Band-structure calculation Atomistic methods: Hartree-Fock, Density Functional theory (DFT): Walter Kohn(Nobel Prize in chemistry in 1998), Tight Binding Non-atomistic: k.P theory, Effective mass approximation: Analytic solution of Schrödinger equation), Numerical (FD, FEM e.g. COMSOL) A method to find the energy levels and wave functions of a cluster or periodic solid without solving a complicated multi-electron Hamiltonian. • The method described involves the calculation of energy levels and wave functions of an N-atom system based on parameters: Tight Binding:

M. P. Anantram , U of Washington

M. P. Anantram , U of Washington

Effective mass

Quantum Confinement (Zone Folding)

Exercise:

Bulk (3D) silicon vs. Si nanowire Si nanowire d = 0.6nm