An ellipsometer is described which is capable of measuring one of the related ellipsometric parameters N, S, or C as a function of time. The ellipsometer is of the standard polarizer–compensator–sample–analyzer type, in which the analyzer is a Wollaston prism. An analysis is presented of the errors resulting from misalignment of the azimuths of the various elements from an incorrect phase shift of the compensator and from sample surface effects. The time resolution of the ellipsometer is limited only by the rise time of the photodetector and by the digitization rate of the data acquisition system. Picosecond time resolution is possible, in principle, using a streak camera as both detector and digitizer. Submicrosecond operation of the time-resolved ellipsometer is demonstrated in a study of pulsed excimer laser cleaning of a silicon surface in air.

Joungchel Lee and Robert W. Collins Appl. Opt. 37(19) 4230-4238 (1998)

References

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Intensity Ratio as a Function of θ_{p}, θ_{b}, and θ_{a}, where θ_{b} = θ_{p} − θ_{c}^{a}

θ_{a}

θ_{p} =

Case I

+90°

Case II

Linearly polarized light

Circularly polarized light

−45°

0°

+45°

θ_{b} =

−45°

+45°

−45°

1 + C

1 + N

1 − C

1 − N

1 − S

1 + S

0°

1 + N

2(1 + N)

1 + N

0

1 + N

1 + N

+45°

1 − C

1 + N

1 + C

1 − N

1 + S

1 − S

+90°

1 − N

0

1 − N

2(1 − N)

1 − N

1 − N

Case I represents incident light that is linearly polarized, for which the compensator is either absent or aligned at 0 or 90° with respect to the polarizer. Case II represents incident circularly polarized light, for which the compensator is aligned at ±45° with respect to the polarizer and the phase shift δ = 90°. Each element in the table is to be multiplied by R/4 to obtain the output/input intensity ratio.

Table II

Values for F_{0} and the Derivatives of F_{0} with Respect to the Azimuthal Angles of the Polarizer Minus the Compensator (∂F_{0}/∂θ_{b}), the Compensator (∂F_{0}/∂θ_{c}), the Analyzer (∂F_{0}/∂θ_{a}), and the Phase Shift of the Compensator (∂F_{0}/∂δ)^{a}

These values are shown for all azimuthal angles of θ_{p} and θ_{c} modulo 45° and for θ_{a} of 0 and 45°; the values for θ_{a} = 90 and −45° can be obtained from this table by simply changing the sign of the appropriate entry for θ_{a} = 0 and 45°, respectively. Also shown in this table are the corrections, K arising from off-diagonal elements in the sample Jones matrix (see text and Table III). The phase shift δ = 90° for configurations that list a value of θ_{c}.
∂F_{0}/∂θ_{b} ≡ ∂F/∂θ_{p} for θ_{c} = — (no compensator).

Table III

First-Order Contribution to F Resulting from Off-Diagonal Elements of the Sample Jones Matrix [see Eq. (17) for Definitions]^{a}

The values of θ_{b} = ±_{b}45° correspond to right- and left-hand circularly polarized incident light, while θ_{b} = −,0°,90°, correspond to linearly polarized incident light (θ_{b} = −corresponds to the absence of the compensator). The values of K change sign when θ_{a} is increased by 90°.

Tables (3)

Table I

Intensity Ratio as a Function of θ_{p}, θ_{b}, and θ_{a}, where θ_{b} = θ_{p} − θ_{c}^{a}

θ_{a}

θ_{p} =

Case I

+90°

Case II

Linearly polarized light

Circularly polarized light

−45°

0°

+45°

θ_{b} =

−45°

+45°

−45°

1 + C

1 + N

1 − C

1 − N

1 − S

1 + S

0°

1 + N

2(1 + N)

1 + N

0

1 + N

1 + N

+45°

1 − C

1 + N

1 + C

1 − N

1 + S

1 − S

+90°

1 − N

0

1 − N

2(1 − N)

1 − N

1 − N

Case I represents incident light that is linearly polarized, for which the compensator is either absent or aligned at 0 or 90° with respect to the polarizer. Case II represents incident circularly polarized light, for which the compensator is aligned at ±45° with respect to the polarizer and the phase shift δ = 90°. Each element in the table is to be multiplied by R/4 to obtain the output/input intensity ratio.

Table II

Values for F_{0} and the Derivatives of F_{0} with Respect to the Azimuthal Angles of the Polarizer Minus the Compensator (∂F_{0}/∂θ_{b}), the Compensator (∂F_{0}/∂θ_{c}), the Analyzer (∂F_{0}/∂θ_{a}), and the Phase Shift of the Compensator (∂F_{0}/∂δ)^{a}

These values are shown for all azimuthal angles of θ_{p} and θ_{c} modulo 45° and for θ_{a} of 0 and 45°; the values for θ_{a} = 90 and −45° can be obtained from this table by simply changing the sign of the appropriate entry for θ_{a} = 0 and 45°, respectively. Also shown in this table are the corrections, K arising from off-diagonal elements in the sample Jones matrix (see text and Table III). The phase shift δ = 90° for configurations that list a value of θ_{c}.
∂F_{0}/∂θ_{b} ≡ ∂F/∂θ_{p} for θ_{c} = — (no compensator).

Table III

First-Order Contribution to F Resulting from Off-Diagonal Elements of the Sample Jones Matrix [see Eq. (17) for Definitions]^{a}

The values of θ_{b} = ±_{b}45° correspond to right- and left-hand circularly polarized incident light, while θ_{b} = −,0°,90°, correspond to linearly polarized incident light (θ_{b} = −corresponds to the absence of the compensator). The values of K change sign when θ_{a} is increased by 90°.