7.2. MODULATION AND SWITCHING OF AP-NDIODE: AC RESPONSE 315
whereV 1 is the voltage across the diode and is related to the minority charge by the relation (see
Eqn. 5.3.5)
V 1 (t)=kBTln(
p(Wn)
pn)
(7.2.46)
Since turn on voltage of the diode is small compared toVF
i(t)∼VF
R
(7.2.47)
It is important to note that upon turn-on, the diode current reaches its peak value almost instantly,
as shown in figure 7.4b.
The minority charge in then-region increases gradually, and is controlled by diffusion, as
shown in figure 7.4c. From equation 7.2.46 we see that the voltage across the diode also increases
and saturates at
V 1 =kBTln(
IF
Io)
(7.2.48)
The time taken for the voltage to saturate toV 1 is approximately 2 τp. The voltage across the
diode starts from zero and grows toV 1 as shown in figure 7.4d.
Tu r n - O F F
We now discuss the turn-off behavior of the diode as shown in figure 7.5a. The voltage is
switched fromVFtoVRatt=t 2. To understand the diode response to this turn-off, we note the
relation between the excess hole density on then-side and the voltage across the diode:
δp(Wn)=pn[
exp(
eV
kBT)
− 1
]
(7.2.49)
An important outcome of this equation is that as long asδp(Wn)is positive, the voltage across
the diode is essentially the forward bias voltage (∼0.7 V). The diode current is
t<t 2 : i(t)=IF=VF−V 1
R
t=t 2 : i(t)=IR=VR−V 1
R
(7.2.50)
Since the diode is in the forward-biased state before the diode is reverse biased, there is excess
minority charge (holes) stored in then-side. The diode response is controlled by the rate at
which this charge is removed. Ift 3 is the time at which the excess minority charge is extracted,
then up to this time, the diode cannot be reverse biased (see equation 7.2.49). To examine the
time response, let us examine the charge control equations
t<t 2 : i(t)=IF=Qp
τpt=t 2 : i(t)=IR=Qp
τp+
dQp
dt