Modeling the optical dielectric function of semiconductors: Extension of the critical-point parabolic-band approximation

Abstract

A model is proposed for the line shape of the optical dielectric function of zinc-blende semiconductors. For comparison with previously proposed models, this model is used primarily with spectroscopic ellipsometry data (but also transmission data below 1.5 eV) to obtain an analytic room-temperature dielectric function for GaAs. It is found to be more generally valid than the harmonic-oscillator model, the critical-point (CP) model, or the model of Adachi. It is applicable over the entire range of photon energies, below and above the lowest band gaps, incorporates the electronic band structure of the medium, and exactly satisfies the Kramers-Kronig transformation.It goes beyond the CP parabolic-band approximation in that it correctly takes into account the full analytic form of the electronic density of states and thus does not require the use of arbitrary cutoff energies. Also, it allows one to go beyond the usual approximation of Lorentzian broadening, which is known to be incorrect for elements and compounds above very low temperatures. For these reasons, it results in excellent quantitative agreement with experimental results for the dielectric function and for its derivatives with respect to photon energy, much better than that given by earlier models. Finally, the parameters of the model are physically significant and are easily determined as functions of composition for semiconductor alloys. Application of the model to the fitting of spectroscopic data on GaAs strongly suggests that spectroscopic ellipsometry does not measure the true bulk dielectric function. It also supports the conclusion that the line-shape broadening in GaAs at room temperature is more nearly Gaussian than Lorentzian.

Optical constants of Cu2ZnGeS4 bulk crystals

“…The inclusion of an additional term, 1ϱ , in the ͑E͒ expression improves the fit of experimental data. [11][12][13][14][15][16] This term contains the contributions of higher lying interband transitions. The 1ϱ parameter may take a second order polynomial dependence of the photon energy 16 or may even be constant [11][12][13][14][15] in the studied spectral range.…”

Oxygen plasma effects on optical properties of ZnSe films

“…Kim and Garland have developed a KK consistent model that adequately describes the semiconductor dielectric function above, below, and through the fundamental direct gap. 50,51 It can accurately describe the dielectric function and higher order derivatives. However, to determine the required internal parameters a two stage fitting process is needed.…”

Modeling the optical constants of GaP, InP, and InAs

“…The fact that Lorentzian broadening does not describe the optical spectrum accurately has already been recognized and discussed by several groups. [20][21][22][23] Rakić and Majewski 23 have shown that the Adachi model, with a Gaussian-like broadening function, can describe accurately the dispersion and absorption of GaAs and AlAs even in the vicinity of the E 0 , where the original model of Ozaki and Adachi 9 is highly inaccurate. In this work, we use a similar model, which considers the contribution of exitonic terms only at E 0 , E 0 ϩ⌬ 0 CPs, since the excitonic effects are usually more pronounced at E 0 than at any other CPs.…”