Mathematical assessment of the thermal band gap variation of semiconductors

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.

Sensitive Thermochromic Behavior of InSeI, a Highly Anisotropic and Tubular 1D van der Waals Crystal

“…The inset depicts the relationship of spectral range with respect to calculated (dE g /dT) max value. [30,[81][82][83][84][85][86][87][88][89][90][91][92][93] linewidth broadening (FWHM), the lattice anharmonicity was also manifested in the SC-XRD data as anomalous shortening of bond lengths and the tilting of the Se thermal ellipsoids with temperature. The behavior described can be ascribed to the unique aspects of the InSeI structure: the highly anisotropic 1D structure and the tubular geometry of the chains.…”

“…Comparative representation of the thermochromic behavior and electron-phonon coupling strength of InSeI to conventional semiconductors.Relationship of UV-vis-infrared spectral range with extrapolated electron-phonon coupling constant, S, across several known semiconductors and insulators. The inset depicts the relationship of spectral range with respect to calculated (dE g /dT) max value [30,[81][82][83][84][85][86][87][88][89][90][91][92][93].…”

Sensitive thermochromic behavior of InSeI, a highly anisotropic and tubular 1D van der Waals Crystal

“…The inset depicts the relationship of spectral range with respect to calculated (dEg/dT)max value. [30,[81][82][83][84][85][86][87][88][89][90][91][92][93] In order to contextualize the potential of InSeI for thermometric applications, we compared its thermochromic metrics to conventional covalent-and vdW-bound semiconductors and known materials 30 utilized for optical thermometry. In Figure 5, the hypothetical energy ranges covered by various solids from the literature and their S and (dEg/dT)max values are compared with InSeI.…”

Thermal tuning of light-emitting diode wavelength as an implication of the Varshni equation

“…In the literature, Varshini's relation (VR) has been fitted to many semiconductors, both elemental e.g. Si and Ge, and compound [11,12,13,14]. Recently, it was demonstrated for nanowires [13], in the context of wavelength tuning, quantum dots [15], and high-voltage and high-temperature (wide bandgap) devices [16].…”