مقاله پژوهشی: شبیه‌سازی تنش‌های گرماکشسانی در بلور ژرمانیوم رشدیافته به روش چُکرالسکی در طول‌های متفاوتِ بلور

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی دکترا، گروه فیزیک، دانشکدۀ علوم پایه، دانشگاه بوعلی سینا، همدان، ایران

2 دانشیار، گروه فیزیک، دانشکدۀ علوم پایه، دانشگاه بوعلی سینا، همدان، ایران

چکیده

در فرایند رشد بلور به روش چُکرالسکی قسمت پایین و هستۀ بلور گرم­تر از قست­های دیگر بلور و محیط آن است که این گرادیان دمایی سبب انبساط در قسمت‌های مختلف بلور می‌شود. نتیجۀ این گرادیان گرمایی، کرنش است که در نهایت باعث ایجاد تنش گرماکشسانی در بلور می‌شود. افزایش این تنش به گذار ماده از حد کشسان و وارد شدن به منطقۀ پلاستیک می‌انجامد. برای نشان دادن تنش گرماکشسانی در بلورها از معیاری با نام تنش فون‌مایسس استفاده می‌کنند. در این مقاله، با استفاده از معادلات ساختاری مناسب، شبیه‌سازی عددی میدان دمایی، تنش گرماکشسانی (گرماکشسانی) و چگالی نابه‌جایی­های بلور درحال رشد ژرمانیوم توسط روش چُکرالسکی برای طول­های مختلف بلور انجام شده است. برای بررسی تراکم نابه‌جایی از یک تقریب سادۀ درجۀ یک، که در آن چگالی نابه‌جایی متناسب با گرادیان شعاعی دماست، استفاده کرده‌ایم. این روش در تمام محاسبات، روش عناصر متناهی حالت پایای دو بُعدی است. نتایج حاکی از آن است که میدان دمایی و تنش گرمایی و چگالی نابه‌جایی بلور به طور صریح وابسته به ارتفاع بلور و انتقال گرمای تابشی و جریان گاز در سامانۀ رشد است. با افزایش ارتفاع بلور و تغییر شکل فصل مشترک بلورـ‌مذاب، تنش گرمایی و چگالی نابه‌جایی افزایش می‌یابد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Research Paper: Numerical Simulation of Thermo-elastic Stresses in Germanium Crystal Grown by Czochralski Technique during Different Lengths of Crystal

نویسندگان [English]

  • Mehdi Jamebozorgi 1
  • Mohammad Hossein Tavakoli 2
1 Ph. D. Student, Department of Physics, Bu-Ali Sina University, Hamedan, Iran.
2 Associate Professor, Department of Physics, Bu-Ali Sina University, Hamedan, Iran
چکیده [English]

In the process of crystal growth by Czochralski technique, lower part and core of the crystal are warmer than other parts of crystal and its environment, which leads to expansion in different parts of the crystal. The result of this thermal gradient is strain, which eventually causes thermo-elastic stress in the crystal. Increasing this stress leads to transition of the material from elastic limit and entering plastic area. To show thermo-elastic stress in crystals, a criterion called Von Misses stress is used. Using the solid mechanics approach, the mechanical response of crystal to the stresses can be determined through appropriate structural equations. In this paper, using appropriate structural equations, a set of numerical simulations of temperature field, thermal stress and dislocation density for a Czochralski setup used to grow Ge single crystal have been done for different heights of crystal. In order to investigate dislocation density, using a simple first-order approximation, in which the dislocation density is proportional to radial gradient of temperature is used. A two-dimensional steady state finite element method has been applied for all calculations. The numerical results reveal that the thermal field and thermal stress are mainly dependent on the crystal height, heat radiation and gas flow in the growth system. As the height of the crystal increases and the shape of the crystal-melt interface changes, we see an increase in thermo-elastic stress and dislocation density.

کلیدواژه‌ها [English]

  • Numerical Simulation
  • Thermo-elastic Stress
  • Czochralski Technique
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