Finite difference method for solving the Schroedinger equation with band nonparabolicity in mid-infrared quantum cascade lasers

Journal Article · Wed Dec 01 00:00:00 EST 2010 · Journal of Applied Physics

DOI:https://doi.org/10.1063/1.3512981· OSTI ID:21537949

Cooper, J D; Valavanis, A; Ikonic, Z; Harrison, P; Cunningham, J E ^[1]

---

1. Institute of Microwaves and Photonics, School of Electronic and Electrical Engineering, University of Leeds, Leeds LS2 9JT (United Kingdom)

The nonparabolic Schroedinger equation for electrons in quantum cascade lasers (QCLs) is a cubic eigenvalue problem (EVP) which cannot be solved directly. While a method for linearizing this cubic EVP has been proposed in principle for quantum dots [Hwang et al., Math. Comput. Modell., 40, 519 (2004)] it was deemed too computationally expensive because of the three-dimensional geometry under consideration. We adapt this linearization approach to the one-dimensional geometry of QCLs, and arrive at a direct and exact solution to the cubic EVP. The method is then compared with the well established shooting method, and it is shown to be more accurate and reliable for calculating the bandstructure of mid-infrared QCLs.

• OSTI ID: 21537949
• Journal Information: Journal of Applied Physics, Vol. 108, Issue 11; Other Information: DOI: 10.1063/1.3512981; (c) 2010 American Institute of Physics; ISSN 0021-8979
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EIGENFUNCTIONS
EIGENVALUES
ELECTRONS
EXACT SOLUTIONS
FINITE DIFFERENCE METHOD
QUANTUM DOTS
SCHROEDINGER EQUATION
THREE-DIMENSIONAL CALCULATIONS
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
ELEMENTARY PARTICLES
EQUATIONS
FERMIONS
FUNCTIONS
ITERATIVE METHODS
LEPTONS
MATHEMATICAL SOLUTIONS
NANOSTRUCTURES
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
WAVE EQUATIONS