材料パラメータと、それらがソルバー内でどのように使用されるか

Every quantum-well solver is only as good as the material parameters it is given. This page explains what each parameter means physically, which Hamiltonian term it controls, its units and the common sign or convention traps — rather than listing numerical values, which belong in the material database and in the compilations cited on the references page. Parameters are grouped by the solver that uses them.

1. エネルギーおよびエネルギーの基準値

The most common source of error is the energy reference. OghmaNano measures energies from the structure valence-band maximum (placed at zero), and each material's valence edge \(E_v\) is supplied on a common absolute scale so that band offsets are correct. The multiband solvers derive the conduction edge as \(E_c = E_v + E_g\) and, internally, an average valence energy that the spin-orbit and crystal-field terms then split back to the physical band edge.

2. 有効質量

The band-edge electron mass fixes the conduction curvature and, in the multiband models, is used to back out the remote-band parameter. Hole masses appear directly only in the parabolic solver; in the k·p models the valence masses are encoded in the Luttinger (or wurtzite \(A_i\)) parameters instead. Silicon's valleys are anisotropic and need two masses each.

3. 亜鉛ブレンデ構造における価電子帯パラメータおよび結合パラメータ

The Luttinger parameters describe the coupled heavy-, light- and split-off holes; the Kane energy sets the conduction–valence coupling. In the 8-band model OghmaNano combines these into the internal \(A_c, L, M, N, P\) parameters, renormalising \(L\) and \(N\) (and, in the standard mode, \(A_c\)) to avoid double-counting the explicit Kane coupling.

4. 亜鉛鉱型構造における変形ポテンシャルと弾性剛性

Strain enters through the deformation potentials and requires the elastic constants and lattice constants to compute the strain tensor. The conduction and valence hydrostatic potentials combine into the gap deformation potential; the shear potentials \(b\) and \(d\) split the valence bands.

5. ウルツァイト構造のパラメータ

Wurtzite needs more parameters because of its lower symmetry: six valence parameters, three splitting energies, two Kane energies, two conduction-mass parameters and separate hydrostatic and shear deformation potentials.

6. シリコンのΔバレー・パラメータ

7. 希薄窒化物材料（10バンドモデル）のパラメータ

8. 光学パラメータおよび輸送パラメータ

The gain and scattering calculations need a few further inputs: the refractive index and Lorentzian broadening for gain, and the mass density, sound velocity and acoustic deformation potential for scattering. These are properties of the medium and the phonons rather than of the band structure.