Generalized gradual channel modeling of field-effect transistors

The flow of current in the channel of the field-effect transistor (FET) is abstracted into a generalized curvilinear coordinate system that allows the transverse and longitudinal processes to be separated. By integrating over the conducting cross section of the channel, a set of generalized channel equations is derived that formally one-dimensionalizes the analysis of a FET for a Boltzmann balance equation transport model. Two mode approximations on the curvature of the channel and the uniformity of the velocity distribution across the channel allow the system of channel equations to be reduced to an extension of the gradual channel approximation of Schockley. The applicability of the formulation is demonstrated through the modeling of a GaAs metal-semiconductor FET (MESFET) that includes all of the Boltzmann equation terms for high-field electron transport as well as a small gate-length-to-channel-thickness ratio. The results indicate that gradual channel models, with suitable geometric modifications, can be used to study FETs using higher internal fields and smaller gate/channel dimensions than previously thought