We have developed a model describing the non-proportional response in scintillators based on non-thermalised carrier and phonon transport. We show that the thermalization of e-h distributions produced in scintillators immediately after photon absorption may take longer than the period over which the non-proportional signal forms. The carrier and LO-phonon distributions during this period remain non-degenerate at quasi-equilibrium temperatures far exceeding room temperature. We solve balance equations describing the energy exchange in a hot bipolar plasma of electrons/holes and phonons. Taking into account dynamic screening we calculate the ambipolar diffusion coefficient at all temperatures. The non-proportional light yields calculated for NaI are shown to be consistent with experimental data. We discuss the implications of a non-equilibrium model, comparing its predictions with a model based on the transport of thermalised carriers. Finally, evidence for non-equilibrium effects is suggested by the shape of non-proportionality curve and wide dispersion in data observed in K-dip spectroscopy near the threshold. A comparison of the predicted curves shows good agreement for deformation potential value in the range 7-8 eV.
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