The Measurement of Thin Film Thickness by Interferometry
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JOURNAL OF THE OPTICAL SOCIETY OF AMERICA VOLUME 41, NUMBER 6 JUNE, 1951
Letters to the Editor The Measurement of Thin Film Thickness
by Interferometry S. TOLANSKY
Royal Holloway College, University of London, Egham, Surrey, England (Received December 12, 1950)
IN a recent paper, Schulz1 has proposed, as an interferometrc method for measuring thin film thickness, a procedure in-volving a stepped Fabry-Perot interferometer, according to which the thin film is put down over half of an optical flat, and the whole flat is then coated with a transmitting silver film. The combination is matched against a silvered flat to form a stepped transmission Fabry-Perot interferometer, and, from the staggered ring patterns, the film thickness is obtained. Schulz compares this method with one of the (several) methods now in use in the author's laboratory,2 claiming advantages for the Fabry-Perot procedure.
Although, in fact, I considered a Fabry-Perot method several years ago, it was rejected on account of some optical defects to which attention may be drawn here in view of the proposal made by Schulz. The use of a related system using a stepped plane parallel interferometer with nonlocalized fringes of equal inclina-tion not differing effectively in practice from Fabry-Perot fringes, apart from localization, has already been described by the author3 mainly because of the peculiar intrinsic feature of offering enor-mous dispersion and not because it is in any way an improvement over other methods for measuring thin films.
The objections about to be raised to the system employed by Schulz do not apply to the methods described in reference 2, for which adequate descriptions have already been published; and in the following, the method of Schulz is compared with these other techniques.
Nature of the film.Schulz describes a transmission Fabry-Perot procedure which will be considered in the first instance. If a trans-mission Fabry-Perot method is to be used, then it should be restricted to the measurement of transparent nonmetallic films of low inherent reflectivity. For if the thin film to be measured is of metal, then
(a) The resulting reflecting coefficients in the two halves of the composite interferometer can often differ considerably on the composite plate leading to two fringe patterns with different fringe widths;
(b) The reflected light from the composite metal film will suffer a phase change different to that experienced by the light reflected from the region of single film, introducing thereby false thickness values;
(c) If the film to be measured is thicker than perhaps 75 A, then the intensities of the fringe system passing through the composite film will be considerably reduced relative to that passing through the single film, an undesirable feature from every point of view. Practically no light will pass through a compound metal film whose thickness exceeds 700 A, and it is clear that this alone re-stricts applicability to films thinner than 250 A; for the film which is to be less than 700 A thick is built up from the original film together with a superposed film that should certainly be no thinner than 450 A if reasonable definition is required from the single-film region of the composite plate;
(d) Since the compound film must be transparent, there is even the distinct possibility that the effective phase change on reflec-tion will be affected by the substrate, be it either metallic or non-metallic. (Without further exploration, it is dangerous to use the method even for transparent dielectric films if their refractive indices differ appreciably from that of the glass flat);
(e) Serious is the fact that the thicker the metal film to be measured the thinner must be the superposed silver film, which means poor definition in the single-film region, with progressive fall-off in sensitivity, and progressive increasing difference in the sharpness of the two sets of fringes.
Localization.A defect which Schulz does not neglect is the fact
that the fringes are at infinity, while the film step edge is localized on the interferometer. With normal camera apertures, both fringes and step edge cannot be simultaneously photographed. The inter-ferometer could, of course, be removed to a considerable distance from the camera lens, which in turn could be stopped to a small aperture, producing thereby a depth of focus which could extend from the interferometer to infinity. So inefficient a system is not practical for photography. I t is in effect put forward by Schulz, who is obliged to place a pinhole before his eye in order to see both fringes and step edge in reasonable focus. This focal defect ex-cludes the use of microscopy and thus prevents examination of small local areas. I t restricts the Schulz procedure to direct visual observation.
Fringe width.It has been established in this laboratory that for a given reflectivity, the best attainable Fabry-Perot fringe width is somewhat inferior to that of correctly produced localized fringes, for which there are several reasons. In the first instance, errors in flatness and in parallelism integrate to affect all the Fabry-Perot fringes. It has been established that good quality plate glass, or even merely fire drawn unpolished glass, is fre-quently locally smooth and flat to better than /300, often over areas of many square millimeters. As a result of this, one obtains, with localized fringes, practically the theoretical fringe width for a given reflectivity, and it is not at all difficult for this width to be l/50th of an order (i.e., /100), permitting high accuracy in setting on a fringe (see, for example, the fringes shown on p. 149 of reference (2)).
A further point is that of chromatic resolving power and line width of the source, the familiar problem in the study of hyper-fine structure with the Fabry-Perot interferometer. A Fabry-Perot interferometer with plate separation of 500 yellow wavelengths, which is the minimum required by Schulz, has the appreciable chromatic order separation of 17 cm-1, from which it follows that a natural line width of only 0.24A (for the sodium lines) alone produces a broadening of l/20th of an order, and this has to be added to the instrumental width which in itself exceeds the theoretical width calculated from the reflectivity. With the hot bright sources frequently needed for thin film inter-ferometry (particularly if microscopy is also used in the examination of small areas), line widths often far exceed this value. The notoriously broad resonance D lines are perhaps not too happy a choice by Schulz in this respect. I t is primarily because of the use of very small plate separations in work with localized multiple-beam fringes that the chromatic resolving power in the latter case can often be some hundreds of times less than the figure given above, with correspondingly proportionate large tolerance in line width, thus permitting the use of intense sources, which in their turn allow the use of very dense silverings, leading to fringe sharpness normally unattainable by Fabry-Perot instruments using much larger plate separations. With single silver layers (i.e., excluding multiple sandwich films), I have never succeeded in producing Fabry-Perot fringes with sharpness at all approaching that attainable with localized fringes.
Computation.A primary distiguishing feature of the method proposed by Schulz is the use of the two NaD lines for computation, together with a displacing screw. This, of course, demands a certain degree of mechanical accuracy in design. The method is optically of some interest but is not a very great improvement on existing simple methods of measuring steps interferometrically, either visually or photographically, or indeed for the highest precision by microphotometry.
Limitations.Apart from other minor defects noted already by Schulz, there remains a further objection. For by the very method of fringe formation, all variations in film thickness within the area illuminated combine to give an average value. The accuracy of 15A given by Schulz is therefore a mean value only. I t is not helpful to note that the method is excellent with uniform films, for on what criterion can it be stated that a given film is uniform if the technique is unable to reveal local lack of uniformity? In this respect, localized fringes are superior, because quite small local variations are immediately revealed.
426 L E T T E R S T O T H E E D I T O R Vol. 41
In this laboratory, considerable experience has now been gained in interferometric thin film measurements, using both reflection and transmission systems with multiple-beams including Fizeau fringes, fringes of equal chromatic order, localized white light fringes of superposition, nonlocalized circular fringes, fringes with curved films, and finally Fabry-Perot fringes. Of these, the most satisfactory are the reflected fringes of equal chromatic order. Reflected multiple-beam Fizeau fringes are a very reliable alternative.
It may perhaps be added that Schulz is not quite correct in con-sidering that the separations between the surfaces, as used in this laboratory, are not under control. Control is generally achieved to within small fractions of a light wave by simple mechanical jigs, such control being a self-evident necessity when operating with high dispersion. Perhaps he has been misled by statements I have made on the difficulty of control in the specific instance of match-ing flexible thin wrinkled mica sheets against optical flats.
If the Fabry-Perot system is at all to be used, then some of the above objections are removed if it be used in reflection in accord-ance with the principles already developed for high resolution-reflection Fabry-Perot spectroscopy,4 but several of the objections still remain. It is concluded that while the Schulz method is un-doubtedly of some interest, it is not equal in flexibility or precision to methods already in use. Perhaps it offers a little advantage in speed, but, in general, no case has been made for discarding other methods in favor of this proposed new technique.
1 L. G. Schulz, J. Opt. Soc. Am. 40, 690 (1950). 2 S. Tolansky, Multiple-Beam Interferomelry (Clarendon Press, Oxford, 1948).
3 S. Tolansky, Multiple-Beam Interferomelry (Clarendon Press, Oxford, 1948), p. 179. 4 S. Tolansky and J. D. Ranade, Monthly Notices Roy. Astron. Soc. 109, 86 (1949).