SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

4.5. REVERSE BIAS CHARACTERISTICS 173

np0 Wp Wn pn0

np(x) Pn(x)

VR

x=wn

+ x

x=-wp x=0

• x

Figure 4.16: Here the minority carriers are electrons injected from thep-region to then-region
(opposite to the forward-biased case)

We also know that the minority carrier concentration in the bulk isnp 0 (p−type) andpn 0
(n−type). Therefore, the shape of the curve will be qualitatively as shown (figure 4.16) re-
ducing from the bulk value to zero at the depletion region edge. We now consider the flow of
minority holes. The charge distribution is obtained by solving:

Dp

d^2 pn

dx^2

+Gth−R=0 (4.5.1)

WhereGthis the generation due to thermal emission of carriers, andRis the recombination
rate for excess carriers. The process of carrier recombination is driven by excess carriers. This
dependence may be written as: (whereαris a material-dependent rate constant).

R=npαr=

pn

τp

(4.5.2)

where in ap-type semiconductorτp= α^1 rn. Clearly, in an intrinsic semiconductor without
excess minority carriers the expressions forRandGthbecome equivalent - expressing the equi-
librium of the system:
Gth−R=0