Editing Capacitance (section)

==Capacitance in electronic and semiconductor devices==

In electronic and semiconductor devices, transient or frequency-dependent current between terminals contains both conduction and displacement components. Conduction current is related to moving charge carriers (electrons, holes, ions, etc.), while displacement current is caused by a time-varying electric field. Carrier transport is affected by electric fields and by a number of physical phenomena - such as carrier drift and diffusion, trapping, injection, contact-related effects, impact ionization, etc. As a result, device [[admittance]] is frequency-dependent, and a simple electrostatic formula for capacitance <math>C = q/V,</math> is not applicable. A more general definition of capacitance, encompassing electrostatic formula, is:<ref name=LauxCapacitance>{{cite journal |first=S.E. |last=Laux |title=Techniques for small-signal analysis of semiconductor devices |journal=IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems |volume=4 |issue=4 |pages=472–481 |doi=10.1109/TCAD.1985.1270145 |date=Oct 1985|s2cid=13058472 }}</ref>
<math display="block">C =  \frac{\operatorname{Im}(Y(\omega))}{\omega} ,</math>
where <math>Y(\omega)</math> is the device admittance, and <math>\omega</math> is the angular frequency.

In general, capacitance is a function of frequency. At high frequencies, capacitance approaches a constant value, equal to "geometric" capacitance, determined by the terminals' geometry and dielectric content in the device.
A paper by Steven Laux<ref name=LauxCapacitance /> presents a review of numerical techniques for capacitance calculation. In particular, capacitance can be calculated by a Fourier transform of a transient current in response to a step-like voltage excitation:
<math display="block">C(\omega) = \frac{1}{\Delta V} \int_0^\infty [i(t)-i(\infty)] \cos (\omega t) dt.</math>