69
Review of Basic Device Physics
to 2 τ τ
p n . Thus, the total diode saturation current, I s , is the sum of Equations
2.120 and 2.123. In general, until V d reaches a value of about 0.4 V, the neutral
region diffusion current will be less than I rec .
At high current levels, the injected minority carrier density is comparable
to the majority carrier concentration (high-level injection), and therefore,
assumption 3 is invalid. For high-level injection, majority carrier concentration increases significantly above its equilibrium value, giving rise to an electric field. Thus, in such cases both drift and diffusion components must be
considered. The presence of the electric field results in a voltage drop across
this region and thus reduces the applied voltage across the junction, resulting in a lower current than expected. It can be shown that under high-level
injection the diode current I d is
I
qA n D
W
V
v
d
d i p
d
kT
=
(
)
exp 2
high-level injection
(2.124)
which indicates that high-level current depends on 1/2v kT rather than on 1/v kT as
shown in Figure 2.25. Thus, depending on the magnitude of the applied forward
voltage, the current through a pn-junction can be represented by an empirical
expression
I
I
V
n v
d
s
d
E kT
=
−
exp
1
(2.125)
where n E is called the ideality factor and is a measure of the deviation of the
real and the ideal I–V plots. When recombination current dominates or when
there is high-level injection n E = 2 and when diffusion current dominates
n E = 1.
In the case of a reverse-biased pn-junction, Figure 2.26 shows the current
through the pn-junction where I s is the current due to an ideal pn-junction
(Equation 2.119). Clearly, the current in a real pn-junction does not saturate
at −I s as predicted by Equation 2.119. This is because when the pn-junction
is reverse biased, generation of electron–hole pairs in the depletion region
takes place, which was neglected in the ideal pn-junction equation. In fact,
the generation current dominates because carrier concentrations are smaller
than their thermal equilibrium values. Again, using SRH theory, it can be
shown that the generation current I gen is
I
qA nW
gen
d i d
gen
= 2τ
(2.126)
where:
τ gen is the generation lifetime of the carriers in the depletion region and is
approximately equal to 2τ p if we assume τ p = τ n
Review of Basic Device Physics
to 2 τ τ
p n . Thus, the total diode saturation current, I s , is the sum of Equations
2.120 and 2.123. In general, until V d reaches a value of about 0.4 V, the neutral
region diffusion current will be less than I rec .
At high current levels, the injected minority carrier density is comparable
to the majority carrier concentration (high-level injection), and therefore,
assumption 3 is invalid. For high-level injection, majority carrier concentration increases significantly above its equilibrium value, giving rise to an electric field. Thus, in such cases both drift and diffusion components must be
considered. The presence of the electric field results in a voltage drop across
this region and thus reduces the applied voltage across the junction, resulting in a lower current than expected. It can be shown that under high-level
injection the diode current I d is
I
qA n D
W
V
v
d
d i p
d
kT
=
(
)
exp 2
high-level injection
(2.124)
which indicates that high-level current depends on 1/2v kT rather than on 1/v kT as
shown in Figure 2.25. Thus, depending on the magnitude of the applied forward
voltage, the current through a pn-junction can be represented by an empirical
expression
I
I
V
n v
d
s
d
E kT
=
−
exp
1
(2.125)
where n E is called the ideality factor and is a measure of the deviation of the
real and the ideal I–V plots. When recombination current dominates or when
there is high-level injection n E = 2 and when diffusion current dominates
n E = 1.
In the case of a reverse-biased pn-junction, Figure 2.26 shows the current
through the pn-junction where I s is the current due to an ideal pn-junction
(Equation 2.119). Clearly, the current in a real pn-junction does not saturate
at −I s as predicted by Equation 2.119. This is because when the pn-junction
is reverse biased, generation of electron–hole pairs in the depletion region
takes place, which was neglected in the ideal pn-junction equation. In fact,
the generation current dominates because carrier concentrations are smaller
than their thermal equilibrium values. Again, using SRH theory, it can be
shown that the generation current I gen is
I
qA nW
gen
d i d
gen
= 2τ
(2.126)
where:
τ gen is the generation lifetime of the carriers in the depletion region and is
approximately equal to 2τ p if we assume τ p = τ n