Non-Ideal Diode Behavior
Diode junction capacitance
An ideal diode is completely characterized by its I-V curve.
It conducts current in the forward direction and essentially no current in the
reverse direction. Its behavior is the same independent of frequency. In
addition to this static behavior, there are additional effects in real diodes
due to two charge storage mechanisms. The first charge storage mechanism is
charge storage in the depletion region of the P-N junction and in the neutral
regions adjacent to the depletion region. The circuit manifestation of stored
charge is capacitance. The capacitance associated with the P-N junction
depletion region is called junction capacitance and is in parallel with the
ideal diode. Recall that capacitance relates an increase in voltage to the
charged stored (Q = C V). The junction capacitance is not important when the
diode is forward biased for two reasons. The first reason is that the voltage
across the diode and thus junction capacitance is essentially constant (0.7V)
and thus no current flows through the capacitance. The second reason is that
what little current does go through the junction capacitance is much smaller
than the forward current and thus can be neglected. On the other hand, the
junction capacitance can be important when a diode is reversed biased for two
reasons. The first reason is that the reverse diode voltage is not in general
constant. The second reason is that the reverse leakage current through a diode
is very small and thus the current through the junction capacitance can be much
larger than the reverse leakage current. The junction capacitance is important
in power electronic circuits when the diode turns off due to the very fast
changes in reverse voltage, square waves ideally have infinite dV / dt at their
edges. Also, including junction capacitance in Spice models reduces convergence
problems.The capacitance of a P-N junction is not a constant (unlike capacitors
you are used to) but depends on the reverse bias voltage on the junction. This
is because the positive and negative charge in the depletion region is not all
separated by the same distance as in a conventional capacitor. As the depletion
region grows, the added positive and negative charge is further and further
apart. Thus, the capacitance of a P-N junction is a function of the P-N
junction’s reverse voltage and it decreases as the reverse voltage increases
(distance between the charge increases 
). The junction capacitance of a reversed biased junction as
a function of the reverse bias voltage is given by
(1)
Note that it takes three numbers (constants) to specify the junction capacitance (CJO, VJ, and m) rather than the one number required for a conventional capacitor (C). Here CJO has the units of Farads and is the zero bias (VR = 0V) junction capacitance. It is proportional to the area of the diode so that high current diodes have more capacitance than low current diodes. The junction potential VJ has the units of Volts and is sometimes called the built in potential. The junction potential’s value is about 0.7V for silicon (Si) junctions. Its value for Si changes slightly from the 0.7V value depending on the doping levels on both sides of the junction. Its value changes significantly from one semiconductor material to another. The grading coefficient m is a unit-less number and typically about 0.5. Its value depends on the nature of the P-N junction. If the P region changes abruptly (a step change) to the N region at the junction, m = 0.5 (square root) and the junction is called an abrupt P-N junction. If the P region changes linearly into the N region (graded junction) at the junction, m = 0.333 (cubed root). High voltage power diodes often go from P to intrinsic semiconductor to N semiconductor (PIN diode) in which case m is close to 0, a constant capacitance. The parameter m is found by plotting the log of the capacitance versus the log of the voltage (m is the slop of this curve for voltages >>Vj).
The circuit in Fig. 1 can be used to measure the junction capacitance of a diode (P-N junction) as a function of its reverse bias voltage. The diode is reverse biased by using a DC source to which is added a relatively small sinusoidal AC signal. The DC voltage is called the bias voltage while the AC voltage is called the incremental voltage. The word incremental implies the AC voltage is small. With a known value and frequency of the AC voltage, the diode’s reverse current (it’s a sinusoidal current) is measured to determine the junction capacitance at the DC value of reverse voltage.
Fig. 1
Diode reverse recovery
The second charge storage mechanism at a P-N junction is charge stored in the neutral regions adjacent to the junction. The amount of charge stored is proportional to the forward current and the proportionality constant is called the transit time and has the units of seconds.
(2)
The transit time varies from ms to about 10’s of ns depending on junction processing. This charge storage mechanism is very nonlinear leading to a very nonlinear capacitance. The stored charge is significant for forward bias and nearly zero for reverse bias. This charge storage has a significant effect when the diode is supposed to turn off, delaying the diode turn off. This turn off delay is called reverse recovery and the delay time is called the reverse recovery time. This effect is very important in power electronic circuits. The reverse recovery time is close in value to the transit time, but not exactly equal to it. The reverse recovery time depends on the circuit the diode is used in while the transit time is a characteristic of the diode. The basic diode rectifier circuit shown in Fig. 2 can be used to study diode reverse recovery. The resistor Rsense can be thought of as the load for the circuit or as a resistor used to sense the current in the diode. Ideally the voltage across the resistor can never go negative. With a real diode the voltage can go negative for a short time called the reverse recovery time.
Fig. 2