Ellipsometry of reflected and scattered fields for the analysis of substrate optical quality

Transcription

1 Ellipsometry of reflected and scattered fields for the analysis of substrate optical quality Carole Deumié, Oliver Gilbert, Gaelle Georges, Laurent Arnaud, and Claude Amra Specular ellipsometry is a well-known and efficient technique to characterize surfaces and coatings. This technique has been extended to the measurement of scattered light. We present an experimental setup, using a polarization modulator, which permits us to characterize transition layers and roughness without a calibration procedure. Experimental results are presented concerning transition layers for damage threshold applications and for rough surfaces or bulks Optical Society of America OCIS codes: , , , Introduction Ellipsometry is a technique that has been used for decades to study specular reflection and transmission from surfaces and coatings. 1 6 In this case the analysis of intensity and phase terms provides information about low-frequency averaged parameters such as thickness, indices or effective indices, etc. These techniques have been extended to the study of diffuse reflectance; that is to say, the quantity of light scattered by a rough surface at specular directions. 4,7 This tool was then completed by a study of the scattered field at each direction in space This complementary technique is called ellipsometry of angle-resolved scattering and was illustrated for the analysis of interferential microcomponents. In the case of high-quality optics and multilayers, and thanks to first-order electromagnetic theories, some key results and predictions concerning the discrimination of surface and bulk effects in substrates and multilayers were obtained. In the present paper we describe an evolution of the experimental method of the phase parameter measurement. The precision and rapidity of measurements have been increased owing to the addition of a polarization modulator, and we show that the relative study of harmonics permits us to analyze the reflected or the The authors are with the Institut Fresnel, Unité Mixte de Recherche Centre National de la Recherche Scientifique 6133, Ecole Généraliste d Ingénieurs de Marseille, Université Paul Cézanne Aix- Marseille III, Université de Provence Aix-Marseille I, Domaine Universitaire de St. Jérôme, Marseille Cedex 20, France C. Deumiè s address is carole.deumie@fresnel.fr. Received 2 March 2005; revised 25 July 2005; accepted 13 August /06/ $15.00/ Optical Society of America scattered field without calibration of levels. Conclusions appear to be successful and offer a complementary tool to further the investigation of the optical quality of substrates (transition layer, roughness, bulk effects, etc.). 2. Principle of Measurements with Polarization Modulation Let us consider a sample lighted under an incidence angle i by a monochromatic plane wave. A polarizer and a piezo-optic polarization modulator are introduced on the incident beam. This component is made of a Homosil silica bar modulated at its resonance frequency 51 Hz. The mechanical fixation of this component can produce a residual static anisotropy, represented in the following equation by the phase term m between the proper polarization states s and p, defined with the incidence plane (Fig. 1). The reflected intensity is measured after an analyzer. The polarization modulator was added to increase the acquisition data speed. Such a device introduces a phase difference M t between its proper polarization states: M t 0 sin t M. The modulation frequency is 51 khz. The modulation amplitude 0 can be modified with electric voltage; M is the residual birefringence (order of magnitude of 1 to 2 ). The analyzer introduced on the reflected beam permits us to project both components E s and E p of the field in the same direction and produces interference. The resulting intensity depends on the angular direction of each polarization component, and its level can 1640 APPLIED OPTICS Vol. 45, No. 7 1 March 2006

2 Fig. 1. Basic principles of specular ellipsometry. The illumination angle is denoted by i.. be optimized by an adequate choice of these orientations, which is not detailed here. The intensity measured after the analyzer is shown to be given by I I 0 I C I sin t I 2 cos 2 t, I C 1 4 R S R P 2J 0 0 R S R P 1 2 cos M, Fig. 2. Harmonics measurement and determination of the phase difference as a function of the incidence angle i in the case of Schott RG1000 glass (n 1.5). I R S R P 1 2 J 1 0 sin M, I 2 R S R P 1 2 J 2 0 cos M, (1) where J 0, J 1, and J 2 design the Bessel functions of the orders 0, 1, or 2; is the phase difference between the proper polarization states s and p of the reflected field; and R s and R p design the intensity-reflection coefficients. Let us note the presence of two harmonics in the signal. They are measured by a lock-in amplifier as a function of the incidence angle. In the expressions of Eqs. (1) the orientations of the optical elements (polarizer, analyzer, modulator) are defined from the s linearly polarized direction. The polarizer and the analyzer are fixed during measurement. They have the same orientation of 45 from the s direction to optimize the measurement conditions. The proper states of the modulator are positioned in the s and p directions. The investigation of ellipsometric measurements is usually performed 1 by the parameters r s r p R s R p exp j s p tan exp j, where is relative with the modulus ratio and is the polarimetric phase difference. In this paper we use only the parameter to emphasize its added value. We should extract the value of from these measurements, but the unknowns are R s, R p,, 0, and M. The extraction-parameters procedure consists of taking measurements both with and without the sample and with and without a calibrated anisotropic plate 8 at 633 nm to obtain more measurements than unknowns. The details of this procedure are not given in this paper, but let us just note that the parameters are extracted by using the ratio I I 2 of the harmonics, which permits us to use the relative values and to avoid a calibration procedure. This provides a key advantage to the measurement method. Harmonics are then represented on graphics without unities (Fig. 2). The measurement in the specular reflected direction permits us to deal with information relative to low spatial frequencies, that is to say at macroscopic scale However, in the case of a real surface, the interface may support several kinds of defects resulting from polishing or cleaning procedures. The contribution of all spatial frequencies can be determined from the specular directions. It is then necessary to measure and analyze the repartition of light in all directions of space, that is to say the angular-resolved scattering The measurement technique presented above can be extended to the measurement of light scattering to analyze the scattered-field polarization state. The experimental setup is built upon the same principle. In this case the incidence angle is fixed and measurements are performed in the variable direction, defined relative to the sample normal (Fig. 3). In the case of slightly heterogeneous samples, the extraction of the scattered-field phase difference can be accomplished in the same way as for that of the reflected field, owing to the absence of cross-polarized scattering in the incidence plane. The intensity after the analyzer can be written as in Eqs. (1), with the scattering coefficients C s and C p in place of the reflection coefficients R s and R p and with as the phase difference of the scattered field. It is possible to in- 1 March 2006 Vol. 45, No. 7 APPLIED OPTICS 1641

3 Fig. 3. Ellipsometry of angular-resolved scattering. The illumination and scattered angles are denoted by i and, respectively. troduce these scattering coefficients C s, C p, and for the interpretation of ellipsometric measurements even if we do not develop any theoretical considerations about the description of scattering. They simply permit us to compare with the experimental results, and they will be studied in a future, more detailed paper on this subject. Measurements are performed according to the same principle, and we can represent the harmonics and the phasedifference variations as a function of the scattered angle. The incidence angle i is fixed during the measurements. Using the same principle as before, we extract parameters from the ratios of harmonics. This allows us to avoid a calibration procedure and to work with relative values, which are represented on graphics without unities (Fig. 4). The case of highly heterogeneous samples must be considered by using more parameters that take into Fig. 5. Definition of the geometrical parameters in the case of a thin film (index n, thickness e) deposited on a substrate (index n s ). account the presence of depolarization. 19 These types of samples are not detailed in this paper. We can then present some experimental results on different optical substrates, which can allow us to investigate the quality of the surfaces. 3. Study of Harmonics Behavior at the Brewster Angle for the Detection of Transition Layers: Theoretical Investigations During ellipsometric measurements, the Brewster angle, which is defined by the zero value of R p, corresponds with the zero value of both harmonics I and I 2, according to Eqs. (1). It is then possible to measure this angular position and to deduce the substrate index. 1,2 However, when the substrate is covered by a thin film, even in the case of a thin transition layer, the reflected coefficient R p does not present a zero value any more. It is possible to calculate the theoretical expressions of the harmonics I and I 2, by using a simple thin-film electromagnetic calculation and by using approximations in the case of thin films. The expressions then become I 2J 1 0 gf he e f 2, I 2 J 2 e2 f 2 0 e f 2, (2) with e 0 n 0 2 n s 2, Fig. 4. Harmonics measurement and determination of the phase difference as a function of the scattering angle in the case of Schott RG1000 glass (n 1.53). The incidence angle is 56. f 0 n 0 n s cos 0 cos s cos s cos 0, g 0 n 2 sn 0 n s nn cos s cos cos cos s, 1642 APPLIED OPTICS Vol. 45, No. 7 1 March 2006

4 Fig. 6. Theoretical variations of harmonics (denoted by I1) and 2 (denoted by I2) in the case of a layer whose index is n 1.6 as deposited on a substrate of index n 1.5. h 0 n 2 s n 0 n 0 nn cos 0 cos (3) cos cos 0, and 2 ne cos is the optical thickness of the thin film. The geometrical parameters (angles and thickness) are defined in Fig. 5. Moreover, the experimental procedure gives us access to the absolute value of these harmonics. We can then study the theoretical variations of the harmonics values as a function of the incidence angle, as shown in Fig. 6. This figure shows that the harmonic I is still positive and that I 2 changes its sign for an incidence angle close but different to the Brewster angle. Because we plotted the absolute value, the sign change is illustrated by the minimum of the curve. It is then interesting to calculate the angular variations of both harmonics for different thin films to study the possibility of characterizing a transition layer on a substrate. Selected results are presented in Fig. 6 for films of different thicknesses with an index n 1.6, deposited on a standard glass substrate n 1.5. As is illustrated in Fig. 6, the angular variations of I 2 do not depend on the presence of a deposited layer. The level of I is proportional to the layer s optical thickness. The determination of this thickness from I measurements needs a calibration procedure. When we introduce an anisotropic plate (phase difference L and transmission T L ) on the incident beam, the expression of both harmonics must be modified as Fig. 7. Theoretical variations of absolute values of harmonics and 2 in the presence of an anisotropic plate. 1 March 2006 Vol. 45, No. 7 APPLIED OPTICS 1643

5 Fig. 8. Theoretical variations of the distance between zero values of the two harmonics as a function of the thin-film thickness (film of index n 1.6 on a substrate of n 1.5). gf he I J 1 0 T L 2 e f cos L 2 e2 f 2 e f 2 sin L, I 2 J 2 0 T L e2 f 2 e f cos L 2 2 gf he e f 2 sin L. (4) In the same way as before, it is possible to calculate and to simulate the angular variations of these harmonics in the presence of a thin layer on the substrate. In this case the introduction of the anisotropic plate 8 at 633 nm, T L 0.9) creates a zero value on each harmonic. Each harmonic presents a sign change at different angles, as we can see in Fig. 7. It is then possible to study the angular distance between zero values of both harmonics I and I 2 as a function of the characteristics of the layer on the substrate. This study is illustrated in Fig. 8. On the other hand, the angular variations of the phase difference presents a curved shape that varies with the thickness of the layer. The perfect stair corresponds to a perfect substrate, and the slope decreases when the thickness of the layer on the substrate increases (Fig. 9). Let us remark that an effect of the imaginary part of the index could lead to the same result. We have shown, for example, that a transition layer of index n 1.2 on a substrate of n 1.5 could lead to the same result as a substrate of n 1.5 j0.1 in the case of a 50 nm thick layer. But the investigations in this paper were performed in the context of nonabsorbant materials. In the case of layers with thicknesses lower than 100 nm, the distance between the harmonics zero values varies linearly with thickness. But this is not the case for higher thicknesses, as is illustrated in Fig. 10. Thus the method seems to be attractive only in the case of thin transition layers. Numerous developments have been published concerning the exploitation of ellipsometric measurements close to the Brewster angle. 2 To our knowledge, the advantage of the method presented in this paper is its use of relative measurements of a distance between two zero values, which does not necessitate use of a calibration procedure. From an experimental point of view, a zero value corresponds to a change in sign of the harmonic, which is easy to measure with a lock-in amplifier. An angular interpolation allows us to obtain precisely the value of the angle corresponding to the zero value of the harmonic. As an illustration, let us consider the measurement of a silica sample (Fig. 11). We have represented in Fig. 9. Phase difference as a function of the incidence angle in the case of a thin-film layer (n 1.6) deposited on a glass substrate (n 1.5) APPLIED OPTICS Vol. 45, No. 7 1 March 2006

6 Fig. 10. Theoretical variations of the distance between zero values of the two harmonics as a function of the thin film (film of index n 1.3 on a substrate of n 1.5). this figure the measurement of both harmonics and of the difference phase variations as a function of the incidence angle. The theoretical interpretation presented above leads to the deduction of the presence of a thin layer (thickness of 10 nm) on the surface of the sample. 4. Measurement of Transition Layers for Damage-Threshold Applications As an illustration of this method, we study the surfaces of YAG prisms for laser-damage applications. We use samples that were polished with different components and by different methods, which are not precisely known to us. These components have to be introduced in a laser cavity. The surfaces look different (microscopic observations), and differences must be quantified. The laser-induced damage threshold of the surfaces can be measured by a one-on-one procedure, defined in the International Organization of Standardization (ISO) Standard The curves obtained with this procedure are given in Fig. 12. The same samples can be characterized by ellipsometric measurements, as presented in Section 3. Experimental results are represented in Fig. 13, and the results can be investigated by using the description of the transition layer on each sample. From the phase measurements, one notes that the four samples are slightly different between prism 2 and prism 7: The angle difference rises from 3.8 to 4.7. Theoretical developments show that these results are connected with a slight degradation of the surface state. These results confirm those made by laser-induced damage-threshold measurements. Fig. 11. Silica sample. Deduced optical thickness of the transition layer, n e 10 nm. 1 March 2006 Vol. 45, No. 7 APPLIED OPTICS 1645

7 Fig. 12. Laser-damage threshold for the different samples. To confirm these measurements, we performed numerical simulations to obtain the optical thickness of the transition layer. The method is detailed in Section 3. The YAG refractive index is n s The characteristics of the transition layers are given in Table 1. The densities of the nanoprecursors in Table 1 were extracted from a classical surface model that was shown to fit the laser-induced damage-threshold curves perfectly. The assumption is that laser damage is initiated by isolated nanodefects distributed at low density under the spot size. We note a successful correspondence between the results given by both methods. The thicker the transition layer is, the lower the damage threshold is. A further series of measurements and theoretical simulations will complete this study and confirm these results. 5. Case of Rough Samples: Ellipsometric Analysis of the Scattered Field In the last step we use the ellipsometric technique to characterize rough samples. Specular ellipsometric measurements were performed on samples with different roughness. Results are given in Figs. 14 and 15. We consider the slope of the polarimetric phaseterm curve as a function of the incidence angle and it is connected with the thickness of the transition layer, as shown in Section 3. These curves confirm in another way that the roughness on the sample is similar to the presence of a transition layer. 2,3 The Fig. 13. Specular ellipsometric measurements of the samples APPLIED OPTICS Vol. 45, No. 7 1 March 2006

8 Table 1. Comparison of Laser-Induced, Damage-Threshold Measurements and Specular Ellipsometric Measurements Prism Number Laser-Induced Damage Threshold (J cm 2 ) Nanoprecursor Density ( m 2 ) Angular Difference of Harmonic Zero Values Optical Thickness (nm) rougher the sample is, the thicker the transition layer is. When the substrate index becomes complex (metallic substrate), the thickness of the equivalent transition layer increases, and this layer may become absorbent. However, these results must be completed and quantified by the application of an adequate theory of light scattering. It is well known that the roughness of samples has to be characterized by light-scattering angleresolved measurements. 15,16 Ellipsometric measurements were then performed on the same samples used for the analysis of angular-resolved scattering. The principle was presented in Section 2. Experimental results are given in Figs. 16 and 17. In the case of the polished sample, experimental results can be interpreted by numerical simulations. The theory used is first-order electromagnetic theory. 15,23 As represented in Fig. 16, we may note a difference between the measured phase curve (small-slope curve) and the calculated phase curve in the case of a nonabsorbent substrate (perfect step curve). This effect could be first attributed to the imaginary index n of the opaque glass, but the resulting value would be too high n 0.2. Further calculation with first-order theory involving a single layer (Fig. 16) shows that the departure from a step function can be explained by the presence of a transition layer with optical thickness n e 70 nm at the substrate surface of the opaque glass. This result is similar to those found with classical ellipsometry on the specular beams. In summary, we here conclude that the phase-term behavior of this polished sample detects the presence of a transition layer. In the case of a highly rough sample, the slope of the phase curve decreases, and even more so when the index is complex (metallic sample) (Fig. 17). The comparison of the results obtained for these different samples shows that ellipsometric measurements of the scattered field allow us to deal with the characterization of the surface roughness and with those behaviors comparable with the tran- Fig. 14. Specular ellipsometric measurements on a polished glass substrate (n 1.5; roughness, 1 nm). Fig. 15. Specular ellipsometric measurements on (a) a rough glass substrate (n 1.5; roughness, 1 m) and (b) a metallic rough surfaces (gold; roughness, 1 m). 1 March 2006 Vol. 45, No. 7 APPLIED OPTICS 1647

9 Fig. 16. Ellipsometric measurements of angular-resolved scattering on a polished glass substrate (n 1.5; roughness, 1 nm). The stair curve corresponds to a theoretical simulation without a transition layer, and the dashed curve corresponds to a theoretical simulation with a transition layer (n e 70 nm). The incidence angle is equal to 50. Fig. 17. Ellipsometric measurements of angular-resolved scattering on a rough glass substrate (curve 1, n 1.5; roughness, 1 m), a metallic rough surface (curve 2; gold; roughness, 1 m), and a bulk heterogeneous sample (curve 3). The incidence angle is equal to 50. sition layers. Moreover, bulk scattering samples present specific angular variations of the phase difference (Fig. 17). All these results will be completed and theoretically interpreted in a future paper. 6. Conclusion We have presented in this paper a particular method for ellipsometry of the specular or scattered field that is based on the measurement of both harmonics. The extraction procedure based on the ratios of harmonics does not need any calibration procedure. This permits us to obtain rapid access to the characterization of transition layers. We presented preliminary results for the characterization of rough samples and then conducted ellipsometric measurements of the angular-resolved field. These preliminary results must now be confirmed by lightscattering theoretical investigations. We acknowledge B. Bertussi, J. Y. Natoli, and L. Gallais for providing the laser-induced damagethreshold characterizations. References 1. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North Holland, 1977), pp H. G. Tompkins, A User s Guide to Ellipsometry (Academic, 1997), pp D. Rönnow, S. K. Anderson, and G. A. Niklasson, Surface 1648 APPLIED OPTICS Vol. 45, No. 7 1 March 2006

10 roughness effects in ellipsometry: comparison of truncated sphere and effective medium models, Opt. Mater. 4, (1995). 4. S. J. Fang, W. Chen, T. Yamanaka, and C. R. Helms, Comparison of Si surface roughness measured by atomic force microscopy and ellipsometry, Appl. Phys. Lett. 68, (1996). 5. S. N. Jasperson and S. E. Schnatterly, An improved method for high reflectivity ellipsometry based on a new polarization modulation technique, Rev. Sci. Instrum. 40, (1969). 6. B. Drevillon, Phase modulated ellipsometry from the ultraviolet to the infrared: in situ application to the growth of semiconductors, in Progress in Crystal Growth and Characterization of Materials (Pergamon, 1993), Vol. 27, pp G. Videen, J.-Y. Hsu, W. S. Bickel, and W. L. Wolfe, Polarized light scattered from rough surfaces, J. Opt. Soc. Am. A 9, (1992). 8. C. Deumié, H. Giovannini, and C. Amra, Ellipsometry of light scattering from multilayer coatings, Appl. Opt. 35, (1996). 9. T. A. Germer and C. C. Asmail, Goniometric optical scatter instrument for out-of-plane ellipsometry measurements, Rev. Sci. Instrum. 70, (1999). 10. C. Deumié, H. Giovannini, and C. Amra, Angle-resolved ellipsometry of light scattering: discrimination of surface and bulk effects in substrates and optical coatings, Appl. Opt. 41, (2002). 11. C. Deumié, R. Richier, P. Dumas, and C. Amra, Multiscale roughness in optical multilayers: atomic force microscopy and light scattering, Appl. Opt. 35, (1996). 12. P. Dumas, B. Bouffakhredine, C. Amra, O. Vatel, E. André, R. Galindo, and F. Salvan, Quantitative microroughness using near field microscopies and optical, Europhys. Lett. 22, (1993). 13. C. Amra, From light scattering to the microstructure of thin film multilayers, Appl. Opt. 32, (1993). 14. R. D. Jacobson, S. R. Wilson, G. A. Al-Jumaily, J. R. McNeil, J. M. Bennett, and L. Mattson, Microstructure characterization by angle-resolved scatter and comparison to measurements made by other techniques, Appl. Opt. 31, (1992). 15. C. Amra, Light scattering from multilayer optics. Part A: Investigation tools, J. Opt. Soc. Am. A 11, (1994). 16. C. Amra, Light scattering from multilayer optics. Part B: Application to experiment, J. Opt. Soc. Am. A 11, (1994). 17. J. M. Elson, J. P. Rhan, and J. M. Bennet, Relationship of the total integrated scattering from multilayer-coated optics to angle of incidence, polarization, correlation-length, and roughness cross-correlation properties, Appl. Opt. 22, (1983). 18. J. M. Elson, J. P. Rahn, and J. M. Bennett, Light scattering from multilayer optics: comparison of theory and experiment, Appl. Opt. 19, (1980). 19. O. Gilbert, C. Deumié, and C. Amra, Angle-resolved ellipsometry of scattering patterns from arbitrary surfaces and bulks, Opt. Express 13, (2005). 20. L. Gallais and J. Y. Natoli, Optimized metrology for laser damage measurement application to multiparameter study, Appl. Opt. 42, (2003). 21. L. Gallais Endommagement laser dans les composants optiques: métrologie, analyse statistique et photo-induite des sites initiateurs, Ph.D. dissertation (Université d Aix- Marseille III, Marseille, France, 2002). 22. International Organization for Standardization, Lasers and equipment associated with the lasers determination of the threshold of damage caused by laser on optical surfaces part 1: test 1 out of 1, ISO Standard 11254, (ISO, Geneva, 2000). 23. C. Amra, First order vector theory of bulk scattering in optical multilayers, J. Opt. Soc. Am. A 10, (1993). 1 March 2006 Vol. 45, No. 7 APPLIED OPTICS 1649