EFFECTIVE-MASS HAMILTONIAN FOR STRAINED SUPERLATTICES

For an abrupt heterojunction between two otherwise homogeneous semicon ductors in one dimension, the effective-mass Hamiltonian H=-<(h)over b ar (2)>/2 m(z)(alpha) alpha(z)(v) d/dz m(z)(beta) alpha(z)(-2v) d/dz m (z)(alpha) alpha(z)(v)+E(c)(z) is examined with 2 alpha+beta=-1, where m(z), a(z), and E(c)(z), are the position dependent effective mass. t he local lattice parameter, and tile local conduction band edge, respe ctively. Tile exact Schrodinger equation is compared with that for the effective-mass equation in the case of an analytically solvable model . In the asymptotic limit of the energy close to the hand edge, the co nclusions obtained are shown to be dependent on tile parity of the ban ds.