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Influence of thermal expansion on the lattice parameter of silicona)

Published online by Cambridge University Press:  10 January 2013

Fengchao Liu
Fengchao Liu
Affiliation:
Department of Physics, South China Normal University, Guangzhou 510631, China
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Abstract

Considering the thermal expansion of silicon at ambient conditions, the lattice parameter will change 0.00032 Å for a 10 °C range. This range is measurable with modern diffraction instrumentation illustrating the importance of knowing the accurate lattice parameter, the temperature of measurement, and the thermal expansion coefficient. The best value for the expansion coefficient is 2.45×10−6/°C.

Keywords

coefficient of thermal expansionlattice constantsilicon
Type
Research Article
Information
Powder Diffraction , Volume 9 , Issue 4 , December 1994 , pp. 260 - 264
Copyright
Copyright © Cambridge University Press 1994

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References

Barns, R. L. (1967). “A Survey of Precision Lattice Parameter Measurements as a Tool for the Characterization of Single-Crystal Materials,” Mat. Res. Bull. 2, 273–282.CrossRefGoogle Scholar
Barns, R. L. (1972). “A strategy for rapid and accurate (P.P.m.) measurement of lattice parameters of single crystals by Bond's method,” Adv. X-Ray Anal. 15, 330–338.Google Scholar
Batchelder, D. N., and Simmons, R. O. (1964). “Lattice Constants and Thermal Expansivities of Silicon and of Calcium Fluoride between 6° and 322° K,” J. Chem. Phys. 41(8), 2324–2329.CrossRefGoogle Scholar
Batchelder, D. N., and Simmons, R. O. (1965). “X-Ray Lattice Constants of Crystals by Rotating-Camera Method: Al, Ar, Au, CaF2, Cu, Ge, Ne, Si,” J. Appl. Phys. 36, 2864–2868.CrossRefGoogle Scholar
Becker, K. (1926). “Eine röntgenographische Methode Zür Bestimmung des Wärmeausdehnungskoeffizienten bei hohen Temperaturen,” Z. Physik 40, 37–41.CrossRefGoogle Scholar
Becker, P., Dorenwendt, K., Ebeling, G., Lauer, R., Lucas, W., Probst, R., Rademacher, H.-J., Reim, G., Seyfried, P., and Siegert, H. (1981). “Absolute Measurement of the (220) Lattice Plane Spacing in a Silicon Crystal,” Phys. Rev. Lett. 46(23), 1540–1543.CrossRefGoogle Scholar
Birss, R. R., and Home, R. J. (1960). “The Thermal Expansion of a Silicon Single Crystal,” Proc. Phys. Soc. LXXV 5, 3E-3E2, 793–795.CrossRefGoogle Scholar
Bond, W. L. (1960). “Precision Lattice Constant Determination,” Acta Cryst. 13, 814–818.CrossRefGoogle Scholar
Burkhardt, P. J., and Marvel, R. F. (1969). “Thermal Expansion of Sputtered Silicon Nitride Films,” J. Electrochem. Soc.: Solid State Science 116(6), 864–866.CrossRefGoogle Scholar
Carr, R. H., McCammon, R. D., and White, G. K. (1965). “Thermal Expansion of Germanium and Silicon at Low Temperature,” Philos. Mag. 12, 157–163.CrossRefGoogle Scholar
Chen, L. et al. (1981), (1982), (1983), (1984), and (1986). “Explanation of the state standard of the People's Republic of China of No. GB8360-87” (internal report, unpublished).Google Scholar
Deslattes, R. D. (1980a). “The Avogadro Constant,” Ann. Rev. Phys. Chem. 31, 435–461.CrossRefGoogle Scholar
Deslattes, R. D. (1980b). “Reference Wavelengths. Infra-red to Gamma-Rays, Avogadro's Constant, Mass and Density,” in Metrology Fundamental Constants, edited by Milone, A. Ferro and Giacomo, P. (North-Holland, Amsterdam, 1980), pp. 38–113.Google Scholar
Deslattes, R. D., and Henins, A. (1973). “X-Ray to Visible Wavelength Ratios,” Phys. Rev. Lett. 31(16), 972–975.CrossRefGoogle Scholar
Deslattes, R. D., Henins, A., Schoonover, R. M., Carroll, C. L., and Bowman, H. A. (1976). “Avogadro Constant—Corrections to an Earlier Report,” Phys. Rev. Lett. 36(15), 898–900.CrossRefGoogle Scholar
Deslattes, R. D., Henins, A., Bowman, H. A., Schoonover, R. M., Carroll, C. L., Barnes, I. L., Machlan, L. A., Moore, L. J., and Shields, W. R. (1974). “Determination of the Avogadro Constant,” Phys. Rev. Lett. 33(8), 463–466.CrossRefGoogle Scholar
Deslattes, R. D., Kessler, E. G., Sauder, W. C., and Henins, A. (1980). “Remeasurement of γ-Ray Reference Lines,” Ann. Phys. 129, 378–434.CrossRefGoogle Scholar
Dismukes, J. P., Ekstrom, L., and Paff, R. J. (1964). “Lattice Parameter and Density in Germanium-Silicon Alloys,” J. Phys. Chem. 68(10), 3021–3027.CrossRefGoogle Scholar
Dutta, B. N. (1962). “Lattice Constants and Thermal Expansion of Silicon up to 900 °C by X-Ray Method,” Phys. Stat. Sol. 2, 984–987.CrossRefGoogle Scholar
Erfling, H. D. (1942). See Table I in Ref. 42.Google Scholar
Fizeau, H. (1869). See Table I in Ref. 42.Google Scholar
GB8360-87 (1987). The State Standard of the People's Republic of China of No. GB8360-87.Google Scholar
Gibbons, D. F. (1958). “Thermal Expansion of Some Crystals with the Diamond Structure,” Phys. Rev. 112(1), 136–140.CrossRefGoogle Scholar
Godwod, K., Kowalszyk, R., and Szmid, Z. (1974). “Application of a Precise Double X-Ray Spectrometer for Accurate Lattice Parameter Determination,” Phys. Stat. Solids A 21, 227–234.CrossRefGoogle Scholar
Hall, R. O. A. (1961). “The thermal expansion of silicon,” Acta Cryst. 14, 1004–1005.CrossRefGoogle Scholar
Hom, T., Kiszenick, W., and Post, B. (1975). “Accurate Lattice Constants from Multiple Reflection Measurement II. Lattice Constants of Germanium, Silicon and Diamond,” J. Appl. Cryst. 8, 457–458.CrossRefGoogle Scholar
Hubbard, C. R., Swanson, H. E., and Mauer, F. A. (1975). “A Silicon Powder Diffraction Standard Reference Material,” J. Appl. Cryst. 8, 45–48.CrossRefGoogle Scholar
Isherwood, B. J., and Wallace, C. A. (1966). “The Solid State Measurement of the Lattice Parameter of Silicon, Using a Double-Diffraction Effect,” Nature (London) 212(5058), 173–175.CrossRefGoogle Scholar
Jette, E. R., and Foote, F. (1935). “Precision Determination of Lattice Constants,” J. Chem. Phys. 3, 605–616.CrossRefGoogle Scholar
King, H. W., and Preece, C. M. (1970). “Precision Lattice Parameter Determination at Liquid Helium Temperatures by Double-Scanning Diffractometry,” Adv. X-ray Anal. 10, 354–365.Google Scholar
King, H. W., and Russell, C. M. (1968). “Double-Scanning diffractometry in the back-reflection region,” Adv. X-ray Anal. 8, 1–10.Google Scholar
Lipson, H., and Rogers, L. E. R. (1944). “LXI. The Measurement of X-ray Wavelengths by the Powder Method: CrKβ 1, and MnKβ 1,” Philos. Mag. 35(7), 544–549.CrossRefGoogle Scholar
Lisiovan, V. I., and Dikovskaya, R. R. (1969). “Local Precision Determination of Lattice Constants of a Single Crystal,” Instruments and Exper. Tech. (Eng. translation) 4, 992–994.Google Scholar
Liu, Fengchao (1993). “Confirmation of the new technique for measuring the linear thermal expansion of silicon,” Powder Diffr. 8, 36–38.Google Scholar
Liu, Fengchao, and Zheng, Bin (1991). “The Linear Coefficient of Thermal Expansion of Silicon at Room Temperature,” Powder Diffr. 6(3), 147–152.Google Scholar
Maissel, L. (1960). “Thermal Expansion of Silicon,” J. Appl. Phys. 31, 211.CrossRefGoogle Scholar
Nan, S., and Yi-Huan, L. (1965). “X-Ray Measurement of the Thermal Expansion of Germanium, Silicon, Indium Antimonide, and Gallium Arsenide,” Scientia Sinica 14(11), 1582–1589.Google Scholar
(Xiao, Nan and Liu, Yi-Huan first published in Chinese in Acta Physica Silica, Vol. 20, No. 8, 699–703 (1964).)Google Scholar
Nasekovsky, A. P. (1967). “On the Temperature Dependence of the Thermal Expansion Coefficient for Cubiform Crystals,” Ukrain. Fiz. Zh. 12(8), 1353–1356.Google Scholar
Parrish, W. (1960). “Results of the I.U.Cr. Precision Lattice-Parameter Project,” Acta Cryst. 13, 838–850.CrossRefGoogle Scholar
Segmüller, A. (1970). “Automated lattice Parameter determination on single crystal,” Adv. X-ray Anal. 13, 455–467.Google Scholar
Smakula, A., and Kalnajs, J. (1955). “Precision Determination of Lattice Constants with a Geiger-Counter X-Ray Diffractometer,” Phys. Rev. 99(6), 1737–1743.CrossRefGoogle Scholar
Straumanis, M. E., and Aka, E. Z. (1952). “Lattice Parameters, Coefficients of Thermal Expansion, and Atomic Weights of Purest Silicon and Germanium,” J. Appl. Phys. 23(3), 330–334.CrossRefGoogle Scholar
Straumanis, M. E., Borgeaud, P., and James, W. J. (1961). “Perfection of the Lattice of Dislocation-Free Silicon, Studied by the Lattice-Constant and Density Method,” J. Appl. Phys. 32(7), 1382–1384.CrossRefGoogle Scholar
Tao, K. (1980). “The Precision and Accuracy in Measuring the Lattice Constant of Silicon With X-Ray Powder Diffractometry,” Chin. J. Tsing Hua Univ. 20(2), 103–113.Google Scholar
Weyerer, H. (1960). “Discussion of error in lattice-parameter measurements,” Acta Cryst. 13, 821–823.CrossRefGoogle Scholar
White, G. K. (1973). “Thermal expansion of reference materials: Copper, Silica and Silicon,” J. Phys. D: Appl. Phys. 6, 2070–2078.CrossRefGoogle Scholar
Yim, W. M., and Paff, R. J. (1974). “Thermal expansion of AlN, Sapphire and Silicon,” J. Appl. Phys. 45(3), 1456–1457.CrossRefGoogle Scholar