Abstract
In this paper, the two-dimensional electron gas (2DEG) concentration is numerically calculated for single and double heterostructure band profiles by solving Schroödinger's and Poisson's equations self-consistently. An expected energy level is introduced to enhance the speed of calculation in obtaining quantized energy levels through the iteration process. Conventional AlGaAs/GaAs and AlGaAs/InGaAs/GaAs structures are selected to prove the validity of this calculation. Three different concentrations, namely, positively ionized donors, free electrons in the conduction band and 2DEG, are considered through the band profiles. Both the 2DEGs in the narrow bandgap and free electrons in the wide bandgap have been calculated and compared with the data available in the literature. Furthermore, positively ionized donors are also obtained and correlated with 2DEG and free electrons to predict the gate capacitance characteristics of the devices, and showed good agreement with the experimental data.
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