SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

162 CHAPTER 4. JUNCTIONS IN SEMICONDUCTORS:P-NDIODES

p n

V

I

I

I

Io V

Diode symbol

Reverse current due

to drift current in the

depletion region

Forward-bias current

dominated by minority

carrier injection

Figure 4.8: Rectifying I-V current of thep-ndiode.

cannot assume that the injected excess minority carrier density will simply decay exponentially
asexp{−(x−Wn)/Lp}(for holes). In fact, for the narrow diode one has to consider theohmic
boundaryconditionswhereatthecontactstheexcessminoritycarrierdensitygoestozero.
In figure 4.9 we show a case where the diode extends a distanceWlnandWlnas shown in the
n-andp-sides. We know from section 3.9 if the diode is narrow the injected minority carrier
concentration goes from its value at the depletion edge toward zero at the contact in a linear
manner. The hole current injected acrossWnbecomes (note thatδpn(Wn)=0)

Ip(Wn)=−eADp

d(δp(x))

dx

=−eADp

[

δpn(Wn)−δpn(Wn)

Wn−Wn

]

=

−eADp

Wn−Wn

pn

[

exp

(

eV

kBT

)

− 1

]

(4.3.17)

A similar expression results in this linear approximation for the electron distribution. The net
effect is that the prefactor of the diode current changes (i.e., the termLnorLpin the denominator
is replaced by a smaller term(Wn−Wn)or(|Wp−Wp|). The prefactor becomes

Io=eA

[

Dppn 0

(Wn−Wn)

+

Dnnp 0

(|Wp−Wp|)

]

(4.3.18)

The narrow diode therefore has a higher saturation current than a long diode. The advantage of
the narrow diode lies in its superior time-dependent response—a topic we will consider later.