Abstract

The problem of determining the roughness of the A model is used based on the SiO2/Si interface is treated. Fresnel formalism and scalar scattering theory. The resulting formulas express the diffuse reflectance as a function of the optical constants of the two materials, the oxide thickness and the rms roughness of the interfaces. Using the roughness values as adjustable parameters, quantitative information about the interface roughness is obtained from the diffuse reflectance spectra for an SiO2/Si double layer. Excellent agreement between calculated and experimental spectra is obtained for an rms roughness of 9.0 nm at the front surface and 2.2 nm at the oxide substrate interface for the case of a low-pressure low-temperature CVD film of SiO2 on Si.

© 1988 Optical Society of America

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References

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  1. J. M. Bennett, “Scattering and Surface Evaluation Techniques for the Optics of the Future,” Opt. News 11, 17 (1985).
    [CrossRef]
  2. H. E. Bennett, J. O. Porteus, “Relation Between Surface Roughness and Specular Reflectance at Normal Incidence,” J. Opt. Soc. Am. 51, 123 (1961).
    [CrossRef]
  3. A. Roos, M. Bergkvist, C-G. Ribbing, “Observation of Diffuse Interference in Reflectance from Oxide-Coated Metals,” Thin Solid Films 125, 221 (1985).
    [CrossRef]
  4. A. Roos, M. Bergvist, C-G. Ribbing, in manuscript.
  5. P. Temple, “Thin Film Absorptance Measurements Using Laser Calorimetry,” in Handbook of Optical Constants of Solids, E. D. Palik, Ed. (Academic, New York, 1985), Chap. 7.
  6. M. Bergkvist, A. Roos, C-G. Ribbing, “Interference Structure in Optical Scattering from Oxide/Metal Interfaces,” J. Vac. Sci. Technol. A 5, 1661 (1987).
    [CrossRef]
  7. O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1954), Chap. 4.
  8. A. Roos, C-G. Ribbing, “Oxidation Induced Roughness as Observed by Diffuse Optical Reflectance,” Phys. Lett. A 108, 225 (1985).
    [CrossRef]
  9. D. F. Edwards, “Silicon (Si),” in Handbook of Optical Constants of Solids, E. D. Palik, Ed. (Academic, New York, 1985), Chap. 2:2, p. 547; H. R. Philipp, “Silicon Dioxide (SiO2) (Glass),” in Hand-book of Optical Constants of Solids, E. D. Palik, Ed. (Academic, New York, 1985), Chap. 3:3. p. 749.

1987 (1)

M. Bergkvist, A. Roos, C-G. Ribbing, “Interference Structure in Optical Scattering from Oxide/Metal Interfaces,” J. Vac. Sci. Technol. A 5, 1661 (1987).
[CrossRef]

1985 (3)

A. Roos, C-G. Ribbing, “Oxidation Induced Roughness as Observed by Diffuse Optical Reflectance,” Phys. Lett. A 108, 225 (1985).
[CrossRef]

J. M. Bennett, “Scattering and Surface Evaluation Techniques for the Optics of the Future,” Opt. News 11, 17 (1985).
[CrossRef]

A. Roos, M. Bergkvist, C-G. Ribbing, “Observation of Diffuse Interference in Reflectance from Oxide-Coated Metals,” Thin Solid Films 125, 221 (1985).
[CrossRef]

1961 (1)

Bennett, H. E.

Bennett, J. M.

J. M. Bennett, “Scattering and Surface Evaluation Techniques for the Optics of the Future,” Opt. News 11, 17 (1985).
[CrossRef]

Bergkvist, M.

M. Bergkvist, A. Roos, C-G. Ribbing, “Interference Structure in Optical Scattering from Oxide/Metal Interfaces,” J. Vac. Sci. Technol. A 5, 1661 (1987).
[CrossRef]

A. Roos, M. Bergkvist, C-G. Ribbing, “Observation of Diffuse Interference in Reflectance from Oxide-Coated Metals,” Thin Solid Films 125, 221 (1985).
[CrossRef]

Bergvist, M.

A. Roos, M. Bergvist, C-G. Ribbing, in manuscript.

Edwards, D. F.

D. F. Edwards, “Silicon (Si),” in Handbook of Optical Constants of Solids, E. D. Palik, Ed. (Academic, New York, 1985), Chap. 2:2, p. 547; H. R. Philipp, “Silicon Dioxide (SiO2) (Glass),” in Hand-book of Optical Constants of Solids, E. D. Palik, Ed. (Academic, New York, 1985), Chap. 3:3. p. 749.

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1954), Chap. 4.

Porteus, J. O.

Ribbing, C-G.

M. Bergkvist, A. Roos, C-G. Ribbing, “Interference Structure in Optical Scattering from Oxide/Metal Interfaces,” J. Vac. Sci. Technol. A 5, 1661 (1987).
[CrossRef]

A. Roos, C-G. Ribbing, “Oxidation Induced Roughness as Observed by Diffuse Optical Reflectance,” Phys. Lett. A 108, 225 (1985).
[CrossRef]

A. Roos, M. Bergkvist, C-G. Ribbing, “Observation of Diffuse Interference in Reflectance from Oxide-Coated Metals,” Thin Solid Films 125, 221 (1985).
[CrossRef]

A. Roos, M. Bergvist, C-G. Ribbing, in manuscript.

Roos, A.

M. Bergkvist, A. Roos, C-G. Ribbing, “Interference Structure in Optical Scattering from Oxide/Metal Interfaces,” J. Vac. Sci. Technol. A 5, 1661 (1987).
[CrossRef]

A. Roos, C-G. Ribbing, “Oxidation Induced Roughness as Observed by Diffuse Optical Reflectance,” Phys. Lett. A 108, 225 (1985).
[CrossRef]

A. Roos, M. Bergkvist, C-G. Ribbing, “Observation of Diffuse Interference in Reflectance from Oxide-Coated Metals,” Thin Solid Films 125, 221 (1985).
[CrossRef]

A. Roos, M. Bergvist, C-G. Ribbing, in manuscript.

Temple, P.

P. Temple, “Thin Film Absorptance Measurements Using Laser Calorimetry,” in Handbook of Optical Constants of Solids, E. D. Palik, Ed. (Academic, New York, 1985), Chap. 7.

J. Opt. Soc. Am. (1)

J. Vac. Sci. Technol. A (1)

M. Bergkvist, A. Roos, C-G. Ribbing, “Interference Structure in Optical Scattering from Oxide/Metal Interfaces,” J. Vac. Sci. Technol. A 5, 1661 (1987).
[CrossRef]

Opt. News (1)

J. M. Bennett, “Scattering and Surface Evaluation Techniques for the Optics of the Future,” Opt. News 11, 17 (1985).
[CrossRef]

Phys. Lett. A (1)

A. Roos, C-G. Ribbing, “Oxidation Induced Roughness as Observed by Diffuse Optical Reflectance,” Phys. Lett. A 108, 225 (1985).
[CrossRef]

Thin Solid Films (1)

A. Roos, M. Bergkvist, C-G. Ribbing, “Observation of Diffuse Interference in Reflectance from Oxide-Coated Metals,” Thin Solid Films 125, 221 (1985).
[CrossRef]

Other (4)

A. Roos, M. Bergvist, C-G. Ribbing, in manuscript.

P. Temple, “Thin Film Absorptance Measurements Using Laser Calorimetry,” in Handbook of Optical Constants of Solids, E. D. Palik, Ed. (Academic, New York, 1985), Chap. 7.

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1954), Chap. 4.

D. F. Edwards, “Silicon (Si),” in Handbook of Optical Constants of Solids, E. D. Palik, Ed. (Academic, New York, 1985), Chap. 2:2, p. 547; H. R. Philipp, “Silicon Dioxide (SiO2) (Glass),” in Hand-book of Optical Constants of Solids, E. D. Palik, Ed. (Academic, New York, 1985), Chap. 3:3. p. 749.

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Figures (4)

Fig. 1
Fig. 1

Schematic representation of the SiO2/Si double layer and the electric fields of the light wave used in the formulation of the model.

Fig. 2
Fig. 2

Calculated diffuse and specular reflectance spectra for the double layer. Parameters: h = 1100; σ1 = 9.0; and σ2 = 2.2 nm.

Fig. 3
Fig. 3

Calculated diffuse reflectance spectra for 1100-nm SiO2 on Si according to the present model. Optical constants where taken from Ref. 9. (a) Variations in front surface rms roughness and constant interface roughness as indicated. (b) Constant front surface roughness and varying interface roughness values as indicated.

Fig. 4
Fig. 4

Experimental diffuse and specular reflectance spectra for a SiO2/Si double layer prepared by (a) 1100°C oven oxidation and (b) 400°C CVD deposition on silicon wafers.

Equations (8)

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E 0 + = A exp [ i ( w t + ϕ ) ] ,
( z , h ) = E ( z ) 2 / E 0 + 2 ,
R D = R T - R S ( σ ) ,
R s = r r *
r = r 1 + r 2 exp ( - 2 i δ ) 1 + r 1 r 2 exp ( - 2 i δ ) ,
exp [ - 2 ( 2 π n σ / λ ) 2 ] ,
R D = { 1 - exp [ - ( 4 π n σ / λ ) 2 ] } R S .
R D = ( h , h ) ( SiO 2 ) R D 1 + ( 0 , h ) ( Si ) · R D 2 · exp ( - α h ) .

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