Application of transfer matrices to surface states in finite periodic systems of quantum wells

2005 2005

Other formats: Order a copy

Abstract (summary)

For a system of N coupled quantum wells an exact energy-dispersion relation in terms of composite functions was derived by Liboff and Seidman 1 (1990). The essential qualitative feature of this equation was the emergence of a band structure for only a few quantum wells. Therefore one can consider this an embryonic band structure of any lattice with short range peridocity. Using transfer matrices one can find a parallel result for the wave function, that is, an exact closed form solution with N as an explicit variable. Based on a result of Abelès2 (1950), the transfer matrix for N arbitrary barriers can be expressed in terms of the transfer matrix of a single barrier multiplied by Chebyshev polynomials of degree N - 1 and N - 2. This expression for the wavefunction allows one to write an exact energy-dispersion relation for a finite-periodic system of N-coupled quantum wells for a general barrier shape. Once the transfer matrix for this barrier is determined, an exact algebraic expression can be written, the roots of which are the eigenenergies. This result represents a generalization of the expression in Liboff & Seidman (1990) since there the expression was specifically for rectangular quantum wells whereas this expression will work for any particular quantum well so long as the transfer matrix across the barrier separating the wells is known. From the eigenergies, the wavefunctions can then be written in terms of the recursive expression for the transfer matrix to determine if there are surface states (or surface resonances). A comparison of this methodology is made to that of Tamm's direct matching procedure for a semi-infinite lattice.

1R. L. Liboff & S. R. Seidman, "Exact energy-dispersion relations for N-well superlattice configurations," Phys Rev B, vol. 42, 1990, p. 9552. 2F. Abelès, "Reserches sur la propagation des onde électromagnétiques sinusoidales dans les milieux stratifiés", Ann. Phys. Paris, vol. 5, 1950 p. 706.

Indexing (details)

Electrical engineering;
0544: Electrical engineering
0611: Condensation
Identifier / keyword
Applied sciences; Pure sciences; Finite periodic; Quantum wells; Surface states; Transfer matrices
Application of transfer matrices to surface states in finite periodic systems of quantum wells
Seidman, Steven Russell
Number of pages
Publication year
Degree date
School code
DAI-B 66/09, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
9780542351273, 0542351277
Liboff, Richard L.
Cornell University
University location
United States -- New York
Source type
Dissertations & Theses
Document type
Dissertation/thesis number
ProQuest document ID
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
Access the complete full text

You can get the full text of this document if it is part of your institution's ProQuest subscription.

Try one of the following:

  • Connect to ProQuest through your library network and search for the document from there.
  • Request the document from your library.
  • Go to the ProQuest login page and enter a ProQuest or My Research username / password.