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Keywords: Substitutional solid solution, epitaxial film, generalized moment of molecules, photoluminescence, current-voltage characteristic, energy band.

1. Introduction

In recent years, the growth of epitaxial films for the needs of the semiconductor industry has been growing at a fast pace, and it is expected that during 2022-2027, the compound annual growth rate (CAGR) will be 11.60% [1]. In this regard, the growth of GaN epitaxial films on foreign substrates is of great importance, since the demand for such films in the semiconductor industry is increasing every year. Sapphire (Al₂O₃), silicon carbide (SiC), and silicon (Si) are commonly used as foreign substrates for growing GaN epitaxial films [2]. Each of these materials as a substrate for growing GaN epitaxial films has its own advantages and disadvantages. When epitaxial films are grown on a foreign substrate, the similarity of lattice constants, thermal expansion coefficients and the similarity of the crystal structure of the substrate and film material are of great importance. These parameters have a great influence on the quality of the grown epitaxial films. And also the important factor is the availability, perfection of growing technology and the substrate material price. The availability of high-quality silicon substrates and the perfection of the growth technology make it a promising substrate material for epitaxial GaN layers growing. But a significant difference in lattice constants and thermal expansion coefficients makes it difficult to grow high-quality GaN films directly on Si substrates. Therefore, the development of a technology for high-quality GaN layers growing on Si substrates is an urgent task of modern semiconductor materials science.
We study the possibilities of growing epitaxial films of the (Si₂)_1-x(GaN)_x solid solution on Si substrates. It is known that the semiconductor devices quality: light emitting diodes; - high electron mobility transistors; power semiconductor devices and micro-electromechanical systems created on the basis of epitaxial films, depends on the crystallographic perfection of the epitaxial films [3]. In turn, the quality of the epitaxial GaN film grown on a foreign substrate strongly depends on the choice of the material of the buffer layer that is located between the substrate and the epitaxial film, which reduces the harmful effect of the mismatch between the thermal expansion coefficients and the lattice constants of the substrate and the film materials. The use of a graded-gap (Si₂)_1-x(GaN)_x solid solution with a smoothly varying composition located between the Si substrate and the GaN epitaxial film as a buffer layer makes it possible to significantly reduce the defects concentration and obtain higher-quality GaN epitaxial layers. For growing an epitaxial film of the (Si₂)_1-x(GaN)_x solid solution, we used the method of liquid-phase epitaxy. As it is known, the method of liquid-phase epitaxy from a limited volume of a metallic solution-melt makes it possible to smoothly change the composition of the solid solution. In our case, the composition of the solid solution smoothly changes in the growth direction from Si to GaN.
We have not found a substitutional solid solution formed between Si and GaN in literature. In this regard, the possibility of the formation of a substitutional solid solution according to the rules of generalized moments is analyzed in this paper.

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