Amorphous germanium I. A model for the structural and optical properties

Abstract

The structural properties (radial distribution function, small angle scattering, density), optical properties (complex dielectric function versus energy), and other characterizing parameters (scanning electron microscope examination, chemical analysis, recrystallization behaviour, transport phenomena), have been determined for a series of amorphous Ge films sputtered at different substrate temperatures. Various of these properties (e.g. refractive index, density, room temperature conductivity) show only slowly varying values for low and high substrate temperatures, with a rapid changeover in a critical temperature range. A model has been developed which relates this behaviour to the probability that an adatom configuration be able to change to a configuration of lower local free energy in the time for the deposition of a monolayer, and it is suggested that such behaviour may be a general feature of disordered films prepared by any deposition method. The structural and optical properties at a given deposition temperature, their differences from the properties of the FC-2 crystal, and the small changes in them as the deposition temperature is increased, are examined in terms of the Phillips spectroscopic theory of bonding. It is found that the changes in the gross optical properties from crystal to disordered film and among disordered films may be very satisfactorily explained in terms of changes in the bond length and the coordination number or density. The changes in these parameters are quantitatively related to the changes in the void density by the structural measurements. The special importance of the coordination number—and so of the void density distribution—both for the basic theory and for attempted extrapolation to the properties of the fully coordinated continuous random network without impurities is emphasized. The complex dielectric function is used, along with published data on the conduction band density of states and arguments concerning the dependence of the transition matrix element on energy, to derive densities of states for the valence band and in the pseudogap, and their changes with deposition temperature. These state densities are then used to calculate the conductivity due to transport in the delocalized valence band states using the random phase approximation and also the conductivity due to hopping near the Fermi level, and the results compared with preliminary data on conductivity. Finally, a review is given of pertinent earlier work on structure and its dependence on preparatory method and annealing treatment, the relation of the experimental structure measurements to atomic models, calculations of the electronic band structure, and earlier measurements of optical properties derived from photoemission, reflectivity and absorption edge data. An attempt is made to correlate the new data with earlier measurements, and to assess to what extent the properties reported here approach those of the hypothetical chemically pure, perfectly coordinated continuous random network.