40
Compact Models for Integrated Circuit Design
The equilibrium condition of a semiconductor is disturbed by optically
or electrically introducing free carriers exceeding their thermal equilibrium
values resulting in pn n i
>
2 or by electrically removing carriers resulting in
pn n i
<
2 . The process of introducing carriers in access of thermal equilibrium
values is called the carrier injection and the additional carriers are called the
excess carriers. In order to inject excess carriers optically, we shine light with
energy E = hν > E g on an intrinsic semiconductor so that the valence electrons
can be excited into the CB by the excess energy ΔE = (hν–E g ), where h and ν
are Planck’s constant and frequency of light, respectively. In this process, we
get optically generated excess electrons (n L ) and holes (p L ) in the semiconductor as shown in Figure 2.10. Therefore, the total nonequilibrium values of
carrier concentration is given by
n n n
p n p
i
L
i
L
= +
= +
Injection of carriers by light
(2.47)
2.2.6.1 Injection Level
From Equation 2.47, we observe that both n and p are greater than the intrinsic carrier concentration of the semiconductor, and therefore, pn n i
>
2 for
injection of carriers into the semiconductor. If the injected carrier density
is lower than the majority carrier density at equilibrium so that the latter
remains essentially unchanged while the minority carrier density is equal
to the excess carrier density, then the process is called the low-level injection.
If the injected carrier density is comparable to or exceeds the equilibrium
value of the majority carrier density, then it is called the high-level injection.
To illustrate the injection levels, we consider an n-type extrinsic semiconductor with N d = 10 15 cm –3 . Then from Section 2.2.4.1, the equilibrium majority carrier electron concentration is given by n no = 1 × 10 15 cm –3 , whereas
from Equation 2.21, the minority carrier hole concentration is given by
Electrons
hv > E g
E c
E g
E v
Holes
h = Planck’s constant
v = Frequency of incident light
FIGURE 2.10
Band-to-band generation of electron–hole pairs under optical illumination of photon energy
hν, where h and ν are the Planck’s constant and the frequency of incident light, respectively.
Compact Models for Integrated Circuit Design
The equilibrium condition of a semiconductor is disturbed by optically
or electrically introducing free carriers exceeding their thermal equilibrium
values resulting in pn n i
>
2 or by electrically removing carriers resulting in
pn n i
<
2 . The process of introducing carriers in access of thermal equilibrium
values is called the carrier injection and the additional carriers are called the
excess carriers. In order to inject excess carriers optically, we shine light with
energy E = hν > E g on an intrinsic semiconductor so that the valence electrons
can be excited into the CB by the excess energy ΔE = (hν–E g ), where h and ν
are Planck’s constant and frequency of light, respectively. In this process, we
get optically generated excess electrons (n L ) and holes (p L ) in the semiconductor as shown in Figure 2.10. Therefore, the total nonequilibrium values of
carrier concentration is given by
n n n
p n p
i
L
i
L
= +
= +
Injection of carriers by light
(2.47)
2.2.6.1 Injection Level
From Equation 2.47, we observe that both n and p are greater than the intrinsic carrier concentration of the semiconductor, and therefore, pn n i
>
2 for
injection of carriers into the semiconductor. If the injected carrier density
is lower than the majority carrier density at equilibrium so that the latter
remains essentially unchanged while the minority carrier density is equal
to the excess carrier density, then the process is called the low-level injection.
If the injected carrier density is comparable to or exceeds the equilibrium
value of the majority carrier density, then it is called the high-level injection.
To illustrate the injection levels, we consider an n-type extrinsic semiconductor with N d = 10 15 cm –3 . Then from Section 2.2.4.1, the equilibrium majority carrier electron concentration is given by n no = 1 × 10 15 cm –3 , whereas
from Equation 2.21, the minority carrier hole concentration is given by
Electrons
hv > E g
E c
E g
E v
Holes
h = Planck’s constant
v = Frequency of incident light
FIGURE 2.10
Band-to-band generation of electron–hole pairs under optical illumination of photon energy
hν, where h and ν are the Planck’s constant and the frequency of incident light, respectively.