207 96 3MB
Russian Pages 312 Year 2004
«
» « »
. .
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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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