Hierarchy of Effective-Mass Equations for Semiconductor Nanostructures
Abstract
It has been developed a generalization of the Kohn Luninger envelope-function method that is applicable for description of the electron and hole states in many-layer (001) heterostructures, composed of related lattice-matched III-V semiconductors, with atonmcally abrupt heterointerfaces. It was shown that additional contributions to the standard one-band effectiveness equations may be classified with powers of the parameter ka(max) << 1, wher1/k is the characteristic size of the envelope function, and the length a is of the order of the lattice constant. It was formulated a hierarchy scheme for the effective-mass equations, the nth level of which accounts for taking into consideration all corrections up to (ka(max)). Zero level of the hierarchy corresponds to the standard effectiveness equations with position-independent effective mass. On the first level of the hierarchy each heterointerface gives an additional d4bncfion contribution to the potential energy. Only on the second level the position-dependent effective nmss appears as weU as corrections for the weak non-parabolicity of the spectrum and spin- orbit interface interaction. At higher levels of the hierarchy non-local contributions appear, and a one-band differential effective-mass equation does not exist.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1998
- Accession Number
- ADP012802
Entities
People
- E. E. Takhtamirov
- V. A. Volkov
Organizations
- Russian Academy of Sciences