Doping effects and compositional grading in AlxGa1-xAs/GaAs heterojunction bipolar transistors

Abstract

First-order analytical calculations were made for the energy-band diagrams for n-Al <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> Ga <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</inf> As/p-GaAs heterojunctions for x = 0.15, 0.3, and 0.5 employing different compositional gradings and doping densities specifically for heterojunction-bipolar-transistor (HBT)applications. In the calculations most recently determined, conduction-band discontinuity ΔE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</inf> of 65 percent of the bandgap difference ΔE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</inf> between the Al <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> Ga <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</inf> As and GaAs, and the donor activation energies in n-Al <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> Ga <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</inf> As of 60 and 160 meV for x = 0.3 and 0.5, respectively, were used. The results show that the position of the heterojunction spike barrier, and the depth and width of the notch in the conduction-band edge for a compositionally abrupt heterointerface depend on the respective doping densities on the p and n sides of the heterojunction. Also, for an abrupt heterointerface the difference in barrier heights for electron and hole injections varies between ΔE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</inf> and ΔE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</inf> (the valence-band discontinuity), depending on the doping densities and the applied bias, and is not necessarily the generally accepted value of ΔE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</inf> . Analytical expressions and curves were obtained to estimate the minimum compositional grading L for eliminating the spike barrier and the notch as a function of the doping densities and the applied bias.