Accession Number : ADA260294


Title :   Quantum Mechanics of Electrons in Crystals with Graded Composition


Descriptive Note : Technical rept. 1 Jan-31 Dec 1992


Corporate Author : CALIFORNIA UNIV SANTA BARBARA DEPT OF PHYSICS


Personal Author(s) : Geller, M R ; Kohn, W


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/a260294.pdf


Report Date : Mar 1993


Pagination or Media Count : 16


Abstract : We construct the effective Hamiltonian describing the motion of electrons in compositionally graded crystals which is valid throughout a given energy band and part way into the gaps. The effective Hamiltonian, constructed from the band structures of uniform crystals, also includes the effects of a slowly varying applied scalar potential U(r). Near the edges of a nondegenerate band, this effective Hamiltonian reduces to an effective mass Hamiltonian with position dependent mass (one of several forms previously appearing in the literature): H sub eff = 1/2 pi(1/m*(r)) sub ij pj + Epsilon(r) + U(r), where Epsilon(r) is the energy of the band edge as a function of position. The analogous effective mass Hamiltonian for degenerate bands is also derived. Next, we examine more general states-not restricted to the vicinity of a band edge in crystals with composition and applied potential variation in one direction. We obtain a WKB-type solution for the envelope functions, as well as the appropriate turning point connection rules.


Descriptors :   *CRYSTAL LATTICES , *MECHANICS , *QUANTUM ELECTRONICS , EDGES , STRUCTURES , SEMICONDUCTORS , LATTICE DYNAMICS , BAND SPECTRA , HAMILTONIAN FUNCTIONS , ENERGY BANDS , ELECTRONS , CHEMICAL COMPOSITION , ALLOYS , MOTION , MASS


Subject Categories : Theoretical Mathematics
      Crystallography
      Atomic and Molecular Physics and Spectroscopy
      Quantum Theory and Relativity


Distribution Statement : APPROVED FOR PUBLIC RELEASE