pn junction under Forward bias condition
Positive of bias applied to the p-side → Forward bias
A current flows in external circuit from n to p
ID
p-side
⟹
 e- enter the n-side from the external circuit
 h+ enter the p-side to from external circuit
 more bound charges are neutralized in both sides
Wdepl
ID
 voltage across DR decreases by V the applied
reverse bias
e- e- eWdepl
I
I
V
V(x)
 Potential barrier across DR decreases
(Vo-V);
IS
h+ h+ h+
 width of the depletion region (DR) decrease
Barrier =
n-side
IS
V
ID increase
Vo
Vo - V
I = ID-IS
-xp
xn
x
Diffusion of majority carriers increases
⟹
⟹
more and more of these carriers can cross the
decreased barrier to pass to the other side:
 h+ are injected across the junction to n-side
 in the n-side they are minority
 pn > pno; excess minority carrier (holes)
 excess is highest at edge of DR
 Decreases as we move away from the edge.
 e- are injected across the junction to p-side
 in the p-side they are minority
 np > npo; excess minority carrier (electrons)
 excess is highest at edge of DR
 Decreases as we move away from the edge.
Holes
ppo = NA
Carrier
Concentration
Potential barrier across DR decreases
Electrons
nno = ND
p region
npo = ni2/NA
n region
pno = ni2/ND
Depletio
n region
-xp 0
xn
x
Details of injected minority carriers
p n, n p
Steady state → excess minority carriers remain
constant as shown,
p region
n region
This distribution gives a diffusion current,
pn(xn)
 Law of the junction:
Excess
concentration
Depletio
n region
𝑉
 𝑝𝑛 𝑥𝑛 = 𝑝𝑛0 exp( )
𝑉𝑇
pn(x)
holes in n region
np(-xp)
𝑉
 𝑛𝑝 −𝑥𝑝 = 𝑛𝑝0 exp( ) electrons in p region
pno
np(x)
Thermal equilibrium
value
𝑉𝑇
npo
-xp
 Minority carriers concentrations:
𝑥−𝑥 𝑛

𝑝𝑛 𝑥 = 𝑝𝑛0 + 𝑝𝑛 𝑥𝑛 − 𝑝𝑛0 exp(−

𝑛𝑝 𝑥 = 𝑛𝑝0 + 𝑛𝑝 −𝑥𝑝 − 𝑛𝑝0 exp(
𝐿𝑝
𝑥+𝑥 𝑝
𝐿𝑛
) holes in the n region
) electrons in the p region
0
xn
x
Lp ≡ diffusion length of holes in the n region
Ln ≡ diffusion length of electrons in the p region
They are related to the excess minority carrier lifetime:
p for holes in the n region
𝐿𝑝 =
𝜏𝑝 ∼ 1 → 10000 𝑛𝑠
n for electrons in the p region
𝐿𝑛 =
𝐷𝑝 𝜏𝑝
→
𝐿𝑝 ∼ 1 → 100𝜇𝑚
𝐷𝑛 𝜏𝑛
Current voltage relationship
Holes in the n region:
p n, n p
 The hole concentration:
𝑥−𝑥 𝑛
𝑝𝑛 𝑥 = 𝑝𝑛0 + 𝑝𝑛 𝑥𝑛 − 𝑝𝑛0 exp(−
)
𝐽𝑝 𝑥 = 𝑞
𝐷𝑝
𝐿𝑝
n region
𝐿𝑝
 Hole diffusion current:
𝐽𝑝 𝑥 = −𝑞𝐷𝑝
p region
pn(xn)
Excess
concentration
Depletio
n region
𝑑𝑝 𝑛 (𝑥)
𝑑𝑥
𝑝𝑛𝑜 𝑒 𝑉
pn(x)
𝑉𝑇
−1 𝑒
−
𝑥 −𝑥 𝑛
𝐿𝑝
np(-xp)
pno
np(x)
Jp decays exponentially with x;
Thermal equilibrium
value
npo
Total current should be constant everywhere in the pn
junction
-xp
0
xn
x
J = Jelec + Jhole
Majority carriers electrons supplied by external circuit
to n region will keep total current constant
Total current
Electrons in the p region:
Very similar expressions are obtained for electrons in
the p region
Majority carrier
drift current
Jp(x)
Jn(x)
-xp
0
xn
Minority carrier
diffusion current
Holes diffusion current in the n-side
+
Electrons diffusion current in the p-side = in same direction
They are added to give the total current:
𝐼 = 𝐴 𝐽𝑝 + 𝐽𝑛
𝐼=
𝐴𝑞𝑛𝑖2
𝑞𝐷𝑝 𝑝𝑛𝑜 𝑞𝐷𝑛 𝑛𝑝𝑜 𝑉
= 𝐴(
+
)𝑒
𝐿𝑝
𝐿𝑛
𝐷𝑝
𝐷𝑛
+
𝐿𝑝 𝑁𝐷 𝐿𝑛 𝑁𝐴
𝐼𝑆 =
IS
IS
≡

IS(T)
saturation current;
𝐴𝑞𝑛𝑖2
𝑒𝑉
Scale current
→ strong dependence on temperature
IS doubles in value for every 5o rise in temperature,
− 1 = 𝐼𝑆 𝑒 𝑉
𝐷𝑝
𝐷𝑛
+
𝐿𝑝 𝑁𝐷 𝐿𝑛 𝑁𝐴
A (junction area) → Scale current
 𝑛𝑖2
𝑉𝑇
𝑉𝑇
−1
𝑉𝑇
−1
Diffusion capacitance
In Forward Bias region:
 Amount of excess minority carrier charges
p n, n p
 It changes with applied bias → capacitance
Hole distribution changes
with forward applied bias
V
Qp= qA× shaded area under pn(x) profile.
𝑄𝑝 = 𝑞𝐴
∞
𝑥𝑛
𝑝𝑛 𝑥 𝑑𝑥 = 𝑞𝐴 𝑝𝑛 𝑥𝑛 − 𝑝𝑛𝑜 . 𝐿𝑝
𝑄𝑝 = 𝑞𝐴𝑝𝑛𝑜 𝐿𝑝
𝑒 𝑉 𝑉𝑇
−1 =
𝐿2𝑝
𝐼
𝐷𝑝 𝑝
= 𝜏𝑝 𝐼𝑝
np(-xp)
pno
np(x)
Similarly:
npo
𝑄𝑛 = 𝜏𝑛 𝐼𝑛
-xp
The total charge is:
𝑄 = 𝑄𝑛 + 𝑄𝑝 = 𝜏𝑛 𝐼𝑛 + 𝜏𝑝 𝐼𝑝 = 𝜏 𝑇 𝐼;
0
xn
𝜏 𝑇 ≡ mean transit time
Case NA >> ND, most practical devices one sided pn junction
𝐼𝑝 ≫ 𝐼𝑛 ⟹ 𝐼 = 𝐼𝑝 + 𝐼𝑛 ≅ 𝐼𝑝
𝑄𝑝 ≫ 𝑄𝑛 ⟹ 𝑄 = 𝑄𝑝 + 𝑄𝑛 ≅ 𝑄𝑝
⟹ 𝜏 𝑇 ≅ 𝜏𝑝
𝐶𝑑 =
𝑑𝑄
𝑑𝑉
=
𝜏𝑇
𝑉𝑇
𝐼
I is the diode current at the bias point,
Cd is proportional to the current I
At forward bias:
Cj ≈ 2 Cjo
x