| Silicon crystal is the basic material of integrated circuit and light converse products, it plays a important role in the21th century information industry and solar industry. In2002, the silicon yield of China account for less than0.4%of the world, after ten years’development, single crystal industry of China has turned to export-oriented. However, it is still unable to keep up with international development trend of high purity, high integrity, high uniformity and large diameter. At present, CZ silicon defects becomes the main restrictive factor of its development and adhibition, but some defects in silicon crystal also help increase the yield and electrical parameter, people’s cognition has turned from "eliminate" to "control, utilize", which impel people to focus more on the defect engineering. In view of the increase of silicon crystal diameter and the rise of defect engineering, indicating and managing the evolution law and existing state of silicon crystal defects such as voids and oxygen precipitation to guarantee the performance property of silicon crystal have become a practical problem that cannot be ignored.Recently, using computer numerical simulation as a supplementary mean in defect engineering of CZ silicon has become a new trend, CZ silicon defect engineering has turned to experimental observation-theoretical analysis parallel with computer numerical simulation. However, computer numerical simulation is restricted to macro simulation which uses finite element method at present, it cannot be used in mesoscopic and microcosmic simulation of defect evolution. Exploring a macroscopic-mesoscopic-microcosmic multi-scale coupling simulation method, coupling model, application program and key simulation technology to realize CZ silicon defect multi-scale coupling simulation is imperative.Phase-field method is based on Ginzburg-Landau free energy theory, using differential equation to show the comprehensive action of ordering potential and thermodynamics drive. After more than20years’development, it has become a very important method in mesoscopic-microcosmic simulation. At present, domestic scholars have been using phase-field method to simulate dendrite growth, dynamic recrystallization and single crystal growth, but using phase-field method to simulate the evolution of defects in single silicon crystal has not been reported. Therefore, this paper adopt phase-field method to simulate the evolution of CZ silicon defects, this research has great theoretical significance and actual value.Firstly, based on crystal growth physics and phase-field simulation theory, fully considered the diffusion and compound behavior of point defects and the effect growth speed did to void defects’ evolution, built phase-field model of single silicon void evolution, took time as the link, through scale transformation of spatial and mesh subdivision etc., temperature field and point defect concentration field which were simulated by finite element software (CGSim) were introduced into phase-field model so finite element method and phase-field method were coupled, in this way, the organic combination of the macroscopic analysis of silicon crystal and mesoscopic morphology observation could be realized. Successfully simulated the0400mm CZ silicon axial void defects evolution of different areas, revealed the effects of different intrinsic point defects concentration and different crystal growth speed do to the evolution of void defects:when intrinsic point defects concentration is high, the number, average size and area fraction of void defects were generally increased, incubation stage was shortened, nucleation stage and growth stage were both increased; the segregation, combination and growth of void defects were obvious; two different growth speed had little effect on the evolution of voids, void still followed incubation, nucleation, growth and static at different temperature intervals, the concentration increased and average size decreased with low growth speed. The reliability of phase-field model and the simulation result were verified by experimental observation and finite element simulation results.Secondly, based on the phase-field model of void dynamics during CZ silicon crystal growth, created a multiple phase-field model of micro defects dynamics during CZ silicon crystal growth and analysis process, simulated the effects different state of initial point defects did to the evolution of axial micro defects and discussed the related mechanism, the results showed that:①under the condition of pure concentration of initial interstitial oxygen, as temperature decreased, concentration of oxygen precipitate increased, average diameter increased at first then decreased slowly; as concentration of initial interstitial oxygen increased, the average diameter of voids increased (more significantly at temperature), the density of voids decreased (low temperature), but average diameter enlarged.②under low temperature, the maximum and the minimum initial void defects concentration correspond to the maximum and the minimum multi-type void defects concentration, under the condition of maximum initial vacancy concentration, the average diameter of voids was relatively large; as initial vacancy concentration increased, oxygen precipitate concentration changed little, the average diameter of oxygen precipitate increased and got bigger when temperature fell.③under low temperature, concentration and average diameter of vacancies decreased as interstitial silicon concentration increased, interstitial silicon concentration did little effect on oxygen precipitate evolution. This phase-field model and simulation results were verified by the relative macroscopic simulation results.Subsequently, In consideration of the axial and radial diffusion and convection of point defects, further perfected the vacancy-oxygen precipitate dynamics multiple phase-field model and its application program, through the finite element macroscopic simulation and multiple phase-field mesoscopic simulation, realized double level simulation of global micro defects dynamics in CZ silicon, revealed the influence low of micro defects state affected by growth speed and initial interstitial oxygen concentration. The results showed that:①The radial distribution laws of vacancy and oxygen precipitate in different axial position of silicon were the same, namely except for the decreasing of vacancy density on the edge of silicon or the zero-vacancy area, with the increasing of radial radius, vacancy density increased and average diameter decreased; oxygen precipitate density changed little along radial direction in most areas, only increased at first then dropped rapidly near the lateral surface, oxygen precipitate average diameter decreased along radial direction and its general change range was bigger than voids.②With axial position raising, vacancy density decreased, average diameter increased and zero-vacancy area decreased; the radial change of oxygen precipitate decreased and average diameter’s change increased.③Growth speed did no effect on micro defects’ radial distribution. As growth speed increased, vacancy density curve and average diameter curve moved toward lateral surface, vacancy density decreased, average diameter increased and zero-vacancy area decreased; the density and radial change trend of oxygen precipitate were both decreased.④The phase-field simulation results not only provided the morphology, distribution etc. mesoscopic information of micro defects, but also indicated the vacancy radial evolution law, which was the same as finite element simulation result, to combine the two simulations could realize multi-scale global simulation of micro defect dynamic during the growth process.Finally, based on the void-oxygen precipitate multiple phase-field model, this paper introduced complementary function to calculate macroscopic point defects diffusion in CZ silicon heat treatment, simulated the silicon microscopic defects’ evolution during furnace cooling, traditional High-Low-High temperature isothermal annealing, RTA annealing and neutron irradiation annealing and results were compared with theory and experiments. Defects evolution law in different annealing process:①Furnace cooling did no effect on CZ silicon micro defect distribution law, only made vacancy average diameter increased slightly, oxygen precipitate size decreased and oxygen precipitate density increased.②Under the condition of reasonable interstitial oxygen concentration distribution acquired from the first high temperature annealing, a intrinsic gettering structure of denuded zone on the surface and oxygen precipitate accumulation area in the core part could be made through subsequent high and low temperature annealing, the third step high temperature annealing could promote the accumulation of oxygen precipitate.③Silicon under high initial temperature annealing had much smaller micro defect density and size than which was under low initial temperature annealing and the thickness of denuded zone was larger at the same time; silicon after RTP annealing plus Ramping annealing had smaller micro defect size and density than that after traditional RTP annealing plus low-high temperature annealing, annealing condition had greater influence on vacancy dynamics than oxygen precipitate.④Under the condition of reasonable neutron irradiation vacancy concentration, the vacancy concentration distribution of high on the surface and low in core part could be realized by phase-field simulation. |
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