Modeling AlxGa1−xAs optical constants as functions of composition

Abstract

Three models for the dielectric function εx(hν) of AlxGa1−xAs are reviewed. All are based on measured optical constants at discrete compositions. The validity of each model near critical point energies, and otherwise, is evaluated. Only the energy-shift model is appropriate over the entire available spectrum (1.5–6.0 eV), including the band-gap (E0) region.

Spectroscopic ellipsometry for monitoring and control of surfaces, thin layers and interfaces

“…If the mixing is on an atomic scale, however, the EMA cannot be used because alloying produces a change in the band structure and shifts in the critical point energies. 13 This is illustrated in Fig. 5, which shows reference spectra for strained Si 1 x Ge x alloys determined by spectroscopic ellipsometry.…”

“…An interpolation procedure is used to represent the alloy, based on polynomials for each critical point variation with composition. 13,15 The critical point energies also are affected by strain and temperature through changes to the band structure. For example, in Si 1 x Ge x and other strained layer alloys the effect of strain is to increase splitting of the E 1 and E 1 C  1 peaks.…”

Plasma-Assisted Atomic Layer Deposition of SrTiO3: Stoichiometry and Crystallinity Studied by Spectroscopic Ellipsometry

“…Snyder et al used a linear interpolation for the wavelength shift algorithm for Al x Ga 1-x As optical constants. 39 Parameters such as the resolution (i.e. the B-spline node spacing) and the maximum degree of the polynomials should be optimized accordingly to the case to obtain the best results.…”

“…The library is then built by interpolating these dielectric functions. The interpolation is based on the critical point shifting algorithm described by Snyder et al for Al x Ga 1-x As optical constants, 39 where the dielectric function of a film with unknown composition is estimated by shifting the closest two dielectric functions of known compositions in energy to align their critical points. The unknown composition is then determined by taking a weighted average of the two dielectric functions of known composition.…”

Spectroscopic ellipsometric monitoring of electron cyclotron resonance plasma etching of GaAs and AlGaAs

“…Dielectric function models include the Bruggeman effective medium approximation ͑EMA͒ for composite or porous materials, 4 a simple harmonic oscillator approximation that uses a set of Lorentz oscillator functions to approximate critical point structure, 5 and an AlGaAs alloy model that allows x to be varied continuously. 6 The general procedure is to develop the simplest model that gives a good fit to the data, is physically reasonable, and is consistent with whatever is independently known about the sample.…”