On the Validity of the Parabolic Effective-Mass Approximation for the Current-Voltage Calculation of Silicon Nanowire Transistors

Abstract

This paper examines the validity of the widely-used parabolic effective-mass approximation for computing the current-voltage (I-V) characteristics of silicon nanowire transistors (SNWTs). The energy dispersion relations for unrelaxed Si nanowires are first computed by using an sp3d5s* tight-binding model. A semi-numerical ballistic FET model is then adopted to evaluate the I-V characteristics of the (n-type) SNWTs based on both a tight-binding dispersion relation and parabolic energy bands. In comparison with the tight-binding approach, the parabolic effective-mass model with bulk effective-masses significantly overestimates SNWT threshold voltages when the wire width is <3nm, and ON-currents when the wire width is <5nm. By introducing two analytical equations with two tuning parameters, however, the effective-mass approximation can well reproduce the tight-binding I-V results even at a \~1.36nm wire with.