A parametrization of the density of states (DOS) near the band edge of phosphorus-doped crystalline silicon is derived from photoluminescence and conductance measurements, using a recently developed theory of band gap narrowing. It is shown that the dopant band only “touches” the conduction band at the Mott (metal-insulator) transition and that it merges with the conduction band at considerably higher dopant densities. This resolves well-known contradictions between conclusions drawn from various measurement techniques. With the proposed DOS, incomplete ionization of phosphorus dopants is calculated and compared with measurements in the temperature range from 300to30K. We conclude that (a) up to 25% of dopants are nonionized at room temperature near the Mott transition and (b) there exists no significant amount of incomplete ionization at dopant densities far above the Mott transition. In a forthcoming part II of this paper, equations of incomplete ionization will be derived that are suitable for implemen...

A simulation model for the density of states and for incomplete ionization in crystalline silicon. I. Establishing the model in Si:P

High-quality ZnS, ZnSe, and ZnTe epitaxial films were grown on (001)-GaAs-substrates by molecular beam epitaxy. The 1s-exciton peak energy positions have been determined by absorption measurements from 2 K up to about room temperature. For ZnS and ZnSe additional high-temperature 1s-exciton energy data were obtained by reflectance measurements performed from 300 up to about 550 K. These complete E1s(T) data sets are fitted using a recently developed analytical model. The high-temperature slopes of the individual E1s(T) curves and the effective phonon temperatures of ZnS, ZnSe, and ZnTe are found to scale almost linearly with the corresponding zero-temperature energy gaps and the Debye temperatures, respectively. Various ad hoc formulas of Varshni type, which have been invoked in recent articles for numerical simulations of restricted E1s(T) data sets for cubic ZnS, are discussed.

Temperature dependence of exciton peak energies in ZnS, ZnSe, and ZnTe epitaxial films

vanishing dispersion, D>0, up to the limiting regime of extremely large dispersion, D 5/4 for Varshni’s model is the fundamental reason for the usual inadequacy ~large degree of arbitrariness! of parameter values resulting from conventional fittings of E(T) data sets using Varshni’s formula.

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Dispersion-related description of temperature dependencies of band gaps in semiconductors

We perform numerical analyses of the temperature dependences of fundamental band gaps, Eg(T), and/or exciton peak positions, Egx(T), for a large variety of group IV, III–V, and II–VI (including wide band gap) materials using a two-oscillator model. This model assumes a fixation of the low-energy oscillator in the vicinity of the dominant TA peak, whereas the location of the high-energy oscillator is taken as an adjustable parameter depending on the relative weights of the contributions of short-wavelength LA and LO/TO phonons. The material-specific sets of empirical parameters have been estimated from fittings of measured E(T) dependences. The results indicate significant changes of the relative contributions of optical versus acoustical phonons from one material to the other. The degree of dispersion is found to increase significantly with contribution of low-energy acoustical phonons.

Temperature dependence of fundamental band gaps in group IV, III–V, and II–VI materials via a two-oscillator model

AlN Bandgap Temperature Dependence from its Optical Properties

Novel analytical descriptions of the temperature dependence of the indirect energy gap in silicon are compared with conventional models due to Varshni [ Physica 34 , 149 (1967)] and Vina et al. [ Phys. Rev. B 30 , 1979 (1984)]. A high-precision fit is shown to be given by an empirical expression of the type E g (T) = E g (0) − ( α·Θ 2 )·( 1 + ( 2T Θ ) − 1 ) where α is the limiting gap shrinkage coefficient and Θ ≡ hω k represents the effective phonon temperature. For silicon, the empirical model parameter p is found to be significantly higher than 2, which is in analogy to many other semiconductor materials. The principal physical causes and analytical aspects of this common feature are briefly discussed on the background of forthcoming analytical results.

R. Pässler

Papers

Comparison of different analytical descriptions of the temperature dependence of the indirect energy gap in silicon