Varshni equation

The influence of the electron-phonon interaction on the band-to-band transition energies Eq at low temperatures is often addressed by the Varshni equation [165]... 

The T dependence of bandgaps is generally given in terms of an empirical Varshni equation... 

G = shear or torsional modulus / = specimen length 5 = parameter in Varshni equation t = transit time, Einstein temperature T = temperature, Kelvin... 

The potential energy curves for the states of most diatomics are generally known with high accuracy from the analysis of spectroscopic or scattering data. Many analytical functions have been proposed which reproduce the main features of attractive and repulsive potentials and we have already mentioned the Morse potentials of equations (32) and (33) as typical of these. Comprehensive reviews of other functions have been given by Varshni 121) and Goodisman 122). 

Dunham (1932) was the first who understood the ideas and force of this method, and applied the WKBJ approach to the derivation of the second and third nonzero energy terms of the one-dimensional Schrddinger equation with the D-version of an anharmonic potential (see also Krieger et ah, 1967). Afterward and up to recent times, so many authors have applied the WKBJ method that if we attempt to enumerate them all, then quite half of the present article would be represented by the references alone. For the inquisitive reader we refer to some papers (Krieger et al., 1967 Kesarwani and Varshni, 1978, 1980 Zwaan, 1929 Kirschner and Watson, 1973 Stettler and Shatas, 1971 Froman and Froman, 1965 Kil-lingbeck, 1980 Hecht and Mayer, 1957) in which, without any difficulties, a whole body of literature devoted to the problem may be found i.e., by the principle of the Russian popular tale, which in our version becomes a reference, by reference, by reference, etc.,. . . , the reader will extract a turnip, i.e., a key to the essence. 

Further equating the coefficients of successive powers of h to zero, one can determine recurrently (Kesarwani and Varshni, 1980) ... 

A considerable contribution to the theoretical study of isoelectronic diatomic molecules was made by Laurenzi (1969, 1972, 1976, 1981), who obtained the equations describing the behavior of Re, De, and k2 as functions of nuclear charges in both cases of homo- and heteronuclear diatomic molecules. In particular, Laurenzi (1976, 1981) solved exactly these equations for one-electron diatomics with some empirical diatomic potential functions (Morse and Varshni III). 

Figure 3.15 Temperature-dependent peak positions of the A-free exciton, FX (r5) and its ILO- and 2LO-phonon replicas. Also shown are the temperature evolutions ofthe peak positions oftwo major neutral donor-bound exciton transitions at 3.3606 and 3.3650eV. The FX (r5) data were fit using Varshni s equation and LO-phonon replicas were fit to the equation shown in the figure. (After Ref [50].)...

---