Temperature dependence of the absorption coefficient in doped quantum wells

Abstract

In this work we present a calculation of the infrared optical absorption coe cient for a Ga1,xAlxAs quantum well QW as a function of donor impurity concentration, compensation and temperature. We treat this problem using a Self-Consistent Method SC calculation taking into account donors as major impurities. The Variational Method was used to obtain the ground state wave-function of an electron bound to a donor impurity in a QW. The results show a shift of energy in the absorption coe cient. I IntroductionMany applications in opto-electronic devices are due to optical properties of quasi-two-dimensional systems. In particular the GaAlAs-GaAs quantum well is a popular system to study these properties. This kind of system is generated by several techniques by growing a layer of GaAs between two l a yers of GaAlAs.The infrared absorption coe cient for a doped quantum well has been calculated by several authors 1 , 10 . Recently Serra et al. 11 calculated thermal properties of a lightly doped and compensated QW showing the Shottky anomaly in the speci c heat. In this work we present the calculation of the optical absorption coe cient O AC for this kind of QW and we show its dependence on temperature and compensation. One important result is the presence of a threshold in the absorption energy. II The ModelWe consider a lightly doped compensated QW. The compensation is de ned by k = N A =N D , where N A and N D are the acceptor and donor densities respectively. Once there is a low concentration of dopants, donor impurities are far away from each other and we neglect the superposition of the electron wave-functions, so the unique kind of interaction present in our model is the electrostatic interaction between ionized impurities.With this assumption the transitions are of intra-site type, in other words transitions between energy levels belong to the same impurity. A t su ciently low temperature all acceptors and an equal number of donors are ionized. The energy of the system depends on the distribution of neutral D 0 and ionized D + donors and ionized acceptors A , :The electrostatic potential acts on the electron energy as a weak perturbation. As the temperature increases the tendency of electrons is to move from center to periphery of the QW, modifying the impurity conguration and increasing the energy of the system. 11 The calculation was made using the self consistent method to determine the thermal properties of the system. From the initial charge density 10 the electrostatic potential z is obtained via Poisson's equation. Once calculated the density of states, the chemical potential is obtained with the assumption of neutrality and the density of states is recalculated. The process continues until the convergence of the chemical potential is achieved.The Hamiltonian of an electron bound to a shallow donor, placed inside a QW is given by 5 H z k = , h 2 2m r 2 , e 2