A Comprehensive Theoretical Analysis of Hole Ballistic Velocity in Si, SiGe, and Ge: Effect of Uniaxial Strain, Crystallographic Orientation, Body Thickness, and Gate Architecture

This paper presents a detailed theoretical analysis of the implications of nanoscale device structures on the average hole ballistic velocity calculated from quantum-mechanical strain-dependent 6×6 k · p bandstructure simulations. The simulations show that the crystallographic orientation of the uniaxial strain, channel, and surface affect the average ballistic velocity by modifying the energy-momentum (E - k) dispersion of the subbands (from which the ballistic velocity is calculated). Conversely, the analysis shows that semiconductor-body thickness and gate architecture influence the ballistic velocity by modifying the quantum confinement in the structure, which ultimately affects the relative hole occupation of k-states across different subbands. Key results of the work show that a 5-nm-body thickness yields a 6%-12% increase in the ballistic velocity compared to a 10-nm body. Likewise, a single-gate architecture gives up to an 11% increase over a double gate, but the improvement is dependent on the crystallographic surface orientation. Strained Ge shows a significantly enhanced ballistic velocity relative to strained Si for both {100}and {110}-surface orientations with a predicted hole ballistic velocity exceeding 2 × 10
⁷
cm/s at n
^v+
_s
= 5 × 10
¹²
#/cm2.