In this paper an analytical model has been optimized to represent similar AlGaN/GaN high electron mobility transistor epitaxially grown on different substrates of sapphire and silicon in view of the effect of epitaxial growth driven crystalline quality of buffer on device I-V characteristics. We have observed its important role on electrical and thermal characteristics of the device. Starting with the standard model for AlGaN/GaN HEMT on sapphire, we have employed a novel thermal modeling approach on this metamorphic buffer to derive the device temperature in different epilayers. The optimized mobility model has been enriched with two defect scatterings for their potential role at high lattice temperature. The electrical and thermal characteristics, obtained from present model, are well agreed with the published experimental data and other existing models. We have observed the inclusion of high parasitic resistance to reduce the dissimilarity in I-V characteristics at linear region between experimental and the present model data for the HEMT on Si; which is possibly related to the growth morphology. Perhaps this dissimilarity can be a collaborative effect of various factors like traps, thermal expansion coefficient mismatch and change in critical electric field. Finally, we have observed the significant influence of device dimension on thermal characteristics of the device; which leads to scaling. (C) 2014 Elsevier Ltd. All rights reserved.