SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

4.5. REVERSE BIAS CHARACTERISTICS 175

∴Δpn(x−Wn)=pn 0 exp

(

−

x−Wn

Lp

)

which can be rewritten forx≥Wn

pn(x)=pn 0

[

1 −exp

(

−

x−Wn

Lp

)]

(4.5.7)

which implies that the flux of holes entering the depletion region is

Jp(Wn)=eDp

dpn(Wn)

dx

=e

Dp

Lp

pn 0

and similarly,Jn=eDLnn·np 0. Assuming no generation in the depletion region, the net current
flowing is:

Js=e

(

Dp

pn 0

Lp

+Dn

np 0

Ln

)

(4.5.8)

This result is remarkable because we get the same answer if we took the forward bias equation
(valid only in forward bias) and arbitrarily allowedVto be large and negative (for reverse bias)-
i.e.
J=Js[ exp (qV/kT)−1] (4.5.9)

ifVis large and negative,JR=−JSwhich is the answer we derived in equation 4.5.8. This
can be understood as follows. As shown in figure 4.17 any minority carrier electrons generated
within a diffusion length of thendepletion edge can diffuse to the edge of the junction and be
swept away. Minority electrons generated well beyond a lengthLnwill recombine with holes
resulting in the equilibrium concentration,np 0. Similarly holes generated withinLp, a diffusion
length, of the depletion region edge could diffuse into the depletion region. It is important to
note (from the first term of equation 4.5.8) that the slope of the minority carrier profile at the
depletion region edge :

slope=

pn 0

Lp

=

difference from bulk value

Lp

(4.5.10)

This is always true when recombination and generation dominate. Recall that even in forward
bias (shown in figure 4.18) the slope of the carrier profile is again

difference from bulk value

Lp

=

Δpn(Wn)

Lp

(4.5.11)

4.5.2 QuasiFermiLevels.............................

The Quasi Fermi Level is a very useful concept as it accurately represents the occupancy of
states of the system that it refers to. It is important to recognize that semiconductor devices
are composed of several interacting systems. For example, the conduction band containing free
electrons, the valence band containing free holes and trap states in the gap have an occupancy,