64
Compact Models for Integrated Circuit Design
• These majority carriers neutralize the injected carriers and reestablish the charge neutrality
• While this process is going on, the injected minority carriers diffuse
into the n- and p-regions; that is, recombination process takes place
over some distance
The distribution of carriers in the n-region of the pn-junction is shown
in Figure 2.23. The majority carrier concentration shown by broken line
remains unchanged whereas the minority carrier concentration decays
exponentially and approaches to the equilibrium concentration in each side
of the junction.
The injected excess carriers set up a momentary electric field, E, in the
regions of excess carrier concentration. Then the current due to this drift
electric field in the n-region is I drift = qμ n nE for majority carrier electrons and
I drift = qμ p pE for minority carrier holes. Since n >> p, the hole drift current is
negligible in the n-region. Similarly, electron drift current is negligible in the
neutral p-region. The minority carriers move primarily by diffusion while
the majority carriers are pulled to the junction by drift. Since the injected
p-type
p p
n p
n po
n n
Unaffected by injection
Related exponentially to
n po and p no as exp(V d /v kT )
Related exponentially to
n n and p p as exp(ϕ bi /v kT )
p n
p no
n-type
FIGURE 2.22
Carriers in a pn-junction under applied bias showing the corresponding dependence on builtin potential and applied bias.
The injected hole concentration
decays to equilibrium level
over some distance
Majority carrier concentration
is essentially unchanged
n n
qΔn(x)
N d = n n o
= 10 15 >> 10 12 = p n
qΔp(x)
x
x
Δn(0) = 10 12 cm
−3
Δp(0) = 10
12 cm
−3
n n o
= 10
15
p n
p n o = 10
05
FIGURE 2.23
The carrier profile in the n-region of a pn-junction with applied bias; the majority carrier electron concentration, n no is 1 × 10 15 cm −3 and injected carrier concentration is 1 × 10 12 cm –3 describing low-level injection.
Compact Models for Integrated Circuit Design
• These majority carriers neutralize the injected carriers and reestablish the charge neutrality
• While this process is going on, the injected minority carriers diffuse
into the n- and p-regions; that is, recombination process takes place
over some distance
The distribution of carriers in the n-region of the pn-junction is shown
in Figure 2.23. The majority carrier concentration shown by broken line
remains unchanged whereas the minority carrier concentration decays
exponentially and approaches to the equilibrium concentration in each side
of the junction.
The injected excess carriers set up a momentary electric field, E, in the
regions of excess carrier concentration. Then the current due to this drift
electric field in the n-region is I drift = qμ n nE for majority carrier electrons and
I drift = qμ p pE for minority carrier holes. Since n >> p, the hole drift current is
negligible in the n-region. Similarly, electron drift current is negligible in the
neutral p-region. The minority carriers move primarily by diffusion while
the majority carriers are pulled to the junction by drift. Since the injected
p-type
p p
n p
n po
n n
Unaffected by injection
Related exponentially to
n po and p no as exp(V d /v kT )
Related exponentially to
n n and p p as exp(ϕ bi /v kT )
p n
p no
n-type
FIGURE 2.22
Carriers in a pn-junction under applied bias showing the corresponding dependence on builtin potential and applied bias.
The injected hole concentration
decays to equilibrium level
over some distance
Majority carrier concentration
is essentially unchanged
n n
qΔn(x)
N d = n n o
= 10 15 >> 10 12 = p n
qΔp(x)
x
x
Δn(0) = 10 12 cm
−3
Δp(0) = 10
12 cm
−3
n n o
= 10
15
p n
p n o = 10
05
FIGURE 2.23
The carrier profile in the n-region of a pn-junction with applied bias; the majority carrier electron concentration, n no is 1 × 10 15 cm −3 and injected carrier concentration is 1 × 10 12 cm –3 describing low-level injection.