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Material models which incorporate the basic characteristics of the underlying physics in a given semiconductor material are the core of device modeling. We employ a Monte Carlo (MC) technique to investigate stationary electron transport in GaN and AlGaN [1]. We obtain a set of model parameters which gives agreement with experimental data available for different physical conditions (doping, temperature, electric field, etc.). Such a calibrated set of models and model parameters delivers valuable data for low-field mobility, velocity saturation, energy relaxation times, etc. We use these data as a basis for the development of analytical models for the numerical simulation of GaN-based electron devices. As a particular example we analyze an AlGaN/GaN HEMT with lg=300 nm from IAF using the two-dimensional device simulator Minimos-NT [2]. We study the impact of different models and efects (polarization charge, thermionic field emission, self-heating effects).