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A physics based analytical model is presented to describe the bare surface barrier height and the two-dimensional electron gas density in AlGaN/GaN heterostructures versus barrier layer thickness and Al content. Details of the model rely on the extraction of the critical thickness for strain relaxation based on the identification of a signature cusp in experimentally obtained bare surface barrier heights. This information is used to obtain the residual strain and total effective polarization when strain relaxation takes place. The model, which covers both unrelaxed and relaxed barriers, shows good agreement with reported experimental results and promises to become a useful tool in advanced design and characterization of GaN based heterostructures.