SEMICONDUCTOR PHYSICS

Inter valley phonon scattering mechanism in strained Si/(101) Si1-xGex

Zhao Jin1, , Liping Qiao2, Ce Liu1, Chen Guo1, Lidong Liu1 and Jiang'an Wang1

+ Author Affiliations

 Corresponding author: Jin Zhao, Email:jinzhaogeorge@126.com

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Abstract: Inter valley scattering has a great impact on carrier mobility of strained Si materials, so based on Fermi's golden rule and the theory of Boltzmann collision term approximation, inter valley phonon scattering mechanism of electrons in nano scale strained Si (101) materials is established under the influence of both energy and stress. It shows that inter valley phonon f2, f3, g3 scattering rates decrease markedly in nano scale strained Si (101) materials with increasing stress. The quantized models can provide valuable references to the understanding of strained Si materials and the research on electron carrier mobility.

Key words: inter valley scatteringstrained Simodel



[1]
Yang L F, Jeremy R W, Rechard C W, et al. Si/SiGe heterostructure parameters for device simulations. Semicond Sci Technol, 2004, 19(10):1174 doi: 10.1088/0268-1242/19/10/002
[2]
Song Jianjun, Zhang Heming, Hu Huiyong, et al. Determination of conduction band edge characteristics of strained Si/Si1-xGex. Chin Phys, 2007, 16(12):3827 doi: 10.1088/1009-1963/16/12/045
[3]
Zhao Lixia, Zhang Heming, Xuan Rongxi, et al. Scattering rates of electrons in strained Si1-xGex (100). Journal of Xidian University, 2012(3):86, 105
[4]
Liu H H, Duan X F, Xu Q X. Finite-element study of strain field in strained-Si MOSFET. Micron, 2009, 40:274 doi: 10.1016/j.micron.2008.06.005
[5]
Song Jianjun, Zhang Heming, Hu Huiyong, et al. Valence band structure of strained Si/(111) Si1-xGex. Science in China, Series G:Physics, Mechanics and Astronomy, 2010, 53(3):454 doi: 10.1007/s11433-010-0093-2
[6]
Olsen S H, Yan L, Aqaiby R, et al. Strained Si/SiGe MOS technology:improving gate dielectric integrity. Microelectron Eng, 2009, 86(3):218 doi: 10.1016/j.mee.2008.08.001
[7]
Smirnov S, Kosina H. Monte Carlo modeling of the electron mobility in strained Si1-xGex layers on arbitrarily oriented Si1-yGey substrates. Solid-State Electron, 2004, 48(8):1325 doi: 10.1016/j.sse.2004.01.014
[8]
Aubry F V, Dollfus P, Galdinn R S. Electron effective mobility in strained-Si/Si1-xGex MOS devices using Monte Carlo simulation. Solid-State Electron, 2005, 49(8):1320 doi: 10.1016/j.sse.2005.06.013
[9]
Driussi F, Esseni D, Selmi L, et al. On the electron mobility enhancement in biaxially strained Si MOSFETs. Solid-State Electron, 2008, 52(4):498 doi: 10.1016/j.sse.2007.10.033
[10]
Ye L X. Monte Carlo simulation for nano-scaled semiconductor devices. Beijing:Science Press, 1997:364
[11]
Song Jianjun, Zhang Heming, Shu Bin, et al. K.P dispersion relation near Δ_i valley in strained Si1-xGex/Si. Journal of Semiconductors, 2008, 29(3):442 http://www.jos.ac.cn/bdtxben/ch/reader/view_abstract.aspx?file_no=07042404&flag=1
[12]
Song Jianjun, Zhang Heming, Hu Huiyong, et al. Calculation of band structure in (101)-biaxially strained Si. Science in China, Series G:Physics, Mechanics and Astronomy, 2009, 52(4):546 doi: 10.1007/s11433-009-0078-1
[13]
Ye L X. Monte Carlo simulation for nano-scaled semiconductor devices. Beijing:Science Press, 1997:472
[14]
Wang Z C. Thermodynamics and statistical physics. 3rd ed. Beijing:National Defense Industry Press, 2003:263
[15]
Tang J Y, Hess K. Theory of hot electron emission from silicon into silicon dioxide. J Appl Phys, 1983, 54(9):5145 doi: 10.1063/1.332738
Fig. 1.  $P_{\rm f2}$ versus energy and Ge fraction at 300 K. (a) Absorption. (b) Emission

Fig. 2.  $P_{\rm f3}$ versus energy and Ge fraction at 300 K. (a) Absorption. (b) Emission

Fig. 3.  $P_{\rm g3}$ versus energy and Ge fraction at 300 K. (a) Absorption. (b) Emission

Fig. 4.  The electron scattering rates $P_{\rm f2}$ of inter valley phonon-$f_{2}$ in strained Si/(101) Si$_{1-x}$Ge$_{x}$ versus energy and Ge fraction at 300 K. (a) Absorption. (b) Emission

Fig. 5.  The electron scattering rates $P_{\rm f3}$ of inter valley phonon-$f_{3}$ in strained Si/(101) Si$_{1-x}$Ge$_{x}$ versus energy and Ge fraction at 300 K. (a) Absorption. (b) Emission

Fig. 6.  The electron scattering rates $P_{\rm g3}$ of inter valley phonon-$f_{2}$ in strained Si/(101) Si$_{1-x}$Ge$_{x}$ versus energy and Ge fraction at 300 K. (a) Absorption. (b) Emission

Fig. 7.  Conduction band splitting by tensile stress in strained Si/Si$_{1-x}$Ge$_{x}$

Fig. 8.  Breaking of symmetry induced by stress, $\alpha$, $\beta$ and $\gamma $ are angles between lattice vectors

Fig. 9.  Splitting energy in strained Si /(101) Si$_{1-x}$Ge$_{x}$

Table 1.   Scattering parameters used in this paper

[1]
Yang L F, Jeremy R W, Rechard C W, et al. Si/SiGe heterostructure parameters for device simulations. Semicond Sci Technol, 2004, 19(10):1174 doi: 10.1088/0268-1242/19/10/002
[2]
Song Jianjun, Zhang Heming, Hu Huiyong, et al. Determination of conduction band edge characteristics of strained Si/Si1-xGex. Chin Phys, 2007, 16(12):3827 doi: 10.1088/1009-1963/16/12/045
[3]
Zhao Lixia, Zhang Heming, Xuan Rongxi, et al. Scattering rates of electrons in strained Si1-xGex (100). Journal of Xidian University, 2012(3):86, 105
[4]
Liu H H, Duan X F, Xu Q X. Finite-element study of strain field in strained-Si MOSFET. Micron, 2009, 40:274 doi: 10.1016/j.micron.2008.06.005
[5]
Song Jianjun, Zhang Heming, Hu Huiyong, et al. Valence band structure of strained Si/(111) Si1-xGex. Science in China, Series G:Physics, Mechanics and Astronomy, 2010, 53(3):454 doi: 10.1007/s11433-010-0093-2
[6]
Olsen S H, Yan L, Aqaiby R, et al. Strained Si/SiGe MOS technology:improving gate dielectric integrity. Microelectron Eng, 2009, 86(3):218 doi: 10.1016/j.mee.2008.08.001
[7]
Smirnov S, Kosina H. Monte Carlo modeling of the electron mobility in strained Si1-xGex layers on arbitrarily oriented Si1-yGey substrates. Solid-State Electron, 2004, 48(8):1325 doi: 10.1016/j.sse.2004.01.014
[8]
Aubry F V, Dollfus P, Galdinn R S. Electron effective mobility in strained-Si/Si1-xGex MOS devices using Monte Carlo simulation. Solid-State Electron, 2005, 49(8):1320 doi: 10.1016/j.sse.2005.06.013
[9]
Driussi F, Esseni D, Selmi L, et al. On the electron mobility enhancement in biaxially strained Si MOSFETs. Solid-State Electron, 2008, 52(4):498 doi: 10.1016/j.sse.2007.10.033
[10]
Ye L X. Monte Carlo simulation for nano-scaled semiconductor devices. Beijing:Science Press, 1997:364
[11]
Song Jianjun, Zhang Heming, Shu Bin, et al. K.P dispersion relation near Δ_i valley in strained Si1-xGex/Si. Journal of Semiconductors, 2008, 29(3):442 http://www.jos.ac.cn/bdtxben/ch/reader/view_abstract.aspx?file_no=07042404&flag=1
[12]
Song Jianjun, Zhang Heming, Hu Huiyong, et al. Calculation of band structure in (101)-biaxially strained Si. Science in China, Series G:Physics, Mechanics and Astronomy, 2009, 52(4):546 doi: 10.1007/s11433-009-0078-1
[13]
Ye L X. Monte Carlo simulation for nano-scaled semiconductor devices. Beijing:Science Press, 1997:472
[14]
Wang Z C. Thermodynamics and statistical physics. 3rd ed. Beijing:National Defense Industry Press, 2003:263
[15]
Tang J Y, Hess K. Theory of hot electron emission from silicon into silicon dioxide. J Appl Phys, 1983, 54(9):5145 doi: 10.1063/1.332738
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    Received: 03 December 2012 Revised: 22 February 2013 Online: Published: 01 July 2013

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      Zhao Jin, Liping Qiao, Ce Liu, Chen Guo, Lidong Liu, Jiang'an Wang. Inter valley phonon scattering mechanism in strained Si/(101) Si1-xGex[J]. Journal of Semiconductors, 2013, 34(7): 072002. doi: 10.1088/1674-4926/34/7/072002 Z Jin, L P Qiao, C Liu, C Guo, L D Liu, J A Wang. Inter valley phonon scattering mechanism in strained Si/(101) Si1-xGex[J]. J. Semicond., 2013, 34(7): 072002. doi:  10.1088/1674-4926/34/7/072002.Export: BibTex EndNote
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      Zhao Jin, Liping Qiao, Ce Liu, Chen Guo, Lidong Liu, Jiang'an Wang. Inter valley phonon scattering mechanism in strained Si/(101) Si1-xGex[J]. Journal of Semiconductors, 2013, 34(7): 072002. doi: 10.1088/1674-4926/34/7/072002

      Z Jin, L P Qiao, C Liu, C Guo, L D Liu, J A Wang. Inter valley phonon scattering mechanism in strained Si/(101) Si1-xGex[J]. J. Semicond., 2013, 34(7): 072002. doi:  10.1088/1674-4926/34/7/072002.
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      Inter valley phonon scattering mechanism in strained Si/(101) Si1-xGex

      doi: 10.1088/1674-4926/34/7/072002
      Funds:

      the National Natural Science Foundation of China 61162025

      the Fundamental Research Funds for the Central Universities of China CHD2011ZD004

      the Fundamental Research Funds for the Central Universities of China CHD2013JC120

      the Fundamental Research Funds for the Central Universities of China 2013G1240120

      Project supported by the National Natural Science Foundation of China (Nos. 51277012, 61162025) and the Fundamental Research Funds for the Central Universities of China (Nos. 2013G1240120, CHD2011ZD004, CHD2013JC120)

      the National Natural Science Foundation of China 51277012

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      • Corresponding author: Jin Zhao, Email:jinzhaogeorge@126.com
      • Received Date: 2012-12-03
      • Revised Date: 2013-02-22
      • Published Date: 2013-07-01

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