Unified nonquasi-static modeling of the long-channel four-terminal MOSFET for large- and small-signal analyses

Abstract

An iterative technique based on device transport and continuity equations is used to formulate a unified nonquasi-static model for the long-channel four-terminal MOSFET for both transient and small-signal analyses in all regions of operation (weak, moderate, and strong inversion). The model is physically derived without resorting to the concept of channel charge partitioning or the use of a priori assumptions about the functional form of the channel charge density. It is shown that the Ward charge-based model is only a 0th-order solution of this formulation. The first-order solution presented here holds for arbitrary time-varying input voltages and can be reduced exactly to a recently proposed small-signal nonquasi-static admittance model. Relaxation due to the channel resistance is included to account for the device nonquasi-static transient behavior. The first-order model consists of simple ordinary differential equations, which can be easily discretized for solution. Results from the proposed model are examined and compared with numerical simulation results and experimental data. Good agreement has been obtained. I. INTRODUCTIONYNAMIC modeling of the long-channel four-termi-D nal MOSFET for large-and small-signal analyses of MOS integrated circuits has always been undertaken as two separate tasks. This is due to the fact that the coupled device current transport and continuity equations are extremely difficult to solve under arbitrary time-varying input voltages. Only under the simplified case of a threeterminal MOSFET with the bulk effect neglected and with small sinusoidal signals superimposed on the terminal bias voltages can the coupled equations be solved [1]- [3]. In order to include the bulk effect, a linearized bulk-charge density was recently used by Bagheri and Tsividis [4] to formulate, for the first time, a small-signal nonquasi-static admittance model for the four-terminal MOSFET that is valid in all regions of operation (weak, moderate, and strong inversion). The formulation of large-signal models for transient analysis under arbitrary time-varying input voltages is therefore a formidable task, and existing ,

A Nonquasi-Static Empirical Model of Electron Devices

“…Their relationship is investigated in Appendix A. In particular, under the hypothesis of small voltage deviations, it is proven that (18) where represents the voltage-dependent differential conductance matrix of the resistive part of the associated quasi-static device.…”

“…This approach is also adopted and simplified by Fernandez-Barciela et al [14]. Finally, device models mainly oriented to time-domain nonquasi-static transient analyses are more often based on charge functions derived from accurate analytical equations describing the carrier transport phenomena [16]- [18].…”

A nonquasi-static table-based small-signal model of heterojunction bipolar transistor

“…The aforementioned characteristics can be found in a T-model, which is widely used for small-signal modeling in HBT. All model-parameters of the model can be directly tied to the physical structure of HBT and the model also has a nonquasi-static parameter such as the emitter-collector phasedelay time [16]. By comparing with the T-model, the proposed model will be verified to be acceptable physically.…”

A non-quasi-static model for nanowire gate-all-around tunneling field-effect transistors

“…For example, both the spline collocation method [32] and the channel segmentation [31] are accurate, and they are also significantly more complex. Despite not high accuracy, the popular simplified relaxation time approximation (RTA) method [25,[33][34][35][36][37] using a characteristic time to approximately describe the redistribution process of the channel carriers can reduce execution time and improve convergence. Therefore, the RTA method is employed in this study to develop the NQS model for GAA TFETs.…”