Quantum well infrared photodetector design using Transfer Matrix Method

This paper demonstrates the use of the transfer matrix method (TMM) to estimate the confined energy levels and their respective wavefunction of complex heterostructures in both valence and conduction band. The potential profile of the structure is sliced and made constant within each layer. By solving the Schro¿dinger equation for a constant potential in each slice and using the continuity of the wavefunction at the interfaces it is possible to handle virtually any potential profile. Comparison between numerical results and analytical solutions of potentials such as modified Posch-Teller hole shows errors smaller than 0.1%. The method is employed to estimate the photoluminescence peaks in different GaAs/AlGaAs/InGaAs samples. Comparison between measurements and TMM numerical results shows that the error rises as the indium concentration increases. Finally, the method is used to estimate the responsivity wavelength peak of QWIPs that uses intersubband transitions to detect mid- and long infrared (MWIR, LWIR). The TMM predictions are found in good agreement with the average error no bigger than 2%. The errors are most likely due to uncertainties in semiconductor parameters such as bandgap and junction band offsets. Those results indicate that the method, despite its simplicity, is a suitable tool to be used in QWIP design.