1. k*p method and Kane model: Starting from Bloch wave function derive k*p Hamiltonian. Retain S and Px,Py,Pz basis functions at k=0 with Ec and Ev as corresponding energies. Derive k*p Hamiltonian in this basis retaining only one non vanishing matrix element coupling S conduction orbital with 3 p orbitals. Plot conduction and valence bands as a function of k assuming Kane P parameter eq. 1eV and Energy gap of 2eV.
2. Light and heavy holes: Construct basis functions as eigen functions of total angular momentum J=L+S where L=1 is angular momentum and S=1/2 is electron spin. Classify your states into heavy and light holes and a spin split-off band. Use four J=3/2 hole functions to write Luttinger - Kohn Hamiltonian for holes. Consider a hole with J=3/2 on a disk with radius R=300A, height H=120A and infinite confining potential. Use Luttinger-Kohn parameters for SiGe from attached paper Rego et al. Construct Luttinger spinors and compute energy spectrum of a hole.
3. Strain and elastic energy:
i) Introduce displacement field.
Ii) Define strain tensor.
Iii) Compute total energy.