68
Compact Models for Integrated Circuit Design
Equation 2.119 becomes inaccurate over a significant range of device operations
both in the forward- and reverse-biased modes.
The current voltage characteristics of a forward-biased silicon pn-junction
diode are shown in Figure 2.25 where the ideal diode current is shown by
the broken line. Two different regions of nonideal behavior are shown in
this plot. At a very low value of the forward bias (V d < 0.3 V), the injected
carrier densities are relatively small. When these carriers move through the
depletion region, some of them may be lost by recombination in this region,
thereby forming a recombination current I rec , which is added to the ideal
diode diffusion current. The result is a larger total current than that predicted
by the ideal diode Equation 2.119, particularly in the low current level, and
violates assumption 4. Thus, I rec dominates in the silicon diode at very low
current levels and negligibly small at higher current levels.
In deriving Equation 2.119, we have assumed that all the minority carriers
cross the depletion region. In practice, some recombine through trapping
centers. Then, using the SRH theory of generation and recombination, it can
be shown that the space-charge recombination current I rec is
I
qA nW
V
v
rec
d i
rec
d
kT
=
2
2
τ
exp
(2.123)
In Equation 2.123, τ rec is the lifetime associated with the recombination of
excess carriers in the depletion region. τ rec is analogous to, but usually greater
than, τ n and τ p for the neutral regions and is generally approximately equal
0.0
1.E−15
1.E−13
1.E−11
1.E−09
Generation
recombination
Current (A)
1.E−07
1.E−05
1.E−03
1.E−01
0.1
I s
0.2 0.3 0.4
I d e a l p n - j u n c t i o n
e q u a t i o n
h o l d s
H ig h -l e v el
in je ct io n
0.5
Voltage (V)
0.6 0.7 0.8 0.9
FIGURE 2.25
Forward characteristics of a real pn-junction: plot shows the deviation of ideal current equation
at the low- and high-current levels due to generation–recombination and high-level injections,
respectively.
Compact Models for Integrated Circuit Design
Equation 2.119 becomes inaccurate over a significant range of device operations
both in the forward- and reverse-biased modes.
The current voltage characteristics of a forward-biased silicon pn-junction
diode are shown in Figure 2.25 where the ideal diode current is shown by
the broken line. Two different regions of nonideal behavior are shown in
this plot. At a very low value of the forward bias (V d < 0.3 V), the injected
carrier densities are relatively small. When these carriers move through the
depletion region, some of them may be lost by recombination in this region,
thereby forming a recombination current I rec , which is added to the ideal
diode diffusion current. The result is a larger total current than that predicted
by the ideal diode Equation 2.119, particularly in the low current level, and
violates assumption 4. Thus, I rec dominates in the silicon diode at very low
current levels and negligibly small at higher current levels.
In deriving Equation 2.119, we have assumed that all the minority carriers
cross the depletion region. In practice, some recombine through trapping
centers. Then, using the SRH theory of generation and recombination, it can
be shown that the space-charge recombination current I rec is
I
qA nW
V
v
rec
d i
rec
d
kT
=
2
2
τ
exp
(2.123)
In Equation 2.123, τ rec is the lifetime associated with the recombination of
excess carriers in the depletion region. τ rec is analogous to, but usually greater
than, τ n and τ p for the neutral regions and is generally approximately equal
0.0
1.E−15
1.E−13
1.E−11
1.E−09
Generation
recombination
Current (A)
1.E−07
1.E−05
1.E−03
1.E−01
0.1
I s
0.2 0.3 0.4
I d e a l p n - j u n c t i o n
e q u a t i o n
h o l d s
H ig h -l e v el
in je ct io n
0.5
Voltage (V)
0.6 0.7 0.8 0.9
FIGURE 2.25
Forward characteristics of a real pn-junction: plot shows the deviation of ideal current equation
at the low- and high-current levels due to generation–recombination and high-level injections,
respectively.