Explicit continuous models of drain current, terminal charges and intrinsic capacitance for a long-channel junctionless nanowire transistor

Abstract

An explicit charge-based solution for the drain current, terminal charges and intrinsic capacitance of a long-channel junctionless nanowire transistor (JNT) incorporating the importance of an interface trap density that affect the threshold voltage and the subthreshold slope is presented in this study. Initially, a continuous implicit solution of the unified charge-based control model (UCCM) is derived from the 1D Poisson equation by invoking the parabolic potential approximation. The the continuous solution of the mobile charge density at the source/drain is obtained by adding the decoupled UCCM expression for the depletion and complementary parts, where each part is explicitly solved using the Lambert function without having an additional smoothing function to unify the two limits. The omission of an additional smoothing function could lead to a shorter computation time. Secondly, by solving Pao-Sah's dual integral, a continuous charge-based expression for the drain current is derived. The expressions for the terminal charge are then derived based on the decoupled drain current model that also becomes an input for computing all four independent capacitances of the JNT. The explicit continuous models show a good agreement with numerical simulation over practical terminal voltages, doping levels, and geometry effects. For a given maximum surface potential error of 5%, the model is accurate for a dopant-geometry ratio of 0.001 < qN D R 2/4 Si < 0.3 and it is also independent of fitting parameters that may vary for different terminal biases or dopant geometries. The nonpiecewise models for drain current, terminal charges and intrinsic capacitance are significantly resolved by decoupling the mobile charge into depletion and complementary parts with no additional smoothing function to unify between operating regions, and omitting fitting parameters that have no physical meaning.