Results of measurements of infrared reflectivity and micro-Raman scattering on the undoped GaN high pressure grown single crystals are reported. These crystals have usually a high electron concentration due to unintentional doping by oxygen. We show, by the shift of the plasma edge (infrared reflectivity measurements), that the free electron concentration is always higher on the (0 0 0 1)N face of the GaN single crystal than on the (0 0 0 I)Ga face. In order to determine the profile of the free carrier concentration, we performed transverse micro-Raman scattering measurements along the (0 0 0 1) c-axis of the crystal with spatial resolution of 1 mum. Micro-Raman experiments give a quantitative information on the free carrier concentration via the longitudinal optical phonon-plasmon (LPP) coupling modes. Thus, by studying the behavior of the LPP mode along the c-axis, we found the presence of a gradient of free electrons. We suppose that this gradient of electrons is due to the gradient of the main electron donor, in undoped GaN single crystals, i.e. oxygen impurity. We propose a growth model which explains qualitatively the incorporation of oxygen during the growth of GaN crystal under high pressure of nitrogen.