4.1.1.1 Contributions to ${\it C}_{\mathrm{gs}}$

The basic contribution to ${\it C}_{\mathrm{gs}}$ arises from the interaction of the channel charge and the gate metal. Additionally, fringe capacitances [13] are added due to coupling between the semiconductor caps, the ohmic metal, and the gate metal. The capacitance ${\it C}_{\mathrm{gs}}$ is therefore written as:

$${\it C}_{\mathrm{gs}} ({\it V}_{\mathrm{GS}},{\it V}_{\mathrm{DS}... ...nge} + {\it C}_{\mathrm{traps}} ({\it V}_{\mathrm{GS}},{\it V}_{\mathrm{DS}},f)$$ (4.4)

The additional term ${\it C}_{\mathrm{traps}}$ is added to point out the effect of the generation/recombination of additional carriers when applying a third terminal voltage. The difference between RF- and DC- ${\mit g}_{\mathrm{m}}$ due to the activation of traps and carrier generation/recombination in a dynamic process with time constants of the order of $\mu$s is generally acknowledged [211]. Above frequencies of excitation of a few MHz (see Chapter 6) this results in a stable, time invariant equilibrium which is extracted in RF-measurements [196]. Above a few MHz it is further independent of the frequency, yet, not of the applied bias. It is very desirable to reduce the effects of generation/recombination. The inclusion of these effects into device modeling [248] is helpful to explain the dependence of device properties on ${\it V}_{\mathrm{DS}}$ bias. The bias dependence of ${\it C}_{\mathrm{gs}}$ is further strongly related to the shape and the carrier charge concentration distribution of the space charge region. The compact model assumes a charge at an effective distance d $_\mathrm {eff}$, yet, the center of this charge varies as a function of ${\it V}_{\mathrm{DS}}$.