. .

,

- , , 010700 010701

2005

539.2 539.2 : - ( ) . ., , . ., - , , .., - , , , . . : . / . . . , 2005. 492 . , . , - . , , , - , , , Si, GaAs, GaN, SiC . , , . , , . . 539.2 . . , 2005 2

........................................... 13 ............................................. 14 1. ............................. 161.1. ..................................................................16 1.2. ...................................................................17 1.3. ....................................19 1.3.1. .................................................19 1.3.2. ......................21 1.4. ..........23 1.5. ............24 1.6. ............................................................26 1.7. ........................................................................27 1.8. ......................................................................................28 1.9. .....................................................................................29 1.10. ................................................................................32 .................................................................................................33 .............................................................................................................................34

2. , P-N ........................................................... 362.1. ..........................................................................36 2.2. p- n-........38 2.3. ...........................................................................................................40 2.4. 42

3

2.5. ......................................................................43 2.6. ......................................................................................................45 2.7. ..................46 2.8. ......47 2.9. - ........................................50 2.10. - -n .................................................................51 2.10.1. p-n ..................................53 2.10.3. p-n ...................................................................54 2.11. -n .............................58 2.12. - -n ..............................................61 2.13. ....................................................................................................66 .................................................................................................73 .............................................................................................................................74

3. - .................. 763.1. () ..........76 3.1.1. ......................................................................................76 3.2. ......................................................81 3.2.1. ..........................................................................81 3.2.2. ...........................................................................83 3.2.3. ............................................................84 3.2.4. .................................................................................................88 3.2.5. ...............90 3.3. ....................................................92 3.4. ................95 3.5. ...................................................................................97 3.5.1. .....................................................................................97 3.5.2. ................................................................98 3.5.3. ..............................................................................99 3.6. - .........................................101

4

3.6.1. - ......................101 3.6.2. .................................................................103 3.6.3. - ..................................................................................107 3.6.4. - ..109 C-V ...................................................................................110 C-V .........................................................111 3.6.5. - C-V ..........................................................................................112 3.6.6. .........................................................................116 3.7. -....................121 3.7.1. ...........................................121 3.7.2. .......................................................................................................124 3.7.3. , .........................................................................126 3.7.4. , , ...................................................................................................127 3.7.5. - ................................................................................................................131 3.7.6. ...133 3.7.7. - ..............................................................................................135 3.7.8. ..........................137 3.7.9. ..........................................................142 ...............................................................................................144 ...........................................................................................................................144

4. ..................................... 147 .......................................................................................................................147 4.1. p-n .........................147 4.1.1. .....................................................................................148 4.1.2. ..............................................................149 4.1.3. ...........................................................................150 4.2. ..............................................................................................................151 4.3. , ....................................................................152 4.3.1. p-n .........................................................................................154

5

4.3.2. p-n ............................................................................................156 4.3.3. ...........................................................................................................................158 4.3.4. .......................................160 4.4. ......................................................................................................161 4.4.1. ......................................................162 4.4.2. ..........................................................165 4.4.3. .................................................166 4.5. ..................................................................167 4.5.1. - ...................................169 4.5.2. - ..................................172 4.5.3. 173 4.6. ..................................174 ...............................................................................................178 ...........................................................................................................................179

5. ......................................... 1805.1. ...................................................................................................180 5.2. ...................183 5.2.1. . ...........................................................................................................................185 5.3. ..................................................................................186 5.4. - ...........................................................................188 5.5. ........................................................................................................190 5.5.1. .................................................................................191 5.5.2. ...................................................................................192 5.5.3. ........................195 5.5.4. .....................195 5.5.5. ........................................................................197 5.5.6. ......................................................................199 5.5.7. ................................................................................200 5.6. ..................................201 5.7. ..........................................204

6

5.8. ...................................................................206 5.9. .....................................................................................208 5.10. ..................................................................................210 5.11. .......................................215 5.11.1. z-, y-, h-.........................................................................................215 5.11.2. h- ......................................218 5.12. ......................................220 5.12.1. ...............223 5.12.2. RC-....................................................................................................226 5.12.3. .....229 5.12.4. ............................232 5.13. ............................................233 5.13.1. GaAS .................................................................233 5.13.2. ................................................................................................................234 ...............................................................................................235 ...........................................................................................................................235

6. ................................................ 2366.1. .....................................................236 6.2. - ................................................................237 6.3. - ...........................................239 6.4. - ...............241 6.5. - ...............................245 6.6. - -..............................................................................................249 6.7. .............................................................................250 6.8. ............................................................................252 6.9. - ......................254 6.10. ................256

7

6.11. -........................................257 6.12. -...................................................260 6.13. - ....................................264 6.13.1. .............................................................266 6.13.2. ............................................................267 6.13.3. .................269 6.13.4. - - ...........................................................................................273 6.14. - ...........................................................278 6.14.1. - ........................................................................................281 6.14.2. .................................................................282 6.15. -n ..................................285 6.16. ..........................................289 6.16.1. GaAs ...........................................289 6.16.2. GaN ..............................................293 6.16.3. .......295 ...............................................................................................296 ...........................................................................................................................297

7. ......................................................................... 2987.1. ...................................................................................................298 7.2. - .................................301 7.2.1. ..........................................302 7.2.2. ......305 7.2.3. ...........................307 7.2.4. VG. ..................................................................................308 7.3. .............................................................................................................309 7.3.1. ........................................311 7.3.2. ...........................................................................312 7.4. ..........................................................................313 ...............................................................................................315

8. - ...................................... 316 8

8.1. ...................................................................................................316 8.2. .......................................................................317 8.3. ...................................................................319 8.4. -...................................323 8.5. pin-..............................................................................326 ...............................................................................................330

9. ..................................................................... 3319.1. ...................................................................................................331 9.2. .......................................331 9.3. .................................................................334 9.4. .............................................................337 9.5. - ...................................................342 ...............................................................................................344

10. ................................. 34510.1. .......................................................................................345 10.2. ........................................................................347 10.3. .............................................................................................347 10.3.1. p-n ....................................347 10.3.2. ................................348 10.4. .........................................................................................................348 10.4.1. ................................................................349 10.4.2. .......................................................355 10.4.3. ..............................355 10.5. ...........................................................................357 10.5.1. ................359 10.5.2. .........................................................................361 ...............................................................................................365

9

...........................................................................................................................366

11. ............................................................ 36711.1. ...............................................367 11.2. ...................................................................369 11.3. ...................................................................................................371 11.4. p-n .................................................................374 11.4.1. .............................................................................................374 11.4.2. - ...............................................377 11.4.3. ..................................................................380 11.4.4. p-i-n .............................................................................................382 11.4.5. ...................................................................................385 11.5. ..............................................................................................388 11.6. - .................................390 11.6.1. ..............................................................................390 11.6.2. ...........................................404 11.6.3. -..............................................................408 11.6.4. () ...........................410 ...............................................................................................414 ...........................................................................................................................414

12. .......................................................... 41512.1. ......................................................................................415 12.1.1. ............................................415 12.1.2. ...............................................417 12.1.3. n(z) .......................................418 12.1.4. .......................................419 12.1.5. ...........425 12.2. ................................................................................426 12.2.1. ...............426 12.2.2. ..................................................................................427 12.2.3. ..428 12.2.4. ..................................429 12.2.5. 2D ...........................................................................................................................430

10

12.2.6. 2D .................430 ...............................................................................................432

13. ................................ 43313.1. .................................................................................................................................433 13.2. SiC......................................................................437 13.3. GaN....................................................................439 ...............................................................................................440

14. .......................................................... 44114.1. - ......................................................442 14.2. , ...........444 14.3. .......................447 ...............................................................................................451

..................................................................... 452 ................................................................................. 462 1. .................................................................................................462 2. , p-n ..............................467 3. ...............................................470 4. ......................................................................475 5. .........................................................................475 6. ................................................................................477 10. .........................................478

11

11. ........................................................................................478

.............................................................. 480 .................................. 483 ....................................................................................... 487 ...............................................................489 .............................................................................................489

................................ 490 ..............................................................................490 ..................................................................................491 .........................................................................................................493 ..................................................................................494

................................................................. 495

12

, - . , , , . . . /.. . 4- . .: , 1977, 671 .; . /. . .: , 1984. .1, 456 ; .2, 456 ; , Sah C.-T. Fundamentals of solid-state electronics /C.-T. Sah. World Scientific, 1991. 1011 p; . , , , , , , , . , , , , . - . . . . .. , . . , . 84 . 31 [1 31], 37 [32 69], 5 [70 74], 10 [75 84]. , . , . . . . . , 15 2005 ,

13

, - . 071400 ..08 . , , , . , . 510400 : 510403 ; 510404 . . 553100 , : 553105 , ; 553117 . 552800 : 552826 ; 552824 - . 010400 ; 071400 ; 220200 ; 190900 - . , p-n , , . , , 14

. . , , - , -. . . . . , . , , . . . , , - . , - . , . , , . . . . . . . , 28 2003 ,

15

1. 1.1. . , . N , N- . , , , . , , . . , [35, 82, 83]. . , , . ( ) 3 , . , , Eg (0,1 3,0) , . , , , , . 1.1 , , . , , . . . EC, EV, Eg. 16

, . , 10-8 106 -1-1, , : , (), .. g > 3 , < 10-8 -1-1, 8 = 1/ > 10 . > 106 -1-1. (Eg)

x

V(x)

Ec' Ec Ev

V0(x)

3p2 - 6,53 3s2 - 13,57

Ev'2,35 A

Si

Si+42p6-150,84 -108,21

/ Si

2s2

a = a0 = 2,35 A

a=

. 1.1. , , [30]

1.2. , , . , ( ). (ni) ( n p, n = p = ni). 17

8

= 0 (n = p = 0). > 0 . . ( 1023 -3) . , . (, ), . , . , 4 (, ), 5 , ( ), n-. 3 , , (-) (. 1.2).

Eg

Eg

+4

+5

+4

+4

+3

+4

. 1.2. n- () p- ()

, , mn* mp* . a = F/m*, dp/dt = F, , ( ) m0 mn* (p = mn*). , .

18

1.3. , , . , . . : , . 1.3.1. . dpx, dpy dpz: dx dpx h , dy dpy h , (1.1)

dz dpz h . . dp dV h3 , (1.2) dp = dpxdpydpz dV = dxdydz, dp px, py, pz, , dV . dV . . ( ) dV = 1 3. (1.2) dp h3. dp = h3 . , h3 , . , dp , , dp/h3 dp. . (. 1.3). (px, py, pz) (. 1.3). p. dp , 19

(. 1.3). p dp :

dN =E

4p 2 dp . h3pz

(1.3)

p 0 p+dp px py

dE

EC

k

. 1.3. :) ; )

+ d, . N(E)dE, N(E) .

E = EC +

p2 , 2m n

(1.4)

C , . mn . (1.4) dE =

m dE p dp , dp = n p 2 = 2mn ( E E C ) . mn p 4m 3 / 2 2 (E E C ) dN = N ( E )dE = h31/ 2

(1.3),

dE

.

(1.5)

N (E) =

3/ 4 mn 2 2 ( E EC )1/ 2 . h3

(1.6)

20

, ( C) (V ), mn mp. (1.6), . 1.3.2. , , , . , , :

f ( E, T ) =

1 1+ eEF kT

.

(1.7)

F , . (1.7) , , 1/2. 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) . :

f (E, T ) = e . :

EF kT

(1.8) (1.9)

n = 2 N C ( E ) f ( E , T )dE .EC

21

E N(E)

EC f3 f2 F f1 f3 EV0 0,5 1

N EC - F f f2

f

. 1.4. N(E), f1 (T1 = 0), f2 (T2 > 0), f3 (T3 > T2) f

, . , f E > F E, . (1.9) (1.6) (1.8). :

n = NC e

EC F kT

,3/ 2

(1.10)

2 mn kT NC = 2 2 h

.

(1.11)

NC . , 2kT, F EC > 2kT ( F EC > kT), fp :

fp = e

F E kT

,

(1.12)

p = NV e22

F EV kT

,

(1.13)

EV , , NV (1.11), mn mp. NV . , (1.9) 2, , ( ). n p (1.10) (1.13) F. , : (1.14) p n , , n p. ni . [82]

n p = (ni ) = N C N V e

2

Eg kT

.

1.4. , , . , n = p (. 1.5).

EC F EV. 1.5. ,

(, ..) , n0 p0 . n0 = p0 (1.14) :

n0 = p0 = ni = N C N V e

Eg 2 kT

.

(1.15)

, ni . 23

NC NV (1.11). (1.15), . 1.6 , , . , 0,6 2,8 , ni 1013 -3 10 -3.1020

T, 0C600 500 400 300 200 100 50 25 0 -25 -55 -75 -100 -125

1018

1016

ni, -3

1014

Ge

1012

1010

Si

108

GaP1,0 2,0 3,0

GaAs4,0 5,0 6,0 7,0

106 0,5

(1000 / T), K. 1.6. , , [30, 82]

1.5. (1.14) , . 24

(1.16) ND. , . (. 1.7) n0 = N D . (1.17) (1.16):

n0 p0 = (ni ) 2 .

p0 =

ni 2 . ND

(1.18)

1.7 n-, ED ( ) n0 p0 ( ).

ED

EC F Ei EV

. 1.7. n-

NA, p0 n0

p 0 = N A n0 =

ni . NA

2

(1.19)

1.8 p-, EA ( ) p0 n0 .

25

EC Ei F EA EV. 1.8. p-

1.6. , . , . p n = 0 p = n. (Eg kT), mn mp , (EC F > 2kT F EV > 2kT) . (1.10) (1.13), . (1.20) F. (1.20) F

NC e

F EC kT

= NV e

EV F kT

e kT .

N 1 F = Ei kT ln C N 2 V Ei =

m* 3 = Ei kT ln n , m* 4 p

(1.21)

1 ( EV + EC ) . 2

F (NC/NV) (mn/mp) (1.11). mn* = mp*

F=

EC + EV . 2

(1.22)

, . n p 26

, F (1.10) (1.13). , n- :

N F = EC kT ln C . n0 p-

(1.23)

N F = EV + kT ln V . p0

(1.24)

(1.23 1.24) , , . n0 = ND.

N F = EC kT ln C . N D p0 = NA (1.19),

(1.25)

N F = E V + kT ln V . N A

(1.26)

1.7. . n p : = n + p. : n = n n 0 q; p = p p 0 q , (1.27) n p . ,

n =

q , * mn

(1.28)

. , , 27

. , n =n +p n . (1.29) , , :

=

1

=

1 1 . n +p n

(1.30)

, []. , , = (110) . (1.27) (1.30),

=

1

n

=

1qn n0

=

1 , ND q n N D

n- , n0. : 4,5. , , . , , . , 0,2 , , , = 0,2 ; 4,5 , , , = 4,5 [38, 39].

1.8. , , , . , , , . : (1.31) j = jp + jn = jpE + jpD + jnE + jnD , j , jp , jn , jnE , jnD , jpE , jpD . 28

: jnE = q n nE = n E; (1.32)

jpE = qp pE = p E; jnD = qDn jpD dn ; dx dp , = qDp dx

(1.33) (1.34) (1.35)

Dn , n Dn =

kT n [35 40]. q

Dp p.

1.9. . , . , . , . , , . , , , , , () . . . , : n = n0 + n ; (1.36)

p = p 0 + p ,

(1.37)

n0 p0 , n p . , , : n = p . (1.38) 29

, , . , () , . . , , . 1.9 G , R .

EC ED G EV. 1.9.

n

R

p

() R : R = n p, (1.39) . ( ) G = G0 R = R0 = n0p0, n0 p0 . (1.39) (1.14) : (1.40) Eg = EC EV . , R0 . , :

R0 = N C N V e

Eg kT

,

dn dp = =GR. dt dt

(1.41)

() : G = G + G0 , R = R + R0 , (1.42) 30

G, R , G , R0 = n0p0 R = np. (1.36), (1.37) (1.39), (1.41) :

d (n) = (n0 + p0 + n)n. dt

(1.43)

( t = 0). (1.43) . . n >>n0 +p0. (1.43) :

p = n =

(n )0 , 1 (n )0 t

(1.44)

n0 . . n0 = ND, p0 NA) ln n 1/T. , n ND NA , ED = EC 0,05 . 34

1.13. p-Si, = 300 , x: N A ( x ) = N e 0 , x0 = 0,5 . p(x) = NA(x), Ei N. Dp = 10 2-1 p = 400 2-1-1. 1.14. n-Si 0,6 Nt = 1015 -3 , . t = 10-15 2, t = 107 -1. 1) , ; 2) , . 1.15. , ND = 1016 -3. 1021 -3-1 - . . 1015 -3 - Et = Ei, 10-14 2. : 1) , 2) p 0. 1.16. GaAs , 1020 -3c-1 - . ND = 21015 -3, 0 = 5.10-8 , = 300 . : 1) ; 2) . 1.17. n-Si 1017 -3 x = 0 61016 -3 x = 2 . . = 1000 2-1-1. 1.18. /0 I = 51015 -2-1 . = 100 -1, -1. , 0 = 210-4 , n0 = 1015 -3. x x

35

2. , p-n 2.1. . . :

f0 ( E, T ) = e

EF kT

.

, E , F, . , f, E > 0, . , , . , , . . dp px, py, pz. , , : (pxx)(pyy)(pzz) h3. xyz = 1 : (pxpypz) h3. dz dp = dpxdpydpz :

dz = 2

dpx dpy dpz h3

=

2(m* )3 d x d y dz . h3

(2.1)

dn, dz f (E,T): dn = f ( E , T ) dz . (2.2) . , (E F >> kT), : 36

f0 ( E, T ) = e

1EF kT

e 1

EF kT

.

(2.3)

, , d, S = 1 l = x: dN = x dn . (2.4) J :

J = q dN = q x dn = q e

EF kT

x

2(m* )3 d x d y dz . h3

(2.5)

, (2.5), . ( ) :

E = EC +

m* 2 m 2 2 = EC + (x + y + z2 ) . 2 2

(2.6)2 m*x 2 kT

J :

2q (m* )3 J= e h3

F EC kT

e

2 m* y

2 kT

d y e

2 m*z 2 kT

dz

x e

d x .

(2.7)

x min

(2.7)

e

2

d = , ,

(2.7) . : m 2 E m 2 * x kT x min kT C x e 2 kT d x = * e 2 kT = * e kT . (2.9) m m Vx min (2.8) (2.9) (2.7), :

e

2 m* y

2 kT

d y =

2kT . m*

(2.8)

jx =

4 em*k 2T 2 e h3

F Ec + Ec kT

F

= AT 2 e kT .

(2.10)

(2.10) . A = . 37

4em * k 2 ; h3

A = 120

m , 2 . * 2 m

F < 0, F, = 0, . : = F . (2.11) , . : . (2.12) , (2.12) , jt . , jt, , . . , , : = 2,5 , 1 = 300 , 2 = 1500 , kT1 = 0,025 , kT2 = 0,125 . , (2.12), : jt1 = 10-36 /2, jt2 = 0,8 /2. , 5 36 .

j x = j t = AT 2 e

kT

2.2. p- n- p- n-. 2.1 : , Eg , 0n 38

n-, 0p p-.

E0

E0

EC F Ei EV

n EC

p

0n

Eg 2

Ei F EV

Eg 2 0p

. 2.1. :) n-; ) p-

= F, n- n p- p:

Eg 0n , n = F = + 2 Eg + 0p . p = F = + 2

(2.13) (2.14)

( , , mp* = mn*. (2.13), (2.14)

kT 2 lnNC NV

n- p-.) (2.13) (2.14) , p- , n-, , n- , p-. 39

2.3. . , , . , . , , . ( ) . 2.2 .n- n-

VG > 0

VG < 0

. 2.2. n-

, , , . ND = 1015 -3, ( ) = ND1/3 = 10-5 = 1000 . = 1012 -2 1012 / 1015 = 10-3 , 10 . , [10, 30]. [30, 39, 45]. . , , , (). E(z) 40

. , , . :

U = U ( x) U () = E ( x)dx ,

x

(2.15)

U() . (k = 0, E =

k2 = 0 ), 2 m*

2

EC ( EV). . :

=

1 E ( x)dx . q x

(2.16)

s. s , . s > 0 , s < 0 (. 2.3).

41

S EC F S 0(x) 0n Ei S EV S S > 0 S S EC F Ei

EV

S < 0

. 2.3. n-:) ; )

2.4. , . n-. nn0 pn0 :

nn0 = N C e

- (EC -F ) kT

= NC e

- (EC -F + q0n q0n ) kT

= NC e

- (EC -F + q0n ) kT

e

q0n kT

= ni e

q0n kT

, (2.17)

EC F + q0n = Eg/2.

q = , kT

nn0 = ni e 0n . (2.18) (x) : (x) = 0 n + ( x ) , nn0(x) p0n(x) . (x), 2.3, 0n. (x) = 0n + (x) :

42

(2.19) (2.18), n-: nn0 ( x) = ni e ( z ) = ni e (0 n + ( x )) = nn0 e ( x ) , (2.20) (2.21) pn0 ( x ) = pi e ( z ) = pi e (0 n + ( x )) = nn0 e ( ( x )+ 20 n ) . ns ps nn0 : (2.22) ns = nn0 e s ; ps = nn0 e ( s + 20 ) . (2.20 2.22) .

nn 0 ( x) = ni e ( x ) ,

2.5. , , . , . , , s kT/q. s , , z :

d 2 ( z) = , 2 s 0 dz (z) , s .

(2.23)

: + ( z ) = q[ N D n( z )] . (2.24) + ND = n0, n(z) (2.19). s =

zf ( z )dz0

f ( z )dz0

= z0 .

(2.33)

, LD , .

44

2.6. . (p- n- ) . . , . ( p- n-), . , , , , . , . . , : . (2.34) n- , / , . (2.34) j/ , : > / ; j Me < j / . , . , . . , . 2.4 . , 45

jT = AT 2 e

kT

, : ms = ( /). p- , / , . j/ , , (2.34). p- .

jMe

/

j/

Me

jMeE=0

/

j/

Me

Me

/ < Me EC Ei EV F/ S = ms EC Ei EV

FMe

F/

(Au)

(n-Si)

W Au n-Si Au

n-Si

. 2.4. ,

p- n-.

2.7. , VG, 46

. VG > 0 ms, VG < 0 . 2.5 . , .VG = 0S = ms

VG > 0S = ms - VG

VG < 0S = ms - VG

VG

VG

E(x) VG VG

E(x) VG

E(x)

W0

W1

W2

. 2.5. :) VG = 0; ) VG > 0, ; ) VG < 0, ; . ( ), s = ms - VG

2.8. , . n-. , , . , 47

, . . :

2 ( x) ( x) , = 2 s 0 x

(2.35)

(x) , (x) , s , 0 . n- ND+. + ( x ) = qN D . (2.36) , E ( x) = :

d d ( x) = , s 0 dx dx+ dE qN D = . dx s 0

(2.37)

(2.38)

(2.38). , x = W ,

E ( x) =

+ qN D

s 0

(W x) .

(2.39)

(2.39) , (x = 0), (x = W). ( , ) (2.39) : x = W, (W) = 0. (. 2.6):+ ( x) = qN D

(W x) 2 . 2 s 0

(2.40)

x = 0 : max = s VG = ms VG , ms = Me / . (2.41) 48

W, (2.41) (2.40):

W=

2 s 0 ( ms VG ) . + qN D

(2.42)

(2.42) . , W VG ND . 2.6 , , (2.39) (2.40).E(x) VG < 0

0 E W 0 x W x

Emax || S

0 W x

. 2.6. , :) ; ) ; )

49

2.9. - - () . E C =2 m min 2

:2 m min = q ( ms VG ) . 2

(2.43)

(2.5) (2.7), :

j

=

4 em*k 2T 2 e h3

EC F kT

e

q (ms VG ) kT

=

1 qnso e VG , 41

(2.44)

8kT 2 , 0 , 0 = m ns ns = n0 e ms , n0 , -

2 m kT 2 EC F kT . n0 = e h2 VG = 0 j j =

3

1 qns0 . 4

. , - : 1 J = J J M = qns0 (e VG 1). (2.45) 4 : 1 J = J 0 (e VG 1); J 0 = qns0 . (2.46) 4 2.7 - .

50

J

J/

Me

JMe

/

= J0

VG

. 2.7. -

- . . . , , . , . - . , . , .

2.10. - -n -, p-n , ( ). p-n : n-Si p-Si, n-Ge p-Ge. n- p-. . p- p , n n-. (2.13) (2.14) , (2.47) = p n = n + p > 0 . n- p- (- 51

) n- p- . n- p- . n- , p- . , . n- p-, p- , n- . p- n-, , . 2.8 , - .Jpn

Jn

p

Jp E=0

n

Jn

p

E=0

pSi

nSiEC F Ei EV

F

EC F Ei EV

p-Si

n-Si

W

. 2.8. , p-n

p-n . , , p-n .

52

2.10.1. p-n p-n , , , NA > ND; n < p. (VG = 0) p-n :

= n + p =

kT N A N D ln . q ni2

(2.48)

p-n .

pp0 = ni e

0p

= N A ; np0 = ni e

0p

=

ni2 ; NA ni2 . ND

(2.49) (2.50)

nn0 = ni e 0n = N D ;

pn0 = ni e 0n =

, 0p 0n x, 0p(x) 0n(x). , x: pp(x), np(x), nn(x), pn(x).

pp ( x) = ni e

0p ( x )

; np (x) = ni e

0p ( x )

;

(2.51)

(2.52) , 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 .

nn ( x) = ni e

0n ( x )

; pn ( x) = ni e

0n ( x )

.

53

IIn0, p0 , , -31018 1016 1014 1012

I

p-Si pp0 = NA-

W

n-Si

nn0 = ND+

1010 108 106 10 104 2

p = n = ni

pn0

np0Wp Wn

p-n p-n

p-

n-

E. 2.9. p-n :

) ; ) ,

, , p-n p-n . , ni.

2.10.3. p-n p-n . : 54

2 ( x) ( x) , = 2 s 0 x

(2.53)

(x) , (x) , s , 0 . p-n . x > 0 ( I), x < 0 ( II). p-n n- ND+, p- NA. I (x) = qND+, II (x) = qNA. I II. I:

E ( x) = II:

+ qN D

s 0 qN A

(Wn x) ,

(2.54)

E ( x) =

s 0

(Wp + x) .

(2.55)

(2.54, 2.55) , x. , . ND = ND+, NA = NA+, . (2.54, 2.55) , p-n (x = 0), (x = Wn; x = Wp). Emax :

Emax =

qN AWp

s 0

=

+ qN DWn

s 0

.

(2.56)

( , ) (2.55) : x = -Wp, (W) = 0. : qN A x 2 ( x) = + Wp x + const , x < 0 . s 0 2

(2.57)

x = Wp; = 0, : 55

const =

2 2 qN A Wp qN A Wp Wp2 + 0 = + 0 . s 0 2 s 0 2

(2.58)

(2.57), (x) x < 0.

W qN ( x) = A x 2 + 2Wp x + p 2 s 0

2

qN A ( x + Wp ) 2 + 0 . = 2 s 0

(2.59)

x > 0, :+ qN D x 2 ( x) = Wn x + const , x > 0 . s 0 2

(2.60)

x = Wn; = 0 :+ + qN D Wn2 qN D Wn2 2 , Wn = const = s 0 2 s 0 2

(2.61)

(2.60), (x) x > 0:

):

qN D 2 qN D ( x 2Wn x + W 2 ) = ( x + Wn ) 2 . (2.62) 2 s 0 2 s 0 , p- (

( x) =

1 ( x) = , n-:

qN A ( x + Wp ) 2 , x < 0, 2 s 0

(2.63)

+ qN D 2 ( x) = ( x Wn ) 2 , x > 0. 2 s 0

(2.64)

2.10 , p-n , (2.54), (2.55), (2.60) (2.62).

56

E p-Si n-Si 0 x1(x)

2(x)

Emax-Wp 0 Wn Wp Wn Wp Wn

. 2.10. , p-n :) p-n ; ) ; )

p-n x = 0 1 + 2 = 0 = n0 + p0, q 0 = ( N AWp2 + N DWn2 ) . (2.65) 2 s 0 : QD = QA ; qN AWp = qN DWn . (2.66) ,

Wn = q

N AW p ND

.

(2.67)

(2.67) (2.65), :

0 =

N W N2 q N AWp2 + N AWp A p = Wp2 N A + A = N D 2 s 0 2 s 0 ND q 1 2 1 Wp2 N A = (2.68) N + N . 2 s 0 D A

Wp Wn p- n- :

Wp =

2 s 0 ; Wn = 1 2 1 qN A N + N D A

2 s 0 . 1 2 1 qN D N + N D A

(2.69)

57

, p- p-n Wp . p-n W, W = Wp + Wn, :

W =

2 s 0 0 q

1 1 N + N D A

.

(2.70)

p+-n ( ) (2.69) , p- , n-: N A >> N D Wp 0

p

n ID = -IS E VG < 0

p

Ei EV

. 2.12. p-n , :) ; )

p-n Fn Fp. Fn Fp VG. p-n (. 2.13).

q(0 -VG)59

EC

q qVG

qVG

Fn - Fp = qVG EC EC Ei VG > 0 Fp EV Lp W Ln Fn Ei EV

. 2.13. , Fn Fp VG > 0

p-n . , Fp - Fn = qVG, nn, pn :Fn Fp

(2.73) .

nn pn = n e

2 i

kT

= ni2 e VG .

nn = nn0 ; pn =

ni2 VG e = pn0 e VG . nn0

(2.74)

2.14 p-n . , , . , (2.74), .. .

60

VG = 0 VG = + 0,25 B (+10 kT/q)1020 1018

VG = 0 VG = - 0,25 B (-10 kT/q)1020 1018

p-

n-

p-

n-

pp0 nn0 , , -3

pp0 nn0

, , -3

1016 1014 1012 1010 108 106 104 102 100 10-2 10-4

1016 1014 1012 1010 108 106 104 102 100 10-2 10-4

p = n = ni pn(x) pn0

p = n = ni

np(x) np0

pn0 np0 np(x)Wp0,Wp Wn0 Wn

pn(x)

Wn Wn0 Wp0,Wp

. 2.14. p-n ( ) ( ) ) (VG = +0,25 ); ) (VG = -0,25 )

2.12. - -n - p-n . :

dp 1 = G R div ( j ) . dt q dp =0. dt

(2.75)

n- p-n (x > 0). G : G = 0. E : E = 0. : IE = 0, -

61

, j = qD

dp . R dx

:

R=

p n p n0

, , : D = Lp2. :

.

(2.76)

d 2 p n p n p n0 = 0. dx 2 L2 p:V

(2.77)

p-n x = 0, p n = p n0 e G ; x , p n = p n0 . (2.78) (2.77) (2.78) : . (2.79) (2.79) n- (. 2.15). p-n , p-n . , (2.79) , (. 2.16):

pn pn0 = pn0 (e

VG

1)e

x LD

j pD = qDp

dp n dx

x =0

=q

Dp p n0 Lp

e VG .

(2.80)

(2.80) p-n , . p-n : D n n p0 VG (2.81) j nD = q e . Ln VG = 0 . (2.80) ,

j pE = q

Dp p n0 Lp

;

j nE = q

Dn np0 Ln

.

(2.82)

p-n p-n : 62

qD p qD n j = p n0 + n p0 (e VG 1) . Lp Ln

(2.83)

p-n . , VG < 0 . Ln Ln/p. :

jn =pn

qLn n p0

n

=

qLn n p0 L2 / Dn n

=

qDn n p0 Ln

.

(2.84)

VG3 > VG2 > VG1 VG3 VG2 VG1 pn0 0 Lp x

. 2.15. p-n

, . (, ), (2.83) , np0 p-. , p- n-: NA >> ND. p-n (. 2.16).

63

p-Si

np(x)

jnD

n-Si

EC F Ei jpD NA >> ND, jpD >> jnD pn(x) EV

. 2.16. p-n n

, p-n : J = J s (e VG 1) . Js :

(2.85)

Js =

qDn np0 Ln

+

qDp p n0 Lp

=

qLn np0

n

+

qLp p n0

p

.

(2.86)

p-n , (2.85), 2.17.

J

J = JpD + JnD

VG J = JpE + JnE

. 2.17. - p-n

(2.85) 2.17, - p-n . p-n . p-n .

p-n 64

, Q, . : C =

Q .

p-n : QB Qp. p-n . p-n CB CD. CB p-n VG < 0, .

CB =

QB . VG

(2.87)

QB p-n :

QB = qN DW = qN D

2 s 0 (0 VG ) = 2qN D s 0 (0 VG ) . qN D

(2.88)

(2.65), :

CB =

2qN D s 0 2 0 VG

=

s 0W

.

(2.89)

(2.89) , CB , W. VG, . , . B VG . , , . VG. . . VG. ND(x), 65

C(VG) , . CD p-n VG > 0, Qp .

CD =

Qp VG

.

(2.90)

(2.79) , Qp .

Qp = q pn ( x)dx = q pn o e0 0

VG

e

x

Lp

dx =

qpn 0 e VG Lp

L2 = p

qpn 0 Dp p Lp

e VG .

(2.91)

, CD

C=

J dQ qpn 0 Dp = p e VG = p . kT dVG Lp q

(2.92)

, .

2.13. , , pGe nGaAs. p-n , p-n , , pSi nSi. , , : () [10, 27, 30]. . Ge, GaAs, InP, InGaAsP. Eg, Eg . 2.18 .

66

1 EC1

2EC

E=0 EC2 EC1 F EV2 EV1 1 > 2 1EC

2

E=0 EC2

EV1 1 > 2

EV

EV

1 - 2 > Eg q

1 = 2E=0

1 - 2 < Eg q

EV2

EC1

1EC

2 EC2

EC1

1EC

E=0 2 EC2EV

EV1 1 < 2

EV

EV2

EV2

1 - 2 < Eg q

EV1 1 < 2

1 - 2 > Eg q

. 2.18. Eg 1 = 2 [61]

, , , , g s. (pGe nGaAs). , , 2.1. pGe nGaAs. : 1. = 0 . 2. Ge GaAs . 3. Eg .

67

2.1. , , 10-6 -1 , -3 , , , , a NA,D W0 (pGe) 5,654 5,9 31016 0,14 0,21 4,05 0,66 (nGaAs) 5,658 6,0 1016 0,17 0,55 4,07 1,43

0 Eg

EC . EC : EC = Ge GaAs . (2.93) V EV. : EV = Ge Eg Ge + GaAs + Eg GaAs = EC + ( Eg GaAs Eg Ge ) . (2.94) , EC EV EC + EV = ( Eg GaAs Eg Ge ) . (2.95) 2.19 p-Ge n-GaAs. ( ), p-GaAs n-Ge (. 2.20). . , EC : EC = Ge GaAs . (2.96) 68

EV. EV : EV = Ge Eg Ge + GaAs + Eg GaAs = EC + ( Eg GaAs Eg Ge ). (2.97)E=0 1 EC 2 EC F Eg1 Ei EV

Eg2

EV

. 2.19. p-Ge n-GaAs

qVD qV1

qV2

E=0

EC EC0 Eg2 F Eg1 EV0 x1 0 x2 x EV

. 2.20. n-Ge p-GaAs

, . 2.21 . , EV, EC [27, 30, 61]. 69

E=0 qVD

E=0 qVD

EC0

ECn

EC0

EC F EVEV0 EVn

ECn

EC F EVEV0 EVn

1 > 2

1 - 2 > Eg q

1 < 2E=0 EC

1 > 2

1 - 2 < Eg q

E=0 ECEC0

qVDECn

qVDEC0 ECn

F EVEV0 EVn

FEV0

EV 1 < 2 1 - 2 < Eg q 1 < 2

EVn

1 - 2 > Eg q

. 2.21. , , (1 < 2), ( )

p-n , s . E, W1n W2p :

E1max =

qN DW1n

1 0

; E2max =

qN AW2p

2 0

,

(2.98) (2.99)

2 2 qN AW2p qN DW1n , V1n = ; V2p = 2 1 0 2 2 0

70

. (2.100) 1 2 2 2 1 + + qN qN A NA ND NA ND W, W = W1n + W2p, :2 D

W1n =

21 2 0 ( 0 V )

; W2p =

21 2 0 ( 0 V )

21 2 0 ( 0 V ) 1 1 + (2.101) . q N A 1 N D 2 0 : 0 = V1n + V2p . (2.102) W= , p-n . 1 2. , , 1 E1 max = 2 E 2 max . (2.103) 2.22 .E(x)

x1

0 V(x) V1

x2

x

V1

V2 V2 x1 0 x2 x

. 2.22. n-Ge p-GaAs

V. p-n , p- . 71

2.23 n-Ge p-GaAs. V = 0.q'b2 qV1 q'b1EC0

qV1 EC q'b1 qV2EC0

q'b2 EC qV2

EV0 EV0

V>0

EV

V 0 V < 0 . V = 0

- . - . , - : J = J s (e VG 1) . (2.104) (2.104) , Js . p-Ge n-GaAs , p-Ge n-GaAs . , Jp Jn :

qLp pn Jp Jn =

p

2 pn ni2 = qLn np n ND p

n

2 2 ni1 ni2 = 2 . N A ni1

(2.105)

, , (ni2) , (ni1), , Jp , Jn. 72

p-Ge n-GaAs . , . , E ~ 106 /. . [1, 29, 30]. , (. 2.24).EC qVn EC F E2 E1 EV qVp F

EV AlGaAs

GaAs

. 2.24.

,

. , , ( , ). . 9.

2.1. ? 2.2. ? 73

2.3. n-. 2.4. ? 2.5. ? 2.6. p-n ? 2.7. . 2.8. p-n . 2.9. ? 2.10. ?

2.1. , n-Ge Au. . = 1 . 2.2. , V = +0,4 , V = 2 n-Si Pt. . 2.3. GaAs Au , V = +0,3 , V = 0 V = 100 . ND = 1016 -3. 2.4. n-Si Au V = 5 z = 1,2 . = 10 . 2.5. , j n-GaAs Pt V = +0,5 V = 5 . ? = 50 . 2.6. p-n n-Ge p-Ge = 2 . V = +0,15 V = 5 . . 2.7. Wn Wp p-n . n = 10 , p = 1 . 2.8. p-n n-Si p-Si = 10 74

V = +0,4 V = 2 z = +0,2 . 2.9. (z) p-n+ n+-Si p-Si V = 1 z = 0,1 . n = 0,001 , p = 4,5 . . 2.10. I p-n V = +0,5 V = 0,5 . : NA = 1016 -3, ND = 1014 -3, S = 1 2. 2.11. n-Ge p-GaAs. ND,A = 1016 -3. 2.12. p-n = 300 K S = 10-3 2 ND = NA = 1018 -3. , 0 10 , 1 .

75

3. -3.1. () 3.1.1. . , , , .. , . , . ND = 1015 -3 , < a >= N D 3 = 1000 . E , . , qN M E= = , (3.1) 2 0 2 0 NM , . , 10 E = 106107 /, NM = 10121013 -2. , 10121013 . , n 1022 -3, , , , . , 105 -3, ( ) . . , NM = 1011 -2 W = NM/ND = 10-4 = 1 . 761

. . , - , , . . . , . , (). , , .. E(x) . , , . , U ( x) U () = E ( x)dx , U() . , , . , 3.1, 3.2, .

x

1 = E ( x)dx . qx

(3.2)

s. (. 3.1) s .

77

E=0

qs

q

q

q0

s < 0

EC F Ei

EV

. 3.1. n-

n p .

n0 = ni e 0 , p0 = pi e 0 , n = ni e = ni e ( + 0 ) = n0 e , p = ni e = ni e ( + 0 ) = p 0 e . ns = n0 e s , ps = p 0 e s .

(3.3)

= q/kT, 0 . n p : (3.4)

ns ps (3.5)

, 4 : , , . 3.2 n-. , , (. 3.2). n- 78 ns > n0 s > 0

p-

ps > p0

s < 0

, , , , (. 3.2).n- p- ps < ns < n0 ns < ps < p0 s < 0 s > 0

0 < s < 0 0 < s < 0

s = 0, . . , , , , (. 3.2). n- p- ns < ps < n0 ps < ns < p0 s < 0 s > 0

0 < s < 2 0 0 < s < 2 0

|s| =0, ns = p s = ni . , , (. 3.2).

79

E

EC

E

EC

q0

qs

Ei

qs

q0

F

F Ei

EV s > 0 s < 0

EV

s < 0 EC

s < 0 EC

qs

q0

Ei

q0

F

qs

F Ei

E

EV

E

EV

. 3.2. n- :) ; ) ; ) ; )

n- p-

ps > n0 ns > p0

s < 0 s > 0

s > 2 0 s > 2 0

s = 20, . . , , , . , , , . 80

3.2. (x), , Qs, p,n, Cs . .

3.2.1. p-:

d 2 ( x) = . 2 0 s dz

(3.6)

(x) , , : + ( z ) = q ( N D N A + p n) . (3.7) , , (x) = 0. + N D N A = n0 p 0 . (3.8) , (3.3 3.5), n = n0 e , p = p 0 e ,

n0 = ni e 0 , (z) :0

p 0 = pi e 0 ,

(3.9) (3.9) (3.6), (z) :

( x) = qp0 [e 2 (e 1) e + 1] .d 2 qp0 2 0 = [e (e 1) e + 1] . dz 2 s 0

(3.10)

, 2.5 (2.23),

d . dz

d d 2 1 d d = . dz dz 2 2 dz dz ,

2

(3.11)

81

qp0 2 0 d d [e (e 1) e + 1]d . = dz s 0 qp0 1 d + 1) + e 2 0 (e 1)] . [(e = dz s 0 (2.23), E ( z ) = 2 2 2

2

(3.12)

(3.12) , : (3.13)

LD

d , : dz

kT 1 + 1) + e 2 0 (e 1)] . E = 2 [(e q LD

(3.14)

F ( , 0 ) [(e + 1) + e 2 0 (e 1)] 2 . (3.14) (3.15) :

1

(3.15) (3.16)

E=.

d kT 1 = F ( ,0 ) . dz q LD

(3.16) . s > 0 ( ), z . s < 0 E z . Es :

Es =

kT 2 F ( s , 0 ) . q LD

(3.17)

Es Qsc, :

Qsc = s 0 Es =

2 s 0 kT F ( s , 0 ) . qLD

(3.18)

, (3.16 3.18), , .

82

3.2.2. (3.18) , , . F(, 0) (3.15). Qsc, (3.18) . (s < 0). p- Qsc Qp,

s >

kT ; q

s > 1 .2 s 0 kT e qLD s2

Qsc = Qp =

.

(3.19)

(0 > s > 0). Qsc QB. (3.16, 3.18) ,

kT = Qsc = QB = 2 s 0 qN A q

2 s 0 kT ( s 1) 12 . qLD

(3.20)

W =

QB = qN A

2 s 0 qN A

kT . s q

(20 > s > 0). Qsc, , QB, Qn 20). Qsc Qn,

Qsc = QW + QB Qn =

s 0 kT2qLD

( s 2 0 )

e

2

.

(3.22)

QB W s :

QB = 2q s 0 N A (2 0

kT ); W = q

2 q s 0 kT (2 0 ) . qN A q

(3.23)

, , 3.2 (3.19 3.22), , 83

. 3.3 Qsc s, .-10 0 10 20 30 s QSC, /2 10-5 40

10-6

NA = 1016 -3 T = 290 K 0 = 0,35 B 20 = 28

10-7

QW

10-8

EV 10-9 -0,4 -0,2 0 0,2

Ei 0,4 0,6 0,8

EC 1,0

s,

. 3.3. s, p-

3.2.3. ( ) Qp,n , 84

, p,n . p

p = ( p ( z ) p 0 )dz ,0

(3.24)

p(z) , p0 . , . p,n . , , . p,n , . (3.24) ,

p = p 0 (e 1)dz = p0 0

e 1 d . d s dz

0

(3.25)

n :

n = n0

e 1 d . d s dz

0

(3.26)

p,n , . (3.25, 3.26), (3.15), |s| > 3 :

p = n =

s 0 kT2 q 2 LD

e

2

, .

(3.27) (3.28)

s 0 kT2 q LD2

e

2

p,n , (3.25, 3.26). , , , , Qn Qsc QB, : Qn = Qsc QB . (3.29)

85

(3.18) Qsc :

2 kT ( s 2 0 ) e 1 . Qsc = 2q s 0 N A s + q

(

)

1

(3.30)

QB (3.20) (3.23), Qn :1 2 1 kT 2 kT e ( s 2 0 ) 1 , 1 + Qn = 2q s 0 N A s kT q q s q 1 kT 2 1 2 ( s 2 0 ) 2 0 q kT kT e 1 + Qn = 2q s 0 N A s kT q q kT s s q q

(3.31)

1

2

.

(3.32) (3.32),

(1 + x ):

1

2

x 1 + , x 7 : . (3.34) , (3.33) Qn (3.22). n = Qn/q :

Qn = [2kT s 0 N A ] 2 e1

( s 2 0 )2

86

n = Cp

kT ( s 2 0 ) e , q21

(3.35)

, , = (110) n(s = 20) = (1091010) -2. n, , n max = (12)1013 -2 . (3.35, 3.36) , s . 3.4 3.5 Qn n s.10-6 Qn, /2 10-7 1015 10-8 10-9 10-10 10-11 10-12 15 s 20 25 30 35 40 s = 20 ND = 1014 -3 1017 1016

kT 2 ( s 2 0 ) 2 2 s 0 N A e 2 . n = (3.36) q (3.36) s = 20, ..

. 3.4. Qn s, p-

87

1013

n, -2 NA = 1015 -3

1012

1011 1010

80 140 230 320

10

9

108 107 -4 0 4

+(s - 20)8 12

. 3.5. n s, p-

3.2.4. , , c, , , . c :

c =

( z ) zdz0

,

(3.37)

( z )dz0

(z) , . ,

( z )dz = Q0

p, n

(3.38)

88

. ( p- ) c :

c =

s LD . F ( s , 0 )

(3.39)

, (3.39) , c Qsc . E(z) Es. : = s Es z . (3.40) n(z) : n( z ) = n0 e ( s Es z ) = ns e Es z . (3.41) (3.39) (3.41) (3.4, 3.5) (3.18) :

c =

kT 1 = s 0 . qQB E z

(3.42)

(3.42), c s, , . c T . , Qn >> QB, (3.39). c , , (3.37). 3.6 . , c (20300) , . s = 0, c , .

89

, A250 T = 320 K 290 260 150 230 200 100 170 140 110 80

o

NA = 1015 -3 VSS = 0 s = 20

200

50

0 107 108 109

n, -21010 1011 1012 1013

. 3.6. c n . T = 300 p-

3.2.5. 3.2.1 (3.16). , .. (z), (3.16) :

F ( , ) = s

ds

0

kT 1 z. q LD

(3.43)

(3.43) (z) . .

1. : p = n = ni; 0 = 0 (3.15) , F(, 0)

F ( , 0 ) = (e + e 2) (3.44) (3.43), :

1

2

=

1 sh . 2 2

(3.44)

90

z = LD

2kT

q

dz s sh 2

.

(3.45)

, (3.45) :

2z = ln LD

th th

s 4 4

(3.46)

2z s th exp = th L . 4 4 D

(3.47)

(3.47) . (z) z.

2. , (3.15), F(, 0) . :

d1 2

kT s q

=

kT 1 z. q LD

(3.48)

, z = W, .. = 0, :

( z ) = s 1

z . W

2

(3.49)

, (3.49) , . ,

( z) = s

2 s z = s Es z . W

(3.50)

, .

91

3. s, (3.19) (3.22). (z) , . (3.44) (3.15) , > 7

s

e

( 20 )2

d

=

kT 2 z. q LD

(3.51)

(3.51) :

( z ) = 2 0

2kT 2 z + e ( s 20 ) . ln q LD s 2kT 2 z +e 2 . ln q LD

(3.52)

:

( z) =

(3.53)

(z) , .

3.3. Qsc s, Csc. Csc, (3.18), :

C sc

1 e s + e 2 0 e s 1 Qsc . = s 0 F ( s , 0 ) s 2 LD

[(

)

(

)]

(3.54)

, (, , ), (3.54), Qsc, 3.2.2. , p.

(s < 0) Csc Cp:

C sc = C p =92

s 0LD

e

s2

.

(3.55)

(20 > s > 0) Csc CB:

C sc = C B =

s 0 qN A kT 2 s q

=

s 0W

.

(3.56)

(3.56) , Csc s, . Csc . , s, W, .

(s = 0) (3.55) (3.56) s 0, .. . s = 0 (3.55) . CFB (3.55) :

C sc = C FB =

s 0LD

=

s 0 qN AkT q

.

(3.57)

, .

(s > 20) Csc Cn (s 20) 7 :

Cn =

s 02 LD

( s 2 0 )

e

2

.

(3.58)

(3.55) (3.58) , s , s = 20. 93

3.7 Csc s, (3.55 3.58).10 0 10 20 30 40

CSC, /

2

s

10-4

NA = 1016 -3 T = 290 K 0 = 0,35 B 20 = 2810-5

10-6

10-7

EV 10-8 -0,4 -0,2 0 0,2

Ei 0,4 0,6 0,8

EC 1,0

s,

. 3.7. Csc , ( ) ( )

94

3.4. . , , , . p-, 2 kT W0 Eg n0 = N C F 1 W0 = N C e , kT 2 p 0 = N V F1 (W0 ) = N V e W0 , Eg

kT , q

2

(3.59)

F 1 2

1 , W0 2

. n p :

E n = N C F1 g s W0 , kT 2 p = N V F1 ( s W0 ) .2

(3.60)

(3.60) (3.7) (3.6) (z), Qsc Csc . :

2 kT Qsc = s 0 qLDC sc =

e W0 F ( W ) + 1 2 , 3 s 0 s 2 e W0 F 1 ( s W0 ) + 12

1

(3.61)

s 0

1 LD W0 2 e F3 ( s W0 ) + s 1 2

.

(3.62)

Qsc =

2 s 0 kT (Eg W0 2 0 ) e F3 ( s E g + W0 ) + s 1 2 q

1

2

, (3.63) 95

-10

0

10

20

30

40

QSC, /210-5

s

EV 10-6

EC

10-7

10-8

10-9 -0,4 -0,2 0 0,2 0,4 0,6 0,8 1,0

s,

. 3.8. Qsc s p-

1 LD (Eg W0 2 0 ) 2 e F3 ( s E g + W0 ) + s 1 2 F3 ( ) F 1 ( ) : 2 2

C sc =

s 0

e

(Eg W0 2 0 )

F1 ( s E g W0 ) + 12

, (3.64)

96

x 2 dx F3 ( ) = x , 2 3 0 1+ e

4

3

(3.65)

x 2 dx . F 1 ( ) = 2 1 + e x 0

2

1

(3.66)

(3.613.64) s 0 . s 0 , 3.2. 3.8 Qsc, . Csc 3.6.

3.5. 3.5.1. , - , . (). , - (, , , , ), . , , . , , , . , , , . , , . 3.9 , . 97

EC

{

Ei F EV EC

s = 0 QSS > 0

Fs

Ei F EV

s = 0 > 0 QSS = 0

EC Fs Ei s = 20 > 0 QSS < 0

{

F EV

. 3.9. p-,

3.9 , Qss . ( Qss surface states ). , , -, , . . , , , , .

3.5.2. [28, 30, 45]: 98

1) ; 2) ; 3) , ; 4) , . . - , , , , . , , . , .. 1015 -2. , , . , , , , . , , . , . (, , ) . , .

3.5.3. , s. . Fs : Fs = F q s . (3.67) Fs Et, , : E = Et + q0 q s , (3.68) 99

Et , . Et > 0, Et < 0. :

f =

1 1+ eE t Fs kT

=

1 1+ e E t + 0 s q

.

(3.69)

Qss : Qss = qN ss f , (3.70) Nss , .. . Fs

kT , (3.69) f = 1 Qss = -qNss. Fs q , f = 1 Qss = 1 qN ss . , 2 2 kT , f = 0 Qss = 0. (2 3) q

(2 3)

, 3.1, (3.70) . , , Nss(E), [-2-1]. Nss(E) dE = 1 E, Nss(E)dE (E; E+dE). Nss(E) , .. , Qss :

Qss = q N ss ( E ) f ( E )dE = qN ss ( s 0 ) .

(3.71)

(3.71) , 3.9, s < 0 Qss , s = 0 Qss s > 0 Qss . , (3.70) (3.71), s , Css, . : 100

Css =

Qss q 2 N ss = f (1 f ) . s kT

(3.72)

(3.72) , Css(s) , 4

kT q

, s = 0 + Et/q.

f = 1 , 2

Css max =

1 q 2 N ss . 4 kT

(3.73)

Css , (3.71),

C ss =

Qss = qN ss . s

(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. - , -, , , , , .. - , 101

, . - . - , , . , , , . , . - , -. , -, 3.10, , , .1 2

3 4

. 3.10. -1 , 2 , 3 , 4

- . , : ) ; ) ; ) . 3.11 -. - , : - , - , - , - , . 102

3.11, - VG .

qD

M MD

SD

F

VG < 0

EC Ei F EV

VG > 0

EC Ei F EV F EC Ei F EV V,

qn

F

(z)

QM -d W QB Qn z

VG > 0

VSC > 0s > 0 -d 0 W z

. 3.11. - p-:) VG = 0; ) VG > 0; ) VG < 0; ) - VG > 0; ) VG

-, , , , n-Si , p-Si . -, , -, .

3.6.2. VG - s. VG - 103

, , s. , VG = Vox + s . (3.75) (3.75) 3.11 , s, a priori, VG. , n- p-, . VG , s. , QM Qsc, - Qss Qox. QM = Qsc + Qss + Qox . (3.76) Cox,

C ox =

QM , Vox

(3.77)

Vox =

Q Q Q QM = sc ss ox . C ox C ox C ox C ox Qsc Qss Qox . C ox C ox C ox

(3.78)

, ms, :

VG = ms + s

(3.79)

(3.79) , VG > 0, s > 0, Qsc < 0, Qss < 0, .. Vox > 0. VG < 0. , Qss = qN ss ( s 0 ) , (3.80) (3.80) (3.79), :

VG = ms

Qox qN ss Q qN + 0 + s sc + ss s . Cox Cox Cox Cox

(3.81)

VFB (Flat Band). VFB 104

-, , : VFB VG ( s = 0) . (3.82) (3.82) (3.81) :

VFB = ms

Qox qN ss + 0 . Cox CoxqN ss Q s sc . C ox C ox

(3.83)

, VG s (3.83) :

VG = VFB + s +

(3.84)

(3.84) .

(s < 0) Qsc (3.19). (3.19) (3.75), :

VG VFB

qN ss 2 s 0 kT s = s 1 + e 2 . C ox qLD C ox

(3.85)

s (|s| > 1), Qsc >> Qss, (3.85) :

VG VFB

s 0 kTC ox qLD

e

s2

.

(3.86)

s =

qL C 2kT ln (VG VFB ) D ox , q s 0 kT Qsc = Qp C ox (VG VFB ) .

(3.87)

(3.86) (3.87) , , , s VG , Qsc VG .

(0 < s < 20) Qsc QB (3.20). QB s = 0:

QB = QB (

s = 0 )

+

QB * * ( s 0 ) = QB + C B ( s 0 ) , s105

QB*, CB* s = 0. QB (3.84) CB* (3.57), : VG VFB = n s , (3.88)

n = 1+

* qN ss C B . + C ox C ox

(3.89)

(3.88) , s VG , tg =

dVG = n d s

Nss, dox NA.

(s > 20) Qsc , QB Qn . (3.22) Qn, :

VG = ms

kT Qox qN ss qN Q 0 B + 2 0 s + ss s + s 0 e C ox C ox C ox C ox qLD C ox

s2

,

(3.90) s = s 20. VT VG, s 20. VT VG ( s = 2 0 ) . (3.91) (3.90) (3.91) ,

VT = ms + 2 0 VFB

Qox qN ss Q 2 0 B , + C ox C ox C ox QB qN ss 2 0 . + C ox C ox

(3.92)

VT = VFB + 2 0

(3.93)

(3.93) , VT VFB, 20 . s, s > 1, : 106

VG VT

s 0 kTC ox qLD

s

e

2

.

(3.94)

s = 2 0 =

(3.96) (3.95) (3.96) , , , VG, Qn VG. 3.12 s VG, dox.1,0 0,8 0,6 0,4 0,2 0 -0,2 -0,4 -5 -4 -3 -2 -1 0 1 2 3 10

qL C 2kT ln (VG VT ) D ox , q s 0 kT Qsc Qn C ox (VG VT ) .

(3.95)

s ,

dox = 40 Ao

o

s

40 30 20

1000 A

200 A

o

NA = 1,5.1015 -3 T = 290 K Si-SiO2 VG - VFB, B

0 -10 -20

4

5

6

. 3.12. s VG, (3.84) -

3.6.3. - , - C VG, - () C-V . -. 107

- C . ,

C

QM . VG .

(3.97)

QM (3.77) Vox (3.75), :

d s C = C ox 1 dV G

(3.98)

, C - s(VG), 3.12. (3.86) (3.98) , C VG, VG. , (4.14), . . (3.84) VG (3.79) s.

dVG C C = 1 + ss + sc , d s C ox C ox

(3.99)

Css, Csc , . (3.99) (3.98) , :

C ox C = C ox 1 C +C +C ox sc ss

(3.100)

1 1 1 = + . C C ox C sc + C ss

(3.101)

(3.101) -, Cox Csc Css. 3.13 -. , -.

108

COX

COX

CSS

CSC

CB+Cp

. 3.13. -

3.14 C-V - , (3.109).1,0C /Cox

1000 A 0,8 0,6 NA = 1,5.1015 -3 T = 290 K Si-SiO2 200 A 0,2 0o o

o

0,4

dox = 40 A -3 -2 -1 0 1 2

VG - VFB, B 3 4

. 3.14. C-V - p-

3.6.4. - - - . , , , Css Csc, , . , Qn 109

- n . . C-V C-V .

C-V , n (-1 >> n, ), - , (3.99). - , , C-V . (. . 3.14). , C-V . , - VG, I -. , VG (t ) = t , (3.102) I, (3.97),

I =

dQM dQM dVG = = C . dt dVG dt

(3.103)

- C = C(VG), I = I(VG). -1 >> n, =

= 10-410-2 /. - (I 10-91012 ) . 3.15 . , -.

dU (3.103). dt

110

1

C

XY

. 3.15. -:

-

1 , , XY , C -

C-V , - , , (-1 > RH . C ~ - U = U 0 e it , kT . C R : U< q RC =

111

~ ~ U i = = z

~ U 1 R + 2 2 C2

~ C (VG )U .

(3.104)

2 R1

1

R2

C R XY

. 3.16. -

-

U RH : (3.105) , URH -. , Y, -. VG VG - X , - . - .

~

~ U RH = iRH = URHC (VG ) .

3.6.5. - C-V - -: (n- p-); ; - ; ; 112

. .

- . , 3.13, C-V - . - . , C-V , , n-, C-V , p-. 3.17 n- p- . , , - Cox, :

C = C ox =

ox d ox

,

(3.106)

ox .1,0

C/Cox0,8

p- Si VFB = -0,9 NA = 1015 -3

CFB

0,6

n- Si VFB = -0,25 ND = 1016 -3

0,4

0,2

dox = 1000 A T = 300 K Si-SiO2-Al-3 -2 -1 0

VG, B1

0

. 3.17. -, n- p-

113

, :

d ox =

oxC ox

,

(3.107)

, Cox , .. . (3.107) , .. S -. 3.14, VG VFB (2 3) - C 2-3% . dox < 100 , VG , 10 %.

C-V -: Cmin CB Cox.

1 1 1 = + . C min C ox C B

(3.108)

Cox (3.106) (3.57), :

C min =

ox 0 . s d ox + W ox2

(3.109)

(3.109), (1.67) , :

kT C ox 2 2 0 C 1 q min . NA = C s 0 q ox

(3.110)

3.18 Cmin/Cox dox Si-SiO2 NA . 3.18 , , . NA 114

z C-V , . , . s > 20, , . - , , Vox , .. Vox 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. - . .

, , - - 116

. 3.19 C-V .C/COX 0,8-6 -5 -4 -3

VFB

-2 -1 0 2

CFB

VG 0,6

0,4 T = 295 K NA = 1,5.1015 -3 Si-SiO2-Al 0,2. f = 1

4 6 8 12

.

16 20

0

-4

-3 VFB

-2

-1

0

1

2

VG, B 2 1012

NSS, -2.-1

1 S 0 10 20 1011 EV F Ei EC

0 -10

. 3.19. :) - Si-SiO2-Al; ) VG s, C = const -; ) E , VG(s) (3.115)

, s. C = const, s. 117

VG C-V , ( , s), (3.84):

VG = VG VG = VFB +

qN ss s. C ox

(3.114)

(3.114) :

N ss =

ox 0 d (VG VG ) . qd ox d s

(3.115)

, (3.114), , . , Nss E . 3.19 VG(s), 3.19 , .

, , - . C-V (3.98),

d s C . = 1 dVG C oxVG

(3.116)

(3.116) s = si, VG = VGi, :

s si = 1 C dVG . VGi

C ox

(3.117)

C(VG) , (3.117) ( ) VG. s1 VG1 . s1 (s1 = 0) VG1 VFB. C-V . VG(s), (3.99) :

N ss = ox 0 qd ox

C

C ox C sc . 1 C C ox C ox

(3.118)

118

(3.118) , .

C, 100

.

= 10-2

CFB (S = 0)

80

60

.

= 106

. .

40

Si-SiO2 ND = 1015 -3 o dox = 1400 A

20 -14

-12

-10

VFB

-6

-4

-2

0

S, B-0,8 -0,6 -0,4 -0,2 0 0,2 -12 -10 -8 1012

NSS, -2-1

VG, B1011 -6 EV Ei F EC

. 3.20. :) - Si-SiO2-Al; ) s VG, (3.117); ) E , (3.117)

(3.117) , (1 - /ox) C-V . C Cox , , 119

C-V . 3.20, , C-V .

, , VFB - T. . 0(T), 0(E), . (3.83) VFB ,

VFB (T1 ) VFB (T2 ) =

qN ss [ 0 (T1 ) 0 (T2 )] . C ox

(3.119)

(3.119) Nss:

N ss =

ox 0 d (VFB ) . qd ox d (0 )

(3.120)

, Nss . T = (77400) , . 3.21, , C-V , .

120

C/COX 0,8T=400 K 300 200 100

0,6 0,4 0,2 0 -0,8 CFB Si-SiO2-Al ND = 1015 -3 o dox = 50 A VG, B 2,0

-0,4

0

0,4

0,8

1,2

1,6

NSS, -2-1

EC ED F EiT = 400 K T = 100 K

EC ED 12 F 10 Ei1011

0(T = 100 K) 0(T = 400 K)

EV

EV

EV

Ei

EC

. 3.21. :) - Si-SiO2-Al T; ) VFB 0 ; ) Nss E , (3.120)

3.7. -3.7.1. - , , Qox, dox, ND,A, 121

-. s,

VG = ms + s +

Qox qN ss Q ( s 0 ) + sc , + C ox C ox C ox

(3.121)

. , , Qox, dox, ND,A , , . , VG s . s VG - [28, 41]. , - , . , -. , - dox W. - , -, s . - (3.121). . - , . , Nox = 1012 -2 a = 100 . ND = 1015 -3 a = 1000 . , , . . 122

(3.121). .+10 +4 +2 2 0 3 12 11 10 9 8 7 6 5 4 3 2 1 80 60 4 20 0 20 40 60 0 80 100 40 +2 +4 +10 +20 100s, kT/q

C,

100 80 60 12C,

40 0 20 40 60 80 100 0 20

11 10

7 6 5C,

100 80 60 40 0 20 40 60 80 100 0 20

4 3 2 1

. 3.22. -:) , ; ) , dox; ) , . () .

123

3.22 - , (0,1x0,1) 2 . , C, , s, . . , C G -. s s -.

3.7.2. Qox = qNox. dox ND,A, 3.22, , . , P(s) s . N , s. s , -, . N , P(N) :

N Qox :

P ( N ) = (2N )

1

. (3.122) s 2

e

( N N )2 2N

N=

s Qoxq

.

(3.123)

(3.122) (3.123), P(Qox):

124

2 s (Qox Qox ) q P (Qox ) = exp . 2qQox 2 s Qox :

1

(3.124)

P ( s ) = P (Qox )

dQox . d s

(3.125)

(3.121) ,

Qsc = C sc , qN ss = C ss , , dVG = 0, s dQ = (C ox + C sc + C ss )d s ;

VG s, :

Qox Qox = (C ox + C sc + C ss )( s s ),

(3.126)

Qox , s Qox s. (3.125) P(s) (3.126) (3.124), :

1 2 P ( s ) = e 2 2 s

1

( s s ) 2 s

,

(3.127)

s =

q kT

:

qQox s = C ox + C sc + C ss s

2 .

1

(3.128)

, s s , :

kT 1 = s = q C ox + C sc + C ss

qQox

2 .

1

(3.129)

(3.128) , . dox, Nss, Qox . s, (3.128), . 125

Gp/ , s - (. 3.23).1,8 1,7 1,6 1,5 1,4 1,3 1,2 W, 10-5 1,1 0,6 0,7 0,8 0,9 1,0 1,1 1,2 1,3 s, 10-5

. 3.23. s W

3.7.3. , , . a . N 0 = a 2 , N ox . dox, a = N ox 2 . s :

P ( s ) =

1 2 s

e

( s s ) 2 2 2 s

,

(3.145)

s s . (3.141 3.144) , P(s) , 3.7.5. n , , . . 3.28 s - dox = (501000) . , . 133

30 100 200 24 49 100 1,0 0,8 0,6 0,4 0,2 0 100 200 f

500 235

1000 dox, A 455 ,

o

Si-SiO2-Me NSS = 1011o-2 z = 50 A

300

400

500 U,

. 3.28. f -

, dox . . 3.29 N ox .

0,3 1,0 8,0 24 1,0 0,8 0,6 0,4 0,2 f

3,0 68

10,0 250

Nss, 1011 -2 ,

Si-SiO2-Me o dox = 50 A o z = 50 A

U, 0 100 200 300 400

. 3.29. f -

, N ox , N ox . 134

3.30 . , , , , . , s , , r r.n 1500 = 1,0 = 0,01 1000

Si-SiO2-Me dox = 50 A NSS = 1011-2

500

U, 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 N ox 2 d ox q ( , d ox ) = ln1 + 2 + 2d . (3.146) ( s + ox ) 0 2 ox ox s , (, dox) . 135

1

1

3.31 () . , . () . , , ., 30 dox=1000 A 500 20 200o

74 10 50

, A 20 40 60 80100 200 400 600 800

o

. 3.31. , dox

(3.146) , 0 . , r 0 . , P(s) . , . , , . min = (5100) (3.136) min. 136

(, dox) U(, ) (3.141) (, dox) (3.136) . (, dox) (3.152). - , :2 2 N ox ( s + ox ) 0 q ( , d ox ) = , ln 1 + ( s + ox ) 0 4 (C ox + C ss + C sc ) 1 2 1

(3.147) Cox, Css, Csc , , . (3.147) . (3.147) :

N ox q ( , d ox ) = ( s + ox ) 0 4

1

2

+ d 2 s ox ox ln 1 + . (3.148) ox

>> dox (3.148) (3.146) ~ -1 2 . ~ dox () .

3.7.8. , -. Nox. . L, , . , , , . - . 137

, . , , , . :

=

Qox qN ox = . S S

(3.149)

N

N = N = N ox S = L N ox ,

(3.150)

N S L, N ox . , L. , U, , , :

L U= * 2 0

2 1 . L L

(3.151)

U0 = 0 :

U0 =

L . 2 * 0

(3.152)

(3.151) (3.152), U0 U0 ~ L. (3.149) (3.150) :

q[N ox ] 2 . U0 = 2 * 01

(3.153)

(3.153) , U0 L, N ox . . (x, y), :

( x, y ) = 0 sin 138

x y sin . L L

(3.154)

, , :

( x, y, z ) = (x, y, z) .

( x, y , z ) , 0 *

(3.155)

(x, y, z):

( x, y , z ) =

2 ( x, y ) L exp 2 , * 4 0 L

(3.156)

L , , . , -, U, :

U =

2 ( x, y ) L ( + 2d ox ) exp 2. * L 4 0

, 3.32, :

U ( x, y , z ) =

2 ( x, y ) L + 2d ox 2 . exp 2 exp L 4 * 0 L (3.157)

3.32 U(x, y, z) , (3.157).

139

1,0 0,8 0,6 2dox 0,4 0,2 0 U 1 - 0,2 - 0,4 - 0,6 - 0,8 - 1,0

U/U0 2 2 U U 1 100 2 200 U

, A300o

o

dox = 50 AL1 = 200 A o L2 = 1000 Ao

. 3.32. U/U0 -

3.33 L. , , .1,0

U/U0

6 4 0,1 5

2 1 3 , A 102 103 1040

0,01 101

. 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

140

3.34 L dox .1,0 U/U 0 1000 Ao

200 A 0,1 = 50 A 100 A 200 Aoo

o

o

o

dox = 50 A

o

0,01

L, A 10 0 10 1 10 2

. 3.34. U/U0 L dox

, U L . (3.157) , L, (U/U0)max, :

L =

2 2d ox + 2d ox ln

.

(3.158)

3.35 L, (3.158) . L ~ dox, L >> dox.

141

10 4

L, A

o

= 200 A 10 3 100 A 50 A 20 A dox, A 10 2 10 1 10 2 10 3o o o o

o

. 3.35. L, U/U0, dox

3.7.9. U(), (3.157) L, (). , L U0 , (3.123). , , L = L, (3.158). U0 , U . . 3.36 , . , U . , dox , , . 0, , 142

, , U0. U L 3.34. , , .

Lmin a = N ox 2 . N ox = 10 Lmin 1000, N ox = 1012-2 Lmin 100.30 25 20 15 10 5 0 1 10o

1

(3.159)

10

-2

U, u,

1000 A 200 A dox= 50 A , A 10 2 10 3o o

o

. 3.36. U0 U

, . -: Lmax L. , Lmin Lmax. , (3.158). - - RC-, . 143

. . . dnn Csc s dnn. :

C sc =

sd nn

.

(3.160)

dnn . p,n dnn , 3.36, . , 3.36, . -, (p) T = (77350) , = (200300) . , 3.35, , - . - , .

3.1. = 15 , = 300 K. 3.2. LD Si, Ge, GaAs, InSb .

144

3.3. ns, ps n-Si c = 1 s = 0,3 ; 0,2 , 0,5 , 0,9 B. . 3.4. Qsc Csc 10 s, s = 0; 0, 20. 3.5. c, p-Si = 0,1 . s =

3 0 2

= 300 K = 77 . 3.6. Si, Ge, GaAs InSb T = 300 = 77 . 3.7. n-Si s = 20 NA = 1016 -3. lc Ni = 77 . 3.8. , Qss : s = 0; s = 0; s = 20 p- = 300 NA = 11018 -3. Nss = 2.1012 -2-1. Qss Qsc . 3.9. n-Si = 7,5 . () Ns = 8.1012 -2 t = 10-16 2, Et = 0,45 . , Cs Rs s, , = 300 . 3.10. Nss - p-Si Si3N4 Si(/) , NA = 1,51015 -3, S = 0,5 2, dn = 1,210-5 ,

=

3.11. Nss, = 2.105

C . = 42 V

Gp

Gp

= 2 109max

. 2145

t, ns0 ns0 = 11012 -3. 3.12. - - p-Si SiO2 Al, dox = 150 , NA = 1,5105 3, T = 300 K Nox = 41011 -2 Ns = 61011 -2 0,1 .

146

4. . , , - . : p-n , , , .

4.1. p-n . 2, - , 4.1, (4.1). , . . , , .

147

210

1,53

M5

14

2 10 11,5

2 11

J

8,8

4

20

pD nD

J=J +J

VG J = JpE + JnE

. 4.1. :) ( ); ) - ; )

J = J s (e VG 1),jpE jnD + jnE jpD = 0.

5,35

(4.1) (4.2)

, , .

4.1.1. p-n - : . . 4.2 , .

148

I V +VG

I, V

4 3 2 1

R

V t

V-3 -2 -1 0 1 2

VG, 3

t

. 4.2. , [60, 68]

, p-n . (4.1) U = 0,01 ; 0,025 ; 0,1 ; 0,25 ; 1 B. :

K=1

, -1 = 0,025 . .VG, B K, . . 0,01 1,0 0,025 1,1 0,1 55 0,25 2,3104 1 2,81020

e VG 1 J+ = V . J e G 1

(4.3)

(4.3), , VG , kT/q, . VG 4 , kT/q, = 300 VG = 0,1 .

4.1.2. : rD RD.

rD =

1 dU dI kT / q 1 V = = js e + js js = [ ( I + I s ) ] = I + I . dI dU s

1

(4.4)

- rD . , I = 25 149

kT/q = 25 rD rD = 1 . - rD , . RD VG I :

RD =

U U = . I I 0 (e U 1)

(4.5)

- , RD > rD, RD < rD. VG np0

np < np0

Fn Fp

Fp Fn

R>G

R 0) pn , p1n1 (pn > p1n1). , 4.7 , dn/dt . , . (VG < 0) , . .

153

4.3.1. p-n (VG < 0) p-n 2.73 , pn = ni2 e kT = ni2 e U 0) p-n 1.20 , pn = ni2 e U >> ni2 . (4.16) 4.7 1.20 , (VG > 0) pn , p1n1 (pn > p1n1). , Et Et = Ei. p1 = n1 = ni, : n = p. 4.7 :

N t ni2 e U dn = . dt n + p + 2ni

(4.17)

(4.17) ,

dn dt

, . , , 0 n,p Ei Fn Fp 0 n,p = VG/2. 4.17 VG

2ni e156

2

.

, :

dn 1 = N t ni2 e dt 2

VG2

.

(4.18)

4.7 p-n , p-n . - p-n . J W :

J = q0

W

VG dn qW N t ni e 2 . dx = 2 dt

(4.19)

:

J = J + J =

qLp ni2

p ND

e

VG

qW N t ni e 2

VG2

.

(4.20)

(4.13) , U

J ~ e n , n = 1 , n = 2 . 4.7 , ( 1) . - ( 2). 4.7 , 2

dU d (ln J )

0,028 ,

kT/q, 0,026 , 1 .

157

I, 10-2 10-4 2

JnD EC Ei Fn Jn

10

-6

1 10-8 10-10

VG > 0

Fp EV Jp U, JpD

0

0,1

0,2

0,3

. 4.7. p-n :) (1 ; 2 ) [56 59]; ) p-n .

4.3.3. p-n , . r, : r =

l , S

, l , S . = 1 , l = 10-1 , S = 10-2 2, r = 10 . U I : U = Ir . (4.21) , p-n , V. (4.21) - : I = I 0 (e (U Ir ) 1). (4.22) (4.22) , p-n , , , . 158

, , : 1 1 dI r = (4.23) = [ I ] = I = r . dU , , - , : I = T/r. r = 10 ; = 0,025 : I = 2,5 A. 4.8 , , .I, 2925

VGIDp-n

100 80 60

T=+1000C +250C -600C

rS rSID

40 20

0

0,2

0,4

0,6 0,8

U, rSID

ln(ID ())

ID,

8 6 4 2 0 0,5 0,6 0,7 0,8 0,9

-5

-10

rS = 0 rS = 15W

-15 0,5

0,6

0,7

0,8

0,9

VG,

VG,

. 4.8. , - [60, 62, 77]:) ; ) ; ) ; ) 2925

, - , , , rI. 2925 , . , 159

.

4.3.4. , , . (. 4.9). : J = J s (e VG 1) . p-n+ NA > pn0. Eg Eg n2 np0 = i ~ e kT , ni = N C N V e 2 kT . nn0 I 0 = const e kT . 1 1 T ~ , : T T T : I 0 (T ) I R (T )eT . (4.24) : Ge = 0,09 -1 T = 700, Si = 0,13 -1 = 1200. . (4.24) , Eg

I 0 (T ) = I 0 (T0 ) 2 T * =

T , T*

(4.25)

(4.25) T* = 10 : 10 . [51, 52]

ln 2 , a : T* = 10; 8; 7; 5, = 0,03; 0,07; 0,1; 0,13.

160

I, 20 16 12 8 4 107(,)+60 C +25 C -60 C0 0 0

I, 107(,) 300 200 100+25 C0

I, 60 107(,) 50 40 30 20 -60 -30 0 30 T, C0

+60 C -60 C0

0

0 0,2 0,4 0,6 U,

0 5 10 15 20 U,

. 4.9. - 107 [77, 80]:) ; ) ; )

4.4. , - - . , 4.10.2156

0,6

28

12

4

28

J

V J . 4.10. (), - () ()

VG

161

, U, . R , R : R 250 . , . , . . U , . , , p-n . U 5 : U < 5 . 8 : U > 8 .

4.4.1. . p-n , (. 4.11).

n

p EC Ei F EV VG < 0

. 4.11. p-n

162

- , , , , . p-n . 4.12 .

I

II

III

. 4.12.

? ? ? H = E , H

? H =

2 + U ( x) , . 2m x 2

2

2 =

2m2

E; =

2m2

( Eg E ) .

(4.26)

:

d 2 + 2 = 0 . 2 dx

(4.