SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

164 CHAPTER 4. JUNCTIONS IN SEMICONDUCTORS:P-NDIODES

p n

+

+

+

-wp 0 wn

In

Ip

IR

IG

Figure 4.10: Qualitative diagram of all current components flowing in ap-ndiode.

We g e t

U=

1

τ

·

pn−n^2 i

n+p+2ni

(4.4.1)

where

τ=

1

σvthNt

andpn−n^2 i=driving force for recombination andn+p+2ni=resistance to recombination.
This applies to any semiconductor with or without band bending. Note that the values ofnandp
are functions of band bending, photon flux, etc. Also, note thatUis maximized for a certain level
of perturbation when the denominator is minimized. As electrons and holes enter the depletion
region, one possible way they can cross the region without overcoming the potential barrier is to
recombine with each other. This leads to an additional flow of charged particles. This current,
called the generation-recombination current, must be added to the current calculated so far. In
figure 4.10 we show a qualitative diagram of all current components flowing in the diode.

4.4.1 Generation-Recombination Currents .................

To calculate the recombination currents in a diode, the Sah-Noyce-Shockley current,JSNS,
we consider a forward biased diode shown in figure 4.11b. Under a forward bias ofV,the
product ofnpis a constant across the depletion layer and is

np=n^2 iexp

(

eV

kBT

)

This is easily seen by recognizing that

n(x)=nn 0 exp

(

−eψ′(x)

kBT

)

(4.4.2)