Abstract
Thin film technology is an area of great importance in current applications of opto-electronics, electronics, MEMS and computer technology. A critical issue in thin film technology is represented by residual stresses that arise when thin films are applied to a substratum. Residual stresses can be very large in magnitude and may result in detrimental effects on the role of the thin film must play. For this reason it is very important to perform "online" measurements in order to control variables influencing residual stress. The research work presented in the paper represents the first step towards the practical solution of such a challenging problem. A methodology to measure residual stresses utilizing reflection/projection moire interferometry to measure deflections of thin coated specimens is developed. Results are in good agreement with experimental values provided by well established measurement techniques. A special optical circuit for the in situ measurement of residual stresses is designed trying to satisfy the constraints deriving from the tight geometry of the vacuum system utilized to carry out the deposition.
INTRODUCTION
Thin film technology has great importance in opto-electronics, electronics, MEMS and computer technology applications. A critical issue in thin film technology is represented by the presence of residual stresses that develop when thin films are applied to a substratum. Residual stresses arise because of the existence of discontinuous interfaces, inhomogeneous thermal history during deposition or subsequent fabrication process, and various imperfections by ion bombardment [1]. Residual stresses may affect significantly mechanical properties and reliability of the thin film as well as the performance of thin-film based devices: in particular, high residual stresses will result in detrimental effects on the role that the thin film is designed to play.
Experimental techniques for measuring residual stresses in thin films are critically revised in Ref. [2]. In general, there are two possible approaches to this problem: (i) lattice strain based methods, including X-ray diffraction and neutron diffraction; (ii) physical surface curvature-based methods. However, the measured values of residual stress may be quite different because the former methods provide local information while the latter methods provide average values. Lattice-based methods rely on the principle that residual strains and hence residual stresses are caused by the relative displacement between atomic planes: therefore, the variations of lattice spacing are measured. However, these methods are rather expensive in terms of experimental equipment and can be used only if the films are crystalline. Determination of residual stress through curvature measurements is relatively easy to perform by the experimental point of view. The average level of residual stress can be found by using the classical Stoney’s equation [3,4] which is valid when the coating is much thinner than the substrate. Nanoindentation is the most recent approach to the problem of measuring residual stresses in thin films: this is done by observing how the force-indentation curve changes with respect to a stress free surface (see, for example, the discussion presented in Ref. [1] and the references cited in that paper). Among curvature measurement methods, non-contact optical techniques are preferable in view of their high sensitivity and because they do not alter the specimen surface. Classical interferometry (i.e., Newton’s rings) [5] or moire techniques [6] can be used for measuring curvatures. Reflection moire allows to measure the slope of a reflective surface and, through differentiation of the fringe pattern in the frequency space, the curvature of the surface. Projection moire measures the height of a surface with respect to a reference plane. A system of lines is projected onto the specimen surface and modulated by the curved specimen. The topography of the surface can be obtained from the phase difference generated by the modulation of the grating lines due to the surface curvature. The reconstructed surface can be fitted by a mathematical function and then differentiated in order to compute curvature values.
Variables influencing residual stress could be controlled by performing in situ measurements of quantities such as deflections and curvatures that are directly related to stress. This work represents a first step towards the practical solution of such a challenging problem. For that purpose, a reflection moire interferometry setup is developed. The novelty is in the fact that the optical setup is now utilized in the projection moire mode: therefore, the experimental setup measures displacements but not slopes. The validity of the optical setup developed in this paper is tested in the measurement of residual stress developed in a diamond-like-carbon (DLC) thin film deposited on a quartz substratum via Plasma Enhanced Chemical Vapor Deposition (PECVD). The value of residual stresses developed in the film and in the substrate are finally derived from the average curvature of the DLC specimen determined via moire measurements. The optical circuit is then adapted to the vacuum system utilized to make the deposition taking care to satisfy the tight geometry constraints posed by the layout of the deposition reactor.
STRESS ANALYSIS OF THE THIN FILM
In the Plasma Enhanced Chemical Vapor Deposition (PECVD) process for thin films, an electric discharge generates film precursors, such as neutral radicals and ions, by electron-impact decomposition. Significant residual stresses can develop in the coated specimen because the atoms passing from the gas phase to the substrate during the adsorption process do not reach their correct position in the reticular structure finally formed. The energetic ions cause atoms to be incorporated into spaces in the growing film which are smaller than the usual atomic volume. This leads to expansion of the film outwards from the substrate. In the plane of film, however, the film is not free to expand and the entrapped atoms cause macroscopic compressive stresses. Figure 1 shows the stress distributions developed in the coating and in the substrate by the deposition process. The coating/substrate system can be considered as a plate subject to bending. Since the substrate is much thicker than the coating, it will present the classical bi-triangular stress distribution while the compressive stress field in the coating can be considered uniform.
Figure 1. Schematic representation of stresses developed in the coating and in the substrate Following the Kirchhoffs plate theory, stress components can be expressed as:
where: w(x,y) is the out-of-plane displacement experienced by the middle plane of the substrate; z is the distance from the middle plane measured in the direction of the curvature radius; Es and vs are respectively the Young modulus and the Poisson ratio of the substrate material. If the thickness of the deposited film ff is much smaller than the thickness of the substrate ts (i.e. tf<<ts), tensile stresses developed at the top surface of the substrate will be 4/3 times as the corresponding stress values computed with Eq. (2) while compressive stresses developed at the bottom surface of the substrate will be 2/3 times the corresponding stress values computed with Eq. (2).
The average value of compressive residual stress afilm developed in the thin film can be computed with the modified Stoney’s equation:
where R is the radius of curvature taken by the specimen after the deposition process while Ro is the radius of curvature prior to deposition. If one assumes that the initial curvature is not significant, Eq. (3) simplifies to:
EXPERIMENTAL SETUP
In this study, a reflection moire setup was developed in order to precisely measure the deflection produced by the deposition process. However, the novelty is that the reflection moire setup is used in the projection moire mode thus providing displacement values rather than surface slopes. Figure 2 shows the schematic of the optical set-up adopted for determining the out-of-plane displacement field w.
Figure 2. Schematic of the optical set-up used in the residual stress measurements
The set-up is comprised of two principal systems: the projection system (PS) and the acquisition system (AS). The optical axis of the projection system is inclined with respect to the optical axis of the acquisition system by the angle a=20°. The projection system includes the laser source L, the polarizer P, the microscope pin-hole system PH, a first lens L1, a grating G, a second lens L2, the iris IR and a third lens L3. The acquisition system includes a microscope M fixed on a CCD camera. The acquired images have been processed by means of the Holo Moire Strain Analizer (HMSA) software developed by Sciammarella and his collaborators [7].
The coherent and polarized light beam generated by the 35 mW He-Ne laser, passes through the polarizer P that decreases its intensity. A 40* magnification microscope expands the laser beam and a pin-hole system removes the noise effects produced by the diffraction phenomena which may occur in beam expansion. The pin-hole diameter is 10 |m. The exit pupil of the pinhole system is located in the focal plane of the first lens L1 and therefore the wave front that comes out from lens L1 is plane. The collimated beam passes through a Ronchi Ruling grating G including 500 lines/in (this corresponds to a nominal pitch of 50.8 |m). The beam passes through a second lens L2 that in its own focal plane, placed at the f2 distance, produces the Fourier transform of the light wave diffracted by the grating G. In that focal plane, there is placed an iris IR opened in such a way to let pass orders 0 and/or ±1. Higher diffraction orders were filtered out in order to reduce the noise. The lens L3, that has the same focal length of lens L2 and is placed in such a way to have the iris lying in its focal plane, collimates again the light beam. The collimated wave front carrying the filtered spectrum of the grating is projected onto the reference plane which is basically a mirror onto whose surface is attached the specimen SP to be analyzed.
The light wave front that hits the mirror or the sample is reflected back to the sensor of the CCD camera. However, this does not mean that the utilized set-up works in the reflection moire mode. In fact, the CCD camera is focused right on the plane of the sample and not in the reference plane. Consequently, the distribution of light intensity I(x,y) recorded by the camera at each pixel (x,y) of the image can be expressed as:
where: Io is the background intensity; I1 is the amplitude, pj is the pitch of the projected grating onto the specimen; a is the angle between the optical axis of the projection system and the optical axis of the acquisition system, ^c(x,y) is the phase modulation term. Therefore, the intensity distribution I(x,y) corresponds to the out-of-plane displacement of the plate with respect to the reference plane, not to the surface slope as it would be in the classical case of reflection moire. Preliminary analyses indicated that if the refection moire were to be adopted, fringe orders related to slope surface and fringe orders related to out-of-plane displacement cannot be distinguished. This leads to incorrectly evaluate phase. The reason for this is that, in general, when surface curvature is large, fringe orders can be very distorted to such an extent that it is practically impossible to correctly reconstruct the phase signal.
It should be noted that the iris aperture was regulated in such a way that orders 0 and ±1 could pass. The choice to allow the passage of the order +1 or the passage of the order -1 (in addition to the background order 0) was done in purpose to account for the Talbot effect, i.e. the physical phenomenon that regulates the process of projection of a grating onto the surface to be investigated. The Talbot effect produces a periodic propagation in the space of the projected grating. Periodicity depends on the grating pitch and wavelength of light. Another effect strictly related to this phenomenon is that at the focal distance f2 the diffraction orders ±1 will recombine thus generating one grating. At a distance different from f2, diffraction orders ±1 will separate thus generating two different fringe orders that interfere and produce moire fringes. Since the plane containing the specimen cannot be perpendicular to the laser beam but must rotated in order to allow light to be reflected back to the sensor, it can be understood that because of Talbot effect, if both orders ±1 were allowed to pass different fringe orders would create and interfere thus altering the signal of the function w(x,y). Conversely, since only the order +1 or the order -1 was allowed to pass together with the background order, such a problem was eliminated thus making it easier to reconstruct the phase function. The sensitivity As of the moire setup is:
where: pj is the pitch of the projected grating; 01 is the angle formed by the optical axis of the projection system with the direction normal to the reference plane; 02 is the angle limited by the optical axis of the recording system and the direction normal to the reference plane. From the schematic of the moire setup shown in Figure 2 it follows a=01+02. Since 01=02 it is a=201.
As is mentioned above, the classical reflection moire technique gives in output directly the slope of the surface, i.e. the first derivative of the displacement function w(x,y). This quantity is obtained optically following a principle similar to finite differences. Consequently, the coordinate where derivative takes a given value remains indefinite within the range where finite difference is determined. Since the specimen is very small the error that could be introduced by following this approach would be very significant. For this reason, it was chosen to use reflection moire as a method to determine displacements and not derivatives.
A microscope (denoted as M in the schematic of Figure 2) was coupled with a CCD camera able to focus planes located at a distance greater than 50 cm. The field of view of the sensor was as large as the DLC specimen (i.e. 1 cm2) under investigation. The microscope includes an auxiliary lens and a 2X lens to maximize resolution. Figure 3a shows the assembly view of the optical setup while Figure 3b shows the detail of the reference plane with the specimen attached. A high precision frame onto which the reference plane is fixed allowed the reflected beam to be lined up with the axis of the CCD camera.
MOIRE LABORATORY MEASUREMENTS IN SITU IMPLEMENTATION OF THE MOIRE SETUP
The moire setup described in Section 3 was tested in the residual stress measurement of a diamond-like carbon thin film deposited on a quartz substrate. The specimen was circular in shape with a diameter of 1 cm. The nominal thickness of the substrate was 2 mm (i.e. 2000 |m) while the nominal thickness of the coating was 500 nm. Average values of elastic properties of the quartz substrate were selected from material databases as follows: E=94 GPa and v=0.17.
The grating utilized in the experiments included 500 lines/in: the corresponding nominal pitch hence is 50.8 |m. The angle of illumination 01«13° was measured by analyzing the change in spatial frequency of the projected grating when no specimen is mounted onto the reference mirror. Cares were taken so to realize the nominal condition of reflection where 61=92 the most as it was feasible. The corresponding projected pitch pj=p/cos91 is 52.14 |m. From Eq. (5), sensitivity can be computed as pj/(2tan01), that is 112.9 |m.
Figure 3. Moire setup utilized in the residual stress measurement: a) 3D assembly view; b) Detail of the reference plane and the DLC specimen .
Prior to executing the moire test, the curvature of the DLC specimen was measured by means of the Newton’s rings interferometric technique. A total of 33 rings were seen to form on the specimen surface. The specimen was properly positioned so to lie in the center of the image field. The total deflection 8DLC of 10.44 |m was measured as the product of the number of interference fringes formed (i.e. 33) and the measurement sensitivity which is half of the wavelength of the He-Ne laser light (X=632.8 nm) used in the experiments. Therefore, we have 8DLC=33×0.3164=10.44 |m. Since the maximum deflection to be measured was about 1/10 of the sensitivity of the moire setup, the nominal grating pitch was rated good for carrying out the moire experiments.
Figures 4a and 4b show respectively the phase maps obtained for the specimen surface and the reference plane. The corresponding phase difference is shown in Figure 4c. As expected, the phase difference is less than one order. However, it is very difficult to achieve the condition of parallelism between the specimen surface and the reference plane. This effect was corrected with a MATLAB routine and the displacement map finally obtained is shown in Figure 5. The resulting out-of-plane displacement measured by the moire setup hence is 11 |m, which is a value very close to the corresponding displacement measured by means of the Newton’s rings interferometric technique. It should be noted some distortion was observed in the shape of the rings but no correction routine was implemented for that pattern as the goal of the interferometric measurement was just to have information on the order of the magnitude of the expected deflection. However, this may explain the difference observed between the two measurements.
The MATLAB datafile was further processed in order to extract profiles and derive the value of the radius of curvature. The radius of curvature of the DLC specimen extrapolated from MATLAB is 1.598 m. By substituting this value in the Stoney’s formula (3mod) and assuming a film thickness of 500 nm, which is a rather usual value for DLC coatings, it follows that the compressive residual stress afilm developed in the film is 93.9 GPa. This value seems to be very large compared with data usually reported in literature which indicate film stress values in the range of few GPa. The out-of-plane displacement measured with moire 11 ^m is very close to the deflection computed with the Newton’s rings 10.44 ^m, the difference is 5 %. Since the two measurements are completely independent, one can consider the value obtained
Figure 4. a) Phase of the specimen surface; b) Phase of the reference plane; c) Phase difference
Figure 5. Distribution of out-of-plane displacement determined for the DLC specimen
Since the two measurements are completely independent, one can consider the value obtained from the moire as correct. The discrepancy in the value of the residual stresses obtained with the utilized sample is currently under investigation.
IN SITU IMPLEMENTATION OF THE MOIRE SETUP
A special optical circuit was designed for the in situ monitoring of residual stress developed during the thin film deposition process. Figure 6a shows the device for film deposition equipped with the moire system developed in this research. The moire device is now physically located in the Thin Films Laboratory of the Italian National agency for new technologies, Energy and sustainable economic development (ENEA), Mesagne (Italy). The tight constraints on geometric layup of the deposition device have required some modifications of the optical setup with respect to the laboratory setup described in the preceding paragraphs.
The reactor includes two large windows that have been used as an access window for carrying the illuminating wave front and as outlet window for recording fringe patterns. The projection system has been mounted onto a prismatic arm rigidly supported in order to realize an angle of illumination of 10° with respect to the horizontal plane. The grating is then projected onto the specimen to be analyzed by the composite prism system schematized in Figure 6b. Preliminary analyses have indicated that the optimal range of grating spatial frequency is 300 lines/in, which corresponds to a nominal pitch of 84.7 |m. Although this decreases the sensitivity to about 200 |m per fringe, it is still possible to sense displacements of the order of few microns [8].
Figure 6. a) Device for thin film deposition with 3D view of the projection system; b) Schematic of the prism that carries the projected grating onto the specimen surface.
The deposition reactor has three plates that can rotate about their vertical axis. These plates are in turn placed on a rotating platform. The composite prism system was fixed above the plate closest to the exit window. In order to simplify measurements and avoid damage of the prism surface, film deposition was allowed only in correspondence of the plate located at the longest distance from the exit window. Furthermore, revolution of plates about their axis was disabled. One concern was that the eventuality that the luminescence induced by the deposition process would have affected the intensity distribution of the modulated grating recorded by the CCD sensor. However, this was found not to be a problem either because deposition was done far away from the prism and the color of light emitted in the deposition process was light violet, thus not overlapping with the CCD camera spectrum.
SUMMARY AND CONCLUSIONS
The research work presented in the paper is the first step towards the application of moire to the in situ measurements of residual stresses generated in thin films during the deposition process. A reflection moire method working in the projection mode was developed and tested in the case of diamond-like carbon film. The largest deflection measured for that specimen was found to be in good agreement with interferometric measurements independently carried out. The corresponding stress value in the film is however large compared to values usually reported in literature. This does not invalidate the present measurements which were totally consistent with other experimental data in terms of values of deflection and radius of curvature. The device was then implemented in a real device for thin film deposition. The original setup was adapted to the rigid geometric layout of the reactor. Measurements carried out on four ZrN specimens with different film thickness (from 200 to 400 nm) and different temperature of deposition (from room temperature to 600°C) indicated the presence of compressive residual stress values of about 30 GPa. The corresponding measurements with Newton’s rings provided instead values of residual stress ranging between 22 and 50 GPa. These values are now of the same order of magnitude of data recently reported in literature [9]. Furthermore, significant statistical dispersion is reported for different conditions of deposition.
