Abstract

A general analysis of the effect of cell windows shows more error terms in each of the four ellipsometry zones than is found in the conventional small-retardation wave-plate approximation. The value of ψ from a two-zone average requires a correction that is generally dependent on both the window and the reflecting surface under study. A difference of the flux transmission in the <i>s</i> direction from that in the <i>p</i> direction as small as 10<sup>-6</sup> leads to an appreciable correction ~0.06°. An experimental procedure to correct for window error is described and is applied to three different types of windows with Δ errors from 0.05° to 1.5°.

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  1. R. J. King, J. Sci. Instr. 43, 924 (1966).
  2. F. L. McCrackin, J. Opt. Soc. Am. 60, 57 (1970).
  3. R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 61, 600 (1971).
  4. W. A. Shurcliff, Polarized Lighit (Harvard University Press, Cambridge, Mass., 1962).
  5. Exceptions (ψ>45°, | tanA | > 1) can be encountered when the reflecting surface is composed of a substrate with an overlay film whose thickness is an appreciable fraction of a wavelength. In this case, the imperfection parameter Tsp′ of the exit window is amplified by tanA and if ψ is sufficiently close to 90° then higherorder powers of Tsp′ tanA might be necessary in Eq. (5). Going to the other limit of small values of ψ, e.g., near the Brewster angle of a bare substrate, we see that Tps′ is amplified by cotA [Eqs. (4) and (5)] and large correction factors might again be needed. In short, the exit window W′ in the PCWSW′A ellipsometric arrangement can introduce large anomalous errors in both limits of ψ near zero or 90°. There is no similar effect due to the entrance window in this case.
  6. These are 2Pi+(-)i Δ=⊫π/2, Ai=±ψ (i=l, 2, 3, or 4), where the upper signs on the right are for i = 1 or 2.
  7. The results for the SRWP representation can, of course, be deduced from those of the general representation given here. The matrix of an SRWP in its principal frame is diagonal with diagonal elements 1 and 1 -jδ, δ being the small retardation. Pre- and postmultiplying this matrix by the counter-rotater and rotater matrices R(-θ) and R(θ), respectively, we get the matrix of the SRWP in the ps frame as in Eq. (1), where Tps = Tsp = ½ jθ sin2θ and Tss = 1 - jδ cos2θ. Using Eqs. (9), (10), and (16), we get the results for the SRWP case.

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 61, 600 (1971).

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 61, 600 (1971).

King, R. J.

R. J. King, J. Sci. Instr. 43, 924 (1966).

McCrackin, F. L.

F. L. McCrackin, J. Opt. Soc. Am. 60, 57 (1970).

Shurcliff, W. A.

W. A. Shurcliff, Polarized Lighit (Harvard University Press, Cambridge, Mass., 1962).

Other (7)

R. J. King, J. Sci. Instr. 43, 924 (1966).

F. L. McCrackin, J. Opt. Soc. Am. 60, 57 (1970).

R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 61, 600 (1971).

W. A. Shurcliff, Polarized Lighit (Harvard University Press, Cambridge, Mass., 1962).

Exceptions (ψ>45°, | tanA | > 1) can be encountered when the reflecting surface is composed of a substrate with an overlay film whose thickness is an appreciable fraction of a wavelength. In this case, the imperfection parameter Tsp′ of the exit window is amplified by tanA and if ψ is sufficiently close to 90° then higherorder powers of Tsp′ tanA might be necessary in Eq. (5). Going to the other limit of small values of ψ, e.g., near the Brewster angle of a bare substrate, we see that Tps′ is amplified by cotA [Eqs. (4) and (5)] and large correction factors might again be needed. In short, the exit window W′ in the PCWSW′A ellipsometric arrangement can introduce large anomalous errors in both limits of ψ near zero or 90°. There is no similar effect due to the entrance window in this case.

These are 2Pi+(-)i Δ=⊫π/2, Ai=±ψ (i=l, 2, 3, or 4), where the upper signs on the right are for i = 1 or 2.

The results for the SRWP representation can, of course, be deduced from those of the general representation given here. The matrix of an SRWP in its principal frame is diagonal with diagonal elements 1 and 1 -jδ, δ being the small retardation. Pre- and postmultiplying this matrix by the counter-rotater and rotater matrices R(-θ) and R(θ), respectively, we get the matrix of the SRWP in the ps frame as in Eq. (1), where Tps = Tsp = ½ jθ sin2θ and Tss = 1 - jδ cos2θ. Using Eqs. (9), (10), and (16), we get the results for the SRWP case.

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