In modeling bipolar transistors the charge-control concept provides a means to predict dynamic behavior from a detailed knowledge of the steady state. As such, it is a first-order approximation lacking accuracy. It is shown that a considerable improvement can be obtained when the concept is extended by allowing time delays in the relations between controlling charges and terminal voltages and currents. It suffices to introduce two delays whose magnitudes can be determined or estimated from the steady-state solution. The increased range of validity of the extended charge-control model is demonstrated in detail, by confronting it with a rigorous model and comparing small-signal parameters.

Extended charge-control model for bipolar transistors

The behavior of MOS transistors from d.c. to frequencies where the operation is non-quasistatic is investigated, with emphasis on four-terminal operation and including the substrate effect. The aspects considered are: (a) development of expressions for the y parameters, with closed-form expressions for the associated series terms of any order; and (b) development of expressions for the induced thermal noise currents at the drain, gate, and substrate as well as the drain thermal noise voltage. The results presented are verified through extensive comparisons to measured results, and to results obtained by simulation of a many-segment device. Such comparisons extend up to frequencies two orders of magnitude above the intrinsic cutoff frequency with positive results.

Small-signal parameters and thermal noise of the four-terminal MOSFET in non-quasistatic operation

The inductive nature of short-base p - n junction diodes at high forward bias is explained by means of a novel equivalent circuit featuring separate paths for charging currents and convection currents. As suggested by other authors, also conductivity modulation turns out to play a role. The general conclusion is, that the a.c. diode capacitance changes sign when the (modulated) total series resistance of the diode becomes equal to its differential resistance.

Modelling the inductive behaviour of short-base p-n junction diodes at high forward bias

The derivation of a simple expression for the capacitance C(V) associated with the transition region of a p-n junction under a forward bias is derived by phenomenological reasoning. The treatment of C(V) is based on the conventional Shockley equations, and simpler expressions for C(V) result that are in general accord with the previous analytical and numerical results. C(V) consists of two components resulting from changes in majority carrier concentration and from free hole and electron accumulation in the space-charge region. The space-charge region is conceived as the intrinsic region of an n-i-p structure for a space-charge region markedly wider than the extrinsic Debye lengths at its edges. This region is excited in the sense that the forward bias creates hole and electron densities orders of magnitude larger than those in equilibrium. The recent Shirts-Gordon (1979) modeling of the space-charge region using a dielectric response function is contrasted with the more conventional Schottky-Shockley modeling.

Simple phenomenological modeling of transition-region capacitance of forward-biased p-n junction diodes and transistor diodes

Physical insight regarding charge-based transient MOSFET modeling is developed to reveal the significance of the channel-charge partition. Components (charging, displacement, transport, and convection) of transient channel current are discussed in terms of charge (actual and model), and clarification concerning "nonreciprocal capacitance" and origins of error in quasi-static models is given.

Significance of the channel&#8212;Charge partition in the transient MOSFET model

The charge-control capacitance ∂Q/∂V looking into a device port is not in general equal to the intrinsic small-signal capacitance found from the low-frequency admittance ratios up to 7:1 occur in practice. This paper explains why the discrepancy occurs, and derives the condition for the discrepancy to be zero. Finally, it is shown that charge-control theory does correctly predict the gain-bandwidth product of an active device.

Active-device capacitances

A complete solution is presented for the small-signal high-frequency response of an idealized model of the insulated-gate field-effect transistor. The y parameters are found by solving Bessel's equation and are plotted as functions of signal frequency and the quiescent conditions. In addition to these general results, simple approximate results that apply only beyond the point of pinch-off are derived for operation at moderately low frequencies.

E.M. Cherry

Papers

Active-device capacitances

Small-signal high-frequency response of the insulated-gate field-effect transistor