pn junction under reverse bias condition
Positive of bias applied to the n-side → reverse bias
A current flows in external circuit from p to n
p-side
ID
IS
n-side
⟹
 e- exit the n-side to the external circuit
 h+ exit the p-side to the external circuit
 more bound charges are uncovered in both sides
Wdepl
ID
IS
e- e - e-
h+ h+ h+
 width of the depletion region (DR) increase
 voltage across DR increases by VR the applied
reverse bias
Wdepl
I
I
VR
 Potential barrier across DR increase
V(x)
VR
VR + Vo
Vo
-xp
xn
x
 Diffusion current ID decrease to zero ( it depends on barrier)
 Drift current IS remain unchanged (it does not dependent on barrier)
The total reverse current at equilibrium (steady state) is given by:
𝐼 = 𝐼𝑆 − 𝐼𝐷 ≅ 𝐼𝑆
 This current flows in the external circuit from p to n.
 inside the junction the current flows from n to p ( same as IS)
Since the reverse current is equal to IS it is independent of the reverse bias applied:
reverse current is constant it depends on temperature
Depletion capacitance
 width of SCL changes with applied reverse bias
⟹
 +qj and -qj charges stored at both side of junction change with bias
⟹ pn junction behaves like a capacitor
This is similar to a capacitor:
An expression for qj is: 𝑞𝑗 = 𝑞𝑁𝐷 𝑥𝑛 𝐴 ; A ≡ cross sectional area of the junction
𝑊𝑑𝑒𝑝𝑙 = 𝑥𝑛 + 𝑥𝑝
and
To get qj in terms of Wdepl, as:
Where Wdepl is given by:
𝑥𝑝
=
qj
𝑁𝐴
𝑁𝐷
𝑞𝑗 = 𝑞𝐴
𝑁 𝐴 𝑁𝐷
𝑁𝐴 +𝑁𝐷
𝑊𝑑𝑒𝑝𝑙
2 s  1
1 

(V0  VR )
wdepl 


q  N A ND 
𝑞𝑗 = 𝐴 2𝑞𝜀𝑠
𝑁𝐴 𝑁𝐷
(𝑉 + 𝑉𝑅 )
𝑁𝐴 + 𝑁𝐷 𝑜
Charge stored in Depl. Region
Use:
𝑥𝑛
Slope = Cj
Q
Bias Point
VQ
Reverse voltage VR
Curve of stored charge qj versus
applied reverse bias VR.
→
qj
 Capacitor is not constant, it depends on the bias point
 "Depletion capacitance" or "Junction capacitance" is the slope of
qj – VR curve at the bias point Q:
𝐶𝑗 =
𝑑𝑞 𝑗
𝑑𝑉𝑅
𝑉𝑅 =𝑉𝑄
=
𝜀𝑠 𝐴
𝑊 𝑑𝑒𝑝𝑙
Where Cj0 is the value of Cj at VR = 0: 𝐶𝑗 0
;
𝐶𝑗 =
𝐶𝑗 0
𝑉
1+ 𝑅
𝑉𝑜
=𝐴
𝑞𝜀 𝑠
𝑁𝐴 𝑁𝐷
2
𝑁𝐴 +𝑁𝐷
Charge stored in Depl. Region
 qj – VR is nonlinear
Slope = Cj
Q
Bias Point
VQ
1
( )
𝑉𝑜
Reverse voltage VR
𝐶𝑗 0
𝐶𝑗 =
𝑉
1+ 𝑅
𝑉𝑜
𝑚