Reverse bias causes majority carriers to move away from the junction, thereby creating more ions. Hence the thickness of depletion region increases. This region behaves as the dielectric material used for making capacitors. The p-type and n-type conducting on each side of dielectric act as the plate. The incremental capacitance CT is defined by
where, dQ is the increase in charge caused by a change dV in voltage. CT is not constant, it depends upon applied voltage, there fore it is defined as dQ / dV.
When p-n junction is forward biased, then also a capacitance is defined called diffusion capacitance CD (rate of change of injected charge with voltage) to take into account the time delay in moving the charges across the junction by the diffusion process. It is considered as a fictitious element that allow us to predict time delay.
If the amount of charge to be moved across the junction is increased, the time delay is greater, it follows that diffusion capacitance varies directly with the magnitude of forward current.
An exponential relationship exists between the carrier density and applied potential of diode junction as given in equation E-3. This exponential relationship of the current iD and the voltage vD holds over a range of at least seven orders of magnitudes of current - that is a factor of 107.
iD= Current through the diode (dependent variable in this expression)
vD= Potential difference across the diode terminals (independent variable in this expression)
IO= Reverse saturation current (of the order of 10-15 A for small signal diodes, but IO is a strong function of temperature)
q = Electron charge: 1.60 x 10-19 joules/volt
k = Boltzmann's constant: 1.38 x l0-23 joules /° K
T = Absolute temperature in degrees Kelvin (°K = 273 + temperature in °C)
n = Empirical scaling constant between 0.5 and 2, sometimes referred to as the Exponential Ideality Factor
The empirical constant, n, is a number that can vary according to the voltage and current levels. It depends on electron drift, diffusion, and carrier recombination in the depletion region. Among the quantities affecting the value of n are the diode manufacture, levels of doping and purity of materials. If n=1, the value of k T/ q is 26 mV at 25°C. When n=2, k T/ q becomes 52 mV.
For germanium diodes, n is usually considered to be close to 1. For silicon diodes, n is in the range of 1.3 to 1.6. n is assumed 1 for all junctions all throughout unless otherwise noted.
Equation (E-3) can be simplified by defining VT =k T/q, yielding
At room temperature (25°C) with forward-bias voltage only the first term in the parentheses is dominant and the current is approximately given by
The current-voltage (l-V) characteristic of the diode, as defined by (E-3) is illustrated in fig. 1. The curve in the figure consists of two exponential curves. However, the exponent values are such that for voltages and currents experienced in practical circuits, the curve sections are close to being straight lines. For voltages less than VON, the curve is approximated by a straight line of slope close to zero. Since the slope is the conductance (i.e., i / v), the conductance is very small in this region, and the equivalent resistance is very high. For voltages above VON, the curve is approximated by a straight line with a very large slope. The conductance is therefore very large, and the diode has a very small equivalent resistance.
Fig.1 - Diode Voltage relationship
The slope of the curves of fig.1 changes as the current and voltage change since the l-V characteristic follows the exponential relationship of relationship of equation (E-4). Differentiate the equation (E-4) to find the slope at any arbitrary value of vDor iD,
This slope is the equivalent conductance of the diode at the specified values of vD or iD.
We can approximate the slope as a linear function of the diode current. To eliminate the exponential function, we substitute equation (E-4) into the exponential of equation (E-7) to obtain
A realistic assumption is that IO<< iD equation (E-7) then yields,
The approximation applies if the diode is forward biased. The dynamic resistance is the reciprocal of this expression.
Although rd is a function of id, we can approximate it as a constant if the variation of iD is small. This corresponds to approximating the exponential function as a straight line within a specific operating range.
Normally, the term Rf to denote diode forward resistance. Rf is composed of rd and the contact resistance. The contact resistance is a relatively small resistance composed of the resistance of the actual connection to the diode and the resistance of the semiconductor prior to the junction. The reverse-bias resistance is extremely large and is often approximated as infinity.