1

2

Si: 0.543 nm

3

sp3 , r. ,

4

Si , Ge GaAs

Si: , EG= 1.12 eV

5

Ge : L , EG= 0.67 eV

GaAs : EG= 1.43eV

6

E-k

12

2 2

1n

Emk

= =

12

2 2

1p

Emk

= =

7

Fermi

( ) /

1( )e 1FE E kT

f E = +

Fermi-Dirac

. Fermi

( )

Maxwell-Boltzmann

( ) .

8

1.5kT Fermi

100( ) /MB FD MBf f f = Fermi Maxwell-Boltzmann

10%.

:

3 3V F CE kT E E kT+ :

1( )

ex p [( ) / ] 1F D Ff E

E E kT= +

( ) ex p [ ( ) / ]M B Ff E E E kT =

9

( ) ( )t o p

C

E

C C bE

f E g E d E N n = =

10

:

[1 ( )] ( )V

bottom

E

V VbE

f E g E dE N p = = :

3/ 2

2 3 3

2 ( ) 8 2( ) n n C nC Cm m E E mg E E

h

= = =

:

3/ 2

2 3 3

2 ( ) 8 2( ) p p V pV V

m m E E mg E E

h

= = =

11

:

2 3

21 exp[( ) / ]

top

C

En n C

CbF

m m E E dEn N

E E kT = = =+ =

2 30

21 exp[( ) / ]

n n C

F

m m E E dEE E kT

= + = 2 3

0

2exp[( ) / ]

exp[( ) / ]n n C

C F CF

m m E E dEN E E kT

E E kT = =

3/ 2

22 2n

Cm kTN = =

. :

3/ 2

2exp[( ) / ] 2 exp[( ) / ]2p

V V F V F

m kTp N E E kT E E kT

= = =

3/ 2

22 2p

V

m kTN

= = .

12

n p :

exp[( ) / ] exp[( ) / ]C F C V V Fnp N E E kT N E E kT= =i

exp[( ) / ] exp( / )C V V C C V GN N E E kT N N E kT= = ni = pi :

3/ 2exp( / 2 ) exp( / 2 )i i C V G Gn n p N N E kT AT E kT= = = =

5/ 2 3/ 2

21 3 3/ 23

2 ( ) 4.83 10 /m kA m Kh = =

Fermi

exp[( ) / ] exp[( ) / ]i i C F C V V Fn p N E E kT N E E kT= =

ln 2C C V FV

NkT E E EN

= +

1/ 21 ( ) ln2

VF C V

C

NE E E kTN

= + +

1/ 21 ( ) ln2

pF C V

n

mE E E kT

m = + +

13

1 ( ) ( )2F C V C V p n

E E E N N m m= + = =

( )n pe n p = +

( ) ( 1) ni i n i p i pp

e n p en b b = + = + =

( 1) exp( / 2 )i p C V Ge b N N E kT = + =

3/ 2

22 ( 1) exp( / 2 )2p n

p G

m m kTe b E kT

= + = =

exp( / 2 )GC E kT= H C :

n

p

b = , 3/ 2

p T , 3/ 2n T

14

2

( ) (0)g gaTE T E

T = +

GaAs EG(0) (eV) 0.7437 1.166 1.519 (meV/K) 0.477 0.473 0.541

() 235 636 204

15

3/ 2exp( / 2 ) exp( / 2 )i C V G Gn N N E kT AT E kT= = =

3/ 4 3/ 219

0 0

(2.510 10 ) exp( / 2 )300

pnG

mm T E kTm m

=

200 700 :

4 7 2

0

1.028 (6.11 10 ) (3.09 10 )nm T Tm

= +

4 7 2

0

0.610 (7.83 10 ) (4.46 10 )pm

T Tm

= +

ni, mn/m0 , mp/m0 (m0

)

.

.

16

( )

17

( ):

11 exp[( ) ]2

DD

D F

NnE E kT

=+

( ):

11 exp[( ) ]2

AA

F A

NnE E kT

=+

:

D A D AN N n n p p = + , ( ) :

D AN N n p = :

exp[( ) / ] exp[( ) / ] 0V V F C F C D AN E E kT N E E kT N N + =

18

2 exp( / )[exp( / )] exp( / ) 0exp( / ) exp( / )

V VD AF F

C C C C

N E kTN NE kT E kTN E kT N E kT

= :

1

1( )1 3 2( ) ln sinh2 4 exp( / )

F i

D ApF V C

n C V G

E

N NmkTE E E kTm N N E kT

= + + +

Fermi :

1sinh2

D AF Fi

i

N NE E kTn

= +

1 2sinh ln( 1)x x x = + +

10 sinhD AA N N x x

2D A

F Fi Fii

N NE E kT En= +

1sinh ln 2D A iA N N n x x

19

ln D AF Fii

N NE E kT

n=

: n-type : p-type Fermi :

Fermi n

20

Fermi p

21

2 23( )16g

e e NNkT = =11.7 :

18 3( ) 22.5 10gNN meVcm

=

22

:

2( ) /P P

dp xJ qD A mdx

= p(x) q

.

n(x) :

2( ) /n ndn xJ qD A m

dx=

V(x)

:

2( )( ) /P Pdp xJ q p x E qD A m

dx=

2( )( ) /n n ndn xJ q n x E qD A m

dx= +

Einstein:

23

11600nP

Tn

DD TV = = = . ,

,

.

.

,

, .

.

24

Jp=0 :

2( )0 ( ) /Pdp xq p x E qD A m

dx=

Einstein

:

( ) ( ) /( )TVdV x dp xE V m

dx p x dx= =

:

121 2 1

2

( )( ) lnT Tpdp xdV x V V V V V

dx p= = =

( )1 2 21exp / Tp p V V = ( Boltzmann)

V21 1 2

, x2-x1.

:

25

( )1 2 21exp / Tn n V V=

1 1 2 2n p n p= np x.

.

.

(NA ND ).

:

2

1 0 2 0i

p A nD

np p N p pN

= = = =

26

:

Millman J. & Halkias C. Integrated Electronics. Analog and Digital

Circuits and Systems. McGraw Hill (1972).

Millman J. & Grabel A. , 2 , ,

, (1996).

. . & . .

, (1980).

Pierret, R. F. Semiconductor Device Fundamentals, Addison-Wesley ,

International Edition (1996).

012

2 0

ln ln lnp A DT T Tn i

pp N NV V V Vp p n

= = =