Application of the Alexander–Haasen Model for Thermally Stimulated Dislocation Generation in FZ Silicon Crystals
Source abstract
Abstract
Numerical simulations of the transient temperature field and dislocation density distribution for a recently published silicon crystal heating experiment were carried out. Low- and high-frequency modelling approaches for heat induction were introduced and shown to yield similar results. The calculated temperature field was in very good agreement with the experiment. To better explain the experimentally observed dislocation distribution, the Alexander–Haasen model was extended with a critical stress threshold below which no dislocation multiplication occurs. The results are compared with the experiment, and some remaining shortcomings in the model are discussed.
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Research context
OpenAlex topics: Silicon and Solar Cell Technologies · Advanced ceramic materials synthesis · Microstructure and mechanical properties
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Institute of Numerical Modelling, University of Latvia, Jelgavas Street 3, LV-1004 Riga, Latvia
Leibniz-Institut für Kristallzüchtung, Max-Born-Str. 2, 12489 Berlin, Germany
Funding
European Regional Development Fund
References (27)
Show source-provided references
1. Growth of silicon crystals free from dislocations10.1063/1.1702390 ↗
2. Defect formation in Si-crystals grown on large diameter bulk seeds by a modified FZ-method10.1016/j.jcrysgro.2018.08.005 ↗
3. Float-zone growth of silicon crystals using large-area seeding10.1016/j.jcrysgro.2019.02.061 ↗
4. NeoGrowth silicon: A new high purity, low-oxygen crystal growth technique for photovoltaic substrates10.1002/pip.2984 ↗
5. A comparative study of thermal stress induced dislocation generation in pulled GaAs, InP, and Si crystals10.1063/1.329154 ↗
6. Thermal stress analysis of silicon bulk single crystal during Czochralski growth10.1016/0022-0248(92)90325-D ↗
7. Stress-induced dislocation generation in large FZ- and CZ-silicon single crystals—Numerical model and qualitative considerations10.1016/S0022-0248(01)01322-7 ↗
8. Dislocations and plastic flow in the diamond structure10.1016/S0081-1947(08)60031-4 ↗
9. Dislocation dynamics during the growth of silicon ribbon10.1063/1.337221 ↗
10. A new model for the calculation of dislocation formation in semiconductor melt growth by taking into account the dynamics of plastic deformation10.1016/0022-0248(89)90255-8 ↗
11. The constitutive equation for silicon and its use in crystal growth modeling10.1115/1.2903305 ↗
12. Development of finite element computer program for dislocation density analysis of bulk semiconductor single crystals during Czochralski growth10.1016/S0022-0248(97)00388-6 ↗
13. Numerical simulation of stresses and dislocations in quasi-mono silicon10.1016/j.jcrysgro.2016.06.007 ↗
14. Study on the usage of a commercial software (Comsol-Multiphysics®) for dislocation multiplication model10.1016/j.jcrysgro.2016.05.027 ↗
15. Dislocation dynamics in the plastic deformation of silicon crystals I. Experiments10.1002/pssa.2210500239 ↗
16. Dislocation dynamics in the plastic deformation of silicon crystals. II. Theoretical analysis of experimental results10.1002/pssa.2210510124 ↗
17. Applicability of the three-dimensional Alexander-Haasen model for the analysis of dislocation distributions in single-crystal silicon10.1016/j.jcrysgro.2014.11.011 ↗
18. Thermally stimulated dislocation generation in silicon crystals grown by the Float-Zone method10.1016/j.jcrysgro.2020.125842 ↗
19. The deal.II library, version 8.510.1515/jnma-2017-0058 ↗
20. (2021, November 16). MACPLAS: MAcroscopic Crystal PLAsticity Simulator. Available online: https://github.com/aSabanskis/MACPLAS.
21. Ratnieks, G. (2007). Modelling of the Floating Zone Growth of Silicon Single Crystals with Diameter up to 8 Inch. [Ph.D. Thesis, University of Latvia].
22. The calculation of 3D high-frequency electromagnetic fields during induction heating using the BEM10.1109/20.250703 ↗
23. Thermal conductivity, electrical resistivity, and Seebeck coefficient of silicon from 100 to 1300°K10.1103/PhysRev.167.765 ↗
24. Sabanskis, A., Plāte, M., Sattler, A., Miller, A., and Virbulis, J. (2021). Evaluation of the performance of published point defect parameter sets in cone and body phase of a 300 mm Czochralski silicon crystal. Crystals, 11.10.3390/cryst11050460 ↗
25. Simulation of the influence of gas flow on melt convection and phase boundaries in FZ silicon single crystal growth10.1016/j.jcrysgro.2014.07.041 ↗
26. Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities10.1002/nme.2579 ↗
27. Precise determination of lattice parameter and thermal expansion coefficient of silicon between 300 and 1500 K10.1063/1.333965 ↗