Numerical simulation of quantum dots and self ...

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Aug 26, 2015 - 1 Institute of Mechanics, Ural Branch of the Russian Academy of Science, Izhevsk, Russia. 2 Kalashnikov Izhevsk State Technical University, ...
Third Asian School-Conference on Physics and Technology of Nanostructured Materials Vladivostok, Russia, 19 ± 26 August, 2015

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Numerical simulation of quantum dots and selforganization of nanostructures of special purpose A.V. Vakhruchev*,1,2, A.Y. Fedotov1, A.V. Severyukhin1 1 Institute

of Mechanics, Ural Branch of the Russian Academy of Science, Izhevsk, Russia Izhevsk State Technical University, Izhevsk, Russia

2 Kalashnikov

*e-mail: [email protected] Abstract. A mathematical model obtaining special nanostructured layers in epitaxial structures for thin photoelectric converters (PEC) is presented. The results of computer simulation of the production of nanostructured objects in epitaxial structures for the refined PEC are given. The silicon atoms, gallium, indium and gold are considered as the initial forming elements. The results of test calculations are shown, which consider autocorrelation, radial functions and temperature graph. Different mechanisms of formation nanostructures in epitaxial structures for thin photoelectric converters are demonstrated.

1. Introduction In recent literature there are more information on the use of nanostructured elements to improve the energy and mass characteristics of thin photoelectric converters (PEC). Low efficiency silicon solar cell due to the fact that he works in a narrow range of the solar spectrum, in the orange-red light. The remainder of the spectrum is not involved in the production of electricity, but only causes undesired heating of the device. In the latest solar cell efficiency improvement is achieved by expanding the range of "efficient" solar radiation by complicating the structure and 4-layer cake. But in this case only action involved in green, yellow, orange, red, and infrared rays of sunlight. The rest of the solar spectrum, from ultraviolet to green, including purple, blue and blue, completely excluded from the "useful" photoelectric conversion. The aim is to describe the methodology of modeling processes of special nanostructured layers in epitaxial structures for sophisticated photovoltaic cells. It is interesting to conduct computational experiments on creation and use of nanostructured and nanoscale elements that can be used in solar cells and other photovoltaic devices. 2. Experiment The problem of modeling processes of special nanostructured layers for solar cells in the structures solved by molecular dynamics (MD). MD method is widely used in modeling the behavior of nanosystems due to the ease of implementation, satisfactory accuracy and low cost computing resources. The basis of this method is the solution of the differential equations of motion for each particle Newton. Depending on the type of building and external forces in the system, the problem of modeling processes of special nanostructured layers in the structures for solar cells will have different accuracies and various thermodynamic parameters. The correct description of the properties of solids is necessary to use many-body potentials. It is known that none of the current capabilities is not capable of reproducing the full set of characteristics of the solids. In the simulation of metal and semiconductor systems most widely modified embedded atom method [1]. When used in the simulation with the orientation of the silicon substrate (100) and (111) having a minimum size of length - 11 nm, 11 nm, width, height - 3 nm. The substrate is not rigidly fixed, this indicates that the substrate atoms are free to move in any direction. Formation of

heterostructures can occur by several mechanisms: mechanism Volmer-Weber (islet growth model), the Frank-van der Merwe, (layer growth) and mixed StranskiKrastanov. Simulation algorithm in this case is as follows. The silicon substrate is heated to a fixed temperature T 0. This process is described by the equation of motion in the form of Newton, with the initial conditions, where the rate is set according to the Maxwell distribution. On the resulting system of deposited atoms of the modeled system. The equations for this phase will be similar to the description of the first stage, but other than that given by the velocity vector for each of the deposited atoms and their direction is opposite to the direction of the axis z, ie velocities are directed to the substrate. In the next step of modeling on the resulting system epitaxially deposited atoms of the second of this type. The equations for this phase will be similar to the description of the first stage. The size and number of epitaxial islands formed depend on the size of the substrate, and the layer thickness of the deposited materials. More detail simulation methodology and parameters used force fields are shown in published studies [2-4]. 3. Results and discussions For the simulation of epitaxial processes used silicon substrate with (100) orientation. Deposited on a substrate, gold atoms in an amount of 1000 units. Then, the resulting system deposited silicon atoms in an amount of 3000 pieces. The temperature of the simulated system was kept constant and equal to 800 K. The size of the formed nanostructures varies from 0.7 to 2.7 nm. The shape of nanostructures prepared by a variety. Diffusion of gold atoms into the substrate is not observed. Interesting dynamics of the physical process of formation of photovoltaic cells made of gold and silicon. First, the gold atoms are deposited on a silicon substrate, and then begin to organize themselves, going to drop. For modeling processes of PEC in the structure Si-Au-Ga used silicon substrates with (100) orientation. The dimensions of the substrate were defined as follows: width - 16 nm, length 16 nm, the height - 2 nm. Deposited on the substrate atoms of gold in 4500. Then, in the amount of the resulting system deposited gallium atoms in an amount of 33,000 pieces. The temperature of the simulated system was kept constant by a thermostat and was equal to 300 K. As can be seen from Fig. 1, on a substrate formed of gold drops of different

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VIII.21.03p diameters and shapes. There is an overlap silting nanostructures special purpose gallium atoms. Gallium atoms do not form pronounced quantum dots on the distribution of the silicon surface is uneven. Diffusion of the gold and gallium atoms in the silicon substrate is observed. The surface structure of gallium atoms and gold deposition on the substrate after forming the relief, there are fluctuations in the heights. Nanocomposite Au-Ga

Nanocomposite Au-Ga

Fig. 1. Result of simulating is nanocomposites Au-Ga.

For modeling processes of PEC in structures Si-In-Ga was used silicon substrates with (100) orientation. Substrate size parameters were the following quantities: width ± 16 nm, length ± 16 nm, the height ± 2 nm. Deposited on the substrate indium atoms in an amount of 4500 pieces. Then, the resulting system deposited gallium atoms in an amount of 33,000 pieces. The temperature of the simulated system was kept constant by a thermostat and was equal to 300 K. The process of formation and deposition of nanostructures of indium atoms differ from similar processes of gold atoms. If gold atoms initially deposited on the substrate, and then gathered in quantum dots, the clustering of indium atoms began and continued mainly in the gaseous environment. Deposited on a substrate already formed nanostructures India. India is trying to form conglomerates spherical. In the next step of modeling deposited gallium atoms. The resulting gas pairs of gallium and indium nanoparticles attracted by the silicon substrate. The simulation of two atoms of deposition of indium and gallium get the picture shown in Fig. 2. indium atoms form a quantum expressed a special form of education in the form of a hemisphere. Gallium is distributed over the entire substrate, sometimes covering the indium nanoparticles. The diffusion of atoms of indium and gallium in the silicon substrate, similarly to the case of gold quantum dots are not observed. The average size of indium nanostructures is 3±3.5 nm and exceeds the size of the quantum dots of gold of the simulation in such a system. 4. Conclusions The paper presents the theoretical foundations of computer simulation to obtain special nanostructured layers in epitaxial structures for sophisticated photovoltaic cells, which include the mathematical model and the formulation of the problem. epitaxial affect: the interaction of atoms and

nano-objects with each other and with the surface of the deposition; a process of self-assembly of nanostructures and self-organization in a gaseous medium and, in contact with solid elements; coated nanostructures special purpose nanolayer films for the emergence of photoelectron effects. As a source of generating elements considered silicon atoms, gallium, indium and gold. Demonstrate different mechanisms of special nanostructures in epitaxial structures for sophisticated photovoltaic cells. Epitaxial and self-organization processes have shown that disruption of the internal order of nanostructures and the substrate is observed. During the deposition of individual atoms was observed partial Silting nanostructures on the substrate. The simulation showed that the characteristic form of a hemisphere of gold on the surface of silicon. Indium atoms begin to assemble into nanoparticles is still in a gaseous medium into contact with the silicon substrate. Gold nanoparticles are hemispherical and extended education. For indium nanoparticles are characterized as spherical and hemispherical. The resulting system was covered with gallium atoms. For the case of indium is typical of almost uniform distribution of gallium atoms on the substrate. Occurs indium gallium tilting nanoparticles (PEC). In the case of gold, gallium characteristic uneven distribution of the substrate is formed pronounced quantum dots. Diffusion of gold atoms of indium, gallium into the upper substrate layers is not observed.

Nanocomposite In-Ga

Fig. 2. Result of simulating is nanocomposites Au-Ga.

Acknowledgements The work was supported by the Russian Foundation for Basic Research (grant 13-08-01072). and by state DVVLJQPHQWRI.DODVKQLNRY,]K678ʋ-1239. References [1] M.I. Baskes. Phys. Rev. B 46(1992)2727. [2] A.V. Vakhrouchev, A.V. Severyukhin, O.Y. Severyukhina. International Journal of Nanomechanics Science and Technology 3(2012)211. [3] A.V. Vakhrouchev, O.Y. Severyukhina, A.V. Severyukhin, A.A. Vakhrushev, N.G. Galkin. International Journal of Nanomechanics Science and Technology 3(2012)51. [4] A.V. Vakhrushev, A.Y. Fedotov, A.A. Vakhrushev, V.B. Golubchikov, A.V. Givotkov. International Journal of Nanomechanics Science and Technology 2(2011)105.

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