Abstract
The thermal band gap variation of ZnS, GaAs, GaP, and ZnSe is mathematically discussed by means of curve discussion. We investigated the most used expressions, i.e. the formulas of Varshni (1967 Physica 34 148) and Fan (1951 Phys. Rev. 82 900). The first and specifically the second derivative of both expressions reveal that Fan’s theory describes the physics behind the thermal affairs, while Varshni’s formula does not. In fact, the second derivative of Fan’s expression pinpoints the temperature at which the maximum of the formation entropy of electron hole pairs takes place, representing the semiconductor’s refractoriness. The work shows that curve discussion verifies whether a mathematical expression describes indeed the physics behind the phenomenon investigated or rather represents simply fitting efficiency.
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