In this paper we present a precise physics based analytical model for the two-dimensional electron gas density n(s) in AlGaAs/GaAs high electron mobility transistors. The model is developed by considering the variation of Fermi-level E-f, the first sub-band E-0, the second sub-band E-1, and n(s) with the applied gate voltage V-g. Taking into account the interdependence between E-f and n(s), we have developed an explicit expression for n(s) in terms of bias voltages. The developed expression for n(s) is valid in all the regions of device operation, with gate-voltage ranging from below to above the cut-off voltage. The proposed model is in very good agreement with numerical calculations. (C) 2012 Elsevier Ltd. All rights reserved.