Accurate Single Beam, Single Optical Path Reflectometer for Continuous Reflectance Measurements Ola Hunderi

Physics Department, Victoria University, Wellington, New-Zealand. Received 27 December 1971.

A simple modification of the single beam reflectometer de­veloped by Beaglehole1 (hereafter referred to as [1]), using two samples instead of one, has allowed us to eliminate all the main systematic errors in that system. Reflecting the light off two samples allowed us to make all mirrors in the system common to both the direct mode of the beam and the reflected mode. We recorded the quantity (1 - R2)/(l + R2) when R approached unity and R2/(1 + R2) when R was small compared to unity. Even more than in [1], the null character of the system when R approached unity made it very sensitive to small changes in the reflectance.

Figure 1 shows (a) the sample holder and (b) the sample. Two identical samples (1 and 2) were mounted back to back in the same type rotating disk as used by [1]. Figure 2 shows the optical arrangement. Light from the exit slit of a monocromator MC was focused onto one side of the sample by a toroidal mirror M4. The reflected light was then1 focused onto the other side of the sample by the spherical mirrors M5 and M6 and finally focused onto the detector D by the toroidal mirror Ml and the

flat mirror MS. The light path is shown by the fully drawn line in Fig. 2 (hereafter referred to as the IR beam). As the plate rotated, the light fell first on the sample and then passed through the hole and reached the detector along the path shown as the dotted line in Fig. 2 (hereafter referred to as the I beam). Note that all mirrors are common to both beams. The ratio of the first harmonic ac signal to the average dc signal was proportional to (1 - R2)/(l + R2). The ac signal was measured using phase sensitive detection. A reference signal was derived by the rotating disk. The ratio of the ac to dc signal was taken automatically by keeping the dc level constant, using the circuit in [1]. The system was calibrated by mounting a black card in the hole in the rotating disk.

Both this system and the system [1] measured the average reflectance over a band across the sample. Since the two samples were evaporated thin films prepared simultaneously, the effect of

Fig. 1. (a) Rotating disk sampleholder and (b) sample.

Fig. 2. The optical arrangement.

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using two samples was to average over twice as large area as in [1].

The main sources of errors in [1] was caused by difference in reflectivities of pairs of mirrors, by beam inversion between the I beam and the IR beam on the detector, and by the I beam and IR beam reaching the detector from different directions. This limited the absolute accuracy to about 1 X 10-3 in (1 - R)/(1 + R), or 2 X 1 0 3 in 1 – R when R approached unity. All these sources of errors have been elimi­nated in this system. The only remaining sources of optical errors were beam inversion and a small difference in size (due to imperfect focusing) between the I beam and the IR beam on the mirrors M5 and M6, a difference between the foci of the two beams equal to the total sample thickness, and imperfect alignment of the mirrors. Note however that there was no beam inversion on the detector. The substrates used by us were mica substrates 0.125 mm thick so that the shift of the focus of one beam relative to the other from the sample thickness became unimportant. As an added precau­tion, the focus was in front of the detector, and a scatterplate was inserted in the beam. If the size of the detector prevents defocus-ing, the images of the two beams on the detector can be made identical by placing the detector half-way between the two foci. This introduces only a partial form of beam inversion on the detector, determined by the sample thickness and f number of the optics. The effect of sample thickness and imperfect alignment of the system was studied by looking at both the reproducibility of the signal upon realignment of the system and by changing the position of the scatterplate. Both showed that the effect of im­perfect alignment and sample thickness was at most ± 3 X 10~4.

The asymmetry of the illumination of the mirrors M5 and M6 can probably be kept less than 1%. Assuming in the worst case 10% and assuming the asymmetry of the reflectivities of the mirrors to be 1 X 10-3, beam inversion would contribute less than 2 X 10 -4 to the total errors in the system. The effect of beam inversion and beam size was studied by rotating the mirrors M5 and M6 180° around an axis through the center of curvature of the mirrors. We found that the variation of the signal with the setting of the mirrors was less than the effect of small realignment necessary after rotation of the mirrors.

If the holes in the rotating disk for the I beam and the IR beam were not identical an error would arise. The holes were carefully machined; any differences could be compensated for by changing the sample from one hole in the rotating disk to the other, taking the average. The difference between the holes was measured by removing the sample. An additional thin coat of black paint on the inside edge of one of the holes in the rotating disk allowed us to reduce the difference to less than 2 × 10–4.

For first harmonic signals (∝1 — R2) much smaller than second harmonic signals (∝1 + R2) an error may arise from the sensitivity of the lockin amplifier to coherent harmonic signals. This can be eliminated by using a notch filter in conjunction with the lockin amplifier to remove the large second harmonic signal. This is better than operating with a very high Q on the tuned amplifier since the latter requires a very high stability of the rotation frequency of the sampleholder.

When R was small (say less than 0.5), (1 - R2)/(l + R2) became rather insensitive to changes in the reflectance. It was then advantageous to gate the signal so that only the part propor­tional to R2 was passed by the gate. The ratio of the first har­monic ac signal to the dc signal was then proportional to R2/(l + R2). The calibration factor was the same as above. The gating was accomplished by driving a mercury wetted relay with the reference signal after an appropriate phase shift and amplification. A convenient gating circuit has also been described by Gerhardt and Rubloff.2

As in [1] the system could also be used to measure the dif­ference in reflectivities between two pairs of samples, measuring in

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this case (R12 — R2

2)/(R12 + R2

2). Here however only a factor of about 2 in sensitivity was gained compared with [1].

In conclusion we can say that the absolute accuracy was deter­mined by imperfect alignment and for, low light intensities, by photon noise. This limited the accuracy of (1 — R2)/(1 + R2) to about 3 X 10 -4 so the absolute accuracy of A = 1 — R was also about 3 × 10–4 when R approached unity.

References 1. D. Beaglehole, App. Opt. 7, 2218 (1968). 2. TJ. Gerhardt and G. Rubloff, Appl. Opt. 8, 305 (1969).