THIN-FILM THICKNESS MEASUREMENTS WITH THERMAL WAVES A. Rosencwaig, J. Opsal, D. Willenborg To cite this version: A. Rosencwaig, J. Opsal, D. Willenborg. THIN-FILM THICKNESS MEASUREMENTS WITH THERMAL WAVES. Journal de Physique Colloques, 1983, 44 (C6), pp.c6-483-c6-489. <10.1051/jphyscol:1983679>. <jpa-00223238> HAL Id: jpa-00223238 https://hal.archives-ouvertes.fr/jpa-00223238 Submitted on 1 Jan 1983 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
JOURNAL DE PHYSIQUE Colloque C6, suppl6ment au no1o, Tome 44, octobre 1983 page C6-483 THIN-FILM THICKNESS MEASUREMENTS WITH THERMAL WAVES A. Rosencwaig, J. Opsal and D.L. Willenborg Therma-Wave, Inc., Fremont, CA 94539, U.S.A. Rgsumg - Nous avons utilisg une technique nouvelle de dgflexion laser induite par des ondes thermiques haute frgquence alli6e 2 un modgle tridimensionnel d'analyse en profondeur pour mesurer ll&paisseur de films opaques et tra;sparents.*des sensibilitgs de 2% dans la gamme d16paisseur 500A - 25000 A ont 6t6 obtenues pour des films d'aluminium et de silice d6pos6s sur des substrats de silicium. Abstract - We have combined a new laser beam deflection technique using high frequency thermal waves with a three-dimensional depth-profiling theoretical model to measure the thickness of opaque and transpargnt films.o Thickness sensitivities of - +2% over the range 500~ - 25,000A have been obtained for A1 and Si02 films on Si substrates. It is well known from photoacoustic theorylr2 that one can, with thermal waves, obtain information about the thermal characteristics of a sample as a function of depth beneath its surface. Although 3,4 there has been some experimentation in thermal-wave depth-profiling, this capability has not been extensively exploited, primarily be- cause of the lack of adequate theoretical models. A recent model of Opsal and ~osencwaig, (0-R model) shows how depth-prof iling and multi-layer thickness analysis can be performed from thermal-wave measurements using either surface temperature or thermoacoustic probes, and allows for a fuller exploitation of this depth-profiling capability. There have also been several experimental impediments to thermal-wave profiling. For example, one would like, in many cases to operate outside of a photoacoustic cell, to employ a completely contactless method for thermal-wave generation and detection, and to couple thickness measurements with high spatial resolution, this last requirement necessitating the use of high-frequency (>100kHz) thermal waves. Recently we have been able to satisfy all three requirements by em- ploying a laser deflection technique6 whereby one laser is used for generating and another for detecting the thermal waves. In our method, depicted in Figure 1, the heating and probe laser beams are focused to 2-4ym diameter spot sizes and directed normal to the sample surface where they are separated by approximately 2ym. This Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983679
C6-484 JOURNAL DE PHYSIQUE is quite different than the conventional optical beam deflection technique where the probe beam skims over the surface of the although similar to the recently reported technique used at low spatial resolution and low modulation frequency to perform + spectroscopic investigations. The heating is from an Ar ion laser whose beam is acousto-optically modulated at frequencies as high as lomhz and with an incident peak power of approximately 30mW at the sample surface. The probe is an unmodulated 5mW He-Ne laser beam (2mW is incident on the sample surface) which is reflected off the sample surface and diverted by a polarizing beam splitter, in combination wit-h a quarter-wave plate, onto a knife-edge (eg. bicell) photodiode) detector. The probe beam undergoes periodic deflection of the order of - rad by the thermal-wave induced changes in the local slope of the sample surface. This is analogous to the 12 use of a laser probe for the detection of surface acoustic waves, although here the surface deformation are due to the thermal waves. We are able to detect, at a lmhz modulation frequency, changes in the local surface slope that result from local surface displacements of approximately ~O-~~/JK, a sensitivity that is considerably BICELL A-0 MODULATOR HeNe FILTER MICROSCOPE Flg. 1 - Schematic depiction of laser beam deflection technique used for the thin-film thickness measurement experiments
greater than that reported in recent experiments done at much lower 9,11,13 modulation frequencies with laser interferometry and laser probe deflection. 9-11 However, before we could combine the 0-R model with our laser probe technique to perform quantitative thin-film thickness measurements, we had to extend it to three dimensions and to include thermoelastic surface deformations. In addition to three dimensional effects, and thermoelastic deflections, we found that in our experiments we also have to include thermal lens, optical effects, and nonlinear effects arising from the temperature dependence of the various material parameters. The thermal lens effects 7r8i14 occur in the air above the sample surface and within any layer of the sample that is not optically opaque. Even though these thermal lenses have only micron-sized dimensions at the high modulation frequencies employed, their refractive power is still considerable since the normalized refractive index gradient, n-i (dn/dx) = n-i (dn/dt) (dt/dx) across the lens is now quite high and of the same order as the thermal expansion coefficient of a solid. Also, even though the probe laser beam is incident normal to the sample surface, it strikes the thermal lens off-axis and thus undergoes refraction in both incident and reflected directions. Consequently, the theory predicts, and we find experimentally, that thel5 thermal lens effect is appreciable for some materials such as Si. Figure 2 presents comparisons with experiments for a complete calculation which includes optical reflectivities, finite absorption depths and finite probe beam diameters, under vacuum, where there is no thermal lens effect (dashed curves), and in air (solid curves). The agreement between theory and experiment is excellent. FREQUENCY (MHz) Fig. 2 - Relative amplitude of laser beam deflection signal as a function of thermal-wave (modulation) frequency for A1 and Si under air (with thermal lens) and vacuum (no thermal lens) conditions. Experimental data are plotted as open (vacuum) and closed (air) circles and theoretical results as dashed (vacuum) and solid (air) curves.
C6-486 JOURNAL DE PHYSIQUE In these thermal-wave experiments DC and AC temperature excursions can range from 30 c to several hundred degrees depending on the sample's thermal characteristics. With such temperature excursions, the dependence on temperature of the various thermal, optical and elastic parameters has to be considered as well. In general, the most critical parameters appear to be the refractive index and the thermal conductivity. These temperature effects introduce appreciable nonlinearities in the model that cannot be neglected. Optical effects will, of course, play an important role in these experiments as well. For example, in Si we have to take into+ account the optical absorption length (=lum) for the 488nm Ar ion laser light. Absorption and reflectivities must also be included. In addition, when dealing with optically transparent films such as Si02, optical interference effects within the film have to be included as well. Figure 3 schematically depicts the situation encountered for an Si02 film on Si. Here we see the thermoelastic deformations of both the Si-Si02 and the Si02-air surfaces, the thermal lenses in both the Si02 and the air, and the optical interference effects on the probe beam in the Si02 film. Note that the thermal lenses have opposite signs in air and SiO2 because of the opposite signs of their respective dn/dt1s. HEATING BEAM...'.., ' 1 THERMAL LENS IN A I R 7 :" AIR THERMOELASTIC DEFORMATION THERMAL LENS IN SiO, Fig. 3 - Schematic depiction of physical processes affecting laser probe beam for Si02 on Si, including thermoelastic deformations of Si-Si02 and SiO2-air interfaces, thermal lenses of opposite sign in air and Si02, and optical interference effects in the Si02 film.
When all of the thermal lens, optical and nonlinear effects are properly included into the 0-R model, we have a quantitative tool for measuring the thickness of thin films. This is illustrated in Figure 4 where we show theoretical curves and data obtained for single films of A1 on Si and for double films of A1 and Si02 on Si. We have used the magnitude of the thermal-wave signal rather than the phase in these measurements, since the magnitude has a greater dynamic range and can be measured more precisely. The data in Figure 4 are in excellent agreement with the theory both for the single and the double films. The precision of the readings obtained with a 1-sec averaging time translates to a thickness sensitivity of +2% over the thickness range of 500a - 25,0008 for these films. - THICKNESS (microns) Fig. 4 - Relative amplitude at 1 MHz of laser beam deflection signal as a function of A1 film thickness for a series of Al-on-Si and Alon-Sio2-on-Si films. Circles are experimental data and curves are from the extended Opsal-Rosencwaig model
C6-488 JOURNAL DE PHYSIQUE In Figure 5 we show the theoretical curves and the data for a series of transparent Si02 films on Si. Although Si02 on Si is only a single film problem, the theory in this case must include thermoelastic deformations at both the Si-Si02 and Si02-air interfaces, thermal lens effects in both the Si02 and the air, and optical inter ference effects in the Si02 (see Figure 31. The fit between theory and experiment is, with all this complexity, quite good, indicating that transparent as well as opaque films can be measured with this thermal-wave technique. The thickness sensitivity for Si02 films on Si appears to be 52% over the range 5002-15,0002. THICKNESS (microns) Fig. 5 - Relative amplitude at lmhz of laser beam deflection signal as a function of Si02 film thickness for a series of Si02-on-Si films. Circles are experimental data and curves are from the extended Opsal- Rosencwaig model.
References A. Rosencwaig and A. Gersho, J. Appl. Phys. 5, 64 (1976). A. Rosencwaig, Photoacoustics and Photoacoustic Spectroscopy, FTiley, Interscience, New York, 1980. M.J. Adams and G.F. Kirkbright, Analyst 102, 678 (1977). A. Rosencwaig, J. Appl. Phys. 2, 2905 (1978). J. Opsal and A. Rosencwaig, J. Appl. Phys. 53, 4240 (1982). Further experimental details will be supplied in another paper. W.B. Jackson, N.M. Amer, A.C. Boccara and D. Fournier, Appl. Opt. 20, 1333 (1981). J.C. Murphy and L.C. Aamodt, Appl. Phys. Lett. 38, 196 (1981). M.A. Olmstead, S.E. Kohn and N.M. Amer, Bull. Am. Phys. Soc., - 27, 227 (1982). M.A. Olmstead and N.M. Amer, J. Vac. Sci. Technol., accepted for publication. M.A. Olmstead, N.M. Amer, S. Kohn, D. Fournier and A.C. Boccara, Appl. Phys. A, accepted for publication. R.L. Whitman and A. Korpel, Appl. Optics 8, 1567 (1969). S. Ameri, E.A. Ash, V. Nueman and C.R. Petts, Electron. Lett. 11, 337 (1981). R. L. Swofford, M.E. Long and A.C. Albrecht, J. Chem. Phys. 65, 179 (1979). Thermal lens effects in the air appear to play a much smaller role in the laser probe method described in refs. 9-11, because the probe beam in this method is not normal to the sample surface and thus there is considerable cancellation of the thermal lens deflection as the probe beam traverses different regions of the thermal lens.