Spatially varying effective mass effects on energy level populations in semiconductor quantum devices

For the analysis and design of semiconductor intersubband devices, accurate values for the Fermi energy and the subband electron population are needed. The effect of the position-dependent electron effective mass m*(z) is commonly neglected in the determination of these two intersubband device parameters. This approach is nearly valid for single-well devices in the GaAs/AlxGa1-xAs material system. However, in multiple-coupled-well devices, the variable nature of the effective mass must be taken into account. In material systems other than the ones based on GaAs, failure to include the position-dependence of the electron mass may give rise to significant errors in the values of the Fermi energy and other device parameters such as the intersubband absorption coefficient. In this paper, the effects of m* (z) on the Fermi level and the intersubband charge distribution are explored and quantified. Theoretical formulation for the intersubband Fermi energy and the subband electron distribution, with the inclusion of position-dependent electron mass, is presented. The eigenenergies of the intersubband structures are obtained by solving the single-band effective-mass Schroedinger equation using the argument principle method. The electron distribution and the Fermi energy are calculated using both the approximate method (m(0)*) and the rigorous formulation [m*(z)], and the relative differences in the corresponding values are presented. It is demonstrated that these differences are small in the GaAs/AlxGa1-xAs material system, but can become very significant in other materials. In addition, the variable nature of carrier effective mass plays an important role in other types of devices such as interband quantum well photodetectors and lasers that employ optical transitions between the valence and the conduction bands. Electronic devices such as the resonant tunneling diode are also affected by the position-dependence of carrier mass and thus the results are applicable to both optoelectronic and electronic quantum devices. (C) 2002 Elsevier Science Ltd. All rights reserved.