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研究生:曾意真
研究生(外文):Yi-ChenTseng
論文名稱:石墨的電子比熱
論文名稱(外文):Electronic specific heat of graphites
指導教授:林明發林明發引用關係
指導教授(外文):Ming-Fa Lin
學位類別:碩士
校院名稱:國立成功大學
系所名稱:物理學系碩博士班
學門:自然科學學門
學類:物理學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:中文
論文頁數:53
中文關鍵詞:緊束模型石墨能帶電子比熱態密度化學位
外文關鍵詞:tight-binding modelenergy band of graphiteelectronic specific heatdensity of statechemical potential
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中文摘要
在本篇論文中,我們用緊束模型探討不同堆疊方式的石墨塊材,其能帶、態密度、化學位及電子比熱的異同。我們所探討的石墨堆疊方式,分別為單層、AA堆疊、AB堆疊及ABC堆疊。不同的幾何結構,造成其能帶有所差異,能帶的對稱性及簡併度亦會反應在態密度及化學位上,並進而影響電子比熱的溫度相依性。
單層石墨的能帶為上下完美對稱,且有兩條線性能帶交叉於費米能,故其態密度值於費米能處為零,化學位亦為零,比熱則為溫度平方正比關係。AA堆疊石墨的能帶亦為上下對稱,且其線性能帶重疊程度大,故其態密度於費米能處仍有一可觀的值,化學位幾乎不隨溫度變化,比熱與溫度一次方成正比。AB堆疊石墨的能帶上下較不對稱,且在H層發生雙重簡併,故其態密度對稱性較低,化學位隨溫度上升而遞減,低溫時比熱與溫度呈線性關係,高溫為非線性關係。ABC堆疊石墨的能帶上下略為對稱,線性能帶分別於K層及H層交叉於費米能上下,其態密度具有對稱性,化學位隨溫度上升而遞增,比熱與溫度平方略呈正比。

Abstract
In this paper, we use the tight-binding model to study the density of states (DOS), the chemical potential, and the electronic specific heat of graphite. Different stacking sequences are taken into consideration, including monolayer, AA-, AB-, and ABC-stacked configurations. The different geometric structures result in the various energy bands. The band symmetry and degeneracy also reflect in the density of states and chemical potential, and thus affect the temperature-dependence of electronic specific heat.
The energy bands of monolayer graphite (graphene) present a complete symmetry with respect to the Fermi level where two linear bands intersect. As a result, the DOS at the Fermi energy and the chemical potential are both zero, and the electronic specific heat is proportional to the square of the temperature. The energy bands of AA-stacked graphite are also symmetric about the Fermi level with more overlapping between linear bands. The DOS at the Fermi energy is therefore a considerable value, while the chemical potential hardly changes with the temperature. Its electronic specific heat is in direct proportion to the temperature. As for AB-stacked graphite, the energy bands are asymmetric, and the double degeneracy occurs on H-layer. Consequently, it reveals less symmetry in the DOS, and the chemical potential decreases with the increasing temperature. The electronic specific heat at low temperatures can be described by a linear relation, but such relationship no longer exists at high temperatures. The conduction and valence bands of ABC-stacked graphite show slight symmetry with two intersections of linear bands above and below the Fermi level on K- and H-layers respectively. The DOS is symmetric, the chemical potential rises with the temperature, and the specific heat is roughly proportional to the square of the temperature.

目錄
中文摘要……………………………………………………i
Abstract ……………………………………………………ii
誌謝…………………………………………………………iii
目錄…………………………………………………………v
圖目錄………………………………………………………vii
第一章 緒論…………………………………………………1
第二章 理論和方法…………………………………………3
2.1 石墨的幾何結構……………………………………3
2.1.1 單層石墨幾何結構…………………………3
2.1.2 AA堆疊石墨幾何結構………………………6
2.1.3 AB堆疊石墨幾何結構…………………… 10
2.1.4 ABC堆疊石墨幾何結構……………………15
2.2 態密度…………………………………………… 19
2.3 比熱……………………………………………… 20
第三章 結果討論………………………………………… 22
3.1 單層石墨………………………………………… 22
3.1.1 單層石墨能帶…………………………… 22
3.1.2 單層石墨態密度………………………… 23
3.1.3 單層石墨比熱…………………………… 25
3.2 AA堆疊的石墨…………………………………… 28
3.2.1 AA堆疊石墨能帶………………………… 28
3.2.2 AA堆疊石墨態密度……………………… 30
3.2.3 AA堆疊石墨比熱………………………… 32
3.3 AB堆疊的石墨…………………………………… 34
3.3.1 AB堆疊石墨能帶………………………… 34
3.3.2 AB堆疊石墨態密度……………………… 37
3.3.3 AB堆疊石墨比熱………………………… 38
3.4 ABC堆疊的石墨……………………………………41
3.4.1 ABC堆疊石墨能帶…………………………41
3.4.2 ABC堆疊石墨態密度………………………44
3.4.3 ABC堆疊石墨比熱…………………………45
第四章 結論……………………………………………… 48
References ……………………………………………… 52




圖目錄
Fig.1 單層石墨的結構圖 …………………………………3
Fig.2 AA堆疊石墨的結構圖 ………………………………6
Fig.3 AB堆疊石墨的結構圖 …………………………… 10
Fig.4 ABC堆疊石墨的結構圖 ……………………………15
Fig.5 單層石墨的能帶圖…………………………………22
Fig.6 單層石墨K點附近的能帶圖 ………………………23
Fig.7 單層石墨的態密度圖(-1eV~1eV)…………………24
Fig.8 單層石墨的態密度圖(-0.1eV~0.1eV)……………24
Fig.9 單層石墨的比熱圖…………………………………26
Fig.10 單層石墨的比熱與T2關係圖………………………27
Fig.11 AA堆疊石墨的能帶圖………………………………29
Fig.12 AA堆疊的石墨能帶圖(K點及H點附近)……………29
Fig.13 AA堆疊的石墨沿kz方向的能帶圖…………………30
Fig.14 AA堆疊的石墨態密度圖(-1eV~1eV)………………31
Fig.15 AA堆疊的石墨態密度圖(-0.1eV~0.1eV)…………31
Fig.16 AA堆疊的石墨比熱圖(0~10K) ……………………33
Fig.17 AA堆疊的石墨比熱圖(0~400K)……………………33
Fig.18 AB堆疊的石墨能帶圖………………………………35
Fig.19 AB堆疊的石墨能帶圖(K點及H點附近)……………35
Fig.20 AB堆疊的石墨能帶圖(K點附近的能帶重疊) ……36
Fig.21 AB堆疊石墨沿kz方向的能帶圖……………………36
Fig.22 AB堆疊的石墨態密度圖(-1eV~1eV)………………37
Fig.23 AB堆疊的石墨態密度圖(-0.1eV~0.1eV)…………38
Fig.24 AB堆疊的石墨化學位圖……………………………39
Fig.25 AB堆疊的石墨比熱圖(0~10K) ……………………39
Fig.26 AB堆疊的石墨比熱圖(0~400K)……………………40
Fig.27 ABC堆疊的石墨能帶圖 ……………………………42
Fig.28 ABC堆疊的石墨能帶圖(kz=0~1) …………………42
Fig.29 ABC堆疊的石墨能帶圖(K點及H點附近的線性關係)
………………………………………………………………43
Fig.30 ABC堆疊石墨沿kz方向的能帶圖 …………………43
Fig.31 ABC堆疊的石墨態密度圖(-1eV~1eV) ……………44
Fig.32 ABC堆疊的石墨態密度圖(-0.1eV~0.1eV) ………45
Fig.33 ABC堆疊的石墨化學位圖 …………………………46
Fig.34 ABC堆疊的石墨比熱圖(0~10K)……………………46
Fig.35 ABC堆疊的石墨比熱圖(0~400K) …………………47
Fig.36 ABC堆疊的石墨比熱與T2關係圖 …………………47
Fig.37 石墨態密度比較圖(-1eV~1eV)……………………49
Fig.38 石墨態密度比較圖(-0.1eV~0.1eV)………………49
Fig.39 石墨比熱比較圖(0~400K)…………………………50
Fig.40 石墨比熱比較圖(0~10K) …………………………51

References
[1]J. C. Charlier amd J. P. Michenaud, “Tight-binding model for the electronic properties of simple hexagonal graphite, Phys. Rev. B 44, 13237-13248(1991)
[2]P. R. Wallace, “The band theory of graphite, Phys. Rev. 71, 622-633(1946)
[3]M. F. Lin and Kenneth W. K. Shung, “Electronic specific heat of single-walled carbon nanotubes, Phys. Rev. B 54, 2896-2900(1996)
[4]C. W.Chiu, M. F. Lin, F. L. Shyu, “Electronic specific heat of nanographite ribbons, Phys. E 11, 356-361(2001)
[5]J. C. Charlier and J. P. Michenaud, “First-principles study of the elelctronic properties of simple hexagonal graphite, Phys. Rev. B 46, 4531-4539(1992)
[6]B. Partoens and F. M. Peeters, “From graphene to graphite:Electronic structure around the K point, Phys. Rev. B 74, 075404-1-11(2006)
[7]C. L. Lu, C. P. Chang, and M. F. Lin, “Magneto-electronic properties of the AA- and ABC-stacked graphites, Eur. Phys. J. B. 60, 161-169(2007)
[8]Chih-Wei Chiu, Yuan-Cheng Huang, Szu-Chao Chen, Ming-Fa Lin and Feng-Lin Shyu, “Low-frequency electronic and optical properties of rhombohedral graphite, Phys. Chem. Chem. Phys. 13, 6036-6042(2011)
[9]Shih-Yang Lin, Yen-Hung Ho, Yuan-Cheng Huang and Ming-Fa Lin, “Magneto-electronic specific heat of graphene, JPSJ (accepted)


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