61
Review of Basic Device Physics
The quasi-Fermi potentials and the current densities for doped semiconductors
given by Equations 2.73, 2.74, and 2.78 can be expressed as
J
qn
d
dx
J
qp
d
dx
n
n
n
p
p
p
= −
= −
µ
φ
µ
φ
(2.105)
where:
φ
φ
φ
φ
n
i
kT
i
p
i
kT
i
v
n
n
v
p
n
= −






= +






ln
ln
(2.106)
where:
f n and f p are the quasi-Fermi potentials for electrons and holes, respectively
2.3.5.1 Relationship between Minority Carrier
Density and Junction Voltage
Under forward bias V d , the barrier to majority carrier flow is reduced. And,
electrons are injected from n-region to p-region and holes are injected from
p-region to n-region. The electrons going from n-region to p-region become
minority carriers in the p-region. Similarly, holes going from p-region to
n-region become minority carriers in the n-region. Therefore, the minority
carrier behavior is of fundamental importance to understand the behavior
of a pn-junction. The minority carriers injected across the barrier will tend to
recombine if given sufficient time. They will also tend to diffuse away from
the region of the junction.
In order to calculate diode current in thermal equilibrium, let us consider
n no and p po are the equilibrium majority carrier concentrations in the neutral n- and p-regions, respectively; and n po and p no are the equilibrium minority carrier electron and hole concentrations in the neutral p- and n-regions,
respectively, as shown in Figure 2.21. Then from carrier statistics discussed in
Section 2.2.7.2, we have in the neutral n-region
n
N p
n
N
no
d
n o
i
d
≅
≅
;
2
(2.107)
and, in the neutral p-region
p
N n
n
N
po
a
p o
i
a
≅
≅
;
2
(2.108)