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

摘要： In this paper, we study the effect of energy-dependent effective mass on optical properties of GaAs/GaxIn1?xAs and GaAs/AlxGa1?xAs quantum well systems through the compact density matrix approach. We solved the resulting non-linear Schro¨dinger 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 coef?cient peak height increases with increasing the total system length L while in the constant effective mass limit, absorption coef?cient peak heights have not been in?uenced by changing L. In the GaAs/AlxGa1?xAs system, by increasing the number of wells, the linear absorption coef?cient amplitude at ?rst increases and then decreases in the ?xed effective mass approximation and monotonically decreases in the energy-dependent effective mass case. By increasing the number of wells, the linear absorption coef?cient peak position at ?rst shows a blue shift and then shows a redshift. In the GaAs/GaxIn1?xAs system, the situation is more complicated and it is described in more detail in the text. However, GaAs/GaxIn1?xAs quantum well systems have larger values of absorption coef?cient peak heights than GaAs/AlxGa1?xAs ones.