70
Compact Models for Integrated Circuit Design
Note that while I s is proportional to n i
2 , I gen is proportional to n i only. Thus, I gen
will dominate when n i is small as is the case at room and low temperatures.
Further, since the space charge width W d increases as the square root of the
reverse bias (Equation 2.103), the generation current increases with reverse
bias voltage as shown in Figure 2.26. Thus, taking into account I gen , the total
reverse current I r becomes I r ≡ –I d = –(I s + I gen ). This value of I r agrees well
with the measured value of reverse current and also it provides proper voltage dependence of the reverse current in properly constructed silicon planar
pn-junctions.
In real pn-junctions there is a third component of leakage current, called
the surface leakage current I sl . This current can be treated as a special
case of I gen modeled at the surface where a high concentration of dislocations at the oxide-silicon interface, often referred to as fast surface states,
provides additional generation centers over those present in the bulk. It is
very much process dependent and is responsible for large variation in the
leakage current. Both process-induced and electrically induced defects at
the surface generally increase the generation rate by an order of magnitude compared with the bulk recombination–generation rate. In that case
I sl dominates over the other components of I r and is thus responsible for
higher leakage current for a pn-junction compared to that predicted by
the sum of I gen and I s . Leakage current is highly temperature dependent
due to the presence of n i term. Also, note that the generation limited leakage current is proportional to n i while diffusion limited leakage current is
proportional to n i
2 .
Reverse bias
C
B
A
V br
I d
V d
I gen
I s
I br
Forward bias
FIGURE 2.26
Reverse characteristics of a real pn-junction; V br and I br are the breakdown voltage and current,
respectively; I s is the ideal reverse saturation current; and I gen is the generation current in the
depletion region.
Compact Models for Integrated Circuit Design
Note that while I s is proportional to n i
2 , I gen is proportional to n i only. Thus, I gen
will dominate when n i is small as is the case at room and low temperatures.
Further, since the space charge width W d increases as the square root of the
reverse bias (Equation 2.103), the generation current increases with reverse
bias voltage as shown in Figure 2.26. Thus, taking into account I gen , the total
reverse current I r becomes I r ≡ –I d = –(I s + I gen ). This value of I r agrees well
with the measured value of reverse current and also it provides proper voltage dependence of the reverse current in properly constructed silicon planar
pn-junctions.
In real pn-junctions there is a third component of leakage current, called
the surface leakage current I sl . This current can be treated as a special
case of I gen modeled at the surface where a high concentration of dislocations at the oxide-silicon interface, often referred to as fast surface states,
provides additional generation centers over those present in the bulk. It is
very much process dependent and is responsible for large variation in the
leakage current. Both process-induced and electrically induced defects at
the surface generally increase the generation rate by an order of magnitude compared with the bulk recombination–generation rate. In that case
I sl dominates over the other components of I r and is thus responsible for
higher leakage current for a pn-junction compared to that predicted by
the sum of I gen and I s . Leakage current is highly temperature dependent
due to the presence of n i term. Also, note that the generation limited leakage current is proportional to n i while diffusion limited leakage current is
proportional to n i
2 .
Reverse bias
C
B
A
V br
I d
V d
I gen
I s
I br
Forward bias
FIGURE 2.26
Reverse characteristics of a real pn-junction; V br and I br are the breakdown voltage and current,
respectively; I s is the ideal reverse saturation current; and I gen is the generation current in the
depletion region.