6×6effective mass Hamiltonian for heterostructures grown on (11N)-oriented substrates

Abstract

The 6ϫ6 effective mass Hamiltonian for semiconductor heterostructures grown on (11N)-oriented substrates is derived and is compared with the 4ϫ4 model. The hole subbands of InGaAs/InP single quantum wells grown on (11N)-oriented substrates with Nϭϱ ͑that is, ͑001͔͒, 0, 1 are calculated using the effective mass Hamiltonian as an example. The spin-orbit coupling affects the light-hole subband at k ͉͉ ϭ0, but it affects all subbands at finite k ͉͉ for all substrate orientations. In the 4ϫ4 model ͑without spin-orbit coupling͒, the coupling between the heavy hole and the light hole is overestimated. At a critical uniaxial stress, the position of the first heavy hole and the first light hole as the highest energy level cross over. The separation between the first heavy hole and the first light hole is overestimated at the uniaxial stress below the critical value and is underestimated above the critical stress in the 4ϫ4 model. The spin-orbit coupling greatly affects the valence band structures of the semiconductor heterostructures resulting in the modifications of the optical transitions anisotropy for structures grown on (11N)-oriented substrates.

Microscopic modeling of hole inversion layer mobility in unstrained and uniaxially stressed Si on arbitrarily oriented substrates

“…In order to verify the proposed approach, the coefficients P, Q, R, S of the Luttinger-Kohn Hamiltonian b H 0 kp are calculated and compared with the results by [8] for (1 1 N) surface orientations. As shown in Fig.…”

“…[11]. The deformation potentials and optical phonon frequencies are adjustable parameters which are extracted by fitting the simulated channel mobility to specially selected mea- H 0 kp calculated by this work compared with the calculation results by [8] surements for (0 0 1) surface orientation. The treatment of surface roughness scattering in the framework of thek Áp theory is similar to [10].…”

“…Matrix b A contains only constants and depends neither on the crystallographic orientation nor on the wave vectors [7,8].0 is the 3 Â 3 zero matrix. The coordinate transformation matrix b U depends on the crystallographic orientation given by…”

Quantum simulations of electrostatics in Si cylindrical nanowire pinch-off nFETs and pFETs with a homogeneous channel including strain and arbitrary crystallographic orientations

“…The k · p Hamiltonian for the 3 main valence bands (VB) (heavy hole, light hole, and split off) is a 6 × 6 matrix which takes into account spin-orbit coupling, the interaction within these 3 bands, and the interaction of these 3 bands with the other bands. Stress/strain is handled by adding a Pikus-Bir strain Hamiltonian to the total Hamiltonian [6][7][8]. The rotation of the 6 × 6 k · p Hamiltonian [6,7] or of the inverse effective mass tensor [8] is required in order to handle different crystallographic orientations.…”

Orientation Effects in Ballistic High-Strained P-type Si Nanowire FETs

“…In this paper, based on the theory developed by Luttinger and Kohn [ 17 ], the bandstructures of p-type silicon nanowires are calculated by using a two-dimensional (2-D) discrete six-band k.p method [ 18 – 22 ] that quantitatively takes into account hole quantization effect, band mixing effect, spin-orbit coupling effect as well as mechanical strain. Then we apply a top-of-the-barrier ballistic FET model [ 23 ] to explore the effects of the orientation and the stress on ballistic hole transport properties of the p-type SiNW FETs.…”