Measuring Young's modulus of low-k dielectrics using surface acoustic waves

Michael Gostein, Alex Mazurenko, and Alex A. Maznev, Philips Advanced Metrology Systems; and Michelle T. Schulberg, Novellus Systems

The adoption of low-k dielectrics for advanced interconnects has enabled higher circuit speed, and smaller wiring pitches, but has also created a variety of processing challenges. One of the drawbacks of such materials is that they are mechanically weak and therefore do not withstand the stresses of postdeposition processing steps as well as silicon dioxide does. Problems are most likely to arise during chemical-mechanical polishing (CMP) of copper and during packaging of the finished chips.¹ The materials' low stiffness may even contribute to reliability problems from electromigration-induced voiding.²

To optimize the strength of a low-k film, it is important to have methods for characterizing mechanical properties such as hardness, which is a measure of deformation resistance, and Young's modulus, which is a measure of stiffness. The emerging use of laser-induced surface acoustic wave (SAW) spectroscopy for measuring the Young's modulus of low-k materials offers several advantages over the more traditional approach of nanoindentation.^3–8 These include the ability to measure films at actual process thicknesses and the ability to determine additional elastic parameters, such as Poisson's ratio and anisotropy factors, which are important for complete material characterization. Furthermore, SAW measurements are rapid and nondestructive, which will enable the semiconductor industry to use the technique for process monitoring.

To date, a variety of laser-induced acoustic wave techniques have been developed to measure the stiffness of film materials. In one instrument configuration, femtosecond laser pulses create wave packets that travel perpendicularly to the film and reflect back from film interfaces. The reflected pulses are detected at the surface by a laser probe, and the travel time is used to determine sound velocity, which is related to film stiffness. However, this method determines only the material's longitudinal acoustic velocity; it cannot be used to measure transverse (shear) velocity or to detect elastic anisotropy.

Another technique uses surface acoustic waves traveling in the plane of the film, which makes it possible to create waves over a range of acoustic wavelengths and to measure a full acoustic dispersion spectrum from which film properties can be determined. Philips Advanced Metrology Systems (Natick, MA) offers such SAW instruments for laser excitation and detection in a small measurement spot over a range of wavelengths. A variety of other tool configurations are in use in research laboratories. The study described in this article investigated the capabilities of Philips AMS's proprietary SAW technology.

Figure 1: Schematic diagram of laser-based surface acoustic wave excitation and detection process.

Surface Acoustic Wave Measurement

Figure 1 is a schematic diagram of the Philips Surface Wave SAW technique, which has been described in detail elsewhere.^3,4 A phase-mask grating (not shown) splits a laser excitation pulse into two beams, which are then combined at the sample surface to produce an interference grating pattern. Each excitation pulse launches acoustic waves in the plane of the film with an acoustic wavelength equal to the period of the grating pattern. Surface ripples from the passing acoustic waves in turn cause diffraction of a probe beam into a detector, and this diffracted intensity is measured versus time to capture a signal waveform. Acoustic wavelength can be controlled easily by using different phase-mask patterns.

Figure 2: Signal waveform and frequency spectrum (inset) for a low-k dielectric film on Si substrate. (Sample 2C measured at acoustic wavelength of 2.09 µm.)

Figure 2 shows a typical signal waveform from a low-k dielectric film on a silicon substrate, with the signal's frequency spectrum in the inset. The passing acoustic waves cause oscillations in the detected signal at a frequency equal to the wave velocity divided by the wavelength. In this case, the oscillation pattern contains two acoustic modes—i.e., waves traveling at two different velocities—which appear as two frequencies in the spectrum. Figure 3 shows the displacement patterns corresponding to two surface wave modes. Note that in the second, higher-order mode (Figure 3b), the direction of displacement may reverse sign as a function of depth. Additional higher-order modes have even-more-complex displacement patterns.

Figure 3: Sketches of displacement patterns for low-k films on an Si substrate corresponding to different surface wave modes: (a) a fundamental, and (b) a second, higher-order mode. Note that the direction of displacement in the second, more-complex mode reverses sign as a function of depth.

Because the details of a wave motion pattern depend on the elastic properties of the film and vary with wavelength, various elastic parameters can be determined by modeling the acoustic response as a function of wavelength. The response is measured over the full wavelength range of the instrument and the wave velocities observed at each wavelength are plotted versus wavelength or wave number (2 π/wavelength), as shown in Figure 4. A first-principles computer model can simulate this dispersion spectrum, calculating the acoustic response as a function of the thickness and mechanical properties of the film. Known parameters such as substrate properties and film thickness are fixed in the analysis, and then a best-fit comparison with the measured data is performed to determine the unknown elastic parameters of the film.

Figure 4: Plotted acoustic dispersion curves for a low-k dielectric film (Sample 2C). Circles represent the experimental data, and lines indicate the best-fit model. Mode 1 corresponds to a fundamental displacement pattern; Modes 2 and 3 correspond to higher-order patterns.

The mechanical properties of an elastically isotropic material can be described by three parameters: density (ρ) and two elastic constants, Young's modulus (E) and Poisson's ratio (σ). An equivalent representation of the elastic constants, more common in acoustics, uses two independent components of the elastic stiffness tensor (C_ij): compressional modulus (C₃₃) and shear modulus (C₄₄). If the film density is known, it is fixed during the best-fit procedure. If not, it may be determined through analysis if an additional, metal-coated sample wafer is also measured.⁵ In such cases, the dispersion spectra of the bare and metal-coated dielectric samples are simultaneously fit to determine density, yielding a typical accuracy of approximately 10% (e.g., with 500 Å of tantalum).

Experimental Methods and Results

In the first phase of this study, the SAW technique was used to examine two 1-µm samples of Coral, a carbon-doped oxide or organosilicate glass low-k material made by Novellus (San Jose). The Coral films were deposited on 200-mm bare-silicon wafers by a Novellus Sequel plasma-enhanced chemical vapor deposition (PECVD) tool. One sample was a first-generation Coral and the other was a second-generation high-mechanical-strength (HMS) version of the material, which had been optimized to improve its mechanical properties.⁹ The two films have known dielectric constants of 2.9–3.0 and moduli of 9 and 15 GPa, respectively, as measured with nanoindentation. Sample film thickness was assessed with a spectroscopic ellipsometer.

The acoustic spectra of the two samples were measured on a Series 3000 SurfaceWave instrument (Philips AMS, Natick, MA). For the analysis, a value of 1.31 g/cm³ was used for the density of the films, while E and σ were varied in order to provide the best fit to the data. The resulting Young's moduli for the two samples were 6.0 and 10.9 GPa, respectively, as listed in Table I (Samples 1 and 2). It was estimated that the absolute error of the surface wave method, which includes the error in the SAW velocity measurements, the error in film-thickness measurements by the spectroscopic ellipsometer, and the error in the assumed density, is of the order of several percent. The repeatability of the modulus measurements was <0.3%.

The surface wave results confirmed the nanoindentation finding that the modulus of the second-generation-material sample was approximately twice as large as that of the original-material sample. However, the readings were somewhat lower than those achieved using nanoindentation, which generally yields significantly higher values for low-stiffness materials such as low-k films. The correlation between results for the two techniques is shown in Figure 5, which includes data from earlier research efforts as well as from this study.^6–8

Figure 5: Correlation of Young's modulus measurements made using surface acoustic waves and nanoindentation.6–8

Nanoindentation likely overestimates the modulus of thin, weak films for a variety of reasons. One of these is the substrate effect, in which the stiff silicon wafer contributes to the resistance felt by the indenter tip. In order to isolate the film properties from this substrate effect, film thicknesses of at least 1 µm are usually needed. In addition, for porous materials, the film may undergo densification as the indenter tip compresses it during the indentation process, which may also raise the modulus reading.

Measuring Thin Low-k Films. To examine the effect of film thickness on SAW modulus measurements, a set of five HMS Coral samples with thicknesses varying from approximately 1500 to 8000 Å was prepared using PECVD. Film-thickness maps were obtained for each sample with a spectroscopic ellipsometer, and acoustic dispersion spectra were measured using the SAW instrument. The acoustic dispersion data were analyzed to determine the Young's modulus and Poisson's ratio of each sample. Ellipsometer thickness data were used as input to the model and film density was again fixed at 1.31 g/cm³.

Because the only process condition that was varied was the deposition time, the mechanical properties of all five films were expected to be identical and independent of film thickness. As shown in Table I (Samples 2A–2E), the acoustic wave method was able to determine properties for even the thinnest films, and all of the samples' measured properties were nearly identical (with differences of <1%). These results indicate that the SAW technique is capable of determining the Young's modulus of low-k films in the typical deposited-thickness range of <1 µm, which is difficult to do with nanoindentation.

Contour Mapping. Ideally, elastic properties of low-k films should be uniform across the wafer, but process conditions may lead to within-wafer modulus variations. Thus, it would be desirable for process engineers to be able to detect film nonuniformities. Because the surface wave technique for measuring modulus yields good repeatability, and because a dispersion spectrum can be measured rapidly, requiring only about 30 seconds per site, the technique seems well suited for mapping the modulus across a wafer.

To verify that capability, the SAW instrument was used to create 49-point maps of Young's modulus on Samples 2A–2E described above. Figure 6 shows the resulting map for Sample 2C. The measurements showed excellent within-wafer uniformity, with a standard deviation of only 1.5%. The measured pattern is a true modulus variation and not a result of thickness nonuniformity, because thickness and modulus variations at the 49 points did not correlate.

Figure 6: A 49-point contour map of Young's modulus measured by surface waves on a Coral low-k dielectric film (Sample 2C). Modulus is plotted as percent deviation from the wafer average. White circles show sites also measured by nanoindentation.

To confirm the observed pattern in the Sample 2C modulus map, five points that together showed a modulus range of ~5% in the surface wave results were selected for follow-up testing; these sites are shown as white circles in Figure 6. Nanoindentation was performed at these points—using the average of 15 individual indentations spaced 15 µm apart at each site—and the results were correlated to the SAW measurements, as shown in Figure 7. Because the sample's film thickness was less than that considered acceptable for nanoindentation, three different methods were used to analyze the measurement results and to extract a modulus value from the force/displacement curves. Each set of values in the figure is plotted in terms of percent deviation from the wafer average. Error bars indicate the repeatability of each technique: 1.3% for nanoindentation and 0.3% for SAW. The variation in the nanoindentation results at the five sites was similar to that of the surface wave measurements, which therefore roughly confirmed the observed pattern of modulus nonuniformity. This ability of surface wave measurements to generate accurate uniformity maps should provide useful information for optimizing low-k film performance.

Figure 7: Correlation of surface wave and nanoindentation (NI) modulus measurements for five sites on Sample 2C. Results are plotted as percent deviation from the wafer average for each technique. Site locations are shown in Figure 6. Error bars indicate the repeatability of each measurement technique.

Measuring Porous Films. Future generations of integrated circuits will require ever-lower dielectric constants. To achieve a k-value of ≤2.4, it is generally necessary to incorporate porosity into the material. The most common method for creating such films is to codeposit a network-forming precursor and a sacrificial pore generator, or porogen, thereby forming a hybrid film. Because the porogen is less thermally stable than the network backbone, it desorbs from the film during heating, leaving behind empty spaces, or pores.

Incorporating porosity into a low-k material inherently weakens it, and film stiffness, as measured by Young's modulus, also decreases with increasing porosity. Therefore, to meet the rigorous demands of IC processing, the film's pores should be configured in such a way as to make the material as robust as possible. An ordered array of uniformly sized pores may be the best arrangement to optimize strength for a given porosity. Mesoporous silica, with ordered pores in the 1–10-nm range, is considered a promising material for ultra-low-k interconnects.¹⁰

The next phase of this study thus investigated the use of the surface wave method to measure a sample of mesoporous silica film. This material, which has a k of 2.25 and a density of 1.0 g/cm³, is made by infusing a solution of methyl triethoxysilane (MTEOS) and tetraethyl orthosilicate (TEOS) in supercritical CO₂ into a block copolymer template.¹¹ Following depressurization, the hybrid film is subjected to a thermal or plasma treatment to remove the porogen, and the resulting porous oxide maintains the ordered structure of the phase-segregated block copolymer. When the template is extracted, however, the film shrinks in the direction normal to the wafer such that the final thickness is ~30% smaller than the thickness following infusion. The resulting pores are therefore isotropic within the plane of the film, but compressed along the axis perpendicular to the film, as shown in the TEM micrograph in Figure 8.

Figure 8: TEM micrograph of ultra-low-k mesoporous silica material deposited on a wafer by a supercritical fluid infusion process.

Nanoindentation measurements of the 1-µm mesoporous film sample used in this study gave a modulus of 7.8 GPa, while the modulus determined by surface wave analysis was 1.8 GPa, as shown in Table I (Sample 3). The surface wave analysis of Sample 3 also revealed an elastic anisotropy, as discussed below. The large discrepancy between the nanoindentation and SAW results is typical for porous low-k films.^6–8

Detecting and Measuring Elastic Anisotropy. In the deposition of a film material onto a substrate, the substrate defines a plane that may cause preferential orientation of any microstructure present in the film as illustrated in Figure 9. For example, polycrystalline films may preferentially orient their grains with certain axes perpendicular to the substrate. The PECVD Coral film material examined in this study (Samples 1–2E) should be amorphous, with no apparent microstructure. In contrast, spin-on dielectric materials may contain a residual microstructure corresponding to the spin and baking processes, which cause movement of material in-plane and out-of-plane, respectively.

Figure 9: Schematic that shows how in-plane film properties may differ from out-of-plane properties if processing results in a preferential orientation of the microstructure.

Porous films that undergo one-dimensional shrinkage during porogen removal may be asymmetric, and if the pores are ordered, that may add further orientation to the microstructure. If a film's microstructure is preferentially oriented with respect to the substrate, then in general it can be expected that its properties will be anisotropic and differ between in-plane and out-of-plane directions. If the in-plane properties do not further depend on direction within the plane (which is the case for most film deposition processes), then the symmetry is described as transverse-isotropic.

The acoustic response of transverse-isotropic materials can be described completely by five independent components of the elastic stiffness tensor C_ij, but SAW measurements are sensitive to only four of those parameters. Defined with the z-axis perpendicular to the film, these are: C₁₁ (in-plane compressional modulus), C₃₃ (out-of-plane compressional modulus), C₄₄ (shear modulus for xz or yz shear deformation), and C₁₃ (sidewall pressure modulus in the wave propagation direction). The effective Young's modulus in the out-of-plane direction can be calculated from these four components, assuming that the fifth component, C₁₂ (sidewall pressure modules perpendicular to the wave propagation direction), equals C₁₃ (i.e., that the sidewall pressure modulus is isotropic in-plane), which yields an error on the order of 5% at most.

Analysis of the dispersion data from the mesoporous silica film, Sample 3, revealed that this material is best modeled as transverse-isotropic, as shown in Figure 10. The sample's C₁₁ and C₃₃ values, which are given in Table I, indicate that the film material was significantly stiffer within the film plane (6.4 GPa) than perpendicular to the film plane (2.1 GPa).

Figure 10: Dispersion spectra with best-fit models for mesoporous silica film (Sample 3). Fitting the data required a transverse-isotropic symmetry model, revealing the elastic anisotropy of the film.

The elastic anisotropy of the sample is easy to understand given the film's microstructure, which can be seen in Figure 8. The pores have an elliptical cross section that is longer in the film plane. The surface wave stiffness measurement results suggest that such a structure is easier to compress perpendicular to its long axis. Surface wave analysis has also revealed elastic anisotropy in other film materials, particularly porous low-k dielectrics. The mechanism of this anisotropy may vary from one material to another.

The ability of surface wave analysis to detect and measure elastic anisotropy presents a characterization capability that may have relevance to wafer processing or device performance. Different types of failures associated with low-modulus films may be caused by stresses in different directions. For example, failures at CMP may be related to in-plane stresses placed on the film; the fact that the mesoporous silica material studied in this work can successfully withstand CMP may be attributable to its high in-plane compressional modulus.¹⁰ Similarly, it is possible that a film's ability to withstand the stresses of the packaging process or the forces that lead to electromigration may depend differently on in-plane and out-of-plane stiffness properties. These issues all need further study, but the ability of the SAW technique to determine the anisotropy of elastic properties provides another tool for examining these failure mechanisms.

Conclusion

Study findings have confirmed that surface acoustic wave measurements are well suited for the nondestructive characterization of low-k films. The technique is able to determine Young's modulus and Poisson's ratio, as well as elastic anisotropy parameters that depend on the details of the film microstructure. Furthermore, SAW instruments can measure low-k films deposited at process thicknesses in the 1500–8000-Å range, unlike nanoindentation, which generally requires thicker films to achieve meaningful results.

In addition, the surface wave measurement technique is precise and can be performed rapidly enough to enable full-wafer mapping of elastic modulus properties. This capability opens the possibility of more-detailed characterization of deposition processes. The nondestructive determination of the uniformity of elastic properties across a wafer makes the technique applicable for deposition tool qualification or for routine process monitoring, enabling improved metrology of future low-k materials.

Acknowledgments

The authors wish to thank their colleagues at IMEC's copper/low-k program, particularly Sywert Brongersma, for helpful discussions and research results that contributed to the ideas presented here. They also would like to acknowledge the contribution of Haiying Fu of Novellus, who provided the HMS Coral samples and related data.

References

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Michael Gostein, PhD, is chief technologist at Philips AMS and works in the company's Austin, TX, office. He joined the company in 1999 and leads the SurfaceWave technology R&D effort. Previously, he was staff scientist and technology development manager. Gostein received an SB in physics from the Massachusetts Institute of Technology (MIT) in Cambridge, MA. In 1997, he received a PhD in physics from the University of Texas in Austin for research using laser spectroscopy to study molecular dynamics of gas-phase reactions at metal surfaces. (Gostein can be reached at 512/231-2295 or michael.gostein@philips.com.)

Alex Mazurenko, PhD, is staff scientist at Philips AMS (Natick, MA) and has been with the company since 2001. He has focused on the design and development of next-generation optical heads for SurfaceWave technology and applications of the system for thin-film metrology, especially in the area of low-k dielectric material evaluation. Mazurenko received an MS in physics from the Moscow Institute of Physics and Technology in Russia. In 2001, he received a PhD in physics from MIT. (Mazurenko can be reached at 508/647-1151 or alex.mazurenko@philips.com.)

Alex A. Maznev, PhD, is senior scientist at Philips AMS (Natick, MA) and has worked with the company since 1999 to develop SurfaceWave technology. He has been active in the field of laser photoacoustics and photothermal research for more than 15 years. He has produced more than 50 technical publications and holds seven patents in that field. Before joining Philips, Maznev was a postdoctoral fellow at MIT and the Freie Universität in Berlin, Germany, where he performed fundamental research in photoacoustics. He received a degree in physics from the Moscow Institute of Physics and Technology in Russia and a PhD in physics from the General Physics Institute in Moscow. (Maznev can be reached at 508/647-1128 or alex.maznev@philips.com.)

Michelle T. Schulberg, PhD, is a senior technologist in the corporate R&D group at Novellus Systems (San Jose). She has led a variety of projects to develop ultra-low-k materials and has specialized in investigating new metrology techniques. Previously, she did research at Sandia National Laboratories (Livermore, CA). She received an AB in chemistry from Harvard College in Cambridge, MA, and a PhD in physical chemistry from MIT. (Schulberg can be reached at 408/570-2743 or michelle.schulberg@novellus.com.)