57
Review of Basic Device Physics
It can be seen from Equation 2.93 that f m is equal to the area under the E(x)
versus x plot, that is, Figure 2.18. Eliminating E max from Equations 2.91 and
2.93, we can show that
W
K N N
qN N
d
si
a
d
a d
m
=
+
(
)
2 0
ε
φ
(2.94)
In order to derive expressions for x p and x n , we integrate Equations 2.89 and
2.90 once again. Remembering that E = –df/dx, and the potential difference
between the p and n sides is f bi , it can be shown that
x
K
q
N
N N N
p
si
d
a
a
d
bi
=
+
(
)
2
0
ε
φ
(2.95)
And,
x
K
q
N
N N N
n
si
a
d
a
d
bi
=
+
(
)
2
0
ε
φ
(2.96)
0
−x p
qN d
−qN a
E
E max
ϕ
ϕ bp
ϕ bn
x
x n
ρ
FIGURE 2.18
Depletion approximation of a pn-junction: the equilibrium distribution of charge, ρ; electric
field, E; and electrostatic potential, f within the depletion region.