On the transfer matrix method and WKB approximation for systems with spatial-dependent effective mass

POSTER

Abstract

A set of coupled differential equations is derived by considering the continuous limit of the transfer matrix method, which is a numerical approach for the one-dimensional structures such as the semiconductor heterostructures. By decoupling such a set of equations, an extension to the Wentzel-Kramers-Brillouin (WKB) method is obtained to incorporate effects due to the spatial-dependent effective mass. For a traveling wave, the decoupling is to ignore the reflection resulting from the variations of both the potential and effective mass. By considering a solvable fully-quantized system, it is shown that the extended WKB method provides good approximation for the states with the high eigenenergies.

Authors

  • Chun-feng Huang

    • National Measurement Laboratoy, Center for Measurement Standards, Industrial Technology Research Institue
    • National Measurement Laboratory, Center for Measurement Standards, Industrial Technology Research Institute, Hsinchu 200, Taiwan, R. O. C.

  • S.D. Chao

    • Institute of Applied Mechanics, National Taiwan University, Taipei, Taiwan, R. O. C.

  • D.R. Hang

    • Department of Materials Science and Optoelectronic Engineering, National Sun Yat-sen University, Kaohsiung 804, Taiwan, R. O. C.

  • Y.C. Lee

    • Institute of Materials Science and Engineering, National Sun Yat-sen University, Kaohsiung 804, Taiwan, R. O. C.