Abstract

An absence of correlation between parameters, indicated by invariance of the normalized ratio of the first derivatives of Δ, makes it possible to make optimal use of the overdetermined set of equations, which are available from multiple-angle measurements. Accurate estimates of the parameters are not needed for the correlation test so that experimental conditions can be chosen to minimize correlation. Also, the second derivatives of the least-squares residuals are useful in deciding on the best method of searching for a solution, in error analysis and in illustrating the critical importance of initial estimates of the unknown parameters in obtaining accurate least-squares solutions.

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  1. F. L. McCrackin and J. P. Colson, in Ellipsometry in the Measurements of Surfaces and Thin Films, edited by E. Passaglia, R. R. Stromberg, and J. Kruger, Natl. Bur. Std. (U.S.) Misc. Pubi. 256 (U. S. Govt. Printing Office, Washington, D. C., 1964), p.61.
  2. D. K. Burge and H. E. Bennett, J. Opt. Soc. Am. 54, 1428 (1964).
  3. This is not to be construed to mean that MAI cannot be used to characterize film and/or substrate properties.
  4. D. G. Schueler, Surface Sci. 16, 104 (1969); also in Proceedings on Recent Developments in Ellipsometry, edited by N. M. Bashara, A. B. Buckman, and A. C. Hall (North-Holland, Amsterdam, 1969).
  5. W. G. Oldham, Surface Sci. 16, 97 (1969).
  6. J. A. Johnson and N. M. Bashara, J. Opt. Soc. Am. 61, 457 (1971).
  7. John R. Rice, in Numerical Solutions of Nonlinear Problems (Computer Sci. Center, Univ. of Maryland, College Park, 1970), p.80.
  8. J. Kowalk and M. R. Osborne, Methods for Unconstrained Optimization Problems (American Elsevier, New York, 1968).
  9. H. R. Philipp and E. A. Taft, Phys. Rev. 120, 37 (1960).
  10. R. J. Archer, Ellipsometry (Gaertner Scientific Corporation, Chicago, 1968).
  11. L. S. Bartell and D. Churchill, J. Phys. Cherm. 65, 2242 (1961); 66, 2719 (1962).
  12. D. L. Marquardt, J. Soc. Indus. Appl. Math. 2, 431 (1963).

Archer, R. J.

R. J. Archer, Ellipsometry (Gaertner Scientific Corporation, Chicago, 1968).

Bartell, L. S.

L. S. Bartell and D. Churchill, J. Phys. Cherm. 65, 2242 (1961); 66, 2719 (1962).

Bashara, N. M.

J. A. Johnson and N. M. Bashara, J. Opt. Soc. Am. 61, 457 (1971).

Bennett, H. E.

D. K. Burge and H. E. Bennett, J. Opt. Soc. Am. 54, 1428 (1964).

Burge, D. K.

D. K. Burge and H. E. Bennett, J. Opt. Soc. Am. 54, 1428 (1964).

Churchill, D.

L. S. Bartell and D. Churchill, J. Phys. Cherm. 65, 2242 (1961); 66, 2719 (1962).

Colson, J. P.

F. L. McCrackin and J. P. Colson, in Ellipsometry in the Measurements of Surfaces and Thin Films, edited by E. Passaglia, R. R. Stromberg, and J. Kruger, Natl. Bur. Std. (U.S.) Misc. Pubi. 256 (U. S. Govt. Printing Office, Washington, D. C., 1964), p.61.

Johnson, J. A.

J. A. Johnson and N. M. Bashara, J. Opt. Soc. Am. 61, 457 (1971).

Kowalk, J.

J. Kowalk and M. R. Osborne, Methods for Unconstrained Optimization Problems (American Elsevier, New York, 1968).

Marquardt, D. L.

D. L. Marquardt, J. Soc. Indus. Appl. Math. 2, 431 (1963).

McCrackin, F. L.

F. L. McCrackin and J. P. Colson, in Ellipsometry in the Measurements of Surfaces and Thin Films, edited by E. Passaglia, R. R. Stromberg, and J. Kruger, Natl. Bur. Std. (U.S.) Misc. Pubi. 256 (U. S. Govt. Printing Office, Washington, D. C., 1964), p.61.

Oldham, W. G.

W. G. Oldham, Surface Sci. 16, 97 (1969).

Osborne, M. R.

J. Kowalk and M. R. Osborne, Methods for Unconstrained Optimization Problems (American Elsevier, New York, 1968).

Philipp, H. R.

H. R. Philipp and E. A. Taft, Phys. Rev. 120, 37 (1960).

Rice, John R.

John R. Rice, in Numerical Solutions of Nonlinear Problems (Computer Sci. Center, Univ. of Maryland, College Park, 1970), p.80.

Schueler, D. G.

D. G. Schueler, Surface Sci. 16, 104 (1969); also in Proceedings on Recent Developments in Ellipsometry, edited by N. M. Bashara, A. B. Buckman, and A. C. Hall (North-Holland, Amsterdam, 1969).

Taft, E. A.

H. R. Philipp and E. A. Taft, Phys. Rev. 120, 37 (1960).

Other (12)

F. L. McCrackin and J. P. Colson, in Ellipsometry in the Measurements of Surfaces and Thin Films, edited by E. Passaglia, R. R. Stromberg, and J. Kruger, Natl. Bur. Std. (U.S.) Misc. Pubi. 256 (U. S. Govt. Printing Office, Washington, D. C., 1964), p.61.

D. K. Burge and H. E. Bennett, J. Opt. Soc. Am. 54, 1428 (1964).

This is not to be construed to mean that MAI cannot be used to characterize film and/or substrate properties.

D. G. Schueler, Surface Sci. 16, 104 (1969); also in Proceedings on Recent Developments in Ellipsometry, edited by N. M. Bashara, A. B. Buckman, and A. C. Hall (North-Holland, Amsterdam, 1969).

W. G. Oldham, Surface Sci. 16, 97 (1969).

J. A. Johnson and N. M. Bashara, J. Opt. Soc. Am. 61, 457 (1971).

John R. Rice, in Numerical Solutions of Nonlinear Problems (Computer Sci. Center, Univ. of Maryland, College Park, 1970), p.80.

J. Kowalk and M. R. Osborne, Methods for Unconstrained Optimization Problems (American Elsevier, New York, 1968).

H. R. Philipp and E. A. Taft, Phys. Rev. 120, 37 (1960).

R. J. Archer, Ellipsometry (Gaertner Scientific Corporation, Chicago, 1968).

L. S. Bartell and D. Churchill, J. Phys. Cherm. 65, 2242 (1961); 66, 2719 (1962).

D. L. Marquardt, J. Soc. Indus. Appl. Math. 2, 431 (1963).

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