Two-Band k·p Model for the Conduction Band in Silicon: Impact of Strain and Confinement on Band Structure and Mobility

For analytical calculations the conduction band of Si is usually approximated by three pairs of equivalent valleys located near the X-points of the Brillouin zone. It is commonly assumed that the valley dispersion is well approximated by a non-parabolic dispersion with the transversal mass mt and the longitudinal mass ml. A constant non-parabolicity parameter α is introduced to describe deviations in the density of states from the purely parabolic dispersion. There are experimental indications that the effective masses depend on shear strain [1] and the silicon film thickness [2]. The parabolic band structure ignores these effects completely. In this work we demonstrate that the recently proposed [3] two-band k·p model describes accurately dependences of the valley shifts and the effective masses on the shear strain component. The theory includes non-parabolicity effects due to the interaction between the two lowest conduction bands and provides an analytical expression for the dependence of the effective masses on shear strain. Within the two-band k·p model the dispersion relation in a [001] valley is of the form [3,4] ( ) 2 2 2 2 2 2 / δ + − + + = z t l y x z k m m k k k E , (1) where all the wave vectors are normalized by a k / 2 15 . 0 0 π × = , the position of the minimum relative to the X point. Energies are in units of ) 2 /( 2 0 2 l m k h , and