Abstract

We present a new method based on fast Fourier transform (FFT) for evaluating the thermal expansion coefficient and thermomechanical properties of thin films. The silicon nitride thin films deposited on Corning glass and Si wafers were prepared by plasma-enhanced chemical vapor deposition in this study. The anisotropic residual stress and thermomechanical properties of silicon nitride thin films were studied. Residual stresses in thin films were measured by a modified Michelson interferometer associated with the FFT method under different heating temperatures. We found that the average residual-stress value increases when the temperature increases from room temperature to 100°C. Increased substrate temperature causes the residual stress in SiNx film deposited on Si wafers to be more compressive, but the residual stress in SiNx film on Corning glass becomes more tensile. The residual-stress versus substrate-temperature relation is a linear correlation after heating. A double substrate technique is used to determine the thermal expansion coefficients of the thin films. The experimental results show that the thermal expansion coefficient of the silicon nitride thin films is 3.27×106°C1. The biaxial modulus is 1125 GPa for SiNx film.

© 2012 Optical Society of America

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  1. J. H. Kim and K. W. Chung, “Microstructure and properties of silicon nitride thin films deposited by reactive bias magnetron sputtering,” J. Appl. Phys. 83, 5831–5839 (1998).
    [CrossRef]
  2. R. K. Pandey, L. S. Patil, J. P. Bange, and D. K. Gautam, “Growth and characterization of silicon nitride films for optoelectronics applications,” Opt. Mater. 27, 139–146 (2004).
    [CrossRef]
  3. L. S. Patil, R. K. Pandey, J. P. Bange, S. A. Gaikwad, and D. K. Gautam, “Effect of deposition temperature on the chemical properties of thermally deposited silicon nitride films,” Opt. Mater. 27, 663–670 (2005).
    [CrossRef]
  4. P. L. Ong, J. Wei, E. H. Tay, and C. Iliescu, “A new fabrication method for low stress PECVD–SiNx layers,” J. Phys. Conf. Ser. 34, 764–769 (2006).
    [CrossRef]
  5. C. C. Lee, K. H. Lee, C. J. Tang, C. C. Jaing, and H. C. Chen, “Reduction of residual stress in optical silicon nitride thin films prepared by radio-frequency ion beam sputtering deposition,” Opt. Eng. 49, 063802 (2010).
    [CrossRef]
  6. V. Joglekar, R. N. Karekar, and K. Sathianandan, “Stress in thin films due to volume change on solidification,” Phys. Status Solidi 17, K89–K92 (1973).
    [CrossRef]
  7. R. W. Hoffman, “Stress distributions and thin film mechanical properties,” Surf. Interface Anal. 3, 62–66 (1981).
    [CrossRef]
  8. X. Dong, X. Feng, K. C. Hwang, S. Ma, and Q. Ma, “Full-field measurement of nonuniform stresses of thin films at high temperature,” Opt. Express 19, 13201–13208 (2011).
    [CrossRef]
  9. G. Suchaneck, V. Norkus, and G. Gerlach, “Low temperature PECVD-deposited silicon nitride thin films for sensor applications,” Surf. Coat. Technol. 142–144, 808–812 (2001).
    [CrossRef]
  10. J. Flewitt, A. P. Dyson, J. Robertson, and W. I. Milne, “Low temperature growth of silicon nitride by electron cyclotron resonance plasma enhanced chemical vapor deposition,” Thin Solid Films 383, 172–177 (2001).
    [CrossRef]
  11. Z. B. Zhao, S. M. Yalisove, and J. C. Bilello, “Stress anisotropy and stress gradient in magnetron sputtered films with different deposition geometries,” J. Vac. Sci. Technol. A 24, 195–201 (2006).
    [CrossRef]
  12. W. J. Chang, T. H. Fang, and C. I. Weng, “Thermoviscoelastic stresses in thin films/substrate system,” Thin Solid Films 515, 3693–3697 (2007).
    [CrossRef]
  13. L. B. Freund, and S. Suresh, Thin Film Materials: Stress, Defect Formation and Surface Evolution (Cambridge University, 2004).
  14. J. Thurn, and M. P. Hughey, “Evaluation of film biaxial modulus and coefficient of thermal expansion from thermoelastic film stress measurements,” J. Appl. Phys. 95, 7892–7897 (2004).
    [CrossRef]
  15. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [CrossRef]
  16. M. Takeda and K. Mutoh, “Fourier-transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22, 3977–3982 (1983).
    [CrossRef]
  17. W. W. Macy, “Two-dimensional fringe-pattern analysis,” Appl. Opt. 22, 3898–3901 (1983).
    [CrossRef]
  18. C. L. Tien and H. D. Zeng, “Measuring residual stress of anisotropic thin film by fast Fourier transform,” Opt. Express 18, 16594–16600 (2010).
    [CrossRef]
  19. C. L. Tien, T. W. Lin, S. S. Jyu, H. D. Tseng, C. S. Lin, and M. C. Liu, “The measurement of anisotropic stress in obliquely-deposited thin films by fast Fourier transform and Gaussian filter,” Phys. Procedia 19, 21–26 (2011).
    [CrossRef]
  20. G. G. Stoney, “The tension of metallic films deposited by electrolysis,” Proc. R. Soc. Lond. A 82, 172–175 (1909).
    [CrossRef]
  21. R. W. Hoffman, Physics of Thin Films, G. Hass and R. E. Thun, eds. (Academic, 1966), Vol. 3, pp. 211–223.
  22. R. Swanepoel, “Determination of the thickness and optical constants of amorphous silicon,” J. Phys. E 16, 1214–1222 (1983).
    [CrossRef]
  23. M. Maeda and K. Ikeda, “Stress evaluation of radio-frequency-biased plasma-enhanced chemical vapor deposited silicon nitride films,” J. Appl. Phys. 83, 3865–3870 (1998).
    [CrossRef]

2011

C. L. Tien, T. W. Lin, S. S. Jyu, H. D. Tseng, C. S. Lin, and M. C. Liu, “The measurement of anisotropic stress in obliquely-deposited thin films by fast Fourier transform and Gaussian filter,” Phys. Procedia 19, 21–26 (2011).
[CrossRef]

X. Dong, X. Feng, K. C. Hwang, S. Ma, and Q. Ma, “Full-field measurement of nonuniform stresses of thin films at high temperature,” Opt. Express 19, 13201–13208 (2011).
[CrossRef]

2010

C. L. Tien and H. D. Zeng, “Measuring residual stress of anisotropic thin film by fast Fourier transform,” Opt. Express 18, 16594–16600 (2010).
[CrossRef]

C. C. Lee, K. H. Lee, C. J. Tang, C. C. Jaing, and H. C. Chen, “Reduction of residual stress in optical silicon nitride thin films prepared by radio-frequency ion beam sputtering deposition,” Opt. Eng. 49, 063802 (2010).
[CrossRef]

2007

W. J. Chang, T. H. Fang, and C. I. Weng, “Thermoviscoelastic stresses in thin films/substrate system,” Thin Solid Films 515, 3693–3697 (2007).
[CrossRef]

2006

Z. B. Zhao, S. M. Yalisove, and J. C. Bilello, “Stress anisotropy and stress gradient in magnetron sputtered films with different deposition geometries,” J. Vac. Sci. Technol. A 24, 195–201 (2006).
[CrossRef]

P. L. Ong, J. Wei, E. H. Tay, and C. Iliescu, “A new fabrication method for low stress PECVD–SiNx layers,” J. Phys. Conf. Ser. 34, 764–769 (2006).
[CrossRef]

2005

L. S. Patil, R. K. Pandey, J. P. Bange, S. A. Gaikwad, and D. K. Gautam, “Effect of deposition temperature on the chemical properties of thermally deposited silicon nitride films,” Opt. Mater. 27, 663–670 (2005).
[CrossRef]

2004

R. K. Pandey, L. S. Patil, J. P. Bange, and D. K. Gautam, “Growth and characterization of silicon nitride films for optoelectronics applications,” Opt. Mater. 27, 139–146 (2004).
[CrossRef]

J. Thurn, and M. P. Hughey, “Evaluation of film biaxial modulus and coefficient of thermal expansion from thermoelastic film stress measurements,” J. Appl. Phys. 95, 7892–7897 (2004).
[CrossRef]

2001

G. Suchaneck, V. Norkus, and G. Gerlach, “Low temperature PECVD-deposited silicon nitride thin films for sensor applications,” Surf. Coat. Technol. 142–144, 808–812 (2001).
[CrossRef]

J. Flewitt, A. P. Dyson, J. Robertson, and W. I. Milne, “Low temperature growth of silicon nitride by electron cyclotron resonance plasma enhanced chemical vapor deposition,” Thin Solid Films 383, 172–177 (2001).
[CrossRef]

1998

J. H. Kim and K. W. Chung, “Microstructure and properties of silicon nitride thin films deposited by reactive bias magnetron sputtering,” J. Appl. Phys. 83, 5831–5839 (1998).
[CrossRef]

M. Maeda and K. Ikeda, “Stress evaluation of radio-frequency-biased plasma-enhanced chemical vapor deposited silicon nitride films,” J. Appl. Phys. 83, 3865–3870 (1998).
[CrossRef]

1983

1982

1981

R. W. Hoffman, “Stress distributions and thin film mechanical properties,” Surf. Interface Anal. 3, 62–66 (1981).
[CrossRef]

1973

V. Joglekar, R. N. Karekar, and K. Sathianandan, “Stress in thin films due to volume change on solidification,” Phys. Status Solidi 17, K89–K92 (1973).
[CrossRef]

1909

G. G. Stoney, “The tension of metallic films deposited by electrolysis,” Proc. R. Soc. Lond. A 82, 172–175 (1909).
[CrossRef]

Bange, J. P.

L. S. Patil, R. K. Pandey, J. P. Bange, S. A. Gaikwad, and D. K. Gautam, “Effect of deposition temperature on the chemical properties of thermally deposited silicon nitride films,” Opt. Mater. 27, 663–670 (2005).
[CrossRef]

R. K. Pandey, L. S. Patil, J. P. Bange, and D. K. Gautam, “Growth and characterization of silicon nitride films for optoelectronics applications,” Opt. Mater. 27, 139–146 (2004).
[CrossRef]

Bilello, J. C.

Z. B. Zhao, S. M. Yalisove, and J. C. Bilello, “Stress anisotropy and stress gradient in magnetron sputtered films with different deposition geometries,” J. Vac. Sci. Technol. A 24, 195–201 (2006).
[CrossRef]

Chang, W. J.

W. J. Chang, T. H. Fang, and C. I. Weng, “Thermoviscoelastic stresses in thin films/substrate system,” Thin Solid Films 515, 3693–3697 (2007).
[CrossRef]

Chen, H. C.

C. C. Lee, K. H. Lee, C. J. Tang, C. C. Jaing, and H. C. Chen, “Reduction of residual stress in optical silicon nitride thin films prepared by radio-frequency ion beam sputtering deposition,” Opt. Eng. 49, 063802 (2010).
[CrossRef]

Chung, K. W.

J. H. Kim and K. W. Chung, “Microstructure and properties of silicon nitride thin films deposited by reactive bias magnetron sputtering,” J. Appl. Phys. 83, 5831–5839 (1998).
[CrossRef]

Dong, X.

Dyson, A. P.

J. Flewitt, A. P. Dyson, J. Robertson, and W. I. Milne, “Low temperature growth of silicon nitride by electron cyclotron resonance plasma enhanced chemical vapor deposition,” Thin Solid Films 383, 172–177 (2001).
[CrossRef]

Fang, T. H.

W. J. Chang, T. H. Fang, and C. I. Weng, “Thermoviscoelastic stresses in thin films/substrate system,” Thin Solid Films 515, 3693–3697 (2007).
[CrossRef]

Feng, X.

Flewitt, J.

J. Flewitt, A. P. Dyson, J. Robertson, and W. I. Milne, “Low temperature growth of silicon nitride by electron cyclotron resonance plasma enhanced chemical vapor deposition,” Thin Solid Films 383, 172–177 (2001).
[CrossRef]

Freund, L. B.

L. B. Freund, and S. Suresh, Thin Film Materials: Stress, Defect Formation and Surface Evolution (Cambridge University, 2004).

Gaikwad, S. A.

L. S. Patil, R. K. Pandey, J. P. Bange, S. A. Gaikwad, and D. K. Gautam, “Effect of deposition temperature on the chemical properties of thermally deposited silicon nitride films,” Opt. Mater. 27, 663–670 (2005).
[CrossRef]

Gautam, D. K.

L. S. Patil, R. K. Pandey, J. P. Bange, S. A. Gaikwad, and D. K. Gautam, “Effect of deposition temperature on the chemical properties of thermally deposited silicon nitride films,” Opt. Mater. 27, 663–670 (2005).
[CrossRef]

R. K. Pandey, L. S. Patil, J. P. Bange, and D. K. Gautam, “Growth and characterization of silicon nitride films for optoelectronics applications,” Opt. Mater. 27, 139–146 (2004).
[CrossRef]

Gerlach, G.

G. Suchaneck, V. Norkus, and G. Gerlach, “Low temperature PECVD-deposited silicon nitride thin films for sensor applications,” Surf. Coat. Technol. 142–144, 808–812 (2001).
[CrossRef]

Hoffman, R. W.

R. W. Hoffman, “Stress distributions and thin film mechanical properties,” Surf. Interface Anal. 3, 62–66 (1981).
[CrossRef]

R. W. Hoffman, Physics of Thin Films, G. Hass and R. E. Thun, eds. (Academic, 1966), Vol. 3, pp. 211–223.

Hughey, M. P.

J. Thurn, and M. P. Hughey, “Evaluation of film biaxial modulus and coefficient of thermal expansion from thermoelastic film stress measurements,” J. Appl. Phys. 95, 7892–7897 (2004).
[CrossRef]

Hwang, K. C.

Ikeda, K.

M. Maeda and K. Ikeda, “Stress evaluation of radio-frequency-biased plasma-enhanced chemical vapor deposited silicon nitride films,” J. Appl. Phys. 83, 3865–3870 (1998).
[CrossRef]

Iliescu, C.

P. L. Ong, J. Wei, E. H. Tay, and C. Iliescu, “A new fabrication method for low stress PECVD–SiNx layers,” J. Phys. Conf. Ser. 34, 764–769 (2006).
[CrossRef]

Ina, H.

Jaing, C. C.

C. C. Lee, K. H. Lee, C. J. Tang, C. C. Jaing, and H. C. Chen, “Reduction of residual stress in optical silicon nitride thin films prepared by radio-frequency ion beam sputtering deposition,” Opt. Eng. 49, 063802 (2010).
[CrossRef]

Joglekar, V.

V. Joglekar, R. N. Karekar, and K. Sathianandan, “Stress in thin films due to volume change on solidification,” Phys. Status Solidi 17, K89–K92 (1973).
[CrossRef]

Jyu, S. S.

C. L. Tien, T. W. Lin, S. S. Jyu, H. D. Tseng, C. S. Lin, and M. C. Liu, “The measurement of anisotropic stress in obliquely-deposited thin films by fast Fourier transform and Gaussian filter,” Phys. Procedia 19, 21–26 (2011).
[CrossRef]

Karekar, R. N.

V. Joglekar, R. N. Karekar, and K. Sathianandan, “Stress in thin films due to volume change on solidification,” Phys. Status Solidi 17, K89–K92 (1973).
[CrossRef]

Kim, J. H.

J. H. Kim and K. W. Chung, “Microstructure and properties of silicon nitride thin films deposited by reactive bias magnetron sputtering,” J. Appl. Phys. 83, 5831–5839 (1998).
[CrossRef]

Kobayashi, S.

Lee, C. C.

C. C. Lee, K. H. Lee, C. J. Tang, C. C. Jaing, and H. C. Chen, “Reduction of residual stress in optical silicon nitride thin films prepared by radio-frequency ion beam sputtering deposition,” Opt. Eng. 49, 063802 (2010).
[CrossRef]

Lee, K. H.

C. C. Lee, K. H. Lee, C. J. Tang, C. C. Jaing, and H. C. Chen, “Reduction of residual stress in optical silicon nitride thin films prepared by radio-frequency ion beam sputtering deposition,” Opt. Eng. 49, 063802 (2010).
[CrossRef]

Lin, C. S.

C. L. Tien, T. W. Lin, S. S. Jyu, H. D. Tseng, C. S. Lin, and M. C. Liu, “The measurement of anisotropic stress in obliquely-deposited thin films by fast Fourier transform and Gaussian filter,” Phys. Procedia 19, 21–26 (2011).
[CrossRef]

Lin, T. W.

C. L. Tien, T. W. Lin, S. S. Jyu, H. D. Tseng, C. S. Lin, and M. C. Liu, “The measurement of anisotropic stress in obliquely-deposited thin films by fast Fourier transform and Gaussian filter,” Phys. Procedia 19, 21–26 (2011).
[CrossRef]

Liu, M. C.

C. L. Tien, T. W. Lin, S. S. Jyu, H. D. Tseng, C. S. Lin, and M. C. Liu, “The measurement of anisotropic stress in obliquely-deposited thin films by fast Fourier transform and Gaussian filter,” Phys. Procedia 19, 21–26 (2011).
[CrossRef]

Ma, Q.

Ma, S.

Macy, W. W.

Maeda, M.

M. Maeda and K. Ikeda, “Stress evaluation of radio-frequency-biased plasma-enhanced chemical vapor deposited silicon nitride films,” J. Appl. Phys. 83, 3865–3870 (1998).
[CrossRef]

Milne, W. I.

J. Flewitt, A. P. Dyson, J. Robertson, and W. I. Milne, “Low temperature growth of silicon nitride by electron cyclotron resonance plasma enhanced chemical vapor deposition,” Thin Solid Films 383, 172–177 (2001).
[CrossRef]

Mutoh, K.

Norkus, V.

G. Suchaneck, V. Norkus, and G. Gerlach, “Low temperature PECVD-deposited silicon nitride thin films for sensor applications,” Surf. Coat. Technol. 142–144, 808–812 (2001).
[CrossRef]

Ong, P. L.

P. L. Ong, J. Wei, E. H. Tay, and C. Iliescu, “A new fabrication method for low stress PECVD–SiNx layers,” J. Phys. Conf. Ser. 34, 764–769 (2006).
[CrossRef]

Pandey, R. K.

L. S. Patil, R. K. Pandey, J. P. Bange, S. A. Gaikwad, and D. K. Gautam, “Effect of deposition temperature on the chemical properties of thermally deposited silicon nitride films,” Opt. Mater. 27, 663–670 (2005).
[CrossRef]

R. K. Pandey, L. S. Patil, J. P. Bange, and D. K. Gautam, “Growth and characterization of silicon nitride films for optoelectronics applications,” Opt. Mater. 27, 139–146 (2004).
[CrossRef]

Patil, L. S.

L. S. Patil, R. K. Pandey, J. P. Bange, S. A. Gaikwad, and D. K. Gautam, “Effect of deposition temperature on the chemical properties of thermally deposited silicon nitride films,” Opt. Mater. 27, 663–670 (2005).
[CrossRef]

R. K. Pandey, L. S. Patil, J. P. Bange, and D. K. Gautam, “Growth and characterization of silicon nitride films for optoelectronics applications,” Opt. Mater. 27, 139–146 (2004).
[CrossRef]

Robertson, J.

J. Flewitt, A. P. Dyson, J. Robertson, and W. I. Milne, “Low temperature growth of silicon nitride by electron cyclotron resonance plasma enhanced chemical vapor deposition,” Thin Solid Films 383, 172–177 (2001).
[CrossRef]

Sathianandan, K.

V. Joglekar, R. N. Karekar, and K. Sathianandan, “Stress in thin films due to volume change on solidification,” Phys. Status Solidi 17, K89–K92 (1973).
[CrossRef]

Stoney, G. G.

G. G. Stoney, “The tension of metallic films deposited by electrolysis,” Proc. R. Soc. Lond. A 82, 172–175 (1909).
[CrossRef]

Suchaneck, G.

G. Suchaneck, V. Norkus, and G. Gerlach, “Low temperature PECVD-deposited silicon nitride thin films for sensor applications,” Surf. Coat. Technol. 142–144, 808–812 (2001).
[CrossRef]

Suresh, S.

L. B. Freund, and S. Suresh, Thin Film Materials: Stress, Defect Formation and Surface Evolution (Cambridge University, 2004).

Swanepoel, R.

R. Swanepoel, “Determination of the thickness and optical constants of amorphous silicon,” J. Phys. E 16, 1214–1222 (1983).
[CrossRef]

Takeda, M.

Tang, C. J.

C. C. Lee, K. H. Lee, C. J. Tang, C. C. Jaing, and H. C. Chen, “Reduction of residual stress in optical silicon nitride thin films prepared by radio-frequency ion beam sputtering deposition,” Opt. Eng. 49, 063802 (2010).
[CrossRef]

Tay, E. H.

P. L. Ong, J. Wei, E. H. Tay, and C. Iliescu, “A new fabrication method for low stress PECVD–SiNx layers,” J. Phys. Conf. Ser. 34, 764–769 (2006).
[CrossRef]

Thurn, J.

J. Thurn, and M. P. Hughey, “Evaluation of film biaxial modulus and coefficient of thermal expansion from thermoelastic film stress measurements,” J. Appl. Phys. 95, 7892–7897 (2004).
[CrossRef]

Tien, C. L.

C. L. Tien, T. W. Lin, S. S. Jyu, H. D. Tseng, C. S. Lin, and M. C. Liu, “The measurement of anisotropic stress in obliquely-deposited thin films by fast Fourier transform and Gaussian filter,” Phys. Procedia 19, 21–26 (2011).
[CrossRef]

C. L. Tien and H. D. Zeng, “Measuring residual stress of anisotropic thin film by fast Fourier transform,” Opt. Express 18, 16594–16600 (2010).
[CrossRef]

Tseng, H. D.

C. L. Tien, T. W. Lin, S. S. Jyu, H. D. Tseng, C. S. Lin, and M. C. Liu, “The measurement of anisotropic stress in obliquely-deposited thin films by fast Fourier transform and Gaussian filter,” Phys. Procedia 19, 21–26 (2011).
[CrossRef]

Wei, J.

P. L. Ong, J. Wei, E. H. Tay, and C. Iliescu, “A new fabrication method for low stress PECVD–SiNx layers,” J. Phys. Conf. Ser. 34, 764–769 (2006).
[CrossRef]

Weng, C. I.

W. J. Chang, T. H. Fang, and C. I. Weng, “Thermoviscoelastic stresses in thin films/substrate system,” Thin Solid Films 515, 3693–3697 (2007).
[CrossRef]

Yalisove, S. M.

Z. B. Zhao, S. M. Yalisove, and J. C. Bilello, “Stress anisotropy and stress gradient in magnetron sputtered films with different deposition geometries,” J. Vac. Sci. Technol. A 24, 195–201 (2006).
[CrossRef]

Zeng, H. D.

Zhao, Z. B.

Z. B. Zhao, S. M. Yalisove, and J. C. Bilello, “Stress anisotropy and stress gradient in magnetron sputtered films with different deposition geometries,” J. Vac. Sci. Technol. A 24, 195–201 (2006).
[CrossRef]

Appl. Opt.

J. Appl. Phys.

J. H. Kim and K. W. Chung, “Microstructure and properties of silicon nitride thin films deposited by reactive bias magnetron sputtering,” J. Appl. Phys. 83, 5831–5839 (1998).
[CrossRef]

J. Thurn, and M. P. Hughey, “Evaluation of film biaxial modulus and coefficient of thermal expansion from thermoelastic film stress measurements,” J. Appl. Phys. 95, 7892–7897 (2004).
[CrossRef]

M. Maeda and K. Ikeda, “Stress evaluation of radio-frequency-biased plasma-enhanced chemical vapor deposited silicon nitride films,” J. Appl. Phys. 83, 3865–3870 (1998).
[CrossRef]

J. Opt. Soc. Am.

J. Phys. Conf. Ser.

P. L. Ong, J. Wei, E. H. Tay, and C. Iliescu, “A new fabrication method for low stress PECVD–SiNx layers,” J. Phys. Conf. Ser. 34, 764–769 (2006).
[CrossRef]

J. Phys. E

R. Swanepoel, “Determination of the thickness and optical constants of amorphous silicon,” J. Phys. E 16, 1214–1222 (1983).
[CrossRef]

J. Vac. Sci. Technol. A

Z. B. Zhao, S. M. Yalisove, and J. C. Bilello, “Stress anisotropy and stress gradient in magnetron sputtered films with different deposition geometries,” J. Vac. Sci. Technol. A 24, 195–201 (2006).
[CrossRef]

Opt. Eng.

C. C. Lee, K. H. Lee, C. J. Tang, C. C. Jaing, and H. C. Chen, “Reduction of residual stress in optical silicon nitride thin films prepared by radio-frequency ion beam sputtering deposition,” Opt. Eng. 49, 063802 (2010).
[CrossRef]

Opt. Express

Opt. Mater.

R. K. Pandey, L. S. Patil, J. P. Bange, and D. K. Gautam, “Growth and characterization of silicon nitride films for optoelectronics applications,” Opt. Mater. 27, 139–146 (2004).
[CrossRef]

L. S. Patil, R. K. Pandey, J. P. Bange, S. A. Gaikwad, and D. K. Gautam, “Effect of deposition temperature on the chemical properties of thermally deposited silicon nitride films,” Opt. Mater. 27, 663–670 (2005).
[CrossRef]

Phys. Procedia

C. L. Tien, T. W. Lin, S. S. Jyu, H. D. Tseng, C. S. Lin, and M. C. Liu, “The measurement of anisotropic stress in obliquely-deposited thin films by fast Fourier transform and Gaussian filter,” Phys. Procedia 19, 21–26 (2011).
[CrossRef]

Phys. Status Solidi

V. Joglekar, R. N. Karekar, and K. Sathianandan, “Stress in thin films due to volume change on solidification,” Phys. Status Solidi 17, K89–K92 (1973).
[CrossRef]

Proc. R. Soc. Lond. A

G. G. Stoney, “The tension of metallic films deposited by electrolysis,” Proc. R. Soc. Lond. A 82, 172–175 (1909).
[CrossRef]

Surf. Coat. Technol.

G. Suchaneck, V. Norkus, and G. Gerlach, “Low temperature PECVD-deposited silicon nitride thin films for sensor applications,” Surf. Coat. Technol. 142–144, 808–812 (2001).
[CrossRef]

Surf. Interface Anal.

R. W. Hoffman, “Stress distributions and thin film mechanical properties,” Surf. Interface Anal. 3, 62–66 (1981).
[CrossRef]

Thin Solid Films

J. Flewitt, A. P. Dyson, J. Robertson, and W. I. Milne, “Low temperature growth of silicon nitride by electron cyclotron resonance plasma enhanced chemical vapor deposition,” Thin Solid Films 383, 172–177 (2001).
[CrossRef]

W. J. Chang, T. H. Fang, and C. I. Weng, “Thermoviscoelastic stresses in thin films/substrate system,” Thin Solid Films 515, 3693–3697 (2007).
[CrossRef]

Other

L. B. Freund, and S. Suresh, Thin Film Materials: Stress, Defect Formation and Surface Evolution (Cambridge University, 2004).

R. W. Hoffman, Physics of Thin Films, G. Hass and R. E. Thun, eds. (Academic, 1966), Vol. 3, pp. 211–223.

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Figures (6)

Fig. 1.
Fig. 1.

Schematic representation of the stress measurement system of thin film.

Fig. 2.
Fig. 2.

Surface profiles of SiN x coated on Si wafer at different heating temperatures: (a) 2D and (b) 3D contours.

Fig. 3.
Fig. 3.

Surface profiles of SiN x coatings on Corning glass at different heating temperatures: (a) 2D and (b) 3D contours.

Fig. 4.
Fig. 4.

Residual stress of SiN x coatings on dual substrates versus temperature.

Fig. 5.
Fig. 5.

Variation in residual stress on different axes as a function of temperature change for SiN x coated on Si wafer.

Fig. 6.
Fig. 6.

Variation in residual stress on different axes as a function of temperature change for SiN x coated on Corning glass.

Equations (9)

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i ( x , y ) = a ( x , y ) + b ( x , y ) cos [ 2 π f 0 x + ϕ ( x , y ) ] ,
i ( x , y ) = a ( x , y ) + c ( x , y ) exp ( 2 π i f 0 x ) + c * ( x , y ) exp ( 2 π i f 0 x ) ,
I ( u , v ) = A ( u , v ) + C ( u , v ) + C * ( u , v ) ,
ϕ ( x , y ) = tan 1 ( Im [ c ( x , y ) ] Re [ c ( x , y ) ] ) ,
h ( x , y ) = λ 4 π ϕ ( x , y ) ,
σ = σ i + σ th = 1 6 E s ( 1 ν s ) t s 2 t f ( 1 R 2 1 R 1 ) ,
σ th = ( α s α f ) B f ( T 2 T 1 ) ,
Δ σ Δ T = B f ( α 2 α 1 ) ,
Δ σ σ = ( Δ λ λ ) 2 + ( Δ t f t f ) 2 + ( Δ ϕ ϕ ) 2 + ( Δ n n ) 2 + ( Δ T T ) 2

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