Diffusion capacitance
Encyclopedia
Diffusion capacitance is the capacitance
due to transport of charge carrier
s between two terminals of a device, for example, the diffusion of carriers from anode to cathode in forward bias mode of a diode
or from emitter to base (forward-biased junction
in active region) for a transistor
. In a semiconductor device
with a current flowing through it (for example, an ongoing transport of charge by diffusion
) at a particular moment there is necessarily some charge in the process of transit through the device. If the applied voltage changes to a different value and the current changes to a different value, a different amount of charge will be in transit in the new circumstances. The change in the amount of transiting charge divided by the change in the voltage causing it is the diffusion capacitance. The adjective "diffusion" is used because the original use of this term was for junction diodes, where the charge transport was via the diffusion mechanism. See Fick's laws of diffusion.
To implement this notion quantitatively, at a particular moment in time let the voltage across the device be
. Now assume that the voltage changes with time slowly enough that at each moment the current is the same as the DC current that would flow at that voltage, say 
(the quasistatic
approximation). Suppose further that the time to cross the device is the forward transit time
. In this case the amount of charge in transit through the device at this particular moment, denoted 
, is given by
Consequently, the corresponding diffusion capacitance:
. is
In the event the quasi-static approximation does not hold, that is, for very fast voltage changes occurring in times shorter than the transit time
, the equations governing time-dependent transport in the device must be solved to find the charge in transit, for example the Boltzmann equation
. That problem is a subject of continuing research under the topic of non-quasistatic effects. See Liu
, and Gildenblat et al.
Capacitance
In electromagnetism and electronics, capacitance is the ability of a capacitor to store energy in an electric field. Capacitance is also a measure of the amount of electric potential energy stored for a given electric potential. A common form of energy storage device is a parallel-plate capacitor...
due to transport of charge carrier
Charge carrier
In physics, a charge carrier is a free particle carrying an electric charge, especially the particles that carry electric currents in electrical conductors. Examples are electrons and ions...
s between two terminals of a device, for example, the diffusion of carriers from anode to cathode in forward bias mode of a diode
Diode
In electronics, a diode is a type of two-terminal electronic component with a nonlinear current–voltage characteristic. A semiconductor diode, the most common type today, is a crystalline piece of semiconductor material connected to two electrical terminals...
or from emitter to base (forward-biased junction
P-n junction
A p–n junction is formed at the boundary between a P-type and N-type semiconductor created in a single crystal of semiconductor by doping, for example by ion implantation, diffusion of dopants, or by epitaxy .If two separate pieces of material were used, this would...
in active region) for a transistor
Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals and power. It is composed of a semiconductor material with at least three terminals for connection to an external circuit. A voltage or current applied to one pair of the transistor's terminals changes the current...
. In a semiconductor device
Semiconductor device
Semiconductor devices are electronic components that exploit the electronic properties of semiconductor materials, principally silicon, germanium, and gallium arsenide, as well as organic semiconductors. Semiconductor devices have replaced thermionic devices in most applications...
with a current flowing through it (for example, an ongoing transport of charge by diffusion
Diffusion
Molecular diffusion, often called simply diffusion, is the thermal motion of all particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size of the particles...
) at a particular moment there is necessarily some charge in the process of transit through the device. If the applied voltage changes to a different value and the current changes to a different value, a different amount of charge will be in transit in the new circumstances. The change in the amount of transiting charge divided by the change in the voltage causing it is the diffusion capacitance. The adjective "diffusion" is used because the original use of this term was for junction diodes, where the charge transport was via the diffusion mechanism. See Fick's laws of diffusion.
To implement this notion quantitatively, at a particular moment in time let the voltage across the device be
. Now assume that the voltage changes with time slowly enough that at each moment the current is the same as the DC current that would flow at that voltage, say (the quasistaticQuasistatic
Quasistatic can refer to:* Quasistatic process* Quasistatic equilibrium* Quasistatic loading* Quasistatic approximation...
approximation). Suppose further that the time to cross the device is the forward transit time
. In this case the amount of charge in transit through the device at this particular moment, denoted , is given by-
.
Consequently, the corresponding diffusion capacitance:
. is-
.
In the event the quasi-static approximation does not hold, that is, for very fast voltage changes occurring in times shorter than the transit time
, the equations governing time-dependent transport in the device must be solved to find the charge in transit, for example the Boltzmann equationBoltzmann equation
The Boltzmann equation, also often known as the Boltzmann transport equation, devised by Ludwig Boltzmann, describes the statistical distribution of one particle in rarefied gas...
. That problem is a subject of continuing research under the topic of non-quasistatic effects. See Liu
, and Gildenblat et al.