If I understand correctly your question, you want to replace the conduction channel region of a device (for example, HEMT) with InGaN instead of pure GaN. If you have a ternary material where electron conduction takes place, then you should consider alloy scattering as one of the mechanisms. It is not clear from your question if you are are actually looking for a formula and you do not specify which device or application you are interested in. More details would help to understand what you need.

For III-V compound materials, the early approach by Harrison and Hauser (Phys Rev B, vol. 13, p. 5347, 15 June 1976) is probably where you want to start.

Thank you sir for the response. This question is related to HEMT.

When HEMT is formed by AlxGa1-xN/GaN than the mathematical expression of relaxation time for alloy disorder scattering (ADS) is t= 16*h^3/(3*b*x*(1-x)*m*D*U^2). I wished to enquire the expression of relaxation time of electron in ADS for HEMT formed by AlxGa1-xN/InyGa1-yN.

A recent paper you may consult is:

Sohi, Carlin, Grandjean "Alloy disorder limited mobility of InGaN two-dimensional electron gas" Applied Physics Letters, vol. 112, 262101 (2018); https://doi.org/10.1063/1.5030992

Since the formula you quote is an empirical approximation for ternary compounds, you should be able to apply the same formula to a material like InGaN with appropriate parameters. The paper by Sohi et al provides a link to supplementary material

ftp://ftp.aip.org/epaps/appl_phys_lett/E-APPLAB-112-001826

which you should find useful to answer your original question and it discusses also the effect of finite quantum well thickness.

If you want to consider in more depth about alloy scattering for AlGAN and InGaN you can look at this paper:

Bellotti, Bertazzi and Goano, "Alloy scattering in AlGaN and InGaN: A numerical study" Journal of Applied Physics, vol. 101, p. 123706 (2007); https://doi.org/10.1063/1.2748353