Temperature dependence of the band gap of silicon

Abstract

The band-gap energy Eg of silicon has been reevaluated with high precision between 2 and 300 K by the following method: the derivative of the absorption coefficient, resulting from free-exciton absorption, has a well-defined singularity, which can be detected unambiguously by wavelength-modulation spectroscopy. The energy of this singularity yields the band gap. Our data deviated by more than 5 meV from the earlier results of MacFarlane et al. and Haynes et al. and fell between their Eg(T) curves. The approximation of Eg(T) = A + BT + CT2 gives A = 1.170 eV, B = 1.059×10−5 eV/K, and C = −6.05×10−7 eV/K2, for 0<T≤190 K, and A = 1.1785 eV, B = −9.025×10−5 eV/K, and C = −3.05×10−7 eV/K2, for 150≤T≤300 K, which fits our data within 0.2 meV. The major uncertainty of about 1 meV lies in the energies of exciton and TO phonon.

Schottky barrier height measurements of Cu/Si(001), Ag/Si(001), and Au/Si(001) interfaces utilizing ballistic electron emission microscopy and ballistic hole emission microscopy

“…The band gap of the substrate is more fundamental and a better number to compare to since it has been measured using optical methods to be 1.1669 eV at 77 K for Si. 31 The sum of the p and n type barriers tabulated in the tables are in good agreement with the gap and independent of the metal overlayer. It appears that fits using n = 2 give the best agreement to the gap and best R 2 values overall.…”

Electron–phonon interaction in tetrahedral semiconductors

“…In the case of germanium, not only the Γ→L indirect gap, but also the Γ→ Γ direct gap and its spinorbit split component are accessible to experiments [41]. Figure 5 shows the indirect gap of silicon vs. T. The points are experimental [44,45]. The curve drawn through them represents a fit with the empirical expression [11,40]:…”

Comparison of some theoretical models for fittings of the temperature dependence of the fundamental energy gap in GaAs

“…This variation of α expn is relatively large (∼ 17%) considering the predicted linear behavior of E g (T ) at high temperatures. The non-linear behavior of E g (T ) was already foreseen by Bludau et al [25] who used second order polynomes to fit the temperature dependence of Si indirect-energy gap. Cardona and Thewalt [16] also point out the importance of anharmonic terms (which leads to higher order terms in T) in the electron-phonon interaction to analyze the temperature dependence of the lattice parameter of Si.…”

“…Experimental data from Panish [22], Shen [23] and Lautenschlager [11], usually used in the literature to describe E g (T ) at high temperatures [3,24], covers a wide temperature range but have a reduced number of data points with a large numerical dispersion, which does not allow us to infer about the non-linear behavior of E g (T ). In a relatively old work, Bludau et al [25] analyzing the dependence on temperature of the indirect energy gap of Si have mentioned that it seems that the predicted linearity of E g (T ) is not a precise description of the behavior of energy gap at high temperatures. Cardona and Thewalt [16] also make remarks about the accuracy of the results deriving from perturbation theory that keeps only up to the second order terms of the atomic displacements (proportional to < u 2 >) in the Hamiltonians used to describe the electron-phonon interactions.…”