Electrical properties of p-n junction

Course: Electronic Devices
paper code: EC301
Course Coordinator: Arpan Deyasi
Department of Electronics and Communication Engineering
RCC Institute of Information Technology
Kolkata, India
8/27/2020 1Arpan Deyasi, RCCIIT, India
Topic: p-n Junction-II

Classification of p-n junction based on doping profile
Abrupt Linearly-graded
ND
NA
zn
-zp
ND
NA
W/2
-W/2
W

D n A pN z N z=
Electrical Properties of Abrupt Junction
From charge neutrality condition
Total depletion width
n pz z W+ =

A
n
D A
N
z W
N N
=
+
D
p
D A
N
z W
N N
=
+

From Poisson’s equation
dE
dz
ρ
ε
=
n DqNρ =
p AqNρ = −
D AdE qN qN
dz ε ε
= = −

D AqN qN
E dz dz
ε ε
= = −∫ ∫
1 2
D AqN qN
E z C z C
ε ε
= + =− +

at z = zn , E = 0 1
D
n
qN
C z
ε
= −
( )D
n
qN
E z z
ε
=− −
at z =-zp , E = 0 2
A
p
qN
C z
ε
= −
( )A
p
qN
E z z
ε
=− +

Maximum electric field
max
D A
n p
qN qN
E z z
ε ε
=− =−
max . . . .D A A D
D A D A
qN N qN N
E W W
N N N Nε ε
=− =−
+ +

Junction potential
n
p
z
j
z
V Edz
−
= − ∫
0
0
n
p
z
j
z
V Edz Edz
−
=− −∫ ∫

0
0
( ) ( )
n
p
z
A D
j p n
z
qN qN
V z z dz z z dz
ε ε−
= + + −∫ ∫
2 2
2 2
A D
j p n
qN qN
V z z
ε ε
= +

2 2
2 2
A D D A
j
D A D A
qN N qN N
V W W
N N N Nε ε
   
+   
+ +   
2
2
D A
j
D A
q N N
V W
N Nε
 
=  
+ 

Depletion width
1/2
2 D A
j
D A
N N
W V
q N N
ε  +
=   
  
For externally applied voltage VA
1/2
2
( )D A
j A
D A
N N
W V V
q N N
ε  +
−  
  

8/27/2020 13
Arpan Deyasi, RCCIIT, India
Depletion Capacitance
Wp n

j
j
dQ
C
dV
=
D n A pQ V qN Az qN Azρ= = =
where
A
D
D A
WN
Q qN A
N N
=
+

1/2
2A D A
D j
D A D A
N N N
Q qN A V
N N q N N
ε  +
=   
+   
1/2
2
2 D A
j
D A
N N
Q qA V
N N
ε
  
=   
+  

1/2
2
2
D A
j
j D A
qA N N
C
V N N
ε  
=   
+   
j
A
C
W
ε
=

Electrical Properties of Linear-Graded Junction
From Poisson’s equation
dE
dz
ρ
ε
=
where kzqρ =
dE kzq
dz ε
=

8/27/2020 Arpan Deyasi, RCCIIT, India 18
kzq
E dz
ε
= ∫
2
1.
2
kq z
E C
ε
= +

at z = ±W/2, E = 0
2
1 .
8
kq z
C
ε
= −
2
2
2 4
kq W
E z
ε
 
=− − 
 

at z = 0, E = Emax
2
max
8
kq
E W
ε
= −

Junction potential
/2
/2
W
j
W
V Edz
−
= − ∫
/2 2
2
/2
2 4
W
j
W
kq W
V z dz
ε−
 
= − 
 
∫

3
12
j
qk
V W
ε
=
Depletion width
1/3
12 jV
W
qk
ε 
=  
 

Depletion Capacitance
j
j
dQ
C
dV
=
where
dQ A dz Aqkzdzρ= =
/2 2
0
8
W
qAkW
Q A qkzdz= =∫

2/3
12
8
jVqAk
Q
qk
ε 
=  
 
1/3
2
12
j
j
qk
C A
V
ε 
=   
 

8/27/2020 25
Arpan Deyasi, RCCIIT, India
Wp n
Diffusion Capacitance (for Abrupt and Linear-graded)

Diode current due to holes
0 exp 1p
n
p T
AqD V
I p
L V
  
−  
  
If applied voltage is high
0 expp
n
p T
AqD V
I p
L V
 
=  
 

Charge stored at the junction due to holes
pQ Iτ=
0 expp
n p
p T
AqD V
Q p
L V
τ
 
=  
 
0 expp n
T
V
Q AqL p
V
 
=  
 

T
dQ
C
dV
=
0 expT p n
T
d V
C AqL p
dV V
  
=   
  
0
exp
p n
T
T T
AqL p V
C
V V
 
=  
 

0
exp
n p
T
T T
AqL n V
C
V V
 
=  
 
If we consider electron current

Electrical properties of p-n junction

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