Making the hamiltonian for gamma valley only is simple because of its isotropic effective mass. But if I want to consider gamma, X and L valleys all together, how can i construct the matrix for [001] direction? How to take care of longitudinal and transverse masses (for X and L valley) as well as the energy offset between two valleys (between gamma and L for example).
Another thing is, there are 6 L valleys. So how to take care of that (in case of thin film channel)?
You should calculate the inverse of the effective-mass tensor (that is the Hessian matrix of the band dispersion) at the extremum of the band you are interested in (this you can do by adopting an appropriate finite-difference formalism), and subsequently diagonalise it. The resulting eigenvalues are the inverses of the sought-after effective masses and the eigenvectors provide you with the principal basis for the representation of the band energies in the neighbourhood of the band extremum at issue.
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