-
Dynamic behavior determines the maximum operational frequency.
-
It is dependent on how fast charge can be moved around.
-
Two capacitances
:
-
Depletion
and
diffusion
.
-
Depletion
region and
Junction
capacitance:
-
Under the ideal model, the depletion region is void of mobile carriers.
-
Its charge is determined by the immobile donor and acceptor ions.
-
Intuitively:
-
Forward bias
: Potential barrier is reduced which means that
less
space charge
is needed to produce the potential difference.
-
This corresponds to a
reduced
depletion-region width.
-
Reverse bias
: Potential barrier increased, increase in space charge,
wider
depletion width.
-
Expressions that convey this fact.
-
Depletion region charge
(V
D
is positive for forward bias):
-
The ratio of the n-side versus p-side depletion region width is determined by the doping level ratios:
-
The model
(for an abrupt junction)
:
-
Imagine the depletion region as the
dielectric
of a capacitor with dielectric constant of silicon.
-
And the n- and p-neutral regions act as the capacitor plates:
-
A small change in the voltage applied to the junction (dV
D
) causes a change in the space charge (dQ
j
).
-
Junction
capacitance:
-
Junction capacitance is easily computed by taking the derivative of equation (1) with respect to V
D
. For an abrupt junction:
-
C
j0
is the capacitance under
zero-bias
conditions and is only a function of the
physical parameters
of the device:
-
The same result can be obtained using the standard parallel-plate capacitor equation:
-
Junction
capacitance plotted as a function of applied voltage bias:
-
Capacitance
decreases
with an
increasing
reverse bias.
-
For -5V, the cap. is reduced by more than a factor of 2 over the zero bias case.:
-
Where
m
is the grading coefficient.
-
For an abrupt junction, m = 1/2.
-
For a linearly graded junction, m = 1/3.
-
For digital circuits, operating voltages tend to move rapidly over wide ranges.
-
In these cases, we can replace the voltage-dependent, nonlinear capacitance C
j
with an equivalent, linear capacitance C
eq
.
-
Diffusion
Capacitance:
-
Under
forward bias
, the pn-junction exhibits a capacitive effect
much larger
than just the junction capacitance.
-
This is due to the
excess minority carrier
charge stored at the boundaries of the depletion region.
-
The total
excess minority charge
can be derived by integrating our previous expression for pn(x). For the n-region, we obtain:
-
Diffusion
Capacitance:
-
The ratio of the
squared width
of the neutral region and the
diffusion coefficient
is another important device parameter called the
mean transit time
:
-
The
total diode current
can now be expressed as a function of the excess minority carrier charge:
-
Which simply states that, in steady state, the current I
D
is inversely proportional to the time it takes a carrier to transport from the junction to the metallic contact.
-
For the long-base diode, replace the
transit time
with the
excess minority carrier lifetime
parameter:
-
Diffusion
Capacitance:
-
Under
transient
conditions, a change in current translates into a change in the excess minority carrier charge.
-
We model this charge by an equivalent capacitance called diffusion capacitance:
-
For reverse bias, C
d
can be ignored.
-
Similar to junction capacitance, the average
diffusion
capacitance can be defined for a voltage range of interest.
-
For a forward bias of 0.75V, the diffusion capacitance evaluates to:
-
So how long does it take to switch the diode?
