Mechanical Spectroscopy of Silicon as a Low Loss Material for High Precision Mechanical and Optical Experiments


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The paper summarises systematic studies of the mechanical loss of crystalline silicon at low temperatures from 300 to 5 K. Thermo-elastic loss is discussed as a main contribution in thin samples. A numerical method based on a finite element analysis is presented to determine the thermo-elastic loss of arbitrarily shaped samples. Additionally, mechanical loss associated with oxygen is investigated in Czochralski grown silicon bulk samples. The process has the activation energy of about 168 meV. An orientation dependency of the loss is observed. The lowest loss reported in this paper was achieved with a cylindrical bulk sample having a diameter of 110 mm and a length of 200 mm at around 5 K and a resonant frequency of about 22.3 kHz.



Solid State Phenomena (Volume 184)

Edited by:

Robert Schaller and D. Mari




C. Schwarz et al., "Mechanical Spectroscopy of Silicon as a Low Loss Material for High Precision Mechanical and Optical Experiments", Solid State Phenomena, Vol. 184, pp. 443-448, 2012

Online since:

January 2012




[1] H.B. Callen, T.A. Welton, Phys. Rev. 83 (1951) 34-40.

[2] S. Seel, R. Storz, G. Ruoso, J. Mlynek, S. Schiller, Phys. Rev. Lett. 78 (1997) 4741-4744.


[3] M. Aspelmeyer, K. Schwab, New J. Phys. 10 (2008) 095001.

[4] S. Rowan, J. Hough and D.R.M. Crooks, Phys. Lett. A 347 (2005) 25-32.

[5] D.F. McGuigan, C.C. Lam, R.Q. Gram, A.W. Hoffman, D.H. Douglass, H.W. Gutche, J. Low Temp. Phys. 30 (1978) 621-629.

[6] R. Nawrodt, A. Zimmer, S. Nietzsche, M. Thürk, W. Vodel, P. Seidel, Cryogenics 46 (2006) 718-723.


[7] C. Zener, Phys. Rev. 52 (1937) 230-235.

[8] A.N. Norris, D.M. Photiadis, Q. J. Mech. Appl. Math. 58 (2005) 143-163.

[9] L.D. Landau, E.M. Lifshitz, Course of Theoretical Physics. Elasticity Theory, Butterworth-Heinemann, (1970).

[10] L. Landau, G. Rumer, Physik. Z. Sowjetunion 11 (1937) 18-25.

[11] A. Akhiezer J. Phys. USSR 1 (1939) 277-287.

[12] W.P. Mason, Physical Acoustics, Vol. 3, Academic Press, New York (1965).

[13] A.S. Nowick, B.S. Berry, Anelastic Relaxation in Crystalline Solids, Academic Press, New York (1972).

[14] C.C. Lam, D.H. Douglas, J. Low Temp. Phys. 44 (1981) 259-264.

[15] A. Borghesi, B. Pivac, A. Sassella, A. Stella, J. Appl. Phys. 77 (1995) 4169-4244.