Page 103 - Microsensors, MEMS and Smart Devices - Gardner Varadhan and Awadelkarim

84 STANDARD MICROELECTRONIC TECHNOLOGIES

The depletion region has an associated depletion or junction capacitance that is given by

E r E 0 A A
C (4 10)
d = — = *OT '

where E 0 is the dielectric permittivity of free space and E T is the relative dielectric constant
that is about 12 for silicon. The space charge region / is related to the depletion voltage
V d and the external voltage V, and for an ideal junction it is given by

= \l p\ + |/nl = .— ( ~ + ^] x V[V d - V] (4.11)
q N d N a

where N d and N a are the donor and acceptor concentrations in the semiconducting mat-
erial. Thus, the capacitance of a junction diode is, in general, expressed by

= K ( V d - V ] - m (4.12)
C d

where the constant K is a function of the impurity profile and area A, and m depends on
the exact distribution of the impurities near the junction; in the ideal case, m takes a value
of 0.5, that is, a plot of 1/C 2 versus V would be a straight line. Typical characteristics
of a silicon junction diode with the conductivity of the p-type and n-type regions being
100 S/cm and 1 S/cm, respectively, are a space charge layer / of 0.5 urn at V = 0 and
1.2 um at V = —5.0 (reverse-biased) and a junction capacitance of 23 pF at 0 V and
8.3 pF at —5.0 V. The nonlinear C- V characteristic of a junction diode, together with
its significant leakage current, makes its use better suited to digital rather than analogue
circuitry.
When the junction is forward-biased (i.e. V > 0), the height of the potential barrier
is reduced, and more holes flow through diffusion from the p-type region to the n-type
region and more electrons flow through diffusion from the n-type region to the p-type
region. In a simple diffusion model, in which the transition width / is much smaller
than the diffusion length, the recombination in the depletion region can be ignored and
then the net current flow is determined from the continuity equation with an exponential
probability of carriers crossing the barrier:

where J is the current density, D denotes the diffusion coefficient of the carrier and L is
its diffusion length. The V-I characteristic of a p-n junction diode is usually rewritten
in the slightly more general form of