Electronic properties of two dimensional semiconducting Nano-systems, by using few numerical approaches: meshless, finite element and finite difference methods

Document Type : Full length research Paper


1 Department of mathematics, faculty of sciences, Qom University of technology, Qom, IRAN Iran

2 Department of Physics, Faculty of sciences, Qom University of Technology, Qom, Iran


در این مقاله، با استفاده از سه روش عددی تفاضلات متناهی، عناصر متناهی و بدون شبکه ساختار الکترونی تعدای از نانو سیستم‌های دو بعدی با کمک حل عددی معادله شرودینگر دو بعدی مورد بررسی و مقایسه قرار می‌گیرد. برای حل مسائل کاربردی حوزه الکترونیک کوانتومی محاسباتی نیم رساناها اغلب نیاز به حل عددی معادلات شرودینگر دو بعدی می‌باشد که این مسائل عموما بخاطر عدم وجود جواب های تحلیلی دارای پیچیدگی‌های محاسباتی خاص خود می‌باشند. محاسبه ویژه مقادیر، یکی از مهمترین چالش‌های این حوزه می‌باشد. در اینجا، با کمک پنج مثال متنوع کابردی، نشان داده شده است که تحت شرایط مفروض، اندازه ویژه مقادیر مسئله، در روش تفاضلات محدود از پایین و در روش المان محدود از بالا به مقادیر واقعی نزدیک می‌شود. بنابراین در صورت نیاز به دقت بالا برای یک مسئله عمومی کاربردی که حل تحلیلی آن وجود ندارد، با کمک این دو روش می‌توان تقریبی از کران بالا و پایین و بازه‌ای برای ویژه مقادیر یافت. در ادامه نشان داده شده، روش بدون شبکه بالاترین دقت را در بین روش‌های ارائه شده برای مثال‌های مورد بررسی دارد.


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