The InGaAs/GaAs Quantum Dots under Effective and Ab Initio Treatments: Comparison and Results I. Filikhin, V. M. Suslov, H. Melikyan, and B. Vlahovic North Carolina Central University, 1801 Fayetteville St. Durham, NC 27707, ifilikhin@nccu.edu ABSTRACT The 3D model for InGaAs/GaAs quantum dots (QD), based on a single sub-band approach taking into account the effect of non-parabolicity of the conduction band is presented. We apply an effective approach in which the combined effect of strain, piezoelectricity and interband interactions are simulated by an effective potential. The strength of the effective potential is determined by analysis of capacitance-gate-voltage (CV) data and photoluminescence spectra for QDs and quantum rings (QR). The model is compared with one based on the 8- band kp-theory, which takes into account interband interactions, strain and piezoelectric effects in an ab initio manner. The atomistic pseudopotential approach is also taken for comparison. It is found that disagreements between predictions obtained in the framework of our model and of these models are related to strength of the electron confinement. It is shown that our approach accurately reproduces photoluminescence measurements for excitons when there is a significant Ga fraction in the QDs s V Keywords: quantum dots and rings, single carrier levels, optical properties, excitons, Coulomb shifts, 1 INTRODUCTION The theoretical modeling for semiconductor InGaAs/GaAs quantum dots (QDs) must take into account such effects as strain, piezoelectric and interband interactions [1]. In addition, the effect of non-parabolicity of the conduction band also has to be taken into account for QDs having base size of few nanometers [2]. As an example of a realistic model one can consider the 3D model [1,3] based on the 8-band kp-theory, which takes into account the interband interactions and in which strain and piezoelectric effects are treated in an ab initio manner. In another realistic model [4] the atomistic pseudopotential approach was considered. Until now there is no direct comparison of these two models. Here we present an effective approach in which the combined effect of strains, piezoelectricity and interband interactions are simulated by an effective potential. Additionally, in the model, an analog of the Kane formula is implemented to take into account the effect of non-parabolicity of the conduction band. Based on our model, we performed an analysis of capacitance- gate-voltage (CV) data [5] and photoluminescence spectra for QDs, QRs, and double concentric QRs. We show that our approach reproduces both the few electron energy level spectra and the increase of the electron effective mass relative its bulk value due to non-parabolicity. We compare our model with the 8-band kp-theory [1,3], which takes into account interband interactions, strain and piezoelectric effects in an ab initio manner. It is shown that our effective approach allows us to reproduce results calculated with the realistic kp-model for pure InGaAs/GaAs QDs. It accurately reproduces the CV experimental data when there are significant Ga fractions in the QDs. The calculations for the QDs with 22% -25% Ga fractions match both the CV data and the photoluminescence measurements [5-6] for Coulomb shifts of exciton complexes (X ,X + ,XX). We compared our results with those obtained within the framework of the atomistic pseudopotential approach [4, 7]. It was found that the considerable disagreements between predictions obtained in the framework of our model and predictions of the pseudopotential model are related to strength of the electron confinement. Our calculations allow us to formulate a conclusion about the strength of confinements of the realistic models. These confinements are quite different; the atomistic pseudopotential approach produces a stronger confinement for electrons and heavy holes. - 2 EFFECTIVE APROACH A 3D heterostructure is modeled utilizing a kp- perturbation single subband approach with an energy dependent quasi-particle effective mass [2,8,9]. The energies and wave functions of a single carrier in a semiconductor structure are solutions of the nonlinear Schrödinger equation: ψ ψ E r V r V E r m s c = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + + ∇ ∇ - ) ( ) ( ) ) , ( 2 ( * 2 h (1) where is the band gap potential, proportional to the energy misalignment of the conduction (valence) band edges of the InAs QD (index 1) and the GaAs substrate (index 2). Inside the substrate and inside the quantum dot . The electron effective mass ) ( r V c c V r V = ) ( 0 ) ( = r V NSTI-Nanotech 2009, www.nsti.org, ISBN 978-1-4398-1782-7 Vol. 1, 2009 578