Simulation of the Inversion of the Aluminum Profile Gradient at Liquid Phase Epitaxy of GaAl(P, As, Sb) Heterostructures
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Abstract
The inversion of the aluminum profile gradient in the epitaxial Ga-Al-Nm (Nm=P, As, Sb) heterostructures grown by the forced cooling from a liquid phase were investigated.
Simulation of the liquid phase epitaxy is carried out in the Pfann approximation in the following assumptions. The problem is one-dimensional, the epitaxial film grows in Frank–van der Merwe growth mode. The diffusion in the solid phase is frozen. The decrease in temperature is so slow that the diffusion in the liquid phase significantly exceeds the solid film growth rate. The degree of supersaturation of the liquid solution is so small that the composition of growing solid layers is determined by the equilibrium phase diagram. Given that in the liquid phase gallium predominates and the fraction of aluminum and phosphorus, arsenic or stibium do not exceed several percent, the liquid phase is considered as a dilute quasi-regular solution. The crystalline phase is considered as an ideal solid solution due to almost identical crystalline lattices in each pair GaP-AlP, GaAs-AlAs, GaSb-AlSb.
Numerical calculations are carried out for growth processes in several different initial compositions of the growth solution: for Ga-Al-P – from 1500 K liquidus isoterm, for Ga-Al-As – from 1200 K and for Ga-Al -Sb – from 850 K. The results are presented in the graphs of the solid phase composition depended of the crystallization temperature and of the film layer depth, as well as on the diagram of moving the liquid phase figurative point during the growth process. Comparison of simulation results with experimental data confirms the correctness of the applied model.
It is shown that at each temperature there is an inverse composition characterized by a certain content of aluminum in the solid phase. If, on cooling, the figurative point of the growth solution intersects the inverse curve then an inversion of the aluminum profile gradient occurs: the epitaxial film, which previously was growing with a decrease in the aluminum, increases further with its increase. The reason for such a phenomenon is the possible compensation of two interconnected competing factors when the growth solution cools: a decrease in the amount of nonmetal in the liquid phase and an increase in the aluminum segregation coefficient. The relationship between the inverse curve shape and the phase diagram parameters is established. The principal possibility of growing in a single technological process of Ga-Al-P and Ga-Al-As (but not Ga-Al-Sb) planar heterostructures suitable for the manufacturing of microelectronic waveguide devices is shown.
Ref. 22, fig. 9, tabl. 1.
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