On the validity of the parabolic effective-mass approximation for the I-V calculation of silicon nanowire transistors

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 (TB) model. A seminumerical ballistic field-effect transistor model is then adopted to evaluate the I-V characteristics of the (n-type) SNWTs based on both a TB dispersion relation and parabolic energy bands. In comparison with the TB approach, the parabolic effective-mass model with bulk effective-masses significantly overestimates SNWT threshold voltages when the wire width is <3 nm, and ON-currents when the wire width is <5 nm. By introducing two analytical equations with two tuning parameters, however, the effective-mass approximation can well reproduce the TB I-V results even at a ∼1.36-nm wire width.