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.
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Intensity Ratio as a Function of θp, θb, and θa, where θb = θp − θca
θa
θp =
Case I
+90°
Case II
Linearly polarized light
Circularly polarized light
−45°
0°
+45°
θb =
−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 F0 and the Derivatives of F0 with Respect to the Azimuthal Angles of the Polarizer Minus the Compensator (∂F0/∂θb), the Compensator (∂F0/∂θc), the Analyzer (∂F0/∂θa), and the Phase Shift of the Compensator (∂F0/∂δ)a
These values are shown for all azimuthal angles of θp and θc modulo 45° and for θa of 0 and 45°; the values for θa = 90 and −45° can be obtained from this table by simply changing the sign of the appropriate entry for θa = 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 θc.
∂F0/∂θb ≡ ∂F/∂θp for θc = — (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 θb = ±b45° correspond to right- and left-hand circularly polarized incident light, while θb = −,0°,90°, correspond to linearly polarized incident light (θb = −corresponds to the absence of the compensator). The values of K change sign when θa is increased by 90°.
Tables (3)
Table I
Intensity Ratio as a Function of θp, θb, and θa, where θb = θp − θca
θa
θp =
Case I
+90°
Case II
Linearly polarized light
Circularly polarized light
−45°
0°
+45°
θb =
−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 F0 and the Derivatives of F0 with Respect to the Azimuthal Angles of the Polarizer Minus the Compensator (∂F0/∂θb), the Compensator (∂F0/∂θc), the Analyzer (∂F0/∂θa), and the Phase Shift of the Compensator (∂F0/∂δ)a
These values are shown for all azimuthal angles of θp and θc modulo 45° and for θa of 0 and 45°; the values for θa = 90 and −45° can be obtained from this table by simply changing the sign of the appropriate entry for θa = 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 θc.
∂F0/∂θb ≡ ∂F/∂θp for θc = — (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 θb = ±b45° correspond to right- and left-hand circularly polarized incident light, while θb = −,0°,90°, correspond to linearly polarized incident light (θb = −corresponds to the absence of the compensator). The values of K change sign when θa is increased by 90°.