Anisotropy and nonlinearity in superlattices II

Abstract

This paper uses the anisotropic medium approach to calculate nonlinear optical absorption in semiconductor superlattices. The study confirms that the nonlinearities increase with anisotropy suggesting that strongly anisotropic materials such as those used for solar cells may also play a relevant role for nonlinear optical applications.

Analytical Expressions for Numerical Characterization of Semiconductors per Comparison with Luminescence

“…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 .…”

“…At quasi-equilibrium, used in Refs. [ 7 , 8 , 9 , 14 , 15 , 16 , 22 ], the total chemical potential is calculated self-consistently with the many body renormalization of the bandgap and can be written exactly as , where is the total free carrier chemical potential calculated from the bottom of each band. In other words, the inversion factor can be equivalently written as , and it is now clear why Figure 4 has the detuning in the x -axis.…”

“…These can be calculated from the corresponding free carrier Hamiltonian, and full details of the method, which has led to good agreement with experimental data, can be found in Refs. [ 15 , 16 , 21 , 29 ]. Figure 5 shows calculated luminescence using the modified parameters determined by anisotropic medium theory for a short period GaAs–Al 0.3 Ga 0.7 As superlattice with repeated barrier and well widths equal to 2 nm.…”

“…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 ]. A similar set of equations was also used to study nonlinearities in GaAs–AlGasAs and GaAsN–AlGaAs superlattices [ 14 , 15 , 16 ]. The superlattice case is particularly noteworthy for room temperature GHz nonlinear multiplication into the THz range [ 17 , 18 ].…”

“…This paper has two objectives: to show hitherto unpublished details of the mathematical steps that lead to the equations used in Refs.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.…”