مقایسة تابعی‌های PBE و HSE06 در محاسبه ساختار نواری الکترونی TiO2

نوع مقاله : مقاله پژوهشی کامل


1 گروه فیزیک، دانشکده علوم، دانشگاه زابل، زابل، ایران

2 دانشکدۀ فیزیک، دانشگاه تحصیلات تکمیلی در علوم پایة زنجان، زنجان، ایران


ساختار و گاف نواری الکترونی چند دستۀ مختلف از ساختارهای TiO2 به وسیلۀ نظریۀ تابعی چگالی و با تابعی‌های PBE و HSE06 محاسبه شد. مقادیرگاف نواری محاسبه شده توسط HSE06 برای فازهای روتیل و آناتاس به ترتیب 3.4 و 3.58 الکترون‌ولت بدست آمد که با مقادیر تجربی 3 و 3.2 الکترون‌ولت در توافق است. مدول حجمی نیز برای فازهای روتیل و آناتاس توسطPBE محاسبه گردید و به ترتیب مقادیر 226 و 205 گیگاپاسکال برای آنها به‌دست آمد که با مقادیر متناظر تجربی به ترتیب به اندازة 7 و 14 درصد اختلاف دارد. مقایسۀ دو تابعی مذکور در محاسبۀ ساختار نواری الکترونی ساختارهای مختلف TiO2 نشان داد که شکل ساختار نواری محاسبه شده توسط این دو تابعی، حداقل برای ساختارهای بررسی شده در این‌جا، مشابه است. مخصوصاً قسمت‌های بالایی نوار ظرفیت و قسمت‌های پایینی نوار رسانش دقیقاً یکسان هستند. بنابراین نوع (مستقیم یا غیرمستقیم) گاف نواری محاسبه شده با این دو تابعی یکسان خواهد بود. مهم‌ترین تفاوت این دو تابعی در محاسبۀ ساختار نواری، فاصلۀ بین نوارهای رسانش و ظرفیت و بنابراین اندازۀ گاف نواری است. اختلاف گاف محاسبه شده توسط این دو تابعی برای همۀ ساختارهای بررسی شده در این‌جا مقدار تقریبا یکسان eV 1.6 است.


عنوان مقاله [English]

Comparison between PBE and HSE06 functionals for the calculation of electronic band-structure of TiO2

نویسندگان [English]

  • Hossein Asnaashari Eivari 1
  • Seyed Alireza Ghasemi 2
1 Department of Physics, University of Zabol, Zabol, Iran P.O. Box 98615-538, Zabol 98613-35856, Iran
2 Department of Physics, IASBS, Zanjan, Iran
چکیده [English]

Electronic structure of various structures of TiO2 were calculated using PBE and HSE06 functionals. Calculated band gap in HSE06 level for rutile and anatase phases was 3.4 and 3.58 eV respectively which are in agreement with experimental values of 3 and 3.2 eV. Calculated bulk moduli for the mentioned phases were to be 226 and 205 Gpa. The difference of these values with reported experimental values are %7 and %14 respectively. Comparison between the two mentioned functionals shows that the overall form of band structures is independent of the functional. Especially the top of valence band and the bottom of conduction band are the same in PBE and HSE06. So both functionals give the same result for the type (direct or indirect) of band-gap. Distance between conduction and valence bands, and so the band-gap, is the main difference in calculating the band-structure using these two functionals. Band-gap difference calculated by these functionals is almost 1.6 eV for all structures studied in here. So one can calculate the band-gap of TiO2 with PBE and sum the result by 1.6 eV instead of calculating the band gap in expensive HSE06 level which is close to experimental value.

کلیدواژه‌ها [English]

  • TiO2
  • DFT
  • band-structure
  • GGA functional
  • hybrid functional
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