Complex conductivity in the presence of long range potential fluctuations. Application to the determination of the gap state density in undoped and boron doped a-Si : H films grown by CVD

In compensated crystalline and amorphous semiconductors long range potential fluctuations (PF), at the scale of the mean free path, largely affect the transport properties : they act on free carriers and they change the average degree of ionization of deep centers. The maximum magnitude of PF varies with the applied field, and the corresponding charge and discharge of deep centers in the bulk, at the frequency of the applied field, contribute to the complex conductivity of the sample. The expressions of the total complex conductivity due to lattice, free carriers and deep centers, and of the complex differential capacitance of a MIS diode, are derived in the general case of a compensated semiconductor with potential fluctuations (PF). These expressions differ significantly from those commonly used when ignoring the existence of PF. This ends up in a new method for the determination of the distribution of gap states which, contrary to other methods, allows to separate the contribution of the localized states from the contribution of band carriers. This method is applied to the interpretation of our data on a-Si: H films grown by CVD. The real and the imaginary parts of the conductivity can be fitted in wide ranges of temperatures and frequencies. The variations of the complex conductivity are completely explained by the action of PF on the transport of free carriers and on the ionization of deep centers. There is no evidence of hopping transport. The density of states shows a discrete series of peaks possibly superposed to a lower continuous density.