Investigation of the Electron Energy Spectrum in a Three Dimensional Regimented Tetragonal Quantum Dot Superlattice
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Investigation of the Electron Energy Spectrum in a Three Dimensional Regimented Tetragonal Quantum Dot Superlattice Olga L. Lazarenkova and Alexander A. Balandin Department of Electrical Engineering University of California at Riverside Riverside, CA 92521 U.S.A.
ABSTRACT We analyze the electron energy spectrum in three-dimensional regimented arrays of semiconductor quantum dots. The coupling among quantum dots results in formation of threedimensional electron mini-bands. Changing the size of quantum dots, inter-dot distance, barrier height and regimentation, one can control the electronic band structure of this quantum dot superlattice, which can also be referred to as quantum dot crystal due to its structure and energy spectrum that resemble those of a real crystal. Results of computer simulations carried out for a tetragonal InAs/GaAs quantum dot superlattice show that the electron density of states, effective mass tensor and other properties are different from those of bulk and conventional quantum well superlattices. INTRODUCTION Quantum dots (QDs) represent the ultimate case of spatial confinement for electrons and holes. In comparison to conventional quantum well superlattices [1] or multiple quantum wells [2], the structures that consist of multiple arrays of quantum dots may have many advantages in applications due to their modified density of electronic states and optical selection rules. For example, due to relaxed intraband optical selection rules in quantum dot superlattices (QDS), they are capable of absorbing normally incident radiation while it is not possible in quantum well superlattices. It has been reported that quantum dot lasers based on InAs/GaAs QDs have superior properties with respect to conventional quantum well lasers. High differential gain, ultralow threshold current density and high temperature stability of threshold current density occurs simultaneously. Additionally, ordered arrays of scatters formed in an optical waveguide region may result in the distribution feedback and in the stabilization of single-mode lasing [3]. Many more applications are envisioned for regimented QD’s structures [4]. Although many types of regimented quantum dot superlattices or quantum dot crystal (QDC) had already been fabricated using different self-assembly techniques [4-5], very little attention has been paid to theoretical description of electronic properties of such structures [6]. In this paper we analyze an electron energy spectrum in a three-dimensional regimented array of semiconductor quantum dots. The regimentation, e.g. spatial site correlation, along all three directions results in the formation of three-dimensional mini-bands and significant modification of the electron energy spectrum in such structures. We particularly focus our attention on the tetragonal InAs/GaAs QDS.
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THEORY In order to analyze the electronic structure of the QDS we use our original approach developed for structures of orthorhombic symmetry [6]. The model is based on the envelope function approximation and u
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