9 Optical Methods for thickness measurements

Learning Objective:

1.      The importance of measurement of film thickness.

2.      Multiple-beam Interference based film thickness measurement techniques.

3.      Detail study of Measurement of thickness using ‘Fizeau Fringes (Tolansky Technique).

4.      Fringes of equal chromatic order (FECO) method for the measurement of film thickness.

Introduction

All the films have surface thickness and therefore when the thickness of the surface layer is of the order of a fraction of the millimeter this called the thin films. The thin films may be of metallic it is called metallic thin films. The thin films may be of polymers are called polymers thin films. Thin film is deposited on the smooth surface of substrate in order to get well-defined edge, and a highly reflecting opaque layer. It is important to measure the thickness of thin film as the electrical, optical and structural property of the material varies drastically from the variation in thickness of the film. The most preferred technique for a specific application or process, depends upon the film type, the thickness of the film, the accuracy desired, and the use of the film. The important criteria include properties such as film thickness, film transparency, film hardness, thickness uniformity, substrate smoothness, substrate optical properties, and substrate size. In many cases there is no single best technique. The most useful techniques for determining film thickness include Multiple beam interference – quartz crystal- ellipsometric- stylus techniques.

1. Optical Methods

Optical techniques for the determination of film thickness are mostly used. They are applicable to both opaque and transparent films, yielding high accuracy in thickness values measurement. In addition, measurements are quickly performed, frequently nondestructive, and utilize relatively inexpensive equipment. In the present module Multiple beam Interference will be discussed in details.

2. Multiple-beam Interference

If the interference occurs between two or more beams, the sharpness of the fringes increases markedly, this can be accomplished if the reflectivities at the two interfaces are very high as shown in Fig. 1. In Fig.1, R and T represent the amplitudes of reflection and transmission. In Fig. 1 it can be observed that each of the two parallel glass plates has a thin partially transparent metallic film (e.g. Silver) indicated by CDFE and IJLK deposited on surfaces facing each other. Another condition for multiple-beam interference is small absorptivity (A) of the metal film through which light must be transmitted. In the case of multiple beam reflection, only the metal film CDFE needs to be moderately transparent with low absorp-tivity, whereas for multiple-beam transmission both metal films must have low absorptivities.

 

Phase changes occurring on reflection are not considered in equation (2).

F is the “co-efficient of fineness.” This coefficient is a measure of sharpness of the interference fringes. With properly evaporated metal films, a reflectivity of near 0.95 is possible, which gives a value of F of over 1,200. Thus, as long as sin ( ‘ /2) has any significant value, the intensity of the transmitted light (I) is very small, as can be seen from Eq. (1). If sin ( ‘/2) becomes zero, ‘I’ reaches the maximum intensity of ‘Imax’. This occurs only if ‘ is an integral value of 2π and therefore, very sharp interference fringes with intensity maxima for integral values of N are observed. In the case of multiple-beam interference by reflection, the interference pattern forms interferogram which is just the opposite of that seen in transmission provided the absorptivity is small. In other words, where there are sharp, bright fringes on a dark background in transmission for integral values of N, observation of the reflected light gives sharp, dark fringes on a bright background.

With an increase in the absorption ‘A’, the intensity of the entire transmitted pattern is decreased by [T/(T + A)]². In the reflected-fringe system, however, an increase in the absorption ‘A’ prevents the fringe minimum from going to zero. Hence, with larger ‘A’, the reflected fringes tend to diminish under the same conditions where they would still be seen on transmission. Consequently, to obtain a sharply delineated reflected-fringe system, the absorption ‘A’ should be kept to a minimum. In addition to the requirements of high reflectivity and small absorption for good quality fringes, the distance between the plate i.e. ‘t’ should be kept as small as possible. From Equation (2), it can be seen that there are various factors that contribute to the development of fringes. Fringe systems are recognized according to the method of fringe formation, and two cases are distinguished in multiple-beam interferometry. Fizeau fringes are generated by monochromatic light and represent contours of equal thickness arising in an area of varying thickness t between two glass plates similar to those shown in Fig. 1. This is accomplished by contacting the two glass plates such that they form a slight wedge at an angle ‘α’ so that ‘t’ varies between the two plates. The angle ‘α’ is generally made very small so that consecutive fringes are spaced as far apart as possible. The angle of incidence ‘ ’ is typically kept near 0⁰ and the medium is air (n1 = 1.0). Hence, the spacing between fringes corresponds to a thickness difference of λ/2, where λ is the wavelength of the monochromatic radiation being used.

Second multiple-beam interferometry technique is referred to as fringes of equal chromatic order (FECO). In this case, white light source is made to focus at an angle of incidence of 0o and the reflected or transmitted white light is dispersed by a spectrograph, thus offering a means of varying wavelength ‘λ’. According to equation (2), fringes will form for certain values of t/ λ. Then, FECO fringes can be obtained with the two metal surfaces parallel to each other, whereas the plates must be inclined relative to each other to produce Fizeau fringes. The spacing between fringes on the interferogram (or spectrum) is inversely proportional to the thickness.

Multiple-beam interferometry for the measurement of film thickness can be implemented by the method of Donaldson and Kharnsavi, which is shown in Fig. 2. The arrangement differs from Fig. 1 in that the substrate GHJI supports a film KLMI whose thickness is to be measured. A highly reflective opaque metal film NKJO is evaporated on top of the film KLMI. Silver films of about 1,000 A0 thicknesses are typically used for this purpose. The step LM in the original film may be formed either by etching the film after deposition or by masking the MJ part of the substrate during deposition. Evaporated silver replicates such steps accurately: the bottom surface of the reference plate ABCD has a thin, highly reflective, semitransparent film as in Fig. 1. To produce Fizeau fringes, the reference plate ABCD is inclined at an angle with respect to the substrate underneath it, as shown in Fig. 3 In the case of FECO fringes, the film substrate and optical flat are parallel to each other. The distance between the plates is adjusted according to the film thickness since the magnification, i.e., the spacing between the fringes on the interferogram, increases with decreasing separation between the plates.

The film KLMI may be either opaque or transparent in these techniques. The requirements for the methods are that a step or channel can be made in the film down to the substrate surface, that the substrate is fairly flat and especially smooth, that the film itself has a smooth surface for fringe formation, and that the film should not be altered by the deposition of the reflective coating. For example, some organic films are altered by the heat generated during the evaporation of the reflective metal and should not be measured by this technique.

3. Measurement of thickness using ‘Fizeau Fringes (Tolansky Technique)

The use of Fizeau fringes for thickness measurements is commonly called the Tolansky technique in recognition of Tolansky’s contributions to the field of multiple-beam interferometry. A schematic representation of Fizeau fringes produced by multiple-beam interference is shown in Fig. 3.

The film thickness is given by d = ΔN λ /2 where ΔN is the number of fringes.

 

Fig. 3 Schematic view of apparatus for producing multiple –beam Fizeau fringes

In the interferogram based on Tolansky Technique shown in Fig. 3, the depth of the channel (or the film thickness) is exactly one-half of the separation between fringes (ΔN = 0.5), and therefore the film thickness is λ./4. If the wavelength were that of the green mercury line, the film thickness would be 1365 Å. Commercial microscopes which utilize Fizeau multiple-beam interferometry are available. In addition, conventional metallurgical microscopes can be easily equipped with Fizeau plate attachments for interferometric measurements. These plate attachments are generally equipped with three adjustable screws to determine the tilt of the plate relative to the specimen and thus control the direction and spacing of the interference fringes. Accurate thickness measurements require careful evaluation of fringe fractions which can be measured by a calibrated microscope eyepiece or photomicrograph of the fringe system. Either way, the evaluation requires a linear measurement, the accuracy of which is strongly dependent on the sharpness of the fringes. This would require the optical flat (Fizeau plate) to have high reflectivity and low absorptivity. Two other prerequisites for an accurate thickness measurement are:

(1)   Smooth and flat film surface

(2)   Monochromatic light source.

Thickness measurements from 10 nm to 2 µm can be made with an accuracy of ± 3 nm.

 

4. Fringes of Equal Chromatic Order (FECO)

Fringes of equal chromatic order are more difficult to obtain but yield greater accuracy than Fizeau fringes, especially if the films are very thin. Figure 4 presents the basic principle of the apparatus for FECO.

Collimated white light impinges at normal incidence on the two parallel plates. The reflected light is then focused on the entrance slit of a spectrograph. The image of the channel in the film must be perpendicular to the entrance slit of the spectrograph. Assuming an angle of incidence of = 0°, then sharp, dark fringes occur for integral values of N = 2t/ λ, as shown in Fig. 5 for two different plate spacing t. Fig. 5. (a) represents the interferogram for parallel plate spacing of 2 m, Fig. 5 (b) represents interferogram for the same parallel plate spacing but with a channel 1000 Å corresponding to film thickness of 1000Å .

The fringes are observed as the wavelength λ is varied by the spectrograph and are recorded on a photographic plate corresponding to λ = 2t/N. The resulting interferograms are shown schematically in Fig. 5 where the scale is assumed to be linear in wavelength. With a linear-wavelength scale, the fringes are not equidistant in the interferogram. The order of the fringe increases with decreasing wavelength of the fringe.

 

It is sometimes preferable to give the order as N = 2tѵ, where ѵ is the reciprocal wavelength or the frequency in wave numbers, as this relation shows N to be linear with wave number. However, this linearity is not found to be exactly true if the phase changes at the two reflecting interfaces vary with wavelength. Hence, there may be a slight dispersion with wavelength, but the effect of phase change on the determined fringes is very small. In practical cases, the spacing between plates is not known, so a prior assumption is made as the hypothetical case shown in Fig. 5. It is therefore necessary to deduce‘t’ as well as N from the wavelengths of the observed fringes. If N1 is the order of a fringe corresponding to wavelength λ1 , then N1 + 1 is the order of the next fringe with a shorter wavelength λo on the interferogram. Neglecting the small phase-change dispersion, we have

 

Summary:

5.      In this module we have come to know about the importance of film thickness.

6.      Explored Multiple-beam Interference based film thickness measurement techniques.

7.      Studied about Measurement of thickness using ‘Fizeau Fringes (Tolansky Technique).

8.      Also explored Fringes of Equal Chromatic Order (FECO) method to measure thickness of films.

List of References and Suggested Reading

• Thin Film Materials- Stress, Defect Formation and Surface Evolution By L. B. Freund
• Handbook of Thin Film Technology-By Leon I. Maissel, Reinhard Glang
• The Material Science of Thin film by M. Ohring