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Final Exam
Semiconductor Devices (ELCT503)
Time allowed : Three hours
Faculty of Information
Engineering & Technology (IET)
Electronics Engineering Dept.
Semiconductor Devices: ELCT 503
Final Exam (Fall 2014)
Course Instructor: Dr. Hassan Mostafa
Bar Code
Instructions:
1. Answer all questions.
2. The exam consists of x questions in x pages including this page.
3. A cheat sheet is attached at end of this booklet.
4. The exam allowed time is Three hours.
5. Electronic calculators are allowed.
6. Clearly show all steps used in your solutions.
7. This is a closed book exam.
Please, do not write anything on this page
Final Exam
Semiconductor Devices (ELCT503)
Time allowed : Three hours
Cheat Sheet
Intrinsic Si:
F (E) 
Carriers Transport:
1
3
mn vth2  kT
2
2
1
e ( E  EF )/kT  1
vn   μ n E

n

f(E)N(E)dE
v p  μ pE
EC
N(E) 
N(E) 
4π
( 2me )3 / 2(E  Ec )1/ 2
h3
4π
( 2mh )3 / 2(Ev  E)1/ 2
h3

n  p  ni 
 f(E)N(E)dE
J  J n  J p  e nμn  p μ p E
σ  e nμn  p μ p 
J n  eDn
n  NC e
J n  eμn nE  eDn
(EC  EF )/kT
 2π mn kT 
N C  12

2
 h

3/ 2
p  NV e (EF  EV )/kT
 2π mh kT 
NV  2

2
 h

3/ 2
Extrinsic Si:
n  ni exp (E F  Ei )/kT 
p  ni exp (Ei  EF )/kT 
Mass Action Law:
pn  n
2
i
Charge neutrality:
n  N A p  N D
J p  eμ p pE  eDp
dn
dx
dp
dx
Quasi Fermi Level:
 Ei  EFp 

p  p0  p  ni exp
 kT 
 E  Ei 
n  n0  n  ni exp Fn

 kT 
Continuity equation:
 n 1  Jn

 Gn  Rn 
t e  x
p
1  Jp

 G p  R p 
dt
e x
N A x p  N D xn
kT  N D N A 

ln 
e  ni 2 
xd 
xd 
Dn D p kT


 VT
μn
μp
e
pn junction:
Vbi 

2 N A  N D 
Vbi
e ND N A
pn with forward bias V=Va:
dp
dx
EC
e
2
2
N D xn  N A x p
2
xd  xn  x p
dn
dx
J p  eDp

Vbi 
Cj 
2 N A  N D 
Vbi  V 
e ND N A
e N A N D
2N A  N D Vbi  V 


xd


w
 D p ni2 Dn ni2    qVa  
J t  e

  1
  exp
 L p N d Ln N a    kT  
Ln  Dn n
L p  D p p
  qV  
I d  J t A  I sd exp a   1
  kT  
Reverse bias pn junction:
 D p ni2 Dn ni2 
I (Va )  qA

   I sd
 L p N d Ln N a 
Diffusion capacitance:
Cd 
Ae 2 L p pn 0
kT
 eV 
exp a 
 kT 
Final Exam
Semiconductor Devices (ELCT503)
Time allowed : Three hours
Diode DC model:

Transistor in Saturation region
Constants:
Exponential model:

(VBE >= 0.7V) and (VBC >= 0.4V)

VCE =0.2V
KT = 0.026 eV
at T=300OK

ICsat = βforced IB

IE = IC + IB = (βforced+1) IB
VD 2  VD1  nVT * ln(
I D2
)
I D1
q = 1.6 *10-19 C
0 = 8.85*10-12 F m-1
Diode small signal model:
BJT small signal:
nV
rd  T
ID
I
gm  C
VT
Eg = 1.12 eV
V
V

r  T   T 
IB
IC gm
NV = 3.08*1019 cm-3
BJT Physics:
γ
I pE

IE
T 
α0 
I pC
I pE
I pE
I pE  I nE

1
D N W
1 n B B
D p N EW E
2
1
I BB
W
1 B 2
I pE
2Lp
For Si:
Sio2 = 3.9
s = 4.05 V
V
V

re  T   T 
IE
IC gm
ψ S inv   2ψ B 
IE
2
W
Base _ Transit _ Time :  D  B
2Dp
wm  2
2kT  N A 

ln
e
 ni 
ε0 εS kT ln N A /ni 
e2 N A
Diffusion_ length : L p  D p p
Lp
Si = 11.7
|V |
ro  A
IC
MOSFET Physics:
I pC
Diffusion_ life _ time :  p 
NC = 2.84*1019 cm-3
2
Dp
BJT DC Models:
Transistor OFF
2eε0 ε S N A 2 ψ B

Vth  VFB  2 ψ B 
VFB  ms 
Cox
Qox
Cox
MOSFET DC models:

(VBE < 0.7V) and (VBC < 0.4V)


VGS < Vtn  OFF  ID=0
IB = 0

VGS >= Vtn  ON

VDS < (VGS – Vtn) (Triode)
IC = 0
IE = 0
Transistor in Active region


(VBE >= 0.7V) and (VBC < 0.4V) 
VCE >=0.3V
ID = n Cox (W/L) [(VGS - Vtn) VDS – VDS2/2]

VDS << (VGS – Vtn) (Linear)

IC = IS exp (VBE/VT)

IC = β IB =  IE
ID = n Cox (W/L) [(VGS - Vtn) VDS]

IE = IC + IB = (β+1) IB
RON = VDS/ID = 1/[n Cox (W/L) (VGS - Vtn) ]

β =  / (1- ) and β >> 1


 = β / (β+1) and  <= 1
ID =0.5* n Cox (W/L) (VGS - Vtn)2
VDS >= (VGS – Vtn) (Saturation)