Workshop on Sources of Polarized Electrons and High Brightness Electron Beams

Optimization of Semiconductor Superlattice for Spin-Polarized Electron Source

Leonid G. GerchikovLaboratory of Spin-Polarized Electron Spectroscopy

Department of Experimental PhysicsState Polytechnic University

St. Petersburg, Russia

CollaboratorsCollaborators

Department of Experimental Physics, St. Petersburg State Polytechnic University, Russia, Yuri A. Mamaev, Yuri P.Yashin, Vitaly V. Kuz’michev, Dmitry A. Vasiliev, Leonid G. Gerchikov

A.F. Ioffe Physicotechnical Institute RAS, Russia, Viktor M. Ustinov, Aleksey E. Zhukov, Vladimir S. Mikhrin, Alexey P. Vasiliev

Stanford Linear Accelerator Center, Stanford, CA, USA, James E. Clendenin , Takashi Maruyama

Institute of Nuclear Physics, Mainz University, Mainz, Germany, Kurt Aulenbacher, Valeri Yu. Tioukin

• Introduction– Goals of optimization – Problems of optimization – Best photocathodes

• Calculations of SL parameters– Energy spectrum – Photoabsorption – Transport

• AlInGaAs/AlGaAs SL with strained QW– Optimized design– Results

• Summary&Outlook

OUTLINEOUTLINE

Goals of optimizationGoals of optimization

High maximal P at large QEHigh maximal P at large QE

High polarization of electron emission from High polarization of electron emission from

strained semiconductor SL at the expense of QEstrained semiconductor SL at the expense of QE

0.00 0.04

-0.04

-0.02

1.4

1.5

1.6

lh1

hh1

e1

k001

, A -1

Ene

rgy,

eV

k100

, A -1

valence band

bandbendingregion

electronemission

electrongeneration

heavy holem iniband

light holem iniband

InG aAs AlGaAs

E c

E v

550 600 650 700 750 800 850 900

10-5

10-4

10-3

10-2

10-1

100

101

0

20

40

60

80

100

QE

QE,

%

, nm

Polarization

Pola

rizat

ion,

%

SL Al0.2 In0.155 Ga0.65As(5.1nm)/Al0.36Ga0.64As(2.3nm)

Spectra of electron emission: Polarization P and Quantum Efficiency QE

•Polarization is maximal at photoabsorption threshold where QE is small.•Strain relaxation does not allow to produce thick photocathode with high QE.•Rise of the vacuum level increases P and decreases QE

To get the bestTo get the best

PP QEQE•Large valence band splitting > 60 meV• High strain splitting and offsets in valence band• Effective electronic transport along SL axes• High quality SL, uniform layer composition and thickensses• Low doping in SL

•Thick working layer• High NEA value• Heavy doped BBR layer

Best photocathodesBest photocathodes

Sample Composition Pmax QE(max) Team

SLSP16 GaAs(3.2nm)/ GaAs0.68P0.34 (3.2nm)

92% 0.5% Nagoya University,

2005

SL5-777 GaAs(1.5nm)/

In0.2Al0.23Ga0.57As(3.6nm)

91% 0.14% SPbSPU, 2005

SL7-307 Al0.4Ga0.6As(2.1nm)/

In0.19Al0.2Ga0.57As(5.4nm)

92% 0.85% SPbSPU, 2007

Calculations of SL’s energyCalculations of SL’s energy spectrum and spectrum and photoabsorption within 8-band Kane modelphotoabsorption within 8-band Kane model

Miniband spectrum:qq qEH ,, ),(ˆ

kk k

),(2

exp1

,,

, qAnzd

iued n

n

iqziq kk

k

Photoabsorption coefficient:

Polarization:

0P

P&QE of electron emissionP&QE of electron emission

95.0,/

/

)()(

0

0

etsst

et

KK

P

KKPP

P0 - initial polarization,Kt , Ke – depolarization factors on stages of transport in SL and emission through BBR,s,t – transport and spin relaxation times in SL.

1.0,3.0

)()1()(

BR

BdRQE R – reflection from GaAs ,B – probability of electron emission through BBR.

Polarization spectrum

0,00 0,05 0,10

-0,15

-0,10

-0,05

1,5

1,6

1,7

hh4

lh2

hh3

hh2lh1

hh1

e2

e1

Kz, A-1

GaAs(9nm)/Ga0.6

Al0.4

As(9nm)

Ene

rgy,

eV

K||, A-1

Initial electron polarization Initial electron polarization PP00

Energy band spectrum

Main optical transitionshh1 – e1 lh1 - e1 hh2 - e2 lh2 - e2

Maximal P0 is determined by:• Valence band splitting Ehh-

lh= Ehh1 - Elh1

• Broadening of hole spectrum

Photoabsorption spectrum

1,40 1,45 1,50 1,55 1,60 1,65 1,70 1,750,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

4,0 Total Up Down Partial contributions

e2-lh2

e1-hh1

e1-lh1

e2-hh2

e2-lh1

e1-hh1

GaAs(9nm)/Ga0.6

Al0.4

As(9nm)

Ph

oto

ab

sorp

tion

Co

eff

icie

nt,

10

4 cm-1

Photon Energy, eV

Maximal P0 is limited by:mixture of hh and lh states due to smearing of band edge and broadening of hole spectrum caused by doping and fluctuations of layer composition

1.45 1.50 1.55 1.60 1.65 1.70 1.750

20

40

60

80

100

= 5meV =10meV =20meV

lh2-e2hh2-e2lh1-e1

hh1-e1

Po

lari

zatio

n,

%

Photon Energy, eV

Photoluminescence spectrum

Initial polarization losses amount up to 15% depending on structure quality and design- and Ehh-lh

Initial electron polarization Initial electron polarization PP00

Ehh-lh

Evl

Evh

lh1

hh1

AlInGaAs

AlGaAs

1.45 1.50 1.550

20

40

60

80

100

Po

lari

zatio

n,

%

Photon Energy, eV

Enlarge Ehh-lh to increase maximal P0

by increase of QW deformationE

hh-lh

Evl

Evh

lh1

hh1

AlInGaAs

AlGaAs

1.45 1.50 1.550

20

40

60

80

100

Po

lari

zatio

n,

%

Photon Energy, eV

Large strain deformation leads to structural defects and strain relaxation

1.45 1.50 1.550

20

40

60

80

100

Po

lari

zatio

n,

%

Photon Energy, eV

Optimal combination of strain deformation and quantum confinement effect to provide maximal valence band splitting with minimal risk of strain relaxation and good transport properties

0 10 20 30 40 50 600

10

20

30

40

50

60

70

80

Val

ence

Ban

d S

plitt

ing,

meV

Deformation splitting, meV

Total Quantum effect

20

40

60 QW width

Electronic transport in SLElectronic transport in SL

I=I0T

RI0

I0

Ballistic electron tunneling though SL

Tres exp(-b) Tf exp(-2b) BBR

Tunneling probabilityT = I/I0

Tunneling time = ∫ |Ψ(x)|² dx/I

Tf << Tres

Tunneling resonancesEn = E0 − ∆E/2Cos(qnd) qn = πn/d(N+1)

∆E – width of e1 miniband

N – number of QW in SL

Time of resonant tunnelingSL = ħ/∆E exp(b)

Transport time = ħ/Γ exp(2b)

Γ << ∆E , >> SL

60 62 64 66 68 70 72 74 76 78 800.0

0.2

0.4

0.6

0.8

1.0

E, meV

p

s

T

0.1

1

10

100

Ballistic transportBallistic transport

60 62 64 66 68 70 72 74 76 78 800.0

0.2

0.4

0.6

0.8

1.0

0.1

1

10

100

p

s

E, meV

T

b bb

Optimal choice: bf = b/2

Electronic diffusion in SLElectronic diffusion in SL

ˆˆˆˆ StH

ti

Kinetic equation - electronic density matrixH – effective Hamiltonian of SL in tight binding approximationSt{} – collision term including:• collisions within each QW in constant relaxation time , p, approximation• tunneling through last barrier to BBR• optical pumping

Stationary pumping Approximate solution

fp

NV

NN

26)1)(2/1( N – number of QW in SL

V = E/4 – matrix element of interwell electron transition

Electronic diffusion in Electronic diffusion in SL bulk GaAsSL bulk GaAs

fp

NV

NN

26)1)(2/1(

SL

DL 3

2

D = 40 cm2/s – diffusion coefficient S = 107 cm/s – surface recombination velocity fp dSdVD

periodSLdN

/,2

,122

For SL Al0.2In0.2Ga0.6As(5.4nm)/ Al0.4Ga0.6As(2.1nm)D = 12 cm2/s , S = 3*106 cm/s

Pulse response of SL Pulse response of SL AlAl0.20.2InIn0.160.16GaGa0.640.64As(3.5nm)/ As(3.5nm)/

AlAl0.280.28GaGa0.720.72As(4.0nm) 15 periodsAs(4.0nm) 15 periods

Time dependence of electron emission

0 5 10 15 200.0

0.2

0.4

0.6

0.8

1.0

Inte

nsity

, a.

u.

Time, ps

Experiment* Calculations

D = 16 cm2/s , S = 3.4*106 cm/s

* K. Aulenbacher et al, Mainz, 2006

Strained-well SLStrained-well SL

Unstrained barrierab = a0

GaAs Substrate

Buffer Layera0 - latt. const

GaAs BBR

Strained QWaw > a0

Strained QWaw > a0

Unstrained barrierab = a0

SL

Large valence band splitting due to combination of deformation and quantum confinement effects in QW

MBE grown AlInGaAs/AlGaAs strained-well superlatticeMBE grown AlInGaAs/AlGaAs strained-well superlattice

SPTU & FTI, St.Petersburg

Eg = 1.536 eV, valence band splitting Ehh1 - Elh1 = 87 meV, Maximal polarization Pmax= 92% at QE = 0.85%

Composition Thickness Doping

As cap

GaAs QW 60 A 71018 cm-3 Be

Al0.4Ga0.6As SL

21 A31017 cm-3 Be

In 0.19Al 0.2Ga 0.65As 54 A

Al0.35Ga0.65As Buffer 0.3 m 61018 cm-3 Be

p-GaAs substrate

Choice of SL parametersChoice of SL parameters

• y - In concentration in QW• x - Al concentration in QW• z - Al concentration in barrier• a – QW width• b – barrier width

AlxInyGa1-x-yAs - QW AlxGa1-xAs - Barrier

y = 0.2, Ev = 76 meV x = 0.19, Eg = 1.536 eV a = 5.4 nm, Ehh-lh = 87 meV

z = 0.4, Uhh = 332 meV, Ulh = 258 meV, Ue = 234 meV, b = 2.1 nm, Ee = 31 meV

2 4 6-0.20

-0.15

-0.10

-0.05

0.00

Evl

Evh

Val

ence

Ban

d S

plitt

ing,

meV

Min

iban

d E

dges

, eV

QW (AlInGaAs) width, nm

hh1 lh1 hh2

30

40

50

60

70

80

90

Ehh-lh

SL AlSL Al0.0.1919 In In0.0.22 Ga Ga0.60.611As(5.As(5.44nm)/Alnm)/Al0.0.44GaGa0.60.6As(2.As(2.11nmnm))

Pmax= 92%, QE = 0.85%

650 700 750 800 850 90010-6

10-5

10-4

10-3

10-2

10-1

100

101

0

20

40

60

80

100Q

E,

%

, nm

QE, Experiment QE, Theory

P, Experiment P, Theory

Pol

ariz

atio

n,

%

650 700 750 800 850 9000

1

2

3

4

5

Dn

, Theory

Dn

, Experiment

Up

, Theory

Up

, Experiment

Pho

toab

sorb

tion

coef

ficie

nt,

m-1

, nm

650 700 750 800 850 90010-6

10-5

10-4

10-3

10-2

10-1

100

101

0

20

40

60

80

100

QE

, %

, nm

QE, Experiment QE, Theory

P, Experiment P, Theory

Pol

ariz

atio

n,

%

SL AlSL Al0.0.1919 In In0.0.22 Ga Ga0.60.611As(5.As(5.44nm)/Alnm)/Al0.0.44GaGa0.60.6As(2.As(2.11nmnm))

= 25 meV, P0max = 97%Polarization losses at• photoabsorption – 3%• transport and emission – 5%

h

GaAsSubstrate Buffer BBR SL

e

RGaAs

= 0.3h

GaAsSubstrate DBR Buffer BBR SL

e

RDBR

= 1

Goal: considerable increase of QE at the main polarization maximum and decrease of cathode heatingMethod: Resonance enhancement of photoabsorption in SL integrated into optical resonance cavity

Photoabsorption in the working layer:L << 1, - photoabsorbtion coefficient,L - thickness of SL

Resonant enhancement by factor 2/(1-(RDBRRGaAs) 1/2)2

Heating is reduced by factor L

Photocathode with DBRPhotocathode with DBR

Resonant enhancement of QE Resonant enhancement of QE

550 600 650 700 750 800 850 900 9500

2

4

6

8

10

0

20

40

60

80

QE

En

cha

nce

me

nt

W avelength, nm

QE enchancement

SPTU data

P-4, SL QT 1890 non DBR P-2, SL QT 1890 DBR

Pol

ariz

atio

n,

%

Accepted for publication at Semiconductors, 2008

Summary & OutlookSummary & Outlook

Photocathode based on optimized AlInGaAs/AlGaAs strained-well SL demonstrates Pmax= 92% at QE = 0.85%.

Maximal initial photoelectron polarization P0 = 97%. To increase P0 the higher fabrication quality SL is needed.

Optimization of polarization losses and QE on the stage of electron transport and emission needs an additional investigations.

DBR can considerably increase QE and reduce cathode heating.

Thanks for your attention!Thanks for your attention!

This work was supported by

• Russian Ministry of Education and Science under grant N.P. 2.1.1.2215 in the frames of a program “Development of the High School scientific potential”

• Swiss National Science Foundation under grant SNSF IB7420-11111

SL In0.155Al0.2Ga0.645As(5.1nm)/Al0.36Ga0.64As(2.3nm)

2 4 6 8 10 12 14 16 18 20

0,1

1

50

60

70

80

90

100

QE

, %

thickness, pairs

o QE P

Po

lari

zatio

n,

%

Reproducibility

550 600 650 700 750 800 850 900

10-4

10-3

10-2

10-1

100

101

0

20

40

60

80

100

QE

, %

, nm

QE-1, SL 7-389 T=300K Tht=540C 21,04,2007 Y7-307 Heating 540K

P-1, SL 7-389 T=300K Tht=540C 21,04,2007 P 7-307 Heating 540K 30.11.2006

Pol

ariz

atio

n,

%

Polarization losses caused by mixture of hh and lh states due to smearing of band edge and

broadening of hole spectrum amount 5-10% depending on structural quality, = 10-30meV. dBRQY )()1()(

Initial electron polarization P0 for different values of hole spectrum broadening and smearing of absorption edge

Pol

ariz

atio

n, %

Photon energy, eV

two interval calc.*0.98 basis calc.*0.945 delta=10 meV basis calc.*0.945 delta=20 meV tail 30 meV, delta=25 meV tail 30 meV, delta=45 meV tail 11 meV, delta=25 meV tail 11 meV, delta=7 meV tail 11 meV, delta=7 meV,

gauss=40meV

1.4 1.5 1.6 1.7 1.8 1.9

20

40

60

80

100

SPEC T=540K SPEC T=570K

1.4 1.5 1.6 1.7 1.8 1.9

20

40

60

80

100

Pol

ariz

atio

n, %

Photon energy, eV

two interval calc.*0.98 basis calc.*0.945 delta=10 meV basis calc.*0.945 delta=20 meV tail 30 meV, delta=25 meV tail 30 meV, delta=45 meV tail 11 meV, delta=25 meV tail 11 meV, delta=7 meV tail 11 meV, delta=7 meV,

gauss=40meV SPEC T=540K SPEC T=570K

Polarization lossesPolarization losses

GaAs0.83P0.17/Al0.1In0.18Ga0.72As (5x4nm)x20

1.4 1.5 1.6 1.7 1.81E-5

1E-4

1E-3

0.01

0.1

1

QY

Photon energy, eV

=30 meV, =25 meV =30=30 meV, =45 meV =30=11 meV, =25 meV =30=11 meV, =7 meV SPEC T=540K SPEC T=570K

QE spectrum for different values valence band tails = 10-30meV extsssBPP /)()( 0

s – время спиновой релаксации , при T=300K, Na=4*1017cm-3

s = 7*10-11sext – время выхода электронов из СР в область BBR,ext = d/S + d2/12D, d – ширина СР, S – скорость поверхностной рекомбинации на границе BBR, D – коэффициент диффузии. При T = 300K S = 1/4<v> = 107cm/s.Для тонкого рабочего слоя d = 100nm ext = d/S,ext = 7*10-13sПоляризационные потери ext /s за время транспорта не более 1%

Потери поляризацииПотери поляризации при транспортепри транспорте

extsssBPP /)()( 0

High-Energy physics requirementsHigh-Energy physics requirements

• High electron polarization, P > 80%

Accelerator P, % Beam

MAMI 85% QE > 1%

eRHIC at BNL 70% 50-250 mA, QE > 0.5%

ILC 80% QE > 0.5%

90% is better

• High QE for large beam currents

•Large electronic current requirement•Light energy limitations:•Surface charge saturation•Heating

High QE

ReflectivityReflectivity

750 800 850 900 9500.0

0.2

0.4

0.6

0.8

1.0

Experiment, SL 7-396 DBR Theory, SL 7-396 DBRR

efle

ctiv

ity

W avelength, nm

Spectra of electron emission, P(Spectra of electron emission, P(), QE(), QE())

550 600 650 700 750 800 850 900

10-4

10-3

10-2

10-1

100

101

0

20

40

60

80

W avelength, nm

QE

, %

QE, SL 7-396 DBR QE, SL 7-395 no DBR

P, SL 7-396 DBR P, SL 7-395 no DBR

Pol

ariz

atio

n,

%

550 600 650 700 750 800 850 900

10-4

10-3

10-2

10-1

100

101

0

20

40

60

80

W avelength, nm

QE

, %

QE, Experiment SL 7-396 DBR QE, Theory SL 7-396 DBR

P, Experiment SL 7-396 DBR P, Theory SL 7-396 DBR

Pol

ariz

atio

n,

%

Spectra of electron emission, P(Spectra of electron emission, P(), QE(), QE())

Resonant enhancement of QE Resonant enhancement of QE

750 800 850 9000

10

20

30

W avelength, nm

QE

En

cha

nce

me

nt

Experiment SL 7-396 DBR Theory SL 7-396 DBR

Optimization of Photocathode structureOptimization of Photocathode structure

Buffer

GaAsSubstrate

DBR

SL

BBR

760 780 800 820 840 860 880 9000.0

0.2

0.4

0.6

0.8

1.0

Ref

lect

ivity

Wavelength, nm

• SL structure: layers composition and thickness are chosen to assure Eg= for P()=Pmax

Ehh-lh > 60meV for high polarization Ee1 > 40meV for effective electron transport

• DBR structure: 20x(AlAs(/4)/ (AlxGa1-xAs(/4)) Layer thickness l = /4n() for Bragg reflection x 0.8 for large reflection band width = 2n/n

• Fabry-Perot resonance cavity: BBR + SL + buffer layer Effective thickness = k /2 for QE() = QEmax

Effective thickness of BBR+SL /4

Simulation of resonant photoabsorptionSimulation of resonant photoabsorption

• SL’s energy band structure, photoabsorption coefficient, polarization of photoelectrons.

Method: kp – method within 8-band Kane model.

A.V. Subashiev, L.G. Gerchikov, and A.I. Ipatov. J. Appl. Phys., 96, 1511 (2004).

• Distribution of electromagnetic field in resonance cavity, reflectivity, QE.

Method: transfer matrixes.

M.Born and E.Wolf. Princeples of Optics, Pergamon Press, New York,

1991

Ballistic transportBallistic transport

60 62 64 66 68 70 72 74 76 78 800.0

0.2

0.4

0.6

0.8

1.0

E, meV

ps

T

0.1

1

10

100

60 62 64 66 68 70 72 74 76 78 800.0

0.2

0.4

0.6

0.8

1.0

E, meV

p

s

T

0.1

1

10

100