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Concordia University Example Formula Sheet ELEC321 Chapter 1: For FCC a

2 2 R , For BCC

4R and for di amond, a 3

a

8R 3 3a 2 2

Surface area for cubic crystal, for (100) a2, for (110) 2a 2 , and for (111) is Chapter 2:

E

h , p

h ,

p x

,

, and K.E. of a particle =

E t

Time-independent Schrodi nger equation,

d2 dx

h 2n 2

Infinite potential well: E n Poten tial barrier: T

8ma E V0

16

,

2

n

2

E V x

0

2 n x sin ;0 x a a a

x

E exp V0

1

2m 2

mv 2 . 2

2m

2K 2a , and K 2

2

V0

E

Chapter 3: 4 2m * 3 h

2

m

* 2

d E / dk

2

,g E

32

E , and f E 1 exp

1 E

EF kT

Chapter 4: n0

Nc exp

ni

N cN v e

E Fi

E midgap

(E C E F ) , p0 kT Eg / 2 kT

, n0

n i exp

(E F

1 nd

1

, and N c

EFi ) , and p0 kT

ni exp

2 mn* kT 2 h2

3/ 2

(E Fi E F ) kT

m p* 3 kT ln * , 4 mn

nd n0

N v exp

E F Ev kT

Nc 2Nd

exp

(E c

For compen sated doping: n0

Ed )

, and

1

pa pa

p0

kT Nd

Na 2

Nd

Na 2

1

Nv 4 Na

exp

(E a

Ev )

kT

2

ni2 ,

1

Concordia University Example Formula Sheet ELEC321

Chapter 5: Current den sities:

Jn

en

Jp

ep

p Ex

e(n

n

e , l = vt h , m*

nE x

p

E lectron current

p)

Hole current

1 2

and average Kineti c Energy of carriers, m* vth2

dn ( x ) KT 1 , and Dn . 0 . dx e n0 ( x) n

Induced Electric field, E x Hall effect: p

dn dx dp eD p dx

eD n

Ix BZ and edVH

Dp

3 KT 2

kT e

p

LI x epV xWd

p

Chapter 6: For n-type s emiconduc tors: R n

nt

Rp

,

p0

For direc t recombination,

p0

= 1/( rn0) and for indirect recom binati on,

Shockley-Read-Hall recombination rate: Rn

Rp

C n C p N t np ni2

Ambipolar transport equa tion in n- type semiconductor:

Quasi-Fermi leve ls: n 0

n

ni exp

kT N N ln a d , Emax e n 2i

2Vbi W

Cp p

C n n ni

Ambipolar transport equa tion in p- type semiconductor:

Dielectric re laxati on time con stant,

1 C p Nt

p0

2

n t

Dn

p t

Dp

x

pi

n n

2

2

p

x

2

E

n x

g

E

p x

g

p

n n0

p p0

d

EFn

EFi

and p 0

kT

p

n i exp

E Fi

E Fp kT

Chapter 7:

V bi

W

2 sVbi e

Na

Nd

N aN d

12

, xp

2eVbi s

N dW Na

Nd

12

N aN d Na Nd

and xn

eN d x n s

eN a x p s

Na W Na

Nd

2...