本文使用第一原理之密度泛函理論，對無限管長之BC_2 N奈米管進行場發射特性研究，藉由改變管徑尺寸及增加硼氮層和碳層連續鍊狀鍵結層層數，以了解結構變化對場發射效益帶來之影響。
　　鋸齒型或扶手椅型BC_2 N奈米管，比石墨與六方硼碳氮表現出較低之功函數，因此具有優異場發射特性。使用鋸齒型結構為場發射源時，存在場發射效益最佳之尺寸，分別是ZZ-1(8,0)、ZZ-2(9,0)和ZZ-3(8,0)，雖然管徑越小，特殊的深寬比特徵，越符合以奈米級針尖構造為場發射源時，能具有良好的聚焦性質有易於場發射之需求，但卻大幅降低費米能，導致功函數上升，對於場發射效益沒有助益；使用小管徑之扶手椅型結構為場發射源時，不會因為費米能大幅下降而降低場發射效益，但場發射特性卻不如其他尺寸之鋸齒型結構優異。
　　硼氮層和碳層連續鍊狀鍵結層數變化對於場發射效益之研究中，扶手椅型結構，隨著層數的變化，存在一場發射效益最差之層數，增加層數，能夠降低功函數，提升場發射效益；鋸齒型結構，則具有一場發射效益最佳之層數，增加層數，反而會降低場發射效益。
　　BC_2 N奈米管比奈米碳管與硼氮奈米管表現出較佳之場發射特性， 硼碳氮鍵結層為改善場發射特性重要之原因； 硼氮層和碳層連續鍊狀鍵結層數改變所導致的能隙變化，會影響功函數之大小，並呈現相同之趨勢，但尚需考慮場發射時受激發之電子所處軌域和其他原子成鍵的情形，成鍵所產生束縛的強弱，會造成激發電子需付出較多能量；以場發射所激發之電子而言，鄰近硼的碳所貢獻之電子數最多。
　　除了以功函數判別BC_2 N奈米管、奈米碳管和硼氮奈米管場發射特性之差異外，總狀態密度分析也可做為另一項判斷之觀點，由總狀態密度圖分析可知，BC_2 N奈米管在價帶區趨近於費米能之軌域，局域性較為明顯，表示場發射時所能激發之電子數越多，即所得場發射電流越大，因此具有較佳之場發射特性，具有作為場發射源之潛力。

By first-principles density functional theory, we investigate the field emission properties of the infinite BC_2 N nanotubes with various tube diameter, or different number of carbon and boron-nitride atomic layers.
　　The zigzag and armchair BC_2 N nanotubes with lower work function than the graphite and hexagonal-BC_2 N display excellent field emission properties. For the zigzag structures, ZZ-1(8,0), ZZ-2(9,0) and ZZ-3(8,0) are tube sizes with the best field emission property respectively. And decreasing the diameter of zigzag BC_2 N nanotubes will decrease the Fermi energy and increase the work function, different to the concept of the super tip. Although the armchair structures show low work function with small diameter, they are not better than zigzag structures on field emission properties.
　　By changing the number of C/C and B/N atomic layers, it is found that the ZZ(8,0) with three atomic layers exhibits better field emission property, and the work function of the AC(6,6) with two atomic layers is higher than the others. Therefore, the field emission properties of armchair structures can be improved by increasing number of C/C and B/N atomic layers up to three atomic layers or more.
　　The BC_2 N nanotubes show the better field emission properties than carbon nanotubes and nitride-boron nanotubes due to the elements B, N and C from the B/C and N/C bonding layers. Besides the energy gap of the tubes, the binding forces from another atoms observed by band structures will also affect the work function. Comparing the elements of C/C and B/N atomic layers of BC_2 N nanotubes, the carbon atom near boron atom can contributes much more electrons than the others during the field emission.
　　From the analysis of the total density of states, it is found that if there are more orbital close to the level of Fermi energy, more electrons can be emitted. In other words, more field emission current can be achieved. Therefore, the BC_2 N nanotubes are suitable to be adopted as one of field emission sources.

[1] 楊素華 and 藍慶忠, "奈米碳管場發射顯示器," 科學發展, vol. 382, pp. 68-71, 2004.
[2] S. Kalbitzer and A. Knoblauch, "Multipurpose nanobeam source with supertip emitter," Journal of Vacuum Science & Technology B, vol. 16, pp. 2455-2461, Jul-Aug 1998.
[3] Q. H. Wang, A. A. Setlur, J. M. Lauerhaas, J. Y. Dai, E. W. Seelig, and R. P. H. Chang, "A nanotube-based field-emission flat panel display," Applied Physics Letters, vol. 72, pp. 2912-2913, Jun 1998.
[4] K. S. Yeong and J. T. L. Thong, "Effects of adsorbates on the field emission current from carbon nanotubes," Applied Surface Science, vol. 233, pp. 20-23, Jun 2004.
[5] J. H. Kang, H. C. Jang, J. M. Choi, S. C. Lyu, and J. H. Sok, "Enhanced Field Emission Behavior from Boron-Doped Double-walled Carbon Nanotubes Synthesized by Catalytic Chemical Vapor Deposition," Journal of Magnetics, vol. 17, pp. 9-12, Mar 2012.
[6] R. B. Sharma, D. J. Late, D. S. Joag, A. Govindaraj, and C. N. R. Rao, "Field emission properties of boron and nitrogen doped carbon nanotubes," Chemical Physics Letters, vol. 428, pp. 102-108, Sep 2006.
[7] M. Yang, L. D. Wang, G. D. Chen, B. An, Y. J. Wang, and G. Q. Liu, "First-principles study on field emission of C-doped capped single-walled BNNT," Acta Physica Sinica, vol. 58, pp. 7151-7155, Oct 2009.
[8] X. D. Bai, J. D. Guo, J. Yu, E. G. Wang, J. Yuan, and W. Z. Zhou, "Synthesis and field-emission behavior of highly oriented boron carbonitride nanofibers," Applied Physics Letters, vol. 76, pp. 2624-2626, May 2000.
[9] P. Dorozhkin, D. Golberg, Y. Bando, and Z. C. Dong, "Field emission from individual B-C-N nanotube rope," Applied Physics Letters, vol. 81, pp. 1083-1085, Aug 2002.
[10] H. Pan, Y. Feng, and J. Lin, "Ab initio study of single-wall BC2N nanotubes," Physical Review B, vol. 74, 2006.
[11] E. Zahedi, "Size-dependent electronic structures of boron carbonitride (BC(2)N) nanotubes. A DFT approach," Superlattices and Microstructures, vol. 50, pp. 491-500, Nov 2011.
[12] X. Blase, "Properties of composite BxCyNz nanotubes and related heterojunctions," Computational Materials Science, vol. 17, pp. 107-114, Jun 2000.
[13] X. Blase, J. C. Charlier, A. De Vita, and R. Car, "Structural and electronic properties of composite B(x)C(y)N(z) nanotubes and heterojunctions," Applied Physics a-Materials Science & Processing, vol. 68, pp. 293-300, Mar 1999.
[14] M. Machado, T. Kar, and P. Piquini, "The influence of the stacking orientation of C and BN stripes in the structure, energetics, and electronic properties of BC2N nanotubes," Nanotechnology, vol. 22, p. 205706, May 20 2011.
[15] 李泳達, "一維奈米碳材料電性結構與場發射之研究," 國立成功大學機械所, 博士論文, 2009.
[16] Y. T. Li and T. C. Chen, "Effect of B/N co-doping on the stability and electronic structure of single-walled carbon nanotubes by first-principles theory," Nanotechnology, vol. 20, Sep 2009.
[17] Y. Miyamoto, A. Rubio, M. L. Cohen, and S. G. Louie, "CHIRAL TUBULES OF HEXAGONAL BC2N," Physical Review B, vol. 50, pp. 4976-4979, Aug 1994.
[18] A. Rubio, J. L. Corkill, and M. L. Cohen, "Theory of graphitic boron nitride nanotubes," Phys Rev B Condens Matter, vol. 49, pp. 5081-5084, Feb 15 1994.
[19] Y. Miyamoto, M. L. Cohen, and S. G. Louie, "Theoretical investigation of graphitic carbon nitride and possible tubule forms," Solid State Communications, vol. 102, pp. 605-608, May 1997.
[20] Y. Miyamoto, A. Rubio, S. G. Louie, and M. L. Cohen, "Electronic properties of tubule forms of hexagonal BC3," Phys Rev B Condens Matter, vol. 50, pp. 18360-18366, Dec 15 1994.
[21] O. Stephan, P. M. Ajayan, C. Colliex, P. Redlich, J. M. Lambert, P. Bernier, and P. Lefin, "DOPING GRAPHITIC AND CARBON NANOTUBE STRUCTURES WITH BORON AND NITROGEN," Science, vol. 266, pp. 1683-1685, Dec 1994.
[22] P. Kohler-Redlich, M. Terrones, C. Manteca-Diego, W. K. Hsu, H. Terrones, M. Ruhle, H. W. Kroto, and D. R. M. Walton, "Stable BC2N nanostructures: low-temperature production of segregated C/BN layered materials," Chemical Physics Letters, vol. 310, pp. 459-465, Sep 1999.
[23] A. Y. Liu, R. M. Wentzcovitch, and M. L. Cohen, "ATOMIC ARRANGEMENT AND ELECTRONIC-STRUCTURE OF BC2N," Physical Review B, vol. 39, pp. 1760-1765, Jan 1989.
[24] M. O. Watanabe, S. Itoh, K. Mizushima, and T. Sasaki, "Bonding characterization of BC2N thin films," Applied Physics Letters, vol. 68, pp. 2962-2964, May 1996.
[25] M. Terrones, N. Grobert, and H. Terrones, "Synthetic routes to nanoscale BxCyNz architectures," Carbon, vol. 40, pp. 1665-1684, 2002.
[26] T. W. Odom, J. L. Huang, P. Kim, and C. M. Lieber, "Structure and electronic properties of carbon nanotubes," Journal of Physical Chemistry B, vol. 104, pp. 2794-2809, Apr 2000.
[27] R. Saito, G. Dresselhaus, and M. S. Dresselhaus, Physical properties of carbon nanotubes. London: Imperial College Press, 1998.
[28] A. Modinos, Field, thermionic, and secondary electron emission spectroscopy. New York: Plenum Press, 1984.
[29] R. H. Fowler and L. Nordheim, "Electron emission in intense electric fields," Proceedings of the Royal Society of London. Series A, vol. 119, pp. 173-181, May 1 1928.
[30] 趙成大, "固體量子化學-材料化學的理論基礎." 2nd ed, 北京: 高等教育出版社, 2003.
[31] P. Hohenberg and W. Kohn, "Inhomogenous Electron Gas," Physical Review, vol. 136, pp. B864-B871, 1964.
[32] W. Kohn and L. J. Sham, "SELF-CONSISTENT EQUATIONS INCLUDING EXCHANGE AND CORRELATION EFFECTS," Physical Review, vol. 140, pp. 1133-&, 1965.
[33] D. M. Ceperley and B. J. Alder, "GROUND-STATE OF THE ELECTRON-GAS BY A STOCHASTIC METHOD," Physical Review Letters, vol. 45, pp. 566-569, 1980.
[34] K. C., "Introduction to solid state physics," 2005.
[35] M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, "ITERATIVE MINIMIZATION TECHNIQUES FOR ABINITIO TOTAL-ENERGY CALCULATIONS - MOLECULAR-DYNAMICS AND CONJUGATE GRADIENTS," Reviews of Modern Physics, vol. 64, pp. 1045-1097, Oct 1992.
[36] N. D. Lang and W. Kohn, "THEORY OF METAL SURFACES - WORK FUNCTION," Physical Review B, vol. 3, pp. 1215-&, 1971.