Optical Properties of Energy-Dependent Effective Mass GaAs/GaxIn1−xAs and GaAs/AlxGa1−xAs Quantum Well Systems: A Shooting Method Study

In this paper, we study the effect of energy-dependent effective mass on optical properties of GaAs/Ga x In 1− x As and GaAs/Al x Ga 1− x As quantum well systems through the compact density matrix approach. We solved the resulting nonlinear Schrödinger equation by a simple shooting method and present the algorithm. We show that the energy-dependent effective mass effect is more important for systems with narrower quantum well systems. By an energy-dependent effective mass assumption, absorption coefficient peak height increases with increasing the total system length L while in the constant effective mass limit, absorption coefficient peak heights have not been influenced by changing L. In the GaAs/Al x Ga 1− x As system, by increasing the number of wells, the linear absorption coefficient amplitude at first increases and then decreases in the fixed effective mass approximation and monotonically decreases in the energy-dependent effective mass case. By increasing the number of wells, the linear absorption coefficient peak position at first shows a blue shift and then shows a redshift. In the GaAs/Ga x In 1− x As system, the situation is more complicated and it is described in more detail in the text. However, GaAs/Ga x In 1− x As quantum well systems have larger values of absorption coefficient peak heights than GaAs/Al x Ga 1− x As ones.