Abstract
The suggested model simulates the structural evolution of the SiO m ( m < 2 ) layer with a thickness of the order of 3—30 nm and the formation of Si nanoclusters in that layer during thermal annealing at temperatures of 900—1200 ° C. The model does not take into account the crystallinity or amorphous structure of the nanocluster. The 3D cellular automaton model implemented by means of SoftCAM software (CA) on 3D cubic grid with a cell scale of 0.54 nm is synchronous, does not use Margolus’s block neighborhood and is open to the incorporation of ab initio calculations for Si x O y clusters. The state of the CA cell is determined by three variables ( x , y , z ), taking on 0,1,2 , ..., 255 and corresponding to the number of atoms of silicon and oxygen and the arbitrary “free volume” in a cell and the fourth variable δ , taking on 0, 1, 2 and corresponding to cells belonging to nanoclusters, SiO x matrix or the interface between them. The local transition rules are determined from the following considerations: 1) for each cell, the scalar “free energy” is calculated similar to the thermodynamic potentials, as it depends only on the state of the cell; 2) the “free energy” consists of three parts: the internal U ( x , y ), the elastic G ( z ) and the surface E ( δ ); 3) the matter exchange between cells is determined by probabilities depending on the difference between the “free energy” by the Fermi— Dirac relation. The model traces the total number of nanoclusters, their average size and the average distance between them. The simulation results are consistent with published experimental data.
Highlights
The suggested model simulates the structural evolution of the SiOm (m < 2 ) layer with a thickness of the order of 3—30 nm and the formation of Si nanoclusters in that layer during thermal annealing at temperatures of 900—1200 °C
The state of the CA cell is determined by three variables (x, y, z), taking on 0,1,2, ..., 255 and corresponding to the number of atoms of silicon and oxygen and the arbitrary “free volume” in a cell and the fourth variable δ, taking on 0, 1, 2 and corresponding to cells belonging to nanoclusters, SiOx matrix or the interface between them
The local transition rules are determined from the following considerations: 1) for each cell, the scalar “free energy” is calculated similar to the thermodynamic potentials, as it depends only on the state of the cell; 2) the “free energy” consists of three parts: the internal U(x, y), the elastic G(z) and the surface E(δ); 3) the matter exchange between cells is determined by probabilities depending on the difference between the “free energy” by the Fermi— Dirac relation
Summary
КЛЕТОЧНО–АВТОМАТНАЯ МОДЕЛЬ РАЗДЕЛЕНИЯ ФАЗ ПРИ ОТЖИГЕ СЛОЕВ НЕСТЕХИОМЕТРИЧЕСКОГО ОКСИДА КРЕМНИЯ. Предложена модель, имитирующая эволюцию структуры слоя SiOm (m < 2) толщиной порядка 3—30 нм и формирование в нем нанокластеров кремния в процессе термического отжига при температурах 900—1200 °С. Одним из способов получения такой системы является термический отжиг слоя оксида кремния, обогащенного кремнием (SiOm, m < 2) при температуре T = 900÷1200 °С в течение 30—90 мин в инертной среде [4]. Примем физический размер ячейки за L = = 0,5 нм, что является компромиссом между наименьшим радиусом nc−Si, наблюдаемымэкспериментально (~1 нм), и длиной связи Si—O или Si—Si (~0,17 нм). Е. КА−аналог масштабу времени при дискретизации дифференциальных уравнений, примем за τ = 10−3 с, что является компромиссом между оценкой из соотношения Эйнштейна L2/τ ∼ 6D и приемлемым машинным временем.
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