Automated numerical characterization of dilute semiconductors per comparison with luminescence

Abstract

This paper combines analytical approximations for the optical absorption and luminescence of semiconductors with trust region-reflective methods, delivering a robust numerical characterization method to be used in the study of new bulk semiconductors per direct comparison with experimental spectra. It further extends recent applications of the theory to the case of dilute nitride semiconductors and confirms results for the s-shape of the luminescence peak as a function of temperature.

Analytical Expressions for Numerical Characterization of Semiconductors per Comparison with Luminescence

“…Low temperature luminescence is typically performed with a small density of injected carriers. Very good agreement of this theory with results from different experimental teams for a variety of materials has been obtained with carrier densities around 10 15 carriers/cm 3 [ 7 , 8 , 9 ], further justifying the range of densities in the y -axis. The theory has also been used for high temperatures and high densities to investigate optical nonlinearites [ 14 , 15 , 16 ], and this range is illustrated in Figure 2 .…”

“…The fully numerical solutions of the equations that use this version of the approximation have given very good agreement with both single beam and pump-probe luminescence [ 20 , 25 ]. Its usefulness has been further confirmed recently by the good agreement between the analytical solutions shown here and the experimental luminescence of dilute semiconductors [ 7 , 8 , 9 , 14 ].…”

“…The total dephasing Γ will determine the luminescence linewidth. Thus, it can be treated as a phenomenological parameter used to interpret data, and at the same time estimate the strength of the scattering and dephasing processes [ 7 , 8 , 9 ] by comparison of adjusted data with microscopic calculations derived from the relevant selfenergies [ 17 , 18 ]. At this point, the Kubo–Martin–Schwinger (KMS) relation under the form derived in Ref.…”

“…A recent theoretical effort led to the development of analytical solutions for the interband polarization, which plays the selfenergy role in the Dyson equation for the Photon Green’s functions [ 7 ], which have been applied them to study photoluminescence of Coulomb-correlated semiconductor materials. The accuracy of the resulting easily programmable solutions has been demonstrated by consistently explaining the low temperature s-shape of the luminescence peak of dilute semiconductors, such as ternary GaAsSb, InAsN, and quaternary InAs(N,Sb) [ 7 , 8 , 9 ]. The interplay of homogeneous versus inhomogeneous broadening at low and high temperatures are described, together with the relevance of many body effects, which are in very good agreement with experiments [ 10 , 11 , 12 , 13 ].…”

“…This paper has two objectives: to show hitherto unpublished details of the mathematical steps that lead to the equations used in Refs. [ 7 , 8 , 9 , 14 , 15 , 16 ], and to draw a bridge between the luminescence and nonlinear absorption calculations in superlattices. It is organized as follows: the main steps involving manipulations of hypergeometric functions that characterize the solution of the Hulthén potential problem are delivered.…”