Optical absorption coefficient in n-type double δ-doped layers GaAs quantum wells

Abstract

The superposition principle is one of the cornerstones of physics. In low-dimensional systems, it is routinely used to model the potential profile. That is the case of coupled [Formula: see text]-doped quantum wells, for which, several works have studied the transport and optoelectronic properties. However, the Poisson equation determines the potential profile is not linear, and the superposition principle is not at all valid. The aim of this work is to correct some of the inconsistencies of the mentioned models for coupled [Formula: see text]-doped quantum wells. In the framework of Thomas–Fermi approximation, we calculated the potential profile, the wave functions, the energy values and the relative absorption coefficient for the double system compared to an isolated delta system in terms of impurity density and distance between [Formula: see text]-wells. We found a red shifting in the absorption coefficient when the interlayer distances increase, in addition, an enhancement in the absorption coefficient is detected for a specific separation distance. Our results agree with ab-initio calculations reported for the electronic structure.

Interlayer distance effects on absorption coefficient and refraction index change in p-type double-δ-doped GaAs quantum wells*

“…In a previous work, we calculated the electronic structure of the n-type double-δ -doped model, in the TF approximation. [31] Our potential profile was not constant with interlayer distance, besides this potential is continuous in the center. Using the same physical considerations, here a model for the p-type double-δ -doped (DDD) quantum well system is proposed.…”

“…where E F is the Fermi energy of the system, e is the electron charge, h represents the Plank constant, ε r the dielectric constant, m * hh,hl is the effective mass of the heavy holes and light holes respectively, ρ 2D is the two-dimensional density of impurities, and d represents the interlayer distance. In the previous work, [31] we proposed, as a solution of the double deltadopings, the following expression in effective units for z ≤ 0:…”

“…[35] In Ref. [31] we determined the values of the parameters β and z 1 by applying two physical conditions. In addition, a third parameter γ was introduced, with the condition z 1 = γ(z 0 + αd/2).…”

“…In Ref. [31] there is a detailed analysis of the parameters involved, where M fi represents matrix elements of the dipole moment of the final (f) and initial (i) associated states. In this case m * represents the mass of heavy holes, τ in is the intersubband relaxation time.…”

“…[7,30] The changes in the interlayer distance can significantly affect the electronic structure mainly due to the changes in energy band gap and the dipolar moment. [31] Some previous models have studied the physical properties of double-δ -doped systems. Those approaches assume that the potential profile bottom is constant.…”