Analytical estimation of lifetime of quasi-bound states in iii-v semiconductors quantum well

The lifetime of electrons in the Quasi Bound States in a quantum well formed by III-V semiconductors has been calculated numerically by several researchers in the past. In this work, we obtain an analytical expression for the lifetime by finding the poles of the scattering matrix in small-width approximation. Airy functions which are solutions of the Schrodinger equation for triangular potentials are expanded asymptotically for large arguments and in power series for small arguments. A scattering problem for the triangular potential well is solved with the help of mixed boundary conditions to derive the expression for the decay width that further gives the net tunneling current from the quantum well. Heterostructures of III-V materials are modeled with triangular wells whose experimental measurements are in close approximation with the theoretical calculations presented in this paper. The analytically calculated decay width in this work is also compared with the reported values by different numerical methods and found in close agreement with them.

Automated summary

The lifetime of electrons in a quantum well formed by III-V semiconductors has been obtained analytically by finding the poles of the scattering matrix in a small-width approximation. Airy functions, which are solutions of the Schrodinger equation for triangular potentials, are expanded for large and small arguments. The decay width is determined by solving the scattering problem for the triangular potential well using mixed boundary conditions, and is found to be in agreement with experimental measurements and numerical calculations.