By David Johns Ken Martin
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Additional info for Analog Integrated Circuit Design
Since the channel has disappeared, these capacitors are now due to only overlap and fringing capacitance. 114) However, the reduction of C gs and C gd does not mean that the total gate capacitance is necessarily smaller. We now have a "new" capacitor, C gb , which is the gate- Fig. 23 A small-signal model for aMOSFET that is turned off. 3 Advanced MOS Modelling 39 to-substrate capacitance. This capacitor is highly nonlinear and dependent on the gate voltage. 115) If the gate-to-source voltage is around 0 V, then C gb is equal 10 Cox in series with the channel-to-bulk depletion capacitance and is considerably smaller, especially when the substrate is lightly doped.
These effects include mobility degradation, reduced output impedance, and hot-carrier effects (such as oxide trapping and substrate currents). These short-channel effects will be briefly described here. For more detailed modelling of short-channel effects, see [Wolf, 1995]. Transistors that have short channel lengths and large electric fields experience a degradation in the effective mobility of their carriers due to several factors. One of these factors is the large lateral electric field (which has a vector in a direction perpendicular from the gate into the silicon) caused by large gate voltages and short channel lengths.
The much smaller base current very closely equals the current due to the holes that flow from the base to the emitter. The total emitter current is the sum of the electron collector current and the hole base current, but since the hole current is much smaller than the electron current, the emitter current is approximately equal to the collector current. 127) where I e s is the scale current. This scale current is proportional to the area of the base-emitter junction. The base current, determined by the hole current flowing from the base to the emitter, is also exponentially related to the base-emitter voltage, resulting in the ratio of the collector current to the base current being a constant that, to a first-order approximation, is independent of voltage and current.
Analog Integrated Circuit Design by David Johns Ken Martin