An explicit and precise model for two dimensional electron gas (2DEG) charge density and Fermi level (E-f) in heterostructure high electron mobility transistors (HEMTs) is developed. This model is from a consistent solution of Schrodinger's and Poisson's equations in the quantum well with two important energy levels. With these closed-form solutions, a unified surface potential calculation valid for all the operation regions is derived. With the help of surface potential, a single-piece drain current model is developed which is also capable of describing the current collapse effect by using a semi-empirical expression of source/drain access region resistances. Comparisons with numerical and measured data show that the proposed model gives an accurate description of Ef and drain current in all regions of operation. (C) 2015 Elsevier Ltd. All rights reserved.