SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

308 CHAPTER 7. TEMPORAL RESPONSE OF DIODES AND BIPOLAR TRANSISTORS

The small signal junction capacitance is then

Cj =

∣

∣∣

∣

dQ

dV

∣

∣∣

∣=

A

2

[

2 e

(Vbi−V)

NaNd

Na+Nd

] 1 / 2

=

A

W

=

Cjo

(1−VVbi)^1 /^2

(7.2.6)

whereCjois the capacitance at zero applied bias. Since the depletion width depends upon the
applied bias, the diode capacitance can be tailored electronically. This voltage-dependent diode
capacitor is called a varactor is useful for tuning frequency of a resonant cavity electronically.
In real diodes, the doping in then-side andp-side gradually changes fromn−type top−type.
In such cases, the depletion capacitance of the diode is written as

Cj=

( Cjo

1 −VVbi

)m (7.2.7)

wheremis a parameter called the grading parameter. For abrupt junctions,m=1/ 2 as can be
seen in equation 7.2.6. For linearly graded junctions,m=1/ 3.
For the forward-biased diode, the injected charge density can be large and can dominate the
capacitance. The injected hole charge is (see Eqn. 5.3.12 for the forward bias hole current;
remember that charge isIτpand useτpDp=L^2 p; we also ignore 1 in the forward-bias state)

Qp=Iτp=eA LppneeV /kBT (7.2.8)

The diffusion capacitance is then

dQp

dV

=

e^2

kBT

ALppneeV /kBT=

e

kBT

Iτp (7.2.9)

Using the diode equation for small-signal ac response, the ac conductance of the diode is

Gs=

dI

dV

=

e

kBT

I(V) (7.2.10)

from the definition of theI(V)function. We will show later that this expression only holds at
low frequencies. At room temperature the conductance is (rsis the diode resistance)

Gs=

1

rs

=

I(mA)

25. 86

Ω−^1 (7.2.11)

Consider now ap-ndiode that is forward-biased at some voltageVdc, as shown in figure 7.3a. If
an ac signal is now applied to the diode, the current changes as shown schematically. The small
signal equivalent circuit of the diode is shown in figure 7.3b and consists of the diode resistance
rs(=G−s^1 ), the junction capacitance, and the diffusion capacitance. At first glance, it would