Abstract

Alternate measurement and data analysis procedures are discussed and compared for the application of reflective Nomarski differential interference contrast microscopy for the determination of surface slopes. The discussion includes the interpretation of a previously reported iterative procedure using the results of a detailed optical model and the presentation of a new procedure based on measured image intensity extrema. Surface slope determinations from these procedures are presented and compared with results from a previously reported curve fit analysis of image intensity data. The accuracy and advantages of the different procedures are discussed.

© 1981 Optical Society of America

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References

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  1. G. Nomarski, J. Phys. Rad. 16, 9S (1955).
  2. G. Nomarski, A. R. Weill, Rev. Metall. 52, 121 (1955).
  3. U. Bertocci, T. S. Noggle, Rev. Sci. Instrum. 37, 1750 (1966).
  4. D. L. Lessor, J. S. Hartman, R. L. Gordon, J. Opt. Soc. Am. 69, 357 (1979).
  5. J. S. Hartman, R. L. Gordon, D. L. Lessor, Appl. Opt. 19, 2998 (1980).
  6. J. S. Hartman, R. L. Gordon, D. L. Lessor, Proc. Soc. Photo-Opt. Instrum. Eng. 192, 223 (1980).
  7. Reference to a company or product name does not imply approval or recommendation from the Pacific Northwest Laboratory or the U.S. Department of Energy to the exclusion of others that may be suitable.

1980 (2)

J. S. Hartman, R. L. Gordon, D. L. Lessor, Proc. Soc. Photo-Opt. Instrum. Eng. 192, 223 (1980).

J. S. Hartman, R. L. Gordon, D. L. Lessor, Appl. Opt. 19, 2998 (1980).

1979 (1)

1966 (1)

U. Bertocci, T. S. Noggle, Rev. Sci. Instrum. 37, 1750 (1966).

1955 (2)

G. Nomarski, J. Phys. Rad. 16, 9S (1955).

G. Nomarski, A. R. Weill, Rev. Metall. 52, 121 (1955).

Bertocci, U.

U. Bertocci, T. S. Noggle, Rev. Sci. Instrum. 37, 1750 (1966).

Gordon, R. L.

J. S. Hartman, R. L. Gordon, D. L. Lessor, Appl. Opt. 19, 2998 (1980).

J. S. Hartman, R. L. Gordon, D. L. Lessor, Proc. Soc. Photo-Opt. Instrum. Eng. 192, 223 (1980).

D. L. Lessor, J. S. Hartman, R. L. Gordon, J. Opt. Soc. Am. 69, 357 (1979).

Hartman, J. S.

J. S. Hartman, R. L. Gordon, D. L. Lessor, Proc. Soc. Photo-Opt. Instrum. Eng. 192, 223 (1980).

J. S. Hartman, R. L. Gordon, D. L. Lessor, Appl. Opt. 19, 2998 (1980).

D. L. Lessor, J. S. Hartman, R. L. Gordon, J. Opt. Soc. Am. 69, 357 (1979).

Lessor, D. L.

J. S. Hartman, R. L. Gordon, D. L. Lessor, Appl. Opt. 19, 2998 (1980).

J. S. Hartman, R. L. Gordon, D. L. Lessor, Proc. Soc. Photo-Opt. Instrum. Eng. 192, 223 (1980).

D. L. Lessor, J. S. Hartman, R. L. Gordon, J. Opt. Soc. Am. 69, 357 (1979).

Noggle, T. S.

U. Bertocci, T. S. Noggle, Rev. Sci. Instrum. 37, 1750 (1966).

Nomarski, G.

G. Nomarski, J. Phys. Rad. 16, 9S (1955).

G. Nomarski, A. R. Weill, Rev. Metall. 52, 121 (1955).

Weill, A. R.

G. Nomarski, A. R. Weill, Rev. Metall. 52, 121 (1955).

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

J. Phys. Rad. (1)

G. Nomarski, J. Phys. Rad. 16, 9S (1955).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

J. S. Hartman, R. L. Gordon, D. L. Lessor, Proc. Soc. Photo-Opt. Instrum. Eng. 192, 223 (1980).

Rev. Metall. (1)

G. Nomarski, A. R. Weill, Rev. Metall. 52, 121 (1955).

Rev. Sci. Instrum. (1)

U. Bertocci, T. S. Noggle, Rev. Sci. Instrum. 37, 1750 (1966).

Other (1)

Reference to a company or product name does not imply approval or recommendation from the Pacific Northwest Laboratory or the U.S. Department of Energy to the exclusion of others that may be suitable.

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Figures (4)

Fig. 1
Fig. 1

Relative orientation of Nomarski prism and sample with identification of pertinent angles.

Fig. 2
Fig. 2

Plot of independent phase shift components for three distinct operating regimes (βI, βII, and βIII).

Fig. 3
Fig. 3

Experimental data and calibration curves for the B&N procedure as calculated from the optical model, [Eq. 5], (---) and from a linear regression analysis of the data (—).

Fig. 4
Fig. 4

Relationship between intensity modulation of rotational data and sample slope as determined from the intensity measurement procedure. Solid curves were calculated for 40 and 16× Zeiss objective assemblies with β = π/2 and Q = 0 (zero optical leakage), while dashed curves correspond to β = π/2, Q = 0.037.

Tables (3)

Tables Icon

Table I Theoretical Measurement Sensitivity (dψ/dx) for Surface Slope Determination Using Procedures of Bertocci and Noggle

Tables Icon

Table II Sample Slope Angles Determined by Alternate Techniques

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Table III Linear Regression Coefficients from ψexp Comparison with ψnom (ψexp = a0 + a1 ψnom)

Equations (9)

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I = I min + I ( 1 cos χ ) / 2 ,
χ = f 2 tan 2 ψ ( d β d x ) cos ϕ + β ,
β = β 0 ± x ( d β / d x ) ,
β < | f 2 ( d β d x ) tan 2 ψ |
ψ = ½ tan 1 { 2 [ β 0 ± x ( d β d x ) ] f ( d β d x ) } ,
ψ = β 0 f ( d β d x ) ± x f .
[ I ( max ) I ( min ) I ( max ) + I ( min ) ] = ( 1 Q 1 + Q ) cos χ ex ,
{ I ( max ) I ( min ) I ( max ) + I ( min ) }
Sensitivity ( d ψ d x )

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