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VN Shastin1
RKh Zhukavin1 KA Kovalevsky1 VV Tsyplenkov1 SG Pavlov2 H-W Huumlbers2
NV Abrosimov3 H Riemann 3
1Institute for Physics of Microstructures Russian Academy of Sciences Nizhny Novgorod Russian Federation
2Institute of Planetary Research Germany Aerospace Center Berlin Germany
3Institute of Crystal Growth Berlin Germany
Supported by RAS RFBR (Russia) DFG (Germany)
IPM RAS
IKZ
Кремниевые лазеры для терагерцового диапазона
(Silicon lasers for terahertz domain)
Contents
Unstressed silicon Experimental results Donor state relaxation rates
Stressed silicon Experimental results Donor state relaxation rates
1s(A1)
1s(T2)
1s(E)
-
P As Sb Bi
2p0
2s2pplusmn
10 m
eV
1s(T28)
1s(T27)
Conduction Band
Group V Donors in Silicon
+~1r ~(r)
Состояния мелких доноров в кремнии
1AE
0 0 0 0 1-1=
0 0 1-1 0 0=
1-1 0 0 0 0=
T2
1 1-1-1 0 0
=
1 1 1 1-2-2=
E
1 1 1 1 1 1=
A1 6
1
12
1
2
1
2
1
2
1
2
1
Principle state lifetimes
P As
Pump-probe ~30 ps ~20 ps
FWHM SiN ~26 ps NTD 12х1014 cm-3
FWHM Si28 ~80 ps
2pplusmn state (A1 E)
Exp P As
Pump-probe ~30 ps ~50 ps
FWHM SiN
~32 ps NTD 12х1014 cm-3
~30 ps7х1014 cm-3
FWHM Si28
~160 ps
2p0 state (A1 E)
Theory P As Sb
2р0 (ps)
А1 40 50 50
Е 32 56 50
T2 37 62 54
2рplusmn (ps)
52 47 52
Layout of the experiment
TEA CO2 laser excitation unstressed silicon (Family of experimental data)
Operating temperature
5 10 15 20 25 30 35
SiP SiSb SiBiSiAs
Si l
aser
s em
issi
on a
u
temperature K
Donors concentration 11015 - 5 1015 cm-3
Threshold intensity 10-100 kWcm2
Small signal gain 01-02 cm-1
120 140 160 180 200 220 240
36 42 48 54 60 66 72
Si l
aser
em
issi
on (
au
)
frequency (THz)
wavenumber (cm-1)
SiAs SiBiSiPSiSb
Emission spectra
2times3times7 mm3
THz
Quantum efficiency Exp Theory up to 10
SiP experiment(106 microm TEA CO2 laser excitation)
P donor THz output vs pump intensity under different stress
50 100 150 2000
10
10
0
em
issi
on a
u
frequency cm-1
SiP [100] 023 kbar 065 12
0
00 05 10 15 20 250
100
200
300
400
500
600 180 75 50 25 17 9 5 3 2
stress kbar
emis
sion
mV
SiP [100]
S=493x255 mm2
pump
kWcm2(a)
2 20 2000
100
200
300
400
500
600059
0
043
029118
147
177
221
266
SiP [100]
S=493x255 mm2
em
issi
on
mV
pump CO2 kWcm2
stress kbar
Sb donor THz output vs pump intensity and compressive stress
00 02 04 06 08 10 12 14 160
5
10
15
20
25
30
35
40
45
pump (kWcm2)
200 85 50 30 10 16 023 015
em
issi
on m
V
stress kbar
SiSb [100]
65x49x32 mm3
Nd= 1015cm-3
02 2 20 2000
5
10
15
20
25
30
35
40
45
65x49x32 mm3
SiSb[100]
emis
sion
mV
pump kWcm2
046023
0
081
105117128
stress kbar
SiSb experiment(106 microm TEA CO2 laser
excitation)
150 160 170 180 190 200
00 10 201720
1725
1730
10
0
0
emis
sion
au
frequency cm-1
SiSb [110] 624 bar 936 bar 1872 bar
0
sress kbar
cm-1
2p0 - 1s(B
2)
200kWcm2 correspond 1025quantcm2s
0 1 2 3 400
01
02
03
04 04 06 08
SiSb em
issi
on V
pump intensity 106 m kWcm2
stress [100] kbar 005 01 02 03
00 05 10 15 2(a) photon flux density 1023 quantcm2
SiSb Under Q-switch CO2 laser pump
Least value of threshold intensity ~150Wcm2
0 1 2 3 40
10
20
30
40
50
60
SiAs
[100] 617x(47x275) mm3
emis
sion
mV
stress kbar
200 150 85 50 30 10 16 1
pump (kWcm2)
2 20 2000
10
20
30
40
50
60 3831
283254
196
17
110810530250
SiAs[100]
617x(47x275) mm3
em
issi
on m
V
pump kWcm2
stress kbar
SiAs experiment(106 microm TEA CO2 laser
excitation)
As donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s
As donor THz output vs pump intensity under different stress
160 180 200 220
10
0
0
00 05 10 15 20 25
170
175
180
185
190
195
200
205
210
215
220
2p+-
1s(T2)
2p0 1s(B
2)
давление кбар
част
ота
см
-1SiAs [100]
em
issi
on a
u
frequency cm-1
240 bar 360 600
frequency
cm
-1
stress kbar
0
0 1 2170
220
1 2 3
00
02
04
06 35 38 4 43
11 117 16 22 29
SiAs
emis
sion
V
pump kWcm2
stress [100] kbar
00 05 10 15(b) pump photon density 1023 quantcm2
Least value of threshold intensity ~300Wcm2
SiAs Under Q-switch CO2 laser pump
20 20000
02
04
06
08
10 27
2522
1917
16
15
13
0
05
06
Pump intensity kW cm2
Inte
nsi
ty (
au
)
SiBi [100]
07(052034) mm3
07
Stress kbar
SiBi experiment(106 microm TEA CO2 laser
excitation)
Bi donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s
Sb donor THz output vs pump intensity under different stress
00 05 10 15 20 25 300
200
400
600
800 200 80 60 35 23 15 9
SiBi [100]
07(052034) mm3
em
issi
on
m
V
stress kbar
pump
kWcm2
02 04 06 080
100
200
300 130 100 80 60 53 41
In
tens
ity a
u
0 1 2 3 4 5
-40
-20
0
60
80
TA-g
TA-f
2p0(A
1ET
2)
1s(T2)
1s(A1)
1s(E)
1s(A1)
2p0(A
1+B
2)
Ene
rgy
(meV
)
Stress (kbar)
THz 1s(B2)
LO-g
pum
p en
ergy
117
meV
2 cont
0 1 2 3 4 5-60
-40
-20
0
60
80
LO-g
THz
LA-f
2s2p
+-
LA-gTA-f
4 co
nt
1s(T2)
1s(A1)
1s(E)
1s(A1)
2p0(A
1+B
2) E
ne
rgy
(meV
)
Stress (kbar)
THz1s(B
2)
pum
p en
erg
y 1
17 m
eV
2 cont
Energy levels of donors in stressed Si
As Sb
1211]100[ ss
XE u
X-valley splitting under uniaxial stress X
The stress removes sixfold degeneracy and as a result the energy difference ΔE appears between different groups of valleys
Intervalley phonon scattering of electrons in Si
K111K010
qN
qf
qg
ee[100]
[010][001]
e
Brillouin zonevector of reciprocal lattice normal processumklapp-process f -type umklapp-process g -type
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
21∙109 c-1
46∙1010 c-121∙1010 c-1
68∙109 c-1
2p0(А1+В2)
SiSb
Stress (06 kbar)
Laser state relaxation rates
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
29∙109 c-1
7∙1010 c-144∙1010 c-1
92∙109 c-1
2p0(А1+В2)
SiP
Stress (06 kbar)
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
26∙101035∙1010
42∙109
2p0(А1+В2)
Stress (25 kbar)
2pplusmn2s
15∙109
14∙109
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
55∙109 2∙109
85∙109
2p0(А1+В2)
Stress (18 kbar)
2pplusmn2s
3∙1011
E
E
SiAs
SiBi
Laser state relaxation rates s-1
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
Влияние деформации на эффективность накачки рабочих состояний
(Pump efficiency of the laser states depending on stress)
СО2
Релаксация на фононах
THg
СО2
Релаксация на фононах
THg emission
E
THg emissionE
001 01 1 10 100
1010
1011
1012
1013
1014 Nd=31015 cm-3
popu
latio
n c
m-3
pump kWcm-2
D-centers 2p
0
D-centers under 2p
0 under
001 01 1 10 100
1E-4
1E-3
001
01
1Nd=31015 cm-3
gain
and
abs
orpt
ion
cm
-1
pump kWcm-2
Population gain absorption
SiSb
Donor gain amp D--center absorption
Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)
Blue lines correspond to valley shift 5 meV (06 kbar)
Summary
The axial compressive stress of silicon crystal applied along [100] crystallographic orientation
From the experiment
- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors
- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors
- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress
From the theoretical treatment
- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys
- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states
- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal
Current study amp Further development
1) Spin-orbit interaction amp laser frequencies SiSb SiBi
2) Group-V donor lasing from isotope enriched silicon 28Si
3) Low T donor relaxation in stressed silicon (exp study)
4) Donoracceptor lasing from low dimensional SiSiGe structures
5) CW operation
D- binding energy vs compression
LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve
0 2 4 6 8 10 12 14 16 18 2000
05
10
15
20
25
109 c
-1
SiP
2p0(A
1+B
2) - 1s(A
1
u) LA-g TA-g
Междолинное расщепление мэВ
00 05 10 15 20 25 30 350
2
4
6
8
10
12
14
1
09 c-1
Междолинное расщепление meV
SiP (TA-f)
2p0-1s(E)
2p0-1s(B
1)
2p0-1s(A
1
u)
Сумма
0 10 20 30 400
1
2
3
4
5
6
7
10
10 c
-1
Междолинное расщепление мэВ
SiP 1s(B2) - 1s(A1) TA-g
1s(B2) - 1s(A1) LA-g
1кбар соответствует 85 мэВ
SiP SiP
1s(E)
1s(T2)
1s(A1)
TA-f84∙109 c-1
TA-f124∙109 c-1
LA-g03∙109 c-1
LA-g575109 c-1
TA-g7∙1010 c-1
TA-g36∙1010 c-1
2p0
SiP
Темп внутридолинных переходов
2р0 - 1s 21∙109 с-1
26∙1010 c-1
7∙1010 c-1
36∙1010 c-1
0 10 20 30 40
0
1
2
3
4
5
intervalley splitting meV
10
10 c
-1
1s(B2)-1s(A
1) TА-g
1s(B2)-1s(A
1) LA-g
SiSb
0 2 4 6 8 10 12 14 16 180
1
2
3
4
5
6
7
intervalley splitting meV
109 c
-1
SiSb 2p
0(A
1+B
2)-1s(Au
1) LA-g
2p0(A
1+B
2)-1s(E) TA-f
2p0(A
1+B
2)-1s(Au
1) TA-g
Переходы 2p0-1s(A
1
u) и 2p0-1s(B
1)
на ТА-f фононах пренебрежимо малы
1 kbar yields 85 meV valley shift for [100]
stress
1 kbar yields 85 meV valley shift for [100]
stress
SiSb SiSb
1s(E)
1s(T2)
1s(A1)
TA-f~108 c-1
TA-f142∙109 c-1
LA-g26∙109 c-1
LA-g175∙109 c-1
TA-g46∙1010 c-1
TA-g38∙1010 c-1
2p0
SiSb
Intra valley scattering rate
2р0 - 1s 21∙109 с-1
18∙1010 c-1
38∙1010 c-1
46∙1010 c-1
SiAs SiAs
LA-f079∙1010 c-1
1s(E)
1s(T2)
1s(A1)
TA-f122∙109 c-1
LA-g063∙109 c-1
LA-g07∙109 c-1
TA-f27∙1010 c-1
TA-f16∙1010 c-1
2p0
2s
2pplusmn
LA-g5∙1010 c-1
LA-g33∙1010 c-1
TA-f146 ∙109 c-1
LA-f098∙109 c-1
LA-f27∙1010 c-1
LA-g6∙109 c-1
LA-g6∙109 c-1
Intra valley scattering rates
2р0 - 1s 21∙109 с-1
2s - 1s 52∙109 c-1
2pplusmn - 1s 01 ∙109 c-1
2pplusmn - 2p0 144 ∙109 c-1
2pplusmn - 2s 89 ∙109 c-1
27∙1010 c-1
16∙1010 c-1
77∙1010 c-1
5∙1010 c-1
0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
rate
10
9 s-1
intervalley splitting meV
SiAs 2p(+-)-1s(Al
1) LA-f
2p(+-)-1s(Au
1) LA-g
Relaxation of the lower laser level
f- and g-phonon scattering rates in As donor under stress
0 2 4 6 8 10 12 14 16 18 20 220
1
2
3
4
5
6
intervalley splitting meV
109 c
-1
SiAs 2p
0-1s(Au
1) LA-g
2p0-1s(EB
1) TA-f
2p0-1s(Al
1) LA-f
2p0-1s(Au
1) TA-g
0 5 10 15 20 25 300
1
2
3
4
5
6
7
8
intervalley splitting meV1
010c-1
SiAs 1s(B
2)-1s(A
1
l) LA-g
1s(B2)-1s(A
1
l) TA-f
Relaxation of 2р(+-) and 2р0 states
1s(T2Г7)
1s(T2Г8)
1s(A1)
TA-f52∙109 c-1
LA-g~ 108 c-1
LA-g2∙109 c-1
LA-f47∙109 c-1
TA-f6∙109 c-1
2p0
2s
2pplusmn
LA-g053∙109 c-1
LA-g04∙109 c-1
TA-f14∙1010 c-1
TO-f~32∙1011 c-1
1s(E)
LA-g37∙109 c-1
SiBi SiBi
00 05 10 15 20 25 30 35 400
5
10
15
20
0 59 118 176 235 294 353 412 471
Intervalley splitting meV
1011
c-1
bar
SiBi 2p0-1s(Al
1) TO-f (для верхней ТО ветки) D
15 20 25 30 35 400
1
2
3
4
5
6
7
8
Intervalley splitting meV
1010
c-1
SiBi 2p
0 - 1s(Al
1) LA-f
0000 0493 0986 1479 1972 2465 2958 3451 39440
2
4
6
8
10
12
14
16
18
0 58 116 174 232 290 348 406 464
SiBi LO-g
2p+- - 1s(Al1)
Intervalley splitting meV
1010
c-1
2p+- - 1s(Al1)
with shiftedphonon dispersion on 05 meV
bar
7 8 9 10 11 12 130
5
10
15
20
25
30
35
Intervalley splitting meV
15 kbar
109 c
-1
SiBi2p(+-)-1s(Al
1) TO-f
для верхней ТО-f ветки для нижней ТО-f ветки
1 kbar
f- and g-phonon scattering rates in Bi donor under stress
0 2 4 6 80
2
4
6
8
Intervalley splitting meV
109 c
-1
SiBi 1s(B
2Г
7)-1s(Al
1)
0 20 40 60 800
2
4
6
8
10
12
14
Intervalley splitting meV
1010
c-1
SiBi1s(B
2)-1s(A
1
l) LA-g
Relaxation 1s(B2) state in Bi donor under stressed silicon
Contents
Unstressed silicon Experimental results Donor state relaxation rates
Stressed silicon Experimental results Donor state relaxation rates
1s(A1)
1s(T2)
1s(E)
-
P As Sb Bi
2p0
2s2pplusmn
10 m
eV
1s(T28)
1s(T27)
Conduction Band
Group V Donors in Silicon
+~1r ~(r)
Состояния мелких доноров в кремнии
1AE
0 0 0 0 1-1=
0 0 1-1 0 0=
1-1 0 0 0 0=
T2
1 1-1-1 0 0
=
1 1 1 1-2-2=
E
1 1 1 1 1 1=
A1 6
1
12
1
2
1
2
1
2
1
2
1
Principle state lifetimes
P As
Pump-probe ~30 ps ~20 ps
FWHM SiN ~26 ps NTD 12х1014 cm-3
FWHM Si28 ~80 ps
2pplusmn state (A1 E)
Exp P As
Pump-probe ~30 ps ~50 ps
FWHM SiN
~32 ps NTD 12х1014 cm-3
~30 ps7х1014 cm-3
FWHM Si28
~160 ps
2p0 state (A1 E)
Theory P As Sb
2р0 (ps)
А1 40 50 50
Е 32 56 50
T2 37 62 54
2рplusmn (ps)
52 47 52
Layout of the experiment
TEA CO2 laser excitation unstressed silicon (Family of experimental data)
Operating temperature
5 10 15 20 25 30 35
SiP SiSb SiBiSiAs
Si l
aser
s em
issi
on a
u
temperature K
Donors concentration 11015 - 5 1015 cm-3
Threshold intensity 10-100 kWcm2
Small signal gain 01-02 cm-1
120 140 160 180 200 220 240
36 42 48 54 60 66 72
Si l
aser
em
issi
on (
au
)
frequency (THz)
wavenumber (cm-1)
SiAs SiBiSiPSiSb
Emission spectra
2times3times7 mm3
THz
Quantum efficiency Exp Theory up to 10
SiP experiment(106 microm TEA CO2 laser excitation)
P donor THz output vs pump intensity under different stress
50 100 150 2000
10
10
0
em
issi
on a
u
frequency cm-1
SiP [100] 023 kbar 065 12
0
00 05 10 15 20 250
100
200
300
400
500
600 180 75 50 25 17 9 5 3 2
stress kbar
emis
sion
mV
SiP [100]
S=493x255 mm2
pump
kWcm2(a)
2 20 2000
100
200
300
400
500
600059
0
043
029118
147
177
221
266
SiP [100]
S=493x255 mm2
em
issi
on
mV
pump CO2 kWcm2
stress kbar
Sb donor THz output vs pump intensity and compressive stress
00 02 04 06 08 10 12 14 160
5
10
15
20
25
30
35
40
45
pump (kWcm2)
200 85 50 30 10 16 023 015
em
issi
on m
V
stress kbar
SiSb [100]
65x49x32 mm3
Nd= 1015cm-3
02 2 20 2000
5
10
15
20
25
30
35
40
45
65x49x32 mm3
SiSb[100]
emis
sion
mV
pump kWcm2
046023
0
081
105117128
stress kbar
SiSb experiment(106 microm TEA CO2 laser
excitation)
150 160 170 180 190 200
00 10 201720
1725
1730
10
0
0
emis
sion
au
frequency cm-1
SiSb [110] 624 bar 936 bar 1872 bar
0
sress kbar
cm-1
2p0 - 1s(B
2)
200kWcm2 correspond 1025quantcm2s
0 1 2 3 400
01
02
03
04 04 06 08
SiSb em
issi
on V
pump intensity 106 m kWcm2
stress [100] kbar 005 01 02 03
00 05 10 15 2(a) photon flux density 1023 quantcm2
SiSb Under Q-switch CO2 laser pump
Least value of threshold intensity ~150Wcm2
0 1 2 3 40
10
20
30
40
50
60
SiAs
[100] 617x(47x275) mm3
emis
sion
mV
stress kbar
200 150 85 50 30 10 16 1
pump (kWcm2)
2 20 2000
10
20
30
40
50
60 3831
283254
196
17
110810530250
SiAs[100]
617x(47x275) mm3
em
issi
on m
V
pump kWcm2
stress kbar
SiAs experiment(106 microm TEA CO2 laser
excitation)
As donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s
As donor THz output vs pump intensity under different stress
160 180 200 220
10
0
0
00 05 10 15 20 25
170
175
180
185
190
195
200
205
210
215
220
2p+-
1s(T2)
2p0 1s(B
2)
давление кбар
част
ота
см
-1SiAs [100]
em
issi
on a
u
frequency cm-1
240 bar 360 600
frequency
cm
-1
stress kbar
0
0 1 2170
220
1 2 3
00
02
04
06 35 38 4 43
11 117 16 22 29
SiAs
emis
sion
V
pump kWcm2
stress [100] kbar
00 05 10 15(b) pump photon density 1023 quantcm2
Least value of threshold intensity ~300Wcm2
SiAs Under Q-switch CO2 laser pump
20 20000
02
04
06
08
10 27
2522
1917
16
15
13
0
05
06
Pump intensity kW cm2
Inte
nsi
ty (
au
)
SiBi [100]
07(052034) mm3
07
Stress kbar
SiBi experiment(106 microm TEA CO2 laser
excitation)
Bi donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s
Sb donor THz output vs pump intensity under different stress
00 05 10 15 20 25 300
200
400
600
800 200 80 60 35 23 15 9
SiBi [100]
07(052034) mm3
em
issi
on
m
V
stress kbar
pump
kWcm2
02 04 06 080
100
200
300 130 100 80 60 53 41
In
tens
ity a
u
0 1 2 3 4 5
-40
-20
0
60
80
TA-g
TA-f
2p0(A
1ET
2)
1s(T2)
1s(A1)
1s(E)
1s(A1)
2p0(A
1+B
2)
Ene
rgy
(meV
)
Stress (kbar)
THz 1s(B2)
LO-g
pum
p en
ergy
117
meV
2 cont
0 1 2 3 4 5-60
-40
-20
0
60
80
LO-g
THz
LA-f
2s2p
+-
LA-gTA-f
4 co
nt
1s(T2)
1s(A1)
1s(E)
1s(A1)
2p0(A
1+B
2) E
ne
rgy
(meV
)
Stress (kbar)
THz1s(B
2)
pum
p en
erg
y 1
17 m
eV
2 cont
Energy levels of donors in stressed Si
As Sb
1211]100[ ss
XE u
X-valley splitting under uniaxial stress X
The stress removes sixfold degeneracy and as a result the energy difference ΔE appears between different groups of valleys
Intervalley phonon scattering of electrons in Si
K111K010
qN
qf
qg
ee[100]
[010][001]
e
Brillouin zonevector of reciprocal lattice normal processumklapp-process f -type umklapp-process g -type
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
21∙109 c-1
46∙1010 c-121∙1010 c-1
68∙109 c-1
2p0(А1+В2)
SiSb
Stress (06 kbar)
Laser state relaxation rates
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
29∙109 c-1
7∙1010 c-144∙1010 c-1
92∙109 c-1
2p0(А1+В2)
SiP
Stress (06 kbar)
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
26∙101035∙1010
42∙109
2p0(А1+В2)
Stress (25 kbar)
2pplusmn2s
15∙109
14∙109
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
55∙109 2∙109
85∙109
2p0(А1+В2)
Stress (18 kbar)
2pplusmn2s
3∙1011
E
E
SiAs
SiBi
Laser state relaxation rates s-1
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
Влияние деформации на эффективность накачки рабочих состояний
(Pump efficiency of the laser states depending on stress)
СО2
Релаксация на фононах
THg
СО2
Релаксация на фононах
THg emission
E
THg emissionE
001 01 1 10 100
1010
1011
1012
1013
1014 Nd=31015 cm-3
popu
latio
n c
m-3
pump kWcm-2
D-centers 2p
0
D-centers under 2p
0 under
001 01 1 10 100
1E-4
1E-3
001
01
1Nd=31015 cm-3
gain
and
abs
orpt
ion
cm
-1
pump kWcm-2
Population gain absorption
SiSb
Donor gain amp D--center absorption
Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)
Blue lines correspond to valley shift 5 meV (06 kbar)
Summary
The axial compressive stress of silicon crystal applied along [100] crystallographic orientation
From the experiment
- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors
- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors
- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress
From the theoretical treatment
- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys
- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states
- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal
Current study amp Further development
1) Spin-orbit interaction amp laser frequencies SiSb SiBi
2) Group-V donor lasing from isotope enriched silicon 28Si
3) Low T donor relaxation in stressed silicon (exp study)
4) Donoracceptor lasing from low dimensional SiSiGe structures
5) CW operation
D- binding energy vs compression
LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve
0 2 4 6 8 10 12 14 16 18 2000
05
10
15
20
25
109 c
-1
SiP
2p0(A
1+B
2) - 1s(A
1
u) LA-g TA-g
Междолинное расщепление мэВ
00 05 10 15 20 25 30 350
2
4
6
8
10
12
14
1
09 c-1
Междолинное расщепление meV
SiP (TA-f)
2p0-1s(E)
2p0-1s(B
1)
2p0-1s(A
1
u)
Сумма
0 10 20 30 400
1
2
3
4
5
6
7
10
10 c
-1
Междолинное расщепление мэВ
SiP 1s(B2) - 1s(A1) TA-g
1s(B2) - 1s(A1) LA-g
1кбар соответствует 85 мэВ
SiP SiP
1s(E)
1s(T2)
1s(A1)
TA-f84∙109 c-1
TA-f124∙109 c-1
LA-g03∙109 c-1
LA-g575109 c-1
TA-g7∙1010 c-1
TA-g36∙1010 c-1
2p0
SiP
Темп внутридолинных переходов
2р0 - 1s 21∙109 с-1
26∙1010 c-1
7∙1010 c-1
36∙1010 c-1
0 10 20 30 40
0
1
2
3
4
5
intervalley splitting meV
10
10 c
-1
1s(B2)-1s(A
1) TА-g
1s(B2)-1s(A
1) LA-g
SiSb
0 2 4 6 8 10 12 14 16 180
1
2
3
4
5
6
7
intervalley splitting meV
109 c
-1
SiSb 2p
0(A
1+B
2)-1s(Au
1) LA-g
2p0(A
1+B
2)-1s(E) TA-f
2p0(A
1+B
2)-1s(Au
1) TA-g
Переходы 2p0-1s(A
1
u) и 2p0-1s(B
1)
на ТА-f фононах пренебрежимо малы
1 kbar yields 85 meV valley shift for [100]
stress
1 kbar yields 85 meV valley shift for [100]
stress
SiSb SiSb
1s(E)
1s(T2)
1s(A1)
TA-f~108 c-1
TA-f142∙109 c-1
LA-g26∙109 c-1
LA-g175∙109 c-1
TA-g46∙1010 c-1
TA-g38∙1010 c-1
2p0
SiSb
Intra valley scattering rate
2р0 - 1s 21∙109 с-1
18∙1010 c-1
38∙1010 c-1
46∙1010 c-1
SiAs SiAs
LA-f079∙1010 c-1
1s(E)
1s(T2)
1s(A1)
TA-f122∙109 c-1
LA-g063∙109 c-1
LA-g07∙109 c-1
TA-f27∙1010 c-1
TA-f16∙1010 c-1
2p0
2s
2pplusmn
LA-g5∙1010 c-1
LA-g33∙1010 c-1
TA-f146 ∙109 c-1
LA-f098∙109 c-1
LA-f27∙1010 c-1
LA-g6∙109 c-1
LA-g6∙109 c-1
Intra valley scattering rates
2р0 - 1s 21∙109 с-1
2s - 1s 52∙109 c-1
2pplusmn - 1s 01 ∙109 c-1
2pplusmn - 2p0 144 ∙109 c-1
2pplusmn - 2s 89 ∙109 c-1
27∙1010 c-1
16∙1010 c-1
77∙1010 c-1
5∙1010 c-1
0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
rate
10
9 s-1
intervalley splitting meV
SiAs 2p(+-)-1s(Al
1) LA-f
2p(+-)-1s(Au
1) LA-g
Relaxation of the lower laser level
f- and g-phonon scattering rates in As donor under stress
0 2 4 6 8 10 12 14 16 18 20 220
1
2
3
4
5
6
intervalley splitting meV
109 c
-1
SiAs 2p
0-1s(Au
1) LA-g
2p0-1s(EB
1) TA-f
2p0-1s(Al
1) LA-f
2p0-1s(Au
1) TA-g
0 5 10 15 20 25 300
1
2
3
4
5
6
7
8
intervalley splitting meV1
010c-1
SiAs 1s(B
2)-1s(A
1
l) LA-g
1s(B2)-1s(A
1
l) TA-f
Relaxation of 2р(+-) and 2р0 states
1s(T2Г7)
1s(T2Г8)
1s(A1)
TA-f52∙109 c-1
LA-g~ 108 c-1
LA-g2∙109 c-1
LA-f47∙109 c-1
TA-f6∙109 c-1
2p0
2s
2pplusmn
LA-g053∙109 c-1
LA-g04∙109 c-1
TA-f14∙1010 c-1
TO-f~32∙1011 c-1
1s(E)
LA-g37∙109 c-1
SiBi SiBi
00 05 10 15 20 25 30 35 400
5
10
15
20
0 59 118 176 235 294 353 412 471
Intervalley splitting meV
1011
c-1
bar
SiBi 2p0-1s(Al
1) TO-f (для верхней ТО ветки) D
15 20 25 30 35 400
1
2
3
4
5
6
7
8
Intervalley splitting meV
1010
c-1
SiBi 2p
0 - 1s(Al
1) LA-f
0000 0493 0986 1479 1972 2465 2958 3451 39440
2
4
6
8
10
12
14
16
18
0 58 116 174 232 290 348 406 464
SiBi LO-g
2p+- - 1s(Al1)
Intervalley splitting meV
1010
c-1
2p+- - 1s(Al1)
with shiftedphonon dispersion on 05 meV
bar
7 8 9 10 11 12 130
5
10
15
20
25
30
35
Intervalley splitting meV
15 kbar
109 c
-1
SiBi2p(+-)-1s(Al
1) TO-f
для верхней ТО-f ветки для нижней ТО-f ветки
1 kbar
f- and g-phonon scattering rates in Bi donor under stress
0 2 4 6 80
2
4
6
8
Intervalley splitting meV
109 c
-1
SiBi 1s(B
2Г
7)-1s(Al
1)
0 20 40 60 800
2
4
6
8
10
12
14
Intervalley splitting meV
1010
c-1
SiBi1s(B
2)-1s(A
1
l) LA-g
Relaxation 1s(B2) state in Bi donor under stressed silicon
1s(A1)
1s(T2)
1s(E)
-
P As Sb Bi
2p0
2s2pplusmn
10 m
eV
1s(T28)
1s(T27)
Conduction Band
Group V Donors in Silicon
+~1r ~(r)
Состояния мелких доноров в кремнии
1AE
0 0 0 0 1-1=
0 0 1-1 0 0=
1-1 0 0 0 0=
T2
1 1-1-1 0 0
=
1 1 1 1-2-2=
E
1 1 1 1 1 1=
A1 6
1
12
1
2
1
2
1
2
1
2
1
Principle state lifetimes
P As
Pump-probe ~30 ps ~20 ps
FWHM SiN ~26 ps NTD 12х1014 cm-3
FWHM Si28 ~80 ps
2pplusmn state (A1 E)
Exp P As
Pump-probe ~30 ps ~50 ps
FWHM SiN
~32 ps NTD 12х1014 cm-3
~30 ps7х1014 cm-3
FWHM Si28
~160 ps
2p0 state (A1 E)
Theory P As Sb
2р0 (ps)
А1 40 50 50
Е 32 56 50
T2 37 62 54
2рplusmn (ps)
52 47 52
Layout of the experiment
TEA CO2 laser excitation unstressed silicon (Family of experimental data)
Operating temperature
5 10 15 20 25 30 35
SiP SiSb SiBiSiAs
Si l
aser
s em
issi
on a
u
temperature K
Donors concentration 11015 - 5 1015 cm-3
Threshold intensity 10-100 kWcm2
Small signal gain 01-02 cm-1
120 140 160 180 200 220 240
36 42 48 54 60 66 72
Si l
aser
em
issi
on (
au
)
frequency (THz)
wavenumber (cm-1)
SiAs SiBiSiPSiSb
Emission spectra
2times3times7 mm3
THz
Quantum efficiency Exp Theory up to 10
SiP experiment(106 microm TEA CO2 laser excitation)
P donor THz output vs pump intensity under different stress
50 100 150 2000
10
10
0
em
issi
on a
u
frequency cm-1
SiP [100] 023 kbar 065 12
0
00 05 10 15 20 250
100
200
300
400
500
600 180 75 50 25 17 9 5 3 2
stress kbar
emis
sion
mV
SiP [100]
S=493x255 mm2
pump
kWcm2(a)
2 20 2000
100
200
300
400
500
600059
0
043
029118
147
177
221
266
SiP [100]
S=493x255 mm2
em
issi
on
mV
pump CO2 kWcm2
stress kbar
Sb donor THz output vs pump intensity and compressive stress
00 02 04 06 08 10 12 14 160
5
10
15
20
25
30
35
40
45
pump (kWcm2)
200 85 50 30 10 16 023 015
em
issi
on m
V
stress kbar
SiSb [100]
65x49x32 mm3
Nd= 1015cm-3
02 2 20 2000
5
10
15
20
25
30
35
40
45
65x49x32 mm3
SiSb[100]
emis
sion
mV
pump kWcm2
046023
0
081
105117128
stress kbar
SiSb experiment(106 microm TEA CO2 laser
excitation)
150 160 170 180 190 200
00 10 201720
1725
1730
10
0
0
emis
sion
au
frequency cm-1
SiSb [110] 624 bar 936 bar 1872 bar
0
sress kbar
cm-1
2p0 - 1s(B
2)
200kWcm2 correspond 1025quantcm2s
0 1 2 3 400
01
02
03
04 04 06 08
SiSb em
issi
on V
pump intensity 106 m kWcm2
stress [100] kbar 005 01 02 03
00 05 10 15 2(a) photon flux density 1023 quantcm2
SiSb Under Q-switch CO2 laser pump
Least value of threshold intensity ~150Wcm2
0 1 2 3 40
10
20
30
40
50
60
SiAs
[100] 617x(47x275) mm3
emis
sion
mV
stress kbar
200 150 85 50 30 10 16 1
pump (kWcm2)
2 20 2000
10
20
30
40
50
60 3831
283254
196
17
110810530250
SiAs[100]
617x(47x275) mm3
em
issi
on m
V
pump kWcm2
stress kbar
SiAs experiment(106 microm TEA CO2 laser
excitation)
As donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s
As donor THz output vs pump intensity under different stress
160 180 200 220
10
0
0
00 05 10 15 20 25
170
175
180
185
190
195
200
205
210
215
220
2p+-
1s(T2)
2p0 1s(B
2)
давление кбар
част
ота
см
-1SiAs [100]
em
issi
on a
u
frequency cm-1
240 bar 360 600
frequency
cm
-1
stress kbar
0
0 1 2170
220
1 2 3
00
02
04
06 35 38 4 43
11 117 16 22 29
SiAs
emis
sion
V
pump kWcm2
stress [100] kbar
00 05 10 15(b) pump photon density 1023 quantcm2
Least value of threshold intensity ~300Wcm2
SiAs Under Q-switch CO2 laser pump
20 20000
02
04
06
08
10 27
2522
1917
16
15
13
0
05
06
Pump intensity kW cm2
Inte
nsi
ty (
au
)
SiBi [100]
07(052034) mm3
07
Stress kbar
SiBi experiment(106 microm TEA CO2 laser
excitation)
Bi donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s
Sb donor THz output vs pump intensity under different stress
00 05 10 15 20 25 300
200
400
600
800 200 80 60 35 23 15 9
SiBi [100]
07(052034) mm3
em
issi
on
m
V
stress kbar
pump
kWcm2
02 04 06 080
100
200
300 130 100 80 60 53 41
In
tens
ity a
u
0 1 2 3 4 5
-40
-20
0
60
80
TA-g
TA-f
2p0(A
1ET
2)
1s(T2)
1s(A1)
1s(E)
1s(A1)
2p0(A
1+B
2)
Ene
rgy
(meV
)
Stress (kbar)
THz 1s(B2)
LO-g
pum
p en
ergy
117
meV
2 cont
0 1 2 3 4 5-60
-40
-20
0
60
80
LO-g
THz
LA-f
2s2p
+-
LA-gTA-f
4 co
nt
1s(T2)
1s(A1)
1s(E)
1s(A1)
2p0(A
1+B
2) E
ne
rgy
(meV
)
Stress (kbar)
THz1s(B
2)
pum
p en
erg
y 1
17 m
eV
2 cont
Energy levels of donors in stressed Si
As Sb
1211]100[ ss
XE u
X-valley splitting under uniaxial stress X
The stress removes sixfold degeneracy and as a result the energy difference ΔE appears between different groups of valleys
Intervalley phonon scattering of electrons in Si
K111K010
qN
qf
qg
ee[100]
[010][001]
e
Brillouin zonevector of reciprocal lattice normal processumklapp-process f -type umklapp-process g -type
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
21∙109 c-1
46∙1010 c-121∙1010 c-1
68∙109 c-1
2p0(А1+В2)
SiSb
Stress (06 kbar)
Laser state relaxation rates
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
29∙109 c-1
7∙1010 c-144∙1010 c-1
92∙109 c-1
2p0(А1+В2)
SiP
Stress (06 kbar)
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
26∙101035∙1010
42∙109
2p0(А1+В2)
Stress (25 kbar)
2pplusmn2s
15∙109
14∙109
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
55∙109 2∙109
85∙109
2p0(А1+В2)
Stress (18 kbar)
2pplusmn2s
3∙1011
E
E
SiAs
SiBi
Laser state relaxation rates s-1
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
Влияние деформации на эффективность накачки рабочих состояний
(Pump efficiency of the laser states depending on stress)
СО2
Релаксация на фононах
THg
СО2
Релаксация на фононах
THg emission
E
THg emissionE
001 01 1 10 100
1010
1011
1012
1013
1014 Nd=31015 cm-3
popu
latio
n c
m-3
pump kWcm-2
D-centers 2p
0
D-centers under 2p
0 under
001 01 1 10 100
1E-4
1E-3
001
01
1Nd=31015 cm-3
gain
and
abs
orpt
ion
cm
-1
pump kWcm-2
Population gain absorption
SiSb
Donor gain amp D--center absorption
Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)
Blue lines correspond to valley shift 5 meV (06 kbar)
Summary
The axial compressive stress of silicon crystal applied along [100] crystallographic orientation
From the experiment
- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors
- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors
- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress
From the theoretical treatment
- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys
- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states
- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal
Current study amp Further development
1) Spin-orbit interaction amp laser frequencies SiSb SiBi
2) Group-V donor lasing from isotope enriched silicon 28Si
3) Low T donor relaxation in stressed silicon (exp study)
4) Donoracceptor lasing from low dimensional SiSiGe structures
5) CW operation
D- binding energy vs compression
LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve
0 2 4 6 8 10 12 14 16 18 2000
05
10
15
20
25
109 c
-1
SiP
2p0(A
1+B
2) - 1s(A
1
u) LA-g TA-g
Междолинное расщепление мэВ
00 05 10 15 20 25 30 350
2
4
6
8
10
12
14
1
09 c-1
Междолинное расщепление meV
SiP (TA-f)
2p0-1s(E)
2p0-1s(B
1)
2p0-1s(A
1
u)
Сумма
0 10 20 30 400
1
2
3
4
5
6
7
10
10 c
-1
Междолинное расщепление мэВ
SiP 1s(B2) - 1s(A1) TA-g
1s(B2) - 1s(A1) LA-g
1кбар соответствует 85 мэВ
SiP SiP
1s(E)
1s(T2)
1s(A1)
TA-f84∙109 c-1
TA-f124∙109 c-1
LA-g03∙109 c-1
LA-g575109 c-1
TA-g7∙1010 c-1
TA-g36∙1010 c-1
2p0
SiP
Темп внутридолинных переходов
2р0 - 1s 21∙109 с-1
26∙1010 c-1
7∙1010 c-1
36∙1010 c-1
0 10 20 30 40
0
1
2
3
4
5
intervalley splitting meV
10
10 c
-1
1s(B2)-1s(A
1) TА-g
1s(B2)-1s(A
1) LA-g
SiSb
0 2 4 6 8 10 12 14 16 180
1
2
3
4
5
6
7
intervalley splitting meV
109 c
-1
SiSb 2p
0(A
1+B
2)-1s(Au
1) LA-g
2p0(A
1+B
2)-1s(E) TA-f
2p0(A
1+B
2)-1s(Au
1) TA-g
Переходы 2p0-1s(A
1
u) и 2p0-1s(B
1)
на ТА-f фононах пренебрежимо малы
1 kbar yields 85 meV valley shift for [100]
stress
1 kbar yields 85 meV valley shift for [100]
stress
SiSb SiSb
1s(E)
1s(T2)
1s(A1)
TA-f~108 c-1
TA-f142∙109 c-1
LA-g26∙109 c-1
LA-g175∙109 c-1
TA-g46∙1010 c-1
TA-g38∙1010 c-1
2p0
SiSb
Intra valley scattering rate
2р0 - 1s 21∙109 с-1
18∙1010 c-1
38∙1010 c-1
46∙1010 c-1
SiAs SiAs
LA-f079∙1010 c-1
1s(E)
1s(T2)
1s(A1)
TA-f122∙109 c-1
LA-g063∙109 c-1
LA-g07∙109 c-1
TA-f27∙1010 c-1
TA-f16∙1010 c-1
2p0
2s
2pplusmn
LA-g5∙1010 c-1
LA-g33∙1010 c-1
TA-f146 ∙109 c-1
LA-f098∙109 c-1
LA-f27∙1010 c-1
LA-g6∙109 c-1
LA-g6∙109 c-1
Intra valley scattering rates
2р0 - 1s 21∙109 с-1
2s - 1s 52∙109 c-1
2pplusmn - 1s 01 ∙109 c-1
2pplusmn - 2p0 144 ∙109 c-1
2pplusmn - 2s 89 ∙109 c-1
27∙1010 c-1
16∙1010 c-1
77∙1010 c-1
5∙1010 c-1
0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
rate
10
9 s-1
intervalley splitting meV
SiAs 2p(+-)-1s(Al
1) LA-f
2p(+-)-1s(Au
1) LA-g
Relaxation of the lower laser level
f- and g-phonon scattering rates in As donor under stress
0 2 4 6 8 10 12 14 16 18 20 220
1
2
3
4
5
6
intervalley splitting meV
109 c
-1
SiAs 2p
0-1s(Au
1) LA-g
2p0-1s(EB
1) TA-f
2p0-1s(Al
1) LA-f
2p0-1s(Au
1) TA-g
0 5 10 15 20 25 300
1
2
3
4
5
6
7
8
intervalley splitting meV1
010c-1
SiAs 1s(B
2)-1s(A
1
l) LA-g
1s(B2)-1s(A
1
l) TA-f
Relaxation of 2р(+-) and 2р0 states
1s(T2Г7)
1s(T2Г8)
1s(A1)
TA-f52∙109 c-1
LA-g~ 108 c-1
LA-g2∙109 c-1
LA-f47∙109 c-1
TA-f6∙109 c-1
2p0
2s
2pplusmn
LA-g053∙109 c-1
LA-g04∙109 c-1
TA-f14∙1010 c-1
TO-f~32∙1011 c-1
1s(E)
LA-g37∙109 c-1
SiBi SiBi
00 05 10 15 20 25 30 35 400
5
10
15
20
0 59 118 176 235 294 353 412 471
Intervalley splitting meV
1011
c-1
bar
SiBi 2p0-1s(Al
1) TO-f (для верхней ТО ветки) D
15 20 25 30 35 400
1
2
3
4
5
6
7
8
Intervalley splitting meV
1010
c-1
SiBi 2p
0 - 1s(Al
1) LA-f
0000 0493 0986 1479 1972 2465 2958 3451 39440
2
4
6
8
10
12
14
16
18
0 58 116 174 232 290 348 406 464
SiBi LO-g
2p+- - 1s(Al1)
Intervalley splitting meV
1010
c-1
2p+- - 1s(Al1)
with shiftedphonon dispersion on 05 meV
bar
7 8 9 10 11 12 130
5
10
15
20
25
30
35
Intervalley splitting meV
15 kbar
109 c
-1
SiBi2p(+-)-1s(Al
1) TO-f
для верхней ТО-f ветки для нижней ТО-f ветки
1 kbar
f- and g-phonon scattering rates in Bi donor under stress
0 2 4 6 80
2
4
6
8
Intervalley splitting meV
109 c
-1
SiBi 1s(B
2Г
7)-1s(Al
1)
0 20 40 60 800
2
4
6
8
10
12
14
Intervalley splitting meV
1010
c-1
SiBi1s(B
2)-1s(A
1
l) LA-g
Relaxation 1s(B2) state in Bi donor under stressed silicon
+~1r ~(r)
Состояния мелких доноров в кремнии
1AE
0 0 0 0 1-1=
0 0 1-1 0 0=
1-1 0 0 0 0=
T2
1 1-1-1 0 0
=
1 1 1 1-2-2=
E
1 1 1 1 1 1=
A1 6
1
12
1
2
1
2
1
2
1
2
1
Principle state lifetimes
P As
Pump-probe ~30 ps ~20 ps
FWHM SiN ~26 ps NTD 12х1014 cm-3
FWHM Si28 ~80 ps
2pplusmn state (A1 E)
Exp P As
Pump-probe ~30 ps ~50 ps
FWHM SiN
~32 ps NTD 12х1014 cm-3
~30 ps7х1014 cm-3
FWHM Si28
~160 ps
2p0 state (A1 E)
Theory P As Sb
2р0 (ps)
А1 40 50 50
Е 32 56 50
T2 37 62 54
2рplusmn (ps)
52 47 52
Layout of the experiment
TEA CO2 laser excitation unstressed silicon (Family of experimental data)
Operating temperature
5 10 15 20 25 30 35
SiP SiSb SiBiSiAs
Si l
aser
s em
issi
on a
u
temperature K
Donors concentration 11015 - 5 1015 cm-3
Threshold intensity 10-100 kWcm2
Small signal gain 01-02 cm-1
120 140 160 180 200 220 240
36 42 48 54 60 66 72
Si l
aser
em
issi
on (
au
)
frequency (THz)
wavenumber (cm-1)
SiAs SiBiSiPSiSb
Emission spectra
2times3times7 mm3
THz
Quantum efficiency Exp Theory up to 10
SiP experiment(106 microm TEA CO2 laser excitation)
P donor THz output vs pump intensity under different stress
50 100 150 2000
10
10
0
em
issi
on a
u
frequency cm-1
SiP [100] 023 kbar 065 12
0
00 05 10 15 20 250
100
200
300
400
500
600 180 75 50 25 17 9 5 3 2
stress kbar
emis
sion
mV
SiP [100]
S=493x255 mm2
pump
kWcm2(a)
2 20 2000
100
200
300
400
500
600059
0
043
029118
147
177
221
266
SiP [100]
S=493x255 mm2
em
issi
on
mV
pump CO2 kWcm2
stress kbar
Sb donor THz output vs pump intensity and compressive stress
00 02 04 06 08 10 12 14 160
5
10
15
20
25
30
35
40
45
pump (kWcm2)
200 85 50 30 10 16 023 015
em
issi
on m
V
stress kbar
SiSb [100]
65x49x32 mm3
Nd= 1015cm-3
02 2 20 2000
5
10
15
20
25
30
35
40
45
65x49x32 mm3
SiSb[100]
emis
sion
mV
pump kWcm2
046023
0
081
105117128
stress kbar
SiSb experiment(106 microm TEA CO2 laser
excitation)
150 160 170 180 190 200
00 10 201720
1725
1730
10
0
0
emis
sion
au
frequency cm-1
SiSb [110] 624 bar 936 bar 1872 bar
0
sress kbar
cm-1
2p0 - 1s(B
2)
200kWcm2 correspond 1025quantcm2s
0 1 2 3 400
01
02
03
04 04 06 08
SiSb em
issi
on V
pump intensity 106 m kWcm2
stress [100] kbar 005 01 02 03
00 05 10 15 2(a) photon flux density 1023 quantcm2
SiSb Under Q-switch CO2 laser pump
Least value of threshold intensity ~150Wcm2
0 1 2 3 40
10
20
30
40
50
60
SiAs
[100] 617x(47x275) mm3
emis
sion
mV
stress kbar
200 150 85 50 30 10 16 1
pump (kWcm2)
2 20 2000
10
20
30
40
50
60 3831
283254
196
17
110810530250
SiAs[100]
617x(47x275) mm3
em
issi
on m
V
pump kWcm2
stress kbar
SiAs experiment(106 microm TEA CO2 laser
excitation)
As donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s
As donor THz output vs pump intensity under different stress
160 180 200 220
10
0
0
00 05 10 15 20 25
170
175
180
185
190
195
200
205
210
215
220
2p+-
1s(T2)
2p0 1s(B
2)
давление кбар
част
ота
см
-1SiAs [100]
em
issi
on a
u
frequency cm-1
240 bar 360 600
frequency
cm
-1
stress kbar
0
0 1 2170
220
1 2 3
00
02
04
06 35 38 4 43
11 117 16 22 29
SiAs
emis
sion
V
pump kWcm2
stress [100] kbar
00 05 10 15(b) pump photon density 1023 quantcm2
Least value of threshold intensity ~300Wcm2
SiAs Under Q-switch CO2 laser pump
20 20000
02
04
06
08
10 27
2522
1917
16
15
13
0
05
06
Pump intensity kW cm2
Inte
nsi
ty (
au
)
SiBi [100]
07(052034) mm3
07
Stress kbar
SiBi experiment(106 microm TEA CO2 laser
excitation)
Bi donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s
Sb donor THz output vs pump intensity under different stress
00 05 10 15 20 25 300
200
400
600
800 200 80 60 35 23 15 9
SiBi [100]
07(052034) mm3
em
issi
on
m
V
stress kbar
pump
kWcm2
02 04 06 080
100
200
300 130 100 80 60 53 41
In
tens
ity a
u
0 1 2 3 4 5
-40
-20
0
60
80
TA-g
TA-f
2p0(A
1ET
2)
1s(T2)
1s(A1)
1s(E)
1s(A1)
2p0(A
1+B
2)
Ene
rgy
(meV
)
Stress (kbar)
THz 1s(B2)
LO-g
pum
p en
ergy
117
meV
2 cont
0 1 2 3 4 5-60
-40
-20
0
60
80
LO-g
THz
LA-f
2s2p
+-
LA-gTA-f
4 co
nt
1s(T2)
1s(A1)
1s(E)
1s(A1)
2p0(A
1+B
2) E
ne
rgy
(meV
)
Stress (kbar)
THz1s(B
2)
pum
p en
erg
y 1
17 m
eV
2 cont
Energy levels of donors in stressed Si
As Sb
1211]100[ ss
XE u
X-valley splitting under uniaxial stress X
The stress removes sixfold degeneracy and as a result the energy difference ΔE appears between different groups of valleys
Intervalley phonon scattering of electrons in Si
K111K010
qN
qf
qg
ee[100]
[010][001]
e
Brillouin zonevector of reciprocal lattice normal processumklapp-process f -type umklapp-process g -type
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
21∙109 c-1
46∙1010 c-121∙1010 c-1
68∙109 c-1
2p0(А1+В2)
SiSb
Stress (06 kbar)
Laser state relaxation rates
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
29∙109 c-1
7∙1010 c-144∙1010 c-1
92∙109 c-1
2p0(А1+В2)
SiP
Stress (06 kbar)
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
26∙101035∙1010
42∙109
2p0(А1+В2)
Stress (25 kbar)
2pplusmn2s
15∙109
14∙109
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
55∙109 2∙109
85∙109
2p0(А1+В2)
Stress (18 kbar)
2pplusmn2s
3∙1011
E
E
SiAs
SiBi
Laser state relaxation rates s-1
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
Влияние деформации на эффективность накачки рабочих состояний
(Pump efficiency of the laser states depending on stress)
СО2
Релаксация на фононах
THg
СО2
Релаксация на фононах
THg emission
E
THg emissionE
001 01 1 10 100
1010
1011
1012
1013
1014 Nd=31015 cm-3
popu
latio
n c
m-3
pump kWcm-2
D-centers 2p
0
D-centers under 2p
0 under
001 01 1 10 100
1E-4
1E-3
001
01
1Nd=31015 cm-3
gain
and
abs
orpt
ion
cm
-1
pump kWcm-2
Population gain absorption
SiSb
Donor gain amp D--center absorption
Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)
Blue lines correspond to valley shift 5 meV (06 kbar)
Summary
The axial compressive stress of silicon crystal applied along [100] crystallographic orientation
From the experiment
- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors
- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors
- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress
From the theoretical treatment
- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys
- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states
- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal
Current study amp Further development
1) Spin-orbit interaction amp laser frequencies SiSb SiBi
2) Group-V donor lasing from isotope enriched silicon 28Si
3) Low T donor relaxation in stressed silicon (exp study)
4) Donoracceptor lasing from low dimensional SiSiGe structures
5) CW operation
D- binding energy vs compression
LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve
0 2 4 6 8 10 12 14 16 18 2000
05
10
15
20
25
109 c
-1
SiP
2p0(A
1+B
2) - 1s(A
1
u) LA-g TA-g
Междолинное расщепление мэВ
00 05 10 15 20 25 30 350
2
4
6
8
10
12
14
1
09 c-1
Междолинное расщепление meV
SiP (TA-f)
2p0-1s(E)
2p0-1s(B
1)
2p0-1s(A
1
u)
Сумма
0 10 20 30 400
1
2
3
4
5
6
7
10
10 c
-1
Междолинное расщепление мэВ
SiP 1s(B2) - 1s(A1) TA-g
1s(B2) - 1s(A1) LA-g
1кбар соответствует 85 мэВ
SiP SiP
1s(E)
1s(T2)
1s(A1)
TA-f84∙109 c-1
TA-f124∙109 c-1
LA-g03∙109 c-1
LA-g575109 c-1
TA-g7∙1010 c-1
TA-g36∙1010 c-1
2p0
SiP
Темп внутридолинных переходов
2р0 - 1s 21∙109 с-1
26∙1010 c-1
7∙1010 c-1
36∙1010 c-1
0 10 20 30 40
0
1
2
3
4
5
intervalley splitting meV
10
10 c
-1
1s(B2)-1s(A
1) TА-g
1s(B2)-1s(A
1) LA-g
SiSb
0 2 4 6 8 10 12 14 16 180
1
2
3
4
5
6
7
intervalley splitting meV
109 c
-1
SiSb 2p
0(A
1+B
2)-1s(Au
1) LA-g
2p0(A
1+B
2)-1s(E) TA-f
2p0(A
1+B
2)-1s(Au
1) TA-g
Переходы 2p0-1s(A
1
u) и 2p0-1s(B
1)
на ТА-f фононах пренебрежимо малы
1 kbar yields 85 meV valley shift for [100]
stress
1 kbar yields 85 meV valley shift for [100]
stress
SiSb SiSb
1s(E)
1s(T2)
1s(A1)
TA-f~108 c-1
TA-f142∙109 c-1
LA-g26∙109 c-1
LA-g175∙109 c-1
TA-g46∙1010 c-1
TA-g38∙1010 c-1
2p0
SiSb
Intra valley scattering rate
2р0 - 1s 21∙109 с-1
18∙1010 c-1
38∙1010 c-1
46∙1010 c-1
SiAs SiAs
LA-f079∙1010 c-1
1s(E)
1s(T2)
1s(A1)
TA-f122∙109 c-1
LA-g063∙109 c-1
LA-g07∙109 c-1
TA-f27∙1010 c-1
TA-f16∙1010 c-1
2p0
2s
2pplusmn
LA-g5∙1010 c-1
LA-g33∙1010 c-1
TA-f146 ∙109 c-1
LA-f098∙109 c-1
LA-f27∙1010 c-1
LA-g6∙109 c-1
LA-g6∙109 c-1
Intra valley scattering rates
2р0 - 1s 21∙109 с-1
2s - 1s 52∙109 c-1
2pplusmn - 1s 01 ∙109 c-1
2pplusmn - 2p0 144 ∙109 c-1
2pplusmn - 2s 89 ∙109 c-1
27∙1010 c-1
16∙1010 c-1
77∙1010 c-1
5∙1010 c-1
0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
rate
10
9 s-1
intervalley splitting meV
SiAs 2p(+-)-1s(Al
1) LA-f
2p(+-)-1s(Au
1) LA-g
Relaxation of the lower laser level
f- and g-phonon scattering rates in As donor under stress
0 2 4 6 8 10 12 14 16 18 20 220
1
2
3
4
5
6
intervalley splitting meV
109 c
-1
SiAs 2p
0-1s(Au
1) LA-g
2p0-1s(EB
1) TA-f
2p0-1s(Al
1) LA-f
2p0-1s(Au
1) TA-g
0 5 10 15 20 25 300
1
2
3
4
5
6
7
8
intervalley splitting meV1
010c-1
SiAs 1s(B
2)-1s(A
1
l) LA-g
1s(B2)-1s(A
1
l) TA-f
Relaxation of 2р(+-) and 2р0 states
1s(T2Г7)
1s(T2Г8)
1s(A1)
TA-f52∙109 c-1
LA-g~ 108 c-1
LA-g2∙109 c-1
LA-f47∙109 c-1
TA-f6∙109 c-1
2p0
2s
2pplusmn
LA-g053∙109 c-1
LA-g04∙109 c-1
TA-f14∙1010 c-1
TO-f~32∙1011 c-1
1s(E)
LA-g37∙109 c-1
SiBi SiBi
00 05 10 15 20 25 30 35 400
5
10
15
20
0 59 118 176 235 294 353 412 471
Intervalley splitting meV
1011
c-1
bar
SiBi 2p0-1s(Al
1) TO-f (для верхней ТО ветки) D
15 20 25 30 35 400
1
2
3
4
5
6
7
8
Intervalley splitting meV
1010
c-1
SiBi 2p
0 - 1s(Al
1) LA-f
0000 0493 0986 1479 1972 2465 2958 3451 39440
2
4
6
8
10
12
14
16
18
0 58 116 174 232 290 348 406 464
SiBi LO-g
2p+- - 1s(Al1)
Intervalley splitting meV
1010
c-1
2p+- - 1s(Al1)
with shiftedphonon dispersion on 05 meV
bar
7 8 9 10 11 12 130
5
10
15
20
25
30
35
Intervalley splitting meV
15 kbar
109 c
-1
SiBi2p(+-)-1s(Al
1) TO-f
для верхней ТО-f ветки для нижней ТО-f ветки
1 kbar
f- and g-phonon scattering rates in Bi donor under stress
0 2 4 6 80
2
4
6
8
Intervalley splitting meV
109 c
-1
SiBi 1s(B
2Г
7)-1s(Al
1)
0 20 40 60 800
2
4
6
8
10
12
14
Intervalley splitting meV
1010
c-1
SiBi1s(B
2)-1s(A
1
l) LA-g
Relaxation 1s(B2) state in Bi donor under stressed silicon
Principle state lifetimes
P As
Pump-probe ~30 ps ~20 ps
FWHM SiN ~26 ps NTD 12х1014 cm-3
FWHM Si28 ~80 ps
2pplusmn state (A1 E)
Exp P As
Pump-probe ~30 ps ~50 ps
FWHM SiN
~32 ps NTD 12х1014 cm-3
~30 ps7х1014 cm-3
FWHM Si28
~160 ps
2p0 state (A1 E)
Theory P As Sb
2р0 (ps)
А1 40 50 50
Е 32 56 50
T2 37 62 54
2рplusmn (ps)
52 47 52
Layout of the experiment
TEA CO2 laser excitation unstressed silicon (Family of experimental data)
Operating temperature
5 10 15 20 25 30 35
SiP SiSb SiBiSiAs
Si l
aser
s em
issi
on a
u
temperature K
Donors concentration 11015 - 5 1015 cm-3
Threshold intensity 10-100 kWcm2
Small signal gain 01-02 cm-1
120 140 160 180 200 220 240
36 42 48 54 60 66 72
Si l
aser
em
issi
on (
au
)
frequency (THz)
wavenumber (cm-1)
SiAs SiBiSiPSiSb
Emission spectra
2times3times7 mm3
THz
Quantum efficiency Exp Theory up to 10
SiP experiment(106 microm TEA CO2 laser excitation)
P donor THz output vs pump intensity under different stress
50 100 150 2000
10
10
0
em
issi
on a
u
frequency cm-1
SiP [100] 023 kbar 065 12
0
00 05 10 15 20 250
100
200
300
400
500
600 180 75 50 25 17 9 5 3 2
stress kbar
emis
sion
mV
SiP [100]
S=493x255 mm2
pump
kWcm2(a)
2 20 2000
100
200
300
400
500
600059
0
043
029118
147
177
221
266
SiP [100]
S=493x255 mm2
em
issi
on
mV
pump CO2 kWcm2
stress kbar
Sb donor THz output vs pump intensity and compressive stress
00 02 04 06 08 10 12 14 160
5
10
15
20
25
30
35
40
45
pump (kWcm2)
200 85 50 30 10 16 023 015
em
issi
on m
V
stress kbar
SiSb [100]
65x49x32 mm3
Nd= 1015cm-3
02 2 20 2000
5
10
15
20
25
30
35
40
45
65x49x32 mm3
SiSb[100]
emis
sion
mV
pump kWcm2
046023
0
081
105117128
stress kbar
SiSb experiment(106 microm TEA CO2 laser
excitation)
150 160 170 180 190 200
00 10 201720
1725
1730
10
0
0
emis
sion
au
frequency cm-1
SiSb [110] 624 bar 936 bar 1872 bar
0
sress kbar
cm-1
2p0 - 1s(B
2)
200kWcm2 correspond 1025quantcm2s
0 1 2 3 400
01
02
03
04 04 06 08
SiSb em
issi
on V
pump intensity 106 m kWcm2
stress [100] kbar 005 01 02 03
00 05 10 15 2(a) photon flux density 1023 quantcm2
SiSb Under Q-switch CO2 laser pump
Least value of threshold intensity ~150Wcm2
0 1 2 3 40
10
20
30
40
50
60
SiAs
[100] 617x(47x275) mm3
emis
sion
mV
stress kbar
200 150 85 50 30 10 16 1
pump (kWcm2)
2 20 2000
10
20
30
40
50
60 3831
283254
196
17
110810530250
SiAs[100]
617x(47x275) mm3
em
issi
on m
V
pump kWcm2
stress kbar
SiAs experiment(106 microm TEA CO2 laser
excitation)
As donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s
As donor THz output vs pump intensity under different stress
160 180 200 220
10
0
0
00 05 10 15 20 25
170
175
180
185
190
195
200
205
210
215
220
2p+-
1s(T2)
2p0 1s(B
2)
давление кбар
част
ота
см
-1SiAs [100]
em
issi
on a
u
frequency cm-1
240 bar 360 600
frequency
cm
-1
stress kbar
0
0 1 2170
220
1 2 3
00
02
04
06 35 38 4 43
11 117 16 22 29
SiAs
emis
sion
V
pump kWcm2
stress [100] kbar
00 05 10 15(b) pump photon density 1023 quantcm2
Least value of threshold intensity ~300Wcm2
SiAs Under Q-switch CO2 laser pump
20 20000
02
04
06
08
10 27
2522
1917
16
15
13
0
05
06
Pump intensity kW cm2
Inte
nsi
ty (
au
)
SiBi [100]
07(052034) mm3
07
Stress kbar
SiBi experiment(106 microm TEA CO2 laser
excitation)
Bi donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s
Sb donor THz output vs pump intensity under different stress
00 05 10 15 20 25 300
200
400
600
800 200 80 60 35 23 15 9
SiBi [100]
07(052034) mm3
em
issi
on
m
V
stress kbar
pump
kWcm2
02 04 06 080
100
200
300 130 100 80 60 53 41
In
tens
ity a
u
0 1 2 3 4 5
-40
-20
0
60
80
TA-g
TA-f
2p0(A
1ET
2)
1s(T2)
1s(A1)
1s(E)
1s(A1)
2p0(A
1+B
2)
Ene
rgy
(meV
)
Stress (kbar)
THz 1s(B2)
LO-g
pum
p en
ergy
117
meV
2 cont
0 1 2 3 4 5-60
-40
-20
0
60
80
LO-g
THz
LA-f
2s2p
+-
LA-gTA-f
4 co
nt
1s(T2)
1s(A1)
1s(E)
1s(A1)
2p0(A
1+B
2) E
ne
rgy
(meV
)
Stress (kbar)
THz1s(B
2)
pum
p en
erg
y 1
17 m
eV
2 cont
Energy levels of donors in stressed Si
As Sb
1211]100[ ss
XE u
X-valley splitting under uniaxial stress X
The stress removes sixfold degeneracy and as a result the energy difference ΔE appears between different groups of valleys
Intervalley phonon scattering of electrons in Si
K111K010
qN
qf
qg
ee[100]
[010][001]
e
Brillouin zonevector of reciprocal lattice normal processumklapp-process f -type umklapp-process g -type
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
21∙109 c-1
46∙1010 c-121∙1010 c-1
68∙109 c-1
2p0(А1+В2)
SiSb
Stress (06 kbar)
Laser state relaxation rates
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
29∙109 c-1
7∙1010 c-144∙1010 c-1
92∙109 c-1
2p0(А1+В2)
SiP
Stress (06 kbar)
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
26∙101035∙1010
42∙109
2p0(А1+В2)
Stress (25 kbar)
2pplusmn2s
15∙109
14∙109
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
55∙109 2∙109
85∙109
2p0(А1+В2)
Stress (18 kbar)
2pplusmn2s
3∙1011
E
E
SiAs
SiBi
Laser state relaxation rates s-1
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
Влияние деформации на эффективность накачки рабочих состояний
(Pump efficiency of the laser states depending on stress)
СО2
Релаксация на фононах
THg
СО2
Релаксация на фононах
THg emission
E
THg emissionE
001 01 1 10 100
1010
1011
1012
1013
1014 Nd=31015 cm-3
popu
latio
n c
m-3
pump kWcm-2
D-centers 2p
0
D-centers under 2p
0 under
001 01 1 10 100
1E-4
1E-3
001
01
1Nd=31015 cm-3
gain
and
abs
orpt
ion
cm
-1
pump kWcm-2
Population gain absorption
SiSb
Donor gain amp D--center absorption
Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)
Blue lines correspond to valley shift 5 meV (06 kbar)
Summary
The axial compressive stress of silicon crystal applied along [100] crystallographic orientation
From the experiment
- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors
- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors
- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress
From the theoretical treatment
- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys
- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states
- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal
Current study amp Further development
1) Spin-orbit interaction amp laser frequencies SiSb SiBi
2) Group-V donor lasing from isotope enriched silicon 28Si
3) Low T donor relaxation in stressed silicon (exp study)
4) Donoracceptor lasing from low dimensional SiSiGe structures
5) CW operation
D- binding energy vs compression
LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve
0 2 4 6 8 10 12 14 16 18 2000
05
10
15
20
25
109 c
-1
SiP
2p0(A
1+B
2) - 1s(A
1
u) LA-g TA-g
Междолинное расщепление мэВ
00 05 10 15 20 25 30 350
2
4
6
8
10
12
14
1
09 c-1
Междолинное расщепление meV
SiP (TA-f)
2p0-1s(E)
2p0-1s(B
1)
2p0-1s(A
1
u)
Сумма
0 10 20 30 400
1
2
3
4
5
6
7
10
10 c
-1
Междолинное расщепление мэВ
SiP 1s(B2) - 1s(A1) TA-g
1s(B2) - 1s(A1) LA-g
1кбар соответствует 85 мэВ
SiP SiP
1s(E)
1s(T2)
1s(A1)
TA-f84∙109 c-1
TA-f124∙109 c-1
LA-g03∙109 c-1
LA-g575109 c-1
TA-g7∙1010 c-1
TA-g36∙1010 c-1
2p0
SiP
Темп внутридолинных переходов
2р0 - 1s 21∙109 с-1
26∙1010 c-1
7∙1010 c-1
36∙1010 c-1
0 10 20 30 40
0
1
2
3
4
5
intervalley splitting meV
10
10 c
-1
1s(B2)-1s(A
1) TА-g
1s(B2)-1s(A
1) LA-g
SiSb
0 2 4 6 8 10 12 14 16 180
1
2
3
4
5
6
7
intervalley splitting meV
109 c
-1
SiSb 2p
0(A
1+B
2)-1s(Au
1) LA-g
2p0(A
1+B
2)-1s(E) TA-f
2p0(A
1+B
2)-1s(Au
1) TA-g
Переходы 2p0-1s(A
1
u) и 2p0-1s(B
1)
на ТА-f фононах пренебрежимо малы
1 kbar yields 85 meV valley shift for [100]
stress
1 kbar yields 85 meV valley shift for [100]
stress
SiSb SiSb
1s(E)
1s(T2)
1s(A1)
TA-f~108 c-1
TA-f142∙109 c-1
LA-g26∙109 c-1
LA-g175∙109 c-1
TA-g46∙1010 c-1
TA-g38∙1010 c-1
2p0
SiSb
Intra valley scattering rate
2р0 - 1s 21∙109 с-1
18∙1010 c-1
38∙1010 c-1
46∙1010 c-1
SiAs SiAs
LA-f079∙1010 c-1
1s(E)
1s(T2)
1s(A1)
TA-f122∙109 c-1
LA-g063∙109 c-1
LA-g07∙109 c-1
TA-f27∙1010 c-1
TA-f16∙1010 c-1
2p0
2s
2pplusmn
LA-g5∙1010 c-1
LA-g33∙1010 c-1
TA-f146 ∙109 c-1
LA-f098∙109 c-1
LA-f27∙1010 c-1
LA-g6∙109 c-1
LA-g6∙109 c-1
Intra valley scattering rates
2р0 - 1s 21∙109 с-1
2s - 1s 52∙109 c-1
2pplusmn - 1s 01 ∙109 c-1
2pplusmn - 2p0 144 ∙109 c-1
2pplusmn - 2s 89 ∙109 c-1
27∙1010 c-1
16∙1010 c-1
77∙1010 c-1
5∙1010 c-1
0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
rate
10
9 s-1
intervalley splitting meV
SiAs 2p(+-)-1s(Al
1) LA-f
2p(+-)-1s(Au
1) LA-g
Relaxation of the lower laser level
f- and g-phonon scattering rates in As donor under stress
0 2 4 6 8 10 12 14 16 18 20 220
1
2
3
4
5
6
intervalley splitting meV
109 c
-1
SiAs 2p
0-1s(Au
1) LA-g
2p0-1s(EB
1) TA-f
2p0-1s(Al
1) LA-f
2p0-1s(Au
1) TA-g
0 5 10 15 20 25 300
1
2
3
4
5
6
7
8
intervalley splitting meV1
010c-1
SiAs 1s(B
2)-1s(A
1
l) LA-g
1s(B2)-1s(A
1
l) TA-f
Relaxation of 2р(+-) and 2р0 states
1s(T2Г7)
1s(T2Г8)
1s(A1)
TA-f52∙109 c-1
LA-g~ 108 c-1
LA-g2∙109 c-1
LA-f47∙109 c-1
TA-f6∙109 c-1
2p0
2s
2pplusmn
LA-g053∙109 c-1
LA-g04∙109 c-1
TA-f14∙1010 c-1
TO-f~32∙1011 c-1
1s(E)
LA-g37∙109 c-1
SiBi SiBi
00 05 10 15 20 25 30 35 400
5
10
15
20
0 59 118 176 235 294 353 412 471
Intervalley splitting meV
1011
c-1
bar
SiBi 2p0-1s(Al
1) TO-f (для верхней ТО ветки) D
15 20 25 30 35 400
1
2
3
4
5
6
7
8
Intervalley splitting meV
1010
c-1
SiBi 2p
0 - 1s(Al
1) LA-f
0000 0493 0986 1479 1972 2465 2958 3451 39440
2
4
6
8
10
12
14
16
18
0 58 116 174 232 290 348 406 464
SiBi LO-g
2p+- - 1s(Al1)
Intervalley splitting meV
1010
c-1
2p+- - 1s(Al1)
with shiftedphonon dispersion on 05 meV
bar
7 8 9 10 11 12 130
5
10
15
20
25
30
35
Intervalley splitting meV
15 kbar
109 c
-1
SiBi2p(+-)-1s(Al
1) TO-f
для верхней ТО-f ветки для нижней ТО-f ветки
1 kbar
f- and g-phonon scattering rates in Bi donor under stress
0 2 4 6 80
2
4
6
8
Intervalley splitting meV
109 c
-1
SiBi 1s(B
2Г
7)-1s(Al
1)
0 20 40 60 800
2
4
6
8
10
12
14
Intervalley splitting meV
1010
c-1
SiBi1s(B
2)-1s(A
1
l) LA-g
Relaxation 1s(B2) state in Bi donor under stressed silicon
Layout of the experiment
TEA CO2 laser excitation unstressed silicon (Family of experimental data)
Operating temperature
5 10 15 20 25 30 35
SiP SiSb SiBiSiAs
Si l
aser
s em
issi
on a
u
temperature K
Donors concentration 11015 - 5 1015 cm-3
Threshold intensity 10-100 kWcm2
Small signal gain 01-02 cm-1
120 140 160 180 200 220 240
36 42 48 54 60 66 72
Si l
aser
em
issi
on (
au
)
frequency (THz)
wavenumber (cm-1)
SiAs SiBiSiPSiSb
Emission spectra
2times3times7 mm3
THz
Quantum efficiency Exp Theory up to 10
SiP experiment(106 microm TEA CO2 laser excitation)
P donor THz output vs pump intensity under different stress
50 100 150 2000
10
10
0
em
issi
on a
u
frequency cm-1
SiP [100] 023 kbar 065 12
0
00 05 10 15 20 250
100
200
300
400
500
600 180 75 50 25 17 9 5 3 2
stress kbar
emis
sion
mV
SiP [100]
S=493x255 mm2
pump
kWcm2(a)
2 20 2000
100
200
300
400
500
600059
0
043
029118
147
177
221
266
SiP [100]
S=493x255 mm2
em
issi
on
mV
pump CO2 kWcm2
stress kbar
Sb donor THz output vs pump intensity and compressive stress
00 02 04 06 08 10 12 14 160
5
10
15
20
25
30
35
40
45
pump (kWcm2)
200 85 50 30 10 16 023 015
em
issi
on m
V
stress kbar
SiSb [100]
65x49x32 mm3
Nd= 1015cm-3
02 2 20 2000
5
10
15
20
25
30
35
40
45
65x49x32 mm3
SiSb[100]
emis
sion
mV
pump kWcm2
046023
0
081
105117128
stress kbar
SiSb experiment(106 microm TEA CO2 laser
excitation)
150 160 170 180 190 200
00 10 201720
1725
1730
10
0
0
emis
sion
au
frequency cm-1
SiSb [110] 624 bar 936 bar 1872 bar
0
sress kbar
cm-1
2p0 - 1s(B
2)
200kWcm2 correspond 1025quantcm2s
0 1 2 3 400
01
02
03
04 04 06 08
SiSb em
issi
on V
pump intensity 106 m kWcm2
stress [100] kbar 005 01 02 03
00 05 10 15 2(a) photon flux density 1023 quantcm2
SiSb Under Q-switch CO2 laser pump
Least value of threshold intensity ~150Wcm2
0 1 2 3 40
10
20
30
40
50
60
SiAs
[100] 617x(47x275) mm3
emis
sion
mV
stress kbar
200 150 85 50 30 10 16 1
pump (kWcm2)
2 20 2000
10
20
30
40
50
60 3831
283254
196
17
110810530250
SiAs[100]
617x(47x275) mm3
em
issi
on m
V
pump kWcm2
stress kbar
SiAs experiment(106 microm TEA CO2 laser
excitation)
As donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s
As donor THz output vs pump intensity under different stress
160 180 200 220
10
0
0
00 05 10 15 20 25
170
175
180
185
190
195
200
205
210
215
220
2p+-
1s(T2)
2p0 1s(B
2)
давление кбар
част
ота
см
-1SiAs [100]
em
issi
on a
u
frequency cm-1
240 bar 360 600
frequency
cm
-1
stress kbar
0
0 1 2170
220
1 2 3
00
02
04
06 35 38 4 43
11 117 16 22 29
SiAs
emis
sion
V
pump kWcm2
stress [100] kbar
00 05 10 15(b) pump photon density 1023 quantcm2
Least value of threshold intensity ~300Wcm2
SiAs Under Q-switch CO2 laser pump
20 20000
02
04
06
08
10 27
2522
1917
16
15
13
0
05
06
Pump intensity kW cm2
Inte
nsi
ty (
au
)
SiBi [100]
07(052034) mm3
07
Stress kbar
SiBi experiment(106 microm TEA CO2 laser
excitation)
Bi donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s
Sb donor THz output vs pump intensity under different stress
00 05 10 15 20 25 300
200
400
600
800 200 80 60 35 23 15 9
SiBi [100]
07(052034) mm3
em
issi
on
m
V
stress kbar
pump
kWcm2
02 04 06 080
100
200
300 130 100 80 60 53 41
In
tens
ity a
u
0 1 2 3 4 5
-40
-20
0
60
80
TA-g
TA-f
2p0(A
1ET
2)
1s(T2)
1s(A1)
1s(E)
1s(A1)
2p0(A
1+B
2)
Ene
rgy
(meV
)
Stress (kbar)
THz 1s(B2)
LO-g
pum
p en
ergy
117
meV
2 cont
0 1 2 3 4 5-60
-40
-20
0
60
80
LO-g
THz
LA-f
2s2p
+-
LA-gTA-f
4 co
nt
1s(T2)
1s(A1)
1s(E)
1s(A1)
2p0(A
1+B
2) E
ne
rgy
(meV
)
Stress (kbar)
THz1s(B
2)
pum
p en
erg
y 1
17 m
eV
2 cont
Energy levels of donors in stressed Si
As Sb
1211]100[ ss
XE u
X-valley splitting under uniaxial stress X
The stress removes sixfold degeneracy and as a result the energy difference ΔE appears between different groups of valleys
Intervalley phonon scattering of electrons in Si
K111K010
qN
qf
qg
ee[100]
[010][001]
e
Brillouin zonevector of reciprocal lattice normal processumklapp-process f -type umklapp-process g -type
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
21∙109 c-1
46∙1010 c-121∙1010 c-1
68∙109 c-1
2p0(А1+В2)
SiSb
Stress (06 kbar)
Laser state relaxation rates
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
29∙109 c-1
7∙1010 c-144∙1010 c-1
92∙109 c-1
2p0(А1+В2)
SiP
Stress (06 kbar)
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
26∙101035∙1010
42∙109
2p0(А1+В2)
Stress (25 kbar)
2pplusmn2s
15∙109
14∙109
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
55∙109 2∙109
85∙109
2p0(А1+В2)
Stress (18 kbar)
2pplusmn2s
3∙1011
E
E
SiAs
SiBi
Laser state relaxation rates s-1
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
Влияние деформации на эффективность накачки рабочих состояний
(Pump efficiency of the laser states depending on stress)
СО2
Релаксация на фононах
THg
СО2
Релаксация на фононах
THg emission
E
THg emissionE
001 01 1 10 100
1010
1011
1012
1013
1014 Nd=31015 cm-3
popu
latio
n c
m-3
pump kWcm-2
D-centers 2p
0
D-centers under 2p
0 under
001 01 1 10 100
1E-4
1E-3
001
01
1Nd=31015 cm-3
gain
and
abs
orpt
ion
cm
-1
pump kWcm-2
Population gain absorption
SiSb
Donor gain amp D--center absorption
Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)
Blue lines correspond to valley shift 5 meV (06 kbar)
Summary
The axial compressive stress of silicon crystal applied along [100] crystallographic orientation
From the experiment
- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors
- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors
- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress
From the theoretical treatment
- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys
- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states
- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal
Current study amp Further development
1) Spin-orbit interaction amp laser frequencies SiSb SiBi
2) Group-V donor lasing from isotope enriched silicon 28Si
3) Low T donor relaxation in stressed silicon (exp study)
4) Donoracceptor lasing from low dimensional SiSiGe structures
5) CW operation
D- binding energy vs compression
LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve
0 2 4 6 8 10 12 14 16 18 2000
05
10
15
20
25
109 c
-1
SiP
2p0(A
1+B
2) - 1s(A
1
u) LA-g TA-g
Междолинное расщепление мэВ
00 05 10 15 20 25 30 350
2
4
6
8
10
12
14
1
09 c-1
Междолинное расщепление meV
SiP (TA-f)
2p0-1s(E)
2p0-1s(B
1)
2p0-1s(A
1
u)
Сумма
0 10 20 30 400
1
2
3
4
5
6
7
10
10 c
-1
Междолинное расщепление мэВ
SiP 1s(B2) - 1s(A1) TA-g
1s(B2) - 1s(A1) LA-g
1кбар соответствует 85 мэВ
SiP SiP
1s(E)
1s(T2)
1s(A1)
TA-f84∙109 c-1
TA-f124∙109 c-1
LA-g03∙109 c-1
LA-g575109 c-1
TA-g7∙1010 c-1
TA-g36∙1010 c-1
2p0
SiP
Темп внутридолинных переходов
2р0 - 1s 21∙109 с-1
26∙1010 c-1
7∙1010 c-1
36∙1010 c-1
0 10 20 30 40
0
1
2
3
4
5
intervalley splitting meV
10
10 c
-1
1s(B2)-1s(A
1) TА-g
1s(B2)-1s(A
1) LA-g
SiSb
0 2 4 6 8 10 12 14 16 180
1
2
3
4
5
6
7
intervalley splitting meV
109 c
-1
SiSb 2p
0(A
1+B
2)-1s(Au
1) LA-g
2p0(A
1+B
2)-1s(E) TA-f
2p0(A
1+B
2)-1s(Au
1) TA-g
Переходы 2p0-1s(A
1
u) и 2p0-1s(B
1)
на ТА-f фононах пренебрежимо малы
1 kbar yields 85 meV valley shift for [100]
stress
1 kbar yields 85 meV valley shift for [100]
stress
SiSb SiSb
1s(E)
1s(T2)
1s(A1)
TA-f~108 c-1
TA-f142∙109 c-1
LA-g26∙109 c-1
LA-g175∙109 c-1
TA-g46∙1010 c-1
TA-g38∙1010 c-1
2p0
SiSb
Intra valley scattering rate
2р0 - 1s 21∙109 с-1
18∙1010 c-1
38∙1010 c-1
46∙1010 c-1
SiAs SiAs
LA-f079∙1010 c-1
1s(E)
1s(T2)
1s(A1)
TA-f122∙109 c-1
LA-g063∙109 c-1
LA-g07∙109 c-1
TA-f27∙1010 c-1
TA-f16∙1010 c-1
2p0
2s
2pplusmn
LA-g5∙1010 c-1
LA-g33∙1010 c-1
TA-f146 ∙109 c-1
LA-f098∙109 c-1
LA-f27∙1010 c-1
LA-g6∙109 c-1
LA-g6∙109 c-1
Intra valley scattering rates
2р0 - 1s 21∙109 с-1
2s - 1s 52∙109 c-1
2pplusmn - 1s 01 ∙109 c-1
2pplusmn - 2p0 144 ∙109 c-1
2pplusmn - 2s 89 ∙109 c-1
27∙1010 c-1
16∙1010 c-1
77∙1010 c-1
5∙1010 c-1
0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
rate
10
9 s-1
intervalley splitting meV
SiAs 2p(+-)-1s(Al
1) LA-f
2p(+-)-1s(Au
1) LA-g
Relaxation of the lower laser level
f- and g-phonon scattering rates in As donor under stress
0 2 4 6 8 10 12 14 16 18 20 220
1
2
3
4
5
6
intervalley splitting meV
109 c
-1
SiAs 2p
0-1s(Au
1) LA-g
2p0-1s(EB
1) TA-f
2p0-1s(Al
1) LA-f
2p0-1s(Au
1) TA-g
0 5 10 15 20 25 300
1
2
3
4
5
6
7
8
intervalley splitting meV1
010c-1
SiAs 1s(B
2)-1s(A
1
l) LA-g
1s(B2)-1s(A
1
l) TA-f
Relaxation of 2р(+-) and 2р0 states
1s(T2Г7)
1s(T2Г8)
1s(A1)
TA-f52∙109 c-1
LA-g~ 108 c-1
LA-g2∙109 c-1
LA-f47∙109 c-1
TA-f6∙109 c-1
2p0
2s
2pplusmn
LA-g053∙109 c-1
LA-g04∙109 c-1
TA-f14∙1010 c-1
TO-f~32∙1011 c-1
1s(E)
LA-g37∙109 c-1
SiBi SiBi
00 05 10 15 20 25 30 35 400
5
10
15
20
0 59 118 176 235 294 353 412 471
Intervalley splitting meV
1011
c-1
bar
SiBi 2p0-1s(Al
1) TO-f (для верхней ТО ветки) D
15 20 25 30 35 400
1
2
3
4
5
6
7
8
Intervalley splitting meV
1010
c-1
SiBi 2p
0 - 1s(Al
1) LA-f
0000 0493 0986 1479 1972 2465 2958 3451 39440
2
4
6
8
10
12
14
16
18
0 58 116 174 232 290 348 406 464
SiBi LO-g
2p+- - 1s(Al1)
Intervalley splitting meV
1010
c-1
2p+- - 1s(Al1)
with shiftedphonon dispersion on 05 meV
bar
7 8 9 10 11 12 130
5
10
15
20
25
30
35
Intervalley splitting meV
15 kbar
109 c
-1
SiBi2p(+-)-1s(Al
1) TO-f
для верхней ТО-f ветки для нижней ТО-f ветки
1 kbar
f- and g-phonon scattering rates in Bi donor under stress
0 2 4 6 80
2
4
6
8
Intervalley splitting meV
109 c
-1
SiBi 1s(B
2Г
7)-1s(Al
1)
0 20 40 60 800
2
4
6
8
10
12
14
Intervalley splitting meV
1010
c-1
SiBi1s(B
2)-1s(A
1
l) LA-g
Relaxation 1s(B2) state in Bi donor under stressed silicon
TEA CO2 laser excitation unstressed silicon (Family of experimental data)
Operating temperature
5 10 15 20 25 30 35
SiP SiSb SiBiSiAs
Si l
aser
s em
issi
on a
u
temperature K
Donors concentration 11015 - 5 1015 cm-3
Threshold intensity 10-100 kWcm2
Small signal gain 01-02 cm-1
120 140 160 180 200 220 240
36 42 48 54 60 66 72
Si l
aser
em
issi
on (
au
)
frequency (THz)
wavenumber (cm-1)
SiAs SiBiSiPSiSb
Emission spectra
2times3times7 mm3
THz
Quantum efficiency Exp Theory up to 10
SiP experiment(106 microm TEA CO2 laser excitation)
P donor THz output vs pump intensity under different stress
50 100 150 2000
10
10
0
em
issi
on a
u
frequency cm-1
SiP [100] 023 kbar 065 12
0
00 05 10 15 20 250
100
200
300
400
500
600 180 75 50 25 17 9 5 3 2
stress kbar
emis
sion
mV
SiP [100]
S=493x255 mm2
pump
kWcm2(a)
2 20 2000
100
200
300
400
500
600059
0
043
029118
147
177
221
266
SiP [100]
S=493x255 mm2
em
issi
on
mV
pump CO2 kWcm2
stress kbar
Sb donor THz output vs pump intensity and compressive stress
00 02 04 06 08 10 12 14 160
5
10
15
20
25
30
35
40
45
pump (kWcm2)
200 85 50 30 10 16 023 015
em
issi
on m
V
stress kbar
SiSb [100]
65x49x32 mm3
Nd= 1015cm-3
02 2 20 2000
5
10
15
20
25
30
35
40
45
65x49x32 mm3
SiSb[100]
emis
sion
mV
pump kWcm2
046023
0
081
105117128
stress kbar
SiSb experiment(106 microm TEA CO2 laser
excitation)
150 160 170 180 190 200
00 10 201720
1725
1730
10
0
0
emis
sion
au
frequency cm-1
SiSb [110] 624 bar 936 bar 1872 bar
0
sress kbar
cm-1
2p0 - 1s(B
2)
200kWcm2 correspond 1025quantcm2s
0 1 2 3 400
01
02
03
04 04 06 08
SiSb em
issi
on V
pump intensity 106 m kWcm2
stress [100] kbar 005 01 02 03
00 05 10 15 2(a) photon flux density 1023 quantcm2
SiSb Under Q-switch CO2 laser pump
Least value of threshold intensity ~150Wcm2
0 1 2 3 40
10
20
30
40
50
60
SiAs
[100] 617x(47x275) mm3
emis
sion
mV
stress kbar
200 150 85 50 30 10 16 1
pump (kWcm2)
2 20 2000
10
20
30
40
50
60 3831
283254
196
17
110810530250
SiAs[100]
617x(47x275) mm3
em
issi
on m
V
pump kWcm2
stress kbar
SiAs experiment(106 microm TEA CO2 laser
excitation)
As donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s
As donor THz output vs pump intensity under different stress
160 180 200 220
10
0
0
00 05 10 15 20 25
170
175
180
185
190
195
200
205
210
215
220
2p+-
1s(T2)
2p0 1s(B
2)
давление кбар
част
ота
см
-1SiAs [100]
em
issi
on a
u
frequency cm-1
240 bar 360 600
frequency
cm
-1
stress kbar
0
0 1 2170
220
1 2 3
00
02
04
06 35 38 4 43
11 117 16 22 29
SiAs
emis
sion
V
pump kWcm2
stress [100] kbar
00 05 10 15(b) pump photon density 1023 quantcm2
Least value of threshold intensity ~300Wcm2
SiAs Under Q-switch CO2 laser pump
20 20000
02
04
06
08
10 27
2522
1917
16
15
13
0
05
06
Pump intensity kW cm2
Inte
nsi
ty (
au
)
SiBi [100]
07(052034) mm3
07
Stress kbar
SiBi experiment(106 microm TEA CO2 laser
excitation)
Bi donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s
Sb donor THz output vs pump intensity under different stress
00 05 10 15 20 25 300
200
400
600
800 200 80 60 35 23 15 9
SiBi [100]
07(052034) mm3
em
issi
on
m
V
stress kbar
pump
kWcm2
02 04 06 080
100
200
300 130 100 80 60 53 41
In
tens
ity a
u
0 1 2 3 4 5
-40
-20
0
60
80
TA-g
TA-f
2p0(A
1ET
2)
1s(T2)
1s(A1)
1s(E)
1s(A1)
2p0(A
1+B
2)
Ene
rgy
(meV
)
Stress (kbar)
THz 1s(B2)
LO-g
pum
p en
ergy
117
meV
2 cont
0 1 2 3 4 5-60
-40
-20
0
60
80
LO-g
THz
LA-f
2s2p
+-
LA-gTA-f
4 co
nt
1s(T2)
1s(A1)
1s(E)
1s(A1)
2p0(A
1+B
2) E
ne
rgy
(meV
)
Stress (kbar)
THz1s(B
2)
pum
p en
erg
y 1
17 m
eV
2 cont
Energy levels of donors in stressed Si
As Sb
1211]100[ ss
XE u
X-valley splitting under uniaxial stress X
The stress removes sixfold degeneracy and as a result the energy difference ΔE appears between different groups of valleys
Intervalley phonon scattering of electrons in Si
K111K010
qN
qf
qg
ee[100]
[010][001]
e
Brillouin zonevector of reciprocal lattice normal processumklapp-process f -type umklapp-process g -type
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
21∙109 c-1
46∙1010 c-121∙1010 c-1
68∙109 c-1
2p0(А1+В2)
SiSb
Stress (06 kbar)
Laser state relaxation rates
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
29∙109 c-1
7∙1010 c-144∙1010 c-1
92∙109 c-1
2p0(А1+В2)
SiP
Stress (06 kbar)
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
26∙101035∙1010
42∙109
2p0(А1+В2)
Stress (25 kbar)
2pplusmn2s
15∙109
14∙109
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
55∙109 2∙109
85∙109
2p0(А1+В2)
Stress (18 kbar)
2pplusmn2s
3∙1011
E
E
SiAs
SiBi
Laser state relaxation rates s-1
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
Влияние деформации на эффективность накачки рабочих состояний
(Pump efficiency of the laser states depending on stress)
СО2
Релаксация на фононах
THg
СО2
Релаксация на фононах
THg emission
E
THg emissionE
001 01 1 10 100
1010
1011
1012
1013
1014 Nd=31015 cm-3
popu
latio
n c
m-3
pump kWcm-2
D-centers 2p
0
D-centers under 2p
0 under
001 01 1 10 100
1E-4
1E-3
001
01
1Nd=31015 cm-3
gain
and
abs
orpt
ion
cm
-1
pump kWcm-2
Population gain absorption
SiSb
Donor gain amp D--center absorption
Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)
Blue lines correspond to valley shift 5 meV (06 kbar)
Summary
The axial compressive stress of silicon crystal applied along [100] crystallographic orientation
From the experiment
- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors
- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors
- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress
From the theoretical treatment
- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys
- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states
- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal
Current study amp Further development
1) Spin-orbit interaction amp laser frequencies SiSb SiBi
2) Group-V donor lasing from isotope enriched silicon 28Si
3) Low T donor relaxation in stressed silicon (exp study)
4) Donoracceptor lasing from low dimensional SiSiGe structures
5) CW operation
D- binding energy vs compression
LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve
0 2 4 6 8 10 12 14 16 18 2000
05
10
15
20
25
109 c
-1
SiP
2p0(A
1+B
2) - 1s(A
1
u) LA-g TA-g
Междолинное расщепление мэВ
00 05 10 15 20 25 30 350
2
4
6
8
10
12
14
1
09 c-1
Междолинное расщепление meV
SiP (TA-f)
2p0-1s(E)
2p0-1s(B
1)
2p0-1s(A
1
u)
Сумма
0 10 20 30 400
1
2
3
4
5
6
7
10
10 c
-1
Междолинное расщепление мэВ
SiP 1s(B2) - 1s(A1) TA-g
1s(B2) - 1s(A1) LA-g
1кбар соответствует 85 мэВ
SiP SiP
1s(E)
1s(T2)
1s(A1)
TA-f84∙109 c-1
TA-f124∙109 c-1
LA-g03∙109 c-1
LA-g575109 c-1
TA-g7∙1010 c-1
TA-g36∙1010 c-1
2p0
SiP
Темп внутридолинных переходов
2р0 - 1s 21∙109 с-1
26∙1010 c-1
7∙1010 c-1
36∙1010 c-1
0 10 20 30 40
0
1
2
3
4
5
intervalley splitting meV
10
10 c
-1
1s(B2)-1s(A
1) TА-g
1s(B2)-1s(A
1) LA-g
SiSb
0 2 4 6 8 10 12 14 16 180
1
2
3
4
5
6
7
intervalley splitting meV
109 c
-1
SiSb 2p
0(A
1+B
2)-1s(Au
1) LA-g
2p0(A
1+B
2)-1s(E) TA-f
2p0(A
1+B
2)-1s(Au
1) TA-g
Переходы 2p0-1s(A
1
u) и 2p0-1s(B
1)
на ТА-f фононах пренебрежимо малы
1 kbar yields 85 meV valley shift for [100]
stress
1 kbar yields 85 meV valley shift for [100]
stress
SiSb SiSb
1s(E)
1s(T2)
1s(A1)
TA-f~108 c-1
TA-f142∙109 c-1
LA-g26∙109 c-1
LA-g175∙109 c-1
TA-g46∙1010 c-1
TA-g38∙1010 c-1
2p0
SiSb
Intra valley scattering rate
2р0 - 1s 21∙109 с-1
18∙1010 c-1
38∙1010 c-1
46∙1010 c-1
SiAs SiAs
LA-f079∙1010 c-1
1s(E)
1s(T2)
1s(A1)
TA-f122∙109 c-1
LA-g063∙109 c-1
LA-g07∙109 c-1
TA-f27∙1010 c-1
TA-f16∙1010 c-1
2p0
2s
2pplusmn
LA-g5∙1010 c-1
LA-g33∙1010 c-1
TA-f146 ∙109 c-1
LA-f098∙109 c-1
LA-f27∙1010 c-1
LA-g6∙109 c-1
LA-g6∙109 c-1
Intra valley scattering rates
2р0 - 1s 21∙109 с-1
2s - 1s 52∙109 c-1
2pplusmn - 1s 01 ∙109 c-1
2pplusmn - 2p0 144 ∙109 c-1
2pplusmn - 2s 89 ∙109 c-1
27∙1010 c-1
16∙1010 c-1
77∙1010 c-1
5∙1010 c-1
0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
rate
10
9 s-1
intervalley splitting meV
SiAs 2p(+-)-1s(Al
1) LA-f
2p(+-)-1s(Au
1) LA-g
Relaxation of the lower laser level
f- and g-phonon scattering rates in As donor under stress
0 2 4 6 8 10 12 14 16 18 20 220
1
2
3
4
5
6
intervalley splitting meV
109 c
-1
SiAs 2p
0-1s(Au
1) LA-g
2p0-1s(EB
1) TA-f
2p0-1s(Al
1) LA-f
2p0-1s(Au
1) TA-g
0 5 10 15 20 25 300
1
2
3
4
5
6
7
8
intervalley splitting meV1
010c-1
SiAs 1s(B
2)-1s(A
1
l) LA-g
1s(B2)-1s(A
1
l) TA-f
Relaxation of 2р(+-) and 2р0 states
1s(T2Г7)
1s(T2Г8)
1s(A1)
TA-f52∙109 c-1
LA-g~ 108 c-1
LA-g2∙109 c-1
LA-f47∙109 c-1
TA-f6∙109 c-1
2p0
2s
2pplusmn
LA-g053∙109 c-1
LA-g04∙109 c-1
TA-f14∙1010 c-1
TO-f~32∙1011 c-1
1s(E)
LA-g37∙109 c-1
SiBi SiBi
00 05 10 15 20 25 30 35 400
5
10
15
20
0 59 118 176 235 294 353 412 471
Intervalley splitting meV
1011
c-1
bar
SiBi 2p0-1s(Al
1) TO-f (для верхней ТО ветки) D
15 20 25 30 35 400
1
2
3
4
5
6
7
8
Intervalley splitting meV
1010
c-1
SiBi 2p
0 - 1s(Al
1) LA-f
0000 0493 0986 1479 1972 2465 2958 3451 39440
2
4
6
8
10
12
14
16
18
0 58 116 174 232 290 348 406 464
SiBi LO-g
2p+- - 1s(Al1)
Intervalley splitting meV
1010
c-1
2p+- - 1s(Al1)
with shiftedphonon dispersion on 05 meV
bar
7 8 9 10 11 12 130
5
10
15
20
25
30
35
Intervalley splitting meV
15 kbar
109 c
-1
SiBi2p(+-)-1s(Al
1) TO-f
для верхней ТО-f ветки для нижней ТО-f ветки
1 kbar
f- and g-phonon scattering rates in Bi donor under stress
0 2 4 6 80
2
4
6
8
Intervalley splitting meV
109 c
-1
SiBi 1s(B
2Г
7)-1s(Al
1)
0 20 40 60 800
2
4
6
8
10
12
14
Intervalley splitting meV
1010
c-1
SiBi1s(B
2)-1s(A
1
l) LA-g
Relaxation 1s(B2) state in Bi donor under stressed silicon
SiP experiment(106 microm TEA CO2 laser excitation)
P donor THz output vs pump intensity under different stress
50 100 150 2000
10
10
0
em
issi
on a
u
frequency cm-1
SiP [100] 023 kbar 065 12
0
00 05 10 15 20 250
100
200
300
400
500
600 180 75 50 25 17 9 5 3 2
stress kbar
emis
sion
mV
SiP [100]
S=493x255 mm2
pump
kWcm2(a)
2 20 2000
100
200
300
400
500
600059
0
043
029118
147
177
221
266
SiP [100]
S=493x255 mm2
em
issi
on
mV
pump CO2 kWcm2
stress kbar
Sb donor THz output vs pump intensity and compressive stress
00 02 04 06 08 10 12 14 160
5
10
15
20
25
30
35
40
45
pump (kWcm2)
200 85 50 30 10 16 023 015
em
issi
on m
V
stress kbar
SiSb [100]
65x49x32 mm3
Nd= 1015cm-3
02 2 20 2000
5
10
15
20
25
30
35
40
45
65x49x32 mm3
SiSb[100]
emis
sion
mV
pump kWcm2
046023
0
081
105117128
stress kbar
SiSb experiment(106 microm TEA CO2 laser
excitation)
150 160 170 180 190 200
00 10 201720
1725
1730
10
0
0
emis
sion
au
frequency cm-1
SiSb [110] 624 bar 936 bar 1872 bar
0
sress kbar
cm-1
2p0 - 1s(B
2)
200kWcm2 correspond 1025quantcm2s
0 1 2 3 400
01
02
03
04 04 06 08
SiSb em
issi
on V
pump intensity 106 m kWcm2
stress [100] kbar 005 01 02 03
00 05 10 15 2(a) photon flux density 1023 quantcm2
SiSb Under Q-switch CO2 laser pump
Least value of threshold intensity ~150Wcm2
0 1 2 3 40
10
20
30
40
50
60
SiAs
[100] 617x(47x275) mm3
emis
sion
mV
stress kbar
200 150 85 50 30 10 16 1
pump (kWcm2)
2 20 2000
10
20
30
40
50
60 3831
283254
196
17
110810530250
SiAs[100]
617x(47x275) mm3
em
issi
on m
V
pump kWcm2
stress kbar
SiAs experiment(106 microm TEA CO2 laser
excitation)
As donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s
As donor THz output vs pump intensity under different stress
160 180 200 220
10
0
0
00 05 10 15 20 25
170
175
180
185
190
195
200
205
210
215
220
2p+-
1s(T2)
2p0 1s(B
2)
давление кбар
част
ота
см
-1SiAs [100]
em
issi
on a
u
frequency cm-1
240 bar 360 600
frequency
cm
-1
stress kbar
0
0 1 2170
220
1 2 3
00
02
04
06 35 38 4 43
11 117 16 22 29
SiAs
emis
sion
V
pump kWcm2
stress [100] kbar
00 05 10 15(b) pump photon density 1023 quantcm2
Least value of threshold intensity ~300Wcm2
SiAs Under Q-switch CO2 laser pump
20 20000
02
04
06
08
10 27
2522
1917
16
15
13
0
05
06
Pump intensity kW cm2
Inte
nsi
ty (
au
)
SiBi [100]
07(052034) mm3
07
Stress kbar
SiBi experiment(106 microm TEA CO2 laser
excitation)
Bi donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s
Sb donor THz output vs pump intensity under different stress
00 05 10 15 20 25 300
200
400
600
800 200 80 60 35 23 15 9
SiBi [100]
07(052034) mm3
em
issi
on
m
V
stress kbar
pump
kWcm2
02 04 06 080
100
200
300 130 100 80 60 53 41
In
tens
ity a
u
0 1 2 3 4 5
-40
-20
0
60
80
TA-g
TA-f
2p0(A
1ET
2)
1s(T2)
1s(A1)
1s(E)
1s(A1)
2p0(A
1+B
2)
Ene
rgy
(meV
)
Stress (kbar)
THz 1s(B2)
LO-g
pum
p en
ergy
117
meV
2 cont
0 1 2 3 4 5-60
-40
-20
0
60
80
LO-g
THz
LA-f
2s2p
+-
LA-gTA-f
4 co
nt
1s(T2)
1s(A1)
1s(E)
1s(A1)
2p0(A
1+B
2) E
ne
rgy
(meV
)
Stress (kbar)
THz1s(B
2)
pum
p en
erg
y 1
17 m
eV
2 cont
Energy levels of donors in stressed Si
As Sb
1211]100[ ss
XE u
X-valley splitting under uniaxial stress X
The stress removes sixfold degeneracy and as a result the energy difference ΔE appears between different groups of valleys
Intervalley phonon scattering of electrons in Si
K111K010
qN
qf
qg
ee[100]
[010][001]
e
Brillouin zonevector of reciprocal lattice normal processumklapp-process f -type umklapp-process g -type
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
21∙109 c-1
46∙1010 c-121∙1010 c-1
68∙109 c-1
2p0(А1+В2)
SiSb
Stress (06 kbar)
Laser state relaxation rates
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
29∙109 c-1
7∙1010 c-144∙1010 c-1
92∙109 c-1
2p0(А1+В2)
SiP
Stress (06 kbar)
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
26∙101035∙1010
42∙109
2p0(А1+В2)
Stress (25 kbar)
2pplusmn2s
15∙109
14∙109
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
55∙109 2∙109
85∙109
2p0(А1+В2)
Stress (18 kbar)
2pplusmn2s
3∙1011
E
E
SiAs
SiBi
Laser state relaxation rates s-1
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
Влияние деформации на эффективность накачки рабочих состояний
(Pump efficiency of the laser states depending on stress)
СО2
Релаксация на фононах
THg
СО2
Релаксация на фононах
THg emission
E
THg emissionE
001 01 1 10 100
1010
1011
1012
1013
1014 Nd=31015 cm-3
popu
latio
n c
m-3
pump kWcm-2
D-centers 2p
0
D-centers under 2p
0 under
001 01 1 10 100
1E-4
1E-3
001
01
1Nd=31015 cm-3
gain
and
abs
orpt
ion
cm
-1
pump kWcm-2
Population gain absorption
SiSb
Donor gain amp D--center absorption
Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)
Blue lines correspond to valley shift 5 meV (06 kbar)
Summary
The axial compressive stress of silicon crystal applied along [100] crystallographic orientation
From the experiment
- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors
- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors
- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress
From the theoretical treatment
- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys
- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states
- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal
Current study amp Further development
1) Spin-orbit interaction amp laser frequencies SiSb SiBi
2) Group-V donor lasing from isotope enriched silicon 28Si
3) Low T donor relaxation in stressed silicon (exp study)
4) Donoracceptor lasing from low dimensional SiSiGe structures
5) CW operation
D- binding energy vs compression
LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve
0 2 4 6 8 10 12 14 16 18 2000
05
10
15
20
25
109 c
-1
SiP
2p0(A
1+B
2) - 1s(A
1
u) LA-g TA-g
Междолинное расщепление мэВ
00 05 10 15 20 25 30 350
2
4
6
8
10
12
14
1
09 c-1
Междолинное расщепление meV
SiP (TA-f)
2p0-1s(E)
2p0-1s(B
1)
2p0-1s(A
1
u)
Сумма
0 10 20 30 400
1
2
3
4
5
6
7
10
10 c
-1
Междолинное расщепление мэВ
SiP 1s(B2) - 1s(A1) TA-g
1s(B2) - 1s(A1) LA-g
1кбар соответствует 85 мэВ
SiP SiP
1s(E)
1s(T2)
1s(A1)
TA-f84∙109 c-1
TA-f124∙109 c-1
LA-g03∙109 c-1
LA-g575109 c-1
TA-g7∙1010 c-1
TA-g36∙1010 c-1
2p0
SiP
Темп внутридолинных переходов
2р0 - 1s 21∙109 с-1
26∙1010 c-1
7∙1010 c-1
36∙1010 c-1
0 10 20 30 40
0
1
2
3
4
5
intervalley splitting meV
10
10 c
-1
1s(B2)-1s(A
1) TА-g
1s(B2)-1s(A
1) LA-g
SiSb
0 2 4 6 8 10 12 14 16 180
1
2
3
4
5
6
7
intervalley splitting meV
109 c
-1
SiSb 2p
0(A
1+B
2)-1s(Au
1) LA-g
2p0(A
1+B
2)-1s(E) TA-f
2p0(A
1+B
2)-1s(Au
1) TA-g
Переходы 2p0-1s(A
1
u) и 2p0-1s(B
1)
на ТА-f фононах пренебрежимо малы
1 kbar yields 85 meV valley shift for [100]
stress
1 kbar yields 85 meV valley shift for [100]
stress
SiSb SiSb
1s(E)
1s(T2)
1s(A1)
TA-f~108 c-1
TA-f142∙109 c-1
LA-g26∙109 c-1
LA-g175∙109 c-1
TA-g46∙1010 c-1
TA-g38∙1010 c-1
2p0
SiSb
Intra valley scattering rate
2р0 - 1s 21∙109 с-1
18∙1010 c-1
38∙1010 c-1
46∙1010 c-1
SiAs SiAs
LA-f079∙1010 c-1
1s(E)
1s(T2)
1s(A1)
TA-f122∙109 c-1
LA-g063∙109 c-1
LA-g07∙109 c-1
TA-f27∙1010 c-1
TA-f16∙1010 c-1
2p0
2s
2pplusmn
LA-g5∙1010 c-1
LA-g33∙1010 c-1
TA-f146 ∙109 c-1
LA-f098∙109 c-1
LA-f27∙1010 c-1
LA-g6∙109 c-1
LA-g6∙109 c-1
Intra valley scattering rates
2р0 - 1s 21∙109 с-1
2s - 1s 52∙109 c-1
2pplusmn - 1s 01 ∙109 c-1
2pplusmn - 2p0 144 ∙109 c-1
2pplusmn - 2s 89 ∙109 c-1
27∙1010 c-1
16∙1010 c-1
77∙1010 c-1
5∙1010 c-1
0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
rate
10
9 s-1
intervalley splitting meV
SiAs 2p(+-)-1s(Al
1) LA-f
2p(+-)-1s(Au
1) LA-g
Relaxation of the lower laser level
f- and g-phonon scattering rates in As donor under stress
0 2 4 6 8 10 12 14 16 18 20 220
1
2
3
4
5
6
intervalley splitting meV
109 c
-1
SiAs 2p
0-1s(Au
1) LA-g
2p0-1s(EB
1) TA-f
2p0-1s(Al
1) LA-f
2p0-1s(Au
1) TA-g
0 5 10 15 20 25 300
1
2
3
4
5
6
7
8
intervalley splitting meV1
010c-1
SiAs 1s(B
2)-1s(A
1
l) LA-g
1s(B2)-1s(A
1
l) TA-f
Relaxation of 2р(+-) and 2р0 states
1s(T2Г7)
1s(T2Г8)
1s(A1)
TA-f52∙109 c-1
LA-g~ 108 c-1
LA-g2∙109 c-1
LA-f47∙109 c-1
TA-f6∙109 c-1
2p0
2s
2pplusmn
LA-g053∙109 c-1
LA-g04∙109 c-1
TA-f14∙1010 c-1
TO-f~32∙1011 c-1
1s(E)
LA-g37∙109 c-1
SiBi SiBi
00 05 10 15 20 25 30 35 400
5
10
15
20
0 59 118 176 235 294 353 412 471
Intervalley splitting meV
1011
c-1
bar
SiBi 2p0-1s(Al
1) TO-f (для верхней ТО ветки) D
15 20 25 30 35 400
1
2
3
4
5
6
7
8
Intervalley splitting meV
1010
c-1
SiBi 2p
0 - 1s(Al
1) LA-f
0000 0493 0986 1479 1972 2465 2958 3451 39440
2
4
6
8
10
12
14
16
18
0 58 116 174 232 290 348 406 464
SiBi LO-g
2p+- - 1s(Al1)
Intervalley splitting meV
1010
c-1
2p+- - 1s(Al1)
with shiftedphonon dispersion on 05 meV
bar
7 8 9 10 11 12 130
5
10
15
20
25
30
35
Intervalley splitting meV
15 kbar
109 c
-1
SiBi2p(+-)-1s(Al
1) TO-f
для верхней ТО-f ветки для нижней ТО-f ветки
1 kbar
f- and g-phonon scattering rates in Bi donor under stress
0 2 4 6 80
2
4
6
8
Intervalley splitting meV
109 c
-1
SiBi 1s(B
2Г
7)-1s(Al
1)
0 20 40 60 800
2
4
6
8
10
12
14
Intervalley splitting meV
1010
c-1
SiBi1s(B
2)-1s(A
1
l) LA-g
Relaxation 1s(B2) state in Bi donor under stressed silicon
Sb donor THz output vs pump intensity and compressive stress
00 02 04 06 08 10 12 14 160
5
10
15
20
25
30
35
40
45
pump (kWcm2)
200 85 50 30 10 16 023 015
em
issi
on m
V
stress kbar
SiSb [100]
65x49x32 mm3
Nd= 1015cm-3
02 2 20 2000
5
10
15
20
25
30
35
40
45
65x49x32 mm3
SiSb[100]
emis
sion
mV
pump kWcm2
046023
0
081
105117128
stress kbar
SiSb experiment(106 microm TEA CO2 laser
excitation)
150 160 170 180 190 200
00 10 201720
1725
1730
10
0
0
emis
sion
au
frequency cm-1
SiSb [110] 624 bar 936 bar 1872 bar
0
sress kbar
cm-1
2p0 - 1s(B
2)
200kWcm2 correspond 1025quantcm2s
0 1 2 3 400
01
02
03
04 04 06 08
SiSb em
issi
on V
pump intensity 106 m kWcm2
stress [100] kbar 005 01 02 03
00 05 10 15 2(a) photon flux density 1023 quantcm2
SiSb Under Q-switch CO2 laser pump
Least value of threshold intensity ~150Wcm2
0 1 2 3 40
10
20
30
40
50
60
SiAs
[100] 617x(47x275) mm3
emis
sion
mV
stress kbar
200 150 85 50 30 10 16 1
pump (kWcm2)
2 20 2000
10
20
30
40
50
60 3831
283254
196
17
110810530250
SiAs[100]
617x(47x275) mm3
em
issi
on m
V
pump kWcm2
stress kbar
SiAs experiment(106 microm TEA CO2 laser
excitation)
As donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s
As donor THz output vs pump intensity under different stress
160 180 200 220
10
0
0
00 05 10 15 20 25
170
175
180
185
190
195
200
205
210
215
220
2p+-
1s(T2)
2p0 1s(B
2)
давление кбар
част
ота
см
-1SiAs [100]
em
issi
on a
u
frequency cm-1
240 bar 360 600
frequency
cm
-1
stress kbar
0
0 1 2170
220
1 2 3
00
02
04
06 35 38 4 43
11 117 16 22 29
SiAs
emis
sion
V
pump kWcm2
stress [100] kbar
00 05 10 15(b) pump photon density 1023 quantcm2
Least value of threshold intensity ~300Wcm2
SiAs Under Q-switch CO2 laser pump
20 20000
02
04
06
08
10 27
2522
1917
16
15
13
0
05
06
Pump intensity kW cm2
Inte
nsi
ty (
au
)
SiBi [100]
07(052034) mm3
07
Stress kbar
SiBi experiment(106 microm TEA CO2 laser
excitation)
Bi donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s
Sb donor THz output vs pump intensity under different stress
00 05 10 15 20 25 300
200
400
600
800 200 80 60 35 23 15 9
SiBi [100]
07(052034) mm3
em
issi
on
m
V
stress kbar
pump
kWcm2
02 04 06 080
100
200
300 130 100 80 60 53 41
In
tens
ity a
u
0 1 2 3 4 5
-40
-20
0
60
80
TA-g
TA-f
2p0(A
1ET
2)
1s(T2)
1s(A1)
1s(E)
1s(A1)
2p0(A
1+B
2)
Ene
rgy
(meV
)
Stress (kbar)
THz 1s(B2)
LO-g
pum
p en
ergy
117
meV
2 cont
0 1 2 3 4 5-60
-40
-20
0
60
80
LO-g
THz
LA-f
2s2p
+-
LA-gTA-f
4 co
nt
1s(T2)
1s(A1)
1s(E)
1s(A1)
2p0(A
1+B
2) E
ne
rgy
(meV
)
Stress (kbar)
THz1s(B
2)
pum
p en
erg
y 1
17 m
eV
2 cont
Energy levels of donors in stressed Si
As Sb
1211]100[ ss
XE u
X-valley splitting under uniaxial stress X
The stress removes sixfold degeneracy and as a result the energy difference ΔE appears between different groups of valleys
Intervalley phonon scattering of electrons in Si
K111K010
qN
qf
qg
ee[100]
[010][001]
e
Brillouin zonevector of reciprocal lattice normal processumklapp-process f -type umklapp-process g -type
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
21∙109 c-1
46∙1010 c-121∙1010 c-1
68∙109 c-1
2p0(А1+В2)
SiSb
Stress (06 kbar)
Laser state relaxation rates
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
29∙109 c-1
7∙1010 c-144∙1010 c-1
92∙109 c-1
2p0(А1+В2)
SiP
Stress (06 kbar)
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
26∙101035∙1010
42∙109
2p0(А1+В2)
Stress (25 kbar)
2pplusmn2s
15∙109
14∙109
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
55∙109 2∙109
85∙109
2p0(А1+В2)
Stress (18 kbar)
2pplusmn2s
3∙1011
E
E
SiAs
SiBi
Laser state relaxation rates s-1
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
Влияние деформации на эффективность накачки рабочих состояний
(Pump efficiency of the laser states depending on stress)
СО2
Релаксация на фононах
THg
СО2
Релаксация на фононах
THg emission
E
THg emissionE
001 01 1 10 100
1010
1011
1012
1013
1014 Nd=31015 cm-3
popu
latio
n c
m-3
pump kWcm-2
D-centers 2p
0
D-centers under 2p
0 under
001 01 1 10 100
1E-4
1E-3
001
01
1Nd=31015 cm-3
gain
and
abs
orpt
ion
cm
-1
pump kWcm-2
Population gain absorption
SiSb
Donor gain amp D--center absorption
Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)
Blue lines correspond to valley shift 5 meV (06 kbar)
Summary
The axial compressive stress of silicon crystal applied along [100] crystallographic orientation
From the experiment
- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors
- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors
- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress
From the theoretical treatment
- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys
- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states
- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal
Current study amp Further development
1) Spin-orbit interaction amp laser frequencies SiSb SiBi
2) Group-V donor lasing from isotope enriched silicon 28Si
3) Low T donor relaxation in stressed silicon (exp study)
4) Donoracceptor lasing from low dimensional SiSiGe structures
5) CW operation
D- binding energy vs compression
LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve
0 2 4 6 8 10 12 14 16 18 2000
05
10
15
20
25
109 c
-1
SiP
2p0(A
1+B
2) - 1s(A
1
u) LA-g TA-g
Междолинное расщепление мэВ
00 05 10 15 20 25 30 350
2
4
6
8
10
12
14
1
09 c-1
Междолинное расщепление meV
SiP (TA-f)
2p0-1s(E)
2p0-1s(B
1)
2p0-1s(A
1
u)
Сумма
0 10 20 30 400
1
2
3
4
5
6
7
10
10 c
-1
Междолинное расщепление мэВ
SiP 1s(B2) - 1s(A1) TA-g
1s(B2) - 1s(A1) LA-g
1кбар соответствует 85 мэВ
SiP SiP
1s(E)
1s(T2)
1s(A1)
TA-f84∙109 c-1
TA-f124∙109 c-1
LA-g03∙109 c-1
LA-g575109 c-1
TA-g7∙1010 c-1
TA-g36∙1010 c-1
2p0
SiP
Темп внутридолинных переходов
2р0 - 1s 21∙109 с-1
26∙1010 c-1
7∙1010 c-1
36∙1010 c-1
0 10 20 30 40
0
1
2
3
4
5
intervalley splitting meV
10
10 c
-1
1s(B2)-1s(A
1) TА-g
1s(B2)-1s(A
1) LA-g
SiSb
0 2 4 6 8 10 12 14 16 180
1
2
3
4
5
6
7
intervalley splitting meV
109 c
-1
SiSb 2p
0(A
1+B
2)-1s(Au
1) LA-g
2p0(A
1+B
2)-1s(E) TA-f
2p0(A
1+B
2)-1s(Au
1) TA-g
Переходы 2p0-1s(A
1
u) и 2p0-1s(B
1)
на ТА-f фононах пренебрежимо малы
1 kbar yields 85 meV valley shift for [100]
stress
1 kbar yields 85 meV valley shift for [100]
stress
SiSb SiSb
1s(E)
1s(T2)
1s(A1)
TA-f~108 c-1
TA-f142∙109 c-1
LA-g26∙109 c-1
LA-g175∙109 c-1
TA-g46∙1010 c-1
TA-g38∙1010 c-1
2p0
SiSb
Intra valley scattering rate
2р0 - 1s 21∙109 с-1
18∙1010 c-1
38∙1010 c-1
46∙1010 c-1
SiAs SiAs
LA-f079∙1010 c-1
1s(E)
1s(T2)
1s(A1)
TA-f122∙109 c-1
LA-g063∙109 c-1
LA-g07∙109 c-1
TA-f27∙1010 c-1
TA-f16∙1010 c-1
2p0
2s
2pplusmn
LA-g5∙1010 c-1
LA-g33∙1010 c-1
TA-f146 ∙109 c-1
LA-f098∙109 c-1
LA-f27∙1010 c-1
LA-g6∙109 c-1
LA-g6∙109 c-1
Intra valley scattering rates
2р0 - 1s 21∙109 с-1
2s - 1s 52∙109 c-1
2pplusmn - 1s 01 ∙109 c-1
2pplusmn - 2p0 144 ∙109 c-1
2pplusmn - 2s 89 ∙109 c-1
27∙1010 c-1
16∙1010 c-1
77∙1010 c-1
5∙1010 c-1
0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
rate
10
9 s-1
intervalley splitting meV
SiAs 2p(+-)-1s(Al
1) LA-f
2p(+-)-1s(Au
1) LA-g
Relaxation of the lower laser level
f- and g-phonon scattering rates in As donor under stress
0 2 4 6 8 10 12 14 16 18 20 220
1
2
3
4
5
6
intervalley splitting meV
109 c
-1
SiAs 2p
0-1s(Au
1) LA-g
2p0-1s(EB
1) TA-f
2p0-1s(Al
1) LA-f
2p0-1s(Au
1) TA-g
0 5 10 15 20 25 300
1
2
3
4
5
6
7
8
intervalley splitting meV1
010c-1
SiAs 1s(B
2)-1s(A
1
l) LA-g
1s(B2)-1s(A
1
l) TA-f
Relaxation of 2р(+-) and 2р0 states
1s(T2Г7)
1s(T2Г8)
1s(A1)
TA-f52∙109 c-1
LA-g~ 108 c-1
LA-g2∙109 c-1
LA-f47∙109 c-1
TA-f6∙109 c-1
2p0
2s
2pplusmn
LA-g053∙109 c-1
LA-g04∙109 c-1
TA-f14∙1010 c-1
TO-f~32∙1011 c-1
1s(E)
LA-g37∙109 c-1
SiBi SiBi
00 05 10 15 20 25 30 35 400
5
10
15
20
0 59 118 176 235 294 353 412 471
Intervalley splitting meV
1011
c-1
bar
SiBi 2p0-1s(Al
1) TO-f (для верхней ТО ветки) D
15 20 25 30 35 400
1
2
3
4
5
6
7
8
Intervalley splitting meV
1010
c-1
SiBi 2p
0 - 1s(Al
1) LA-f
0000 0493 0986 1479 1972 2465 2958 3451 39440
2
4
6
8
10
12
14
16
18
0 58 116 174 232 290 348 406 464
SiBi LO-g
2p+- - 1s(Al1)
Intervalley splitting meV
1010
c-1
2p+- - 1s(Al1)
with shiftedphonon dispersion on 05 meV
bar
7 8 9 10 11 12 130
5
10
15
20
25
30
35
Intervalley splitting meV
15 kbar
109 c
-1
SiBi2p(+-)-1s(Al
1) TO-f
для верхней ТО-f ветки для нижней ТО-f ветки
1 kbar
f- and g-phonon scattering rates in Bi donor under stress
0 2 4 6 80
2
4
6
8
Intervalley splitting meV
109 c
-1
SiBi 1s(B
2Г
7)-1s(Al
1)
0 20 40 60 800
2
4
6
8
10
12
14
Intervalley splitting meV
1010
c-1
SiBi1s(B
2)-1s(A
1
l) LA-g
Relaxation 1s(B2) state in Bi donor under stressed silicon
0 1 2 3 400
01
02
03
04 04 06 08
SiSb em
issi
on V
pump intensity 106 m kWcm2
stress [100] kbar 005 01 02 03
00 05 10 15 2(a) photon flux density 1023 quantcm2
SiSb Under Q-switch CO2 laser pump
Least value of threshold intensity ~150Wcm2
0 1 2 3 40
10
20
30
40
50
60
SiAs
[100] 617x(47x275) mm3
emis
sion
mV
stress kbar
200 150 85 50 30 10 16 1
pump (kWcm2)
2 20 2000
10
20
30
40
50
60 3831
283254
196
17
110810530250
SiAs[100]
617x(47x275) mm3
em
issi
on m
V
pump kWcm2
stress kbar
SiAs experiment(106 microm TEA CO2 laser
excitation)
As donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s
As donor THz output vs pump intensity under different stress
160 180 200 220
10
0
0
00 05 10 15 20 25
170
175
180
185
190
195
200
205
210
215
220
2p+-
1s(T2)
2p0 1s(B
2)
давление кбар
част
ота
см
-1SiAs [100]
em
issi
on a
u
frequency cm-1
240 bar 360 600
frequency
cm
-1
stress kbar
0
0 1 2170
220
1 2 3
00
02
04
06 35 38 4 43
11 117 16 22 29
SiAs
emis
sion
V
pump kWcm2
stress [100] kbar
00 05 10 15(b) pump photon density 1023 quantcm2
Least value of threshold intensity ~300Wcm2
SiAs Under Q-switch CO2 laser pump
20 20000
02
04
06
08
10 27
2522
1917
16
15
13
0
05
06
Pump intensity kW cm2
Inte
nsi
ty (
au
)
SiBi [100]
07(052034) mm3
07
Stress kbar
SiBi experiment(106 microm TEA CO2 laser
excitation)
Bi donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s
Sb donor THz output vs pump intensity under different stress
00 05 10 15 20 25 300
200
400
600
800 200 80 60 35 23 15 9
SiBi [100]
07(052034) mm3
em
issi
on
m
V
stress kbar
pump
kWcm2
02 04 06 080
100
200
300 130 100 80 60 53 41
In
tens
ity a
u
0 1 2 3 4 5
-40
-20
0
60
80
TA-g
TA-f
2p0(A
1ET
2)
1s(T2)
1s(A1)
1s(E)
1s(A1)
2p0(A
1+B
2)
Ene
rgy
(meV
)
Stress (kbar)
THz 1s(B2)
LO-g
pum
p en
ergy
117
meV
2 cont
0 1 2 3 4 5-60
-40
-20
0
60
80
LO-g
THz
LA-f
2s2p
+-
LA-gTA-f
4 co
nt
1s(T2)
1s(A1)
1s(E)
1s(A1)
2p0(A
1+B
2) E
ne
rgy
(meV
)
Stress (kbar)
THz1s(B
2)
pum
p en
erg
y 1
17 m
eV
2 cont
Energy levels of donors in stressed Si
As Sb
1211]100[ ss
XE u
X-valley splitting under uniaxial stress X
The stress removes sixfold degeneracy and as a result the energy difference ΔE appears between different groups of valleys
Intervalley phonon scattering of electrons in Si
K111K010
qN
qf
qg
ee[100]
[010][001]
e
Brillouin zonevector of reciprocal lattice normal processumklapp-process f -type umklapp-process g -type
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
21∙109 c-1
46∙1010 c-121∙1010 c-1
68∙109 c-1
2p0(А1+В2)
SiSb
Stress (06 kbar)
Laser state relaxation rates
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
29∙109 c-1
7∙1010 c-144∙1010 c-1
92∙109 c-1
2p0(А1+В2)
SiP
Stress (06 kbar)
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
26∙101035∙1010
42∙109
2p0(А1+В2)
Stress (25 kbar)
2pplusmn2s
15∙109
14∙109
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
55∙109 2∙109
85∙109
2p0(А1+В2)
Stress (18 kbar)
2pplusmn2s
3∙1011
E
E
SiAs
SiBi
Laser state relaxation rates s-1
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
Влияние деформации на эффективность накачки рабочих состояний
(Pump efficiency of the laser states depending on stress)
СО2
Релаксация на фононах
THg
СО2
Релаксация на фононах
THg emission
E
THg emissionE
001 01 1 10 100
1010
1011
1012
1013
1014 Nd=31015 cm-3
popu
latio
n c
m-3
pump kWcm-2
D-centers 2p
0
D-centers under 2p
0 under
001 01 1 10 100
1E-4
1E-3
001
01
1Nd=31015 cm-3
gain
and
abs
orpt
ion
cm
-1
pump kWcm-2
Population gain absorption
SiSb
Donor gain amp D--center absorption
Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)
Blue lines correspond to valley shift 5 meV (06 kbar)
Summary
The axial compressive stress of silicon crystal applied along [100] crystallographic orientation
From the experiment
- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors
- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors
- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress
From the theoretical treatment
- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys
- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states
- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal
Current study amp Further development
1) Spin-orbit interaction amp laser frequencies SiSb SiBi
2) Group-V donor lasing from isotope enriched silicon 28Si
3) Low T donor relaxation in stressed silicon (exp study)
4) Donoracceptor lasing from low dimensional SiSiGe structures
5) CW operation
D- binding energy vs compression
LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve
0 2 4 6 8 10 12 14 16 18 2000
05
10
15
20
25
109 c
-1
SiP
2p0(A
1+B
2) - 1s(A
1
u) LA-g TA-g
Междолинное расщепление мэВ
00 05 10 15 20 25 30 350
2
4
6
8
10
12
14
1
09 c-1
Междолинное расщепление meV
SiP (TA-f)
2p0-1s(E)
2p0-1s(B
1)
2p0-1s(A
1
u)
Сумма
0 10 20 30 400
1
2
3
4
5
6
7
10
10 c
-1
Междолинное расщепление мэВ
SiP 1s(B2) - 1s(A1) TA-g
1s(B2) - 1s(A1) LA-g
1кбар соответствует 85 мэВ
SiP SiP
1s(E)
1s(T2)
1s(A1)
TA-f84∙109 c-1
TA-f124∙109 c-1
LA-g03∙109 c-1
LA-g575109 c-1
TA-g7∙1010 c-1
TA-g36∙1010 c-1
2p0
SiP
Темп внутридолинных переходов
2р0 - 1s 21∙109 с-1
26∙1010 c-1
7∙1010 c-1
36∙1010 c-1
0 10 20 30 40
0
1
2
3
4
5
intervalley splitting meV
10
10 c
-1
1s(B2)-1s(A
1) TА-g
1s(B2)-1s(A
1) LA-g
SiSb
0 2 4 6 8 10 12 14 16 180
1
2
3
4
5
6
7
intervalley splitting meV
109 c
-1
SiSb 2p
0(A
1+B
2)-1s(Au
1) LA-g
2p0(A
1+B
2)-1s(E) TA-f
2p0(A
1+B
2)-1s(Au
1) TA-g
Переходы 2p0-1s(A
1
u) и 2p0-1s(B
1)
на ТА-f фононах пренебрежимо малы
1 kbar yields 85 meV valley shift for [100]
stress
1 kbar yields 85 meV valley shift for [100]
stress
SiSb SiSb
1s(E)
1s(T2)
1s(A1)
TA-f~108 c-1
TA-f142∙109 c-1
LA-g26∙109 c-1
LA-g175∙109 c-1
TA-g46∙1010 c-1
TA-g38∙1010 c-1
2p0
SiSb
Intra valley scattering rate
2р0 - 1s 21∙109 с-1
18∙1010 c-1
38∙1010 c-1
46∙1010 c-1
SiAs SiAs
LA-f079∙1010 c-1
1s(E)
1s(T2)
1s(A1)
TA-f122∙109 c-1
LA-g063∙109 c-1
LA-g07∙109 c-1
TA-f27∙1010 c-1
TA-f16∙1010 c-1
2p0
2s
2pplusmn
LA-g5∙1010 c-1
LA-g33∙1010 c-1
TA-f146 ∙109 c-1
LA-f098∙109 c-1
LA-f27∙1010 c-1
LA-g6∙109 c-1
LA-g6∙109 c-1
Intra valley scattering rates
2р0 - 1s 21∙109 с-1
2s - 1s 52∙109 c-1
2pplusmn - 1s 01 ∙109 c-1
2pplusmn - 2p0 144 ∙109 c-1
2pplusmn - 2s 89 ∙109 c-1
27∙1010 c-1
16∙1010 c-1
77∙1010 c-1
5∙1010 c-1
0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
rate
10
9 s-1
intervalley splitting meV
SiAs 2p(+-)-1s(Al
1) LA-f
2p(+-)-1s(Au
1) LA-g
Relaxation of the lower laser level
f- and g-phonon scattering rates in As donor under stress
0 2 4 6 8 10 12 14 16 18 20 220
1
2
3
4
5
6
intervalley splitting meV
109 c
-1
SiAs 2p
0-1s(Au
1) LA-g
2p0-1s(EB
1) TA-f
2p0-1s(Al
1) LA-f
2p0-1s(Au
1) TA-g
0 5 10 15 20 25 300
1
2
3
4
5
6
7
8
intervalley splitting meV1
010c-1
SiAs 1s(B
2)-1s(A
1
l) LA-g
1s(B2)-1s(A
1
l) TA-f
Relaxation of 2р(+-) and 2р0 states
1s(T2Г7)
1s(T2Г8)
1s(A1)
TA-f52∙109 c-1
LA-g~ 108 c-1
LA-g2∙109 c-1
LA-f47∙109 c-1
TA-f6∙109 c-1
2p0
2s
2pplusmn
LA-g053∙109 c-1
LA-g04∙109 c-1
TA-f14∙1010 c-1
TO-f~32∙1011 c-1
1s(E)
LA-g37∙109 c-1
SiBi SiBi
00 05 10 15 20 25 30 35 400
5
10
15
20
0 59 118 176 235 294 353 412 471
Intervalley splitting meV
1011
c-1
bar
SiBi 2p0-1s(Al
1) TO-f (для верхней ТО ветки) D
15 20 25 30 35 400
1
2
3
4
5
6
7
8
Intervalley splitting meV
1010
c-1
SiBi 2p
0 - 1s(Al
1) LA-f
0000 0493 0986 1479 1972 2465 2958 3451 39440
2
4
6
8
10
12
14
16
18
0 58 116 174 232 290 348 406 464
SiBi LO-g
2p+- - 1s(Al1)
Intervalley splitting meV
1010
c-1
2p+- - 1s(Al1)
with shiftedphonon dispersion on 05 meV
bar
7 8 9 10 11 12 130
5
10
15
20
25
30
35
Intervalley splitting meV
15 kbar
109 c
-1
SiBi2p(+-)-1s(Al
1) TO-f
для верхней ТО-f ветки для нижней ТО-f ветки
1 kbar
f- and g-phonon scattering rates in Bi donor under stress
0 2 4 6 80
2
4
6
8
Intervalley splitting meV
109 c
-1
SiBi 1s(B
2Г
7)-1s(Al
1)
0 20 40 60 800
2
4
6
8
10
12
14
Intervalley splitting meV
1010
c-1
SiBi1s(B
2)-1s(A
1
l) LA-g
Relaxation 1s(B2) state in Bi donor under stressed silicon
0 1 2 3 40
10
20
30
40
50
60
SiAs
[100] 617x(47x275) mm3
emis
sion
mV
stress kbar
200 150 85 50 30 10 16 1
pump (kWcm2)
2 20 2000
10
20
30
40
50
60 3831
283254
196
17
110810530250
SiAs[100]
617x(47x275) mm3
em
issi
on m
V
pump kWcm2
stress kbar
SiAs experiment(106 microm TEA CO2 laser
excitation)
As donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s
As donor THz output vs pump intensity under different stress
160 180 200 220
10
0
0
00 05 10 15 20 25
170
175
180
185
190
195
200
205
210
215
220
2p+-
1s(T2)
2p0 1s(B
2)
давление кбар
част
ота
см
-1SiAs [100]
em
issi
on a
u
frequency cm-1
240 bar 360 600
frequency
cm
-1
stress kbar
0
0 1 2170
220
1 2 3
00
02
04
06 35 38 4 43
11 117 16 22 29
SiAs
emis
sion
V
pump kWcm2
stress [100] kbar
00 05 10 15(b) pump photon density 1023 quantcm2
Least value of threshold intensity ~300Wcm2
SiAs Under Q-switch CO2 laser pump
20 20000
02
04
06
08
10 27
2522
1917
16
15
13
0
05
06
Pump intensity kW cm2
Inte
nsi
ty (
au
)
SiBi [100]
07(052034) mm3
07
Stress kbar
SiBi experiment(106 microm TEA CO2 laser
excitation)
Bi donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s
Sb donor THz output vs pump intensity under different stress
00 05 10 15 20 25 300
200
400
600
800 200 80 60 35 23 15 9
SiBi [100]
07(052034) mm3
em
issi
on
m
V
stress kbar
pump
kWcm2
02 04 06 080
100
200
300 130 100 80 60 53 41
In
tens
ity a
u
0 1 2 3 4 5
-40
-20
0
60
80
TA-g
TA-f
2p0(A
1ET
2)
1s(T2)
1s(A1)
1s(E)
1s(A1)
2p0(A
1+B
2)
Ene
rgy
(meV
)
Stress (kbar)
THz 1s(B2)
LO-g
pum
p en
ergy
117
meV
2 cont
0 1 2 3 4 5-60
-40
-20
0
60
80
LO-g
THz
LA-f
2s2p
+-
LA-gTA-f
4 co
nt
1s(T2)
1s(A1)
1s(E)
1s(A1)
2p0(A
1+B
2) E
ne
rgy
(meV
)
Stress (kbar)
THz1s(B
2)
pum
p en
erg
y 1
17 m
eV
2 cont
Energy levels of donors in stressed Si
As Sb
1211]100[ ss
XE u
X-valley splitting under uniaxial stress X
The stress removes sixfold degeneracy and as a result the energy difference ΔE appears between different groups of valleys
Intervalley phonon scattering of electrons in Si
K111K010
qN
qf
qg
ee[100]
[010][001]
e
Brillouin zonevector of reciprocal lattice normal processumklapp-process f -type umklapp-process g -type
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
21∙109 c-1
46∙1010 c-121∙1010 c-1
68∙109 c-1
2p0(А1+В2)
SiSb
Stress (06 kbar)
Laser state relaxation rates
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
29∙109 c-1
7∙1010 c-144∙1010 c-1
92∙109 c-1
2p0(А1+В2)
SiP
Stress (06 kbar)
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
26∙101035∙1010
42∙109
2p0(А1+В2)
Stress (25 kbar)
2pplusmn2s
15∙109
14∙109
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
55∙109 2∙109
85∙109
2p0(А1+В2)
Stress (18 kbar)
2pplusmn2s
3∙1011
E
E
SiAs
SiBi
Laser state relaxation rates s-1
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
Влияние деформации на эффективность накачки рабочих состояний
(Pump efficiency of the laser states depending on stress)
СО2
Релаксация на фононах
THg
СО2
Релаксация на фононах
THg emission
E
THg emissionE
001 01 1 10 100
1010
1011
1012
1013
1014 Nd=31015 cm-3
popu
latio
n c
m-3
pump kWcm-2
D-centers 2p
0
D-centers under 2p
0 under
001 01 1 10 100
1E-4
1E-3
001
01
1Nd=31015 cm-3
gain
and
abs
orpt
ion
cm
-1
pump kWcm-2
Population gain absorption
SiSb
Donor gain amp D--center absorption
Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)
Blue lines correspond to valley shift 5 meV (06 kbar)
Summary
The axial compressive stress of silicon crystal applied along [100] crystallographic orientation
From the experiment
- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors
- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors
- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress
From the theoretical treatment
- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys
- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states
- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal
Current study amp Further development
1) Spin-orbit interaction amp laser frequencies SiSb SiBi
2) Group-V donor lasing from isotope enriched silicon 28Si
3) Low T donor relaxation in stressed silicon (exp study)
4) Donoracceptor lasing from low dimensional SiSiGe structures
5) CW operation
D- binding energy vs compression
LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve
0 2 4 6 8 10 12 14 16 18 2000
05
10
15
20
25
109 c
-1
SiP
2p0(A
1+B
2) - 1s(A
1
u) LA-g TA-g
Междолинное расщепление мэВ
00 05 10 15 20 25 30 350
2
4
6
8
10
12
14
1
09 c-1
Междолинное расщепление meV
SiP (TA-f)
2p0-1s(E)
2p0-1s(B
1)
2p0-1s(A
1
u)
Сумма
0 10 20 30 400
1
2
3
4
5
6
7
10
10 c
-1
Междолинное расщепление мэВ
SiP 1s(B2) - 1s(A1) TA-g
1s(B2) - 1s(A1) LA-g
1кбар соответствует 85 мэВ
SiP SiP
1s(E)
1s(T2)
1s(A1)
TA-f84∙109 c-1
TA-f124∙109 c-1
LA-g03∙109 c-1
LA-g575109 c-1
TA-g7∙1010 c-1
TA-g36∙1010 c-1
2p0
SiP
Темп внутридолинных переходов
2р0 - 1s 21∙109 с-1
26∙1010 c-1
7∙1010 c-1
36∙1010 c-1
0 10 20 30 40
0
1
2
3
4
5
intervalley splitting meV
10
10 c
-1
1s(B2)-1s(A
1) TА-g
1s(B2)-1s(A
1) LA-g
SiSb
0 2 4 6 8 10 12 14 16 180
1
2
3
4
5
6
7
intervalley splitting meV
109 c
-1
SiSb 2p
0(A
1+B
2)-1s(Au
1) LA-g
2p0(A
1+B
2)-1s(E) TA-f
2p0(A
1+B
2)-1s(Au
1) TA-g
Переходы 2p0-1s(A
1
u) и 2p0-1s(B
1)
на ТА-f фононах пренебрежимо малы
1 kbar yields 85 meV valley shift for [100]
stress
1 kbar yields 85 meV valley shift for [100]
stress
SiSb SiSb
1s(E)
1s(T2)
1s(A1)
TA-f~108 c-1
TA-f142∙109 c-1
LA-g26∙109 c-1
LA-g175∙109 c-1
TA-g46∙1010 c-1
TA-g38∙1010 c-1
2p0
SiSb
Intra valley scattering rate
2р0 - 1s 21∙109 с-1
18∙1010 c-1
38∙1010 c-1
46∙1010 c-1
SiAs SiAs
LA-f079∙1010 c-1
1s(E)
1s(T2)
1s(A1)
TA-f122∙109 c-1
LA-g063∙109 c-1
LA-g07∙109 c-1
TA-f27∙1010 c-1
TA-f16∙1010 c-1
2p0
2s
2pplusmn
LA-g5∙1010 c-1
LA-g33∙1010 c-1
TA-f146 ∙109 c-1
LA-f098∙109 c-1
LA-f27∙1010 c-1
LA-g6∙109 c-1
LA-g6∙109 c-1
Intra valley scattering rates
2р0 - 1s 21∙109 с-1
2s - 1s 52∙109 c-1
2pplusmn - 1s 01 ∙109 c-1
2pplusmn - 2p0 144 ∙109 c-1
2pplusmn - 2s 89 ∙109 c-1
27∙1010 c-1
16∙1010 c-1
77∙1010 c-1
5∙1010 c-1
0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
rate
10
9 s-1
intervalley splitting meV
SiAs 2p(+-)-1s(Al
1) LA-f
2p(+-)-1s(Au
1) LA-g
Relaxation of the lower laser level
f- and g-phonon scattering rates in As donor under stress
0 2 4 6 8 10 12 14 16 18 20 220
1
2
3
4
5
6
intervalley splitting meV
109 c
-1
SiAs 2p
0-1s(Au
1) LA-g
2p0-1s(EB
1) TA-f
2p0-1s(Al
1) LA-f
2p0-1s(Au
1) TA-g
0 5 10 15 20 25 300
1
2
3
4
5
6
7
8
intervalley splitting meV1
010c-1
SiAs 1s(B
2)-1s(A
1
l) LA-g
1s(B2)-1s(A
1
l) TA-f
Relaxation of 2р(+-) and 2р0 states
1s(T2Г7)
1s(T2Г8)
1s(A1)
TA-f52∙109 c-1
LA-g~ 108 c-1
LA-g2∙109 c-1
LA-f47∙109 c-1
TA-f6∙109 c-1
2p0
2s
2pplusmn
LA-g053∙109 c-1
LA-g04∙109 c-1
TA-f14∙1010 c-1
TO-f~32∙1011 c-1
1s(E)
LA-g37∙109 c-1
SiBi SiBi
00 05 10 15 20 25 30 35 400
5
10
15
20
0 59 118 176 235 294 353 412 471
Intervalley splitting meV
1011
c-1
bar
SiBi 2p0-1s(Al
1) TO-f (для верхней ТО ветки) D
15 20 25 30 35 400
1
2
3
4
5
6
7
8
Intervalley splitting meV
1010
c-1
SiBi 2p
0 - 1s(Al
1) LA-f
0000 0493 0986 1479 1972 2465 2958 3451 39440
2
4
6
8
10
12
14
16
18
0 58 116 174 232 290 348 406 464
SiBi LO-g
2p+- - 1s(Al1)
Intervalley splitting meV
1010
c-1
2p+- - 1s(Al1)
with shiftedphonon dispersion on 05 meV
bar
7 8 9 10 11 12 130
5
10
15
20
25
30
35
Intervalley splitting meV
15 kbar
109 c
-1
SiBi2p(+-)-1s(Al
1) TO-f
для верхней ТО-f ветки для нижней ТО-f ветки
1 kbar
f- and g-phonon scattering rates in Bi donor under stress
0 2 4 6 80
2
4
6
8
Intervalley splitting meV
109 c
-1
SiBi 1s(B
2Г
7)-1s(Al
1)
0 20 40 60 800
2
4
6
8
10
12
14
Intervalley splitting meV
1010
c-1
SiBi1s(B
2)-1s(A
1
l) LA-g
Relaxation 1s(B2) state in Bi donor under stressed silicon
1 2 3
00
02
04
06 35 38 4 43
11 117 16 22 29
SiAs
emis
sion
V
pump kWcm2
stress [100] kbar
00 05 10 15(b) pump photon density 1023 quantcm2
Least value of threshold intensity ~300Wcm2
SiAs Under Q-switch CO2 laser pump
20 20000
02
04
06
08
10 27
2522
1917
16
15
13
0
05
06
Pump intensity kW cm2
Inte
nsi
ty (
au
)
SiBi [100]
07(052034) mm3
07
Stress kbar
SiBi experiment(106 microm TEA CO2 laser
excitation)
Bi donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s
Sb donor THz output vs pump intensity under different stress
00 05 10 15 20 25 300
200
400
600
800 200 80 60 35 23 15 9
SiBi [100]
07(052034) mm3
em
issi
on
m
V
stress kbar
pump
kWcm2
02 04 06 080
100
200
300 130 100 80 60 53 41
In
tens
ity a
u
0 1 2 3 4 5
-40
-20
0
60
80
TA-g
TA-f
2p0(A
1ET
2)
1s(T2)
1s(A1)
1s(E)
1s(A1)
2p0(A
1+B
2)
Ene
rgy
(meV
)
Stress (kbar)
THz 1s(B2)
LO-g
pum
p en
ergy
117
meV
2 cont
0 1 2 3 4 5-60
-40
-20
0
60
80
LO-g
THz
LA-f
2s2p
+-
LA-gTA-f
4 co
nt
1s(T2)
1s(A1)
1s(E)
1s(A1)
2p0(A
1+B
2) E
ne
rgy
(meV
)
Stress (kbar)
THz1s(B
2)
pum
p en
erg
y 1
17 m
eV
2 cont
Energy levels of donors in stressed Si
As Sb
1211]100[ ss
XE u
X-valley splitting under uniaxial stress X
The stress removes sixfold degeneracy and as a result the energy difference ΔE appears between different groups of valleys
Intervalley phonon scattering of electrons in Si
K111K010
qN
qf
qg
ee[100]
[010][001]
e
Brillouin zonevector of reciprocal lattice normal processumklapp-process f -type umklapp-process g -type
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
21∙109 c-1
46∙1010 c-121∙1010 c-1
68∙109 c-1
2p0(А1+В2)
SiSb
Stress (06 kbar)
Laser state relaxation rates
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
29∙109 c-1
7∙1010 c-144∙1010 c-1
92∙109 c-1
2p0(А1+В2)
SiP
Stress (06 kbar)
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
26∙101035∙1010
42∙109
2p0(А1+В2)
Stress (25 kbar)
2pplusmn2s
15∙109
14∙109
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
55∙109 2∙109
85∙109
2p0(А1+В2)
Stress (18 kbar)
2pplusmn2s
3∙1011
E
E
SiAs
SiBi
Laser state relaxation rates s-1
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
Влияние деформации на эффективность накачки рабочих состояний
(Pump efficiency of the laser states depending on stress)
СО2
Релаксация на фононах
THg
СО2
Релаксация на фононах
THg emission
E
THg emissionE
001 01 1 10 100
1010
1011
1012
1013
1014 Nd=31015 cm-3
popu
latio
n c
m-3
pump kWcm-2
D-centers 2p
0
D-centers under 2p
0 under
001 01 1 10 100
1E-4
1E-3
001
01
1Nd=31015 cm-3
gain
and
abs
orpt
ion
cm
-1
pump kWcm-2
Population gain absorption
SiSb
Donor gain amp D--center absorption
Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)
Blue lines correspond to valley shift 5 meV (06 kbar)
Summary
The axial compressive stress of silicon crystal applied along [100] crystallographic orientation
From the experiment
- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors
- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors
- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress
From the theoretical treatment
- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys
- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states
- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal
Current study amp Further development
1) Spin-orbit interaction amp laser frequencies SiSb SiBi
2) Group-V donor lasing from isotope enriched silicon 28Si
3) Low T donor relaxation in stressed silicon (exp study)
4) Donoracceptor lasing from low dimensional SiSiGe structures
5) CW operation
D- binding energy vs compression
LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve
0 2 4 6 8 10 12 14 16 18 2000
05
10
15
20
25
109 c
-1
SiP
2p0(A
1+B
2) - 1s(A
1
u) LA-g TA-g
Междолинное расщепление мэВ
00 05 10 15 20 25 30 350
2
4
6
8
10
12
14
1
09 c-1
Междолинное расщепление meV
SiP (TA-f)
2p0-1s(E)
2p0-1s(B
1)
2p0-1s(A
1
u)
Сумма
0 10 20 30 400
1
2
3
4
5
6
7
10
10 c
-1
Междолинное расщепление мэВ
SiP 1s(B2) - 1s(A1) TA-g
1s(B2) - 1s(A1) LA-g
1кбар соответствует 85 мэВ
SiP SiP
1s(E)
1s(T2)
1s(A1)
TA-f84∙109 c-1
TA-f124∙109 c-1
LA-g03∙109 c-1
LA-g575109 c-1
TA-g7∙1010 c-1
TA-g36∙1010 c-1
2p0
SiP
Темп внутридолинных переходов
2р0 - 1s 21∙109 с-1
26∙1010 c-1
7∙1010 c-1
36∙1010 c-1
0 10 20 30 40
0
1
2
3
4
5
intervalley splitting meV
10
10 c
-1
1s(B2)-1s(A
1) TА-g
1s(B2)-1s(A
1) LA-g
SiSb
0 2 4 6 8 10 12 14 16 180
1
2
3
4
5
6
7
intervalley splitting meV
109 c
-1
SiSb 2p
0(A
1+B
2)-1s(Au
1) LA-g
2p0(A
1+B
2)-1s(E) TA-f
2p0(A
1+B
2)-1s(Au
1) TA-g
Переходы 2p0-1s(A
1
u) и 2p0-1s(B
1)
на ТА-f фононах пренебрежимо малы
1 kbar yields 85 meV valley shift for [100]
stress
1 kbar yields 85 meV valley shift for [100]
stress
SiSb SiSb
1s(E)
1s(T2)
1s(A1)
TA-f~108 c-1
TA-f142∙109 c-1
LA-g26∙109 c-1
LA-g175∙109 c-1
TA-g46∙1010 c-1
TA-g38∙1010 c-1
2p0
SiSb
Intra valley scattering rate
2р0 - 1s 21∙109 с-1
18∙1010 c-1
38∙1010 c-1
46∙1010 c-1
SiAs SiAs
LA-f079∙1010 c-1
1s(E)
1s(T2)
1s(A1)
TA-f122∙109 c-1
LA-g063∙109 c-1
LA-g07∙109 c-1
TA-f27∙1010 c-1
TA-f16∙1010 c-1
2p0
2s
2pplusmn
LA-g5∙1010 c-1
LA-g33∙1010 c-1
TA-f146 ∙109 c-1
LA-f098∙109 c-1
LA-f27∙1010 c-1
LA-g6∙109 c-1
LA-g6∙109 c-1
Intra valley scattering rates
2р0 - 1s 21∙109 с-1
2s - 1s 52∙109 c-1
2pplusmn - 1s 01 ∙109 c-1
2pplusmn - 2p0 144 ∙109 c-1
2pplusmn - 2s 89 ∙109 c-1
27∙1010 c-1
16∙1010 c-1
77∙1010 c-1
5∙1010 c-1
0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
rate
10
9 s-1
intervalley splitting meV
SiAs 2p(+-)-1s(Al
1) LA-f
2p(+-)-1s(Au
1) LA-g
Relaxation of the lower laser level
f- and g-phonon scattering rates in As donor under stress
0 2 4 6 8 10 12 14 16 18 20 220
1
2
3
4
5
6
intervalley splitting meV
109 c
-1
SiAs 2p
0-1s(Au
1) LA-g
2p0-1s(EB
1) TA-f
2p0-1s(Al
1) LA-f
2p0-1s(Au
1) TA-g
0 5 10 15 20 25 300
1
2
3
4
5
6
7
8
intervalley splitting meV1
010c-1
SiAs 1s(B
2)-1s(A
1
l) LA-g
1s(B2)-1s(A
1
l) TA-f
Relaxation of 2р(+-) and 2р0 states
1s(T2Г7)
1s(T2Г8)
1s(A1)
TA-f52∙109 c-1
LA-g~ 108 c-1
LA-g2∙109 c-1
LA-f47∙109 c-1
TA-f6∙109 c-1
2p0
2s
2pplusmn
LA-g053∙109 c-1
LA-g04∙109 c-1
TA-f14∙1010 c-1
TO-f~32∙1011 c-1
1s(E)
LA-g37∙109 c-1
SiBi SiBi
00 05 10 15 20 25 30 35 400
5
10
15
20
0 59 118 176 235 294 353 412 471
Intervalley splitting meV
1011
c-1
bar
SiBi 2p0-1s(Al
1) TO-f (для верхней ТО ветки) D
15 20 25 30 35 400
1
2
3
4
5
6
7
8
Intervalley splitting meV
1010
c-1
SiBi 2p
0 - 1s(Al
1) LA-f
0000 0493 0986 1479 1972 2465 2958 3451 39440
2
4
6
8
10
12
14
16
18
0 58 116 174 232 290 348 406 464
SiBi LO-g
2p+- - 1s(Al1)
Intervalley splitting meV
1010
c-1
2p+- - 1s(Al1)
with shiftedphonon dispersion on 05 meV
bar
7 8 9 10 11 12 130
5
10
15
20
25
30
35
Intervalley splitting meV
15 kbar
109 c
-1
SiBi2p(+-)-1s(Al
1) TO-f
для верхней ТО-f ветки для нижней ТО-f ветки
1 kbar
f- and g-phonon scattering rates in Bi donor under stress
0 2 4 6 80
2
4
6
8
Intervalley splitting meV
109 c
-1
SiBi 1s(B
2Г
7)-1s(Al
1)
0 20 40 60 800
2
4
6
8
10
12
14
Intervalley splitting meV
1010
c-1
SiBi1s(B
2)-1s(A
1
l) LA-g
Relaxation 1s(B2) state in Bi donor under stressed silicon
20 20000
02
04
06
08
10 27
2522
1917
16
15
13
0
05
06
Pump intensity kW cm2
Inte
nsi
ty (
au
)
SiBi [100]
07(052034) mm3
07
Stress kbar
SiBi experiment(106 microm TEA CO2 laser
excitation)
Bi donor THz output vs stress under several pump intensity 200kWcm2 correspond 1025quantcm2s
Sb donor THz output vs pump intensity under different stress
00 05 10 15 20 25 300
200
400
600
800 200 80 60 35 23 15 9
SiBi [100]
07(052034) mm3
em
issi
on
m
V
stress kbar
pump
kWcm2
02 04 06 080
100
200
300 130 100 80 60 53 41
In
tens
ity a
u
0 1 2 3 4 5
-40
-20
0
60
80
TA-g
TA-f
2p0(A
1ET
2)
1s(T2)
1s(A1)
1s(E)
1s(A1)
2p0(A
1+B
2)
Ene
rgy
(meV
)
Stress (kbar)
THz 1s(B2)
LO-g
pum
p en
ergy
117
meV
2 cont
0 1 2 3 4 5-60
-40
-20
0
60
80
LO-g
THz
LA-f
2s2p
+-
LA-gTA-f
4 co
nt
1s(T2)
1s(A1)
1s(E)
1s(A1)
2p0(A
1+B
2) E
ne
rgy
(meV
)
Stress (kbar)
THz1s(B
2)
pum
p en
erg
y 1
17 m
eV
2 cont
Energy levels of donors in stressed Si
As Sb
1211]100[ ss
XE u
X-valley splitting under uniaxial stress X
The stress removes sixfold degeneracy and as a result the energy difference ΔE appears between different groups of valleys
Intervalley phonon scattering of electrons in Si
K111K010
qN
qf
qg
ee[100]
[010][001]
e
Brillouin zonevector of reciprocal lattice normal processumklapp-process f -type umklapp-process g -type
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
21∙109 c-1
46∙1010 c-121∙1010 c-1
68∙109 c-1
2p0(А1+В2)
SiSb
Stress (06 kbar)
Laser state relaxation rates
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
29∙109 c-1
7∙1010 c-144∙1010 c-1
92∙109 c-1
2p0(А1+В2)
SiP
Stress (06 kbar)
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
26∙101035∙1010
42∙109
2p0(А1+В2)
Stress (25 kbar)
2pplusmn2s
15∙109
14∙109
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
55∙109 2∙109
85∙109
2p0(А1+В2)
Stress (18 kbar)
2pplusmn2s
3∙1011
E
E
SiAs
SiBi
Laser state relaxation rates s-1
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
Влияние деформации на эффективность накачки рабочих состояний
(Pump efficiency of the laser states depending on stress)
СО2
Релаксация на фононах
THg
СО2
Релаксация на фононах
THg emission
E
THg emissionE
001 01 1 10 100
1010
1011
1012
1013
1014 Nd=31015 cm-3
popu
latio
n c
m-3
pump kWcm-2
D-centers 2p
0
D-centers under 2p
0 under
001 01 1 10 100
1E-4
1E-3
001
01
1Nd=31015 cm-3
gain
and
abs
orpt
ion
cm
-1
pump kWcm-2
Population gain absorption
SiSb
Donor gain amp D--center absorption
Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)
Blue lines correspond to valley shift 5 meV (06 kbar)
Summary
The axial compressive stress of silicon crystal applied along [100] crystallographic orientation
From the experiment
- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors
- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors
- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress
From the theoretical treatment
- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys
- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states
- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal
Current study amp Further development
1) Spin-orbit interaction amp laser frequencies SiSb SiBi
2) Group-V donor lasing from isotope enriched silicon 28Si
3) Low T donor relaxation in stressed silicon (exp study)
4) Donoracceptor lasing from low dimensional SiSiGe structures
5) CW operation
D- binding energy vs compression
LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve
0 2 4 6 8 10 12 14 16 18 2000
05
10
15
20
25
109 c
-1
SiP
2p0(A
1+B
2) - 1s(A
1
u) LA-g TA-g
Междолинное расщепление мэВ
00 05 10 15 20 25 30 350
2
4
6
8
10
12
14
1
09 c-1
Междолинное расщепление meV
SiP (TA-f)
2p0-1s(E)
2p0-1s(B
1)
2p0-1s(A
1
u)
Сумма
0 10 20 30 400
1
2
3
4
5
6
7
10
10 c
-1
Междолинное расщепление мэВ
SiP 1s(B2) - 1s(A1) TA-g
1s(B2) - 1s(A1) LA-g
1кбар соответствует 85 мэВ
SiP SiP
1s(E)
1s(T2)
1s(A1)
TA-f84∙109 c-1
TA-f124∙109 c-1
LA-g03∙109 c-1
LA-g575109 c-1
TA-g7∙1010 c-1
TA-g36∙1010 c-1
2p0
SiP
Темп внутридолинных переходов
2р0 - 1s 21∙109 с-1
26∙1010 c-1
7∙1010 c-1
36∙1010 c-1
0 10 20 30 40
0
1
2
3
4
5
intervalley splitting meV
10
10 c
-1
1s(B2)-1s(A
1) TА-g
1s(B2)-1s(A
1) LA-g
SiSb
0 2 4 6 8 10 12 14 16 180
1
2
3
4
5
6
7
intervalley splitting meV
109 c
-1
SiSb 2p
0(A
1+B
2)-1s(Au
1) LA-g
2p0(A
1+B
2)-1s(E) TA-f
2p0(A
1+B
2)-1s(Au
1) TA-g
Переходы 2p0-1s(A
1
u) и 2p0-1s(B
1)
на ТА-f фононах пренебрежимо малы
1 kbar yields 85 meV valley shift for [100]
stress
1 kbar yields 85 meV valley shift for [100]
stress
SiSb SiSb
1s(E)
1s(T2)
1s(A1)
TA-f~108 c-1
TA-f142∙109 c-1
LA-g26∙109 c-1
LA-g175∙109 c-1
TA-g46∙1010 c-1
TA-g38∙1010 c-1
2p0
SiSb
Intra valley scattering rate
2р0 - 1s 21∙109 с-1
18∙1010 c-1
38∙1010 c-1
46∙1010 c-1
SiAs SiAs
LA-f079∙1010 c-1
1s(E)
1s(T2)
1s(A1)
TA-f122∙109 c-1
LA-g063∙109 c-1
LA-g07∙109 c-1
TA-f27∙1010 c-1
TA-f16∙1010 c-1
2p0
2s
2pplusmn
LA-g5∙1010 c-1
LA-g33∙1010 c-1
TA-f146 ∙109 c-1
LA-f098∙109 c-1
LA-f27∙1010 c-1
LA-g6∙109 c-1
LA-g6∙109 c-1
Intra valley scattering rates
2р0 - 1s 21∙109 с-1
2s - 1s 52∙109 c-1
2pplusmn - 1s 01 ∙109 c-1
2pplusmn - 2p0 144 ∙109 c-1
2pplusmn - 2s 89 ∙109 c-1
27∙1010 c-1
16∙1010 c-1
77∙1010 c-1
5∙1010 c-1
0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
rate
10
9 s-1
intervalley splitting meV
SiAs 2p(+-)-1s(Al
1) LA-f
2p(+-)-1s(Au
1) LA-g
Relaxation of the lower laser level
f- and g-phonon scattering rates in As donor under stress
0 2 4 6 8 10 12 14 16 18 20 220
1
2
3
4
5
6
intervalley splitting meV
109 c
-1
SiAs 2p
0-1s(Au
1) LA-g
2p0-1s(EB
1) TA-f
2p0-1s(Al
1) LA-f
2p0-1s(Au
1) TA-g
0 5 10 15 20 25 300
1
2
3
4
5
6
7
8
intervalley splitting meV1
010c-1
SiAs 1s(B
2)-1s(A
1
l) LA-g
1s(B2)-1s(A
1
l) TA-f
Relaxation of 2р(+-) and 2р0 states
1s(T2Г7)
1s(T2Г8)
1s(A1)
TA-f52∙109 c-1
LA-g~ 108 c-1
LA-g2∙109 c-1
LA-f47∙109 c-1
TA-f6∙109 c-1
2p0
2s
2pplusmn
LA-g053∙109 c-1
LA-g04∙109 c-1
TA-f14∙1010 c-1
TO-f~32∙1011 c-1
1s(E)
LA-g37∙109 c-1
SiBi SiBi
00 05 10 15 20 25 30 35 400
5
10
15
20
0 59 118 176 235 294 353 412 471
Intervalley splitting meV
1011
c-1
bar
SiBi 2p0-1s(Al
1) TO-f (для верхней ТО ветки) D
15 20 25 30 35 400
1
2
3
4
5
6
7
8
Intervalley splitting meV
1010
c-1
SiBi 2p
0 - 1s(Al
1) LA-f
0000 0493 0986 1479 1972 2465 2958 3451 39440
2
4
6
8
10
12
14
16
18
0 58 116 174 232 290 348 406 464
SiBi LO-g
2p+- - 1s(Al1)
Intervalley splitting meV
1010
c-1
2p+- - 1s(Al1)
with shiftedphonon dispersion on 05 meV
bar
7 8 9 10 11 12 130
5
10
15
20
25
30
35
Intervalley splitting meV
15 kbar
109 c
-1
SiBi2p(+-)-1s(Al
1) TO-f
для верхней ТО-f ветки для нижней ТО-f ветки
1 kbar
f- and g-phonon scattering rates in Bi donor under stress
0 2 4 6 80
2
4
6
8
Intervalley splitting meV
109 c
-1
SiBi 1s(B
2Г
7)-1s(Al
1)
0 20 40 60 800
2
4
6
8
10
12
14
Intervalley splitting meV
1010
c-1
SiBi1s(B
2)-1s(A
1
l) LA-g
Relaxation 1s(B2) state in Bi donor under stressed silicon
0 1 2 3 4 5
-40
-20
0
60
80
TA-g
TA-f
2p0(A
1ET
2)
1s(T2)
1s(A1)
1s(E)
1s(A1)
2p0(A
1+B
2)
Ene
rgy
(meV
)
Stress (kbar)
THz 1s(B2)
LO-g
pum
p en
ergy
117
meV
2 cont
0 1 2 3 4 5-60
-40
-20
0
60
80
LO-g
THz
LA-f
2s2p
+-
LA-gTA-f
4 co
nt
1s(T2)
1s(A1)
1s(E)
1s(A1)
2p0(A
1+B
2) E
ne
rgy
(meV
)
Stress (kbar)
THz1s(B
2)
pum
p en
erg
y 1
17 m
eV
2 cont
Energy levels of donors in stressed Si
As Sb
1211]100[ ss
XE u
X-valley splitting under uniaxial stress X
The stress removes sixfold degeneracy and as a result the energy difference ΔE appears between different groups of valleys
Intervalley phonon scattering of electrons in Si
K111K010
qN
qf
qg
ee[100]
[010][001]
e
Brillouin zonevector of reciprocal lattice normal processumklapp-process f -type umklapp-process g -type
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
21∙109 c-1
46∙1010 c-121∙1010 c-1
68∙109 c-1
2p0(А1+В2)
SiSb
Stress (06 kbar)
Laser state relaxation rates
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
29∙109 c-1
7∙1010 c-144∙1010 c-1
92∙109 c-1
2p0(А1+В2)
SiP
Stress (06 kbar)
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
26∙101035∙1010
42∙109
2p0(А1+В2)
Stress (25 kbar)
2pplusmn2s
15∙109
14∙109
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
55∙109 2∙109
85∙109
2p0(А1+В2)
Stress (18 kbar)
2pplusmn2s
3∙1011
E
E
SiAs
SiBi
Laser state relaxation rates s-1
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
Влияние деформации на эффективность накачки рабочих состояний
(Pump efficiency of the laser states depending on stress)
СО2
Релаксация на фононах
THg
СО2
Релаксация на фононах
THg emission
E
THg emissionE
001 01 1 10 100
1010
1011
1012
1013
1014 Nd=31015 cm-3
popu
latio
n c
m-3
pump kWcm-2
D-centers 2p
0
D-centers under 2p
0 under
001 01 1 10 100
1E-4
1E-3
001
01
1Nd=31015 cm-3
gain
and
abs
orpt
ion
cm
-1
pump kWcm-2
Population gain absorption
SiSb
Donor gain amp D--center absorption
Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)
Blue lines correspond to valley shift 5 meV (06 kbar)
Summary
The axial compressive stress of silicon crystal applied along [100] crystallographic orientation
From the experiment
- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors
- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors
- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress
From the theoretical treatment
- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys
- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states
- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal
Current study amp Further development
1) Spin-orbit interaction amp laser frequencies SiSb SiBi
2) Group-V donor lasing from isotope enriched silicon 28Si
3) Low T donor relaxation in stressed silicon (exp study)
4) Donoracceptor lasing from low dimensional SiSiGe structures
5) CW operation
D- binding energy vs compression
LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve
0 2 4 6 8 10 12 14 16 18 2000
05
10
15
20
25
109 c
-1
SiP
2p0(A
1+B
2) - 1s(A
1
u) LA-g TA-g
Междолинное расщепление мэВ
00 05 10 15 20 25 30 350
2
4
6
8
10
12
14
1
09 c-1
Междолинное расщепление meV
SiP (TA-f)
2p0-1s(E)
2p0-1s(B
1)
2p0-1s(A
1
u)
Сумма
0 10 20 30 400
1
2
3
4
5
6
7
10
10 c
-1
Междолинное расщепление мэВ
SiP 1s(B2) - 1s(A1) TA-g
1s(B2) - 1s(A1) LA-g
1кбар соответствует 85 мэВ
SiP SiP
1s(E)
1s(T2)
1s(A1)
TA-f84∙109 c-1
TA-f124∙109 c-1
LA-g03∙109 c-1
LA-g575109 c-1
TA-g7∙1010 c-1
TA-g36∙1010 c-1
2p0
SiP
Темп внутридолинных переходов
2р0 - 1s 21∙109 с-1
26∙1010 c-1
7∙1010 c-1
36∙1010 c-1
0 10 20 30 40
0
1
2
3
4
5
intervalley splitting meV
10
10 c
-1
1s(B2)-1s(A
1) TА-g
1s(B2)-1s(A
1) LA-g
SiSb
0 2 4 6 8 10 12 14 16 180
1
2
3
4
5
6
7
intervalley splitting meV
109 c
-1
SiSb 2p
0(A
1+B
2)-1s(Au
1) LA-g
2p0(A
1+B
2)-1s(E) TA-f
2p0(A
1+B
2)-1s(Au
1) TA-g
Переходы 2p0-1s(A
1
u) и 2p0-1s(B
1)
на ТА-f фононах пренебрежимо малы
1 kbar yields 85 meV valley shift for [100]
stress
1 kbar yields 85 meV valley shift for [100]
stress
SiSb SiSb
1s(E)
1s(T2)
1s(A1)
TA-f~108 c-1
TA-f142∙109 c-1
LA-g26∙109 c-1
LA-g175∙109 c-1
TA-g46∙1010 c-1
TA-g38∙1010 c-1
2p0
SiSb
Intra valley scattering rate
2р0 - 1s 21∙109 с-1
18∙1010 c-1
38∙1010 c-1
46∙1010 c-1
SiAs SiAs
LA-f079∙1010 c-1
1s(E)
1s(T2)
1s(A1)
TA-f122∙109 c-1
LA-g063∙109 c-1
LA-g07∙109 c-1
TA-f27∙1010 c-1
TA-f16∙1010 c-1
2p0
2s
2pplusmn
LA-g5∙1010 c-1
LA-g33∙1010 c-1
TA-f146 ∙109 c-1
LA-f098∙109 c-1
LA-f27∙1010 c-1
LA-g6∙109 c-1
LA-g6∙109 c-1
Intra valley scattering rates
2р0 - 1s 21∙109 с-1
2s - 1s 52∙109 c-1
2pplusmn - 1s 01 ∙109 c-1
2pplusmn - 2p0 144 ∙109 c-1
2pplusmn - 2s 89 ∙109 c-1
27∙1010 c-1
16∙1010 c-1
77∙1010 c-1
5∙1010 c-1
0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
rate
10
9 s-1
intervalley splitting meV
SiAs 2p(+-)-1s(Al
1) LA-f
2p(+-)-1s(Au
1) LA-g
Relaxation of the lower laser level
f- and g-phonon scattering rates in As donor under stress
0 2 4 6 8 10 12 14 16 18 20 220
1
2
3
4
5
6
intervalley splitting meV
109 c
-1
SiAs 2p
0-1s(Au
1) LA-g
2p0-1s(EB
1) TA-f
2p0-1s(Al
1) LA-f
2p0-1s(Au
1) TA-g
0 5 10 15 20 25 300
1
2
3
4
5
6
7
8
intervalley splitting meV1
010c-1
SiAs 1s(B
2)-1s(A
1
l) LA-g
1s(B2)-1s(A
1
l) TA-f
Relaxation of 2р(+-) and 2р0 states
1s(T2Г7)
1s(T2Г8)
1s(A1)
TA-f52∙109 c-1
LA-g~ 108 c-1
LA-g2∙109 c-1
LA-f47∙109 c-1
TA-f6∙109 c-1
2p0
2s
2pplusmn
LA-g053∙109 c-1
LA-g04∙109 c-1
TA-f14∙1010 c-1
TO-f~32∙1011 c-1
1s(E)
LA-g37∙109 c-1
SiBi SiBi
00 05 10 15 20 25 30 35 400
5
10
15
20
0 59 118 176 235 294 353 412 471
Intervalley splitting meV
1011
c-1
bar
SiBi 2p0-1s(Al
1) TO-f (для верхней ТО ветки) D
15 20 25 30 35 400
1
2
3
4
5
6
7
8
Intervalley splitting meV
1010
c-1
SiBi 2p
0 - 1s(Al
1) LA-f
0000 0493 0986 1479 1972 2465 2958 3451 39440
2
4
6
8
10
12
14
16
18
0 58 116 174 232 290 348 406 464
SiBi LO-g
2p+- - 1s(Al1)
Intervalley splitting meV
1010
c-1
2p+- - 1s(Al1)
with shiftedphonon dispersion on 05 meV
bar
7 8 9 10 11 12 130
5
10
15
20
25
30
35
Intervalley splitting meV
15 kbar
109 c
-1
SiBi2p(+-)-1s(Al
1) TO-f
для верхней ТО-f ветки для нижней ТО-f ветки
1 kbar
f- and g-phonon scattering rates in Bi donor under stress
0 2 4 6 80
2
4
6
8
Intervalley splitting meV
109 c
-1
SiBi 1s(B
2Г
7)-1s(Al
1)
0 20 40 60 800
2
4
6
8
10
12
14
Intervalley splitting meV
1010
c-1
SiBi1s(B
2)-1s(A
1
l) LA-g
Relaxation 1s(B2) state in Bi donor under stressed silicon
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
21∙109 c-1
46∙1010 c-121∙1010 c-1
68∙109 c-1
2p0(А1+В2)
SiSb
Stress (06 kbar)
Laser state relaxation rates
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
29∙109 c-1
7∙1010 c-144∙1010 c-1
92∙109 c-1
2p0(А1+В2)
SiP
Stress (06 kbar)
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
26∙101035∙1010
42∙109
2p0(А1+В2)
Stress (25 kbar)
2pplusmn2s
15∙109
14∙109
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
55∙109 2∙109
85∙109
2p0(А1+В2)
Stress (18 kbar)
2pplusmn2s
3∙1011
E
E
SiAs
SiBi
Laser state relaxation rates s-1
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
Влияние деформации на эффективность накачки рабочих состояний
(Pump efficiency of the laser states depending on stress)
СО2
Релаксация на фононах
THg
СО2
Релаксация на фононах
THg emission
E
THg emissionE
001 01 1 10 100
1010
1011
1012
1013
1014 Nd=31015 cm-3
popu
latio
n c
m-3
pump kWcm-2
D-centers 2p
0
D-centers under 2p
0 under
001 01 1 10 100
1E-4
1E-3
001
01
1Nd=31015 cm-3
gain
and
abs
orpt
ion
cm
-1
pump kWcm-2
Population gain absorption
SiSb
Donor gain amp D--center absorption
Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)
Blue lines correspond to valley shift 5 meV (06 kbar)
Summary
The axial compressive stress of silicon crystal applied along [100] crystallographic orientation
From the experiment
- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors
- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors
- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress
From the theoretical treatment
- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys
- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states
- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal
Current study amp Further development
1) Spin-orbit interaction amp laser frequencies SiSb SiBi
2) Group-V donor lasing from isotope enriched silicon 28Si
3) Low T donor relaxation in stressed silicon (exp study)
4) Donoracceptor lasing from low dimensional SiSiGe structures
5) CW operation
D- binding energy vs compression
LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve
0 2 4 6 8 10 12 14 16 18 2000
05
10
15
20
25
109 c
-1
SiP
2p0(A
1+B
2) - 1s(A
1
u) LA-g TA-g
Междолинное расщепление мэВ
00 05 10 15 20 25 30 350
2
4
6
8
10
12
14
1
09 c-1
Междолинное расщепление meV
SiP (TA-f)
2p0-1s(E)
2p0-1s(B
1)
2p0-1s(A
1
u)
Сумма
0 10 20 30 400
1
2
3
4
5
6
7
10
10 c
-1
Междолинное расщепление мэВ
SiP 1s(B2) - 1s(A1) TA-g
1s(B2) - 1s(A1) LA-g
1кбар соответствует 85 мэВ
SiP SiP
1s(E)
1s(T2)
1s(A1)
TA-f84∙109 c-1
TA-f124∙109 c-1
LA-g03∙109 c-1
LA-g575109 c-1
TA-g7∙1010 c-1
TA-g36∙1010 c-1
2p0
SiP
Темп внутридолинных переходов
2р0 - 1s 21∙109 с-1
26∙1010 c-1
7∙1010 c-1
36∙1010 c-1
0 10 20 30 40
0
1
2
3
4
5
intervalley splitting meV
10
10 c
-1
1s(B2)-1s(A
1) TА-g
1s(B2)-1s(A
1) LA-g
SiSb
0 2 4 6 8 10 12 14 16 180
1
2
3
4
5
6
7
intervalley splitting meV
109 c
-1
SiSb 2p
0(A
1+B
2)-1s(Au
1) LA-g
2p0(A
1+B
2)-1s(E) TA-f
2p0(A
1+B
2)-1s(Au
1) TA-g
Переходы 2p0-1s(A
1
u) и 2p0-1s(B
1)
на ТА-f фононах пренебрежимо малы
1 kbar yields 85 meV valley shift for [100]
stress
1 kbar yields 85 meV valley shift for [100]
stress
SiSb SiSb
1s(E)
1s(T2)
1s(A1)
TA-f~108 c-1
TA-f142∙109 c-1
LA-g26∙109 c-1
LA-g175∙109 c-1
TA-g46∙1010 c-1
TA-g38∙1010 c-1
2p0
SiSb
Intra valley scattering rate
2р0 - 1s 21∙109 с-1
18∙1010 c-1
38∙1010 c-1
46∙1010 c-1
SiAs SiAs
LA-f079∙1010 c-1
1s(E)
1s(T2)
1s(A1)
TA-f122∙109 c-1
LA-g063∙109 c-1
LA-g07∙109 c-1
TA-f27∙1010 c-1
TA-f16∙1010 c-1
2p0
2s
2pplusmn
LA-g5∙1010 c-1
LA-g33∙1010 c-1
TA-f146 ∙109 c-1
LA-f098∙109 c-1
LA-f27∙1010 c-1
LA-g6∙109 c-1
LA-g6∙109 c-1
Intra valley scattering rates
2р0 - 1s 21∙109 с-1
2s - 1s 52∙109 c-1
2pplusmn - 1s 01 ∙109 c-1
2pplusmn - 2p0 144 ∙109 c-1
2pplusmn - 2s 89 ∙109 c-1
27∙1010 c-1
16∙1010 c-1
77∙1010 c-1
5∙1010 c-1
0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
rate
10
9 s-1
intervalley splitting meV
SiAs 2p(+-)-1s(Al
1) LA-f
2p(+-)-1s(Au
1) LA-g
Relaxation of the lower laser level
f- and g-phonon scattering rates in As donor under stress
0 2 4 6 8 10 12 14 16 18 20 220
1
2
3
4
5
6
intervalley splitting meV
109 c
-1
SiAs 2p
0-1s(Au
1) LA-g
2p0-1s(EB
1) TA-f
2p0-1s(Al
1) LA-f
2p0-1s(Au
1) TA-g
0 5 10 15 20 25 300
1
2
3
4
5
6
7
8
intervalley splitting meV1
010c-1
SiAs 1s(B
2)-1s(A
1
l) LA-g
1s(B2)-1s(A
1
l) TA-f
Relaxation of 2р(+-) and 2р0 states
1s(T2Г7)
1s(T2Г8)
1s(A1)
TA-f52∙109 c-1
LA-g~ 108 c-1
LA-g2∙109 c-1
LA-f47∙109 c-1
TA-f6∙109 c-1
2p0
2s
2pplusmn
LA-g053∙109 c-1
LA-g04∙109 c-1
TA-f14∙1010 c-1
TO-f~32∙1011 c-1
1s(E)
LA-g37∙109 c-1
SiBi SiBi
00 05 10 15 20 25 30 35 400
5
10
15
20
0 59 118 176 235 294 353 412 471
Intervalley splitting meV
1011
c-1
bar
SiBi 2p0-1s(Al
1) TO-f (для верхней ТО ветки) D
15 20 25 30 35 400
1
2
3
4
5
6
7
8
Intervalley splitting meV
1010
c-1
SiBi 2p
0 - 1s(Al
1) LA-f
0000 0493 0986 1479 1972 2465 2958 3451 39440
2
4
6
8
10
12
14
16
18
0 58 116 174 232 290 348 406 464
SiBi LO-g
2p+- - 1s(Al1)
Intervalley splitting meV
1010
c-1
2p+- - 1s(Al1)
with shiftedphonon dispersion on 05 meV
bar
7 8 9 10 11 12 130
5
10
15
20
25
30
35
Intervalley splitting meV
15 kbar
109 c
-1
SiBi2p(+-)-1s(Al
1) TO-f
для верхней ТО-f ветки для нижней ТО-f ветки
1 kbar
f- and g-phonon scattering rates in Bi donor under stress
0 2 4 6 80
2
4
6
8
Intervalley splitting meV
109 c
-1
SiBi 1s(B
2Г
7)-1s(Al
1)
0 20 40 60 800
2
4
6
8
10
12
14
Intervalley splitting meV
1010
c-1
SiBi1s(B
2)-1s(A
1
l) LA-g
Relaxation 1s(B2) state in Bi donor under stressed silicon
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
26∙101035∙1010
42∙109
2p0(А1+В2)
Stress (25 kbar)
2pplusmn2s
15∙109
14∙109
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
0
2p0
1s(E)1s(T2)
1s(A1)
1s(A1)
1s(B2)
1s(B1)1s(E)1s(A1)
55∙109 2∙109
85∙109
2p0(А1+В2)
Stress (18 kbar)
2pplusmn2s
3∙1011
E
E
SiAs
SiBi
Laser state relaxation rates s-1
intra2pplusmn = 215 ∙1010 c-1
intra2p0= 2 ∙109 c-1
Влияние деформации на эффективность накачки рабочих состояний
(Pump efficiency of the laser states depending on stress)
СО2
Релаксация на фононах
THg
СО2
Релаксация на фононах
THg emission
E
THg emissionE
001 01 1 10 100
1010
1011
1012
1013
1014 Nd=31015 cm-3
popu
latio
n c
m-3
pump kWcm-2
D-centers 2p
0
D-centers under 2p
0 under
001 01 1 10 100
1E-4
1E-3
001
01
1Nd=31015 cm-3
gain
and
abs
orpt
ion
cm
-1
pump kWcm-2
Population gain absorption
SiSb
Donor gain amp D--center absorption
Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)
Blue lines correspond to valley shift 5 meV (06 kbar)
Summary
The axial compressive stress of silicon crystal applied along [100] crystallographic orientation
From the experiment
- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors
- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors
- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress
From the theoretical treatment
- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys
- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states
- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal
Current study amp Further development
1) Spin-orbit interaction amp laser frequencies SiSb SiBi
2) Group-V donor lasing from isotope enriched silicon 28Si
3) Low T donor relaxation in stressed silicon (exp study)
4) Donoracceptor lasing from low dimensional SiSiGe structures
5) CW operation
D- binding energy vs compression
LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve
0 2 4 6 8 10 12 14 16 18 2000
05
10
15
20
25
109 c
-1
SiP
2p0(A
1+B
2) - 1s(A
1
u) LA-g TA-g
Междолинное расщепление мэВ
00 05 10 15 20 25 30 350
2
4
6
8
10
12
14
1
09 c-1
Междолинное расщепление meV
SiP (TA-f)
2p0-1s(E)
2p0-1s(B
1)
2p0-1s(A
1
u)
Сумма
0 10 20 30 400
1
2
3
4
5
6
7
10
10 c
-1
Междолинное расщепление мэВ
SiP 1s(B2) - 1s(A1) TA-g
1s(B2) - 1s(A1) LA-g
1кбар соответствует 85 мэВ
SiP SiP
1s(E)
1s(T2)
1s(A1)
TA-f84∙109 c-1
TA-f124∙109 c-1
LA-g03∙109 c-1
LA-g575109 c-1
TA-g7∙1010 c-1
TA-g36∙1010 c-1
2p0
SiP
Темп внутридолинных переходов
2р0 - 1s 21∙109 с-1
26∙1010 c-1
7∙1010 c-1
36∙1010 c-1
0 10 20 30 40
0
1
2
3
4
5
intervalley splitting meV
10
10 c
-1
1s(B2)-1s(A
1) TА-g
1s(B2)-1s(A
1) LA-g
SiSb
0 2 4 6 8 10 12 14 16 180
1
2
3
4
5
6
7
intervalley splitting meV
109 c
-1
SiSb 2p
0(A
1+B
2)-1s(Au
1) LA-g
2p0(A
1+B
2)-1s(E) TA-f
2p0(A
1+B
2)-1s(Au
1) TA-g
Переходы 2p0-1s(A
1
u) и 2p0-1s(B
1)
на ТА-f фононах пренебрежимо малы
1 kbar yields 85 meV valley shift for [100]
stress
1 kbar yields 85 meV valley shift for [100]
stress
SiSb SiSb
1s(E)
1s(T2)
1s(A1)
TA-f~108 c-1
TA-f142∙109 c-1
LA-g26∙109 c-1
LA-g175∙109 c-1
TA-g46∙1010 c-1
TA-g38∙1010 c-1
2p0
SiSb
Intra valley scattering rate
2р0 - 1s 21∙109 с-1
18∙1010 c-1
38∙1010 c-1
46∙1010 c-1
SiAs SiAs
LA-f079∙1010 c-1
1s(E)
1s(T2)
1s(A1)
TA-f122∙109 c-1
LA-g063∙109 c-1
LA-g07∙109 c-1
TA-f27∙1010 c-1
TA-f16∙1010 c-1
2p0
2s
2pplusmn
LA-g5∙1010 c-1
LA-g33∙1010 c-1
TA-f146 ∙109 c-1
LA-f098∙109 c-1
LA-f27∙1010 c-1
LA-g6∙109 c-1
LA-g6∙109 c-1
Intra valley scattering rates
2р0 - 1s 21∙109 с-1
2s - 1s 52∙109 c-1
2pplusmn - 1s 01 ∙109 c-1
2pplusmn - 2p0 144 ∙109 c-1
2pplusmn - 2s 89 ∙109 c-1
27∙1010 c-1
16∙1010 c-1
77∙1010 c-1
5∙1010 c-1
0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
rate
10
9 s-1
intervalley splitting meV
SiAs 2p(+-)-1s(Al
1) LA-f
2p(+-)-1s(Au
1) LA-g
Relaxation of the lower laser level
f- and g-phonon scattering rates in As donor under stress
0 2 4 6 8 10 12 14 16 18 20 220
1
2
3
4
5
6
intervalley splitting meV
109 c
-1
SiAs 2p
0-1s(Au
1) LA-g
2p0-1s(EB
1) TA-f
2p0-1s(Al
1) LA-f
2p0-1s(Au
1) TA-g
0 5 10 15 20 25 300
1
2
3
4
5
6
7
8
intervalley splitting meV1
010c-1
SiAs 1s(B
2)-1s(A
1
l) LA-g
1s(B2)-1s(A
1
l) TA-f
Relaxation of 2р(+-) and 2р0 states
1s(T2Г7)
1s(T2Г8)
1s(A1)
TA-f52∙109 c-1
LA-g~ 108 c-1
LA-g2∙109 c-1
LA-f47∙109 c-1
TA-f6∙109 c-1
2p0
2s
2pplusmn
LA-g053∙109 c-1
LA-g04∙109 c-1
TA-f14∙1010 c-1
TO-f~32∙1011 c-1
1s(E)
LA-g37∙109 c-1
SiBi SiBi
00 05 10 15 20 25 30 35 400
5
10
15
20
0 59 118 176 235 294 353 412 471
Intervalley splitting meV
1011
c-1
bar
SiBi 2p0-1s(Al
1) TO-f (для верхней ТО ветки) D
15 20 25 30 35 400
1
2
3
4
5
6
7
8
Intervalley splitting meV
1010
c-1
SiBi 2p
0 - 1s(Al
1) LA-f
0000 0493 0986 1479 1972 2465 2958 3451 39440
2
4
6
8
10
12
14
16
18
0 58 116 174 232 290 348 406 464
SiBi LO-g
2p+- - 1s(Al1)
Intervalley splitting meV
1010
c-1
2p+- - 1s(Al1)
with shiftedphonon dispersion on 05 meV
bar
7 8 9 10 11 12 130
5
10
15
20
25
30
35
Intervalley splitting meV
15 kbar
109 c
-1
SiBi2p(+-)-1s(Al
1) TO-f
для верхней ТО-f ветки для нижней ТО-f ветки
1 kbar
f- and g-phonon scattering rates in Bi donor under stress
0 2 4 6 80
2
4
6
8
Intervalley splitting meV
109 c
-1
SiBi 1s(B
2Г
7)-1s(Al
1)
0 20 40 60 800
2
4
6
8
10
12
14
Intervalley splitting meV
1010
c-1
SiBi1s(B
2)-1s(A
1
l) LA-g
Relaxation 1s(B2) state in Bi donor under stressed silicon
Влияние деформации на эффективность накачки рабочих состояний
(Pump efficiency of the laser states depending on stress)
СО2
Релаксация на фононах
THg
СО2
Релаксация на фононах
THg emission
E
THg emissionE
001 01 1 10 100
1010
1011
1012
1013
1014 Nd=31015 cm-3
popu
latio
n c
m-3
pump kWcm-2
D-centers 2p
0
D-centers under 2p
0 under
001 01 1 10 100
1E-4
1E-3
001
01
1Nd=31015 cm-3
gain
and
abs
orpt
ion
cm
-1
pump kWcm-2
Population gain absorption
SiSb
Donor gain amp D--center absorption
Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)
Blue lines correspond to valley shift 5 meV (06 kbar)
Summary
The axial compressive stress of silicon crystal applied along [100] crystallographic orientation
From the experiment
- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors
- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors
- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress
From the theoretical treatment
- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys
- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states
- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal
Current study amp Further development
1) Spin-orbit interaction amp laser frequencies SiSb SiBi
2) Group-V donor lasing from isotope enriched silicon 28Si
3) Low T donor relaxation in stressed silicon (exp study)
4) Donoracceptor lasing from low dimensional SiSiGe structures
5) CW operation
D- binding energy vs compression
LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve
0 2 4 6 8 10 12 14 16 18 2000
05
10
15
20
25
109 c
-1
SiP
2p0(A
1+B
2) - 1s(A
1
u) LA-g TA-g
Междолинное расщепление мэВ
00 05 10 15 20 25 30 350
2
4
6
8
10
12
14
1
09 c-1
Междолинное расщепление meV
SiP (TA-f)
2p0-1s(E)
2p0-1s(B
1)
2p0-1s(A
1
u)
Сумма
0 10 20 30 400
1
2
3
4
5
6
7
10
10 c
-1
Междолинное расщепление мэВ
SiP 1s(B2) - 1s(A1) TA-g
1s(B2) - 1s(A1) LA-g
1кбар соответствует 85 мэВ
SiP SiP
1s(E)
1s(T2)
1s(A1)
TA-f84∙109 c-1
TA-f124∙109 c-1
LA-g03∙109 c-1
LA-g575109 c-1
TA-g7∙1010 c-1
TA-g36∙1010 c-1
2p0
SiP
Темп внутридолинных переходов
2р0 - 1s 21∙109 с-1
26∙1010 c-1
7∙1010 c-1
36∙1010 c-1
0 10 20 30 40
0
1
2
3
4
5
intervalley splitting meV
10
10 c
-1
1s(B2)-1s(A
1) TА-g
1s(B2)-1s(A
1) LA-g
SiSb
0 2 4 6 8 10 12 14 16 180
1
2
3
4
5
6
7
intervalley splitting meV
109 c
-1
SiSb 2p
0(A
1+B
2)-1s(Au
1) LA-g
2p0(A
1+B
2)-1s(E) TA-f
2p0(A
1+B
2)-1s(Au
1) TA-g
Переходы 2p0-1s(A
1
u) и 2p0-1s(B
1)
на ТА-f фононах пренебрежимо малы
1 kbar yields 85 meV valley shift for [100]
stress
1 kbar yields 85 meV valley shift for [100]
stress
SiSb SiSb
1s(E)
1s(T2)
1s(A1)
TA-f~108 c-1
TA-f142∙109 c-1
LA-g26∙109 c-1
LA-g175∙109 c-1
TA-g46∙1010 c-1
TA-g38∙1010 c-1
2p0
SiSb
Intra valley scattering rate
2р0 - 1s 21∙109 с-1
18∙1010 c-1
38∙1010 c-1
46∙1010 c-1
SiAs SiAs
LA-f079∙1010 c-1
1s(E)
1s(T2)
1s(A1)
TA-f122∙109 c-1
LA-g063∙109 c-1
LA-g07∙109 c-1
TA-f27∙1010 c-1
TA-f16∙1010 c-1
2p0
2s
2pplusmn
LA-g5∙1010 c-1
LA-g33∙1010 c-1
TA-f146 ∙109 c-1
LA-f098∙109 c-1
LA-f27∙1010 c-1
LA-g6∙109 c-1
LA-g6∙109 c-1
Intra valley scattering rates
2р0 - 1s 21∙109 с-1
2s - 1s 52∙109 c-1
2pplusmn - 1s 01 ∙109 c-1
2pplusmn - 2p0 144 ∙109 c-1
2pplusmn - 2s 89 ∙109 c-1
27∙1010 c-1
16∙1010 c-1
77∙1010 c-1
5∙1010 c-1
0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
rate
10
9 s-1
intervalley splitting meV
SiAs 2p(+-)-1s(Al
1) LA-f
2p(+-)-1s(Au
1) LA-g
Relaxation of the lower laser level
f- and g-phonon scattering rates in As donor under stress
0 2 4 6 8 10 12 14 16 18 20 220
1
2
3
4
5
6
intervalley splitting meV
109 c
-1
SiAs 2p
0-1s(Au
1) LA-g
2p0-1s(EB
1) TA-f
2p0-1s(Al
1) LA-f
2p0-1s(Au
1) TA-g
0 5 10 15 20 25 300
1
2
3
4
5
6
7
8
intervalley splitting meV1
010c-1
SiAs 1s(B
2)-1s(A
1
l) LA-g
1s(B2)-1s(A
1
l) TA-f
Relaxation of 2р(+-) and 2р0 states
1s(T2Г7)
1s(T2Г8)
1s(A1)
TA-f52∙109 c-1
LA-g~ 108 c-1
LA-g2∙109 c-1
LA-f47∙109 c-1
TA-f6∙109 c-1
2p0
2s
2pplusmn
LA-g053∙109 c-1
LA-g04∙109 c-1
TA-f14∙1010 c-1
TO-f~32∙1011 c-1
1s(E)
LA-g37∙109 c-1
SiBi SiBi
00 05 10 15 20 25 30 35 400
5
10
15
20
0 59 118 176 235 294 353 412 471
Intervalley splitting meV
1011
c-1
bar
SiBi 2p0-1s(Al
1) TO-f (для верхней ТО ветки) D
15 20 25 30 35 400
1
2
3
4
5
6
7
8
Intervalley splitting meV
1010
c-1
SiBi 2p
0 - 1s(Al
1) LA-f
0000 0493 0986 1479 1972 2465 2958 3451 39440
2
4
6
8
10
12
14
16
18
0 58 116 174 232 290 348 406 464
SiBi LO-g
2p+- - 1s(Al1)
Intervalley splitting meV
1010
c-1
2p+- - 1s(Al1)
with shiftedphonon dispersion on 05 meV
bar
7 8 9 10 11 12 130
5
10
15
20
25
30
35
Intervalley splitting meV
15 kbar
109 c
-1
SiBi2p(+-)-1s(Al
1) TO-f
для верхней ТО-f ветки для нижней ТО-f ветки
1 kbar
f- and g-phonon scattering rates in Bi donor under stress
0 2 4 6 80
2
4
6
8
Intervalley splitting meV
109 c
-1
SiBi 1s(B
2Г
7)-1s(Al
1)
0 20 40 60 800
2
4
6
8
10
12
14
Intervalley splitting meV
1010
c-1
SiBi1s(B
2)-1s(A
1
l) LA-g
Relaxation 1s(B2) state in Bi donor under stressed silicon
001 01 1 10 100
1010
1011
1012
1013
1014 Nd=31015 cm-3
popu
latio
n c
m-3
pump kWcm-2
D-centers 2p
0
D-centers under 2p
0 under
001 01 1 10 100
1E-4
1E-3
001
01
1Nd=31015 cm-3
gain
and
abs
orpt
ion
cm
-1
pump kWcm-2
Population gain absorption
SiSb
Donor gain amp D--center absorption
Population of 2p0 states and D- center concentration in unstressed (red lines) amp stressed silicon (blue lines)
Blue lines correspond to valley shift 5 meV (06 kbar)
Summary
The axial compressive stress of silicon crystal applied along [100] crystallographic orientation
From the experiment
- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors
- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors
- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress
From the theoretical treatment
- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys
- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states
- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal
Current study amp Further development
1) Spin-orbit interaction amp laser frequencies SiSb SiBi
2) Group-V donor lasing from isotope enriched silicon 28Si
3) Low T donor relaxation in stressed silicon (exp study)
4) Donoracceptor lasing from low dimensional SiSiGe structures
5) CW operation
D- binding energy vs compression
LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve
0 2 4 6 8 10 12 14 16 18 2000
05
10
15
20
25
109 c
-1
SiP
2p0(A
1+B
2) - 1s(A
1
u) LA-g TA-g
Междолинное расщепление мэВ
00 05 10 15 20 25 30 350
2
4
6
8
10
12
14
1
09 c-1
Междолинное расщепление meV
SiP (TA-f)
2p0-1s(E)
2p0-1s(B
1)
2p0-1s(A
1
u)
Сумма
0 10 20 30 400
1
2
3
4
5
6
7
10
10 c
-1
Междолинное расщепление мэВ
SiP 1s(B2) - 1s(A1) TA-g
1s(B2) - 1s(A1) LA-g
1кбар соответствует 85 мэВ
SiP SiP
1s(E)
1s(T2)
1s(A1)
TA-f84∙109 c-1
TA-f124∙109 c-1
LA-g03∙109 c-1
LA-g575109 c-1
TA-g7∙1010 c-1
TA-g36∙1010 c-1
2p0
SiP
Темп внутридолинных переходов
2р0 - 1s 21∙109 с-1
26∙1010 c-1
7∙1010 c-1
36∙1010 c-1
0 10 20 30 40
0
1
2
3
4
5
intervalley splitting meV
10
10 c
-1
1s(B2)-1s(A
1) TА-g
1s(B2)-1s(A
1) LA-g
SiSb
0 2 4 6 8 10 12 14 16 180
1
2
3
4
5
6
7
intervalley splitting meV
109 c
-1
SiSb 2p
0(A
1+B
2)-1s(Au
1) LA-g
2p0(A
1+B
2)-1s(E) TA-f
2p0(A
1+B
2)-1s(Au
1) TA-g
Переходы 2p0-1s(A
1
u) и 2p0-1s(B
1)
на ТА-f фононах пренебрежимо малы
1 kbar yields 85 meV valley shift for [100]
stress
1 kbar yields 85 meV valley shift for [100]
stress
SiSb SiSb
1s(E)
1s(T2)
1s(A1)
TA-f~108 c-1
TA-f142∙109 c-1
LA-g26∙109 c-1
LA-g175∙109 c-1
TA-g46∙1010 c-1
TA-g38∙1010 c-1
2p0
SiSb
Intra valley scattering rate
2р0 - 1s 21∙109 с-1
18∙1010 c-1
38∙1010 c-1
46∙1010 c-1
SiAs SiAs
LA-f079∙1010 c-1
1s(E)
1s(T2)
1s(A1)
TA-f122∙109 c-1
LA-g063∙109 c-1
LA-g07∙109 c-1
TA-f27∙1010 c-1
TA-f16∙1010 c-1
2p0
2s
2pplusmn
LA-g5∙1010 c-1
LA-g33∙1010 c-1
TA-f146 ∙109 c-1
LA-f098∙109 c-1
LA-f27∙1010 c-1
LA-g6∙109 c-1
LA-g6∙109 c-1
Intra valley scattering rates
2р0 - 1s 21∙109 с-1
2s - 1s 52∙109 c-1
2pplusmn - 1s 01 ∙109 c-1
2pplusmn - 2p0 144 ∙109 c-1
2pplusmn - 2s 89 ∙109 c-1
27∙1010 c-1
16∙1010 c-1
77∙1010 c-1
5∙1010 c-1
0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
rate
10
9 s-1
intervalley splitting meV
SiAs 2p(+-)-1s(Al
1) LA-f
2p(+-)-1s(Au
1) LA-g
Relaxation of the lower laser level
f- and g-phonon scattering rates in As donor under stress
0 2 4 6 8 10 12 14 16 18 20 220
1
2
3
4
5
6
intervalley splitting meV
109 c
-1
SiAs 2p
0-1s(Au
1) LA-g
2p0-1s(EB
1) TA-f
2p0-1s(Al
1) LA-f
2p0-1s(Au
1) TA-g
0 5 10 15 20 25 300
1
2
3
4
5
6
7
8
intervalley splitting meV1
010c-1
SiAs 1s(B
2)-1s(A
1
l) LA-g
1s(B2)-1s(A
1
l) TA-f
Relaxation of 2р(+-) and 2р0 states
1s(T2Г7)
1s(T2Г8)
1s(A1)
TA-f52∙109 c-1
LA-g~ 108 c-1
LA-g2∙109 c-1
LA-f47∙109 c-1
TA-f6∙109 c-1
2p0
2s
2pplusmn
LA-g053∙109 c-1
LA-g04∙109 c-1
TA-f14∙1010 c-1
TO-f~32∙1011 c-1
1s(E)
LA-g37∙109 c-1
SiBi SiBi
00 05 10 15 20 25 30 35 400
5
10
15
20
0 59 118 176 235 294 353 412 471
Intervalley splitting meV
1011
c-1
bar
SiBi 2p0-1s(Al
1) TO-f (для верхней ТО ветки) D
15 20 25 30 35 400
1
2
3
4
5
6
7
8
Intervalley splitting meV
1010
c-1
SiBi 2p
0 - 1s(Al
1) LA-f
0000 0493 0986 1479 1972 2465 2958 3451 39440
2
4
6
8
10
12
14
16
18
0 58 116 174 232 290 348 406 464
SiBi LO-g
2p+- - 1s(Al1)
Intervalley splitting meV
1010
c-1
2p+- - 1s(Al1)
with shiftedphonon dispersion on 05 meV
bar
7 8 9 10 11 12 130
5
10
15
20
25
30
35
Intervalley splitting meV
15 kbar
109 c
-1
SiBi2p(+-)-1s(Al
1) TO-f
для верхней ТО-f ветки для нижней ТО-f ветки
1 kbar
f- and g-phonon scattering rates in Bi donor under stress
0 2 4 6 80
2
4
6
8
Intervalley splitting meV
109 c
-1
SiBi 1s(B
2Г
7)-1s(Al
1)
0 20 40 60 800
2
4
6
8
10
12
14
Intervalley splitting meV
1010
c-1
SiBi1s(B
2)-1s(A
1
l) LA-g
Relaxation 1s(B2) state in Bi donor under stressed silicon
Summary
The axial compressive stress of silicon crystal applied along [100] crystallographic orientation
From the experiment
- increases the gain and decreases the threshold intensity for THz lasing of optically excited group-V donors
- changes the 2pplusmn- upper laser state for the 2p0 one as well as emission frequency for As and Bi donors
- lasing of P and Sb donors is based on the 2p0 ndash 1s(T2) transitions amp laser line does not depend on stress
From the theoretical treatment
- f-phonons give noticeable contribution in relaxation of donor laser states in unstressed silicon and lose meaning even under small splitting of conduction band valleys
- valley shift of the conduction band increases both pump efficiency and the lifetime of the upper laser states
- D- center THz absorption block lasing of donors in silicon under photo-ionizing excitation amp can be eliminated by axial deformation of the host crystal
Current study amp Further development
1) Spin-orbit interaction amp laser frequencies SiSb SiBi
2) Group-V donor lasing from isotope enriched silicon 28Si
3) Low T donor relaxation in stressed silicon (exp study)
4) Donoracceptor lasing from low dimensional SiSiGe structures
5) CW operation
D- binding energy vs compression
LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve
0 2 4 6 8 10 12 14 16 18 2000
05
10
15
20
25
109 c
-1
SiP
2p0(A
1+B
2) - 1s(A
1
u) LA-g TA-g
Междолинное расщепление мэВ
00 05 10 15 20 25 30 350
2
4
6
8
10
12
14
1
09 c-1
Междолинное расщепление meV
SiP (TA-f)
2p0-1s(E)
2p0-1s(B
1)
2p0-1s(A
1
u)
Сумма
0 10 20 30 400
1
2
3
4
5
6
7
10
10 c
-1
Междолинное расщепление мэВ
SiP 1s(B2) - 1s(A1) TA-g
1s(B2) - 1s(A1) LA-g
1кбар соответствует 85 мэВ
SiP SiP
1s(E)
1s(T2)
1s(A1)
TA-f84∙109 c-1
TA-f124∙109 c-1
LA-g03∙109 c-1
LA-g575109 c-1
TA-g7∙1010 c-1
TA-g36∙1010 c-1
2p0
SiP
Темп внутридолинных переходов
2р0 - 1s 21∙109 с-1
26∙1010 c-1
7∙1010 c-1
36∙1010 c-1
0 10 20 30 40
0
1
2
3
4
5
intervalley splitting meV
10
10 c
-1
1s(B2)-1s(A
1) TА-g
1s(B2)-1s(A
1) LA-g
SiSb
0 2 4 6 8 10 12 14 16 180
1
2
3
4
5
6
7
intervalley splitting meV
109 c
-1
SiSb 2p
0(A
1+B
2)-1s(Au
1) LA-g
2p0(A
1+B
2)-1s(E) TA-f
2p0(A
1+B
2)-1s(Au
1) TA-g
Переходы 2p0-1s(A
1
u) и 2p0-1s(B
1)
на ТА-f фононах пренебрежимо малы
1 kbar yields 85 meV valley shift for [100]
stress
1 kbar yields 85 meV valley shift for [100]
stress
SiSb SiSb
1s(E)
1s(T2)
1s(A1)
TA-f~108 c-1
TA-f142∙109 c-1
LA-g26∙109 c-1
LA-g175∙109 c-1
TA-g46∙1010 c-1
TA-g38∙1010 c-1
2p0
SiSb
Intra valley scattering rate
2р0 - 1s 21∙109 с-1
18∙1010 c-1
38∙1010 c-1
46∙1010 c-1
SiAs SiAs
LA-f079∙1010 c-1
1s(E)
1s(T2)
1s(A1)
TA-f122∙109 c-1
LA-g063∙109 c-1
LA-g07∙109 c-1
TA-f27∙1010 c-1
TA-f16∙1010 c-1
2p0
2s
2pplusmn
LA-g5∙1010 c-1
LA-g33∙1010 c-1
TA-f146 ∙109 c-1
LA-f098∙109 c-1
LA-f27∙1010 c-1
LA-g6∙109 c-1
LA-g6∙109 c-1
Intra valley scattering rates
2р0 - 1s 21∙109 с-1
2s - 1s 52∙109 c-1
2pplusmn - 1s 01 ∙109 c-1
2pplusmn - 2p0 144 ∙109 c-1
2pplusmn - 2s 89 ∙109 c-1
27∙1010 c-1
16∙1010 c-1
77∙1010 c-1
5∙1010 c-1
0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
rate
10
9 s-1
intervalley splitting meV
SiAs 2p(+-)-1s(Al
1) LA-f
2p(+-)-1s(Au
1) LA-g
Relaxation of the lower laser level
f- and g-phonon scattering rates in As donor under stress
0 2 4 6 8 10 12 14 16 18 20 220
1
2
3
4
5
6
intervalley splitting meV
109 c
-1
SiAs 2p
0-1s(Au
1) LA-g
2p0-1s(EB
1) TA-f
2p0-1s(Al
1) LA-f
2p0-1s(Au
1) TA-g
0 5 10 15 20 25 300
1
2
3
4
5
6
7
8
intervalley splitting meV1
010c-1
SiAs 1s(B
2)-1s(A
1
l) LA-g
1s(B2)-1s(A
1
l) TA-f
Relaxation of 2р(+-) and 2р0 states
1s(T2Г7)
1s(T2Г8)
1s(A1)
TA-f52∙109 c-1
LA-g~ 108 c-1
LA-g2∙109 c-1
LA-f47∙109 c-1
TA-f6∙109 c-1
2p0
2s
2pplusmn
LA-g053∙109 c-1
LA-g04∙109 c-1
TA-f14∙1010 c-1
TO-f~32∙1011 c-1
1s(E)
LA-g37∙109 c-1
SiBi SiBi
00 05 10 15 20 25 30 35 400
5
10
15
20
0 59 118 176 235 294 353 412 471
Intervalley splitting meV
1011
c-1
bar
SiBi 2p0-1s(Al
1) TO-f (для верхней ТО ветки) D
15 20 25 30 35 400
1
2
3
4
5
6
7
8
Intervalley splitting meV
1010
c-1
SiBi 2p
0 - 1s(Al
1) LA-f
0000 0493 0986 1479 1972 2465 2958 3451 39440
2
4
6
8
10
12
14
16
18
0 58 116 174 232 290 348 406 464
SiBi LO-g
2p+- - 1s(Al1)
Intervalley splitting meV
1010
c-1
2p+- - 1s(Al1)
with shiftedphonon dispersion on 05 meV
bar
7 8 9 10 11 12 130
5
10
15
20
25
30
35
Intervalley splitting meV
15 kbar
109 c
-1
SiBi2p(+-)-1s(Al
1) TO-f
для верхней ТО-f ветки для нижней ТО-f ветки
1 kbar
f- and g-phonon scattering rates in Bi donor under stress
0 2 4 6 80
2
4
6
8
Intervalley splitting meV
109 c
-1
SiBi 1s(B
2Г
7)-1s(Al
1)
0 20 40 60 800
2
4
6
8
10
12
14
Intervalley splitting meV
1010
c-1
SiBi1s(B
2)-1s(A
1
l) LA-g
Relaxation 1s(B2) state in Bi donor under stressed silicon
Current study amp Further development
1) Spin-orbit interaction amp laser frequencies SiSb SiBi
2) Group-V donor lasing from isotope enriched silicon 28Si
3) Low T donor relaxation in stressed silicon (exp study)
4) Donoracceptor lasing from low dimensional SiSiGe structures
5) CW operation
D- binding energy vs compression
LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve
0 2 4 6 8 10 12 14 16 18 2000
05
10
15
20
25
109 c
-1
SiP
2p0(A
1+B
2) - 1s(A
1
u) LA-g TA-g
Междолинное расщепление мэВ
00 05 10 15 20 25 30 350
2
4
6
8
10
12
14
1
09 c-1
Междолинное расщепление meV
SiP (TA-f)
2p0-1s(E)
2p0-1s(B
1)
2p0-1s(A
1
u)
Сумма
0 10 20 30 400
1
2
3
4
5
6
7
10
10 c
-1
Междолинное расщепление мэВ
SiP 1s(B2) - 1s(A1) TA-g
1s(B2) - 1s(A1) LA-g
1кбар соответствует 85 мэВ
SiP SiP
1s(E)
1s(T2)
1s(A1)
TA-f84∙109 c-1
TA-f124∙109 c-1
LA-g03∙109 c-1
LA-g575109 c-1
TA-g7∙1010 c-1
TA-g36∙1010 c-1
2p0
SiP
Темп внутридолинных переходов
2р0 - 1s 21∙109 с-1
26∙1010 c-1
7∙1010 c-1
36∙1010 c-1
0 10 20 30 40
0
1
2
3
4
5
intervalley splitting meV
10
10 c
-1
1s(B2)-1s(A
1) TА-g
1s(B2)-1s(A
1) LA-g
SiSb
0 2 4 6 8 10 12 14 16 180
1
2
3
4
5
6
7
intervalley splitting meV
109 c
-1
SiSb 2p
0(A
1+B
2)-1s(Au
1) LA-g
2p0(A
1+B
2)-1s(E) TA-f
2p0(A
1+B
2)-1s(Au
1) TA-g
Переходы 2p0-1s(A
1
u) и 2p0-1s(B
1)
на ТА-f фононах пренебрежимо малы
1 kbar yields 85 meV valley shift for [100]
stress
1 kbar yields 85 meV valley shift for [100]
stress
SiSb SiSb
1s(E)
1s(T2)
1s(A1)
TA-f~108 c-1
TA-f142∙109 c-1
LA-g26∙109 c-1
LA-g175∙109 c-1
TA-g46∙1010 c-1
TA-g38∙1010 c-1
2p0
SiSb
Intra valley scattering rate
2р0 - 1s 21∙109 с-1
18∙1010 c-1
38∙1010 c-1
46∙1010 c-1
SiAs SiAs
LA-f079∙1010 c-1
1s(E)
1s(T2)
1s(A1)
TA-f122∙109 c-1
LA-g063∙109 c-1
LA-g07∙109 c-1
TA-f27∙1010 c-1
TA-f16∙1010 c-1
2p0
2s
2pplusmn
LA-g5∙1010 c-1
LA-g33∙1010 c-1
TA-f146 ∙109 c-1
LA-f098∙109 c-1
LA-f27∙1010 c-1
LA-g6∙109 c-1
LA-g6∙109 c-1
Intra valley scattering rates
2р0 - 1s 21∙109 с-1
2s - 1s 52∙109 c-1
2pplusmn - 1s 01 ∙109 c-1
2pplusmn - 2p0 144 ∙109 c-1
2pplusmn - 2s 89 ∙109 c-1
27∙1010 c-1
16∙1010 c-1
77∙1010 c-1
5∙1010 c-1
0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
rate
10
9 s-1
intervalley splitting meV
SiAs 2p(+-)-1s(Al
1) LA-f
2p(+-)-1s(Au
1) LA-g
Relaxation of the lower laser level
f- and g-phonon scattering rates in As donor under stress
0 2 4 6 8 10 12 14 16 18 20 220
1
2
3
4
5
6
intervalley splitting meV
109 c
-1
SiAs 2p
0-1s(Au
1) LA-g
2p0-1s(EB
1) TA-f
2p0-1s(Al
1) LA-f
2p0-1s(Au
1) TA-g
0 5 10 15 20 25 300
1
2
3
4
5
6
7
8
intervalley splitting meV1
010c-1
SiAs 1s(B
2)-1s(A
1
l) LA-g
1s(B2)-1s(A
1
l) TA-f
Relaxation of 2р(+-) and 2р0 states
1s(T2Г7)
1s(T2Г8)
1s(A1)
TA-f52∙109 c-1
LA-g~ 108 c-1
LA-g2∙109 c-1
LA-f47∙109 c-1
TA-f6∙109 c-1
2p0
2s
2pplusmn
LA-g053∙109 c-1
LA-g04∙109 c-1
TA-f14∙1010 c-1
TO-f~32∙1011 c-1
1s(E)
LA-g37∙109 c-1
SiBi SiBi
00 05 10 15 20 25 30 35 400
5
10
15
20
0 59 118 176 235 294 353 412 471
Intervalley splitting meV
1011
c-1
bar
SiBi 2p0-1s(Al
1) TO-f (для верхней ТО ветки) D
15 20 25 30 35 400
1
2
3
4
5
6
7
8
Intervalley splitting meV
1010
c-1
SiBi 2p
0 - 1s(Al
1) LA-f
0000 0493 0986 1479 1972 2465 2958 3451 39440
2
4
6
8
10
12
14
16
18
0 58 116 174 232 290 348 406 464
SiBi LO-g
2p+- - 1s(Al1)
Intervalley splitting meV
1010
c-1
2p+- - 1s(Al1)
with shiftedphonon dispersion on 05 meV
bar
7 8 9 10 11 12 130
5
10
15
20
25
30
35
Intervalley splitting meV
15 kbar
109 c
-1
SiBi2p(+-)-1s(Al
1) TO-f
для верхней ТО-f ветки для нижней ТО-f ветки
1 kbar
f- and g-phonon scattering rates in Bi donor under stress
0 2 4 6 80
2
4
6
8
Intervalley splitting meV
109 c
-1
SiBi 1s(B
2Г
7)-1s(Al
1)
0 20 40 60 800
2
4
6
8
10
12
14
Intervalley splitting meV
1010
c-1
SiBi1s(B
2)-1s(A
1
l) LA-g
Relaxation 1s(B2) state in Bi donor under stressed silicon
D- binding energy vs compression
LEOliveira LMFalicov PhysRevB 336990(1986)-solid curve DM Larsen PhysRev B 235521 (1981) ndashdashed curve
0 2 4 6 8 10 12 14 16 18 2000
05
10
15
20
25
109 c
-1
SiP
2p0(A
1+B
2) - 1s(A
1
u) LA-g TA-g
Междолинное расщепление мэВ
00 05 10 15 20 25 30 350
2
4
6
8
10
12
14
1
09 c-1
Междолинное расщепление meV
SiP (TA-f)
2p0-1s(E)
2p0-1s(B
1)
2p0-1s(A
1
u)
Сумма
0 10 20 30 400
1
2
3
4
5
6
7
10
10 c
-1
Междолинное расщепление мэВ
SiP 1s(B2) - 1s(A1) TA-g
1s(B2) - 1s(A1) LA-g
1кбар соответствует 85 мэВ
SiP SiP
1s(E)
1s(T2)
1s(A1)
TA-f84∙109 c-1
TA-f124∙109 c-1
LA-g03∙109 c-1
LA-g575109 c-1
TA-g7∙1010 c-1
TA-g36∙1010 c-1
2p0
SiP
Темп внутридолинных переходов
2р0 - 1s 21∙109 с-1
26∙1010 c-1
7∙1010 c-1
36∙1010 c-1
0 10 20 30 40
0
1
2
3
4
5
intervalley splitting meV
10
10 c
-1
1s(B2)-1s(A
1) TА-g
1s(B2)-1s(A
1) LA-g
SiSb
0 2 4 6 8 10 12 14 16 180
1
2
3
4
5
6
7
intervalley splitting meV
109 c
-1
SiSb 2p
0(A
1+B
2)-1s(Au
1) LA-g
2p0(A
1+B
2)-1s(E) TA-f
2p0(A
1+B
2)-1s(Au
1) TA-g
Переходы 2p0-1s(A
1
u) и 2p0-1s(B
1)
на ТА-f фононах пренебрежимо малы
1 kbar yields 85 meV valley shift for [100]
stress
1 kbar yields 85 meV valley shift for [100]
stress
SiSb SiSb
1s(E)
1s(T2)
1s(A1)
TA-f~108 c-1
TA-f142∙109 c-1
LA-g26∙109 c-1
LA-g175∙109 c-1
TA-g46∙1010 c-1
TA-g38∙1010 c-1
2p0
SiSb
Intra valley scattering rate
2р0 - 1s 21∙109 с-1
18∙1010 c-1
38∙1010 c-1
46∙1010 c-1
SiAs SiAs
LA-f079∙1010 c-1
1s(E)
1s(T2)
1s(A1)
TA-f122∙109 c-1
LA-g063∙109 c-1
LA-g07∙109 c-1
TA-f27∙1010 c-1
TA-f16∙1010 c-1
2p0
2s
2pplusmn
LA-g5∙1010 c-1
LA-g33∙1010 c-1
TA-f146 ∙109 c-1
LA-f098∙109 c-1
LA-f27∙1010 c-1
LA-g6∙109 c-1
LA-g6∙109 c-1
Intra valley scattering rates
2р0 - 1s 21∙109 с-1
2s - 1s 52∙109 c-1
2pplusmn - 1s 01 ∙109 c-1
2pplusmn - 2p0 144 ∙109 c-1
2pplusmn - 2s 89 ∙109 c-1
27∙1010 c-1
16∙1010 c-1
77∙1010 c-1
5∙1010 c-1
0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
rate
10
9 s-1
intervalley splitting meV
SiAs 2p(+-)-1s(Al
1) LA-f
2p(+-)-1s(Au
1) LA-g
Relaxation of the lower laser level
f- and g-phonon scattering rates in As donor under stress
0 2 4 6 8 10 12 14 16 18 20 220
1
2
3
4
5
6
intervalley splitting meV
109 c
-1
SiAs 2p
0-1s(Au
1) LA-g
2p0-1s(EB
1) TA-f
2p0-1s(Al
1) LA-f
2p0-1s(Au
1) TA-g
0 5 10 15 20 25 300
1
2
3
4
5
6
7
8
intervalley splitting meV1
010c-1
SiAs 1s(B
2)-1s(A
1
l) LA-g
1s(B2)-1s(A
1
l) TA-f
Relaxation of 2р(+-) and 2р0 states
1s(T2Г7)
1s(T2Г8)
1s(A1)
TA-f52∙109 c-1
LA-g~ 108 c-1
LA-g2∙109 c-1
LA-f47∙109 c-1
TA-f6∙109 c-1
2p0
2s
2pplusmn
LA-g053∙109 c-1
LA-g04∙109 c-1
TA-f14∙1010 c-1
TO-f~32∙1011 c-1
1s(E)
LA-g37∙109 c-1
SiBi SiBi
00 05 10 15 20 25 30 35 400
5
10
15
20
0 59 118 176 235 294 353 412 471
Intervalley splitting meV
1011
c-1
bar
SiBi 2p0-1s(Al
1) TO-f (для верхней ТО ветки) D
15 20 25 30 35 400
1
2
3
4
5
6
7
8
Intervalley splitting meV
1010
c-1
SiBi 2p
0 - 1s(Al
1) LA-f
0000 0493 0986 1479 1972 2465 2958 3451 39440
2
4
6
8
10
12
14
16
18
0 58 116 174 232 290 348 406 464
SiBi LO-g
2p+- - 1s(Al1)
Intervalley splitting meV
1010
c-1
2p+- - 1s(Al1)
with shiftedphonon dispersion on 05 meV
bar
7 8 9 10 11 12 130
5
10
15
20
25
30
35
Intervalley splitting meV
15 kbar
109 c
-1
SiBi2p(+-)-1s(Al
1) TO-f
для верхней ТО-f ветки для нижней ТО-f ветки
1 kbar
f- and g-phonon scattering rates in Bi donor under stress
0 2 4 6 80
2
4
6
8
Intervalley splitting meV
109 c
-1
SiBi 1s(B
2Г
7)-1s(Al
1)
0 20 40 60 800
2
4
6
8
10
12
14
Intervalley splitting meV
1010
c-1
SiBi1s(B
2)-1s(A
1
l) LA-g
Relaxation 1s(B2) state in Bi donor under stressed silicon
0 2 4 6 8 10 12 14 16 18 2000
05
10
15
20
25
109 c
-1
SiP
2p0(A
1+B
2) - 1s(A
1
u) LA-g TA-g
Междолинное расщепление мэВ
00 05 10 15 20 25 30 350
2
4
6
8
10
12
14
1
09 c-1
Междолинное расщепление meV
SiP (TA-f)
2p0-1s(E)
2p0-1s(B
1)
2p0-1s(A
1
u)
Сумма
0 10 20 30 400
1
2
3
4
5
6
7
10
10 c
-1
Междолинное расщепление мэВ
SiP 1s(B2) - 1s(A1) TA-g
1s(B2) - 1s(A1) LA-g
1кбар соответствует 85 мэВ
SiP SiP
1s(E)
1s(T2)
1s(A1)
TA-f84∙109 c-1
TA-f124∙109 c-1
LA-g03∙109 c-1
LA-g575109 c-1
TA-g7∙1010 c-1
TA-g36∙1010 c-1
2p0
SiP
Темп внутридолинных переходов
2р0 - 1s 21∙109 с-1
26∙1010 c-1
7∙1010 c-1
36∙1010 c-1
0 10 20 30 40
0
1
2
3
4
5
intervalley splitting meV
10
10 c
-1
1s(B2)-1s(A
1) TА-g
1s(B2)-1s(A
1) LA-g
SiSb
0 2 4 6 8 10 12 14 16 180
1
2
3
4
5
6
7
intervalley splitting meV
109 c
-1
SiSb 2p
0(A
1+B
2)-1s(Au
1) LA-g
2p0(A
1+B
2)-1s(E) TA-f
2p0(A
1+B
2)-1s(Au
1) TA-g
Переходы 2p0-1s(A
1
u) и 2p0-1s(B
1)
на ТА-f фононах пренебрежимо малы
1 kbar yields 85 meV valley shift for [100]
stress
1 kbar yields 85 meV valley shift for [100]
stress
SiSb SiSb
1s(E)
1s(T2)
1s(A1)
TA-f~108 c-1
TA-f142∙109 c-1
LA-g26∙109 c-1
LA-g175∙109 c-1
TA-g46∙1010 c-1
TA-g38∙1010 c-1
2p0
SiSb
Intra valley scattering rate
2р0 - 1s 21∙109 с-1
18∙1010 c-1
38∙1010 c-1
46∙1010 c-1
SiAs SiAs
LA-f079∙1010 c-1
1s(E)
1s(T2)
1s(A1)
TA-f122∙109 c-1
LA-g063∙109 c-1
LA-g07∙109 c-1
TA-f27∙1010 c-1
TA-f16∙1010 c-1
2p0
2s
2pplusmn
LA-g5∙1010 c-1
LA-g33∙1010 c-1
TA-f146 ∙109 c-1
LA-f098∙109 c-1
LA-f27∙1010 c-1
LA-g6∙109 c-1
LA-g6∙109 c-1
Intra valley scattering rates
2р0 - 1s 21∙109 с-1
2s - 1s 52∙109 c-1
2pplusmn - 1s 01 ∙109 c-1
2pplusmn - 2p0 144 ∙109 c-1
2pplusmn - 2s 89 ∙109 c-1
27∙1010 c-1
16∙1010 c-1
77∙1010 c-1
5∙1010 c-1
0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
rate
10
9 s-1
intervalley splitting meV
SiAs 2p(+-)-1s(Al
1) LA-f
2p(+-)-1s(Au
1) LA-g
Relaxation of the lower laser level
f- and g-phonon scattering rates in As donor under stress
0 2 4 6 8 10 12 14 16 18 20 220
1
2
3
4
5
6
intervalley splitting meV
109 c
-1
SiAs 2p
0-1s(Au
1) LA-g
2p0-1s(EB
1) TA-f
2p0-1s(Al
1) LA-f
2p0-1s(Au
1) TA-g
0 5 10 15 20 25 300
1
2
3
4
5
6
7
8
intervalley splitting meV1
010c-1
SiAs 1s(B
2)-1s(A
1
l) LA-g
1s(B2)-1s(A
1
l) TA-f
Relaxation of 2р(+-) and 2р0 states
1s(T2Г7)
1s(T2Г8)
1s(A1)
TA-f52∙109 c-1
LA-g~ 108 c-1
LA-g2∙109 c-1
LA-f47∙109 c-1
TA-f6∙109 c-1
2p0
2s
2pplusmn
LA-g053∙109 c-1
LA-g04∙109 c-1
TA-f14∙1010 c-1
TO-f~32∙1011 c-1
1s(E)
LA-g37∙109 c-1
SiBi SiBi
00 05 10 15 20 25 30 35 400
5
10
15
20
0 59 118 176 235 294 353 412 471
Intervalley splitting meV
1011
c-1
bar
SiBi 2p0-1s(Al
1) TO-f (для верхней ТО ветки) D
15 20 25 30 35 400
1
2
3
4
5
6
7
8
Intervalley splitting meV
1010
c-1
SiBi 2p
0 - 1s(Al
1) LA-f
0000 0493 0986 1479 1972 2465 2958 3451 39440
2
4
6
8
10
12
14
16
18
0 58 116 174 232 290 348 406 464
SiBi LO-g
2p+- - 1s(Al1)
Intervalley splitting meV
1010
c-1
2p+- - 1s(Al1)
with shiftedphonon dispersion on 05 meV
bar
7 8 9 10 11 12 130
5
10
15
20
25
30
35
Intervalley splitting meV
15 kbar
109 c
-1
SiBi2p(+-)-1s(Al
1) TO-f
для верхней ТО-f ветки для нижней ТО-f ветки
1 kbar
f- and g-phonon scattering rates in Bi donor under stress
0 2 4 6 80
2
4
6
8
Intervalley splitting meV
109 c
-1
SiBi 1s(B
2Г
7)-1s(Al
1)
0 20 40 60 800
2
4
6
8
10
12
14
Intervalley splitting meV
1010
c-1
SiBi1s(B
2)-1s(A
1
l) LA-g
Relaxation 1s(B2) state in Bi donor under stressed silicon
0 10 20 30 40
0
1
2
3
4
5
intervalley splitting meV
10
10 c
-1
1s(B2)-1s(A
1) TА-g
1s(B2)-1s(A
1) LA-g
SiSb
0 2 4 6 8 10 12 14 16 180
1
2
3
4
5
6
7
intervalley splitting meV
109 c
-1
SiSb 2p
0(A
1+B
2)-1s(Au
1) LA-g
2p0(A
1+B
2)-1s(E) TA-f
2p0(A
1+B
2)-1s(Au
1) TA-g
Переходы 2p0-1s(A
1
u) и 2p0-1s(B
1)
на ТА-f фононах пренебрежимо малы
1 kbar yields 85 meV valley shift for [100]
stress
1 kbar yields 85 meV valley shift for [100]
stress
SiSb SiSb
1s(E)
1s(T2)
1s(A1)
TA-f~108 c-1
TA-f142∙109 c-1
LA-g26∙109 c-1
LA-g175∙109 c-1
TA-g46∙1010 c-1
TA-g38∙1010 c-1
2p0
SiSb
Intra valley scattering rate
2р0 - 1s 21∙109 с-1
18∙1010 c-1
38∙1010 c-1
46∙1010 c-1
SiAs SiAs
LA-f079∙1010 c-1
1s(E)
1s(T2)
1s(A1)
TA-f122∙109 c-1
LA-g063∙109 c-1
LA-g07∙109 c-1
TA-f27∙1010 c-1
TA-f16∙1010 c-1
2p0
2s
2pplusmn
LA-g5∙1010 c-1
LA-g33∙1010 c-1
TA-f146 ∙109 c-1
LA-f098∙109 c-1
LA-f27∙1010 c-1
LA-g6∙109 c-1
LA-g6∙109 c-1
Intra valley scattering rates
2р0 - 1s 21∙109 с-1
2s - 1s 52∙109 c-1
2pplusmn - 1s 01 ∙109 c-1
2pplusmn - 2p0 144 ∙109 c-1
2pplusmn - 2s 89 ∙109 c-1
27∙1010 c-1
16∙1010 c-1
77∙1010 c-1
5∙1010 c-1
0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
rate
10
9 s-1
intervalley splitting meV
SiAs 2p(+-)-1s(Al
1) LA-f
2p(+-)-1s(Au
1) LA-g
Relaxation of the lower laser level
f- and g-phonon scattering rates in As donor under stress
0 2 4 6 8 10 12 14 16 18 20 220
1
2
3
4
5
6
intervalley splitting meV
109 c
-1
SiAs 2p
0-1s(Au
1) LA-g
2p0-1s(EB
1) TA-f
2p0-1s(Al
1) LA-f
2p0-1s(Au
1) TA-g
0 5 10 15 20 25 300
1
2
3
4
5
6
7
8
intervalley splitting meV1
010c-1
SiAs 1s(B
2)-1s(A
1
l) LA-g
1s(B2)-1s(A
1
l) TA-f
Relaxation of 2р(+-) and 2р0 states
1s(T2Г7)
1s(T2Г8)
1s(A1)
TA-f52∙109 c-1
LA-g~ 108 c-1
LA-g2∙109 c-1
LA-f47∙109 c-1
TA-f6∙109 c-1
2p0
2s
2pplusmn
LA-g053∙109 c-1
LA-g04∙109 c-1
TA-f14∙1010 c-1
TO-f~32∙1011 c-1
1s(E)
LA-g37∙109 c-1
SiBi SiBi
00 05 10 15 20 25 30 35 400
5
10
15
20
0 59 118 176 235 294 353 412 471
Intervalley splitting meV
1011
c-1
bar
SiBi 2p0-1s(Al
1) TO-f (для верхней ТО ветки) D
15 20 25 30 35 400
1
2
3
4
5
6
7
8
Intervalley splitting meV
1010
c-1
SiBi 2p
0 - 1s(Al
1) LA-f
0000 0493 0986 1479 1972 2465 2958 3451 39440
2
4
6
8
10
12
14
16
18
0 58 116 174 232 290 348 406 464
SiBi LO-g
2p+- - 1s(Al1)
Intervalley splitting meV
1010
c-1
2p+- - 1s(Al1)
with shiftedphonon dispersion on 05 meV
bar
7 8 9 10 11 12 130
5
10
15
20
25
30
35
Intervalley splitting meV
15 kbar
109 c
-1
SiBi2p(+-)-1s(Al
1) TO-f
для верхней ТО-f ветки для нижней ТО-f ветки
1 kbar
f- and g-phonon scattering rates in Bi donor under stress
0 2 4 6 80
2
4
6
8
Intervalley splitting meV
109 c
-1
SiBi 1s(B
2Г
7)-1s(Al
1)
0 20 40 60 800
2
4
6
8
10
12
14
Intervalley splitting meV
1010
c-1
SiBi1s(B
2)-1s(A
1
l) LA-g
Relaxation 1s(B2) state in Bi donor under stressed silicon
SiAs SiAs
LA-f079∙1010 c-1
1s(E)
1s(T2)
1s(A1)
TA-f122∙109 c-1
LA-g063∙109 c-1
LA-g07∙109 c-1
TA-f27∙1010 c-1
TA-f16∙1010 c-1
2p0
2s
2pplusmn
LA-g5∙1010 c-1
LA-g33∙1010 c-1
TA-f146 ∙109 c-1
LA-f098∙109 c-1
LA-f27∙1010 c-1
LA-g6∙109 c-1
LA-g6∙109 c-1
Intra valley scattering rates
2р0 - 1s 21∙109 с-1
2s - 1s 52∙109 c-1
2pplusmn - 1s 01 ∙109 c-1
2pplusmn - 2p0 144 ∙109 c-1
2pplusmn - 2s 89 ∙109 c-1
27∙1010 c-1
16∙1010 c-1
77∙1010 c-1
5∙1010 c-1
0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
rate
10
9 s-1
intervalley splitting meV
SiAs 2p(+-)-1s(Al
1) LA-f
2p(+-)-1s(Au
1) LA-g
Relaxation of the lower laser level
f- and g-phonon scattering rates in As donor under stress
0 2 4 6 8 10 12 14 16 18 20 220
1
2
3
4
5
6
intervalley splitting meV
109 c
-1
SiAs 2p
0-1s(Au
1) LA-g
2p0-1s(EB
1) TA-f
2p0-1s(Al
1) LA-f
2p0-1s(Au
1) TA-g
0 5 10 15 20 25 300
1
2
3
4
5
6
7
8
intervalley splitting meV1
010c-1
SiAs 1s(B
2)-1s(A
1
l) LA-g
1s(B2)-1s(A
1
l) TA-f
Relaxation of 2р(+-) and 2р0 states
1s(T2Г7)
1s(T2Г8)
1s(A1)
TA-f52∙109 c-1
LA-g~ 108 c-1
LA-g2∙109 c-1
LA-f47∙109 c-1
TA-f6∙109 c-1
2p0
2s
2pplusmn
LA-g053∙109 c-1
LA-g04∙109 c-1
TA-f14∙1010 c-1
TO-f~32∙1011 c-1
1s(E)
LA-g37∙109 c-1
SiBi SiBi
00 05 10 15 20 25 30 35 400
5
10
15
20
0 59 118 176 235 294 353 412 471
Intervalley splitting meV
1011
c-1
bar
SiBi 2p0-1s(Al
1) TO-f (для верхней ТО ветки) D
15 20 25 30 35 400
1
2
3
4
5
6
7
8
Intervalley splitting meV
1010
c-1
SiBi 2p
0 - 1s(Al
1) LA-f
0000 0493 0986 1479 1972 2465 2958 3451 39440
2
4
6
8
10
12
14
16
18
0 58 116 174 232 290 348 406 464
SiBi LO-g
2p+- - 1s(Al1)
Intervalley splitting meV
1010
c-1
2p+- - 1s(Al1)
with shiftedphonon dispersion on 05 meV
bar
7 8 9 10 11 12 130
5
10
15
20
25
30
35
Intervalley splitting meV
15 kbar
109 c
-1
SiBi2p(+-)-1s(Al
1) TO-f
для верхней ТО-f ветки для нижней ТО-f ветки
1 kbar
f- and g-phonon scattering rates in Bi donor under stress
0 2 4 6 80
2
4
6
8
Intervalley splitting meV
109 c
-1
SiBi 1s(B
2Г
7)-1s(Al
1)
0 20 40 60 800
2
4
6
8
10
12
14
Intervalley splitting meV
1010
c-1
SiBi1s(B
2)-1s(A
1
l) LA-g
Relaxation 1s(B2) state in Bi donor under stressed silicon
0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
rate
10
9 s-1
intervalley splitting meV
SiAs 2p(+-)-1s(Al
1) LA-f
2p(+-)-1s(Au
1) LA-g
Relaxation of the lower laser level
f- and g-phonon scattering rates in As donor under stress
0 2 4 6 8 10 12 14 16 18 20 220
1
2
3
4
5
6
intervalley splitting meV
109 c
-1
SiAs 2p
0-1s(Au
1) LA-g
2p0-1s(EB
1) TA-f
2p0-1s(Al
1) LA-f
2p0-1s(Au
1) TA-g
0 5 10 15 20 25 300
1
2
3
4
5
6
7
8
intervalley splitting meV1
010c-1
SiAs 1s(B
2)-1s(A
1
l) LA-g
1s(B2)-1s(A
1
l) TA-f
Relaxation of 2р(+-) and 2р0 states
1s(T2Г7)
1s(T2Г8)
1s(A1)
TA-f52∙109 c-1
LA-g~ 108 c-1
LA-g2∙109 c-1
LA-f47∙109 c-1
TA-f6∙109 c-1
2p0
2s
2pplusmn
LA-g053∙109 c-1
LA-g04∙109 c-1
TA-f14∙1010 c-1
TO-f~32∙1011 c-1
1s(E)
LA-g37∙109 c-1
SiBi SiBi
00 05 10 15 20 25 30 35 400
5
10
15
20
0 59 118 176 235 294 353 412 471
Intervalley splitting meV
1011
c-1
bar
SiBi 2p0-1s(Al
1) TO-f (для верхней ТО ветки) D
15 20 25 30 35 400
1
2
3
4
5
6
7
8
Intervalley splitting meV
1010
c-1
SiBi 2p
0 - 1s(Al
1) LA-f
0000 0493 0986 1479 1972 2465 2958 3451 39440
2
4
6
8
10
12
14
16
18
0 58 116 174 232 290 348 406 464
SiBi LO-g
2p+- - 1s(Al1)
Intervalley splitting meV
1010
c-1
2p+- - 1s(Al1)
with shiftedphonon dispersion on 05 meV
bar
7 8 9 10 11 12 130
5
10
15
20
25
30
35
Intervalley splitting meV
15 kbar
109 c
-1
SiBi2p(+-)-1s(Al
1) TO-f
для верхней ТО-f ветки для нижней ТО-f ветки
1 kbar
f- and g-phonon scattering rates in Bi donor under stress
0 2 4 6 80
2
4
6
8
Intervalley splitting meV
109 c
-1
SiBi 1s(B
2Г
7)-1s(Al
1)
0 20 40 60 800
2
4
6
8
10
12
14
Intervalley splitting meV
1010
c-1
SiBi1s(B
2)-1s(A
1
l) LA-g
Relaxation 1s(B2) state in Bi donor under stressed silicon
1s(T2Г7)
1s(T2Г8)
1s(A1)
TA-f52∙109 c-1
LA-g~ 108 c-1
LA-g2∙109 c-1
LA-f47∙109 c-1
TA-f6∙109 c-1
2p0
2s
2pplusmn
LA-g053∙109 c-1
LA-g04∙109 c-1
TA-f14∙1010 c-1
TO-f~32∙1011 c-1
1s(E)
LA-g37∙109 c-1
SiBi SiBi
00 05 10 15 20 25 30 35 400
5
10
15
20
0 59 118 176 235 294 353 412 471
Intervalley splitting meV
1011
c-1
bar
SiBi 2p0-1s(Al
1) TO-f (для верхней ТО ветки) D
15 20 25 30 35 400
1
2
3
4
5
6
7
8
Intervalley splitting meV
1010
c-1
SiBi 2p
0 - 1s(Al
1) LA-f
0000 0493 0986 1479 1972 2465 2958 3451 39440
2
4
6
8
10
12
14
16
18
0 58 116 174 232 290 348 406 464
SiBi LO-g
2p+- - 1s(Al1)
Intervalley splitting meV
1010
c-1
2p+- - 1s(Al1)
with shiftedphonon dispersion on 05 meV
bar
7 8 9 10 11 12 130
5
10
15
20
25
30
35
Intervalley splitting meV
15 kbar
109 c
-1
SiBi2p(+-)-1s(Al
1) TO-f
для верхней ТО-f ветки для нижней ТО-f ветки
1 kbar
f- and g-phonon scattering rates in Bi donor under stress
0 2 4 6 80
2
4
6
8
Intervalley splitting meV
109 c
-1
SiBi 1s(B
2Г
7)-1s(Al
1)
0 20 40 60 800
2
4
6
8
10
12
14
Intervalley splitting meV
1010
c-1
SiBi1s(B
2)-1s(A
1
l) LA-g
Relaxation 1s(B2) state in Bi donor under stressed silicon
00 05 10 15 20 25 30 35 400
5
10
15
20
0 59 118 176 235 294 353 412 471
Intervalley splitting meV
1011
c-1
bar
SiBi 2p0-1s(Al
1) TO-f (для верхней ТО ветки) D
15 20 25 30 35 400
1
2
3
4
5
6
7
8
Intervalley splitting meV
1010
c-1
SiBi 2p
0 - 1s(Al
1) LA-f
0000 0493 0986 1479 1972 2465 2958 3451 39440
2
4
6
8
10
12
14
16
18
0 58 116 174 232 290 348 406 464
SiBi LO-g
2p+- - 1s(Al1)
Intervalley splitting meV
1010
c-1
2p+- - 1s(Al1)
with shiftedphonon dispersion on 05 meV
bar
7 8 9 10 11 12 130
5
10
15
20
25
30
35
Intervalley splitting meV
15 kbar
109 c
-1
SiBi2p(+-)-1s(Al
1) TO-f
для верхней ТО-f ветки для нижней ТО-f ветки
1 kbar
f- and g-phonon scattering rates in Bi donor under stress
0 2 4 6 80
2
4
6
8
Intervalley splitting meV
109 c
-1
SiBi 1s(B
2Г
7)-1s(Al
1)
0 20 40 60 800
2
4
6
8
10
12
14
Intervalley splitting meV
1010
c-1
SiBi1s(B
2)-1s(A
1
l) LA-g
Relaxation 1s(B2) state in Bi donor under stressed silicon
0 2 4 6 80
2
4
6
8
Intervalley splitting meV
109 c
-1
SiBi 1s(B
2Г
7)-1s(Al
1)
0 20 40 60 800
2
4
6
8
10
12
14
Intervalley splitting meV
1010
c-1
SiBi1s(B
2)-1s(A
1
l) LA-g
Relaxation 1s(B2) state in Bi donor under stressed silicon