A Theoretical Study of Structural Disorder and Photoluminescence Linewidth in InGaAs/GaAs Self Assembled Quantum Dots
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A Theoretical Study of Structural Disorder and Photoluminescence Linewidth in InGaAs/GaAs Self Assembled Quantum Dots Yih-Yin Lin, Hongtao Jiang,1 and Jasprit Singh Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109-2122 1 Broadcom Corporation, Irvine, CA 92618 ABSTRACT The past few years have seen considerable efforts in growth and device application of selfassembled quantum dots. However, the photoluminescence (PL) linewidth, which represents structural fluctuations in dot sizes, is still in the range of 30-50 meV. This large linewidth has deleterious effects on devices such as lasers based on self-assembled dots. In this paper we will examine the configuration-energy diagram of self-assembled dots. Our formalism is based on: (1) an atomistic Monte Carlo method which allows us to find the minimum energy configuration and strain tensors as well as intermediate configurations of dots; (2) an 8-band k·p method to calculate the electronic spectra. We present results on the strain energy per unit cell for various distributions of InAs/GaAs quantum dots and relate them to published experimental results. In particular we examine uncovered InAs/GaAs dots and show that in the uncovered state a welldefined minimum exists in the configuration energy plot. The minimum corresponds to the size that agrees well with experiments. INTRODUCTION The use of strained epitaxy to create quasi-0 dimensional quantum dots has been widely studied over the last decade. Self-assembled quantum dots have now been fabricated using InGaAs/GaAs, SiGe/Ge, and many other strained systems [1-2]. In addition to the study of electronic and optical properties of these dots, devices lower as quantum dot interband lasers [3] and intersubband detectors [4] have been demonstrated. However, in spite of much progress in the area of self assembly, there is still a nagging issue - dot size nonuniformity. The self assembled dots vary in sizes and shapes - a variation that reflects in the electronic spectrum, photoluminescence linewidth, and gain spectrum etc. For many potential device applications, dot size nonuniformity creates deleterious effects. To understand the reason for nonuniformity and its extent, it is important to study the configuration energy of self-assembled dots. There have been several studies on the strain tensor and energy in self-assembled dots. A useful model has emerged the valence force field (VFF) method [5,6], which allows us to calculate the strain tensor at an atomic level. It is found that the strain tensor in dots plays a key role in determining the electronic spectrum [7]. While the strain tensor of quantum dots in the covered state (i.e. with the dot buried in the large bandgap material matrix) has been examined, to our knowledge no work has been done on why certain mean dot sizes are chosen and why there is a distribution in the dot size. In this paper we use an extension of the VFF model to examine the strain tensor and energy of “covered” and “uncovered” InAs/GaAs dots. Then w
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