-
-
. .
2004
22.37 539.2 957 : . ., - , , . . . ; . ., , - ( ) , . . 957 : .
/ . . ; . , 2004. 312 . ISBN 5-8021-0319-1 , . , - . , -, - . -, ,
, - . .
22.37 539.2
. . , 2004 , 2004 ISBN 5-8021-0319-1
-
2
.........................................................................................
4 1. ........................................................... 5
1.1.
.......................................................................
5 1.2.
........................................................................
5 1.3. .......................................... 6 1.3.1.
.......................................................... 6 1.3.2.
............................... 7 1.4. ............... 8 1.5.
.................. 9 1.6.
................................................................. 9
1.7.
...........................................................................
10 1.8.
.........................................................................................
10 1.9.
.........................................................................................
11 1.10.
....................................................................................
12 2. , P-N
...................................................................................................................
13 2.1.
.............................................................................
13 2.2. p- n- ........... 14 2.3. ,
.......................................... 14 2.4. .... 15 2.5.
.........................................................................
16 2.6. . ........................................... 17 2.7.
..................... 17 2.8. .......... 18 2.9. -
............................................ 19 2.10. -n
................................................ 20 2.10.1. p-n
......................................... 20 2.10.3. p-n
.........................................................................
21 2.11. -n ................................. 23 2.12. - -n
................................................. 24 2.14.
.......................................................................................................
27 3. - .................. 31 3.1. () .............. 31 3.1.1.
..............................................................................................................................
31 3.2. .........................................................
33 3.2.1.
.................................................................................
33 3.2.2.
..................................................................................
34 3.2.3.
...................................................................
35 3.2.4.
.................................................................................................................
37 3.2.5. ..................... 38 3.3.
....................................................... 39
3.4. ...................40 3.5.
.......................................................................................41
3.5.1.
............................................................................................41
3.5.2.
.......................................................................42
3.5.3.
.....................................................................................42
3.6. - ..............................................43 3.6.1. -
...............................43 3.6.2.
..........................................................................44
3.6.3. -
...........................................................................................46
3.6.4. - ..........47 C-V
............................................................................................48
C-V
...................................................................48
3.6.5. - C-V 49 3.6.6.
............................................................................................51
3.7. - .........................53 3.7.1.
....................................................53 3.7.2.
..........................................................................................................................55
3.7.3. ,
............................................................................................56
3.7.4. , ,
......................................................................................................................56
3.7.5. -
...................................................................................................................................58
3.7.6. ............59 3.7.7.
-............................................................................................................................60
3.7.8. ...................................61 3.7.9.
.............................................................................63
4. ...................................... 65
.............................................................................................................................65
4.1. p-n ..............................65 4.1.1.
..............................................................................................65
4.1.2.
.......................................................................66
4.1.4.
....................................................................................66
4.2.
....................................................................................................................66
4.3. ,
................................................................................67
4.3.1. p-n
.............................................................................................................................67
4.3.2. p-n
.............................................................................................................................68
4.3.3. .....69 4.3.4.
................................................70
-
3
4.4.
...........................................................................................................
71 4.5.
........................................................................
73 4.6. ........................................ 76 5.
.......................................... 78 5.1. .
........................................................................
78 5.2. ........................ 79 5.2.1. . ....... 80 5.3.
.......................................................................................
81 5.4. -
................................................................................................................................
82 5.5.
....................................................................................................................
82 5.6.
..........................................................................................
83 5.7. . 83 5.8. .............................. 85 5.9.
.......................... 85 5.10.
...............................................................................
86 5.11.
.............................................................................
87 5.12.
......................................................................................
87 5.13. ..................................... 88 5.14.
.............................................. 89 5.15. .
.................................................. 90 5.16.
.......................................................................................
91 5.17. ............................................. 94
h-......................................................................................................................
94 5.18. ............................................ 96 6.
................................................ 102 6.1.
................................... 102 6.2.
................................................... 104 6.3.
................................................................................
105 6.4.
................................................................................
106 6.5. -.......................... 107 6.6.
...................... 108 6.7.
-.......................................... 108 6.8.
.....................................................................
109 6.9.
....................................................................
110 6.10. ................... 111 6.11. - -
..........................................................................................................
113 6.12. -
.............................................................. 115
6.13. -
................................................................................................
116 6.14.
......................................................................
117 6.15.
..............................................................................
118 6.16. -n ...................................... 119 6.17.
-.......................................................... 121
6.18. , .............. 122
6.19. -
......................................................124 7.
.........................................................................
126 7.1.
.......................................................................................................126
7.2. - .....................................................127
7.3. ................................................127 7.4.
........128 7.5. ..............................129 7.6. VG.
............................................................................................................................130
7.7.
.................................................................................................................130
7.8. .............................................131 8.
....................................................................
132 8.1.
.......................................................................................................132
8.2. ..........................................132 8.3.
.....................................................................133
8.4.
..............................................................................................................135
8.5. - .......................................................137
9. ............................................... 139 9.1.
..........................................................................................................................139
9.2.
..........................................................................................................................141
9.3.
..............................................................143
9.4. ...............................................144
.............................................................. 145
.................................. 147
.......................................................................................
149 1. ......................................149 2. ()
..............................................................................149
3.
............................................................................................149
................................ 149
-
4
- , - -. 071400 - - ..08 - . , - , - , - . - . 510400 : 510403 ;
510404 . . 553100 , : 553105 , ; 553117 . 552800 : 552826 ; 552824
- . 010400 ; 071400 ; 220200 ; 190900 - -. , - p-n , , . , , - .
-
. , , - , -. - . . . . , . , - - , . - . . - , , - . - , - . - ,
- . , , . . . . .
-
5
1. 1.1. - . , . N , - N- . , , , -. , , . . , - [1]. . , , - . (
) 3 , - . , , Eg - (0,1 3,0) , . , , , , . 1.1 , , - . , , . . .
EC, - EV, Eg. , -. ,
10-8 106 , , : , (), .. g > 3 ,
< 10-8 , 8101 >= . > 106 .
. 1.1. , , [2] 1.2. , , . , ( ). (ni) - ( - n p, n = p = ni). =
0 (n = p = 0). > 0 . - . ( 1023 -3) . , . -
-
6
(, ), - . , - . , 4 (, ), 5 , ( ), n-. 3 , , - (-) (. 1.2).
+4 +4+5
+4 +4+3
Eg Eg
. 1.2. n- () p- () , , - mn* mp* . -
*mFa = , F
dtdp = , ,
( ) m0 mn* (p = mn*). [3, 4]. 1.3. , , - . - , . -. : - -
. 1.3.1. . - dpx, dpy dpz:
hdpdx x , hdpdy y , (1.1) hdpdz z . . - 3hdVdp , (1.2) zyx
dpdpdpdp = dzdydxdV = , dp px, py, pz, , dV . dV - . . - ( -) dV =
1 3. (1.2) dp h3. dp = h3 , - . , h3 , , -. ,
dp , 3hdp
dp. . (. 1.3). (px, py, pz) (. 1.3). p. dp -, - (. . 1.3). p -
dp :
324
hdppdN = . (1.3)
-
7
d
E
E
N
0
E
EC
py
pz
p dp
. 1.3. : ) ; ) - + d, . N(E)dE, N(E) . -
,2 n
2
C mpEE += (1.4)
C , . - mn . (1.4)
nmdppdE = ,
pdEmdp = n )(2 Cn2 EEmp = . (1.3),
( )
3
2/1C
2/3 24)(
hdEEEmdEENdN == . (1.5)
( )3
2/1C
2/3n 24)(
hEEmEN = . (1.6)
, ( C) (V ), mn mp. (1.6), - . 1.3.2. , , , - . , , :
( )
+=
kTFE
TEfexp1
1, . (1.7)
F , . (1.7) , -, . 1.4. = 0 . E < F 1, , - E < F . E >
F f = 0 . > 0 , kT, E = F 1 0. , . , F C 2kT ( C > kT). -
(1.7) - . - :
( ), exp E Ff E TkT = . (1.8)
:
( ) ( )=C
,2 CE
dETEfENn . (1.9)
-
8
f
ff1
f2
f2
f3
f3
10,50
EV
EC
E
EC - F
ED
F
N
N(E)
. 1.4. N(E), f f , . f E > F E, - . - (1.9) (1.6) (1.8). .
:
,exp CC
=kT
FENn (1.10)
2/3
2n
C22
=
hkTmN . (1.11)
NC . , 2kT, F EC > 2kT ( F EC > kT), fp :
=kT
EFf expp , (1.12)
=kT
EFNp VV exp , (1.13)
EV , , NV - (1.11), mn mp. NV . , (1.9) 2, , - ( ). n p (1.10)
(1.13) F. , :
)exp()( gVC2
kTE
NNnpn i == . (1.14) p n , , n p. ni - . 1.4. , , - . , - n = p
(. 1.5).
. 1.5. (, ..) , n0 p0 . n0 = p0 (1.14) :
.2
exp gVCi00
===
kTE
NNnpn (1.15)
, ni - . NC NV (1.11). (1.15), - . 1.6
-
9
- , , -. , 0,6 2,8 ni 1013 -3 101 -3.
. 1.6. , , [2, 5] 1.5. (1.14) , . 200 )( inpn = . (1.16) ND. - ,
-. (. 1.7) D0 Nn = . (1.17)
(1.16):
D
2
0 Nnp i= . (1.18)
1.7 n-, - ED - n0 p0 .
. 1.7. n- NA, p0 n0
A0 Np = A
2
0 Nnn i= . (1.19)
1.8 p-, - EA - p0 n0 .
. 1.8. p- 1.6. , . - , . - p n = 0 p = n. (Eg kT) - mn mp , (EC
F > 2kT F EV > 2kT) -. (1.10) (1.13) p + pD n nA = 0, :
-
10
=
kT
FENkT
EFN VVCC expexp . (1.20)
F. (1.20) -
kTF
e .
,ln43ln
21
*p
*n
iV
Ci
=
=
mmkTE
NNkTEF (1.21)
Ei = (EV + EC) . F (NC/NV) (mn/mp) (1.11). mn* = mp* F = (EC +
EV)/2. , . - n p, F - (1.10) (1.13). , - n- :
=n
NkTEF CC ln . (1.22)
p-
+=p
NkTEF VV ln . (1.23)
(1.22 1.23) , , . - n0 = ND (1.17),
=
D
CC ln N
NkTEF . (1.24)
p0 = NA (1.19),
+=
A
VV ln N
NkTEF . (1.25)
1.7. - . - - n p :
pn += . - : ,; 0pp0nn qpqn == (1.26) n p [6, 7]. , , - . , n-
npn =+= . (1.27) , , -:
npn
111 =+== . (1.28)
, []. , , = (110) . (1.10) (1.11),
,111
Dn0nn qNqn === ND - n- , - n0. : -4,5. - , -, . , , . , -0,2 , ,
, = 0,2 ; -4,5 , , , - = 4,5 [8]. 1.8. , , , - . , - , , - -. -
:
-
11
nD_
nE
_
pD
_
pE
_
n
_
p
__jjjjJJJ +++=+= , (1.29)
Jr
, nE_j , nD
_j
, pE_j
, pD_j .
-:
;
;
pppE
_
nnnE
_
EpEqj
EnEqj
====
,
;
ppD
_
nnD
_
dxdpqDj
dxdnqDj
=
= (1.30)
Dn , -
n nn qkTD = [4, 9]. -
Dp p. 1.9. - . , - . , . , . - , - , . - , , - , , () . - . , :
nnn += 0 ; (1.31) ppp += 0 , (1.32)
n0 p0 , n p - . - , - , : pn = . (1.33) , - , - . , () - , . . -
, - , . 1.9 G , R .
G R
p
nEC
ED
EV
. 1.9. () R : pnR = , (1.34) . ( )
0GG = 000 pnRR == , n0 p0 . (1.30) (1.14) :
,exp gVC0
=
kTE
NNG (1.35) Eg = EC EV . , G0 .
-
12
, - :
RGdtdp
dtdn == . (1.36)
() : 00 , RRRGGG +=+= , (1.37) G, R -, G , 000 pnR = pnR = .
(1.31), (1.32) (1.34), (1.36) :
( ) .)( 00 nnpndtnd ++= (1.38)
( t = 0). - (1.38) . . 00 pnn +>> . (1.38) :
( )
( ) tnn
np0
0
1 == , (1.39)
n0 . - . n0 = ND, p0
-
13
2. , p-n 2.1. . . :
( ) kTFEeTEf =,0 . , E -, F, . , f, - E > 0, . , , . , , -
[6, 5]. -. d px, py, pz. , , - :
3zyx ))()(( hzpypxp . -
1= zyx : 3zyx )( hppp . - dz - zyx dpdpdpd = : zyx3
3*
3zyx )(22 ddd
hm
hdpdpdp
dz == . (2.1) dn, dz f(E,T): ( )dzTEfdn ,= . (2.2) . , - (E F
>> kT), - :
( ) kTFEkT
FE ee
TEf
=1
1,0 . (2.3)
, , - d, S = 1 l = x: dndN x= . (2.4) J :
( )
zyx3
3*
xx2 ddd
hmeednedNeJ kT
FE
=== . (2.5)
, (2.5), - . ( ) :
( )2z2y2xC2*C 22 +++=+= mEmEE . (2.6) J :
x2xz2y233*
min
2x
*2z
*2y
*C)(2
dededee
hmeJ
x
kTm
kTm
kTm
kTEF
= . (2.7) (2.7)
=
de2
, ,
*y2 2
2y
*
mkTde kT
m
=
. (2.8)
(2.7) . :
kTE
kTW
kTm
V
kTm
emkTe
mkTe
mkTde
x
x
C2
min
min
2x*
**2
*x2
x ===
. (2.9)
(2.8) (2.9) (2.7), - :
kTF
kTEEF
eATeh
Tkemjc
23
22*
x4 ==
+. (2.10)
(2.10)
. 32*4
hkemA = ; -
.
-
14
22*120
mmA
= [11, 8].
F < 0, F, = 0, . : F= . (2.11) , - . :
kT
eATjj== 2tx . (2.12)
, (2.12) , jt - . , jt, - , - . . - , , : = 2,5 , 1 = 300 , 2 =
1500 , kT1 = 0,025 , kT2 = 0,125 . , (2.15), : jt1 = 10-36 /2, jt2
= 0,8 /2. , 5 36 . 2.2. p- n- p- n-. 2.1 : -, Eg , 0n n-, 0p -
p-.
n
E0
Ei
EV
Eg
EC
F20n
p
E0
Ei
EV
Eg
EC
F
2
0p
. 2.1. : ) n-; ) p- F= , - - n- n p- p:
+== ngn 2
EF , (2.13)
++== pgp 2
EF . (2.14)
( , - , mp* = mn*. -
(2.13), (2.14)
V
Cln2NN
kT
n- - p-.) (2.13) (2.14) , p- , n-, , n- , p-. 2.3. , . , - ,
-
15
. , . - , - , . ( ) - . 2.2 .
. 2.2. , - , , - . ND = 1015 -3, - ( ) = ND-1/3 = 10-5 = 1000 .
= 1012 -2 1011 / 1015 = 10-4 , 1 . , [12]. - [13, 14]. . , , - , -
(). E(z) . , - , . :
==z
dzzEUzUU )()()( ,
U() -.
( *22
2mkE h= ),
- EC ( EV). . - :
dzzEq
z
= )(1 . s. s - , . s > 0 , s < 0 (. 2.3).
EV
ECF
Ei
EV
EC
F
Ei
s > 0
s s
s
s
s
s
s < 0 . 2.3. n-: ) ; )
2.4. , - . n-. nn0 pn0 (2.15):
-
16
kTq
ikT
qkT
) q-F-(EkT
)q q-F-(EkT
-F)-(E
enee Ne N e Nn0n0n0nC0n0nCC
CCCn0
= ===
++,
EC F + q0n = Eg/2. =
kTq
,
)exp( 0nn0 inn = . (2.15) (x) : (x) = 0 n (x) , - nn0(x) p0n(x)
. (x) = 0n (x) : )exp( sinn = , )exp())(exp())(exp( 00 nnznn ii
=+== , )exp())(exp())(exp( 00 =+== npzpp ii . (2.16) ns ps :
))2(exp();exp( 0sn0ssn0s == npnn . (2.17) 2.5. , , -. , . , , - s
kT/q. - s -, , z - :
( )
0s2
2
z
dzd = , (2.18)
(z) , s . : D( ) [ ( )]z q N n z += . (2.19) ND+ = n0, n(z)
(2.16). - s
-
17
, LD , . 2.6. . . (p- n- ) . . , . ( p- n-), . , , , , [15, 16].
, . . , :
)exp(2T kTATj = . (2.29)
n- , - / , - . - (2.29) j/ , : /Me/ ; jj . . , . . , .
2.4 . , , : = /. p- , - / , - . - j/ , , (2.29). p- .
S=ms
jMe > /
j/ > Me
Me / < Me
FMe F/
E = 0
EiEi
ECEC
EV
EV
(Au) (n-Si)
W
n-SiAu
jMe > /
j/ > Me
F/
. 2.4. , p- n-. 2.7. , VG, . VG > 0 - ms, VG < 0
-
18
. 2.5 - - . , .
S=ms S=ms - VG
S=ms - VG
VG = 0 VG > 0
VG < 0
VG = 0 VG > 0 VG < 0
E(x) E(x) E(x)
W0 W1W2
. 2.5. : ) VG = 0; ) VG > 0, ; ) VG < 0,
2.8. , . n-. , - , . , , . - . :
( )
0s2
2 )(
xx
x =
, (2.30)
(x) , (x) , s , 0 - . - n- ND+. - += D)( qNx . (2.31) , =)(xE
:
( )0s
xdxd
dxd = , (2.32)
0s
D
+
= qNdxdE
. (2.33)
(2.33). , x = W ,
( )Ds 0
( ) qNE x W x +
= . (2.34) (2.34) , - (x = 0), - - (x = W). ( , ) (2.34) : x =
W, (W) = 0. (. 2.6):
( ) ( )0s
2
D 2 xWqNx = . (2.35)
x = 0 : GmsGsmax VV == , /Mems = . (2.36) W, (2.36) (2.35):
( )
D
Gms0s2qN
VW
= . (2.37)
-
19
(2.37) . - , - W - VG ND . 2.6 , - , - (2.34) (2.35).
S
E(x)
E
Emax
VG < 0
0
0
0
W
W
W
x
x
x
. 2.6. , : ) ; ) ; )
2.9. - - () .
2
min2
Cm
E = - :
)(2 Gms
min2 Vq
m = . (2.38) (2.5) (2.7), :
GGmsC
os
)(
3
22*
4
14 VkTVq
kTFE
eqneeh
Tkemj
==
, (2.39)
0 , 2
1
08
= m
kT ,
ns ms
ss= enn ,
n0 ,
kTFE
eh
kTmn
=
C23
202
[6, 17].
VG = 0 j -
0
41 sqnj = . -
. , - :
)1(41
0 == GVsM eqnJJJ ; (2.40)
:
os00 41);1( qnJeJJ GV == . (2.41)
2.7 - .
J/ > Me
J
VGJMe > / = J0
. 2.7. - - - . .
-
20
. , -, . - , . - . - , - . , - . 2.10. -n -, p-n , - ( ). p-n :
nSi pSi, nGe pGe. n- p-. - . - p- p , n n-. - (2.13) (2.14) , 0pnnp
>+== . n- p- (- ) - n- p- . n- - p- . n- , p- . - , -. - n- p-,
p- , n- -. p- n-, , -. 2.8 , - - .
n-Sip-Si
pSi nSi
Jp > n Jn > p
W
E = 0
EC
EC
EV
EiEV
EiF
F
F
E = 0
Jp > n Jn > p
. 2.8. , p-n - p-n . , , p-n . 2.10.1. p-n p-n , , , NA > ND;
n < p. (VG = 0) p-n :
2DA
pn lninNN
qkT=+= . (2.42)
- p-n .
;)exp(;)exp(A
2
0pp0A0pp0 NnnnNnp iii ====
D
2
n0D0nn00n;)exp(
NnenpNnn iii ==== . (2.43)
, 0p 0n x, 0p(x) 0n(x). , x: pp(x), np(x), nn(x), pn(x).
-
21
.))(exp()());(exp()(
));(exp()());(exp()(
0nn0nn
0pp0pp
xnxpxnxnxnxnxnxp
ii
ii
====
(2.44)
, p-. p-n p , pp -. p-n (p = 0), - , .. pp = ni. , np(x) p-n .
nn(x) pn(x) - n-. 2.9 - p-n p-n .
,
,
-
3
1018
1016
1014
1012
1010
108
106
104
102
n0, p0p-Si n-Si
W
W
Wn
Wn
Wp
Wp
p = n = ni
np0
nn0 = ND+
pp0 = NA-
pn0
p-n
p-n
E
p-
n-
. 2.9. p-n : ) ; ) , - , , p-n p-n . , - ni. 2.10.3. p-n p-n - .
:
( )
0s2
2 )(
xx
x =
, (2.45)
(x) , (x) , s , 0 - . - p-n . - x > 0 ( I), x < 0 ( II).
p-n n- ND+, - p- NA+. I += D)( qNx , II += A)( qNx . I II. - I:
)()( n0s
D xWqNxE =+
, (2.46) II:
)()( p0s
A xWqNxE +=+
. (2.47) (2.46, 2.47) , - x. (2.34) , - p-n (x = 0), - (x = Wn;
x = Wp). Emax :
0s
nD
0s
pAmax
WqNWqNE == . (2.48) ( , ) (2.34) : x = W, (W) = 0. : ( ) 0,
2 p2
0s
A
-
22
02
0s
A22
0s
A
22 +=
= WqNWWqNconst .
(2.49), (x) x < 0. ( ) ( ) 02p
0s
A2
2
0s
A
222 ++=
++= WxqNWWxxqNx .
x > 0, :
( ) 0,2 n
2
0s
A >+
= xconstxWxqNx . (2.50)
0; == nWx ; - :
22
2
0s
D22
0s
D WqNWWqNconst =
= ,
(2.50), (x) x > 0: ( ) ( ) ( )2n
0s
D2n
2
0s
D
22
2WxqNWxWxqNx +=+= . (2.51)
, p- ( ):
( ) ( )2p0s
A1 2
WxqNx += , x < 0, , n-:
( ) ( )2n0s
D2 2
WxqNx = , x > 0. 2.10 , - p-n , (2.46), (2.47), (2.50)
(2.51).
p-Si n-Si
Wp-Wp WpWnWn Wn
E
Emax
0
0
x
2(x)1(x)
. 2.10. , p-n : ) p-n ; ) ; ) - p-n x = 0 1 + 2 = 0 = n0 + p0, (
)2nD2pA
0s0 2
WNWNq += . (2.52) : nDpAAD ; WqNWqNQQ == . ,
D
pAn N
WNW = . (2.53)
(2.45) (2.46), :
=
+=
+=
D
2A
A2
p0sD
pApA
2pA
0s0 22 N
NNWqN
WNWNWNq .
+=
DA
2A
2p
0s
112 NN
NWq Wp Wn p- n- :
+
=
+
=
DA
2D
0sn
DA
2A
0sp 11
2;
112
NNqN
W
NNqN
W . (2.54)
-
23
, p- - p-n Wp . p-n W, W = Wp + Wn, :
+=
DA
00s 112NNq
W
. (2.55)
p+-n ( ) (2.47) (2.48) , p- , n-: npDA WWNN . , p+-n W = Wn.
2.11. -n - (. 2.11) ( , . 2.12) .
-
-
- -
- -
- -
- - -
-n p
E
EC
EV
Ei
F
qVbi
. 2.11. p-n , p-n . - , . - (VG = 0) p-n , - : 0nDnEpDpEDE
=+++=+ JJJJJJ .
, , -, .
q(Vbi - VD)
q
(
V
b
i
-
V
D
)qVD
VF
ID
- -
- -
-
-n p
- -
- -
- -
- -
- -
- - -
--
-
-
-n p
EC
EV
Ei
VD = -VR
VR
ID = -IS E
. 2.12. p-n , : ) ; ) p-n Fn Fp. - Fn Fp - VG [4, 3]. p-n - (.
2.13).
-
24
VG > 0
WLn Lp
Fn - Fp = qVGEc
Ec
EiEi
Fp
Fn
EvEv
. 2.13. , Fn Fp VG > 0 p-n . - , Fp - Fn = qVG, - nn, pn
:
UikTFF
i enenpn22
nn
pn
==
. .
UUi epennpnn n0
n0
2
nn0n ; === . (2.56) 2.14 p-n . , , . , - (2.56), .. .
VG = 0
VG = +0,25 B (+10 kT/q)
VG = 0
VG = -0,25 B (-10 kT/q)
Wp
Wn
Wp
Wn
Wp0Wn0
Wp0Wn0
p = n = ni p = n = ni
np0 np0
pn0 pn0
pn0 pn0
np0 np0
np(x)
np(x)
pn(x)
pn(x)
,
,
-
3
1018
1020
1016
1014
1012
1010
108
106
104
102
100
10-2
10-4
,
,
-
3
1018
1020
1016
1014
1012
1010
108
106
104
102
100
10-2
10-4
. 2.14. p-n ( ) ( ) ) (VG = +0,25 ); ) (VG = -0,25 )
2.12. - -n - p-n . :
)(div1 jq
RGdtdp = .
0=dtdp
.
n- p-n (x > 0). G - : G = 0. E : E = 0. : IE = 0, ,
dxdpqDj = . R -
:
-
25
n0n ppR
= . (2.57) , -, : D = Lp2. :
02p
n0n2
n2
=L
ppdx
pd. (2.58)
p-n : x = 0, Gn0n
Vepp = ; x , n0n pp = . (*) (2.58) (*) :
( ) DG 1n0n0n LxV eeppp = . (2.59) (2.59) n- - (. 2.15). p-n ,
p-n . - , (2.59) , - (. 2.16):
Gp
n0p0
nppD
Vx eL
pDq
dxdpqDj == = . (2.60)
(2.60) p-n , . p-n -:
Gn
p0nnD
VeLnD
qj = . VG = 0
. , n
p0nnE
p
n0ppE ; L
nDqj
LpD
qj == . p-n p-n :
)1(n
p0n
p
n0p
+= Ue
LnqD
LpqD
j . (2.61)
p-n . , VG < 0 -
. - Ln Ln/p. :
n
p0n
n2n
p0n
n
p0nn / L
nqDDLnqLnqL
j === . pn
pn0
VG1
VG2
VG3 > VG2 > VG1
0 Lp x . 2.15. p-n , . (, ), (2.61) , - np0 p-. , p- n-: NA
>> ND. p-n - (. 2.16).
p-Si n-Si
EV
EC
EiF
np(x)
pn(x)
jnD
jpD
NA >> ND, jpD >> jnD . 2.16. p-n n , p-n : )1( Gs =
VeJJ . (2.62)
-
26
Js :
p
n0p
n
p0n
p
n0p
n
p0ns
pqLnqLL
pqDL
nqDJ +=+= . (2.63)
p-n , (2.62), 2.17.
J
J = JpD +JnD
VG
J = JpE +JnE
. 2.17. - p-n (2.16) 2.17, - - p-n . p-n - . - p-n . p-n , - Q,
. -
: = QC .
p-n : - QB - Qp. p-n - . p-n CB - CD.
CB p-n VG < 0, .
G
BB V
QC = . (2.64)
QB p-n :
( ) ( )G00sD
D
G00sDDB
2 VqNqN
VqNWqNQ === . (2.65) (2.65), :
WVqN
C o s
G0
0sDB 2
2 == . (2.66) (2.66) , CB - , W. VG, . , . CD p-n VG > 0, Qp
Qp.
G
pD V
QC
= ,
G0G
0pG
op
ppn
0 0
2p
p
nnnp )(
VV
Lx
V eLDqp
LLeqp
dxeepqdxxpqQ
==== ,
qkT
Je
LDqp
dVdQC V pp
p
pn
G
G0 === .
B VG . , - , . - VG. . - -
-
27
. VG. ND(x), C(VG) , . 2.14. , , pGe nGaAs. p-n , p-n - , , pSi
nSi. , , : () [18, 16, 19]. . Ge, GaAs, InP, InGaAsP. Eg, - Eg .
2.18 - .
Ec1
Ec1Ec1
Ec1
Ec
Ec Ec
Ec
Ev
EvEv
Ev
Ec2
Ec2Ec2
Ec2
Ev1
Ev1
Ev1
Ev1Ev2
Ev2Ev2
Ev2
F
NV NV
NV
1 > 2
1 < 2 1 < 2
1 > 2
e1
e1
e1
e1
e2
e2
e2
e2
1 - 2 > Eg/e
1 - 2 > Eg/e1 - 2 < Eg/e
1 - 2 < Eg/e
NV
1 = = 2
. 2.18. Eg 1 = 2 [18] , - -, ,
, g - s. - (pGe nGaAs). - , , - 1. pGe nGaAs. -: 1. = 0 . 2. Ge
GaAs . 3. Eg . 1.
(pGe) (nGaAs)
, a 5,654 5,658
- , 10-6 -1 5,9 6,0
, -3 NA,D 31016 1016
, W0 0,14 0,17
, 0 0,21 0,55
, 4,05 4,07 EC - . EC : GaAsGeC =E . V - EV. : )(
GegGaAsgCGaAsgGaAsGegGeV EEEEEE +=++= .
-
28
, EC EV )( GegGaAsgVC EEEE =+ . 2.19 - pGe nGaAs. (- ), pGaAs
nGe (. 2.20). . , - EC -: GaAsGeC =E . - EV. EV : )(
GegGaAsgCGaAsgGaAsGegGeV EEEEEE +=++= .
1
2
E = 0
EC
EV
EV
EC
Eg1
Eg2
Ei
F
. 2.19. pGe nGaAs
eV2eV1
eVd
EC
Eg2
Eg1
EC0
EV0
EV
F
x
NV
x1 x20 . 2.20. nGe pGaAs - , . 2.21 . , EV, EC [20, 17].
-
29
NV NV
NVNV
1 < < 21 > 2
1 < 2 1 < 2
1 > 21 - 2 > Eg/e
1 - 2 > Eg/e1 - 2 < Eg/e
1 - 2 < Eg/e
Ec
Ec Ec
Ec
F
F F
F
Ev
Ev
Ev
Ev
eVd eVd
eVdeVd
Ecn
Ecn Ecn
EcnEc0
Ec0 Ec0
Ec0
Ev0
Ev0Ev0
Ev0Evn
EvnEvn
Evn
. 2.21. , , (1 < 2), ( ) - p-n , - s . E, W1n W2p :
A 2pD 1n1max 2max1 0 2 0
;qN WqN WE E = = , (2.67)
02
22pA
2p01
21nD
1n 2;
2 WqN
VWqNV == , (2.68)
( ) ( )
+
=
+
=
D
2
A
12A
00212p
D
2
A
12D
00211n
2;
2
NNqN
VW
NNqN
VW
. (2.69)
W, W = W1n + W2p, :
( )
+=
2D1A
0021 112
NNq
VW . (2.70)
0 : 2p1n0 VV += . (2.71) - , p-n . - - 1 2. , - , max22max11 EE
= . (2.72) 2.22 .
E(x)
V(x)
XX2
V1
V2
V1
V2
X1
0
X1
X2
X0 . 2.22. nGe pGaAs - V. p-n , p- . 2.23 - nGe pGaAs. V =
0.
-
30
V > 0 V < 0
EcEc
EvEv
Ec0Ec0
Ev0
Ev0
eV1
eV1
e'b1
e'b1
e'b2e'b2
eV2eV2
. 2.23. nGe pGaAs V > 0 V < 0 . V = 0 - . - . , - - : (
)1s = VeJJ . (2.73) (2.73) , Js . pGe nGaAs , pGe nGaAs . , Jp Jn -
:
21
22
A
21
D
22
p
n
n
pn
p
np
n
p
i
iii
nn
Nn
Nn
np
nqL
pqL
JJ ===
. (2.74)
, -, (ni2) , (ni1), , Jp , Jn. - pGe nGaAs -. , - . , E ~ 106 /.
- . -
[21, 2, 20]. , (. 2.24).
qVn
qVp
Ec
EC
F
F
EV
E2
E1
AlGaAs GaAs . 2.24. , . , - , ( , - ). - .
-
31
3. - 3.1. () 3.1.1. - - . , - , , .. , . , . ND = 1015 -3 - , -
= ND-1/3 = 1000. E - -, . -,
0
M
0 22 qNE == , (3.1)
NM , . , 10 E = 106107 /, NM = 10121013 -2. -, 10121013 - . , -
n 1022 -3, - , , , . , 105 -3, ( ) . - . , - NM = 1011 -2 -
NNW
D
M 110 4 === . - . - .
, - - , , . - . . , . - - - , - (). , - - , .. E(z) . - , , - .
, -
=z
dzzEUzU )()()( , U() -
. , - , . , 3.1, 3.2, . - -
=z
dzzEq
)(1 . (3.2) s. - (. 3.1) s .
-
32
S
(S n0 s > 0 p- ps > p0 s < 0
, , - , , - (. . 3.2).
n- ps < ns < n0 s < 0 0s0 0 0s0
-
33
EC
ECEC
EC
F
FF
F
EV
EVEV
EV
E
Ei
EiEi
Ei
0
q
0
q
0
q
0
q
(S p- ns > p0 s > 0 0s 2 >
0s 2 = , . -. , - , , . , -
, , -. 3.2. - - (z), , - Qs, p,n, Cs . [2, 14, 21, 13, 11].
3.2.1. p-:
s0
2
2 )(
zdzd = (3.6)
(z) , -, : )()( AD npNNqz += + . (3.7) , , (z) = 0. 00AD pnNN =
+ . (3.8) , (3.3 3.5), == eppenn 00 , , 00 00 ,
eppenn ii == , (z) : ]1)1([)( 020 = eeeqpz . (3.9) (3.9) (3.6),
(z) -:
]1)1([ 020s
02
2
= eeeqp
dzd
. (3.10)
, -
2.5 (2.23), dzd
.
2
2
2
21
=
dzd
dzd
dzd
dzd
. (3.11)
,
-
34
deeeqp
dzdd ]1)1([ 02
0s
02
=
. (3.12) (3.12) , :
)]1()1[(121
02
0s
02
++=
eeeqp
dzd
. (3.13)
LD (2.23),
dzdzE =)( , :
)]1()1[(2
102
2D
22 ++
= eee
LqkTE . (3.14)
212
0 )]1()1[(),( 0 ++ eeeF . (3.15) (3.14) (3.15) :
),(21
0D
FLq
kTdzdE == . (3.16)
(3.16) . . s > 0 ( ), - z . s < 0 E z . Es :
),(21
0sD
s FLqkTE = . (3.17)
- Es - Qsc, :
),(2
0sD
0ss0ssc FqL
kTEQ == . (3.18) , (3.16 3.18), , . 3.2.2. (3.18) , , . -
F(, 0) (3.15). Qsc, (3.18) . (s < 0). p- Qsc Qp,
1; ss >> qkT
.
2D
0spsc
s2 == eqL
kTQQ . (3.19)
(0 > s > 0). Qsc QB. (3.16, 3.18) ,
( ) 21sD
0sA0sBsc 1
22 =
==
qLkT
qkTqNQQ . (3.20)
==
qkT
qNqNQW s
A
0s
A
B 2 . (20 > s > 0). Qsc, - , QB, - Qn 20). Qsc Qn, -
2)2(
D
0snBWsc
0s
2
=+= eqLkT
QQQQ . (3.22)
QB - W s : )2(
2;)2(2 0
A
0s0A0sB q
kTqNq
Wq
kTNqQ == . (3.23) , , 3.2 (3.19 3.22), , - . 3.3 - Qsc s, -
.
-
35
ECEV
Ei
s, B
-0,4 -0,2 0 0,2 0,4 0,6 0,8 1,0
10-5
10-6
10-7
10-8
10-9
NA=1016-3
T=290K
0=0,35B
20=28
QSC
, /2
s-10 0 10 20 30 40
QW
. 3.3. s, p- 3.2.3. ( ) Qp,n , - , p,n . - p =
00p ))(( dzpzp , (3.24)
p(z) , p0 - . , - - . p,n . , - , . p,n , - . (3.24) ,
==0
0
00p
s
1)1(
d
dzd
epdzep . (3.25)
n : = 00n
s
1
d
dzd
en . (3.26)
p,n , - . (3.25, 3.26), (3.15), 3s > : 2
D2
0sp 2
= eLq
kT, (3.27)
2D
20s
n 2
eLq
kT= . (3.28) p,n , - (3.25, 3.26). , , , , - Qn Qsc - QB, : Bscn
QQQ = . (3.29) (3.18) Qsc :
( ) 21)2(sA0ssc 12 0s
+= eq
kTNqQ . (3.30)
-
36
QB (3.20) (3.23), Qn :
+
=
112
21
s
)2(21
sA0sn
0s
qkT
eq
kTq
kTNqQ
, (3.31)
( )
+
=
2
1
s
0
21
s
221
sA0sn
212
0s
qkT
qkT
qkT
eq
kTq
kTNqQ
.
(3.32) (3.32),
1,2
1)1( 21
-
37
1012
1011
1010
109
108
107
-4 0 4 8 12
1013
320230
140
80
NA=1015-3
+( s-20 )
n, -2
. 3.5. n s, p- 3.2.4. , , c, , , . c :
=
0
0c
)(
)(
dzz
zdzz
, (3.37)
(z) , - . ,
=0
np,)( Qdzz (3.38) . - ( p- ) c :
),( 0s
Dsc
F
L= . (3.39) , (3.39) , c Qsc . E(z) - Es. - : zEss = . (3.40)
n(z) : ( ) zEzE enenzn sss s0)( == . (3.41) (3.39) (3.41) (3.4,
3.5) (3.18) :
B
0s
zc
1qQ
kTE
== . (3.42)
(3.42), c - s, , . c T . , Qn >> QB, - (3.39). - c , ,
(3.37). 3.6 . , c (20300) , . s = 0, c , .
-
38
, Ao
NA=10
15-3
VSS=0
T=320K
s=20
80
110
140
170
200
230
260
290
250
200
150
100
50
0
107 108 109 1010 1011 1012 1013
,-2
. 3.6. c n . T = 300 p- [2, 21] 3.2.5. 3.2.1 (3.16). , .. (z), -
(3.16) :
=
s D0s 21
),(z
LqkT
Fd
. (3.43)
(3.43) (z) . . 1. : p = n = ni; 0 = 0 (3.15) , F(, 0)
=+= 22
1)2(),( 21
0 sheeF . (3.44)
(3.44) (3.43), :
=
s2
2D sh
dzkT
qLz
. (3.45)
, (3.45) :
4
4ln2s
D
th
th
Lz = (3.46)
=
DLzthth 2exp
44s . (3.47)
(3.47) . (z) z. 2. , (3.15), F(, 0) . :
=
s D2
1 21 zLq
kT
qkT
d. (3.48)
, z = W, .. = 0, -:
2
s 1)(
=Wzz . (3.49)
, (3.49) , . ,
zEzW
z ssss2
)( == . (3.50) , . 3. - s, (3.19) (3.22).
-
39
(z) , . (3.44) (3.15) , > 7
( ) zLqkT
e
d
D22 2
1
s
0=
. (3.51)
(3.51) :
( )
+= 0s 2
D0 2
ln22)( eLz
qkTz . (3.52)
:
+= 2
D
s
2ln2)(
e
Lz
qkTz . (3.53)
(z) , . 3.3. Qsc - s, - Csc. Csc, (3.18), :
( ) ( )[ ]
),(11
2 0s
2
D
0s
s
scsc
s0s
Feee
LQC +=
. (3.54)
, (, , ), - (3.54), Qsc, 3.2.2. , p-. (s < 0) Csc Cp:
2D
0spsc
s == eL
CC . (3.55)
(20 > s > 0) Csc CB:
W
qkT
qNCC 0s
s
A0sBsc
2
=
== . (3.56)
(3.56) , Csc - s, . - Csc - . , - s, W, . (s = 0) (3.55) (3.56)
s 0, .. . s = 0 (3.55) . CFB - (3.55) :
q
kTqN
LCC A0s
D
0sFBsc
=== . (3.57)
, . (s > 20) Csc Cn -
7)2( 0s : 2
)2(
D
0sn
0s
2
= eL
C . (3.58)
(3.55) (3.58) , - - s , - s = 20. 3.7 Csc s, (3.55 3.58).
-
40
10 0 10 20 30 40
10-4
10-5
10-6
10-7
10-8
-0,4 -0,2 0 0,2 0,4 0,6 0,8 1,0
s
s, B
EC
EV
Ei
NA=1016-3
T=290K
0=0,35B
20=28
CSC
, /2
. 3.7. Csc , ( ) ( ) 3.4. - . - , -
, , - . - p-,
q
kT2 ,
=
= 0
g
C0g
21C0
WkTE
eNWkTE
FNn ,
( ) 0V02
1V0WeNWFNp == , (3.59)
2
1F , W0
. n p :
( ) .
,
0s2
1V
0sg
21C
WFNp
WkTE
FNn
=
=
(3.60)
(3.60) (3.7) (3.6) (z), Qsc Csc . -:
( ) 21s0s2
3D
0ssc 1
20
+= WFe
qLkTQ W , (3.61)
( )
( ) 21s0s2
3
0s2
1
D
0ssc
1
1
0
0
+
+=
WFe
WFe
LC
W
W
. (3.62)
( ) ( ) 21s0gs2
320s
sc 12 00g
++= WEFe
qkTQ WE , (3.63)
-
41
0-10 10 20 30 40
QSC
, K/2 s
ECEV
10-5
10-6
10-7
10-8
10-9
-0,4 -0,2 0 0,2 0,4 0,6 0,8 1,0
s, B
. 3.8. Qsc s p-
( ) ( )( ) ( ) 21s0gs
23
2
0gs2
12
D
0ssc
1
1
00g
00g
++
+=
WEFe
WEFe
LC
WE
WE
, (3.64)
)(2
3 F )(2
1 F :
+= 02
3
23 13
4)( xedxxF , (3.65)
+= 02
1
21 1
2)( xedxxF . (3.66)
(3.613.64) s 0 -. s 0 , 3.2. 3.8 Qsc, - . Csc - 3.6. 3.5. 3.5.1.
, - - , . (). , - (, , , , ), - - . , - , . , , , . - , , , . - , ,
. 3.9 - , .
-
42
EC EC
EC
Ei Ei
Ei
F F
F
EV EV
EV
FS
FS
Qss>0
Qss=0
Qss0
s>0
{{
s=0
s=20
. 3.9. p-, 3.9 , Qss - . ( Qss - surface states ). , , -, - , .
. - , , , , - . 3.5.2. - [13]: 1) ; 2) ; 3) , ; 4) , -. . - ,
, , - , - -. , , . - -, .. 1015 -2. - , , - . , -, , , . , , -.
, . - (, , ) - . , . 3.5.3. , s. -. Fs -: ss qFF = . (3.67) Fs Et,
, : s0t qqEE += , (3.68) Et , . Et > 0, Et < 0. :
+ +
=+
=s0
tst
1
1
1
1
qE
kTFE
eef . (3.69)
Qss :
fqNQ ssss = , (3.70)
-
43
Nss , .. . Fs
( )q
kT32 , (3.69) f = 1 Qss = -qNss. Fs - , 2
1=f ssss 21 qNQ = . , ( )
qkT32 , 0=f 0ss =Q .
, - 3.1, (3.70) . -, , Nss(E), [-2-1]. Nss(E) - dE = 1 E,
Nss(E)dE (E; E+dE). Nss(E) , .. , Qss - :
( )0sssssss )()( ==
qNdEEfENqQ . (3.71)
(3.71) , 3.9, s < 0 Qss , s = 0 Qss s > 0 Qss . , (3.70)
(3.71), s , Css, - . :
)1(ss2
s
ssss ffkT
NqQC == . (3.72)
(3.72) , Css(s)
, q
kT4
, qE t
0s += . 2
1=f ,
kTNqC ss
2
maxss 41= . (3.73)
Css , (3.71),
sss
ssss qN
QC =
= . (3.74) Css - Csc. Csc - s 20. - NA = 1,51015 -3 , (3.57),
Csc = 1,610-8 /2. Nss, Css, Csc, , - (3.74), Nss = 1011 -2-1. , , ,
. 3.6. - 3.6.1. - , -, - - , , , , - .. - , , . - - . - -, , -. , ,
, . - -, . - - , - - [14, 11, 13]. , -, -
-
44
3.10, , , - .
1
2
3
4
. 3.10. - 1 , 2 , 3 , 4 - - - . , : ) ; ) ; ) . 3.11 -. - - , :
- , - , - , - , . 3.11, - VG .
EC
EV
EiF
EC
EV
EiF
EC
EV
EiF
V
g
0
V
S
C
>
0
-d
-d
0 W
W
V,
0 >0
Z
Z
(z)
QB
Qn
Q
V
g
>
0
F
F
D
n
D
q
d
q
n
. 3.11. - p-: ) VG = 0; ) VG > 0; ) VG < 0; ) - VG > 0;
) VG -, , , - , n-Si , p-Si - . -, -, -, - . 3.6.2. VG - s. - VG -
, , - s.
-
45
, soxG += VV . (3.75) (3.75) 3.11 , s, a priori, - VG. , - n-
p-, - . VG , s. , - QM Qsc, - - Qss - Qox. oxssscM QQQQ ++= .
(3.76) Cox,
ox
Mox V
QC = , (3.77)
ox
ox
ox
ss
ox
sc
ox
Mox C
QCQ
CQ
CQV == . (3.78)
, - ms, :
ox
ox
ox
ss
ox
scsmsG C
QCQ
CQ
V += . (3.79) (3.79) , VG > 0, s > 0, Qsc < 0, Qss <
0, .. Vox > 0. - VG < 0. , ( )0sssss = qNQ , (3.80) (3.80)
(3.79), :
sox
ss
ox
scs0
ox
ss
ox
oxmsG C
qNCQ
CqN
CQ
V +++= . (3.81) VFB (Flat Band). - VFB -, -, :
)0( sGFB = VV . (3.82) (3.82) (3.81) :
0ox
ss
ox
oxmsFB C
qNCQ
V += . (3.83) , VG - s (3.83) :
ox
scs
ox
sssFBG C
QCqN
VV ++= . (3.84) (3.84) . (s < 0) Qsc (3.19). - (3.19) (3.75),
:
2oxD
0s
ox
sssFBG
s21
+= e
CqLkT
CqN
VV . (3.85)
s ( 1s > ), Qsc >> Qss, (3.85) :
2Dox
0sFBG
s eqLCkTVV . (3.86)
=kTCqL
VVqkT
0s
oxDFBGs )(ln
2 ,
)( FBGoxpsc VVCQQ = . (3.87) (3.86) (3.87) , , - , s VG , Qsc -
VG . (0 < s < 20) Qsc - QB (3.20). QB s = 0:
)()( 0s*B
*B0s
s
B)0s(BB
+=+= = CQQQQ ,
-
46
QB*, CB* s = 0. QB (3.84) CB* (3.57), -: sFBG nVV = , (3.88)
ox
*B
ox
ss1CC
CqNn ++= . (3.89)
(3.88) , s VG , -
( ) nddV
tg ==s
G
Nss, dox - NA. (s > 20) Qsc , QB Qn . (3.22) Qn, -:
2oxD
0ss
ox
sss0
ox
B0
ox
ss
ox
oxmsG
s
2 e
CqLkT
CqN
CQ
CqN
CQV +++= ,
(3.90) s = s - 20. VT VG, - s 20. )2(GT 0s = VV . (3.91) (3.90)
(3.91) ,
ox
B0
ox
ss
ox
ox0msT 22 C
QCqN
CQ
V ++= , (3.92) VFB
0ox
ss
ox
B0FBT 22 C
qNCQVV ++= . (3.93)
(3.93) , VT - VFB, - 20 -
. - s, s > 1, :
2Dox
0sTG
s eqLCkTVV . (3.94)
( )kTCqL
VVqkT
0s
oxDTG0s ln
22 == , (3.95) ( )TGoxnsc VVCQQ . (3.96) (3.95) (3.96) , , - , -
VG, Qn VG. 3.12 s - VG, dox.
40
30
20
10
0
1,0
0,8
0,6
0,4
0,2
-0,2
-0,4
0
-1-2-3-4-5 1 2 3 4 5 6
0
-10
-20
S, B
dox
=40 Ao
S
1000 Ao
200 Ao
NA
=1,5 1015cm-3.
T=290 K
Si-SiO2
Vg-V
FB ,B
. 3.12. s VG, (3.84) - 3.6.3. - - , - C VG, - () C-V . -. - C .
,
-
47
G
M
VQC
. (3.97) QM (3.77) - Vox (3.75), :
=
G
sox 1 dV
dCC
. (3.98)
, C - - s(VG), 3.12. (3.86) (3.98) , C VG, - VG. , (4.14), -. .
(3.84) VG - (3.79) s.
ox
sc
ox
ss
s
G 1CC
CC
ddV ++= , (3.99)
Css, Csc , . (3.99) (3.98) , :
++= ssscoxox
ox 1 CCCC
CC (3.100)
ssscox
111CCCC ++= . (3.101)
(3.101) -, Cox Csc Css. 3.13 -. -, - -.
COX COX
CSS CSC CB+Cp
. 3.13. - 3.14 C-V - , (3.109).
NA
=1,5 .10 15c -3
T=290 KSi-SiO
2
dox=40 Ao
1000 Ao
200 Ao
Vg-V
FB ,B
C /Cox1,0
0,8
0,6
0,4
0,2
0-3 -2 -1 0 1 2 3 4
. 3.14. C-V - p- 3.6.4. - - - . , , , - Css Csc, , . -, Qn -- -
n . - .
-
48
C-V C-V . C-V , n (-1 >> n, ), - - , (3.99). - , , - C-V .
(. . 3.14). , - C-V . , - - VG, I -. , ttV = )(G , (3.102) I,
(3.97),
=== Cdt
dVdVdQ
dtdQI G
G
MM . (3.103)
- C = C(VG), - I = I(VG). -1 >> n, - -
dt
dU= (3.103). = 10-410-2 /. - (I 10-910-12 ) -. 3.15 -. - ,
-.
1
XYC
. 3.15. - -: 1 , , XY - , C -
C-V , - - , , (-1 >= . - tieUU 0
~ = , q
kTU < . C R :
UVC
CR
Uz
Ui ~)(1
~~~
G
222
+
== . (3.104)
-
49
Y CD XY
1
1
2
R2
R1
RH
C
. 3.16. - - RH
~U : )(~ GHHRH VCRUiRU == . (3.105) , URH - -. - , - Y, -. VG VG
- X , - - . - - . 3.6.5. - C-V - - -: - (n- p-); -; - ; ; - . . - -
. , 3.13, - C-V
- . - - . , C-V , -, n-, C-V , - p-. 3.17 n- p- . , , - Cox,
:
ox
oxox d
CC== , (3.106)
ox .
0,8
0,6
0,4
0,2
0
1,0
-3 -2 -1 0 1
dox
=1000 A
T=300 K
Si-SiO2-Al
0
p - Si
VFB=-0,9 B
Vg , B
NA=1015 -3
n - Si
VFB=-0,25 B
ND=1016-3
C/Cox
CFB
. 3.17. -, n- p- , :
ox
oxox C
d= , (3.107)
, Cox , .. . (3.107) , .. - S -. 3.14, VV )32(FBG
-
50
- C 2-3% - . - dox < 100 , VG - , 10%. - C-V -: Cmin - CB -
Cox.
Boxmin
111CCC
+= . (3.108) Cox (3.106) (3.57), :
Wd
C
ox
sox
0oxmin
+= . (3.109)
(3.109), (1.67) -, :
2
ox
min
ox
0s
0
A
122
=C
CC
qq
kT
N
. (3.110)
3.18 oxmin / CC dox Si-SiO2 - NA . 3.18 , , - . NA z C-V , . - ,
- . s > 20, , . - , , Vox -
, .. Vox
-
51
dox, NA , (3.101) (3.58) CFB - - VFB = ms. C-V -, .. 0ss C , , C
= const = CFB (.), - , s = 0, .. VFB (.). , (3.83),
0ox
ss
ox
oxFBFB C
qNCQ
VV += . (3.113) Qox, Qss > 0, VFB (.) > VFB (.), , Qox,
Qss < 0, VFB (.) < VFB (.). , - (3.113) . - , - (p-, Qss(s =
0) > 0 n-, Qss(s = 0) < 0), - . Nss, - Qss (3.83) Qox. 3.6.6.
- - - - . . , , - - - - . 3.19 - C-V .
2
1
0-10 0 10 20
VG, B
S
1012
1011
EV
F Ei EC
NSS
, -2-1
C/COX-6 -5 -4 -3
-2-1
0
2
4
68
1216
20.
f=1
T=295 K
NA=1,5 . 1015-3
Si-SiO2-Al
VFB
VFB
CFB
VG
.
0,8
0,6
0,4
0,2
0-4 -3 -2 -1 0 1 2
. 3.19. : ) - Si-SiO2-Al; ) - VG s, - C = const -; ) E , VG(s)
(3.115) , - s. C = const, - s. VG - C-V , ( -, s), (3.84):
-
52
sox
ssFBGGG C
qNVVVV +== . (3.114)
(3.114) :
s
GG
ox
0oxss
)(
d
VVdqd
N= . (3.115)
, (3.114), -, . , - Nss E . 3.19 VG(s), 3.19 - , - . , , - . C-V
(3.98),
oxG
s 1CC
dVd = . (3.116)
(3.116) s = si, VG = VGi, :
=
G
Gi
Gox
ss 1V
Vi dVC
C . (3.117) C(VG) , - (3.117) ( ) - VG. s1 VG1 . s1 (s1 = 0) -
VG1 VFB. - C-V . VG(s), (3.99) :
= ox
sc
ox
ox
ox
0oxss
1 CC
CCC
C
qdN . (3.118)
(3.118) - , -
-.
1012
1011
EV
Ei F EC
NSS
, -2-1
Vg , B
S, B
-0,8
-0,6
-0,4
-0,2
0
0,2-12 -10 -8 -6
C,
.=10-2
.=106
.
.
Si-SiO2N
D=1015-3
dOX=1400 Ao
CFBS=0
100
80
60
40
20-14 -12 -10 -6 -4 -2 0 V
FB
. 3.20. : ) - Si-SiO2-Al; ) - s VG, (3.117); ) E , (3.117)
(3.117) , (1 - /ox) C-V . - C Cox - , , C-V -. 3.20, , C-V .
-
53
, , - VFB - T. - . 0(T), 0(E), . (3.83) - VFB ,
[ ])()()()( 2010ox
ss2FB1FB TTC
qNTVTV = . (3.119)
(3.119) Nss:
)()(
0
FB
ox
0oxss
d
Vdqd
N = . (3.120) , Nss . T = (77400) , - . 3.21, , C-V , .
C/COX
Si-SiO2-AuN
D=1015-3
dOX=50 Ao
T=400 K
T=400 K
0(T=400 K)
0(T=100 K)
T=100 K
300 200 100
0,8
0,6
0,4
0,2
0-0,8 -0,4 0 0,4 0,8 1,2 1,6 2,0
CFB
Vg
, B
EV
EV E
VEi EC
Ei Ei
FF
ED
ED
EC
EC
NSS
, -2-1
1012
1011
. 3.21. : ) - Si-SiO2-Al - T; ) VFB 0 ; ) Nss E - , (3.120)
-
3.7. - 3.7.1. - , , Qox, dox, - ND,A, -. s, -
( )ox
sc0s
ox
ss
ox
oxsmsG C
QCqN
CQ
V ++++= , (3.121)
-
54
- . , - -, Qox, dox, - ND,A , , - . , - VG s . s - VG - - -
[22]. , - , . , - -. , - dox - W. - , - -, s . - (3.121). . - , . ,
Nox = 1012 -2 - a = 100 . ND = 1015 -3 a = 1000 . , , . . (3.121).
.
+10
+4
+2
0
+2
+4
+10+20
0
20
40
60
80
100
0 20 40 60 80 100
12
11
10
9 8
7
6
5
4
3
2
2
3
4
1
C
(
p
F
)
s
(
k
T
/
q
)
0 20 40 60 80 100
12
11
10C
(
p
F
)
0
20
40
60
80
100
C
(
p
F
)
7
6
5
4
3
2
10 20 40 60 80 100
0
20
40
60
80
100
. 3.22. -: ) , ; ) , dox; ) -, - . () . 3.22 - , (0,1x0,1) 2 . ,
C, , s, . - . -
-
55
, C - G -. s s -. 3.7.2. - Qox = qNox. dox - ND,A, 3.22, , . ,
P(s) s -. N , s. s , -, . N , P(N) - :
( ) NNNeNNP 2 )(212
2)(= . (3.122)
N Qox s -:
qQN s ox= . (3.123)
(3.122) (3.123), P(Qox):
=
ox
oxoxs2
1
oxox 2
)(exp2
)(qQ
QQQ
qQPs
. (3.124)
:
s
oxoxs )()( d
dQQPP = . (3.125)
(3.121) -
, ssssscs
sc , CqNCQ ==
, , dVG = 0, -
VG s, -:
( )
( )( ),;
ssssscoxoxox
sssscox
++=++=
CCCQQdCCCdQ
(3.126)
sox ,Q Qox s. (3.125) P(s) - (3.126) (3.124), :
( )
s
ss
22
1
2s
s 21)(
= eP , (3.127)
kTq =s :
2
1
s
ox
ssscoxs
++= qQ
CCC. (3.128)
, s s , :
2
1
ox
ssscoxs
1
++== Qq
CCCqkT
. (3.129)
(3.128) , . - dox, Nss, - oxQ . s, (3.128), . Gp/ , s - - (.
3.23).
-
56
s, 10 -5
W, 10 -5
1,8
1,7
1,6
1,5
1,4
1,3
1,2
1,10,6 0,7 0,8 0,9 1,0 1,1 1,2 1,3
. 3.23. s W 3.7.3. , , . a . 20
= aN , oxN .
-
57
- . W , - dox, , . - . , 3.24. q0 I = 1. , - q0 II = 2. , , - I
II. I q1 q2, II q3, , q1. , q0, - I II - . -, q1, q2 q3 - - . q2 =
-q1, - 1, 2 . (En) (E) , 3.24.
q1=qo /1
I ,1
q2= - qo /1
q3= - qo /1
,2II
1<
2
E3
E2 E1
E3E2 E1En1
En2 En3
r r
. 3.24. , I, q1 q2, - - 1,
cos)1(210
2,1+= qEn ,
sin)1(210
2,1= qE . (3.137)
II, q3 1,
cos210
3= qEn ,
sin210
3= qE . (3.138)
-
32,1 EE =
32,1 21 nnEE = , -
: 1 =+ , =1 , (3.139)
1
2
= . ,
11
,1
2
+=+=
. (3.140) , -, q0 I 1 II 2, I - 1 q1 q2, . q2 = -q1, (3.140). II
2 - q3 = q1, q1 I 1. - , - . ( , , ). 3.25 . , . q, , -q, -q . - q,
- .
-
58
q -q. -, - - -. 3.25 . , - +q - -q, +q, -2q .., 2dox, 4dox,
6dox, 8dox - .
Me SiO2 Si
5dox
3dox
4dox6dox
2dox
dox
dox
- 2q
- 2q - q - q q
2q 3q- q q- q q
2
. 3.25. , -: ) ; ) , . , - -,
sox
02
+= qq . , , , -, : =+= iUUU 0),( ( ) ( ) ++++=
= 21ox
1
212122
oxs0
0 2)(2
idqi
i . (3.141) - 1 = 2 = *, = 1, = 0 :
( ) ( )[ ] +++= 212ox22122*00 22),( dqU . (3.142) (3.141)
(3.142), - , - dox, ( ) - , . 3.7.5. - - - . , - , S, - - , N -
S
NN =ox . - (3.141). , , - dox . - - s ,
oxN . 3.26 . , , , - , , , . - , - 500 dox - dox = 50 .
-
59
500 Ao
. 3.26. - . s s . 3.27 s - y , , 3.26. , s -.
Si-SiO2-
dox=50 A
Z = 50 A
Nss=1011 -2
-
+
o
o
60
50
40
30
20
10
024002200200018001600140012001000800600400200
U,
, o
. 3.27. s y , -.
3.7.6. - . - - - , :
NN
eN
NP =!)(
m , (3.143)
N , S, SNN = ox ,
S. i , (3.141):
),(),(1
iN
iiUU
== . (3.144)
(3.141 3.144)
>> dox, 21
ox= Na .
s -:
2
2ss
2)(
ss 2
1)( seP
= , (3.145) s s - . (3.141 3.144) - , P(s) , 3.7.5. n - , , - .
- . 3.28 - s - dox = (501000) . , .
-
60
Si-SiO2-
Nss=1011 -2
Z = 50 Ao
f
30
24
200
100100
49500
235
1000
455 ,
dox, Ao
1,0
0,8
0,6
0,4
0,2
0100 200 300 400 500
. 3.28. f - , dox - . - . 3.29 oxN .
0,3
8,01,0
24
3,0
68
10,0
250Nss, 10
11 -2
,
Si-SiO2-
dox=50 A
Z = 50 A
o
o
U,
1,0
0,8
0,6
0,4
0,2
0100 200 300 400
f
. 3.29. f - , oxN - , oxN . 3.30 . , , -
, , . , s , , - r r.
Si-SiO2-
dox=50 A
Nss=1011 -2
o
U,
=1,0
=0,01
n
1500
1000
500
0 20 40 60 80 100 120 . 3.30. f - 3.7.7. - 3.7.3 3.7.4, - -. U(,
) (3.142) (3.136) . 1 = 2 = * (3.142) - U(, ) (3.136) :
2
1
ox2
ox2
1
ox
0oxsox 2
1ln2)(
),(
++
+= d
dNqd . (3.146)
ox s , (, dox) -. 3.31 - () . , - - . - () . , , -
-
61
.
dox=1000 Ao
o
,
500
200
74
50
, A
30
20
10
20 40 60 80 100 200 400 600 800 . 3.31. , dox (3.146) , 0 - . ,
r 0 . - , P(s) -. , . , - , . min = (5100) (3.136) min. (, dox) -
U(, ) (3.141) (, dox) (3.136) - . - (, dox) (3.152).
- - , :
2
12
scssox
0oxs2
1
ox
0oxsox )(
)(1ln
4)(),(
++
++
+=
CCC
Nqd ,
(3.147) Cox, Css, Csc , -, . (3.147) - . - (3.147) :
++
+=
2
ox
ox
oxs2
1
ox
0oxsox 1ln4)(
),(
dNqd . (3.148)
>> dox (3.148) (3.146) - ~ -1 2 . ~ dox () . 3.7.8. , - -.
Nox. - - . - L, , . , , - , - . - - . , . , , , - . :
SNq
SQ oxox == . (3.149)
N
-
62
oxox NLSNNN === , (3.150) N S L,
oxN . , - L. , U, - , , :
=2
0* 12 LLLU
. (3.151)
U0 = 0 :
0
*0 2 LU = . (3.152)
(3.151) (3.152), U0 U0 ~ L. (3.149) (3.150) :
[ ]
0*
21
ox0 2
NqU = . (3.153)
(3.153) , - U0 L, oxN . - . - (x, y), - :
=Ly
Lxyx sinsin),( 0 . (3.154)
, , :
*0
),,(),,( zyxzyx = , (3.155)
(x, y, z) . (x, y, z):
= 2exp4
),(2),,(0
*
LLyxzyx , (3.156)
L , , - . , - -, U, :
+= 2)2(exp4
),(2 ox0
*
LdLyxU .
, 3.32, :
+
= 22exp2exp4
),(2),,( ox0
*
Ld
LLyxzyxU .
(3.157) 3.32 U(x, y, z) , (3.157).
U/U0
1,0
0,8
0,6
0,4
0,2
0
- 0,4
- 0,2
- 0,6
- 0,8
- 1,0
100 200 300
dox=50 A
L1=200 A
L2=1000 A
0
0
0
0
, AU
U
U
2
2
2
U
1
1
2dox
. 3.32. U/U0 - 3.33 L. , , -.
-
63
U/U0
1
2
3
4 5
6
, A0
1,0
0,1
0,01102101 103 104
. 3.33. U/U0 : dox = 50, 1 L = 100, 2 L = 1000, 3 L = 10000, dox
= 1000, 4 L = 100, 5 L = 1000, 6 L = 10000 3.34 L dox .
1,0
0,1
0,0110 0 10 1 10 2
dox=50 Ao
o
200 A
1000 Ao
=50 Ao
100 Ao
200 Ao
o
AL,
U/U0
. 3.34. U/U0 L dox , U L -. (3.157) , - L, - (U/U0)max, :
+=
ox
ox 2
ln
22d
dL . (3.158)
3.35 L, - (3.158) -. L ~ dox, - - L >> dox.
10 1 10 210 2
10 3
10 4
10 3
L,o
A
dox, o
A
=200 oA
100
50
20
o
A
o
A
o
A
. 3.35. L, U/U0, dox 3.7.9. U(), - (3.157) L, (). , L U0 ,
(3.123). - , , L = L, (3.158). U0 -, U - . .
-
64
3.36 , - . , - U -. , dox , -, . 0, , , - , U0. U L 3.34. , , -
.
21
oxmin= NaL . (3.159)
oxN = 1010-2 Lmin 1000, oxN = 1012-2 Lmin 100.
U, u,
dox=50o
A
,o
A
200o
A
1000o
A
30
25
20
15
10
5
010 1 10 2 10 3
. 3.36. U0 U , - . -: Lmax L.
, Lmin Lmax. , - (3.158). - - RC-, - . . . -. dnn - Csc - s dnn.
:
nn
ssc d
C= . (3.160)
dnn - . p,n dnn , 3.36, . , 3.36, - . -, - (p) T = (77350), =
(200300) . , - 3.35, , - - . - , -.
-
65
4. . , , - - . : - p-n , , , - . 4.1. p-n - . 2, - , 4.1, ,
(4.1). -, . -. , - , .
1
,
0
0
,
8
7
5
9
15
3419
J
J = JpD + JnD
J = JpE + JnEVG
. 4.1. : ) - ; )
Gs ( 1)VJ J e= , (4.1)
0pDnEnDpE =+ jjjj . - , , .
4.1.1. p-n - : - . . 4.2 , - .
V V VD
IDD
R
t
V
t
V
+
I
D
(
m
A
)
VD(V)
4
3
2
1
1 2 30-1-2-3
. 4.2. , [10, 20] , - p-n . (4.1) - - U = 0,01 ; 0,025 ; 0,1 ;
0,25 ; 1 B. :
11
G
G
==
+V
V
ee
JJK
. (4.2)
, -1 1 0,025 = . .
VG, B 0,01 0,025 0,1 0,25 1 K, . . 1,0 1,1 55 2,3104 2,81020
(4.2), -, VG , kT/q, - . - VG 4 , kT/q, = 300 VG = 0,1 .
-
66
4.1.2. : - rD RD.
[ ]1 1D s s s ss
/( )VdU dI kT qr j e j j I IdI dU I I
= = = + = + = + . (4.3) - rD . -, I = 25 - kT/q = 25 rD - rD = 1
. - rD , . RD - VG I :
D0 ( 1)
U
U URI I e
= = . (4.4) - - , RD > rD, - RD < rD. VG
-
67
7
1
5
0
,
5
19
15
9
34
116-1
200
100
50
20
10
1 2 5 10
,
U, B
20
20
25
10
10
15
15
5
50
,
U, B
126-5
f=10
130
20
20
40
6080
100
10
10
8
8
6
6
4
42
2
,
U, B
. 4.4. () ( 116, 126, 130) [23, 25] 4.3. , p-n - - p-n p-n . -
p-n , -- . , , () :
n p t 1 1
n 1 p 1
( )( ) ( )
N pn p ndndt n n p p
= + + + . (4.6) , 4.10, : n, p -; Nt ; n, p ; n1, p1 -, . 4.6
1.20 , (VG > 0) - pn , -
p1n1 (pn > p1n1). , 4.6 , - dn/dt . -, . (VG < 0) , - . .
4.3.1. p-n (VG < 0) p-n 1.20 ,
22 iU
ikT
i nenenpnpn
-
68
J VG, , T (. 4.5). J VG W VG. W
s 0 0
D
2 ( )UW
qN += , J
: G ~ VJ . J0 p+-n - :
A
2
p
p
p
p0p0 N
nqLnqLJ i == . J0 J -, :
in
NLW
JJ D
n0
= . (4.10)
Js
J
J0=J+Js
VG
J
. 4.5. J p-n (Ge) : W = 1 ; Ln = 150 , ni = 1013 -3, ND = 1015
-3. 4.10, , , I ~ Is. (Si) : W = 1 ; Ln = 500 , ni = 1010 -3, ND =
1015 -3. 4.10, -, , , I / Is ~ 2102. , p-n , - . 4.10, ni. ni
( ), , ni ( ), . 4.3.2. p-n (VG > 0) p-n 1.20 , 22 i
Ui nenpn >>= .
4.6 1.20 , (VG > 0) - pn , - p1n1 (pn > p1n1). , Et - Et =
Ei. p1 = n1 = ni, - : n = p. 4.6 :
i
Ui
npnenN
dtdn
2
2t
++=
. (4.11)
(4.11) , dtdn
, . , , 0 n,p - Ei Fn Fp 2pn,0
U= . 4.11
22U
ien
. , :
22t21 U
i enNdtdn = .
J - W :
2t0
2
U
i
W
enNqWdxdtdnqJ
== . (4.12)
- :
2tDp
2p
2
U
iUi enNqWe
NnqL
JJJ
=+= . (4.13)
-
69
(4.13) , -
nU
eJ
~ , n = 1 , n = 2 . 4.6 - - . ,
)(ln Jd
dU 0,028 , -
kT/q, 0,026 .
I,
U, 0
10-10
10-8
10-6
10-4
10-2
0,1 0,2 0,3 . 4.6. [2, 23] 4.3.3. p-n , . - r, -
: Slr = ,
, l , S - . = 1 , l = 10-1 , S = 10-2 2, r = 10 . U - J : IrU =
. (4.14) , p-n , V. (4.14) - : ( )0 ( 1)U IrI I e = ; (4.15)
(4.15) , - p-n , , , . , , - - :
[ ] 11
rII
dUdIr ===
=
. , ,
, :
r
I = . r = 10 ; = 0,025 : I = 2,5 A. 4.7 , - , - .
-
70
T=+1000C
+250C
-600C
I,
2925
U,
100
80
60
40
20
0 0,2 0,4 0,6 0,8
A C
P-N
VD
VD
ID
I
D
I
D
ID
rS
rS IDrS
rS
rS
+
(
m
A
)
(
A
)
]
(V) VD(V)
8 -5
-10
-15
6
4
2
00.5 0.50.6 0.60.7 0.70.8 0.8 0.90.9
l
n
[
= 0
= 15
. 4.7. , - [17, 23, 26]: ) ; ) ; ) ; ) 2925 , - -, , , rI. 2925
, - . , . 4.3.4. , , - - . (. 4.8). :
Gs ( 1)
VJ J e= .
p-n+ NA > pn0.
kTE
i enn
ng
~n0
2
p0
= , kTE
i eNNn 2VCg= .
kTE
econstI 20g= .
-
:
~11TT
TT ,
: 0 R ( ) ( )
TI T I T e . (4.16) : Ge = 0,09 -1 T = 700, Si = 0,13 -1 = 1200.
. (4.16) ,
0 0 0 *( ) ( )2TI T I T
T= , (4.17)
a
T 2ln* = , : T* = 10; 8; 7; 5, = 0,07; 0,03; 0,1; 0,13. (4.17)
T* = 10 : - 10 .
U,
I,
I, 107(,)
+250C
+600C
-600C
300
200
100
0 5 10 15 20
107(,)60
-60 -30 0 30
50
40
30
20T,
0CU,
I,
107(,)
+600C
+250C
-600C
20
16
12
8
4
0,20 0,4 0,6
. 4.8. - 107 [23, 25]: ) ; ) ; )
-
71
4.4. , - - - . , 4.9.
U
J
VG
J
7
1
5
0
,
5
19
15
9
34
. 4.9. - () () , - U, . R 0, R : R 250 . , . - , - . . U , - . ,
, - p-n . - U 5 : U < 5 . - 8 : U > 8 . .
p-n , - (. 4.10).
p n
VG < 0
EV
Ei
ECFn
. 4.10. p-n - , , , - -, . p-n . 4.11 - .
. 4.11. EH = , H -
2 2
2 ( )
2H U x
m x= +
h, .
2 g2 22 2; ( )m mE E E = = h h .
:
0222
=+ dxd
.
-
72
0222
= dxd
.
: ikxikx eBeA += 11 ,
ikxeAs= , xx eBeA 22 += .
dxd , ,
(W >> 1). :
=== hqE
EmAA
T324
exp42/3
g2
1
2s
2I
2III
t
.
- :
[ ]C V t C C V V( ) ( ) 1 ( ) ( )VC
E
E
I AT f E N E f E N E dE = , . p+-n+ : CVVC = II . : C V V C t C
V C V( ) ( ) ( )I I I AT f f N E N E dE = = . (4.18) fC, fV . - J -
:
=
EE
AUI2/3
g8
2
10exp . (4.19)
E , : 0 10 II = .
p-n - E : Si: E = 4105 /; Ge: E = 2105 /. - . Uz, . , E -
p-n W
UE = . -
W D
0s2 UqN
W= ,
, W D
0s2
2qNE
U = , , - [5, 2]:
D
20s
2qN
EU
= . (4.20) , - . ND
eN
1D = , -
:
20sz 2
1 EU = . (4.21) (4.21) , Uz - . Uz : (Ge): Uz = 100n + 50p;
(Si): Uz = 40n + 8p, n, p n- p-, (). . , , , ,
-
73
, , , - . - . - . - 4.12 , . W, , . , , : >> WEEq ;g .
(4.22)
E(x)
VG> NC, NV.
-
74
p+ n+ -.
U,
I,
0,2
0,4
0,8
1,2
1,6
2,0
0,1 0,30
1104(-)
42,8
2
1
,
2
. 4.14. 1104 [25, 23]: ) - ; ) n+- - , p+- . p+-n+ , -,
4.15.
EC
VG=0
I=0
EV
F Fn
p+
n+
. 4.15. p+-n+ () . , ( Eg/2). ()
=
D
2
n0 Nn
p i .
, p-n . , p-n (p+ ). p+-n+ :
12
s 0 g 6s 0 019
D D
22 2 2 1 10 1 ~ 10 ~ 1001.6 10
EW
qN qN = = = .
:
;2
22
mkkTE h== ;2
=k ( ) ;2
22
22
kTm
E == h
mkThh
mkT 212 2 == ,
31 23
342 9,1 10 1,38 10 300 ~ 140
6,3 10
= . , p+-n+ . p+-n+ - , . . p+-n+ - . 4.16 - .
EC
VG
-
75
, - - .
EC
VG1
-
76
U,
I,
0
3
2
1
-600C
+200C
+700C
1403403
-100 -80 -60 -40 -20
3
2
1
-1
-2
0 U, U,
I,
I,
1403403
100 200 300 400
. 4.19. - 403 [23, 25]: ) ; ) , - . - ( -) - -. 4.6. p-n , - - ,
. - -. - -. , - - . . I U . 4.20 - .
0 t
U
U
U
0
t
J
J
J0
b
?
. 4.20. : ) ; ) ( )1G0 = VeJJ . J0. , p-n - . - p-n . - :
22
pp
n0
dxpdDpp
dtdp =+ . (4.25)
t = 0 - :
n0n0n1p)()( peppxp L
x
+= . (4.26) , , . , - , . - - (4.26). , , . t2, - , , . - (4.25)
.
-
77
t = 0 (4.26). - t :
)1( pn0Lx
epp= .
- p-n :
0p == xdxdpqDj . (4.27)
. - , (4.25) - p(x,t) . 4.21 p(x,t) - .
0 x
pn0
pn(x,t)
Lp
t = 0
t
0 < t < ap
t = p
8
. 4.21. p(x,t) [28, 15] p(x,t) (4.27), - J(t). J(t) :
( )
=
pp /
/exp
terfcttjj . (4.28)
pterfc ,
( ) ( ) ( )dyyzerfczerfc z ==0
2exp211 . -
: ( )
p//exp1
tt
.
(4.28) : t > p. [28, 15]: )(
/1
pp
= tt
tjj . (4.30)
(4.30) , t = 0 . , - r U. , - J, : J = U/r.
J
