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METHODOLOGY

1. The condition for the formation of a solid solution

(Si₂)_1-x(GaN)_x

We have studied a two-component substitutional solid solution based on silicon and gallium nitride. GaN is a wide-gap semiconductor with a band gap E_g = 3.4 eV at room temperature, while silicon has the band gap E_g = 1.1 eV. To assess the possibility of a solid solution forming based on GaN and Si₂, we use the rule of generalized moments [4], according to which, a decrease of the absolute value of the difference between the generalized moments of ions, atoms, or molecules of solution-forming substances, leads to an increase in their mutual solubility:

Table 1. Generalized molecular moments and band gap of III-V binary compounds and elementary semiconductors
Chemical formula of semicondutors	Generalized moments of molecules, m∙10^2, C/m	Eg, eV
BN	137.8	5
AlN	114.6	4.9
GaN	109.4	3.4
InN	99.5	0.64
BP	119.9	6
AlP	96.7	2.45
GaP	91.5	2.27
InP	81.6	1.34
Bas	114.7	3.0
AlAs	91.4	2.16
GaAs	86.3	1.43
InAs	76.4	0.35
BSb	85.7	2.60
AlSb	62.5	1.58
GaSb	57.3	0.72
InSb	47.4	0.18
Si2	104.0	1.12
Ge2	78.3	0,67
Sn2	49.5	0.08
αSiC	120.5	3

where c′ and c″ are the mole fractions of the dissolved component in the solid () and liquid () phases,  and  are the average values of the potentials of molecular fields in the phases () and (), m and m₀ are the generalized moments of the solute and solvent, respectively, k is the Boltzmann constant, Т is the absolute temperature, V is the effective volume of the dissolved component. In exp. (1), the exponent is always negative and, therefore, for the  c′ increase, there should be a decrease of generalized moments difference m  m₀.
To estimate the generalized moment of atoms, it was used an expression that takes into account the covalent radius, the shell structure of the atom, and the effective nuclear charge [4]:

where N is the ordinal number of the element in the periodic system of elements,  is the screening coefficient, r_i is the crystallographic radius of the ion, а_о is the Bohr radius, n^* is the effective principal quantum number. As could be seen from exp. (2), the potential of an ion or atom on its surface with radius r_i consists of the sum of potentials created by a nucleus with an effective charge (N - )e and internal electron shells. The screening coefficient  and, consequently, the value of m^*, determined by exp. (2), depends on the type of the considered subshell (s, p, d, f, …), even for the same value of the principal quantum number n, which is probably should be reflected in the physical and chemical properties of the elements. m^* expresses the energy characteristic of an atom during its action with an external field and intermolecular interaction.
The state of the molecules of substances IV-IV, III-V and II-VI in a solution-melt differs little from its molten state. Therefore, during consideration of these molecules solubility in metallic solvents under the conditions of the existence of liquid and solid solutions, it is necessary to take into account the existence of molecules of the AB type that have retained a covalent bond between atoms A and B. Considering these circumstances, the energy characteristic of the molecules of binary compounds III-V in liquid solutions is taken potential on the surface of a sphere with radius R and effective charge Z^*∙ q, and by analogy with exp. (2), and so represents the generalized moment of the III-V molecule in the following form:

where Z^*= (A – γ)_III + (A – γ)_V – 0.35, and R = r_III + r_V (4)