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

TL;DR

This study evaluates the accuracy of the parabolic effective-mass approximation for silicon nanowire transistors by comparing it with tight-binding models, revealing its limitations at very small wire widths and proposing adjustments for improved predictions.

Contribution

The paper provides a detailed comparison between the parabolic effective-mass approximation and tight-binding models for SNWTs, introducing analytical equations to enhance the approximation's accuracy at nanoscale dimensions.

Findings

Effective-mass model overestimates threshold voltages for wires <3nm.

Effective-mass model overestimates ON-currents for wires <5nm.

Adjusted effective-mass approximation can match tight-binding results at ~1.36nm.

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.