## Quantitative Modeling and Simulation of Quantum Dots

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#### Abstract

Quantum dots grown by self-assembly process are typically constructed by 50,000 to 5,000,000 structural atoms which confine a small, countable number of extra electrons or holes in a space that is comparable in size to the electron wavelength. Under such conditions quantum dots can be interpreted as artificial atoms with the potential to be custom tailored to new functionality. In the past decade or so, these nanostructures have attracted significant experimental and theoretical attention in the field of nanoscience. The new and tunable optical and electrical properties of these artificial atoms have been proposed in a variety of different fields, for example in communication and computing systems, medical and quantum computing applications. Predictive and quantitative modeling and simulation of these structures can help to narrow down the vast design space to a range that is experimentally affordable and move this part of nano-Science to nano-Technology. Modeling of such quantum dots pose a formidable challenge to theoretical physicists because: (1) Strain originating from the lattice mismatch of the materials penetrates deep inside the buffer surrounding the quantum dots and require large scale (multi-million atom) simulations to correctly capture its effect on the electronic structure, (2) The interface roughness, the alloy randomness, and the atomistic granularity require the calculation of electronic structure at the atomistic scale. Most of the current or past theoretical calculations are based on continuum approach such as effective mass approximation or k.p modeling capturing either no or one of the above mentioned effects, thus missing some of the essential physics.

The Objectives of this work are: (1) to model and simulate the experimental quantum dot topologies at the atomistic scale; (2) to theoretically explore the essential physics i.e. long range strain, linear and quadratic piezoelectricity, interband optical transition strengths, quantum confined stark shift, coherent coupling of electronic states in a quantum dot molecule etc.; (3) to assess the potential use of the quantum dots in the

real device implementation and to provide the physical insight to the experimentalists. Full three dimensional strain and electronic structure simulations of the quantum dot structures containing multi-million atoms are done using NEMO 3-D. Both single and vertically stacked quantum dot structures are analyzed in detail. The results show that the strain and the piezoelectricity significantly impact the electronic structure of these devices.

This work shows that the InAs quantum dots when placed in the InGaAs quantum well red shifts the emission wavelength. Such InAs/GaAs-based optical devices can be used for optical-fiber based communication systems at longer wavelengths (1.3um – 1.5um). Our atomistic simulations of InAs/InGaAs/GaAs quantum dots quantitatively match with the experiment and give the critical insight of the physics involved in these structures. A single quantum dot molecule is studied for coherent quantum coupling of electronic states under the influence of static electric field applied in the growth direction. Such nanostructures can be used in the implementation of quantum information technologies. A close quantitative match with the experimental optical measurements allowed us to get a physical insight into the complex physics of quantum tunnel couplings of electronic states as the device operation switches between atomic and molecular regimes. Another important aspect is to design the quantum dots for a desired isotropic polarization of the optical emissions. Both single and coupled quantum dots are studied for TE/TM ratio engineering. The atomistic study provides a detailed physical analysis of these computationally expensive large nanostructures and serves as a guide for the experimentalists for the design of the polarization independent devices for the optical communication systems.

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[2] Muhammad Usman*, Yui H. Matthias Tan*, Hoon Ryu, Shaikh S. Ahmed, Hubert Krenner, Timothy B. Boykin, and Gerhard Klimeck, "Quantitative excited state spectroscopy of a single InGaAs quantum dot molecule through multi-million atom electronic structure calculations", under review with IOP Nanotechnology 2011; (Full paper at: http://arxiv.org/abs/1008.3127v1) (*Equal contribution authors)

[3] Muhammad Usman, Hoon Ryu, Insoo Woo, David S. Ebert, and Gerhard Klimeck, "Moving towards nano-TCAD through multi-million atom quantum dot simulations matching experimental data", IEEE Trans. on Nanotechnology, Vol. 8, No. 3, May 2009, pp. 330-344 (Full paper at http://arxiv.org/abs/0812.3814)

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#### Tags

- strain
- Stacked Quantum dots
- Degree of Polarization
- TM-mode
- TE-mode
- Optical Response
- electronic structure
- quantum dots
- nanoelectronics
- Ph.D. thesis
- optics
- Simulation
- InAs
- GaAs
- devices