Shooting Method for Analysis of Quantum Wells with Arbitrary Potential Profiles
Keywords:Shooting Method, Quantum Wells, Arbitrary Potential, Schrodinger equation
This paper presents a simple method for accurately calculating energy eigenvalues and eigenfunctions in quantum wells by using shooting method. This method is applicable to various potential barriers and wells, including continuous variations of potential energy. Various potential structures, i.e., single finite quantum well, triple finite quantum wells and multiple irregular quantum
wells, are analyzed to show the feasibility of this method. This method is useful to find the eigenfunction and energy eigenvalues, which are very important parameters to analyze and design quantum tunneling devices.
Likharev KK. Correlated discrete transfer of single electrons in ultrasmall tunnel junctions. IBM Journal of Research and Development. 1988 Jan;32(1):144-58.
Burhanudin ZA, Nuryadi R, Tabe M. Detection of field-induced single-acceptor ionization in Si by single-hole-tunneling transistor. Applied Physics Letters. 2007 Jul 23;91(4):042103.
Ikeda H, Nuryadi R, Ishikawa Y, Tabe M. Photoinduced effects on single-charge tunneling in a Si two-dimensional multidot field-effect transistor. Japanese journal of applied physics. 2004 May 28;43(6B):L759.
Tabe M, Terao Y, Ishikawa Y, Nuryadi R, Asahi N, Amemiya Y. Simulation of visible light induced effects in a tunnel junction array for photonic device applications. Japanese journal of applied physics. 1999;38(1S):593.
Tsu R, Esaki L. Tunneling in a finite superlattice. Applied Physics Letters. 1973 Jun 1;22(11):562-4.
Ando Y, Itoh T. Calculation of transmission tunneling current across arbitrary potential barriers. Journal of applied physics. 1987 Feb 15;61(4):1497-502.
Harwit A, Harris Jr JS, Kapitulnik A. Calculated quasi?eigenstates and quasi?eigenenergies of quantum well superlattices in an applied electric field. Journal of applied physics. 1986 Nov 1;60(9):3211-3.
Nuryadi R. Simulasi Perhitungan Probabilitas Terobosan pada Struktur Resonance Tunneling Diode. Prosiding Seminar Nasional Ilmu Komputer dan Aplikasinya. 2009 Oct; 4(1): C-88, Bandung, Indonesia.
Lui WW, Fukuma M. Exact solution of the Schrodinger equation across an arbitrary one?dimensional piecewise?linear potential barrier. Journal of Applied Physics. 1986 Sep 1;60(5):1555-9.
Khondker AN, Khan MR, Anwar AF. Transmission line analogy of resonance tunneling phenomena: The generalized impedance concept. Journal of applied physics. 1988 May 15;63(10):5191-3.
Killingbeck J. Shooting methods for the Schrodinger equation. Journal of Physics A: Mathematical and General. 1987 Apr 21;20(6):1411.
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