Thermodynamic Modeling of Island Size Distributions for InGaAs/GaAs Self Assembled Quantum Dots: A Quantitative Effort t
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Thermodynamic Modeling of Island Size Distributions for InGaAs/GaAs Self Assembled Quantum Dots: A Quantitative Effort to Understand Ensemble Size Nonuniformity Jeff Cederberg1, Alexana Roshko2, Brit Hyland2, and Michael Coltrin1 1 Sandia National Laboratory, 1515 Eubank Blvd SE, Albuquerque, NM, 87123 2 Optoelectronics Divison, NIST, 326 Broadway, Boulder, CO, 80305
ABSTRACT Experimental island count histograms as a function of SAQD volume have been evaluated using an established model. The experimental data was obtained for 51 mm wafers grown by MOCVD and analyzed over the center 26 x 26 mm square of the wafer with AFM. More than one distribution is required for all conditions investigated to obtain adequate representations of the experimental data. Consistent parameters are obtained for samples grown with a variable InAs thickness. Higher growth temperatures results in material being converted into relaxed islands. Extended annealing without AsH3 eliminates small islands, suggesting that they are not a stable distribution. INTRODUCTION InGaAs self-assembled quantum dots (SAQD) have been studied extensively over the past 15 years addressing fundamental questions related to their three-dimensional quantum confinement and a variety of applications. Initial research of InGaAs-based SAQD was motivated by the possibility of achieving active regions that emit at 1.3 or 1.55 µm to replace and improve upon InP-based quantum well devices.[1, 2, 3] SAQD discrete characteristics naturally lead into applications utilizing them for single photon detectors.[4] SAQD have been utilized to demonstrate middle infrared detectors [5,6] and emitters [7]. The optimization of InGaAs SAQD on GaAs (100) has been largely an empirical effort. Basic phenomenological models have provided insight into SAQD formation and development as of function of growth parameters.[8, 9, 10] This can be contrasted to the even more widely studied Ge(Si) on Si (100) system, where extensive fundamental modeling has been undertaken.[11] There is a need for quantitative modeling addressing experimentally determined SAQD size distributions in the InAs/GaAs (100) material system. A general thermodynamic model for SAQD size distributions was first posed by Shchukin, et al.[12] With this model they evaluated the stability of SAQD with respect to ripening. They determined the importance of the surface energy and the dipole interaction energy to distribution stabilization and determined regions where distributions would be stable and unstable. Daruka and Barbási extended this model providing a phase plot of the different regimes of island formation as a function of strain and deposit thickness.[13] More recently Rudd, et al. has combined the previous developments into a tractable model that allows fitting experimental histograms of island count versus island size.[14] They applied their model to fitting Ge on Si (100) where the pyramid to dome transition produces bimodal distributions that vary with the growth temperature and Ge thickness deposited. This
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