SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

7.2. MODULATION AND SWITCHING OF AP-NDIODE: AC RESPONSE 313

In the forward-biased state, minority charge is injected across the depletion region. In the
reverse-bias state, the excess minority charge is below the equilibrium value. Thus in diode
switching, minority charge has to be removed and injected, and the diode temporal response is
controlled by the time it takes to inject and remove the minority charge.
To understand the time response of the diode, we use the relationship between the excess
minority charge and the current in the diode. We will assume an asymmetrically doped diode
(p+−n)so that hole lifetime will limit the device response. The total chargeQpinjected into
then-region for a long diode is

Qp=eA

∫∞

Wn

δpn(x)dx (7.2.40)

Using the relation between the charge and the voltage across the diode, we have

Qp=eALppno

(

eeV /kBT− 1

)

(7.2.41)

In steady state the current is related to the charge by

I=

Qp

τp

(7.2.42)

whereτpis the hole recombination time. For a narrow diode the relevant time is the carrier
extraction time from the neutraln-region of widthWln−Wn, which is given by:

τT=

|Wln−Wn|^2

2 Dp

(7.2.43)

A change in density with time defines the current. This give the equation

i(t)=

Qp

τp

+

dQp

dt

(7.2.44)

where the first term is due toe−hrecombination and the second is due to the change in the
minority charge with time.

Turn-ON Response

We will start by examining how ap−ndiode switches to its ON state. Consider the circuit
of figure 7.4 where a diode is driven by a square wave pulse with the voltage switching between
VFandVR. The voltageVFis much larger than the voltage across the diode under forward-bias
conditions. Let us consider how the diode responds when the voltage pulse switches toVF.As
shown in figure 7.4a, the voltage switches att=t 1. Once the diode is forward biased, the
current becomes

i(t)=

VF−V 1

R

(7.2.45)