SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

312 CHAPTER 7. TEMPORAL RESPONSE OF DIODES AND BIPOLAR TRANSISTORS

andGsandCdif fare given by (see equation 7.2.14)

Gs =

eI

kBT

(7.2.34)

Cdif f =

e

2 kBT

Iτp=

1

2

(

dQp

dV

)

(7.2.35)

While the diode conductanceGsis the same for low frequency ac response as its value at dc

(equation 7.2.10), we see that the diffusion capacitanceCdif f=^12

(dQ

p

dV

)

(see equation 7.2.9),

indicating thatonlyhalfoftheinjectedchargeisreclaimedthroughthejunction. The other half
recombines in the neutral region. A similar analysis can be carried out for narrow base diodes to
show that in that case, 2/3 of the injected charge is reclaimed through the junction. In general,
the diffusion capacitance of the small-signal description can be written as

Cdif f=K

e

kBT

Iτp (7.2.36)

whereKis a factor which is 1/2 for long base diodes and 2/3 for narrow base devices.
At high frequencies, the admittance becomes

y

eI

kBT

√

jωτp=

eI

kBT

√

ωτp

2

+jω

eI

kBT

√

τp

2 ω

(7.2.37)

andGsandCdif fare given by

Gs =

eI

kBT

√

ωτp

2

(7.2.38)

Cdif f =

eI

kBT

√

τp

2 ω

(7.2.39)

We see that at high frequencies both the small signal resistancers=G−s^1 and capacitanceCdif f
decrease withωas√^1 ω.
In figure 7.3b we show the equivalent circuit of a packaged diode where we have the additional
series resistanceRsassociated with the diodenandp−type neutral regions and a capacitance
Cpassociated with the diode packaging. As discussed, at forward bias the diffusion capacitance
dominates, while at reverse bias the junction capacitance is dominant.

7.2.2 Switching characteristics of diodes.....................

In many approaches the diode is switched from the conducting state to its non-conducting
state. Large-signal switching occurs in digital technology, in pulse shaping, and in optoelectron-
ics. Accurate time responses of current to voltage switching are complex series solutions to the
time-dependent semiconductor equations. However, simplified approaches give a good insight
to the problem and will be discussed.