High electron mobility transistor (HEMT) made of compound semiconductors exhibit great potential for high-power applications at RF, microwave, and millimeter-wave frequencies. Owing largely to a high electrical breakdown field, electron sheet charge density, and substrate material with high thermal conductivity, these are capable of handling larger power density signals at high temperatures in unfriendly environments. The present work involves the analytical modeling of AlGaN/GaN material system based HEMTs. A polynomial represents Fermi-level as a non-linear function of sheet carrier density at the interface of HEMTs. Using this polynomial, models for finding the temperature dependent gate capacitance, parasitic MESFET dependent transconductance and dc characteristics including self-heating effects were formulated. The effects of spontaneous and piezoelectric polarization fields, have been investigated in detail. All results show reasonable agreement with the experimental data. Our analytical simulation should be useful in device designing, allowing interactive optimization of device configuration and economically complementing experimental investigations.