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通过理论计算与模拟，研究分析了P元素替代掺杂单晶硅纳米梁的谐振频率.计算模拟了两端固支单晶硅纳米梁的谐振频率随尺寸、掺杂浓度与温度的变化.通过对计算结果与模拟结果的分析得到： 单晶硅纳米梁的谐振频率随着硅纳米梁长度尺寸的增大而减小；硅纳米梁的谐振频率随着掺杂浓度的增大而增大，但变化趋势并不明显；最后考虑了温度效应，发现掺杂硅纳米梁的谐振频率随着温度的增大而减小，但从谐振频率的数值来看，硅梁的谐振频率随温度的变化趋势并不明显，即温度对硅梁谐振频率基本无影响.由此得出结论： 掺杂浓度与温度对硅纳米梁谐振频率的影响很小，影响单晶硅纳米梁谐振频率的主要因素是尺寸大小，掺杂单晶硅纳米梁的谐振频率具有尺寸效应.With the rapid development of nanoelectromechanical system technologies, silicon nanostructures have attracted considerable attention for the remarkable mechanical properties. A number of studies have been made on the mechanical properties through theoretical analysis, atomistic or molecular dynamics and experiments. In this paper, the resonance frequency of the doping silicon nano-beam is investigated by a theoretical model based the semi-continuum approach to achieve the goal of accurately capturing the atomistic physics and retaining the efficiency of continuum model. The temperature dependence of the resonance frequency of the nanostructure is important for application design, which is considered by the Keating anharmonic model used to describe the strain energy at finite temperature. The resonance frequencies are also simulated by the molecular dynamics at different temperatures. The studies indicate that the resonance frequency of the P doped silicon nano-beam is influenced by the size, the doping concentration and the temperature. The results show that the resonant frequency decreases with the increase of the length of the beam, and increases with the increase of the doping concentration of the silicon nano-beam. The resonant frequency of silicon nano-beam decreases with the increase of temperature, but the changes of the resonant frequency is not obvious. The doping concentration has a little effect on the resonance frequency of the silicon nano-beam. The conclusion can be drawn that neither the effect of doping concentration nor the effect of temperature on resonant frequency of the silicon nano-beam is obvious, the size is a major factor influencing the resonance frequency of the silicon nano-beam.
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Keywords:
- silicon nano-beam /
- resonance frequency /
- doping /
- temperature
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[19] Krivtsov A M, Morozovv N F 2002 Phys. Solid State 44 2260
[20] Xu Y, Zhang L C, Yu T X 1987 Int. J. Mech. Sci. 29 425
[21] Wang J, Huang Q A, Yu H 2008 J. Phys. D: Appl. Phys. 41 165406
[22] Park S H, Kim J S, Park J H, Lee J S, Choi Y K, Kwon O M 2005 Thin Sol. Films 492 285
[23] Li Y N, Zhao J, Guo T 2008 J. Tianjin Univ. 41 7 (in Chinese) [李艳宁, 赵景, 郭彤 2008 天津大学学报 41 7]
[24] Pishkenari H N, Afsharmanesh B, Akbari E 2015 Curr. Appl. Phys. 15 1389
[25] Tang Z, Alueu N R 2006 Phys. Rev. B 74 235441
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[1] Huang X M H, Ekinci K L, Yang Y T, Zorman C A, Mehregany M, Roukes M L 2002 Appl. Phys. Lett. 81 2253
[2] Yang Y T, Callegari C, Feng X L, Ekinci K L, Roukes M L 2006 Nano Lett. 6 583
[3] Yang Y T, Callegari C, Feng X L, Roukes M L 2011 Nano Lett. 11 1753
[4] Bargatin I, Myers E B, Aldridge J S, Marcoux C, Brianceau P, Duraffourg L 2012 Nano Lett. 12 1269
[5] Arkan E F, Sacchetto D, Yildiz I 2011 J. Micromech. Microeng. 21 125018
[6] Koumela A, Hentz S, Mercier D, Ollier E, Feng P X, Purcell S T 2013 Nat. Nanotech. 24 435203
[7] Li X X, Ono T, Wang Y, Esashi M 2003 Appl. Phys. Lett. 83 3081
[8] Sun C T, Zhang H 2003 J. Appl. Phys. 93 1212
[9] Bao F, Yu H, Lu Q, Huang Q 2007 Chin. J. Semi. 28 1979
[10] Lu Q R, Bao F, Yu H, Huang Q A 2008 Chin. J. Sens. Actuat. 21 469 (in Chinese) [陆清茹, 鲍芳, 于虹, 黄庆安 2008 传感技术学报 21 469]
[11] Wang J, Huang Q A, Yu H 2008 Appl. Surf. Sci. 255 2449
[12] L H L, Wang J 2015 Acta Phys. Sin. 64 236103 (in Chinese) [吕焕玲, 王静 2015 64 236103]
[13] Gong B, Chen Q, Wang D 2012 Mater. Lett. 67 165
[14] Cao G B, Chen Y F, Jiao J W, Wang Y L 2007 Mech. Res. Commun. 34 503
[15] Pishkenari H N, Afsharmanesh B, Tajaddodianfar F 2016 Int. J. Eng. Sci. 100 8
[16] L H L, Wang J 2016 J. Xinjiang Univ. 33 421 (in Chinese) [吕焕玲, 王静 2016 新疆大学学报 33 421]
[17] Rcker H, Methfessel M 1995 Phys. Rev. B 52 11059
[18] Wang J 2012 The Sixth Asia-Pacific Conference on Transducers and Micro/Nano Technologies Nanjing, China, July 8-11, 2012 ac12000109
[19] Krivtsov A M, Morozovv N F 2002 Phys. Solid State 44 2260
[20] Xu Y, Zhang L C, Yu T X 1987 Int. J. Mech. Sci. 29 425
[21] Wang J, Huang Q A, Yu H 2008 J. Phys. D: Appl. Phys. 41 165406
[22] Park S H, Kim J S, Park J H, Lee J S, Choi Y K, Kwon O M 2005 Thin Sol. Films 492 285
[23] Li Y N, Zhao J, Guo T 2008 J. Tianjin Univ. 41 7 (in Chinese) [李艳宁, 赵景, 郭彤 2008 天津大学学报 41 7]
[24] Pishkenari H N, Afsharmanesh B, Akbari E 2015 Curr. Appl. Phys. 15 1389
[25] Tang Z, Alueu N R 2006 Phys. Rev. B 74 235441
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