Твердотельная электроника 5-8021-0319-1, 5-8021-0319-1

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«

» « »

. .

2004

22.37 539.2 957

: . .,

-

,

,

. . . . .,

;

, (

)

, . . :

957

.

/ . .

;

.–

, 2004. – 312 . ISBN 5-8021-0319-1

,

. ,

.

,

-

, . ,

,

,

-

. . К 22.37 К 539.2 © . . © ISBN 5-8021-0319-1

2

, 2004 , 2004

........................................................................................10 Я

1.

............................. 12 1.1.

..................................................................12

1.2.

...................................................................13

1.3. 1.3.1. 1.3.2.

....................................15 .................................................15 ......................17

1.4. К

..........19

1.5. К

............21

1.6.

............................................................22

1.7.

........................................................................23

1.8.

......................................................................................24

1.9.

.....................................................................................25

1.10.

................................................................................28

2.

, P-N ........................................................... 29

2.1.

..........................................................................29

2.2. 2.3. Э

p,

35

2.5.

2.7.

........32

.......................................33

2.4. К

2.6. К

n-

......................................................................36 –

.

.......................................37 ..................39

3

2.8.

......40

2.9.

-

........................................42

2.10. 2.10.1. 2.10.3.

-n

p-n

.............................................44 p-n ..................................45 ...................................................................47

2.11. К

-n

2.12.

-

2.14.

-n

.............................50 ..............................................53

....................................................................................................58

3.

-

3.1. 3.1.1.

(

)

.................. 66 ..........66

......................................................................................66 3.2. 3.2.1. 3.2.2. 3.2.3. 3.2.4.

......................................................71 ..........................................................................71 ...........................................................................73 ............................................................74 .................................................................................................78 ...............80

3.2.5. 3.3.

....................................................82

3.4.

................85

3.5. 3.5.1. 3.5.2. 3.5.3. 3.6. 3.6.1. 3.6.2. 3.6.3. 3.6.4.

...................................................................................87 .....................................................................................87 ................................................................88 ..............................................................................89 -

...........................................91 ........................91 ...................................................................94 ....................................................................................98 ....99 C-V ...................................................................................100 C-V ..........................................................101 ...........................................................................................102 -

3.6.5. C-V 3.6.6.

–

4

.........................................................................106

3.7. 3.7.1. 3.7.2.

....................111 ...........................................111 .......................................................................................................114 , .........................................................................116 , , ...................................................................................................117 ................................................................................................................121 ...123

3.7.3. 3.7.4. 3.7.5. 3.7.6. 3.7.7. -

..............................................................................................125 ..........................127

3.7.8. 3.7.9.

..........................................................132

4.

..................................... 135 .......................................................................................................................135

4.1. 4.1.1. 4.1.2. 4.1.4.

p-n .........................135 .....................................................................................136 ..............................................................137 ...........................................................................138

4.2.

..............................................................................................................139

4.3.

, ....................................................................139 p-n .........................................................................................140 p-n ............................................................................................142

4.3.1. 4.3.2. 4.3.3. 4.3.4.

...........................................................................................................................144 .......................................146

4.4.

......................................................................................................147

4.5.

..................................................................153

4.6.

..................................158

5. 5.1.

Я

......................................... 163 .

...................................................................163

5

5.2. 5.2.1.

...................166 . ...........................................................................................................................167 –Э

5.3. 5.4.

..................................................................................169

...................................................................................................................171

5.5. ........................................................................................................172 5.6. К

.....................................................................................173

5.7. К . .................................................................................................................................174 5.8.

.........................177

5.9.

.....................178

5.10. К

..........................................................................180

5.11.

........................................................................182

5.12.

.................................................................................183

5.13.

................................184

5.14. Э

........................................187

5.15.

.

5.16.

..................................................................................191

5.17.

. ......................................196

h-

................................................................................................................196

5.18.

......................................201

6.

................................................ 213

6.1.

................................214

6.2.

................................................217

6.3. Э

6

.............................................189

.............................................................................219

6.4.

............................................................................221

6.5. Э

-

6.6.

......................223 ..................225

6.7.

-

......................................226

6.8.

.................................................................228

6.9.

................................................................229

6.10.

................231

6.11.

-

6.12.

...............................................................................................235

-

6.13.

...........................................................240 -

............................................................................................242

6.14.

...................................................................244

6.15.

..........................................................................246

6.16.

-n

6.17.

-

6.18.

...........254 -

7.

...................................................257

......................................................................... 261

7.1. 7.2.

......................................................252

,

6.19.

..................................248

...................................................................................................261 -

..................................................263

7.3.

............................................264

7.4.

....266

7.5.

α

..........................268

7.6.

VG. ......................................................................................269

7.7.

.............................................................................................................270

7

7.8.

..........................................271

8.

..................................................................... 273

8.1.

...................................................................................................273

8.2.

.......................................273

8.3.

.................................................................276

8.4. .............................................................279 8.5.

-

...................................................284

Я

9.

Я .............................. 287

9.1. ..........................................................................287 9.2. ................................................................................................................292 9.3.

..........................................................296

9.4. ....................................298

Я .............................................................. 301 Я

.................................. 304

.......................................................................................308 1. 2. 3.

..................................308 (

)...........................................................................308

.........................................................................................308

................................ 309

8

9

«

»

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, . 071400 «

» -

. .08 «

». , ,

,

-

. . 510400 «

»

510403 – 510404 –

: ;

.

. »,

553100 « 553105 –

:

,

-

; 553117 –

. 552800 »

« :

552826 –

;

552824 –

010400 « 071400 « 220200 « »; 190900 «

. »; »; -

-

». , p-n

,

,

-

. ,

, -

10

. . , ,

-

-

, -

. .

-

. –

– -

. . ,

. , , . «

»

-

. . , ,

.

,

-

. -

, . , , .

.

-

. . -

.

11

1.

1.1. . , .

,

N

,

.

N,

,

,

. ,

. . -

,

[1]. .

,

,

-

. (

) . , (0,1 ÷ 3,0) ,

3

,

Eg ,

,

.

, ,

,

. , -

1.1 , . ,

, . .

EC, – Eg . 12

– EV,

щ

. -

,

,

ρ=

σ

1

σ > 106

.

σ

,

10-8

⋅

⋅

,

, (

> 10 8

⋅

106

: . .

),

σ < 10-8

⋅

g

>3

,

-

,

.

.

χ

. 1.1.

, , [2]

1.2. ,

,

-

. – (

).

, (ni) –

13

n =0 (n = p = 0).

( n = p = ni).

p,

>0 . .

– 1023

( .

–

,

-3

. ( -

)

,

–

), . –

,

-

. 4

( 5

,

,

),

,

( ),

.

n-

3

-

,

-

,

( -

)(

. 1.2).

Зона проводимости

Eg

Eg Валентная зона

+4

+5

+4

+3

+4

а

+4

б

. 1.2.

n-

( )

p-

( )

,

-

,

a=

mn*

mp*

.

dp =F, dt

F , m* (

mn* (p = mn*·υ).

, ) m0 -

[3, 4]. 14

1.3. –

,

,

.

,

.

-

. :

-

– – . 1.3.1.

. dpx, dpy

dpz:

dx ⋅ dp x ≤ h , dy ⋅ dp y ≤ h ,

(1.1)

dz ⋅ dp z ≤ h .

.

dp = dp x ⋅ dp y ⋅ dp z

dp ⋅ dV ≤ h 3 , dV = dx ⋅ dy ⋅ dz ,

(1.2) dp –

px, py, pz, dV –

, .

dV – .

.

-

( dp ≤ h .

)

dV = 1

3

(1.2)

.

3

dp = h , “

, h3 –

3

. -

”

, ,

. dp ,

dp – h3

, “

”

dp.

-

15

.

–

( (px, py, pz) (

–

. 1.3 ). p.

,

dp

( . dp

p :

dN =

. 1.3 ).

4πp 2 dp . h3

(1.3) py

E

dE

p

E

dp pz

0

EC

N

а

б

. 1.3.

:

)

; )

+d , N(E)dE,

E = EC + C

–

dE = (1.3),

16

. 1.3 ). -

. .

N(E)

p2 , 2m n

(1.4)

,

p ⋅ dp , mn

dp =

mn ⋅ dE p

mn

dN = N ( E )dE =

. .

p 2 = 2mn ( E − E C ) .

4πm 3 / 2 2 (E − E C ) h3

1/ 2

dE

.

(1.4)

-

(1.5)

N (E) =

4πmn3 / 2 2 (E − E C ) h3

1/ 2

.

(1.6) ,

( –

C)

( V – ), (1.6),

-

mn –

mp.

. 1.3.2. К ,

, –

,

.

,

f (E , T ) =

:

,

-

–

1 . ⎛E−F⎞ 1 + exp⎜ ⎟ ⎝ kT ⎠

F –

(1.7)

,

.

(1.7)

, ,

½. –

1.4.

=0

.

1, E>F

E kT).

(1.7)

–

.

⎛ E−F⎞ f ( E , T ) = exp ⎜ − ⎟. kT ⎠ ⎝ :

n = 2 ⋅ ∫ N C (E ) f (E , T )dE . ∞

(1.8) : (1.9)

EC

17

E N(E)

EC ED

N f3

EC - F

f2 F

fБ

f1 f2 f3

EV 0

0,5

1

f

. 1.4.

N(E), –

f

f

, . f

E>F .

E, .

(1.9)

(1.6)

(1.8).

⎛ E −F⎞ n = N C exp⎜ − C ⎟, kT ⎠ ⎝

:

⎛ 2πmn kT ⎞ N C = 2⎜ ⎟ 2 ⎝ h ⎠

(1.10)

3/ 2

.

(1.11) -

NC . , 2kT, F – EC > kT), :

18

⎛ F −E⎞ f p = exp⎜ − ⎟, kT ⎠ ⎝

F – EC > 2kT ( –

fp (1.12)

⎛ F − EV ⎞ p = N V exp⎜ − ⎟, kT ⎠ ⎝ EV –

(1.13)

,

, (1.11),

mp.

NV – ,

-

NV

mn .

(1.9)

2,

-

, ( n

). (1.10)

p

(1.13)

-

F. , :

n ⋅ p = (ni ) 2 = N C ⋅ N V ⋅ exp(− ,

n

Eg kT

).

(1.14)

p ni

p.

n

,

-

.

1.4. К ,

,

-

. ,

n=p(

. 1.5).

. 1.5.

(

,

. .)

,

n0

p0

.

n0 = p0

(1.14)

:

19

⎛ Eg ⎞ ⎟⎟. n0 = p 0 = ni = N C ⋅ N V exp⎜⎜ − ⎝ 2kT ⎠ ,

(1.15) -

ni .

NC

(1.11).

NV

(1.15), .

1.6 -

–

1

10

-3

. 0,6 ni

,

,

, 2,8 1013

.

. 1.6. – [2, 5]

20

,

,

-3

1.5. К (1.14)

,

n 0 ⋅ p 0 = ( ni ) 2 . .

,

(1.16) ND. -

n0 = N D .

.

p0 =

(

. 1.7) (1.17) (1.16):

2

ni . ND

(1.18)

1.7

n, ED p0

n0

-

.

. 1.7.

n-

NA,

p0 = N A

p0

n0 =

n0 2

ni . NA

(1.19)

1.8

pp0

, EA n0 -

.

21

. 1.8.

p-

1.6. ,

.

, p–n=0 mn

-

p = n. (Eg

kT) , F – EV > 2kT)

mp (EC – F > 2kT . (1.10)

-

⎛ F − EC ⎞ ⎛E −F⎞ N C exp⎜ ⎟ = N V exp⎜ V ⎟. ⎝ kT ⎠ ⎝ kT ⎠ (1.13)

p + pD – n – nA = 0,

F kT

: (1.20)

(1.20) –

F.

e

.

⎛N 1 F = Ei − kT ln⎜⎜ C 2 ⎝ NV

⎛ m* ⎞ ⎞ 3 ⎟⎟ = Ei − kT ln⎜ n* ⎟, ⎜m ⎟ 4 ⎠ ⎝ p⎠

(1.21)

Ei = ½(EV + EC)

. (NC/NV)

F (mn/mp)

(1.11). mn* = mp*

F = (EC + EV)/2. ,

.

n

(1.10)

F n-

22

-

.

:

(1.13).

,

p, -

⎛N ⎞ F = EC − kT ⋅ ln⎜ C ⎟ . ⎝ n ⎠

(1.22)

⎛N ⎞ F = E V + kT ⋅ ln⎜ V ⎟ . ⎝ p ⎠ (1.22

1.23)

p(1.23)

,

.

,

⎛N ⎞ F = EC − kT ⋅ ln⎜⎜ C ⎟⎟ . ⎝ ND ⎠

(1.24)

⎛N ⎞ F = E V + kT ⋅ ln⎜⎜ V ⎟⎟ . ⎝ NA ⎠

(1.25)

n0 = ND (1.17),

p0 = NA (1.19),

1.7. . –

σ = σn +σp .

– n

: -

p

σ n = μ n n 0 q; σ p = μ p p 0 q , :

n

p

–

[6, 7]. ,

,

σ = σn +σp = σn . , :

ρ – [

·

].

(1.26)

.

,

(1.27) ,

ρ=

σ

1

=

1 1 . = σn +σp σn , ,

n-

(1.28)

23

ρ = (1÷10)

·

, . (1.10)

1 1 = = , ρ= σ n μ n n0 q μ n N D q 1

(1.11),

ND –

,

nn0 .

:

-4,5. ,

,

. ,

·

.

,

-0,2 –

,

ρ = 0,2

, ,

, ·

;

,

ρ = 4,5

·

,– -4,5 – ,

[8].

1.8. ,

,

, .

, ,–

, . :

J = J p + J n = j pE + j pD + j nE + j nD , _

r J –

_

_

_

_

_

_

(1.29) _

_

, j nD

, j nE – _

, j pE –

– _

, j pD –

. -

:

j nE = qμ n nE = σ n E;

_

j pE = qμ p pE = σ p E;

_

24

j nD = −qDn

_

_

j pD Dn –

dn ; dx dp = −qDp , dx

Dn =

n

(1.30)

,

kT μ n [4, 9]. q Dp

p.

1.9. .

-

, . ,

.

.

,

,

-

,

. ,

, ,

, (

.

n0

n = n0 + Δn ; p = p 0 + Δp ,

,

p0 –

,

)

. -

: (1.31)

Δn

.

Δp –

(1.32) -

, , :

-

Δn = Δp . ,

(1.33) -

, . , (

)

,

25

. . ,

-

,

. 1.9 G –

, R–

.

n

EC ED G

R

EV

p

. 1.9.

(

)

γ– G = G0

-

R

:

R = R0 = γ ⋅ n 0 ⋅ p 0 ,

R = γ ⋅n⋅ p, .

( n0

(1.34) )

p0 .

(1.30)

(1.14)

:

⎛ Eg ⎞ ⎟⎟, G0 = γ ⋅ N C N V exp⎜⎜ − ⎝ kT ⎠

Eg = EC – EV –

.

(1.35) , G0 .

,

:

dn dp = =G−R. dt dt

( ΔG, ΔR – , 26

) ΔG –

G = ΔG + G0 , R = ΔR + R0 ,

(1.36) : (1.37) -

, R0 = γ ⋅ n0 ⋅ p 0 ΔR = γ ⋅ Δn ⋅ Δp . (1.34), (1.36)

d (Δn) = −γ (n0 + p 0 + Δn )Δn. dt

(1.31), (1.32)

: (1.38) (

t = 0). (1.38)

-

Δn >> n0 + p 0 .

.

(1.38)

:

.

Δp = Δn =

Δn0 –

(Δn )0 , 1 − γ (Δn )0 t

(1.39) . .

n0 = ND, p0 0, .

,

, .

–

,

-

, [6, 5].

. px, py, pz.

-

d

: ( Δp x ⋅ Δx)(Δp y ⋅ Δy )(Δp z ⋅ Δz ) ≥ h .

,

, -

3

Δx ⋅ Δy ⋅ Δz = 1

(Δp x ⋅ Δp y ⋅ Δp z ) ≥ h 3 .

: dz

dτ = dp x dp y dp z :

dz = 2

dp x dp y dp z h3

=

2(m * ) 3 dυ x dυ y dυ z . h3

dn,

(2.1) dz

dn = f (E , T )dz .

f(E,T):

–

–

.

(2.2) -

, 29

(E – F >> kT),

-

f 0 (E , T ) =

:

1

e

E −F kT

,

−1

≈e

J = e ∫ dN = e ∫ υ x dn = e ∫∫∫ e

E−F − kT

E−F kT

.

(2.3)

l = υx:

S=1 :

( )

2 m* υx h3

(2.4)

3

dυ x dυ y dυ z .

,

(

J

∫e

∞

∫e

F − EC ∞ kT

−

m*υ y2 2 kT

−∞

:

dυ y ∫ e ∞

−

m*υ z2 2 kT

−∞

dυ z

∫υ

∞

υ x min

x

e

−

(2.6) m*υ x2 2 kT

dυ x .

(2.7)

(2.7) −ξ 2

−∞

-

dξ = π ,

∫e

∞

−∞

−

, m*υ y2 2 kT

dυ y =

2πkT . m*

(2.8)

(2.7)

∫υ

-

m *υ 2 m = E C + υ x2 + υ y2 + υ z2 . 2 2

E = EC +

2e ( m * ) 3 J= e h3

(

)

υ:

)

∞

x

e

−

Vx min

(2.8) :

30

(2.5)

(2.5), .

:

dτ,

,

dN = υ x dn . J

−

m*υ x2 2 kT

kT − dυ x = * e m

(2.9)

mυ x2 min 2 kT

.

kT − kT C = * e kT = * e kT . m m E

W

(2.7),

4πem * k 2T 2 jx = e h3

-

(2.9) -

F − Ec + E kT

= AT e . 2

F kT

(2.10)

(2.10)

. A=

4πem k ; h3 *

-

2

–

-

.

À ⎛ m⎞ A = 120⎜ * ⎟ 2 [11, 8]. 2 ⎝ m ⎠ ñì ⋅ ãðàä F,

F < 0, = 0,

Φ = −F .

Ф ,

.

-

: (2.11) –

.

j x = j t = AT 2 e ,

Ô − kT

(2.12)

: .

(2.12) , -

jt . , j t,

-

, . . ,

,

: Ф = 2,5

,

1

= 300 ,

2

= 1500 , kT1 = 0,025

, jt1 = 10-36 /

, kT2 = 0,125

(2.15),

2

, jt2 = 0,8 /

,

2

. :

. 5 -

36

.

31

2.2. p-

np-

2.1 , Eg – n-

, φ0n –

, φ0p –

E0

E0

χ

χ

Φn

EC Ei

EC

Eg 2

ϕ0n

Ei F EV

EV

ϕ0p

б

. 2.1.

:

Φ = −F ,

; ) p-

n-

(

Фn

Фp :

⎞ ⎛ Eg − ϕ n ⎟⎟ , Ô n = − F = χ + ⎜⎜ ⎠ ⎝ 2 ⎞ ⎛ Eg + ϕ p ⎟⎟ . Ô p = − F = χ + ⎜⎜ ⎠ ⎝ 2 p-

(2.14)

, (2.13), (2.14)

-

(2.13)

,

32

Φp

Eg 2

а

) n-

. –

.

p-

F

n:

mp* = mn*.

kT ⎛N 2 ln⎜⎜ C ⎝ NV

nn-

⎞ ⎟⎟ ⎠

n-

p.) (2.13) (2.14) p, ,

,

2.3. Э

, ,

-

.

p-

, .

-

, , .

, .

-

, , . (

) . -

2.2 .

. 2.2.

, ,

щ

, –

. ND = 1015

(

-3

, 33

) 1/3

= 10

-5

= 1000 Å.

1011 / 1015 = 10-4

,

= 10 1

.

12

-2

= ND-

, [12]. -

[13, 14]. . (

, ,

, –

).

-

E(z) . , ,

-

.

ΔU = U ( z ) − U (∞) = ∫ E ( z )dz , :

z

∞

U(∞) – .

(E =

h2k 2 ), 2m *

EC (

EV). . -

:

1 ψ = ∫ E ( z )dz . q∞ z

-

ψs > 0

34

ψs

, ,

ψs. ψs < 0

. (

. 2.3).

EC

ψs EC F ψs

ψs F Ei ψs

Ei EV

ψs

ψs EV а

б

ψs > 0

. 2.3.

ψs < 0

:

n-

)

; )

2.4. К , . nnn0

.

nn0 = N C e

pn0 -(EC -F) kT

-(EC -F + qϕ 0n − qϕ 0n ) kT

= NCe = NCe EC – F + qϕ0n = Eg/2. q =β, kT nn0 = ni exp( βϕ 0n ) .

ϕ(x) :

-(EC -F + qϕ 0n ) kT

: ϕ(x) = ϕ 0 n – p0n(x) . ϕ(x) = ϕ0n – ψ(x)

nn0(x)

e

qϕ 0n kT

(2.15):

= ni e

ps –

,

(2.15) (x),

n = ni exp( βψ s ) , n = ni exp( βϕ ( z )) = ni exp( β (ϕ 0 + ψ )) = n0 exp( βψ ) , p = pi exp(− βϕ ( z )) = pi exp(− β (ϕ 0 + ψ )) = n0 exp(− βψ ) . ns

qϕ 0n kT

-

(2.16) –

: 35

ns = nn0 exp( βψ s );

ps = nn0 exp( β (ψ s − 2ϕ 0 )) .

(2.17)

2.5. ,

-

, .

,

.

,

ψs ,

, kT/q. ,

z

ρ (z ) d ψ =− , 2 ε sε 0 dz

ψs

-

:

2

εs –

ρ(z) –

(2.18)

, . -

ρ ( z ) = −q[ N D+ − n( z )] .

:

(2.19)

= n0, n(z) βψs Ф / ;

j Me < j / .

– . .

, .

, .

2.4 – :ϕ =Ф

–

. , , –Ф / . pФ .

Ф /

,

p-

– . 38

, -

j (2.29).

, /

,

jMe > п/п

jп/п > Me

jMe > п/п

jп/п > Me

E=0

ΦMe

Φп/п < ΦMe EC Ei EV

FMe

ψS=Δϕms

Fп/п

EC Ei

Fп/п

EV ОПЗ металл (Au)

полупроводник (n-Si) W Au

n-Si

электроны

. 2.4.

ионизованные доноры

,

– –

pn-

.

2.7. ,

–

-

VG,

.

Δϕms,

-

VG > 0

VG < 0 .

2.5 .

,

. 39

ψS=Δϕms - VG ψS=Δϕms VG = 0

ψS=Δϕms - VG

VG < 0

VG > 0

E(x)

E(x)

VG = 0

E(x)

VG > 0

VG < 0

W0

W2

W1

а

б

в

. 2.5.

:

) VG = 0; ) VG > 0,

; ) VG < 0,

2.8. ,

–

.

,

.

n-

, . , ,

. .

ρ (x ) ∂ ψ ( x) =− , 2 ε sε 0 ∂x

:

2

40

(2.30)

ψ(x) –

, ρ(x) –

, εs –

, ε0 –

.

n-

ND+.

ρ ( x ) = qN D+ .

E ( x) = −∇ϕ :

-

(2.31) -

,

d dψ ρ (x ) =− , ε sε 0 dx dx

(2.32)

qN D+ dE =− . ε sε 0 dx

(2.33) (2.33).

,

E ( x) =

(2.34)

(W − x ) .

x=W + D

ε sε 0

qN

, (2.34)

, (x = 0),

–

–

(x = W). (

) (

(2.34) . 2.6):

ψ ( x ) = qN D

,

: x = W, ψ(W) = 0.

(W − x )2 .

ψ max = ψ s − VG = Δϕ ms − VG ,

-

2ε s ε 0

(2.35)

Δϕ ms = Φ Me − Φ ï/ï . x=0

2ε s ε 0 (Δϕ ms − VG ) . qN D

: (2.36)

(2.36) (2.35):

W,

W =

(2.37)

(2.37)

. , W

VG

-

ND 41

.

2.6

,

,

(2.34)

(2.35).

E(x) VG < 0

а 0

W

x

E W x

0

б

Emax

ψ ψS

в 0

. 2.6.

x

W

, :

)

; ) ; )

2.9.

-

(

mυ õ2 min EC = 2 mυ 2

2 õ min

42

-

:

= q(Δϕ ms − VG ) . (2.5)

)

.

(2.7),

(2.38) :

jï

ï

=

→Ì

4πem * k 2T 2 e h3

EC − F kT

e

−

q ( Δϕ ms −VG ) kT

=

1 qnsυ o e βVG , 4

(2.39)

⎛ 8kT ⎞ 2 υ0 = ⎜ ∗ ⎟ , ⎝ πm ⎠ 1

υ0 –

,

ns = ns e − βΔϕ ms ,

ns –

n0 –

,

⎛ 2πm ∗ kT ⎞ 2 ECkT− F ⎟⎟ e [6, 17]. n0 = ⎜⎜ 2 ⎝ h ⎠

-

3

j

VG = 0 →

j .

,

J=J

: →

2.7

1 qn sυ 0 . 4

-

− JM→

J = J 0 (e βVG

=

→

=

1 qn sυ 0 (e βVG − 1) ; 4

1 − 1); J 0 = qnsυ o . 4 -

(2.40)

: (2.41) -

.

J

Jп/п > Me

JMe > п/п = J0 . 2.7.

VG

-

43

.

ё

. .

–

,

, . , .

-

-

–

.

,

.

-

, .

2.10.

-n -

,

,

p-n

(

). p-n n-

Ф (2.14)

.

n-

ΔΦ = Φ p − Φ n = ϕ n + ϕ p > 0 .

(2.13)

. -

Фp

p-

Фn

,

: nSi – pSi, nGe – pGe. p.

,

n)

p( n-

.

-

pn.

pnp-

,

–

. ,

–

-

. n-

p-

,

p,

n. p-

,

n.

44

,

-

2.8

, -

Jp > n

.

Jn > p

Jp > n

Jn > p

E=0 E=0

ϕpSi

ϕnSi EC F Ei EV

F

EC F Ei EV ОПЗ

p-Si

W

n-Si

ионизированные акцепторы

. 2.8.

,

ионизированные доноры

p-n

.

p-n

,

,

p-n

. 2.10.1.

p-n ,

p-n , (VG = 0)

ϕn < ϕp.

,

-

NA > ND;

ΔÔ = ϕ n + ϕ p =

p-n

kT N A N D . ln 2 q ni

: (2.42)

– p-n

p p0 = ni exp( βϕ 0p ) = N A ; np0

.

ni2 ; = ni exp(− βϕ 0p ) = NA

45

nn0 = ni exp( βϕ 0n ) = N D ; ϕ0p(x)

ϕ0n(x).

ϕ0p

,

p n0 = ni e − βϕ 0n =

ni2 . ND

(2.43)

ϕ0n

x, ,

pp ( x ) = ni exp( βϕ 0p ( x )); np ( x ) = ni exp( − βϕ 0p ( x ));

x: pp(x),

np(x), nn(x), pn(x).

nn ( x ) = ni exp( βϕ 0n ( x ));

pn ( x ) = ni exp( − βϕ 0n ( x )) . ϕp

, .

p, . p-n

p-n pp

(ϕp = 0),

(2.44) -

, . . p p = ni. ,

-

np(x) .

p-n

nn(x) n-

pn(x)

.

2.9 p-n

-

p-n

.

Концентрация электронов, дырок, см-3

n 0, p 0 1018

ОПЗ p-Si

n-Si

W

-

ОПЗ

pp = NA 0

1016

W

+

nn = ND 0

1014

электроны

1012

108

pn

0

106 104

np

дырки

физический p-n переход металлургический p-n переход

0

102

Wn Wp E

Wp

Wn а

б

. 2.9. p-n )

46

квазинейтральный объем n-типа

квазинейтральный объем p-типа

p = n = ni

1010

: ; )

,

-

,

,

p-n

p-n .

-

, ni. 2.10.3.

p-n

∂ ψ ( x) ρ (x ) =− , 2 ε sε 0 ∂x

.

p-n :

2

ψ(x) –

, εs –

, ρ(x) –

, ε0 –

.

I),

ND+, + II ρ ( x) = qN A . II. -

p-n I ρ ( x) = qN D+ ,

–

NA+.

I

E ( x) = − II:

-

II).

np-

-

.

p-n x>0 ( x 0 . ε sε 0 ⎝ 2 ⎠ x = −Wn ; ψ = 0 ; x > 0,

:

2

(2.50) -

⎞ qN W 2 qN D ⎛ W 2 ⎜⎜ − W 2 ⎟⎟ = − D , ε sε 0 ⎝ 2 ε sε 0 2 ⎠ :

ψ(x)

(

ψ 1 (x ) =

)

(2.50),

qN D (x − Wn )2 , x > 0. 2ε s ε 0 , p-n

(2.46), (2.47), (2.50)

(2.51)

qN A (x + Wp )2 , x < 0, 2ε s ε 0

ψ 2 (x ) = − :

-

x > 0:

):

2.10

48

-

+ Δϕ 0 .

qN D 2 qN D ( x + W n )2 . x − 2Wn x + W 2 = − 2ε s ε 0 2ε s ε 0 , ψ p(

, n-

:

2

ψ(x) x < 0. 2 qN A ⎛ 2 W ⎞ qN A ⎜⎜ x + 2Wx + ⎟= ψ (x ) = x + Wp 2 ⎟⎠ 2ε s ε 0 ε sε 0 ⎝

ψ (x ) = −

,

(2.51).

,

-

E p-Si

n-Si

ψ

x

0

ψ1(x)

ψ2(x)

Emax -Wp 0

Wn

Wp Wn

а

б

. 2.10.

в

, :

p-n )

Wp Wn

; )

p-n

; )

ψ1 + ψ2 = Δϕ0 = ϕn0 + ϕp0,

x=0

p-n

Δϕ 0 =

2ε s ε 0 q

(N

-

A

-

)

Wp2 + N DWn2 .

(2.52) -

QD = QA ; qN AWp = qN DWn .

: ,

Δϕ 0 =

Wn =

N AW p ND

.

(2.53)

N W ⎞ ⎛ ⎛ q N2 ⎞ ⎜⎜ N AWp2 + N AWp A p ⎟⎟ = Wp2 ⎜⎜ N A + A ⎟⎟ = . 2ε sε 0 ⎝ N D ⎠ 2ε sε 0 ND ⎠ ⎝ ⎛ 1 q 1 ⎞ ⎟⎟ Wp2 N A2 ⎜⎜ = + 2ε sε 0 ⎝ NA ND ⎠ (2.45) (2.46),

:

q

Wp =

2ε s ε 0 Δϕ ; Wn = 1 ⎞ 2⎛ 1 ⎟⎟ qN A ⎜⎜ + N N D ⎠ ⎝ A Wp

Wn p-

n-

2ε s ε 0 Δϕ . 1 ⎞ 2⎛ 1 ⎟⎟ qN D ⎜⎜ + N N D ⎠ ⎝ A :

(2.54)

49

, p-

p-n

Wp

. p-n

W,

2ε s ε 0 Δϕ 0 q

W =

p+-n

W = Wp + Wn,

:

⎞ ⎟⎟ . ⎠

⎛ 1 1 ⎜⎜ + ⎝ NA ND

(2.55)

( )

(2.47)

(2.48)

,

p-

N A >> N D → Wp 0

Fp Ev

Ev

Ln

. 2.13. Fp

Lp

W

,

Fn VG > 0

p-n . , n n, p n

:

Fn − Fp

nn p n = n e 2 i

kT

-

Fp - Fn = qVG,

= ni2 e βU .

.

nn = nn0 ;

pn =

ni2 βU e = p n0 e βU . nn0

(2.56)

2.14

-

p-n . , ,

.

,

-

(2.56), . . . 52

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

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

pn0

1020

1018

np0

1016 1014 1012

p = n = ni

108

pn(x)

106

pn0

np(x)

104

np0

102 100

Wp Wn

10-2

Концентрация электронов, дырок, см-3

Концентрация электронов, дырок, см-3

1018

1010

pn0

1020

np0

1016 1014 1012 1010

p = n = ni

108 106

pn0

104

100

np(x)

10-2

Wp Wn0 0

10-4

pn(x)

np0

102

10-4

Wp Wn 0

а

б

0

Wp

Wn

. 2.14.

p-n (

)

)

(

(VG = +0,25 ); )

2.12.

) (VG = -0,25 )

-

-n -

p-n

.

-

:

dp 1 = G − R − div ( j ) . dt q dp =0. dt n(x > 0).

p-n : G = 0. : E = 0.

G E : IE = 0,

-

53

j = −qD

,

R=−

dp . dx

R

p n − p n0

:

τ

.

(2.57) : Dτ = Lp2.

,

,

d 2 p n p n − p n0 − = 0. dx 2 L2p

:

(2.58) p-n

x = 0, p n = p n0 e

:

(*)

:

βVG

x → ∞, p n = p n0 . (2.58)

;

(

p n − p n0 = p n0 e (2.59)

βVG

)

−1 e

−

x LD

(*)

.

(2.59) -

n(

. 2.15).

p-n

,

p-n

. ,

, (

. 2.16):

j pD = −qDp

:

=q

Dp p n0 Lp

e βVG .

, j pE = q

. p-n :

(2.60)

-

p-n j nD = q

VG = 0

54

x =0

(2.60) , .

p-n

p-n

dp n dx

D n n p0 Ln

Dp p n0 Lp

-

(2.59)

e βVG .

;

j nE = q

Dn np0 Ln

.

⎛ qD p qDn n p0 ⎞ βU ⎟( e − 1) . j = ⎜⎜ p n0 + ⎟ L L p n ⎝ ⎠

(2.61) p-n

.

,

-

VG < 0 .

Ln/τp.

Ln

-

:

jn =

qLn np0

τn

=

qLn np0 2 n

L / Dn

=

qDn np0 Ln

.

pn VG3 > VG2 > VG1 VG2 pn 0

VG1

0

x

Lp

. 2.15. p-n

, . ( ,

),

(2.61)

, np0

,

-

.

p-

pn-

: NA >> ND.

p-n (

-

. 2.16).

55

p-Si

n-Si jnD

np(x)

EC F Ei EV

jpD pn(x)

NA >> ND, jpD >> jnD . 2.16.

p-n n

,

Js =

p-n

qDn np0 Ln

J = J s (e +

βVG

:

Js

qDp p n0 Lp

=

− 1) .

: (2.62)

qLn np0

τn

+

,

p-n 2.17.

qLp p n0

τp

.

(2.62),

(2.63) -

J

J = JpD +JnD диффузионный ток

VG

J = JpE +JnE дрейфовый ток

. 2.17.

-

p-n

(2.16)

2.17,

-

-

p-n .

p-n .

56

-

–

p-n

-

.

ϕ

p-n , Q,

: C=

∂Q . ∂ϕ

.

-

:

p-n

-

QB Qp.

.

p-n p-n

CB

CD. CB –

-

p-n

VG < 0, .

∂QB . ∂VG

CB =

(2.64) QB

QB = qN DW = qN D

2ε s ε 0 (Δϕ 0 − VG ) = qN Dε s ε 0 (Δϕ 0 − VG ) . qN D :

p-n

(2.65) (2.65),

CB = (2.66)

2qN D ε sε 0

2 Δϕ 0 − VG

:

=

ε sε o W

,

.

(2.66) CB

-

, W. VG,

-

. ,

-

. CD – VG > 0,

p-n Qp

-

Qp. 57

CD =

Qp = q ∫ p n ( x)dx = q ∫ p n o e βVG e ∞

∞

0

0

C=

−x

Lp

∂Qp

∂VG

dx =

,

qp n 0 e βVG

L2p =

Lp

qp n 0 Dpτ p

τpJ dQ qp n 0 Dp = τ p βe βVG = . kT dVG Lp q

Lp

e βVG ,

.

, -

VG.

-

B

.

VG ,

. VG.

. ND(x), C(VG) –

,

-

.

2.14. ,

, pGe – nGaAs. , ,

p-n nSi.

,

, : [18, 16, 19].

(

p-n , pSi – -

) -

. GaAs,

Ge, InP,

InGaAsP. E g,

χ Eg

χ.

2.18

.

58

NV eχ2

eχ1

ΔEc

Ec 1

NV eχ1

Ec 2

Ev 2

ΔEv χ1 > χ2

χ1 - χ2 > ΔEg/e

Ec 1

Ev 1

ΔEv χ1 > χ2

Φ 1 = Φ2 NV

eχ1 ΔEc

ΔEc

Ec 1

F

Ev 1

eχ2

eχ2

ΔEc

Ec

Ec 2

2

Ev 1

ΔEv χ1 < χ2

Ev 2

NV

eχ1

Ec 1

eχ2

χ1 - χ2 < ΔEg/e

Ec 2

Ev 2

Ev 2

ΔEv

Ev 1 χ1 < χ2

χ1 - χ2 < ΔEg/e

. 2.18.

χ1 - χ2 > ΔEg/e

Eg

Ф1 = Ф2 [18]

χ

, ,

χ,

,

εs. –

g

(pGe – nGaAs).

-

,

,

1. pGe

nGaAs.

: 1.

=0

.

2.

χGaAs

χGe

.

3.

Eg . 59

1. (pGe) ,Å

5,654

5,658

5,9

6,0

NA,D

3⋅1016

1016

W0

0,14

0,17

ϕ0

0,21

0,55

χ

4,05

4,07

a -

, 10-6

-1

-3

,

, , ,

(nGaAs)

EC “

” ΔEC

“

ΔE C = χ Ge − χ GaAs .

:

ΔEV.

”.

-

V

ΔE V = − χ Ge − E g Ge + χ GaAs + E g GaAs = −ΔE C + ( E g GaAs − E g Ge ) . ΔEC

“

“

”

:

ΔE C + ΔE V = ( E g GaAs − E g Ge ) .

” ΔEV

,

“

”

2.19 pGe – nGaAs. ( nGe (

), . 2.20). .

,

“

: ΔE C = χ Ge − χ GaAs . “ ”

EV.

” “

“

” ΔEV

:

– pGaAs – ” ΔEC

ΔE V = − χ Ge − E g Ge + χ GaAs + E g GaAs = −ΔE C + ( E g GaAs − E g Ge ) . 60

E=0 χ1

χ2 ΔEC

Eg2

EC F Ei

Eg1

ΔEV

EV

. 2.19.

pGe – nGaAs NV eVd

eΔV2 eΔV1 EC ΔEC0 Eg2 F Eg1

EV ΔEV0

x1 0

x2

. 2.20.

x

nGe – pGaAs

, .

-

2.21

.

, EV, EC

“

”

“

”

-

[20, 17]. 61

NV

NV

eVd

ΔEc0

eVd

ΔEcn

Ec

Ec

F

F ΔEv0

χ1 > χ 2

Ev

ΔEvn

Ev χ1 - χ2 > ΔEg/e

NV

ΔEc0

ΔEcn

ΔEv0

ΔEvn

χ1 > χ 2

Φ1 < Φ2

χ1 - χ2 < ΔEg/e

NV

eVd

Ec

eVd

Ec ΔEc0

F Ev

ΔEcn

ΔEc0

ΔEcn

ΔEv0

ΔEvn

F ΔEv0

ΔEvn Ev

χ1 < χ2

χ1 - χ2 < ΔEg/e

χ1 - χ2 > ΔEg/e

χ1 < χ 2

. 2.21.

, (Ф1 < Ф2), )

, (

. E, W1n

W2p

E1max =

W1n =

62

εs

ψ

p-n

, -

:

ε1ε 0

qN DW1n

; E2max =

qN AW2p

ε 2ε 0

qN AW2p2 qN DW1n2 V1n = , ; V2p = 2ε 1ε 0 2ε 2 ε 0

2ε 1ε 2 ε 0 (Δϕ 0 − V ) ; W2p = ε2 ⎞ 2 ⎛ ε1 ⎟⎟ + qN D ⎜⎜ ⎝ NA ND ⎠

,

2ε 1ε 2 ε 0 (Δϕ 0 − V ) . ε2 ⎞ 2 ⎛ ε1 ⎟⎟ + qN A ⎜⎜ ⎝ NA ND ⎠

(2.67)

(2.68) (2.69)

W = W1n + W2p,

W =

W,

2ε 1ε 2 ε 0 (Δϕ 0 − V ) ⎛ 1 1 ⎞ ⎜⎜ ⎟⎟ . + q ⎝ N Aε 1 N Dε 2 ⎠

(2.70)

Δφ0

Δϕ 0 = V1n + V2p .

: (2.71)

,

p-n

ε 1 E1 max = ε 2 E 2 max .

,

:

ε1

ε2.

-

.

, (2.72)

2.22

. E(x)

0

X1

X2

X

V(x) V1

ΔV1

ΔV2 V2 0

X1

X2

X

. 2.22. nGe – pGaAs

V.

p-n

-

, p-

2.23

. -

nGe – pGaAs. V = 0. 63

eΦ'b2 eV2 eV1 eΦ'b1

eΦ'b2 eV2

eV1

Ec

eΦ'b1

Ec

ΔEc0

ΔEc0

ΔEv0 ΔEv0 Ev

V>0

V p0

np-

-

, . 3.2 ). >0 s0)

EV

q ϕ0

EC E внеш q ψS

q ϕ0

E внеш

(ψS 2ϕ 0

ψ s > 2ϕ 0

ψ s = 2ϕ 0 , «

-

.

» . , ,

, .

70

,

-

,

,

-

.

3.2.

(z), Q s,

,

Γp,n,

Cs –

-

. [2, 14, 21, 13, 11]. 3.2.1.

d ψ ρ ( z) = ε 0ε s dz 2

p-

:

2

ρ(z) ,

(3.6)

,

:

ρ ( z ) = q( N D+ − N A− + p − n) .

(3.7) -

,

, ρ(z) = 0.

N D+ − N A− = n0 − p 0 . n = n0 e ,

,

ρ(z)

βϕ

(3.8)

p = p 0 e − βϕ ,

(3.3 – 3.5),

n0 = ni e − βϕ 0 ,

p 0 = pi e βϕ 0 ,

ρ ( z ) = −qp 0 [e −2 βϕ (e βψ − 1) − e − βψ − 1] . :

(3.9)

0

(3.9) :

(3.6),

(z)

qp 0 − 2 βϕ 0 βψ d 2ψ [e (e − 1) − e − βψ − 1] . = 2 ε sε 0 dz

(3.10) ,

2.5

(2.23),

dψ . dz

71

dψ d 2ψ 1 d ⎛ dψ ⎞ ⋅ = ⎟ . ⎜ dz dz 2 2 dz ⎝ dz ⎠ 2

(3.11)

qp 0 − 2 βϕ 0 βψ ⎛ dψ ⎞ d⎜ [e (e − 1) − e − βψ − 1]dψ . ⎟ = ε ε dz ⎠ ⎝ s 0 ,

2

(3.12)

(3.12) :

,

1 qp 0 1 − βψ ⎛ dψ ⎞ + βψ − 1) + e − 2 βϕ 0 (e βψ − βψ − 1)] . [(e ⎟ = ⎜ 2 ε sε 0 β ⎝ dz ⎠

-

2

dψ , E( z) = − dz

(2.23),

(3.13) LD

:

⎛ kT ⎞ 1 [(e − βψ + βψ − 1) + e −2 βϕ 0 (e βψ − βψ − 1)] . E = ⎜⎜ ⎟⎟ 2 ⎝ q ⎠ 2 LD 2

2

F (ψ , ϕ 0 ) ≡ [(e − βψ + βψ − 1) + e − 2 βϕ 0 (e βψ − βψ − 1)] 2 . 1

(3.14)

(3.15)

E=−

dψ kT =± dz q

:

1 2 LD

F (ψ , ϕ 0 ) .

(3.14)

(3.15)

(3.16)

(3.16)

-

. . ), s0 ( z

E

.

z

Es = ±

Es

kT q

1 2 LD

F (ψ s , ϕ 0 ) .

: (3.17) -

Es Qsc,

Qsc = ε s ε 0 Es = ± , . 72

2ε s ε 0 kT F (ψ s , ϕ 0 ) . qLD :

(3.16 – 3.18),

(3.18) ,

-

3.2.2. (3.18)

,

-

,

. Qsc,

(3.15). F( , φ0) (3.18) щ ( s < 0). Qsc

ψs >

s

pQp,

kT ; q

Qsc = Qp = (φ0 >

.

βψ s > 1 .

2ε s ε 0 kT − e qLD

> 0). QB.

(2φ0 >

.

(3.19) -

Qsc

2ε s ε 0 qN A

QB = qN A

2

2ε s ε 0 kT (βψ s − 1) 12 . qLD

(3.16, 3.18)

⎛ kT ⎞ ⎟= Qsc = QB = 2ε s ε 0 qN A ⎜⎜ψ − q ⎟⎠ ⎝ W =

βψ s

s

,

(3.20)

⎛ kT ⎞ ⎜⎜ψ s − ⎟. q ⎟⎠ ⎝

> φ0).

Qsc,

,

QB,

Qsc = QB = 2ε s ε 0 qN A (ψ s − (

s

1 2ε s ε 0 kT ( βψ s − 1) 2 . qLD

Qn 2φ0).

(3.21) -

Qsc

Qn,

-

Qsc = QW + QB ≈ Qn =

ε s ε 0 kT 2qLD

β (ψ s − 2ϕ 0 )

e QB

W

QB = 2qε s ε 0 N A (2ϕ 0 − ,

,

kT ); W = q 3.2

2

.

ψs

(3.22)

2 qε s ε 0 kT (2ϕ 0 − ) . qN A q :

(3.23)

(3.19 – 3.22),

, 73

–

.

3.3

Qsc . -10

0

10

20

30

ψ s,

-

40 βψs

QSC, Кл/см2 10-5

NA=1016см-3 T=290K ϕ0=0,35B 2βϕ0=28

10-6

Обогащение

Сильная инверсия

Слабая инверсия

Обеднение

10-7

QW

10-8

Плоские зоны

10

-0,4

-0,2

0

0,2

ψs, B

EC

Ei

EV

-9

0,4

0,6

0,8

1,0

ψs,

. 3.3. p-

3.2.3. ( 74

) Qp,n

,

Γp,n

Γp ,

.

Γ p = ∫ ( p( z ) − p 0 )dz , ∞

(3.24)

0

, p0 –

p(z) –

-

. ,

–

Γp,n

.

,

.

Γp,n

.

, .

e − βψ − 1 − 1)dz = p0 ∫ Γ p = p 0 ∫ (e dψ . dψ ψs 0 dz Γn : 0 βψ e −1 Γ n = n0 ∫ dψ . d ψ ψs dz Γp,n ,

(3.24)

,

-

, ∞

− βψ

0

:

Γp = Γn =

(3.26)

-

βψ s > 3

. (3.15),

3.26),

(3.25)

ε s ε 0 kT 2 q 2 LD

ε s ε 0 kT 2

2 q LD

e

−

(3.25,

βψ 2

,

(3.27)

.

(3.28)

βψ

e

2

Γp,n

-

,

(3.25, 3.26). , Qn QB,

,

Qn = Qsc − QB .

,

,

Qsc

-

: (3.29) 75

(3.18)

Qsc

(

:

)

⎧ ⎡ ⎤⎫ 2 kT β (ψ s − 2ϕ 0 ) Qsc = ⎨2qε s ε 0 N A ⎢ψ s + − 1 ⎥⎬ . e q ⎣ ⎦⎭ ⎩ (3.20)

QB

1

(3.30)

(3.23),

-

1 ⎧⎡ ⎫ 2 ⎤ 1 ⎪ ⎪ ⎡ ⎛ kT ⎞⎤ 2 ⎪⎢ kT e β (ψ s − 2ϕ 0 ) ⎥ ⎪ ⎥ − 1⎬ , ⎟⎟⎥ ⎨⎢1 + Qn = ⎢2qε s ε 0 N A ⎜⎜ψ s − kT ⎥ q ⎠⎦ ⎪⎢ q ⎝ ⎣ ⎪ ψs − ⎢ q ⎥⎦ ⎪⎣ ⎪ ⎩ ⎭ 1 ⎧⎡ kT ⎤ 2 ⎡ 1 ⎪ 2ϕ 0 − 2 ⎢ ( ψ s − 2ϕ 0 ) ⎥ ⎢ ⎡ ⎛ kT ⎞⎤ ⎪ kT e q ⎥ −⎢ ⎟⎟⎥ ⎨⎢1 + Qn = ⎢2qε s ε 0 N A ⎜⎜ψ s − kT ⎥ q ⎠⎦ ⎪⎢ q ⎢ ψ − kT ⎝ ⎣ ψs − ⎢⎣ s q q ⎥⎦ ⎪⎢⎣ ⎩

:

Qn

(3.31)

⎤ ⎥ ⎥ ⎥ ⎥⎦

1

2

⎫ ⎪ ⎪ ⎬. ⎪ ⎪ ⎭

(3.32) (3.32),

:

(1 + x )

1

2

x ≈ 1 + , ïðè x 7

1

(3.33)

2

–

.

(3.33) :

Qn = [2kTε s ε 0 N A ] e 1

, Qn

76

(3.33) (3.22).

2

β (ψ s − 2ϕ 0 ) 2

.

Γn =

(3.34) -

Qn q

:

Γ n = Cp

kT β (ψ s − 2ϕ 0 ) , e q2

(3.35)

⎛ kT ⎞ 2 β (ψ s − 2ϕ 0 ) Γ n = ⎜⎜ 2 2 ε s ε 0 N A ⎟⎟ e 2 . ⎝ q ⎠ ψs = 2ϕ0, . . (3.36) 1

,

ρ = (1÷10) (1÷2)⋅10

13

,

⋅

(3.36)

Γn(ψs = 2ϕ0) = (10 ÷10 ) 9

Γn,

-2

3.4

3.5

.

Γn max =

,

-2

-

10

. (1.42 – 1.47)

,

ψs . Qn

10-6

Γn

ψ s.

Qn, Кл/см2

10-7 ND=1014 1015 1016 1017 10-8 βψs=2ϕ0

10-9

10-10

10-11 10-12 15

. 3.4.

βψs

20

ψs,

25

30

35

40

Qn p-

77

Гn, см-2

1013

NA=1015см-3

1012

1011 80 140

1010

230 320

109

108 +β( ψs-2ϕ0 )

107 0

-4

12

Γn

ψs,

. 3.5.

8

4

p-

3.2.4. , ,

λc

λc,

, ,

. :

λc = ρ(z) –

∫ ρ ( z ) zdz

∞

∫ ρ ( z )dz

0 ∞

,

(3.37)

0

,

-

. ,

∫ ρ ( z )dz = Q

∞

0

78

-

p, n

(3.38)

.

λc

(

λc

,

–

p-

βψ s LD λc = . F (ψ s , ϕ 0 )

)

: (3.39)

(3.39)

, .

Qsc E(z) Es. :

ψ = ψ s − Es z .

(3.40)

n(z)

n( z ) = n0 e β (ψ s − Es z ) = ns e − βEs z .

: (3.39)

(3.41)

λc =

(3.41)

ε ε kT 1 = s 0 . qQB βE z (3.4, 3.5)

(3.18)

: (3.42)

λc

(3.42),

ψs,

,

λc

. .

T

,

Qn >> QB, (3.39). -

λc

,

,

(3.37). 3.6 ,

.

λc

(20÷300) Å .

,

λc

s

,

= 0, -

. 79

o

15

NA=10 см-3 VSS=0

λ, A

250

T=320K

ψs=2ϕ0

290

200

260 230

150

200 170 140 110

100

50

80 ГП,см-2

0 7

108

10

109

1010

. 3.6.

1011

1012

1013

Γn T = 300

.

λc

[2, 21]

p-

3.2.5. 3.2.1 (3.16). . .

(z), (3.16)

dψ kT = q s ,ϕ 0 )

∫ ψ F (ψ

:

ψ

s

1

z.

2 LD

, (3.43)

(3.43) (z)

.

.

1. (3.15)

,

: p = n = ni; φ0 = 0 F( , φ0)

F (ψ , ϕ 0 ) = (e − βψ + e βψ − 2) (3.44) (3.43),

80

:

1

2

=

1 ⎛ βψ ⎞ sh⎜ ⎟. 2 ⎝ 2 ⎠

(3.44)

z = LD ,

∫ 2kT ψ ψ

dz ⎛ βψ s sh ⎜ ⎝ 2

q

βψ s

(3.45)

2z = ln LD

⎛ βψ th⎜ ⎝ 4

th

⎞ ⎟ ⎠

.

(3.45)

:

βψ 4

th

(3.46)

4

⎛ 2z ⎞ ⎛ βψ s ⎞ ⎞ ⎟. ⎟ exp⎜⎜ ⎟ = th⎜ ⎟ L ⎠ ⎝ 4 ⎠ D ⎝ ⎠

(3.47)

(3.47)

. (z) z.

2. ,

F( , φ0)

(3.15),

∫ ψ

.

dψ

ψ

s

⎛ kT ⎞ ⎟ ⎜⎜ βψ − q ⎟⎠ ⎝

1

2

=

,

:

kT q

1 2 LD

z.

(3.48)

z = W, . .

-

= 0, :

z⎞ ⎛ ψ ( z ) = ψ s ⎜1 − ⎟ . ⎝ W⎠ 2

,

(3.49)

(3.49)

,

.

ψ ( z) = ψ s − ,

2ψ s z = ψ s − Es z . W

, (3.50) -

.

81

щ

3.

s,

(3.19) ,

(z)

(3.22). -

. (3.44)

∫ ψ

(3.15)

s

dψ

,

ψ

e

=

β (ψ − 2ϕ 0 )

−

>7

2

ψ ( z ) = 2ϕ 0 − ψ ( z) =

1

kT q

z.

2 LD

(3.51)

⎤ 2kT ⎡ z + e − β (ψ s − 2ϕ 0 ) ⎥ . ln ⎢ q ⎢⎣ 2 LD ⎥⎦ (3.51)

2kT ⎡ z +e ln ⎢ q ⎢⎣ 2 LD

:

βψ s 2

: (3.52)

⎤ ⎥. ⎦⎥

(3.53)

(z)

, -

.

3.3. Qsc s,

Csc. Csc,

C sc ≡

[(

ε ε 1− e ∂Qsc = s 0 ∂ψ s 2 LD

− βψ s

)+ e

(3.18), −2 βϕ 0

(e

F (ψ s , ϕ 0 )

βψ s

)] .

−1

: (3.54)

, (

, (3.54),

,

), Qsc,

3.2.2.

,

p-

. щ

(ψs < 0) Csc

82

C sc = C p =

ε sε 0 LD

e

−

Cp:

βψ s 2

.

(3.55)

(2φ0 > ψs > 0) -

Csc CB:

ε s ε 0 qN A

C sc = C B =

⎛ kT ⎞ ⎟ 2⎜⎜ψ s − q ⎟⎠ ⎝

(3.56)

,

=

ε sε 0

.

W

(3.56)

.

Csc s,

Csc . ,

εs, .

W, (ψs = 0) (3.55)

(3.56)

s

→ 0, . .

. s

=0 ».

(3.55)

« CFB

(3.55)

C sc = C FB =

ε sε 0 LD

=

ε s ε 0 qN A kT

: .

(3.57)

q -

,

. (ψs > 2φ0)

Csc

β (ψ s − 2ϕ 0 ) ≥ 7

(3.55) s

Cn

Cn =

(3.58)

ε sε 0

:

2 LD

-

β (ψ s − 2ϕ 0 )

e

2

.

(3.58)

, , s

= 2φ0. 83

3.7

Csc s,

(3.55 –

3.58). 10

0

10

20

30

40 βψs

CSC, Ф/см2 10

-4

NA=1016см-3 T=290K ϕ0=0,35B 2βϕ0=28 10-5

Сильная инверсия

Слабая инверсия

Обеднение

Обогащение 10-6

Плоские зоны 10-7

Ei

EV

EC

ψs , B

10-8 -0,4

-0,2

0

0,2

0,4

0,6

0,8

1,0

. 3.7.

Csc , (

84

( )

)

3.4.

. , ,

.

, – ,

p-

2 ⎟ ⎜ ⎜ kT − βW0 ⎟ ⎞ ⎛ Eg ⎠ ⎝ ⎟ ⎜ , n0 = N C F 1 ⎜ − βW0 ⎟ = N C e 2 kT ⎠ ⎝ p 0 = N V F1 (βW0 ) = N V e − βW0 , ⎞

⎛ Eg

kT , q

(3.59)

2

F1 –

½, W0 –

2

. n

⎞ ⎛E n = N C F1 ⎜⎜ g − βψ s − βW0 ⎟⎟, 2 kT ⎠ ⎝ p = N V F1 (− βψ s − βW0 ) . :

p

(3.60)

2

ρ(z),

(3.6)

(3.60)

2ε ε kT Qsc = s 0 qLD :

C sc =

ε sε 0

2ε ε kT Qsc = s 0 q

-

.

Csc

Qsc

(3.7)

⎡e βW0 F (− βψ − βW ) + βψ − 1⎤ 2 , 3 s 0 s ⎥⎦ ⎢⎣ 2 1

e βW0 F1 (− βψ s − βW0 ) + 1

1 LD ⎡ βW0 2 ⎤ e F3 (− βψ s − βW0 ) + βψ s − 1 ⎢⎣ 2 ⎦⎥ 2

(3.61)

.

⎡e β (Eg −W0 − 2ϕ 0 ) F (βψ − βE + βW ) + βψ − 1⎤ 3 s g 0 s ⎥⎦ ⎢⎣ 2

(3.62)

1

2

, (3.63)

85

-10

0

10

20

30

40 βψs

QSC, Kл/см2 10-5

EC

EV 10-6

10-7

10-8

ψs, B

10-9 -0,4

-0,2

0

0,2

. 3.8.

C sc = F3 (η )

86

0,6

0,8

1,0

Qsc

s

2

0,4

β (Eg −W0 − 2ϕ 0 )

p-

ε sε 0

e

F1 (βψ s − βE g − βW0 ) + 1

1 LD ⎡ β (Eg −W0 − 2ϕ 0 ) 2 ⎤ e F3 (βψ s − βE g + βW0 ) + βψ s − 1 ⎥⎦ ⎢⎣ 2 F 1 (η ) : 2

2

, (3.64)

x 2 dx F3 (η ) = ∫ x−η , 2 3 π 0 1+ e ∞

4

3

(3.65)

x 2 dx . F 1 (η ) = 2 π ∫0 1 + e x −η 2

∞

1

(3.66)

(3.61–3.64) s→0

. ,

s

→0 -

3.2. 3.8

Qsc, .

Csc

3.6.

3.5. 3.5.1. , -

-

, . (

). , -

(

,

,

,

,

), -

. , ,

-

–

.

, ,

,

. ,

,

,

. -

, ,

–

.

3.9 -

, . 87

Поверхностные состояния

EC

акцепторного типа

Ei

{

донорного типа

EC FS

Ei

F EV

EV

ψs>0 ψs=2ϕ0

ψs=0 Qss>0

F

{

EC Qss0 ψs=ϕ0

F EV

Qss=0

. 3.9.

,

p-

3.9

,

Qss

. ( “surface states – , , , .

,

Qss ”). .

,

,

, ,

-

. 3.5.2. [13]: ; ;

1) 2) 3)

, ;

4)

, .

88

-

.

,

-

,

, , -

.

,

,

. -2

1015

, . .

.

,

, .

, ,

, ,

-

.

,

, .

,

(

.

,

,

)

. ,

. 3.5.3. ,

s.

–

.

Fs = F − qψ s .

:

Fs

(3.67) -

Fs

ΔE = E t + qϕ 0 − qψ s ,

Et, Et –

–

,

: (3.68)

,

. Et > 0,

f =

1

1+ e

E t − Fs kT

=

Et < 0. :

1+ e

1

⎞ ⎛ Et +ϕ 0 −ψ s ⎟⎟ ⎠ ⎝ q

β ⎜⎜

.

(3.69)

89

Qss

Qss = − qN ss f ,

:

(3.70)

Nss –

, . . Fs

(2 ÷ 3) kT , .

(3.69) f = 1

q

f =1

Qss = -qNss.

Qss = − 1 qN ss . 2 (2 ÷ 3) kT , f = 0 Qss = 0 . q

,

-

Fs

2

,

, -

3.1, (3.70)

. -

,

,

Nss(E),

[ Nss(E) dE = 1

-2

-1

·

].

Nss(E)

E+dE).

Nss(E)dE (E; Qss

E, , . . ,

Qss = q ∫ N ss ( E ) f ( E )dE = − qN ss (ψ s − ϕ 0 ) . :

∞

(3.71)

−∞

< φ0 s > φ0

(3.71)

, ,

Qss

s

s

3.9,

= φ0

Qss

.

Qss ,

(3.70)

(3.71),

-

s

,

Css, .

Css =

∂Qss q 2 N ss = f (1 − f ) . ∂ψ s kT :

(3.72)

(3.72) Css( s)

, ,

90

4

kT q

ψ s = ϕ0 +

,

f =1 , 2 Css max =

1 q 2 N ss . 4 kT

(3.73) ,

Css (3.71),

C ss =

∂Qss = qN ss . ∂ψ s

(3.74) Css

Csc. 15

NA = 1,5·10 (3.57), Nss, (3.74), Nss = 1011

,

,

Csc

≈ 2φ0.

s

-3

, -2

-1

Csc = 1,6·10-8 Css, .

Et . q

-

2

/

. Csc,

, -

,

.

3.6.

-

3.6.1.

– -

–

,

, ,

, ,

. .

, -

, , .

-

.

,

,

.

, ,

,

-

. 91

, -

-

. , [14, 11, 13]. ,

3.10,

,

, -

,

. 1 2

3

4

. 3.10. 1–

-

,2–

,3–

,4–

.

-

,

:

) )

; ;

)

. -

3.11 .

–

–

,

:

–

,

, -

, , .

92

3.11 , -

VG .

EC

qχn

ФnD

ФМ ФМD

qχd

Уровень вакуума

Ei F EV

Ei F EV

Металл

Vg>0

EC

F

F

Полупроводник

б

Диэлектрик

ρ(z)

а QМ

W -d

Z

QB Qn

г Vg0

VSC >0

Ei F EV

ψ0 >0

в

-d

. 3.11.

0

Z

W

-

) VG = 0; ) VG > 0; ) VG < 0; ) )

-

:

p-

VG > 0;

VG

,

,

,

« , ,

n-Si

» p-Si

. ,

,

-

,

.

93

3.6.2. -

VG -

s.

-

VG ,

, s.

VG = Vox + ψ s .

, (3.75) ,

s,

priori, , n-

, .

p-

VG , s.

(3.75) 3.11 a VG. -

, Qsc,

QM

− QM = Qsc + Qss + Qox .

(3.77)

Q Q Q QM = − sc − ss − ox . C ox C ox C ox C ox

(3.78)

Δφms,

VG = Δϕ ms + ψ s − (3.79)

:

Qsc Qss Qox − − . C ox C ox C ox

,

VG > 0,

Qsc < 0, Qss < 0, . . VG < 0.

Qss = − qN ss (ψ s − ϕ 0 ) , (3.80) (3.79),

94

(3.76)

QM , Vox

,

,

Qss

Cox,

C ox = Vox =

Qox.

:

(3.79) s > 0, Vox > 0.

(3.80)

VG = Δϕ ms −

Qox qN ss Q qN + ϕ 0 + ψ s − sc + ss ψ s . C ox C ox C ox C ox

(3.81)

VFB (Flat Band).

– VFB -

, ,

VFB ≡ VG (ψ s = 0) . :

(3.82)

(3.81)

VFB = Δϕ ms −

(3.82) :

Qox qN ss + ϕ0 . C ox C ox

,

(3.83) -

VG (3.83)

VG = VFB + ψ s +

s

:

qN ss Q ψ s − sc . C ox C ox

(3.84)

(3.84)

-

. щ

(

s

< 0) (3.19).

Qsc

⎛ qN ss ⎞ 2ε s ε 0 kT − βψ2 s ⎟− . e VG − VFB = ψ s ⎜⎜1 + C ox ⎟⎠ qLD C ox ⎝ Qsc >> Qss, s ( βψ s > 1 ),

(3.19) (3.75),

(3.85)

-

:

:

VG − VFB ≈ −

ε s ε 0 kT C ox qLD

e

−

(3.85)

βψ s 2

.

(3.86)

qL C ⎤ − 2kT ⎡ ln ⎢(VG − VFB ) D ox ⎥ , ε s ε 0 kT ⎦ q ⎣ Qsc = Qp ≈ −C ox (VG − VFB ) .

ψs =

(3.86)

(3.87)

,

,

,

VG

s

,

VG

(3.87)

Qsc

. 95

(0
2φ0) Qsc Qn

QB Qn,

:

VG = Δϕ ms −

,

.

(3.22)

ε ε kT Qox qN ss qN Q ϕ 0 − B + 2ϕ 0 − Δψ s + ss Δψ s + s 0 e − C ox C ox C ox C ox qLD C ox Δ

s

=

s

,

- 2φ0.

VT ≡ VG (ψ s = 2ϕ 0 ) .

2φ0. (3.91)

,

VT = Δϕ ms + 2ϕ 0 − VFB

96

2

(3.90) VG,

VT

(3.90)

βΔψ s

s

Qox qN ss Q 2ϕ 0 − B , + C ox C ox C ox

(3.91)

(3.92)

VT = VFB + 2ϕ 0 − (3.93)

QB qN ss + 2ϕ 0 . C ox C ox

(3.93)

,

-

VT VFB,

2φ0 s,

VG − VT ≈

ε s ε 0 kT

C ox qLD

.

Δ

s> βΔψ s

e

2

1,

:

.

(3.94)

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

ψ s = 2ϕ 0 = (3.95)

(3.96) ,

(3.95) (3.96)

,

,

VG,

-

Qn VG.

3.12

s

VG,

-

dox. 1,0

o

β ψS

dox=40 A

ψS, B

40

0,8 0,6

30

o

o

200 A

1000 A

20 0,4 10

0,2

NA=1,5 .1015cm-3

0

0

T=290 K Si-SiO2

-0,2

-10 Vg-VFB ,B

-0,4 -5

-20 -4

-3

-2

-1

. 3.12.

0

1

2

3

5

4

V G,

s

(3.84)

6

-

97

3.6.3.

–

–

, -

VG, . -

C (

)

C-V -

.

-

.

C ,

C≡

∂QM . ∂VG

⎛ dψ s C = C ox ⎜⎜1 − ⎝ dVG

Vox

,

(3.75),

(3.97) (3.77)

QM :

⎞ ⎟⎟ . ⎠

(3.98)

-

C

-

s(VG),

3.12.

(3.86) C VG. (4.14),

VG, ,

(3.98)

, -

. . (3.84) (3.79)

VG

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

(3.99)

Css, Csc – .

,

⎛ ⎞ C ox ⎟⎟ C = C ox ⎜⎜1 − + + C C C ox sc ss ⎠ ⎝

(3.99) (3.98)

,

: (3.100)

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

(3.101)

(3.101) -

, Cox Css.

98

-

s.

Csc

3.13 -

.

, -

.

COX

COX

CSC

CSS

. 3.13.

CB+Cp

-

3.14

C-V

(3.109).

,

C /Cox

1,0

o

1000 A 0,8

NA=1,5 .10 15cм -3

0,6

T=290 K Si-SiO2

0,4

o

200 A 0,2

o

dox=40 A

Vg-VFB ,B

0 -3

-2

. 3.14.

-1

0

1

2

3

4

-

C-V

p-

3.6.4. Э

-

,

. 99

,

, -

Csc,

Css , .

, -

Qn .

n

. –

C-V

К

.

C-V

C-V ,

(

(3.99).

-1

n

>>

n,

),

, -

,

, .

C-V (

.

-

. 3.14). ,

.

C-V

, -

VG,

I

-

VG (t ) = α ⋅ t ,

.

,

I ñì =

I ,

(3.97),

dQM dQM dVG = = C ⋅α . dt dVG dt -1

dU dt

>> n,

α

(3.103).

α = 10-4÷10-2 / .

(I ≤ 10-9÷10-

12

) .

3.15

-

. , 100

(3.103)

C = C(VG), I = I (VG).

-

α=

(3.102)

.

Э

Г1

. 3.15. 1

XY

C

: ,Э–

– ,C–

, XY –

-

-

C-V , ,

,

( -1 > RH . ωC

-

~ U = U 0 e i ωt ,

-

U
2φ0,

, .

,

-

,

Vox , . . Vox 0, .) < VFB ( ,

,

VFB ( .).

, Qss(

s

.).

=−

Qox qN ss ϕ0 . + C ox C ox

.) > VFB (

= 0) > 0 .

-

= 0, . . , (3.83), s

(3.113) (p-

CFB -

.), , VFB (

VFB (

. -

dox,

n-

.),

. , , Qss( Nss,

(3.113) ,

Qox, Qss < 0, -

s

= 0) < 0), (3.83)

Qss Qox. 3.6.6. – -

–

106

.

.

,

,

-

.

3.19

.

C-V

-6

C/COX

-5

-4 -3 ΔVFB

0,8

-2 -1

CFB

0

ΔVG

2

0,6

Теорет.

4 6 8

0,4

12

T=295 K NA=1,5 . 1015см-3 Si-SiO2-Al

0,2

0

-4

ΔVG,

16

Эксперим. f=1 мГц

-3 VFB

-2

20

-1

0

1

2

а NSS, см-2эВ-1

B 1012

2

1 1011 0

βψS

-10

0

10

20

EV

б

F

Ei

EC

в

. 3.19. )

ΔVG C = const , (3.115)

: -

Si-SiO2-Al; ) s,

; )

E ΔVG( s)

-

107

, s.

C = const,

s.

VG ,

C-V

(

,

s),

(3.84):

ΔVG = VG

N ss =

− VG

= VFB +

ε ox ε 0 d (VG qd ox

− VG

qN ss ψs. C ox

(3.114)

(3.114)

dψ s

,

)

:

.

(3.115)

(3.114), .

, , Nss

-

E .

ΔVG( s),

3.19

3.19 – ,

-

. И ,

, C-V

dψ s C . = 1− dVG C ox

-

. (3.98),

(3.116)

(3.116) VGi,

s

⎛

=

C ⎞

⎟dVG . ψ s − ψ si = ∫ ⎜⎜1 − C ⎟

:

VG

VGi

⎝

⎠

ox

C(VG) – (3.117) (

si,

VG =

(3.117) , ) VG.

s1

(

s1

VG1

= 0)

. VG1 –

s1

VFB. C-V

(3.99) 108

. :

VG( s),

⎡ C

⎤ C ox C sc ⎥ − . ⎢1 − C C ox ⎥ C ox ⎥⎦ ⎣⎢

ε ε N ss = ox 0 ⎢ qd ox

(3.118)

(3.118) , . C, пФ

100 Низкочастот. χ=10-2 Гц

CFB ψS=0

80

Теоретич. высокочастот.

Высокочастот. χ=106 Гц

60

Si-SiO2 ND=1015смo-3 dOX=1400 A

40

20 -14

-12

-10

-6

VFB

-4

-2

0

а ψS, B

NSS, см-2эВ-1

-0,8 -0,6 1012

-0,4 -0,2 0

Vg , B 1011

0,2 -12

-10

-8

EV

-6

б

Ei

F

EC

в

. 3.20.

:

)

s

)

Si-SiO2-Al; )

-

VG,

(3.117); E

,

(3.117)

109

(3.117) (1 - /

,

ox)

.

C-V

-

C → Cox ,

, C-V

.

3.20 , ,

C-V .

,

– VFB

-

,

-

-

T. . φ0(E),

φ0(T), . ,

VFB

VFB (T1 ) − VFB (T2 ) =

(3.83)

qN ss [ϕ 0 (T1 ) − ϕ 0 (T2 )] . C ox

-

(3.119)

(3.119) Nss:

N ss =

-

ε ox ε 0 d (ΔVFB ) . qd ox d (Δϕ 0 )

(3.120) , -

.

Nss T = (77÷400)

,

.

3.21 , ,

C-V .

110

,

-

C/C

OX

0,8 T=400 K

200

300

100

0,6

0,4 Si-SiO2-Au -3 ND=1015см o dOX=50 A

CFB

0,2

Vg , B

0 -0,8

-0,4

0

0,4

0,8

1,2

1,6

а

2,0

NSS, см-2эВ-1

EC ED

EC ED 1012 F ϕ0(T=100 K) ϕ0(T=400 K) Ei

F Ei T=400 K

T=100 K

1011

EV

EV

EV

б

Ei в

. 3.21.

:

)

T; )

φ0

EC

Si-SiO2-Al ΔVFB

; )

Nss

,

(3.120)

E -

3.7. 3.7.1. -

, Qox,

, dox,

-

ND,A, -

.

-

s,

111

VG = Δϕ ms + ψ s +

Qox qN ss (ψ s − ϕ 0 ) + Qsc , + C ox C ox C ox

–

(3.121)

.

,

dox,

Qox, ,

, ND,A

, –

.

-

, VG .

s

-

s

VG [22]. , -

-

, .

, -

.

-

– ,

-

–

-

dox

W. -

,

.

s

-

, (3.121).

.

-

. -

, Nox = 1012

,

-2

a = 100 Å. ND = 1015 a = 1000 Å.

-3

, ,

–

. .

(3.121). 112

. +10 +4 +2 0 +2 +4

C (pF)

3 12 11 10 9 8 7 6 5 4 3 2

ψs (kT/q)

2

+10 +20 мкм 100 80

1

60 40

4 20 0

20

40

60

а

мкм 0 80 100

100 мкм 80 60

C (pF)

12

40

11 10

20

мкм 0

20

40

60

80

100

б

0

7 6

мкм 100 80

C (pF)

5 4

60 40

3 2 1

0

20

40

60

. 3.22. )

20

мкм 80

-

100

в

0

:

,

; ) dox; )

,

-

, . (

)

.

3.22 -

, (0,1x0,1)

2

–

. 113

, , s

,

C, . .

-

–

, -

G

C

-

. -

s

s

-

.

3.7.2. К

Qox = qNox.

dox 3.22 , ,

ND,A,

-

. , P( s)

– . -

s

N –

.

–

α s.

,

αs

,

N –

,

P(N) :

P ( N ) = (2πN ) N :

−1

2

e

−

N=

α s Qox q

( N − N )2 2N

.

(3.122) αs

Qox

(3.122) P(Qox):

,

.

(3.123)

(3.123),

⎛ α (Q − Qox ) ⎞ ⎞ 2 ⎛ q ⎟⎟ . ⎟⎟ exp⎜⎜ s ox P (Qox ) = ⎜⎜ πα 2 2 Q qQ ox ox s ⎠ ⎝ ⎠ ⎝ 1

(3.124) :

114

P (ψ s ) = P (Qox ) ∂Qsc = C sc , qN ss = C ss , ∂ψ s

,

VG :

Qox ,ψ s – (3.126)

dQox . dψ s

(3.121) ,

qσ ψ kT

dVG = 0, αs,

dQ = (C ox + C sc + C ss )dψ s ;

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

s.

P( s)

(3.125) :

(3.124),

-

(3.126)

Qox

⎡ 1 ⎤ 2 − P (ψ s ) = ⎢ e 2 ⎥ ⎣ 2πσ s ⎦ 1

σs =

(3.125)

β (ψ s −ψ s ) 2σ s

-

,

(3.127)

⎞ 2 ⎟⎟ . ⎠

(3.128)

:

β

⎛ qQox ⎜ σs = C ox + C sc + C ss ⎜⎝ α s

,

ψs,

s

-

:

1 kT σψ = σs = q C ox + C sc + C ss (3.128)

1

⎛ qQox ⎜⎜ ⎝ α

⎞ 2 ⎟⎟ . ⎠ 1

(3.129)

,

-

. dox,

Nss,

Qox

.

(3.128),

αs ,

. Gp/

,

αs

-

(

. 3.23). 115

1,8 αs, 10 -5 см 1,7 1,6 1,5 1,4 1,3 1,2 W, 10 -5 см 1,1

0,6

0,7

0,8

0,9

1,0

1,1

1,2

1,3

αs

. 3.23.

W

3.7.3.

, , .

N 0 = a −2

,

α = N ox N . 0

α dox, a = N ox 2 . −1

-

s

:

P (ψ s ) = s

2πσ s 1

e

β (ψ s −ψ s ) 2 2σ s2

,

(3.145)

–

s

.

(3.141 – 3.144) , ,

P( s) 3.7.5.

-

n

,

-

, . .

123

3.28

-

dox = (50÷1000) Å.

s

200 100

30 100 24 49

,

.

o

1000 dox, A 455 , мВ

500 235

f

1,0

Si-SiO2-Металл Nss=1011 см-2 o Z = 50 A

0,8 0,6 0,4 0,2 0

100

200

. 3.28.

300

400

500

-

f

,

dox . .

3.29

-

N ox

0,3 1,0 8,0 24 1,0

–

10,0 250

3,0 68

.

Nss, 1011 см-2 , мВ

f Si-SiO2-Металл o dox=50 A o Z = 50 A

0,8 0,6 0,4 0,2

U, мВ 0

. 3.29.

124

100

200

f

300

400

-

N ox

,

-

N ox

,

-

. 3.30 –

. ,

«

-

,

» ,

,

. ,

, r

-

,

s

r. n 1500

λ=1,0

Si-SiO2-Металл o dox=50 A 11 Nss=10 см-2

λ=0,01 1000

500

U, мВ 0

20

40

60

. 3.30.

80

100

120

-

f

3.7.7. 3.7.3

3.7.4, -

U(ρ, )

. (3.142)

(3.136) .

U(ρ, )

(3.136)

⎤ ⎡ N ox ⎤ ⎡ q σ ψ (λ , d ox ) = ⎢ ⎥⎢ ⎥ ⎣ (ε s + ε ox )ε 0 ⎦ ⎣ 2π ⎦

-

ε1 = ε2 = ε*

(3.142) :

1

⎧⎪ ⎛ ⎞⎫⎪ 2 d ox ⎟⎬ . (3.146) ⎨ln⎜⎜1 + 2 ⎪⎩ ⎝ λ + 2d ox λ ⎟⎠⎪⎭ 1

2

125

εox ,

εs

( , dox)

. 3.31

-

( ) .

, . ( )

.

,

-

, -

. σψ, мВ 30 o

dox=1000 A 500 20 200

74 10

50

o

λ, A 20

40 60 80 100

200

400 600 800

. 3.31. , dox

(3.146)

→0

-

.

r→0 , « » .

, ,

-

. P( s)

,

.

, ,

126

-

ρmin = (5÷100) Å

. (3.136)

-

ρmin. ( , dox) U(ρ, )

(3.141) (3.136)

( , dox) . ( , dox)

(3.152).

-

-

,

⎡ ⎤ ⎡ N ox ⎤ q σ ψ (λ , d ox ) = ⎢ ⎥⎢ ⎥ ⎣ (ε s + ε ox )ε 0 ⎦ ⎣ 4π ⎦

:

1

2 2 ⎧⎪ ⎡ ⎡ (ε + ε )ε ⎤ ⎤ ⎫⎪ s ox 0 ⎨ln ⎢1 + ⎢ ⎥ ⎥⎬ , C C C λ ( ) + + ⎢ ss sc ⎦ ⎥⎦ ⎪⎭ ⎪⎩ ⎣ ⎣ ox 1

2

Cox, Css, Csc – ,

(3.147) -

,

–

. (3.147) . (3.147)

:

⎤ ⎡ N ox ⎤ ⎡ q σ ψ (λ , d ox ) = ⎢ ⎥⎢ ⎥ ⎣ (ε s + ε ox )ε 0 ⎦ ⎣ 4π ⎦ >> dox

1

2

⎧⎪ ⎡ ⎡ ε + ε d ⎤ 2 ⎤ ⎫⎪ s ox ox ⎨ln ⎢1 + ⎢ ⎥ ⎥ ⎬ . (3.148) ε λ ⎢ ox ⎦ ⎥⎦ ⎭⎪ ⎣ ⎪⎩ ⎣

(3.148) ~

.

(3.146)

-

-1

2 ( )

~ dox

-

. 3.7.8. , -

.

– Nox.

-

. -

L, ,

–

.

, 127

,

,

.

. -

, . , ,

, :

σ =

ΔQox S

.

=

qΔN ox . S

(3.149) -

ΔN

ΔN = N = N ox ⋅ S = L N ox , N–

S

(3.150) L,

N ox –

. , ,

L. ,

,

σL U= * 2ε ε 0 U0

2 ⎞ ⎛λ ⎜ − 1 − ⎛⎜ λ ⎞⎟ ⎟ . ⎜L ⎝ L ⎠ ⎟⎠ ⎝

:

σL U0 = * . 2ε ε 0 (3.151) –

(3.149)

(3.150)

-

U,

(3.151)

=0

: (3.152)

(3.152),

U0 U0 ~ L. :

q[N ox ] 2 . U0 = 2ε *ε 0

-

1

(3.153)

(3.153)

, – -

U0

N ox .

L, . –

(x, y), :

128

-

⎛ πx ⎞ ⎛ πy ⎞ ⎟ sin ⎜ ⎟ . ⎝L⎠ ⎝L⎠

σ ( x, y ) = σ 0 sin ⎜

(3.154)

, ,

-

Δϕ ( x, y, z ) = −

ρ(x, y, z) –

:

ρ ( x, y , z ) , ε 0ε *

(3.155)

. -

φ(x, y, z):

ϕ ( x, y , z ) =

2σ ( x, y ) L ⎞ ⎛ λ exp⎜ − π 2 ⎟ , * 4πε ε 0 ⎠ ⎝ L

L–

(3.156)

,

–

,

-

. , –

-

, U ,

:

U îòð = −

2σ ( x, y ) L ⎞ ⎛ (λ + 2d ox ) exp⎜ − π 2⎟. * L 4πε ε 0 ⎠ ⎝ ,

3.32,

U ( x, y , z ) =

-

:

2σ ( x, y ) L ⎡ ⎛ λ ⎞⎤ ⎛ λ + 2d ox ⎞ π 2 ⎟⎥ . ⎢exp⎜ − π 2 ⎟ − exp⎜ − * L 4πε ε 0 ⎣ ⎝ L ⎠ ⎠⎦ ⎝ (3.157)

3.32

U(x, y, z) ,

-

(3.157).

129

1,0 0,8

2dox

U/ U

0

0,6

2

0,4

2 Uпр

0,2 0

Uпр U

1

0

200

100

Uобр

- 0,2

1

λ, A 300

2

0

dox=50 A L1=200 A L2=1000 A

- 0,4

0

0

- 0,6 - 0,8 - 1,0

. 3.32.

U/U0

«

» -

3.33 ,

L. . 1,0 U/U

0

6 5

4 0,1

2 1

3 0

λ, A

0,01 1 10

. 3.33.

102

103

«

U/U0 :

dox = 50Å, 1 – L = 100Å, 2 – L = 1000Å, 3 – L = 10000Å, dox = 1000Å, 4 – L = 100Å, 5 – L = 1000Å, 6 – L = 10000Å

130

104

»

,

3.34 L

-

dox . 1,0

U/U

o

0

1000 A

o

200 A

o

0,1

λ=50 A o

100 A

o

dox=50 A o

200 A o

L, A

0,01

10 0

. 3.34.

10 1

10 2

«

U/U0 L

»

dox

,

U

.

L

(3.157)

,

L , (U/U0)max,

:

Lîïò =

2 2πd ox ⎛ λ + 2d ox ln⎜ λ ⎝

⎞ ⎟ ⎠

.

(3.158)

L ,

3.35 (3.158) .

L

L

~ dox,

>> dox. 131

10 4

o

Lопт, A

o

10

3

λ=200 A o

100 A o

50 A o

20 A o

10

dox, A

2

10 1

10 2

10 3

. 3.35.

L , U/U0, dox

3.7.9.

σψ U( ), (3.157) ( ).

L, ,

-

L ,

U0

(3.123).

, L=L , ,

, U0

(3.158).

-

→ ∞.

U

. 3.36 .

, -

, U

. , ,

dox . –

132

, → 0, ,

-

, ,

U 0. U

-

L

3.34. , ,

.

N ox = 1010 N ox = 10

12

Lmin ≈ a = N ox 2 . −1

-2

-2

(3.159) 1000Å,

Lmin

100Å.

Lmin

30 U, σu, мВ 25 20 15

o

1000 A 10

o

200 A o

dox=50 A

5

o

λ, A 0 1 10

10 2

10 3

. 3.36.

U0 U

–

, – .

: Lmax ≈ L .

, Lmin

– Lmax.

,

-

-

(3.158). -

-

RC-

, . . 133

. .

dnn Csc

εs

C sc =

ε sε d nn

dnn.

:

.

(3.160) -

dnn –

.

Γp,n

,

dnn

3.36, . ,

3.36, .

-

, (Γp) = (200÷300) Å.

-

T = (77÷350)° , ,

3.35,

, -

.

-

« .

134

»

,

4.

.

, -

, -

. :

,

p-n

,

,

.

4.1. p-n .

2,

-

,

4.1 , ,

(4.1). ,

. .

, ,

-

.

7

J = JpD + JnD

1,0

5

J

0,8

диффузионный ток 9 15

VG

J = JpE + JnE

19

34

дрейфовый ток

а

б

. 4.1. )

-

: ; )

135

J = J s (e βVG − 1) ,

(4.1)

j pE − j nD + j nE − j pD = 0 . ,

-

, . 4.1.1.

-

p-n -

: . .

4.2 .

, D

Vвх

ID Vвых

Vвх

+ VD

R

V

t

t

ID (mA)

4 3 2 1 -3

-2

-1

0

1

2

3

VD(V)

. 4.2. [10, 20]

,

, p-n

.

(4.1) U = ± 0,01 ; 0,025 ; ±0,1 ; 0,25 ; ±1 B.

K=

136

e −1 J . = − βVG − J −1 e +

βVG

: (4.2)

β -1

β −1 = 0, 025 . ,

VG, B K, .

.

± 0,01 1,0

.

±0,1 55

0,025 1,1

±1 2,8·1020

0,25 2,3·104

(4.2), ,

,

VG

-

kT/q, . VG

4

,

VG = ± 0,1 .

kT/q,

= 300

-

4.1.2. : RD.

rD

dU ⎡ dI ⎤ kT / q −1 =⎢ = β js e βV + js − js = [ β ( I + I s ) ] = . rD = ⎥ dI ⎣ dU ⎦ I + Is

-

−1

(4.3)

rD ,

.

-

rD

-

,

-

I = 25

kT/q = 25 rD = 1 .

rD

. RD VG

U U . RD = = I I 0 (e βU − 1)

:

I

(4.4)

, –

RD > rD, RD < rD. VG 0) p·n , p1·n1 (p·n > p1·n1). , dn/dt

,

,

4.6 ,

. -

. (VG < 0)

,

.

.

4.3.1.

p-n (VG < 0) p-n

,

pn = ni e

Ô n −Ô p kT

1.20

= ni2 e βU 0) p-n

4.6

,

142

1.20

-

pn = ni2 e βU >> ni2 .

, 1.20

: γn = γp.

,

Et = Ei.

(VG > 0) p·n , p1·n1 (p·n > p1·n1). Et p1 = n1 = ni, 4.6 :

-

-

γN t ni2 e βU dn . =− dt n + p + 2ni (4.11)

(4.11)

dn dt

,

-

,

.

-

, , Fn

Ei

4.11

βU

2ni e

2

ϕ 0 n,p

Fp

ϕ0 n,p U = . 2

. ,

−

dn 1 = γN t ni2 e dt 2

:

βU 2

.

J

dn qW = ∫ q dx = γN t ni e dt 2 0 :

W

W

J ðåê

βU 2

.

(4.12) -

:

J = J äèô + J ðåê = (4.13)

qLp ni2

τ p ND

,

e

βU

qW − γN t ni e 2

βU 2

.

(4.13) -

βU

J ~e n=1

,

n

,

n=2 –

.

4.6 . ,

dU ïð d (ln J ) kT/q,

-

0,028 , 0,026

. 143

10-2

I, А

10-4 10-6 10-8 10-10

U, В 0

0,1

0,2

0,3

. 4.6.

[2, 23]

4.3.3. p-n ,

ρ–

. r

l : rá = ρ , S ,l–

ρ=1

.

, V.

⋅

, l = 10-1

, S = 10-2

2

, r = 10

(4.14) -

,

p-n -

I = I 0 (e (4.15)

.

U

(4.14)

:

,

,S–

U á = Irá .

:

J

-

β (U − Irá )

− 1) ;

(4.15) -

, ,

p-n , .

, ,

, -

:

r 144

⎡ dI ⎤ =⎢ ⎣ dU ⎥⎦

−1

= [Iβ ] = −1

ϕ I

=r .

,

, ; ϕ = 0,025

r = 10 :I

=

: I

,

= 2,5 A. 4.7

ϕ r

. -

,

-

, . VD

+

ID C

A

а

rS

P-N переход rSID

rSID

8

-5

экспериментальные данные ln [ ID (A)]

ID (mA)

6 4

rS = 0

-10

rS = 15Ω

2 0 0.5

б

0.6

0.7 VD(V)

0.8

-15 0.5

0.9

0.6

0.7 VD(V)

0.8

0.9

в

Iпр, мкА 2Д925Б 100

0

T=+100 C

80

0

+25 C

60

0

-60 C

40 20 0

0,2 0,4 0,6 0,8

Uпр, В

г

. 4.7.

,

[17, 23, 26]:

) ; )

; ) 2 925

; )

, ,

-

-

,

, r ·I. 145

2 925

, .

, -

. 4.3.4. ,

,

.

:

J = J s (e βVG − 1) . (

. 4.8).

p-n+

NA > pn0.

(4.16) T = 700,

ΔT , T* ,

α = 0,07; 0,03; 0,1; 0,13.

, (4.17) T* = 10

Iобр, мкА

Iпр, мА ГД107(А,Б)

20 16

300

+60 C +25 C

200

0

-60 C

0

+25 C

100

. 4.8.

50 40

0

-60 C

30 20 -60 -30

0 5 10 15 20 Uобр, В б

0 0,2 0,4 0,6 Uпр, В а

ГД107(А,Б)

60

0

+60 C

0

12 8 4

Iпр, мА

ГД107(А,Б)

0

-

0

0 30 T, C

в

107 [23, 25]:

)

; )

; )

4.4. ,

-

-

. ,

4.9.

5

VG

1

Uстаб

0,5

7

J

Jстаб

19

9 15

а

34

б

. 4.9.

-

( )

( )

, U

,

.

-

R R

≈ 2÷50

0, .

R

:

147

– ,

, -

. . . U

, .

, ,–

-

.

p-n

5

U

:U

8 .

U

. p-n , . 4.10).

(

-

p

n EC Fn Ei EV

VG < 0

. 4.10.

p-n

,

, ,

148

-

,

. .

p-n 4.11

-

.

. 4.11.

Hψ = Eψ ,

h ∂ + U ( x) , Hˆ = − 2m ∂x 2 2m 2m α 2 = 2 E ; β = 2 ( Eg − E ) . h h 2

H–

2

–

.

d 2ψ + α 2ψ = 0 . dx 2 d 2ψ − β 2ψ = 0 . 2 dx

:

ψ = A1e ikx + B1e − ikx – ψ = As e ikx – ψ = A2 e − βx + B2 e βx – :

, , .

dψ ψ, dx

,

Tt =

ψ III ψI

(βW >> 1).

2 2

=

⎛ 4 2m E As2 ⎜− 4 exp = ⎜ 3qEh A12 ⎝

3/ 2 g

⎞ ⎟. ⎟ ⎠

:

149

:

I C→V = ATt

∫

EV

EC

f C ( E )N C ( E ) [1 − f V ( E ) ] N V ( E )dE , .

: I C→V

p+-n+ = I V →C .

I = I C→V − I V →C = ATt ∫ ( f C − f V )N C ( E ) N V ( E )dE . :

(4.18)

fC, fV –

-

. J :

I òóí

⎛ 10 8 E g3 / 2 ⎞ ⎟. = AU exp⎜ − ⎟ ⎜ E ⎠ ⎝ 2

(4.19)

E : I òóí = 10 ⋅ I 0 . ,

-

p-n E = 4⋅105 /

:

E Ge: E = 2⋅105 /

;

Si: -

. .

U z, ,

E ïð =

p-n

W =

2ε s ε 0 U îáð , qN D

U îáð W

.

-

W ,

,

W

U îáð E

2 ïð

=

2ε s ε 0 , qN D -

[5, 2]:

150

. -

E

U îáð =

2ε s ε 0 E ïð2 qN D

.

(4.20)

, .

ND =

ρ

ND :

1 ε s ε 0 μ á Eïð2 ρ áàçû . 2

Uz = (4.21)

,

ρ

(Ge): Uz = 100ρn + 50ρp; (Si): Uz = 40ρn + 8ρp, ρn, ρp –

ρμe 1

,

(4.21) -

Uz .

-

Uz :

n-

,

p-

⋅

(

).

. ,

, ,

,

, ,

, -

. -

.

.

-

4.12

,

-

. W, , ,

. :

-

,

qλE ïð ≥ E g ; W >> λ .

(4.22) 151

E(x)

VG> NC, NV.

153

p+

n+

. Iпр, мА

1,6 4

1,2

1,2

2

1И104(А-Е) 2,0

2,8

0,8 0,4 0

0,1 0,2 0,3 Uпр, В

а

. 4.14. )

б

1 104 [25, 23]:

-

; )

n +p +-

, +

p -n

+

–

,

,

4.15. EC

VG=0

p+

EV F

Fn n+

I=0

p+-n+

. 4.15.

(

)

. ,

( Eg/2).

⎛ n ⎞ ⎟ ⎜ p n0 = ⎟ ⎜ N D ⎠ ⎝ 2 i

154

(

) .

. -

, . (p+ – :

E = kT =

p+-n+

).

W=

-

p-n p-n

,

2ε sε 0 Eg 2ε sε 0 2ϕ 0 2 ⋅ 1 ⋅ 10−12 ⋅ 1 = = ~ 10−6 ñì ~ 100Å . 1.6 ⋅ 1019 qN D qN D

2mkT 1 2π h k h (2π ) ; k= ;E= 2mkT , = = kT ; λ = 2 2m h λ h2 2mλ 2 ⋅ 9,1 ⋅ 10−31 ⋅ 1,38 ⋅ 10−23 ⋅ 300 λ= ~ 140Å . 6,3 ⋅ 10−34 2

:

2

2

2

p+-n+ .

,

-

p+-n+ ,

-

. . p+-n+ .

4.16 .

EC

p+

EV Fp VG 0

κIэp

Iэp

а

б

. 5.6.

:

)

; )

5.2.1.

. 5.6 .

(+)

(–)

-

. ( – . ,

p-n-

,

–

)

-

U > 0, U < 0. 167

p-n, ,

, Lp –

W (W 0 -

p-nI n.

I

,

,

I I n. , Lp,

W

-

p-n-

. ,

-

. (U < 0,

Iý = Iê + Iá ,

|U | >> 0): I – .

,I –

,I –

I ý = I ýp + I ýn ,

I, I – . I p = ·Iэ, , I

«

–

,In– » .

κIэ.

, ,

(1 - κ) Iэ I

0

I ê0 168

:

I n = (1 – )·I , I 0. : = I0 + Ig ,

I0 –

, Ig –

.

5.7 ,

. Э

К

W

p

n

p

γIэ

γχIэ

-

IКБ0

UЭ

(1-γ)IЭ

UК

(1-χ)γIЭ

-

+

Iк

+

Iэ

IБ = (1-а)IЭ - IКБ0

. 5.7.

,

–Э

5.3. –

, -

[28, 5, 19]. , 5.8.

αII2

αNI1 JК

JЭ

К

Э J1

JБ

J2

Б . 5.8.

αNI1 –

p-n ,

I1,

I1 , 169

.

αN –

αNI1, .

5.8 α II 2 ,

I2 .

,

αI – J (αNI1

J (I1

I2 )

J ý = I1 − α I I 2 ,

:

J ê = α N I1 − I 2 .

I2

I1

I 0' –

I 0' I 0'

(

-

p-n

)

α II 2 ) (5.1)

′ I 1 = I ý0 (exp( βU ý ) − 1), ′ I 2 = I ê0 (exp( βU ê ) − 1),

:

-

(5.2) .

p-n

,

I 0'

I0 . (J = 0) U. ,

I = 0,

(5.1) I = I 0,

,

I1 = αII2,

, (5.2) I2 = - I ', :

I ê = α Nα I I 2 I 1 = I 2 (α Nα I − 1) = (1 − α Nα I ) = I ê0 , I ê0 ′ I ê0 = . 1 - α Nα I

I 0. U >> kT/q.

(5.3) -

′ I ý0 =

I 0' –

,

170

1 - α Nα I I ý0

.

(5.4)

.

′ ′ J ý = I ý0 (exp( βU ý ) − 1) − α I I ê0 (exp( βU ê ) − 1) , ′ ′ J ê = α N I ý0 (exp( βU ý ) − 1) − I ê0 (exp( βU ê ) − 1) , ′ ′ J á = (1 − α N ) I ý0 (exp( βU ý ) − 1) + (1 − α I ) I ê0 (exp( βU ê − 1)) , (5.2) (5.1),

J –

:

,

:

I

I.

(5.5)

(5.5)

– . -

I0 : J = J (J = 0).

, -

. –

,

, ,

,

. , .

5.4.

, ,

–

.

p-n-p

-

U > 0, U < 0. – J, U (exp( βU ý ) − 1) ,

J = αNI

0

′ ′ I + α I I (exp(βU ) − 1) (exp(βU ) − 1) − I 0 (exp(βU ) − 1) = ′ I0 = α N I − (1 − α Nα I ) = α N I − I 0 (exp(βU ) − 1) . :

J

,

J = α N I − I 0 (exp(βU ) − 1) .

(5.6)

(5.6) I.

I = f(U ) (5.5).

J,U, (5.5)

.

,

I′ α I ê0 = α N , ′ I ý0

U = f(I )

U

:

′ [ I ý + α I I ê0 (exp( βU ê ) − 1)] ; ′ I ý0 + 1 ′ ⎤ ⎡ I I ê0 −1 ý + 1 + αI U ý = β ⋅ ln ⎢ + (exp( βU ê ) − 1)⎥ ; ′ ⎥⎦ ⎢⎣ I ý0′ I ý0 exp( βU ý ) − 1 =

171

U = (5.6)

⎤ kT ⎡ I ln ⎢ + 1 + α N (exp(βU ) − 1)⎥ . q ⎢I ′ ⎥⎦ ⎣ 0

(5.7)

(5.7) 5.9.

,

-

8

I = 6 мА 6

I, мА

5 4

4

3 2 1 0

2

0 -5

0

10

IC0

20

40

30

50

U, В . 5.9.

-

:

, (5.7)

U > 0, U < 0, |U | 0 Ei JЭ EV J Эp

Б

Э . 5.10.

γ

J,J.

dJ Jn

J = J p + J n. J p J n:

Jp

J ýp =

γ =

qp n0 Dp

σp

J

dJ , J

J p +J

=

p

n

⋅ exp(βVG ); J ýn = 1 J 1+ J

= n

:

1+

p

1 = np0 p n0

-

qnp0 Dn

σn

⋅ exp(βVG ) .

N 1 ≈ 1- D . 2 N n N 1 + i D2 N ni

, p-n-p

J

(J p). (N

>> N ).

5.7. К

. α

I

I.

, .

, ,

.

174

-

α=

dJ ê dJ ýð dJ ê ; α = γ ⋅κ . = dJ ý dJ ý dJ ýð γ

(5.9) -

.

κ

.

dp p − p0 1 = + div( j ) dt q τ ,

(5.10)

p d2p p − 2 = − 20 . 2 dx L L

(5.11)

(5.11) :

p ( x) = A1e

J =γJ

x

L

+ A2 e

−x

L

+ p0 .

(5.11)

−

dp dx

x =0

=−

(5.12) -

, U.

I qDS

, x = 0,

(5.13)

p( x) = p0 e βU ê , x = W . 1

(5.14)

2.

(5.12)

dp A1 x L A2 − x L e , e − − = L dx L (5.13)

:

x,

:

J LJ A1 A2 , A1 − A2 = − = , L L qDS qDS (5.15 )

p 0 e βU ê = A1e

:

W

L

+ A2 e

−W

L

(5.15 )

+ p0 .

(5.15 )

(5.15 , ), A1

A2

A1

(5.12)

A2. -

n(

)

: 175

⎡ ⎛ x ⎞ ⎤ ⎛W − x ⎞ ⎟ ch⎜ ⎟ ⎥ sh⎜ ⎢ ⎜L ⎟ ⎥ ⎜ L ⎟ Lp J ⎢ βU p p ⎝ ⎠ p ( x) = + p0 ⎢ e − 1 ⋅ ⎝ ⎠ + 1⎥ . qDS ⎛W ⎞ ⎛W ⎞ ⎢ ch⎜ ⎟ ⎥ ch⎜ ⎟ ⎜L ⎟ ⎥ ⎜L ⎟ ⎢ ⎝ p⎠ ⎦ ⎝ p⎠ ⎣

(

)

(5.16)

(5.16) . , x < W 1),

-

βΣ ≈ β1β2

.

. I1 dI 2, ,

,

,

1

,

2

1-2

. 1

2

. 190

-

βΣ

β1, β2 ~ 30

βΣ ~ 1000.

-

, . ,

,

,

-

, 2.

1

5.16. -

. ,

.

,

υ

=

Lp

τp

-

, ,

. ,

. . . (

). . ,

n(

. 5.20).

-

. -

j D = qD

dn . dx

-

, .

,

. 191

EC F Ei EV E(x)

E(x)

. 5.20. n-

,

E(x) jE

j = j D + j E = qD , E(x)

dn + μE ( x)n( x) = 0 . dx

(5.35)

:

E ( x) =

Dp

μp

⋅

E ( x) = −

(5.34)

,

-

1 dn( x) . ⋅ n( x) dx

μ

D

=

(5.35)

kT , q

:

dN D ( x ) 1 kT 1 dn( x) kT ⋅ ⋅ =− ⋅ ⋅ . q n( x) dx q N D (x ) dx

x N ( x) = N 0 exp(− ) ( L

:

jD

. 5.21)

(5.36)

-

.

1 dn = −n0 e dx L0

−

x L0

=−

(5.37)

E ( x) =

192

:

n( x ) . L0 (5.36),

kT 1 . q L0

(5.37) (5.38)

, ,

(5.38).

.

p-n-p

( , (

–

.

)

) .

ND+ - NA-

Э

N(x)

Б

К EC Ei

0

Эмиттер

W

База

. 5.21.

x

F EV

Коллектор

, ,

, ( ),

-

p − p0 dp d2p dp dE =− + D 2 − μE + μp . dt dx τp dx dx :

, –

(5.39)

η= ,

(5.39)

dp = 0, dt .

W – 2 L0

. ,

E=

-

kT 1 . q L0 :

193

d 2 p 2η dp p − − =0. dx 2 W dx L2p ,

−

J =γJ

dp dx

x =0

=−

p ( x ) = p0 e

N D ( x ) = N D (0) ⋅ e

−

W LD

I ýð qDS

βU ê

(5.40)

U:

, ( x = 0),

, (x = W ) .

η.

: − N D (W ) = e LD . N D ( 0) W

−

.

⎡ N (W ) ⎤ 2 W = ln ⎢ D ⎥ . 2 LD ⎣ N D ( 0) ⎦ 1

,

η=

W 1 N (W ) 1 N D (0) = − ln D = ln . 2 LD 2 N D (0) 2 N D (W )

(5.51)

(5.41)

η

,

η. ND(0) = 1017

.

-3

γ. -

.

ND(0) ND(W) , ND(W) = 1012

η = 2÷4. (5.35)

.

η

η = 5, -

:

− 2η (1−

I W 1− e p ( x) = ⋅ qDS 2η 194

-3

X ) W

.

(5.42)

η.

n(

5.22

)

-

,

p(x) η=0 2 4 0 . 5.22.

W

η

x n(

κ

)

,

-

, .

:

κ=

(5.53)

1 k (η ) ≈ . 1+η

1 . 1W2 k (η ) 1− 2 L2 k(η)

(5.43)

:

η = 2÷5,

k(η) = 0,33÷0,20.

(5.53)

k(η) ,

κ

-

β

.

β

, . :

β= , 3÷5



2 Lp α ≈ 2 (1 + η ) . 1+α W

-

2

β

-

.

195

. t .

t

=

t

W = μE

=

t t

1 t

=

1 t

+

:

kT LD WLD q ; t = kT D D q

W

t

W2 . 2D

W 2 LD 2 D 2 LD 1 = = . η D W2 W

=

1

=

1 t

+

η t

=

1+η ; t t

-

=

t

1+η

.

,

3÷5

,

.

5.17.

. h. I1 U 1 U2 (

I1

I2

. 5.23).

h11

h12

h21

h22

U1

I2

U2

. 5.23.

, ,

,

.

z-

, y-

.

h.

196

,

zI2,

I1 . :

z11 = z12 =

U1

U2 -

U 1 = z11 I 1 + z12 I 2 ; U 2 = z 21 I 1 + z 22 I 2 . :

zik

U1 I1

z 22 =

I 2 =0

.

U1 I2

U2 I2

z 21 =

I1 = 0

I1 = 0

U2 I1

–

I 2 =0

-

–

-

. z(I1 = 0)

(I2 = 0).

I1 = 0 ( -

I1 = 0). I2 = 0 (

). yU1 . :

U2,

I1

I2 -

I 1 = y11U 1 + y12U 2 ; I 2 = y 21U 1 + y 22U 2 . -

y11 = y12 =

I1 U1 I1 U2

U 2 =0

U1 = 0

y 22 = y 21 =

:

I2 U2 I2 U1

U1 = 0

U 2 =0

–

–

.

.

197

y(U1 = 0) (U1 = 0)

(U2 = 0). (

-

, ).

U2 = 0 ( ).

hh, (U2 = 0) hU2 , U1,

(I1 = 0). I1 I2 ,

U 1 = h11 I 1 + h12 I 2 ; I 2 = h21U 1 + h22U 2 .

,

I1, U2

I2, U1

:

h-

-

:

h11 =

U1 I1

U 2 =0

–

-

;

h22 =

I2 U2

I1 = 0

–

;

h12 =

U1 U2

I1 = 0

I2 I1

U 2 =0

–

-

;

h21 =

–

. h5.24 , . 198

,

-

.

h-

а

б

. 5.24.

:

)

; )

h. , 5.24 ,

-

h11 =

U1 I1

U 2 =0

h21 = h12 = h22 =

U1 U2

I2 U2

.

=

I2 I1

U =0

U 2 =0

I1 = 0

=

I1 = 0

:

U I

=

=

U U

I U

I I

≈ r + (1 − α )r ;

U =0

I =0

I =0

=

=

=α ; r +μ ; r

1 1 ≈ . r +r r (

, ,

h-

h11 =

U1 I1

U 2 =0

h21 = h12 =

U1 U2

I1 = 0

=

I2 I1 =

:

U I

U 2 =0

U U

-

U =0

=

I =0

I I =

. 5.24 ) -

≈ r + (1 − β )r ;

U =0

=β;

r r ; +μ = * r 2r 199

h22 =

I2 U2

I1 = 0

=

I U

I =0

=

1 1 ≈ ∗. r +r r ∗

( ,

) h.

2

, ,

h-

-

.

2.

h-

h11á ≈

h11

h12 á

h12 h21 h22

h11ý 1 + h21ý h h − h (1 + h21ý ) ≈ 11ý 22 ý 12 ý 1 + h21ý h h21á ≈ 21ý 1 + h21ý h h22 á ≈ 22 ý 1 + h21ý -

.

h21

. 215

5.25 .

(

)

,

( -

) – . 200

UКБ=1В

h21Э

КТ215Д-1

КТ215В-1, КТ215Г-1, КТ215Е-1

300 250 200 150 100 50 0 0,01

0,1

1

10

Iэ, мА

100

КТ215А-1, КТ215Б-1

. 5.25.

215

h21 I [24, 29]

5.18. .

,

τD =

,

υ

W

~

W ⋅ Lp D

.

.

-

. ,

τD.

t=0

τD, α0I .

, T + τD.

,

t 1.

,

τD + t1 t = T,

-

,

-

α0I 201

Δjэ, Δjк

1

α0

0

t1

t

а

Δjэ, Δjк

1

α0

0

t

б

Δjэ, Δjк

1 α1

0

t

в

. 5.26.

(

)

)

, ; )

)

202

(

,

τD [28, 15]:

) ;

T + τD. (

t1 (

)

,

I = αI I

I

⎛ τ Dω ⎞ ⎟. ⎝ 2π ⎠

ϕ α ~ arctg⎜

τD T

.

=

,

Δj

ϕ

,

tgϕ =

(5.44)

5.26 ) τD.

ϕ

τ Dω . 2π

: (5.44)

τD

Δj

. .

,

T >τD “ 4

I = αI

(

-

-

”

. 5.26 ). -

, (

α(ω).

α(ω)

,

|α|

α(ω) .

-

-

.

2

:

ϕα,

5.27

ω,

|α|

. 5.26 ).

ωα

α (ωα ) 1 . = α0 2

α0,

-

(5.45) 203

Δjэ, Δjк

1

2 1'

3 2'

3'

0

t

τD

. 5.27. )

(

α(ω)

( T/4 < τD

)

α

κ ⋅ α = ⋅κ ,

γ

-

κ (ω). κ (ω)

-

p − p0 dp d2p =− + Dp 2 . dt τp dx ,

U =U

U =U

0 0

(5.46)

+ U exp(iωt ); +U

exp(iωt )

(5.47)

:

exp(i (ω + ϕ )t ). i

(5.47)

i.

,

-

(5.46) p(x,t), .

:

ω=0 (

204

κ (ω ) =

iê = iýð

-

1 W ⎤ ⎡ ch ⎢(1 ± iω Lp ) 2 ⎥ Lp ⎦ ⎣

1

)

.

κ (ω = 0):

(5.48)

(5.48)

κ (ω = 0) =

1 1W2 ≈ 1− . 2 W 2 L p ch Lp

(5.48) κ (ω)

κ (ω ) 1 . = κ0 2

2

(5.49)

ωα = ωχ,

:

(5.48) .

κ (ω ) = 1 − (1 + iωτ p ) ⋅

,

,

-

1W2 1W2 1W2 1W2 = − + ωτ = κ + ωτ . 1 i i p 0 p 2 Lp 2 2 Lp 2 2 Lp 2 2 Lp 2 (5.50)

κ (ω ) = κ 02 − ω 2τ p2 κ (ω ) = κ 02 2

κ 02 − ωα2τ p2 κ

1W4 . 4 Lp 4 ωα

:

4

1W 4 Lp 4

=

2 0

1 . 2

,

1W 1 κ −ω τ = κ 02 . 4 4 Lp 2 2 0

4

2 2 α p

ωα =

G(α0) ≈ 2,53.

, Lp2 = Dpτp,

ωα =

⋅ 2 , 2 W

2

ωα =

Dp

G(α 0 ) Dp W2

ωατ p

κ 0 ~ 1.

=

W2 Lp

2

=

2 2

.

:

2 ⋅ Lp

τ pW 2

ωα: 2 G(α 0 ) ⋅ Lp

τ pW 2

κ

2

.

(5.51) -

,

ωα (5.52) (5.50)

(5.52)

-

: 205

κ (ω ) = κ 0 − j ϕ

ω ⋅ G (α ) . ωα

(5.53)

κ

ω

5.28.

|α| α0 ϕ

ϕα

1,0 100 90

0,8 80 70

0,6 60 50

0,4 40 0,2

30 20 10

0 −2

10

ϕα

2

4

6 10−1

2

4

6

2

1,0

6

10

ω ωα

|κ (ω)|

ω [28, 15]

. 5.28.

4

⎛ 1 G (α 0 ) ⋅ ω ⎞ ⎟⎟ . ωα ⎝ 2π ⎠ ω,

ϕα = arctg ⎜⎜

(ω/ωα = 1,0), |κ (ω)| = 0,71,

ϕα = 60º. ,

ϕ = 55º,

ωα

ω-1 ~ τD,

|κ (ω)|

.

α(ω)

206

R -

α0I ,

(

. 5.29).

α(ω)I .

R

-

R

α 0J э

α(ω)Jэ

С

α(ω)

. 5.29. RC-

,

Z

RC-

1 1 = 2 + ωC 2 , 2 Z R

α0Iý =

, Z =

:

1 + (ωRC ) R

2

.

U~ . Z

Zα 0 I ý U 1 α (ω ) I ý = ~ = = α0Iý . R R 1 + ω 2C 2 R 2 :

IR

α (ω ) 1 = . α0 1 + ω 2C 2 R 2

,

ωα

α (ωα ) 1 , = α0 2

(5.55)

α (ω ) = α0

:

ϕ

R IR IC

C.

ωα = 1/RC.

,

1

1 + ⎛⎜ ω ⎞⎟ ⎝ ωα ⎠

(5.54)

2

-

.

.

U RωC = α0Iý I C = ~ = Zα 0 I ýωC = α 0 I ý RC 1 + ω 2C 2 R 2

(5.55)

α0I

ω

ωα

1 + ⎛⎜ ω ⎞⎟ ⎝ ωα ⎠

2

.

207

,

RC-

:

ϕ,

α0Iý ωω

α

⎞ 1 + ⎛⎜ ω ⎟ ω IC α ⎠ ⎝ = tgϕ = α0Iý IR

⎞ 1 + ⎛⎜ ω ⎟ ω α ⎠ ⎝

:

α (ω ) =

α (ω ) =

α0

(5.57)

⎛ω 1 + ⎜⎜ ⎝ ωα

⎞ ⎟⎟ ⎠

2

α0

ω 1+ i ωα ,

,

(5.56) (5.55). (5.56) , ϕ = 55º.

ω = ωα

⎛

, exp⎜⎜ − i

⎝

⎞ ω ⋅ m ⎟⎟ . ωα ⎠

m = 0,2 Δϕ = 60º.

α (ω ) =

2

=

ω . ωα

(5.56)

2

α(ω)

RC-

.

(5.57)

ω tg (ϕ α ) = , ωα

R α(ω) ,

⎞ ω ⋅ m ⎟⎟ ⎝ ωα ⎠. ω 1+ i ωα

ϕ

-

RC-

ω = ωα

⎛

α 0 exp⎜⎜ − i

(5.58)

-

208

β

.

α

α β= . 1−α ,

:

5.30.

JЭ

JБ

{

JЭ

JК

JБ

ϕα≈600

. 5.30. ,

I

ω 0 (n,

-

,

-

6.18 . VT < 0

6.18 .

241

6.13.

(6.64).

VT ,

-

:

VT )

NA (

φ0 ,

-

φms,

pa

Q ); ) ) )

Nss; Q ; -

VSS (

). ,

Q .

)

)

) . (

-

,

)

,

-

, VT

Q . ,

-

,

– –

–

(

-

)

. 6.16 ,

,

. -

. (dox < 50 Å)

.

-

(d ≈ 1000 Å) Si3N4

. -

ε Si3N 4

, SiO2.

Si3N4

242

,

SiO2.

-

Металл Нитрид Окисел

Al Si3N4 SiO2

n+

n+

а

Al SiO2

Металл Окисел Плавающий затвор n+

Si п/к n+

б

. 6.16. )

:

-

; )

6.17

,

.

-

.

-

+VGS .

,

6.17 ,

.

, .

, .

-

-VGS ,

6.17 . -

,

6.17 ,

.

ε Si3N 4 = 6 .

-

.

, ΔVT = 10 , d Si

= 1000 A ,

-

3N 4

243

Si SiO2 Si3N4 Al ловушки

а

-VGS

+VGS

б

в

. 6.17.

-

)

:

, ; )

ΔN ox =

ΔQox q

; )

=

C ox ΔVT ε ox ε 0 ΔVT = . q qd ox ΔNox ≈ 3·1011

(6.84), ,

(6.84)

1 100 Å,

, 2·1018

Nt

-3

·

-1

-2

.

-

.

6.14. -

.

,

.

,

, 6.18 , , . , 244

.

+VGS б

Si SiO2 Si

SiO2

Al VGS=0

а

в

. 6.18.

:

)

,

VGS

; ) +VGS; )

6.18a

.

-

6.18 . 6.18 . -

.

, . Qox( )

:

Qox (τ ) = ∫ I (t )dt ,

-

τ

(6.85)

0

I(t) –

t. 6.18, . I(t)

⎛ B ⎞ ⎟⎟ . I (t ) = AE ox2 exp⎜⎜ − ⎝ E ox ⎠

-

: (6.86)

(6.86)

– . 245

,

(6.86), . Q( )

-

x

.

,

,

:

E ox =

d SiO

2

VG + d Si

− 3N 4

ε SiO 2

Q(τ ) ⎛ d SiO 2 + ε Si N ⎜ 3 4⎜d ⎝ Si3N 4

-

⎞ ⎟ ⎟ ⎠

.

(6.87)

(6.87) VG, .

–

, -

,

(6.87) . (6.85 – 6.87)

,

,

Q( ) .

I(t)

Q( ).

(6.85 – 6.87)

.

6.15. , ,

(

6.19

).

-

, .

-

.

-

1-2

.

.

246

Me

VG1

VG2

VG3

SiO2

а

p-Si

VG1>0

VG2=0

VG3=0 б

VG1>0

VG2>VG1

VG3=0 в

VG1=0

VG2>0

VG3=0 г

. 6.19.

. 1-

VG1

.

1-

.

,

t -

. -

.

t1 >>

1-

6.19 ). -

t2 > t1, VG2 > VG1,

( . 22-

t2 > NA). , VDS

, .

.

-

VDS

,

-

-n

,

VGS. ,

-n ,

. Затвор

L

x

Сток

W Исток

y

n+ IDS

H

p-канал n+ z

VDS

Затвор

VGS

. 6.20.

248

-n

,

, .

, L, W,

. ,

– (VGS = VDS = 0). VGS > 0 -n

VDS < 0 Δl ,

h( y ) = H − 2Δl îá = H − 2

:

2ε s ε 0 [VGS − VDS ( y )] . qN D

VG0 – ,

qN D H 2 . 2ε s ε 0 4

(6.90)

⎛ V − VDS ( y ) ⎞ ⎟. h( y ) = H ⎜⎜1 − G ⎟ V G0 ⎝ ⎠

dR(y). dVDS(y),

(6.90)

: (6.91)

+dy, dy

IDS

dVDS ( y ) = I DS (dR( y )) .

:

dR(y)

(6.92)

:

V − VDS ( y ) ⎞ ⎟ . dR( y ) = 1− G = ⎟ W ⋅ h( y ) WH ⎜⎝ VG0 ⎠

ρ ⋅ dy

(6.92) (6.93)

∫ I DS dy = L

ρ

WH

0

∫

VDS

0

ρ ⋅ dy ⎛⎜

−1

⎡ VG − VDS ( y ) ⎤ ⎥ dVDS . ⎢1 − VG0 ⎦⎥ ⎣⎢ ρ

ρ

WH

-

-n

VG0 =

(6.89)

(6.89) ,

(VDS = 0) : h(y) = 0. (6.89)

-

:

VDS( ), .

VDS

h(y)

-

2ε s ε 0 [VGS − VDS ( y )] . (6.88) qN D

Δl îá = l îá (VG , VDS ) − l îá (VG = VDS = 0) ≈ -

, z–

(6.93) : (6.94)

ρ = (qμ p p 0 ) −1 ,

: 249

ρ

WH

= Wqμ p ρ 0 H = qWμ p Qp ( y = 0) .

(6.95)

Qp ( y = 0) = qρ 0 H – . (6.95)

(6.94) IDS

,

VG

VDS

3 3 ⎡ 2 VG 2 − (VG − VDS ) 2 ⎤ W ⎥. = μ p Qp ( y = 0) ⎢VDS − 1 3 L ⎢⎣ ⎥⎦ VG02

:

-n

I DS

(6.96)

VDS 1400

6.22 -

.

,

, ,

-

[31]. -

0,25-0,1

,

-

,

.

-

. 253

10

Размер транзистора 2,0 мкм

3,0 мкм

Длина канала, мкм

1,0 мкм

1,5 мкм

1

Длина канала

0,5 мкм

0,8 мкм

0,35 мкм

0,1

0,25 мкм 0,18 мкм 0,13 мкм 90 нм

50 нм

0,01 1970

1980

1990

2000

2010

2020

. 6.22.

6.18.

, ,

.

1960-

,

2000.

,

-

, [32]. , ,

, ,

, .

-

5 .

254

-

5. Ф

-

,

(100x100)

,

-

,

p-n

50 Å kT/q 0,025 , 10-6 /

, 10-12

-

2

/

,

-

f=1 0,03 , -

-

p-n ,

-

108

, VDS. ,

,

l p-n

⎡ 2ε ε (2ϕ 0 + VDS ) ⎤ 2 =⎢ s 0 ⎥ , qN A ⎦ ⎣

-

1

l îá

(6.104) p-n

Lmin > 2l . 6.23

-

Lmin

NA,

V ,

dox

(6.104).

dox = 100 Å

, 17

NA = 10 L = 0,4

-3

-

1-2 .

-

+

p -n

+

. 255

L, мкм dox = 400 A

1,00

300 5.1016

200 100

500 A 3.1016, см-3

1.1017

0,10

L

S

0,01

4

0

. 6.23.

D

VDS, В 12

8

,

L, ,

6.24

. . –

-

,

dox > 50 Å

,

.

L=1

,

,

= 0,03

.

kT/q .

256

, ,

-

-

1020

NA, см-3

1019 туннельный пробой 500 А/см2

1018

5 А/см2 0,05 А/см2

лавинный пробой

1017

VDS, В

1016 0

2

4

6

8

10

12

W

p-n+

. 6.24. NA

6.19.

-

-

,

-

, «

».

,

,

–

. -

(

, VT)

n

. . ,

z

y .

.

,

(6.43)

257

,

-

. ,

-

, .

,

VT

L. 6.25 L

(

-

).

p-n 6.25, . L затвор

SiO2

n-исток

n-сток

p-подложка

. 6.25.

,

,

, ,

,

VT. ,

⎧⎪ ⎡⎛ 2l ⎞ ⎤ x ⎫⎪ QB ýô = ⎨1 − ⎢⎜⎜1 + ⎟⎟ − 1⎥ J ⎬QB , x J ⎠ ⎦ L ⎪⎭ ⎪⎩ ⎣⎝

, -

:

l, QB – p-n+

(6.105)

,

, xJ –

. ,

(6.104),

L,

NA VSS (

l ).

6.26

ΔVT

. 258

-

0,5 0,4 0,3 0,2 0,1 0 -0,1 -0,2 -0,3 -0,4 -0,5

ΔVT, В

W или L, мкм

0

2

4

6

8

10

12

14

16

ΔVT

. 6.26.

L

W

.

6.27

-

.

-

. ,

.

VGS ,

,

Q

,

.

W

затвор

500 А

реальная граница ОПЗ

идеальная граница ОПЗ

p-подложка . 6.27.

,

, . .

,

, 259

, . ,

. ,

, -

. n

. ,

-

n. n

n

–

α, -

(6.10)

260

(6.12)

:

⎛ ⎝

μ n = μ n0 ⎜1 −

α⎞

⎟, L⎠

(6.106)

,

α = 0,35

. .

.

7. 7.1. – ,

-

-n

. 7.1.

(

(

-n ( 1, 2), . 7.1 ).

.

1,

-

, 3).

1-n1- 2-n2 2

– 1

( 1, 2) ,

2

3

–

. Э1

П1

Б1

П3

Б2 П2

Э2

VG = 0 p1

а

n1

p2

n2

VG = 0

EC

б EV

. 7.1.

:

)

; )

(

). .

7.2 ( 1, ,

2)

. -

7.2 . ,

. . .

7.2

261

. .

-

7.2 208.

a1

А

p1

a2

n1

p2

К

n2

+

П1

П2

Катод

а

1 2 Управляющие электроды

Управляющий электрод

4,4

П3

30

40

1,2

Uос, В

4,5

Анод

1,2 40

28

6,0

. 7.2.

5

1,1

4

1,05

3

1,0 о -60 -20 20 60 Т, С

2

б

56

tвыкл, мкс

2У208(А-Г) 6 КУ208(А-Г)

1,15 4отв

28

tвкл, мкс 2У208(А-Г) КУ208(А-Г)

100 90

tвкл tвыкл

80 70 60

0

5

10 15 Iос,и, А

в

( ),

( )

( )

[23]

n-

-

.

-

-

7.3. .

n1

(

-

2.

n2.

) +

+

p1 -n1-p2-n2 . 262

-

Ns, см-3 p1

n1

p2

n2

1020 1018 1016 1014 x=0

x=W

. 7.3.

x (Ns)

7.2.

-

,

7.4,

-

. VG,

p 1-

. 1

2

.

2,

VG .

1

p-n

2

. . VG, U ,

J ,

J, 3

(

).

-

4, 2

3 , . 263

(4)

I

Область прямых смещений (3) ("+" на слое p1)

Iу IB

(2)

(1)

VB

Vу

VG

Область обратных смещений ("-" на слое p1)

. 7.4.

:

VG –

;I,V –

-

;I,V –

7.3. . 7.5 -n-

, n- -n .

,

,

1,

,

2.

. 7.5.

264

Э1

Б1

Б2

p1

n1

p2

n1

p2

n2

Б1

Б2

Э2

-

I,

α1

1-n1-

I

2

.

-

α2 n2- 1-n1 ,

.

IÏ

–

1

3

IÏ

1→Ï 3

IÏ IÏ

3

IÏ ,

1.

,

= α1 I Ï .

1 →Ï 3

–

: (7.1)

1

2,

IÏ

1

= α2IÏ .

2 →Ï 3

: (7.2)

3

–

IÏ

.

I Ï = M (α 1 I Ï + α 2 I Ï + I Ê0 ) ,

:

3

3

I

0

1

–

3

(7.3)

(

). 1,

α = α1 + α2 – (n2-p2-n1) (7.5) « » , VG. (α1 + α2) ∞. » «

3

2

I = M (α 1 I + α 2 I + I Ê0 ) , I=

-

3

2,

,

3

(7.4)

MI Ê0 MI Ê0 , ; I= 1 − Mα 1 − M (α 1 + α 2 )

(7.5) (p1-n1-p2)

. α

-

α 1,

VG, (7.5)

I

,

«

-

». 20-50

U 1000-2000 ,

– ).

I ( ,

« α α

«

»–

-

. (α –

3

»

, ) –

p-n 265

.

7.1,

1)

(«+» 7.6.

VG>0

Э1

Б1

Б2

Э2

p1

n1

p2

n2

П3

П1

П2

jnE

jn рек EC

jn рек

VG>0

EV

jp рек jp рек

EF

Ei

jpE

jp диф

. 7.6.

[5]

,

1

,

3

2

.

– -

.

p-n

7.4. (α –

)

. n 2, p2

.

α2 -n

, ,

n 2-

2-

3,

, n 1-

.

1.

n1-

,

,

. 1

3,

266

-

n1 2.

-n -

2.

,

-

2

. 2

n1

,

3

. 7.7 2.

n1

-

p-n 1-2

. 7.7,

, ,

p-n ,

1

3

2 1

2.

Э 1 + - Б1 - + Б2 + - Э 2 VG>0

+

-

p1

n1

p2

Q0 jnD

α1 jnD

jnD -

n2

-

EC

-

VG>0

F

Ei

+ + +

Ev α1 jpD

jpD

jpD

. 7.7.

( )

,

: ,

,

.

»

, -

, «

» α

1

« 2

-

.

267

α,

J

VG ”

“

“

-

”. ,

,

,

.

-

I, , -n ,

-n

α

,

-

. ,

(

-

,

)

,

.

α

7.5. ,

α

-

,

,

.

, .

α

.

I

–

J . ,

,

JpD. 4.3.2.

,

, 7.6

-

p-n

γ

JpD

-

. α = ·κ.

, ,

-

– ,

α .

268

7.8 – I

p-n

α

1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1

0

10-7 10-6 10-5 10-4 10-3

Iэ, А α

. 7.8.

I

p-n

7.6.

VG. ,

-

, .

p-n , ,

q E, q E>

.

g,

-

.

-

. – ,

,

Ì =

Si

,

U – 3.

:

I âûõîäíîé I âõîäíîé

=

1

⎛ U 1 − ⎜⎜ ⎝UÌ ,

⎞ ⎟⎟ ⎠

n

,

(7.6)

n

, .

Ge, , 269

. ,

-

,

-

4.2, .

»,

α

-

M

.

M (α1 + α2) = 1, . 3,

«

1-2, 2

2, . «

».

»

«

3-4 p-n

-

. .

7.7. ,

, -

n1 2. 1

.

U

-

3 1

,

2

, (

.

. 7.1 ). ,

. U

.

-

7.9 .

-

I I ,

.

,

,

-

. , ,

-

I ,

: .

270

-

I

Iу1

Iу IB

Iу2

Iу=0

Iу=0

Vу

VB

VG

Iу1 Iу2>Iу1

. 7.9.

I

7.10

, .

– . Iу,от,и , мА

Iуд, мА

tвыкл, мкс 2У104(А-Г) КУ104(А-Г)

10

12

3

9

2,5

9

2У104(А-Г) КУ104(А-Г)

8

2

7

1,5 1

6 0

2

4

6 tу, мкс

2У104(А-Г) КУ104(А-Г)

6 3

0 400 800 1200 Iос, мА

0 -60 -40 -20

. 7.10.

о

0 20 Т,

С

104

7.8. , I

I I

2→ 3

1→ 3

= α1 I

= α2I

2

p-n

1

; I

= α1 I , 2

= I + Iy.

,

-

(7.7) 271

,

( I + I y )α 2 + α 1 I + I

=I .

3,

0

7.11

:

,

-

.

П3

П1

А

JА

p

П2

n

p

α1

К

JК

n

JК

α2

Jу

Jу JА

Rn . 7.11.

, :

I=

I 0 +α2I

1 − (α 1 + α 2 )

I = Iý,

,

.

-

(7.9) -

3

α 2 M ( I + I ) + α 1 MI + MI 0 = I . :

I= (7.11)

I 1−

0

α2I . (α 1 + α 2 )

+

: (7.11) ,

α2

, α1 ,

(7.10)

-

VG.

, ,

,

. I, , -n , -n

, .

272

-

8. 8.1. –

,

,

-

. ,

,

, N-

. .

1963 . ≥ 2-3

(E

(J. Gunn)

(GaAs)

. E -

, /

)

n. ,

E>E –«

,

, ~107 ,

», .

/

. ,

.

–

. , . .

,

.

8.2. , [32, 33]. , , •

:

, •

-

ό ; . 273

1,

m1*

-

,

-

. •

2,

m2*

; , . n-

. . .

-

, (

). ,

(

. 8.1). m2*=1,2 ΔE=0,36 эВ

m1*=0,068

Eg=1,43 эВ

GaAs

. 8.1.

, n1.

, n1 (n1 = n0, ):

J = en1υ Ä = enμ1 E .

m1* , n0 –

(8.1)

. . 274

l

-

-

eEl, . E ,

, .

. , . ( J

)(

-

-

. 8.2). enµ1E

enµ2E

0

E1=3,2 кВ/см

. 8.2. N-

E2=20 кВ/см

E, кВ/см

-

: E–

,

;J–

(

. 8.3). ,

,

-

, ,

, «

. »

«

»

.

. 275

E

E < EП

E EП < E < E2

E E > E2

. 8.3.

8.3. υ (E)

J = e(n1 μ1 + n2 μ 2 ) E = en0υ Ä ( E )

-

.

dυ Ä dJ = en0 . dE dE ,

:

dυ Ä dE

-

:

(8.2) -

≡ μD < 0 .

(8.3)

,

:

n2 ⎛ E ⎞ = ⎜⎜ ⎟⎟ ≡ F k , n1 ⎝ E 0 ⎠ k

k–

; E0 –

,

(8.4)

n1 = n 2 . -

:

276

μ2 ≡ B. μ1 ,

1

(8.5) -

2

,

.

, -

, 10-12

.

,

10 [34, 20].

n1

n2

n1 = n0 (1 + F ) ; :

−1

k

(8.6)

n 2 = n0 F (1 + F ) , k

n0 = n1 + n2 .

υ Ä (E) =

-

k

−1

e(n1 μ1 + n 2 μ 2 ) E (n1 μ 1 + n 2 μ 2 ) E μ1 E (1 + BF k ) J . = = = en0 e(n1 + n 2 ) n1 + n2 1+ F k :

(8.7) -

8.4 , (8.7)

.

Скорость дрейфа, см/сек

3.107

2.107

1.107

0

1 2 3 4 5 6 7 8 9 10 11

Напряженность электрического поля, кВ/см2

. 8.4.

GaAs

E , ,

~3,2 ~8000

2

/ · ,

/

.

277

2

~2400

/ · .

,

, 20

/

.

(Te) .

,

-

n2 ⎛ M 2 ⎞⎛ m2∗ ⎞ ⎟ ⎟⎜ =⎜ n1 ⎜⎝ M 1 ⎟⎠⎜⎝ m1∗ ⎟⎠

m1*, m2* –

–

3/ 2

⎛ ΔE 21 ⎞ ⎟⎟ , ⋅ exp⎜⎜ − kT e ⎠ ⎝

, n1, n2 – , M1 –

, M2 –

: (8.8) -

⎛M {GaAs: M1 = 1, M2 = 4, m1 = 0,067m0, m2 = 0,55m0, ⎜⎜ 2 ⎝ M1 *

,

*

⎞⎛ m2∗ ⎞ ⎟⎟⎜⎜ ∗ ⎟⎟ ⎠⎝ m1 ⎠

(n1 μ1 + n 2 μ 2 ) E μE ≅ 1 , ( μ1 >> μ 2 ) ; n n1 + n2 1+ 2 n1 μ1 E . υ Ä (E) = 3/ 2 ⎛ ΔE 21 ⎞ ⎛ M 2 ⎞⎛ m2∗ ⎞ ⎟⎟ ⎟⎟⎜⎜ ∗ ⎟⎟ ⋅ exp⎜⎜ − 1 + ⎜⎜ ⎝ M 1 ⎠⎝ m1 ⎠ ⎝ kTe ⎠

. 3/ 2

= 94 }.

:

υ Ä (E) =

.

(8.9)

(8.10)

-

,

[32]:

e

eEυ Ä = 3k (Te − T ) /( 2τ e ) ,

(8.11)

(~10-12 ).

–

Te ( E ) = T +

2eτ e μ1 E 2 /(3k )

⎛ M ⎞⎛ m 1 + ⎜⎜ 2 ⎟⎟⎜⎜ ⎝ M 1 ⎠⎝ m

∗ 2 ∗ 1

⎞ ⎟⎟ ⎠

3/ 2

⎛ ΔE 21 ⎞ ⎟⎟ ⋅ exp⎜⎜ − kT e ⎠ ⎝

.

8.5 GaAs

, .

278

(8.12)

3 1

υД.10-7, см/с

2

2 3

1

4

0

. 8.5. 1 – 200, 2 – 300, 3 – 350.

5

10 -3 . E 10 , В/см

15

GaAs 4–

E

T, K [32, 35]: 300

8.4.

, (

. 8.6).

E=E .

-

. :

Δn(t ) = Δn(0) ⋅ exp(−

τM t

),

(8.13) -

.

E ,

τM =

ε rε 0 εε = r 0 . σ en0 μ1

: (8.14)

279

-

+ + + + + +

n n0 0

W

x

0

W

x

E

. 8.6.

E .

,

σ − = en0 μ − ,

-

μ− –

, .

,

τM =

Δn(t)

ε rε 0 . en0 μ −

(8.15)

,

-

μ− < 0 .

,

t, . , E ,

E ,

, -

. , 280

-

.

(

)

. , -

, (

E=E

E=E )(

,

. 8.7).

. 8.7.

[5, 32]

, ,

. , , . . – Jmin. E , (d

. .)

-

–E . ,

-

U = E È W = E Ä d Ä.Ì. + E Â (W − d Ä.Ì. ) , , . .

(8.16)

E =E , W–

.

.

n0

d Ä.Ì. =

EÈ − EÂ W. EÄ − EÂ

E = f ( x)

,

(8.17)

.

n0 E

E

x ,

-

. .

,

, 281

t ïð = W / υ Ä ,

υÄ –

(8.18)

,

. -

(

)

.

. .

-

. , , .

,

,

t ïð > τ M

,

n0W >

ε rε 0υ Ä . e μ−

(8.19) [5, 32].

ε rε 0υ Ä ≈ 1012 e μ−

-2

. -

,

n0W > 1012

-2

,

(8.20)

. ,

,

,

( f = υ Ä W ). -

-

, (

. 8.8).

, ,

.

282

, . (n0)

I Imax

Imin t

tпрол

. 8.8.

-

-

,

,

. ( f > υ Ä W ).

-

, ,

-

,

-

.

,

,

E ,

f

−1

>

ε rε 0 , en0 μ1

GaAs

,

,

.

n0 > 10 4 / f

InP

«

n0 ε r ε 0 . > f eμ1 3

(8.21)

.

-

» ,

. E>E

«

.

:

»

-

, ,

ε r ε 0 n0 ε r ε 0 < < , eμ1 f e μ−

. : (8.22) 283

(

).

InP 10 4
E , ,

(E < E )

.

-

,

-

,

.

8.5.

-

, ,

, ,

-

, .

–

,

.

( f = υ l ).

P = U 2 z = E 2l 2 z =

1 Eυ ~ 2 . 2 zf f 2

:

2

(8.23)

-

. -

z , 2

1 f . (

. 8.10).

-

1

50

.

ó

-

ó , . (10,5 ). . 284

ó

– 3,2 ó

/ -

GaInSb, . Типичная зависимость генерируемой диодом Ганна мощности от приложенного напряжения

Зависимость генерируемой диодом Ганна мощности от приложенного напряжения и температуры 250

f = 10,5 ГГц

140

T = 25

120

Выходная мощность, мВт

Выходная мощность, мВт

160 0C

100 80 60 40

-30 0C

200

+25 0C

175 150 +90 0C

125 100

20 0

f = 25 ГГц

225

75 4

6

8

50

10 12 14 16 18 20 Напряжение, В

3

3,5

4

4,5 5 5,5 6 Напряжение, В

6,5 7

Частота и плотность генерируемой мощности диода Ганна в зависимости от степени легирования для случая GaN 106

5.1017 7.1017

N - уровень легирования

3.1017

Плотность мощности, Вт/см2

2.1017 104

1.1017

5.1017

7.1017

N = 8.1016 см-3

3.1017

Основная гармоника

2.1017 102 Вторая гармоника

100 100

150

200

250

1.1017

300

350

Частота, ГГц

. 8.10.

[33, 35]

, CdTe, ZnS, InSb, InAs

GaAs

InP, Ge

.,

-

. (

1

30 %), . . , . .

. ,

.

,

285

,

-

,

. -

.

, . , .

-

. ,

,

.

286

9. К . , ,

-

,

.

-

. 10862-64

1964

10862-72, 11.336.919-81

.

11.336.038-77 .

1972, 1977, 1981 .

[23 –

25, 29, 36 – 38]. , : 9 25529-82 –

.

,

-

;

9 19095-73 –

.

9 20003-74 –

;

9 20332-84 –

;

, .

.

,

,

.

9.1.

. , . .

11.336.919-81 « » 5 . . ( ,

)

4 287

, ,

,

-

. (

,

,)

1

4.

6

. 6

1 2 (

,

(

)

,

)

4

(

. . (

3

)

,

. 7)

7 ,

-

-

,

-

288

(

.

)

-

, . (

) ,

– –

.

,

–

, .

-

–

8 .

8 ,

-

,

,

:

: 1

0,3

2

0,3…10 (

-

,

.)

,

3

: -

4

150…500

5

30…150

6

5…30

7

3

0,3

:

500

2

0,3 ... 10

, ,

1

0,3

4

0,3…10 :

x15 ºC/B ) D

(Rthja15 ºC/B )

L

(Rthja