Contents lists available at ScienceDirect Superlattices and Microstructures journal homepage: www.elsevier.com/locate/superlattices Enhancement of optical gain in quantum dot ensemble with electric field Shampa Guin, Nikhil Ranjan Das * Institute of Radio Physics and Electronics, University of Calcutta, 92, Acharya Prafulla Chandra Road, Kolkata, 700009, W.B, India ARTICLE INFO Keywords: Quantum dot Optical gain Electric field Inhomogeneous broadening FWHM ABSTRACT In this paper, optical gain of quantum dot ensemble is investigated in presence of external electric field for different carrier densities. First, the wave functions and the energy eigenvalues of car- riers are calculated by solving the Schrödinger equation for a quantum dot. Then these electric field dependent wave functions and energies are used to calculate the optical gain using the transition rates based on Fermi's golden rule. The analysis assumes the Gaussian distribution of the density of states to take into account the effect of inhomogeneous broadening due to the size- deviation of dots in ensemble and the Lorentz shape function to take into account the effect of homogeneous broadening. Results show that optical gain is enhanced with electric field de- pending on the carrier densities injected into the dots, indicating applications in optical sources with electrically tunable output power. 1. Introduction SEMICONDUCTOR nanostructures have been the focus of research in recent times due to their novel physical behavior arising out of the quantum size effect. Among these nanostructures, quantum dots (QDs) have drawn special attention because of complete carrier confinement and characteristic density of states and, thus, find applications in diverse areas [1]. As reported in literature, QD-based LEDs offer low turn-on voltage and high quantum efficiency [2], lasers have significantly reduced threshold current density [3,4], solar cells offer high power conversion efficiency [5], quantum dot infrared photodetectors (QDIP) promise less dark current at the same operating temperature than conventional IR detectors or its quantum well counterpart (QWIP) [6–9]. Quantum dots grown on a layer using Stranski-Krastanov method [10,11] are of different sizes. The island-size distribution of quantum dot arrays is investigated in detail by Petrov et al. [12–14]. As a consequence of this nonuniformity in size and position, the density of states (DOS) of the QD ensemble deviates from the ideal delta function of a single quantum dot. This causes the inhomogeneous broadening of the spectral linewidth of the QD ensemble. This broad spectral linewidth makes QD-based optical sources suitable for applications, such as, sub- cellular imaging [15–17]. Such applications, however, require the optical gain to be large for high resolution. The wave functions and energies of carriers in QD play important role to determine the optical gain. In presence of an external electric field, the subband energies and wave functions are modified due to the changed configuration of the potential well [18,19]. Thus, electric field may have an important role on the optical gain of the QD ensemble. To the knowledge of the authors, similar studies have not been reported in literature. A very preliminary study has been reported by authors in a conference [20]. This paper presents a detailed and systematic study on the optical gain of QD ensemble in presence of external electric field for different values of carrier densities injected into the dots. The remaining sections of this paper are organized as follows. A theoretical background is given in Section 2 to https://doi.org/10.1016/j.spmi.2018.11.002 Received 19 September 2018; Received in revised form 2 November 2018; Accepted 5 November 2018 * Corresponding author. E-mail addresses: shampaphysics@gmail.com (S. Guin), nrd@ieee.org (N.R. Das). Superlattices and Microstructures 125 (2019) 151–158 Available online 09 November 2018 0749-6036/ © 2018 Elsevier Ltd. All rights reserved. T