OPERATOR ORDERING IN EFFECTIVE-MASS THEORY FOR HETEROSTRUCTURES .2. STRAINED SYSTEMS

A new kinetic-energy operator -1/2Latin small letter h with stroke2mama-2ma suitable for effective-mass treatment of strained heterostructures is introduced. Here, m(r) is the local effective mass and a(r) is the local lattice constant. By comparison of exact results with effective-mass results for solvable test models, values of , , and , which ensure asymptotic agreement, are determined. Based on qualitative similarities between the test models considered and realistic systems, the boundary conditions [(1/a)=continuous], [(a/m)=continuous] are proposed for abrupt heterointerfaces for conduction-band states in strained systems. When a single-band effective-mass equation is applicable to hole states, however, we propose that the continuity of and (1/m) should be imposed instead. © 1990 The American Physical Society.