Dyson, J. 1958

Physica XXIV Zernike issue

532-537

T H E MEASUREMENT OF T H I N FILMS BY I N T E R F E R O M E T R Y

b y J. DYSON

Synopsis

The measurement of thin films is becoming of increasing technical and scientific importance. In view of the high accuracy of comparison 5f path-differences attainable in polarimeLu-y, experiments have been made to achieve some of this accuracy in thin film measurements.

It is shown experimentally that setting accuracies are obtainable corresponding to an error of thickness measurement of ± 1A.

CONTENTS. Introduct ion, § 1 - A previous at tempt to obtain high accuracy, § 2 - Fur ther exper iments § 3 - Pract ical considerations § 4 - Conclusions

§ 5 - Acknowledgements - Re[erences.

1. Introduct ion. The use of thin films has become widespread in scientific and technical apphcations and the accurate measurement of their thickness is a matter of increasing importance. A very elegant method has been devised by Z e r n i k e 1) for effecting this measurement on films of moderate size and setting accuracies of 0.0048 1 for a single setting and 0.0017 2 for eight settings were claimed by him.

In the article mentioned above, Zernike points out that settings of much higher accuracy, in some cases as high as 10 -5 t, may be attained in polari- metry by the use of half-shadow devices. This point had also occurred to the author, together with the fact that a polarising type of interference micros- cope offered conditions in which a half-shadow device could be used.

2. A previous at tempt to obtain high accuracy. In order to realise some of the potential accuracy of the method, a measuring apparatus was made a) based on a S m i t h 3) type of shearing interference microscope adapted for opaque specimens. The shear was given by a Wollaston prism in the back focal plane of a low-power objective and two coherent images, polarised in mutually perpendicular directions, were obtained. After passage through a quarter-wave plate the two images combined to give an image in plane- polarised light, the azimuth of the plane of polarisation depending on the

- - 5 3 2 - -

THE MEASUREMENT OF THIN FILMS BY INTERFEROMETRY 5 3 3

path-difference between the light of the two sheared images. This azimuth was determined by rotating the plane of polarisation, by means of a rotatable half-wave plate, into a fixed direction such that the half-shadow device gave no contrast.

The film to be measured was deposited, with-a sharp edge, on glass and aluminised. The edge was set at right angles to the direction of shear and so appeared as a strip equal in width to the distance of shear. To effect the measurement the half-shadow edge was made to disappear against the strip and the azimuth angle noted; this was then repeated, but setting for disap- pearance against the background just outside the strip. The difference between the azimuth angles, as a fraction of 180 °, the gave twice then thick- ness of the film in wavelengths.

The half-shadow device consisted of a strip of "Cellophane" selected with a degree of birefringence such that it constituted a half-wave plate and immersed in Canada balsam with a small addition of monobromonaphthalene to match the refractive index of the cement to one of the two indices of the "Cellophane". As disappearance occurs when the plane of polarisation of the light is parallel to one of the principal directions of the "Cellophane", only one of the two indices is operative at disappearance; this avoids the impossible requirement that both indices shall be matched simultaneously, and was the reason for employing this particular optical system.

A dark line at the boundary of the half-shadow plate remained, however, and to reduce this the primary image was received on a rotating ground- glass screen and projected by an optical relay system into the plane of the half-shadow device.

With this system settirig accuracies of 4- 0.0014 ~ were attained under the best conditions. However, in practice, this accuracy was reduced by several considerations. A fine black line was still visible due apparently to imper- fections in cutting of the "Cellophane" sheet. A more disturbing feature was that while setting for disappearance on the strip the eye tended to be distracted by the contrast along the half-shadow edge outside the strip. This led to a setting error varying with the power of concentration of the operator and made the instrument somewhat fatiguing to use. A good observer could still obtain accuracies of 4- 0.0025 ~ in practice, but it was felt that this ~ccuracy was very modest in comparison with what should be obtainable.

3. Further experiments. In view of the above, it seemed necessary to remove altogether the image of the edge of the film from the field of view seen when making the photometric setting. Furthermore, it was desirable to increase the scale of the half-shadow device in order to reduce the effect of imperfections of cutting of the edge.

The system adopted is shown in Figure I. A shearing type of microscope

534 j. DYSON

was used with an objective of about 50 m/m focal length. Illumination was b y a totally reflecting prism occupying half the aperture, in order to avoid the changes of polarisation which would be caused by a half-silvered mirror. The other half of the aperture, from which the returning beam emanates, is imaged b y a lens L2 onto a ground-glass screen which is rotated b y a small motor. The light is scattered b y the ground-glass to fill the aperture of a lens Ls, which images the spot of light on the ground-glass into the pupil

\ yscr

I [ " - Wollaston Half shadow Ti l tabl ( pr ism Device planl parallel plat(

OPTICAL LAYOUT OF FILM MEASURING APPARATUS

FIG:I

of the obser~;er's eye. The observer therefore sees the aperture of L8 filled with light. The half-shadow device is placed in the beam close to L3 at a point where the diameter of the beam is about 15 m/m.

The light source is an illuminated slit which is imaged sharply onto the specimen. Two images are formed, and the edge of the film may lie between them or on either side.

As very high accuracy is aimed at it was desirable to keep the polarisation conditions unchanged throughout for each measurement, in order to avoid errors due to wavelength change or errors in the construction of half- and quarter-wave plates. This involved some form of compensator in the object space of the microscope. The simplest form would consist of means for tilting the object about an axis perpendicular to the plane of Figure 1, for a tilt 0 introduces a path-difference p between the two interfering beams, given by

# = 2s0 (1)

where s is the distance of shear. However, the tilts required are inconvenient- ly small (of the order of 0.1 seconds of arc per angstrom of step-height) and would require quite special mechanical arrangements. The same effect is produced by placing a very weak lens L1 of focal length F between object and objective. The lens can be moved in its own plane by a micrometer drive ; a translation of amount x then introduces a path-difference p given by

p = 2xs/F (2)

THE MEASUREMENT OF THIN FILMS BY INTERFEROMETRY 535

Evidently, the traverse x can be brought to a convenient value by a proper choice of F. The system can be calibrated by traversing the lens, using monochromatic light, and noting the micrometer readings for two successive disappearances of the half-shadow edge.

In order to measure a film it is necessary to make two settings, one with the film edge between the two images of the slit and the other with the edge lying to one side or other of both images. In view of the sensitivity to tilt shown b y (1) above it is undesirable to move the specimen mechanically, so a plane-parallel plate is placed between L1 and the object. Rotation of this plate into a position shown dotted in Figure 1 moves both images of the slit laterally by the required amount. There will be a small variation of the intensities of the two polarised beams due to the varying angles of incidence on the plate surfaces, but it is easy to show that this causes no error in the measurement.

The above apparatus has been set up experimentally and various forms of half-shadow device tried. Perhaps the best was a "Cellophane" sheet mounted as previously described. As this was viewed under much lower magnification than in the previous system the edge imperfections were negligible and it was possible for the first time to obtain a true disapperance of the edge.

With the quarter-wave plate omitted a thin plate of mica, immersed in a mixture of aniline and monobromonaphthalene, was used. A cleavage step of suitable height gave a practically perfect half-shadow edge.

Both these methods gave readings repeatable to within 4= 0.00028 wave- lengths of green light, corresponding to an error in step height of 4- 0.76A. As the errors for the two readings required to measure a film may be expected to add quadratically this corresponds to a thickness error of about 4- 1.0 A.

The system wiU operate in white light, so a half-shadow device consisting of two plates each giving about one wavelength retardation, placed edge to edge and with their principal directions at right angles, will enable the "sensitive t int" technique to be used. No suitable plates were available at the time, however.

The above figures represented the limit of reading of the micrometer screw used and it is possible that they may be improved upon. The utmost care was reqflired to avoid mechanical and thermal deformations of the apparatus during and between measurements; it was not found possible to repeat more than three or four readings to the degree of accuracy quoted because of slow drifts. These were accounted for by lack of rigidity in the experimental apparatus used, which incorporated "Plasticine" at certain points.

4. Practical considerations. In the construction of a practical film- measuring device to operate to this accuracy a number of points need

536 J. DYSON

careful consideration. The glass on which the film is deposited must be fiat to a high degree of accuracy. The minimum radius of curvature R for an accuracy of 1 A is given by

R = 2.107s 2 m/m (3)

This gives R = 800 metres for a shear of 0.2 m/m, corresponding to about 0.12 ~t of spherical curvature over a circle of 1 cm radius.

A wedge error in the plane-parallel plate will give a thickness error, for the angular deviation of the light will vary with the angular position of the plate. The required accuracy of construction can be calculated to be not above what can be achieved by careful optical workmanship. As the plate need only be a few millimetres thick, the required homogeneity and freedom from strain should not be difficult to achieve.

Much the same remarks apply to the lens L1. "The mechanical rigidity of the section holding the objective and object stage must be very carefully considered in view of the great sensitivity of the system to tilt of the object.

The use of the system in white light, employing the "sensitive t int" technique to make settings, offers the possibility of somewhat greater accuracy. However, a disturbing feature in this case is the dispersion with wavelength of the deviation produced by the Wollaston prism, which causes the path-difference introduced by a given shift of the lens L1 to vary with wavelength. The effect of this on the accuracy of measurement must be investigated; the result may well be that the method is limited to the measurement of extremely thin films. It may be possible to eliminate this effect by constructing L1 as a hyperchromatic doublet.

5. Conclusions. Recognising the very high setting accuracies obtainable in polarimetry, at tempts have been made to realise some of this accuracy in the use of a polarising interference microscope for the measurement of thin films.

Experiments have indicated that setting accuracies approaching 214000 can be achieved, corresponding to an error in determination of the film thickness of 4- 1 A approximately. The mean of a number of settings may be expected to give better accuracy if the apparatus be designed to avoid thermal and elastic movements.

It appears possible to use the apparatus in white light for very thin films, or for thicker ones" with certain design modifications. This point requires further consideration. It is evident that with certain obvious changes in arrangement the method can be used for measurements in transmission of transparent objects.

Acknowledgements. The author wishes to thank Dr. T. E. A l l i b o n e ,

T H E M E A S U R E M E N T OF T H I N FILMS BY I N T E R F E R O M E T R ¥ 5 3 7

F.R.S., Director of the Research Laboratory, Associated Electrical Industries for permission to publish this paper.

Received 23-2-58

R E F E R E N C E S

1) Z e r n i k e , F., J. opt. Soc. Amer., 40 (1950) 326. 2) D y s o n , J., J. opt. Soc. Amer., ~" (1957) 557. 3) S m i t h , F. H., Brit. Pat. 639,014, June 21, 1950.