We investigate light emission spectra at different excitation levels of nanoscale thin InGaN film participating in an InGaN/GaN quantum well (QW) with heavily doped barriers for green and blue light emitting diodes (LEDs). We model the spectral shape and energy position in frames of the free electron recombination model created first for highly doped 3D direct gap III-V semiconductor films and applied for QWs at low excitation. The model accounts for the influence on the potential width of the QW of the random impurity potential of the doped barriers which penetrates into the QW. The blue shift at high excitation is supposed to be due to the filling of the conduction band with degenerate 2D nonequilibrium electrons. A structure in the emission bands is observed and it is assumed to be a result from step-like 2D density-of-states (DOS) in the QW. A good agreement is obtained between the calculated and experimental spectra assuming that the barriers are graded.