Anisotropic Thermal Expansion Behavior of Thin Films of

while the in-plane thermal expansion coefficient R| of each film was determined ... films have been shown to exhibit anisotropic thermal expansion beh...
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Anisotropic Thermal Expansion Behavior of Thin Films of Polymethylsilsesquioxane, a Spin-on-Glass Dielectric for High-Performance Integrated Circuits Weontae Oh and Moonhor Ree* Department of Chemistry, Center for Integrated Molecular Systems, BK21 Program, Division of Molecular and Life Sciences, and Polymer Research Institute, Pohang University of Science & Technology, San 31, Hyoja-dong, Pohang 790-784, Republic of Korea Received February 18, 2004. In Final Form: May 13, 2004 Thin films of poly(methylsilsesquioxane) (PMSSQ) are candidates for use as interdielectric layers in advanced semiconductor devices with multilayer structures. We prepared thin films of PMSSQ with thicknesses in the range 25.0-1151.0 nm by spin-casting its soluble precursor onto Si and GaAs substrates with native oxide layers and then drying and curing the films under a nitrogen atmosphere at temperatures in the range 250-400 °C. The out-of-plane thermal expansion coefficient R⊥ of each film was measured over the temperature range 25-200 °C using spectroscopic ellipsometry and synchrotron X-ray reflectivity, while the in-plane thermal expansion coefficient R| of each film was determined over the temperature range 25-400 °C by residual stress analysis. PMSSQ films cured at higher temperatures exhibited reduced thermal expansion, which is attributed to the denser molecular packing and higher degree of cross-linking that arises at higher temperatures. Surprisingly however, all the PMSSQ films were found to exhibit very strong anisotropic thermal expansion; R⊥ and R| of the films were in the ranges 140-329 ppm/°C and 12-29 ppm/°C respectively, depending on the curing temperature. This is the first time that cured PMSSQ thin films have been shown to exhibit anisotropic thermal expansion behavior. This anisotropic thermal expansion of the PMSSQ thin films might be due to the anisotropy of cross-link density in the films, which arises because of a combination of factors: the preferential orientation of methyl groups toward the upper film surface and the preferential network formation in the film plane that occurs during curing of the confined film. In addition, the film electron densities were determined using synchrotron X-ray reflectivity measurements and the film biaxial moduli were obtained using residual stress analysis.

Introduction Advanced semiconductor devices are designed and manufactured as multilayer structures in order to produce dense wiring of metal conductor lines in a compact size, which results in improved electrical performance.1,2 Today’s integrated circuits (ICs) have signal line features e0.15 µm in size, and so signal delays, which are mainly due to interconnect capacitance, resistance, and cross talk between signal lines, are the main focus of research into improving device performance.1,2 Signal delays and power consumption in such devices can generally be reduced by using low dielectric constant materials as the interlayer dielectric.1,2 Thus much research effort has been applied to the development of interlayer dielectrics with an ultralow dielectric constant and a high dielectric strength.2-8 One promising class of candidates for a low dielectric * To whom all correspondence should be addressed. Tel: +8254-279-2120. Fax: +82-54-279-399. E-mail: [email protected]. (1) (a) Tummala, R. R., Rymaszewski, E. J., Eds. Microelectronics Packaging Handbook; van Nostrand Reinhold: New York, 1989. (b) Czornyj, G.; Chen, K. J.; Prada-Silva, G.; Arnold, A.; Souleotis, H.; Kim, S.; Ree, M.; Volksen, W.; Dawson, D.; DiPietro, R. Proc. Electron. Compon. Technol. Conf. (IEEE) 1992, 42, 682. (c) Feng, Z.-C.; Liu, H.-D. J. Appl. Phys. 1983, 54, 83. (2) (a) Singer, P. Semicond. Int. 1997, 21, 73. (b) The National Technology Roadmap for Semiconductors: Technology Needs; Semiconductor Industry Association: San Jose, CA, 1997; p 101. (c) Havemann, R. Proc. Ultra Low k Workshop (ACS Div. Polym. Chem.) 1999, 1-17. (d) Carter, K. R. Proc. Ultra Low k Workshop (ACS Div. Polym. Chem.) 1999, 60-80. (e) Liu, R.; Pai, C.-S.; Martinez, E. SolidState Electron. 1999, 43, 1003. (f) Chiang, S.-K.; Lassen, C. L. Solid State Technol. 1999, 10, 42. (g) Carter, K. R.; Dawson, D. J.; DiPietro, R. A.; Hawker, J.; Hedrick, J. L.; Miller, R. D.; Yoon, D. Y. U.S. Patent No. 5,895,263, April 20, 1999. (h) Romo-Uribe, A.; Mather, P. T.; Haddad, T. S.; Lichtenhan, J. D. J. Polym. Sci., Part B: Polym. Phys. 1998, 36, 1857.

constant material are spin-on-glass materials, i.e., organosilicates.3-8 They are characterized by a low dielectric constant (2.7-2.9), low moisture uptake, and excellent thermal stability up to 500 °C.3-8 The dielectric constant of such a material can be further decreased when an organic pore generator is incorporated into the organosilicate matrix and subsequently calcined out, generating pores in the matrix.3-7 Reliable dielectric thin films require high surface hardness and mechanical toughness in order to withstand the severe mechanical stress conditions, such as chemical mechanical planarization, that occur in the fabrication of integrated circuit (IC) devices.2-7 (3) (a) Ree, M.; Goh, W. H.; Kim, Y. Polym. Bull. 1995, 35, 215. (b) Hedrick, J. L.; Miller, R. D.; Hawker, C. J.; Carter, K. R.; Volksen, W.; Yoon, D. Y.; Trollsas, M. Adv. Mater. 1998, 10, 1049. (c) Ying, J. Y.; Mehnert, C. P.; Wong, M. S. Angew. Chem., Intl. Ed. 1999, 38, 56. (d) Nguyen, C. V.; Carter, K. R.; Hawker, C. J.; Hedrick, J. L.; Jaffe, R. L.; Miller, R. D.; Remenar, J. F.; Rhee, H.-W.; Rice, P. M.; Toney, M. F.; Trollsas, M.; Yoon, D. Y. Chem. Mater. 1999, 11, 3080. (e) Cook, R. F.; Liniger, E. G. J. Electrochem. Soc. 1999, 146, 4439. (f) Nguyen, C. V.; Hawker, C. J.; Miller, R. D.; Huang, E., Hedrick, J. L.; Gauderon, R.; Hilborn, J. G. Macromolecules 2000, 33, 4281. (g) Oh, W.; Hwang, Y.-T.; Park, Y. H.; Ree, M.; Chu, S.-H.; Char, K.; Lee, J. K.; Kim, S. Y. Polymer 2003, 44, 2519. (4) Bolze, J.; Ree, M.; Youn, H. S.; Chu, S. H.; Char, K. Langmuir 2001, 17, 6683. (5) Yang, S.; Mirau, P. A.; Pai, C.-S.; Nalamasu, O.; Reichmanis, E.; Lin, E. K.; Lee, H.-J.; Gidley, D. W. Chem. Mater. 2001, 13, 2762. (6) Yang, S.; Mirau, P. A.; Pai, C.-S.; Nalamasu, O.; Reichmanis, E.; Pai, J. C.; Obeng, Y. S.; Seputro, J.; Lin, E. K.; Lee, H.-J.; Sun, J.; Gidley, D. W. Chem. Mater. 2002, 14, 369. (7) (a) Morgen, M.; Ryan, E. T.; Zhao, J.-H.; Hu, C.; Cho, T.; Ho, P. S. Annu. Rev. Mater. Sci. 2000, 30, 645. (b) Maier, G. Prog. Polym. Sci. 2001, 26, 3. (8) (a) Oh, W.; Shin, T. J.; Ree, M.; Jin, M. Y.; Char, K. Macromol. Chem. Phys. 2002, 203, 791. (b) Oh, W.; Shin, T. J.; Ree, M.; Jin, M. Y.; Char, K. Mol. Cryst. Liquid Cryst. 2001, 371, 397.

10.1021/la049581m CCC: $27.50 © 2004 American Chemical Society Published on Web 06/26/2004

Thermal Expansion of Organosilicate Thin Films

In multilayer IC devices, the dielectric material is commonly interfaced to itself as well as to other device component materials such as silicon, silicon nitride, silicon oxide, ceramic, copper, aluminum, chromium, tungsten, and capping metals.1-11 At such interfaces, high residual stress is often generated, causing problems for the reliability of the devices such as curl, bend, displacement, crack, and delamination.1,8-11 The residual stress at a given interface is primarily dependent on the mismatch of the thermal expansion coefficients (R’s) and mechanical properties (i.e., Young’s modulus E and Poisson’s ratio ν) of the interfaced layers, as well as on the thermal history of the layers.8,10,11 Therefore, mismatches between the properties of the interfaced layers need to be minimized in order to prevent stress-associated reliability problems.1,8,10,11 Of the spin-on-glass dielectrics reported so far,3-8 poly(methylsilsesquioxane) (PMSSQ) has become the subject of both semiconductor industry and academic attention because of its possible use as an interlayer dielectric matrix in advanced IC devices because of its low dielectric constant, excellent thermal stability, and good processability, including spin-on processability, planarization, gap filling, damascene processing, and chemical mechanical polishing.3-8 The residual stress in PMSSQ films has been found to vary with temperature over the range 0-100 MPa during the curing process but increases almost linearly with temperature during subsequent cooling runs.8 The final stress at room temperature was found to range from 30 to 120 MPa and depends on factors such as the number of coatings, film thickness, heating rate and heating protocol, final curing temperature, and degree of curing.8 In particular, during the cooling run after curing, residual stress was found to induce cracks in films of thickness greater than 3 µm.8 Due to this stress-induced cracking, the PMSSQ film thickness is limited to 3 µm. Further, PMSSQ is inherently brittle, so it is very difficult to prepare in free-standing films. Because of these inherent limitations, the thermal expansion behavior of PMSSQ thin films is rarely investigated, despite its great importance to the understanding of their residual stress and stress-associated reliability issues. In this study, we investigate in detail the out-of-plane and in-plane thermal expansion behaviors of PMSSQ films with various thicknesses. The out-of-plane thermal expansion coefficient (TEC) (R⊥) was measured using spectroscopic ellipsometry and X-ray reflectivity, while the in-plane TEC (R|) was determined using residual stress analysis. These TEC results are explained in this study by considering the curing reactions of the PMSSQ precursor and the chemical structure of the cured films. (9) (a) Lee, K.-W.; Viehbeck, A.; Walker, G. F.; Cohen, S.; Zucco, P.; Chen, R.; Ree, M. J. Adhes. Sci. Technol. 1996, 10, 807. (b) Yu, J.; Ree, M.; Shin, T. J.; Wang, X.; Cai, W.; Zhou, D.; Lee, K.-W. J. Polym. Sci., Polym. Phys. Ed. 1999, 37, 2806. (c) Yu, J.; Ree, M.; Park, Y. H.; Shin, T. J.; Cai, W.; Zhou, D.; Lee, K.-W. Macromol. Chem. Phys. 2000, 201, 491. (10) (a) Ree, M.; Shin, T. J.; Park, Y.-H.; Kim, S. I.; Woo, S. H.; Cho, C. K.; Park, C. E. J. Polym. Sci., Part B: Polym. Phys. 1998, 36, 1261. (b) Ree, M.; Park, Y.-H.; Kim, K.; Cho, C. K.; Park, C. E. Polymer 1997, 38, 6333. (c) Elsner, G.; J. Appl. Polym. Sci. 1987. 34, 815. (d) Goldsmith, C.; Geldermans, P.; Bedetti, F.; Walker, G. A. J. Vac. Sci. Technol. 1983, A1 (2), 407. (e) Ree, M.; Kim, K.; Woo, S. H.; Chang, H. J. Appl. Phys. 1997, 81, 698. (f) Ree, M.; Nunes, T. L.; Czornyj, G.; Volksen, W. Polymer 1992, 33, 1228. (g) Ree, M.; Chu, C. W.; Goldberg, M. J. J. Appl. Phys. 1994, 75, 1410. (h) Hoffman, W. R. Physics of Thin Film; Hass, G., Thun, R. E., Eds.; Academic: New York, 1966; Vol. 3, p 211. (11) (a) Jou, J.-H.; Huang, P.-T. Macromolecules 1991, 24, 3796. (b) Jou, J.-H.; Huang, P.-T.; Chen, H.-C.; Liao, C.-N. Polymer 1992, 33, 967.

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Figure 1. Chemical structure of poly(methylsilsesquioxane) (PMSSQ) precursor and its film formation and thermal curing reaction.

Experimental Section Materials and Film Preparation. PMSSQ precursor with a weight-average molecular weight of 10 000 (GR650F) was supplied by Techneglas Company; its chemical structure is shown in Figure 1. Methyl isobutyl ketone (MIBK) was obtained from Aldrich Chemical Co. These materials were used as received without further purification. PMSSQ precursor was dissolved in MIBK at various concentrations, giving completely homogeneous solutions. The solid content of the precursor solutions was 2.525 wt %. The solutions were filtered with PTFE membranes with a pore size of 0.20 µm before use. The solutions were spin-coated onto Si(100) wafers for the ellipsometry and X-ray reflectivity measurements and onto Si(100) and GaAs(100) wafers for the residual stress analyses, followed by drying at 50 °C for 2 h under a nitrogen atmosphere. The resulting films were measured to have a thickness of 25-1150 nm using spectroscopic ellipsometers (models VASE and M-2000, Woollam) and an R-stepper (model Tektak3, Veeco). The Si(100) and GaAs(100) wafers were 76.0 mm in diameter and 400 µm thick. Before the deposit of PMSSQ films, the wafers were precleaned, their initial curvatures were determined using a residual stress analyzer,8 and their ellipsometric parameters were determined for various wavelengths on Woollam spectroscopic ellipsometers12 as a function of temperature. The dried films were cured thermally either in an oven with a nitrogen atmosphere or on the hot stage of the stress analyzer under a nitrogen atmosphere, using various curing protocols in the temperature range 250-400 °C: (1) 250 °C/100 min, (2) 300 °C/60 min, and (3) 400 °C/60 min. A rate of 2.0 °C/min was used for both the heating and the cooling processes. Spectroscopic Ellipsometry. Measurements of the thicknesses of the film samples deposited on Si(100) wafers were carried out using Woollam spectroscopic ellipsometers (models VASE and M-2000) equipped with a hot stage and a Xe lamp light source. For each ellipsometric measurement, the film sample was first heated at 20.0 °C/min up to 200 °C, held at that temperature for 10 min, and then cooled in a stepwise manner. During the stepwise cooling run, the film thickness was measured as a function of temperature; the film sample was held at each temperature for 10 min. The determinations of film thickness for two ellipsometric angles (i.e., Ψ and ∆, which are related to the ratio of the Fresnel reflection coefficients for p- and s-polarized light) at each temperature over the wavelength range 400-800 nm, were performed according to an analytical method based on the Levenbergerg-Marquardt multivariate regression algorithm (12) (a) Guide to using WVASE32: Ellipsometry manual of J.A. Woollam Co.: Lincoln, NE, 2003. (b) Paik, W.-K. Modern Aspects of Electrochemistry, No. 25; Bockris, John O‘M., et al., Eds.; Plenum Press: New York, 1993, p 191. (c) Tompkins, H. G.; McGahan, W. A. Spectroscopic Ellipsometry and Reflectometry; Wiley: New York, 1999.

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and Cauchy model described previously.12 From the film thickness data, the out-of-plane TEC R⊥ was determined using the equation

R⊥ )

1 dt t0 dT

( )

(1)

where the symbols t and T denote the film thickness and the temperature, respectively, and t0 is the initial film thickness. X-ray Reflectivity. Specular X-ray reflectivity (SXR) measurements were conducted at the BL3C2 and BL4C2 beamlines4,13 of the Pohang Accelerator Laboratory at the Pohang University of Science & Technology in Korea. An X-ray beam with a wavelength λ of 1.54 Å and ∆λ/λ ) 5 × 10-4 was selected using a Si(111) double crystal monochromator. The film samples were mounted on a HUBER four-circle goniometer equipped with a hot stage, and a scintillation counter with an enhanced dynamic range (Bede Scientific, EDR) was used as a detector. Film thicknesses were determined from the SXR data obtained as a function of temperature according to a method reported previously,4,14 and then from the measured film thicknesses R⊥ was determined using eq 1; the details of the SXR data analysis are given in ref 4. Residual Stress Analysis. The residual stress σF of each film deposited on a substrate was measured in situ under a nitrogen atmosphere during the heating and subsequent cooling run using a stress analyzer equipped with a hot stage. The film stress σF was determined from the radii (R∞ and RF) of the curvature of the wafer measured before and after film deposition using the equation8,10

σF ) (

EStS2

(

)

1 1 1 6 (1 - νS)tF RF R∞

σF,1 )

∫

σF,2 )

∫

Tf

Ti

Ti

( ) ( )

can be expressed according to the following equations, which have been rewritten from eqs 3a and 3b above

( ) ( )

dσF,1 EF ) (R (F) - RS1) dT 1 - νF |

(4a)

EF dσF,2 ) (R (F) - RS2) dT 1 - νF |

(4b)

(2) The combination of these two equations provides the equations

where the positive and negative signs indicate the residual stress in the tension and compression modes, respectively, and the symbols E, ν, and t represent the Young’s modulus, Poisson’s ratio, and thickness of each layer material, respectively. The film stress σF on a substrate with known TEC is a function of two unknowns, R|(F) and EF/(1 - νF) that are the in-plane TEC and biaxial modulus of the film, respectively:8,10,11 EF and νF are the Young’s modulus and Poisson’s ratio of the film, respectively. These unknowns can be determined independently by measuring the slope of the film stress-temperature plot of the film on two substrates with different TECs.8,10,11 Taking this into account, we chose Si(100) and GaAs(100) substrates which have different TECs:10,11,15 Si(100) substrate, RS ) 2.8 ppm/°C and [ES/(1 - νS)] ) 180.5 GPa; GaAs(100) substrate, RS ) 5.8 ppm/°C and [ES/(1 - νS)] ) 123.9 GPa. The film stresses σF,1 and σF,2 of the two substrates can be expressed by the equations8,10,11 Tf

Figure 2. Representative ellipsometric angle profiles (Ψ and ∆) over the wavelength range 400-800 nm of a PMSSQ film deposited on a Si(100) substrate: symbols are the measured ellipsometric angles and the solid lines are the best-fit results. The PMSSQ film was determined to have a thickness of 219.5 nm. The ellipsometry measurements were conducted with an incident angle of 75° at 25 °C. The PMSSQ film was prepared by curing at 400 °C/60 min under a nitrogen atmosphere.

(

)

dσF,1/dT R - RS1 dσF,2/dT S2 R|(F) ) dσF,1/dT -1 dσF,2/dT

(5a)

EF (dσF,2/dT) - (dσF,1/dT) ) 1 - νF RS2 - RS1

(5b)

(

)

Using eqs 5a and 5b, the in-plane TEC [R|(F)] and biaxial modulus [EF/(1 - νF)] of the films can be obtained from the measured film stress-temperature profiles of the two substrates.

Results and Discussion

EF (R (F) - RS1) dT 1 - νF |

(3a)

EF (R (F) - RS2) dT 1 - νF |

(3b)

where RSi is the TEC of the substrate i, and Ti and Tf are the initial and final temperatures of the film, respectively. In general, the residual stress of a polymer film monotonically increases or decreases with temperature during a heating or cooling run;8,10,11 in the case of PMSSQ films, the residual stress monotonically varies with temperature once the precursor films are thermally cured at a chosen temperature. The linear slopes of stresstemperature profiles measured during heating or cooling runs (13) (a) Bolze, J.; Kim, J.; Huang, J.-Y.; Rah, S.; Youn, H. S.; Lee, B.; Shin, T. J.; Ree, M. Macromol. Res. 2002, 10, 2. (b) Park, B.-J.; Rah, S.-Y.; Park, Y.-J.; Lee, K.-B. Rev. Sci. Instrum. 1995, 66, 1722. (14) (a) Tolan, M. X-ray scattering from soft-matter thin films; Springer-Verlag: Berlin, 1999. (b) Russell, T. P. Mater. Sci. Rep. 1990, 5, 171. (c) Russell, T. P. Physica B 1996, 221, 267. (15) Thermal Expansion, Nonmetallic Solids; Touloukian, Y. S., Ed.; IFI/Plenum: New York, 1977; Vol. 13.

Spectroscopic Ellipsometry. All silicon wafers used in the present study were precleaned, and their ellipsometric parameters were measured as a function of temperature over the range 25-400 °C before the deposition of the PMSSQ precursor. Figure 2 shows typical profiles of the ellipsometric angles Ψ and ∆ of a PMSSQ film, which were measured with an incident angle of 75° at 25 °C; this PMSSQ film was prepared by curing at 400 °C/60 min. The analysis of the variation of these ellipsometric angles with wavelength indicates a thickness of 219 nm for the PMSSQ film. Figure 3 shows typical temperature-dependent refractive index n and extinction coefficient k spectra of a precleaned silicon wafer, which were determined from our analysis of the ellipsometric angles (Ψ and ∆) measured for the silicon wafer as a function of temperature and wavelength. As can be seen in this figure, both the n and k spectra of the silicon substrate increase slightly with increasing temperature. Both n and k of a given material are known to vary with the density and polarizability of the material, and these are both temperature-

Thermal Expansion of Organosilicate Thin Films

Figure 3. Refractive index n and extinction coefficient k spectra of a bare Si(100) substrate as a function of temperature. The measurements were performed in air over the temperature range 25-160 °C. The native oxide layer of the silicon substrate was determined to be 1.8 nm thick. The inset shows a magnification of the region of 500-610 nm.

dependent.16 We believe that the temperature dependence of silicon’s density and polarizability can account for the observed temperature dependence of the n and k spectra of the silicon substrate. All the silicon wafers we used were found to have native oxide layers with a thickness of around 1.8 nm. The thickness of the native oxide layer on the silicon wafers was found to be unaltered by heat treatment up to 400 °C, indicating that the native oxide layer is not further thickened by the heat treatment. Moreover, the variation of the thickness of the native oxide layers was found to be less than 0.1 nm during the heat treatment. The temperature-dependent n-k spectra of the silicon substrates were used for analyzing the ellipsometric angles of the PMSSQ films deposited on the silicon substrates, which were measured as a function of temperature and wavelength. With this method the thickness variations of all the PMSSQ films were determined as a function of temperature. Figure 4 shows representative examples of the temperature dependence of these film thickness variations (∆t), which were determined for PMSSQ films with various thicknesses that were cured at three different temperatures in the range 250-400 °C. The film thickness was measured with a precision of less than (1 Å. As can be seen in Figure 4, the thickness variation increases linearly with increasing temperature, regardless of the curing history and the initial thickness of the PMSSQ film. However, the slope of the thickness variation versus temperature depends on the curing history and the initial thickness of the PMSSQ film. From the temperature dependence of the thickness variations of the PMSSQ films with various thicknesses (16) (a) Thomas, M. E. Handbook of optical constants of solids II; Palik, E. D., Ed.; Academic: New York, 1991; p 177. (b) Akhmanov, S. A.; Nikitin, S. Y. Physical Optics; Clarendon: Oxford, 1997; p 362.

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Figure 4. The out-of-plane thermal expansion coefficients (R⊥’s) of PMSSQ films with thicknesses in the range 90.0-400.0 nm, which were prepared by curing under a nitrogen atmosphere at three different temperatures: 250 °C/100 min, 300 °C/60 min, and 400 °C/60 min. Si(100) wafers were used as substrates. The R⊥ values were determined from the thickness variations measured using ellipsometry by using eq 1. Table 1. Out-of-Plane Thermal Expansion Coefficients (r⊥’s) of PMSSQ Films Cured at Various Temperatures R⊥ (ppm/°C)a cure temp (°C)

film thickness (nm)

ellipsometryb

250

90.0 92.0 174.7 230.0 385.0 400.0 92.0 230.0 376.0 385.0 25.0 46.0 54.0 92.0 192.0 200.8 230.0 334.0 385.0 633.0 1151.0

312 305

300

400

329 311 323 222 230 240 238 157 170 143 166 148 140 159 170 172 142

SXRc -d 304 196 -

a ppm/°C: part per million per °C. b Measured over 30-200 °C by spectroscopic ellipsometry. c Measured over 30-200 °C by specular X-ray reflectivity. d Not available.

which were cured under various conditions, the out-ofplane TEC R⊥ values were estimated using eq 1. The results are summarized in Table 1. As seen in Table 1, the 250 °C cured film with a thickness of 90.0 nm has R⊥ ) 312 ppm/°C ()part per million per °C); other PMSSQ films with thicknesses in the range 90.0-400.0 nm cured at 250 °C have R⊥ values in the range 305-329 ppm/°C, depending on the sample. However, no correlation was

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Figure 5. The variation of the out-of-plane thermal expansion coefficients (R⊥’s) of PMSSQ films with film thickness. The films were cured at 400 °C/60 min under a nitrogen atmosphere; Si(100) wafers were used as substrates. The R⊥ values were determined from the thickness variations measured with ellipsometry by using eq 1. Filled circles (b) are the R⊥ values determined from the thickness-temperature profiles obtained by analysis of the ellipsometric angles, taking into account the temperature-dependent n-k spectra of the silicon(100) substrate; open squares (0) are the R⊥ values determined from the thickness-temperature profiles obtained by analysis of the ellipsometric angles, taking into account the n-k spectra of the silicon(100) substrate measured at 25.0 °C.

found between the thickness and R⊥ of the 250 °C cured films. The 300 °C cured films with thicknesses in the range 92.0-385.0 nm have R⊥ values in the range 222-240 ppm/ °C, depending on the sample; however, there was also no correlation found between the thickness and R⊥ of the 300 °C cured films. The 400 °C cured films with thicknesses in the range 25.0-1151.0 nm have R⊥ values in the range 140-172 ppm/°C, depending on the sample; however, no correlation was found in this case between the thickness and R⊥ of the 400 °C cured films. Overall the R⊥ values of the PMSSQ films range from 140 to 330 ppm/°C, depending on the curing history; higher curing temperatures result in lower R⊥ values of the cured films. According to previous thermogravimetry (TGA) results,8 in films the PMSSQ precursor undergoes a curing reaction at around 200 °C and the yield of the curing reaction increases with increasing temperature. Taking this result into account, we attribute the curing temperature dependency of R⊥ to the variation of the degree of cross-linking in the PMSSQ films with the curing conditions such as the curing temperature and the curing time; higher curing temperatures and curing times result in a larger degree of crosslinking in the PMSSQ films, leading to lower R⊥ values. We now analyze the influence of the temperature dependence of the n-k spectra of the silicon substrate on the R⊥ values of the PMSSQ films by direct comparison of the R⊥ values determined using the temperaturedependent n-k spectra of the substrate to those determined using the temperature-independent n-k spectra of the substrate. As can be seen in Figure 5, the R⊥ values (open squares) that were determined using the temperature-independent n-k spectra of the silicon substrates are in the range 206-242 ppm/°C for films of thickness 90-1100 nm. These values are rather different from those (141-177 ppm/°C) determined using the temperaturedependent n-k spectra of the silicon substrate (see the filled circles in Figure 5). Moreover, this difference is even larger for films less than 90 nm thick; in particular, the 27 nm thick film was found to have R⊥ ) 1504 ppm/°C. In ellipsometry, as films become thinner, the correlation between the thickness and the refractive index of the film generally becomes stronger. In addition, the n-k spectra of the silicon substrate vary with temperature, as discussed above (see Figure 3). Taking these facts into account, the unrealistically large R⊥ values for PMSSQ films of less than 90 nm thickness are attributed to the strong

Figure 6. (a) Representative X-ray reflectivity profiles of a PMSSQ film cured at 400 °C obtained at three different temperatures (198, 120, and 34 °C); the symbols are the experimental data and the solid lines are the fitted curves. (b) The film thicknesses were obtained by fitting the experimental data measured at the three different temperatures; the solid line is a linear regression fit. The thermal expansion coefficient of the film can be calculated using the slope of the line.

correlation between the thickness and the refractive index of thin films and, further, to the correlations of the film thickness and refractive index with the refractive index of the substrate. Therefore, ellipsometric angles measured for PMSSQ films deposited on silicon substrates as a function of temperature must be analyzed using the variation of the n-k spectra of the silicon substrate with temperature determined before film deposition. A similar effect of the temperature dependence of the n-k spectra of the silicon substrate on R⊥ was observed for poly(methyl methacrylate) films deposited on silicon substrates.17 Specular X-ray Reflectivity. The R⊥ values of some PMSSQ films were also determined from specular X-ray reflectivity (SXR) measurements obtained using synchrotron radiation sources. Figure 6a shows representative SXR profiles at three different temperatures (34, 120, 198 °C) of a PMSSQ film cured at 400 °C/60 min. In this figure, the points are the measured SXR data, whereas the solid lines are the SXR profiles generated by the least-squares fitting of parametrized model electron density profiles to the experimental data. These calculations were carried out using the recursive formula provided by the dynamical theory of Parratt,4,18 which properly incorporates absorption, refraction, and multiple scattering effects. Interfacial roughness was taken into account by introducing Ne´votCroce damping factors into the recursive formula and by assuming Gaussian smearing functions.4,19 In Figure 6a we present the variation of the SXR oscillation frequencies and positions as the temperature changes; the vertically dashed lines on the right and left (17) Kahle, O.; Wielsch, U.; Metzner, H.; Bauer, J.; Uhlig, C.; Zawatzki, C. Thin Solid Films 1998, 313-314, 803. (18) Parratt, L. G. Phys. Rev. 1954, 95, 359. (19) Ne´vot, L.; Groce, P. Rev. Phys. Appl. 1980, 15, 761.

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sides indicate the changes of the SXR oscillation frequencies and positions. In particular, the dashed line on the left side indicates the critical angle θc of the PMSSQ film, which is directly related to the electron density Fe of the film as indicated by the equation

θc ) λ(Fere/π)1/2

(6)

where λ is the wavelength of the X-ray radiation source and re is the classical electron radius. As the temperature increases, the SXR profile shifts toward the low q region (q is the magnitude of the scattering vector, which is related to the incident angle θ) and the oscillation frequency increases; these effects with increasing temperature are due to the reduction of the electron density of the film and increases in the film thickness, respectively. The thickness and electron density of the 400 °C cured PMSSQ film were found to be 200.8 nm and 390 nm-3 at 34 °C, 203.8 nm and 383 nm-3 at 120 °C, and 207.5 nm and 376 nm-3 at 198 °C, respectively. From this variation of thickness with temperature, R⊥ was found to be 196 ppm/°C for the 400 °C cured PMSSQ film, as shown in Figure 6b. This R⊥ value is comparable to the values (140172 ppm/°C) obtained for the 400 °C cured PMSSQ film using ellipsometry, as discussed above (Table 1). However, the R⊥ value is approximately five times larger that those (38.0 - 41.2 ppm/°C) of poly(hydrogen silsesquioxane) (PHSSQ) films with 41.6-113.3 nm thickness that were cured at 400 °C.20 SXR profiles of a PMSSQ film cured at 250 °C were also measured and analyzed with this method (SXR data not shown). The 250 °C cured PMSSQ film was found to have a thickness and electron density of 174.7 nm and 376 nm-3 at 30 °C, 178.7 nm and 373 nm-3 at 105 °C, and 184.2 nm and 369 nm-3 at 200 °C, respectively. From this variation of thickness with temperature, R⊥ of the film was found to be 304 ppm/°C, which is comparable to the values (304330 ppm/°C) obtained for the 250 °C cured PMSSQ film using ellipsometry (Table 1). These SXR results show that PMSSQ films cured at higher temperatures have smaller R⊥ values. Overall, the R⊥ results obtained with the SXR technique are in good agreement with those obtained using spectroscopic ellipsometry (Table 1). The SXR technique can also be used to obtain the electron densities of the films. As described above, a higher curing temperature results in an increase in the electron density of the cured PMSSQ film. Taking into account previous TGA results,8 the increased electron densities of PMSSQ films cured at higher temperatures can be attributed to the increased densities of the films produced by the increased degree of cross-linking at higher temperatures. Therefore, the smaller R⊥ values of films cured at higher temperatures are due to the larger electron densities of films, which are in turn due to the higher degree of cross-linking in the films. Residual Stress Analysis. We attempted to measure the in-plane thermal expansion coefficients (R|) of PMSSQ films of around 700 nm thickness using residual stress analysis. Figure 7 shows the residual stress profiles of PMSSQ films deposited on Si(100) and GaAs(100) substrates that were cured at three different temperatures (250, 300, and 400 °C); in the figure, ∆σF at a given temperature indicates the difference between the stresses at the given temperature and at the curing temperature. As can be seen in the figure, all films deposited on the Si(100) and GaAs(100) substrates exhibit positive residual (20) Wu, W.-L.; Liou, H.-C. Thin Solid Films 1998, 312, 73.

Figure 7. Residual stress-temperature profiles of PMSSQ films spun onto Si(100) and GaAs(100) substrates and cured at various temperatures, which can be used to obtain the inplane thermal expansion coefficients of the films. All film thicknesses were around 700 nm. Filled squares (9) and open squares (0) are the stress profiles of the films adhered on Si(100) and GaAs(100) substrates, respectively. These stress profiles with respect to temperature were obtained during cooling at a rate of 2.0 °C/min after curing at the following temperatures: (a) 400, (b) 300, and (c) 250 °C. Table 2. In-Plane Thermal Expansion Coefficients (r|’s) and Mechanical Properties of PMSSQ Films Cured at Various Temperaturesa cure temp (°C)

a| (ppm/°C)

EF/(1 - νF)b (GPa)

EFc (GPa)

250 300 400

29 ((4) 18 ((3) 12 ((3)

5.9 8.3 12.7

3.8 5.3 8.1

a PMSSQ films had a thickness of 700 nm. b Biaxial modulus. Young’s modulus was estimated from the measured biaxial modulus with assuming νF ) 0.36.

c

stresses regardless of the curing temperature, indicating that the films have larger R| values than the substrates. Further, films cured at a given temperature on Si substrates exhibit larger stress than such films on GaAs substrates. As indicated by eq 3, the residual stress of a film on a substrate is proportional to the difference between R| of the film and RS of the substrate (i.e., ∆R ) R| - RS). Therefore, the results in Figure 7 indicate that all the films have R| values that are larger than the RS of the GaAs substrate (which is greater than that of the Si substrate). From the residual stress profiles in Figure 7, the R| values of the PMSSQ films were obtained using eq 5a. The estimated R| values range 12-29 ppm/°C, depending on the curing temperature of the film (Table 2). Collectively these results indicate that higher curing temperatures produce smaller R| values in the cured PMSSQ films; a similar trend was observed in the R⊥ values of the cured

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PMSSQ films. This curing temperature dependence of the R| values of cured PMSSQ films is attributed to the increases in film density and in the degree of cross-linking in the film with curing temperature, as discussed above. In particular, the R| value of the 400 °C cured film is smaller than that (20.5 ppm/°C) of PHSSQ films.7 However, the PMSSQ films still exhibit much larger than that (1.0 ppm/°C) of silicon dioxide made from tetraethylorthosilane.21 Moreover, for the 400 °C cured films the R| value is 12 to 16 times smaller than the R⊥ values determined using ellipsometry and SXR. In the case of the 300 °C cured films, the R| value is 12 to 13 times smaller than the R⊥ values measured by ellipsometry; for the 250 °C cured films the R| value is 10 to 11 times smaller than the R⊥ values determined using ellipsometry and SXR. In addition to the determination of R|, residual stress analysis can provide the biaxial moduli of the cured PMSSQ films. From the residual stress profiles in Figure 7, the biaxial moduli were determined using eq 5b to be 12.7 GPa for the 400 °C cured film, 8.3 GPa for the 300 °C cured film, and 5.9 GPa for the 250 °C cured film (Table 2). These biaxial moduli are comparable to those of aromatic polyimides.11 A PMSSQ film cured at 500 °C was recently reported to have a modulus of 5.8 GPa and a density of 1.3 g/cm3, as measured by nanoindentation.6 This value for the modulus is comparable to those of semirigid or rigid polyimides.10 From this result, the Poisson’s ratio νF of the 400 °C cured film is estimated to be 0.36. This value for νF is comparable to those of aromatic polyimides.10,22 In general, Poisson’s ratio varies in the range 0.15-0.5;10,23 higher modulus and harder materials exhibit smaller Poisson’s ratios.10,23 Assuming other PMSSQ films have the same νF value (0.36), the Young’s modulus is estimated from the biaxial modulus data to be 8.1 GPa for the 400 °C cured film, 5.3 GPa for the 300 °C cured film, and 3.8 GPa for the 250 °C cured film (Table 2). It here is noted that the Young’s modulus value of the 400 °C cured film is comparable to that (7.1 GPa) of PHSSQ films.7 We conclude that higher curing temperatures produce PMSSQ films with larger biaxial and Young’s moduli, and this is attributed to the higher density that results from the higher degree of cross-linking achieved at higher curing temperatures. On the other hand, silicon oxide films are known to have Young’s moduli in the range 67.0-77.0 GPa, biaxial moduli in the range 80.7-92.8 GPa, a Poisson’s ratio of 0.17, and densities in the range 2.0-2.2 g/cm3.24,25 Compared to the silicon oxide films, the PMSSQ films have lower biaxial and Young’s moduli, a higher Poisson’s ratio, and lower density. These differences probably originate in the amorphous network structure of PMSSQ films, which is composed of branch, ladder, polyhedral, and cage units and characteristically exhibits less dense packing and a lower degree of cross-linking.26 These characteristics of PMSSQ films arise because of the methyl (21) Zhao, J.-H.; Ryan, T.; Ho, P. S.; McKerrow, A. J.; Shih, W.-Y. J. Appl. Phys. 1999, 85, 6421. (22) Maden, M.; Farris, R. J. In Advances in Polyimide Science and Technology; Feger, C., Khojasteh, M., Htoo, M., Eds.; Technomic: Lancaster, PA, 1993; p 644. (23) (a) Polymer Handbook, 2nd ed.; Brandrup, J., Immergut, E. H., Eds.; Wiley: New York, 1975; Chapter V. (b) Sylvester, M. F.; Olenick, J. A. Proc. Int. Electron. Packag. Conf. 1991, 833. (24) Kim, M. T. Thin Solid Films 1996, 283, 12. (25) Ryan, E. T.; Fox, R. J. I. Future Fab Int. 2000, 8, 169. (26) (a) Brinker, C. J.; Scherer, C. W. Sol-Gel Science; Academic: San Diego, CA, 1990. (b) Baney, R. H.; Itoh, M.; Sakakibara, A.; Suzuki, T. Chem. Rev. 1995, 95, 1409. (c) Eisenberg, P.; Erra-Balsells, R.; Ishikawa, Y.; Lucas, J. C.; Mauri, A. N.; Nonami, H.; Riccardi, C. C.; Williams, R. J. Macromolecules 2000, 33, 1940.

Oh and Ree

substituent on each chemical repeat unit, which acts as an inherent cross-link defect site. Discussion of the Observed Anisotropic Thermal Expansion. As described in the earlier sections, all the PMSSQ films with 25.0-1151.0 nm thickness exhibit strong anisotropy over the range 250-400 °C in their thermal expansion, regardless of the curing temperature. This is the first time it has been shown that cured poly(alkylsilsesquioxane) thin films exhibit anisotropic thermal expansion behavior. Considering the amorphous network characteristics of cured PMSSQ films,22 the anisotropic thermal expansion behavior observed in the present study is a very surprising result. We now attempt to explain this thermal expansion behavior. First, we consider the analytical techniques used in this study. As described in the above sections, the R⊥ values of the cured PMSSQ films were measured using ellipsometry and SXR, whereas the R| values were determined using residual stress analysis. The resolutions of these methods are different. However, the R⊥ values determined using ellipsometry were cross-checked with those measured using SXR. Further, in the case of aromatic polyimide films the R| values measured using residual stress analysis have been confirmed using thermomechanical analysis. In summary, these techniques provide R values with good resolution, although there are some differences in their respective resolution limits due to the different principles of each technique. Even when these differences are taken into account, the measured R⊥ values are still very different from the R| values of the cured PMSSQ thin films. We conclude that this surprisingly large anisotropy in the R⊥ and R| values is an actual characteristic of PMSSQ thin films cured on Si and GaAs substrates. Second, we examine the chemical structures of PMSSQ precursor molecules in thin films adhered on Si and GaAs substrates and consider the possible orientations of the precursor segments. As can be seen in Figure 1, the PMSSQ precursor molecule is partially networked with Si-O bonds and contains one nonpolar methyl group per every Si atom, as well as polar hydroxyl groups and partially polar ethoxy groups; the PMSSQ is therefore known to be amphiphilic.5 The Si and GaAs substrates have somewhat polar characteristics due to the native oxide layers on their upper surfaces, compared to air or nitrogen gas. When thin films of PMSSQ precursor molecules with these chemical characteristics form through solution coating and subsequent drying on these substrates with native oxide layers under nitrogen atmosphere, the film interface with air and nitrogen gas is likely to be rich with nonpolar methyl groups, while the substrate-film interface is likely to be rich with polar hydroxyl groups and partially polar ethoxy groups. The preferential orientation of methyl groups at the film interface with air and nitrogen gas and of hydroxyl and ethoxy groups at the substrate-film interface are likely to induce the PMSSQ precursor molecules to orient in the film plane. Finally, we consider the curing reactions of PMSSQ precursor molecules in thin films. As shown in Figure 1, the curing reactions occur via the condensation reactions of polar hydroxyl groups and partially polar ethoxy groups, simultaneously generating Si-O networks and water and ethyl alcohol as byproducts; these byproducts are outgassed from the polymer network film. During curing, it is likely that Si-O network formation will occur mainly in the film plane rather than out-of-plane because the reactive hydroxyl and ethoxy groups in the confined thin film will orient most favorably in the film plane as described above. On the other hand, during curing it is

Thermal Expansion of Organosilicate Thin Films

expected that the methyl groups directly bonded to Si atoms will retain their orientation toward the nitrogen atmosphere/film interface because of their nonpolar characteristics. These methyl groups are not involved in any curing reaction and so remain as defects in the networks formed by the condensation reactions of the hydroxyl and ethoxy groups during curing. This preferential orientation of the methyl groups toward the upper film surface and the preferential network formation in the film plane cooperatively lead to relatively high crosslink density in the film plane but low out-of-plane crosslink density. Therefore, we conclude that the observed anisotropic thermal expansion in the cured PMSSQ thin films is due to the anisotropy of cross-link density in the films, which is produced by the combination of the effects of the preferential orientation of methyl groups toward the upper film surface and the preferential network formation in the film plane that occurs during curing. As described above, the R| values of PMSSQ films are only 4-10 times larger than the RS (2.8 ppm/°C) of silicon wafers. Although this difference is not large, it results in a residual stress of 30-120 MPa at the interface of the PMSSQ film and the silicon wafer, depending on the filmprocessing conditions;8 these residual stress values are too large to be ignored. On the other hand, the R| values are comparable to that (20 ppm/°C) of copper metal. Therefore, there is expected to be only low residual stress for PMSSQ films interfaced with copper metals. In contrast, the R⊥ values of the PMSSQ films are 50118 times larger than that of silicon wafers and 7-17 times larger than that of copper metal, which are both used in the semiconductor industry, and these differences have the potential to produce large residual stress in the interfaces with silicon wafers and metal lines along the out-of-plane direction of semiconductor devices with multilayer structures. Conclusions PMSSQ thin films of 25.0-1151.0 nm thickness were prepared by spin-casting PMSSQ soluble precursor onto Si and GaAs substrates with native oxide layers and then drying and curing the films in a nitrogen atmosphere at 250-400 °C. The out-of-plane thermal expansion coef-

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ficients R⊥ of the cured films was measured in the temperature range 25-200 °C using spectroscopic ellipsometry and synchrotron X-ray reflectivity, and the inplane thermal expansion coefficients R| were determined over the range 25-400 °C by using residual stress analysis. PMSSQ films cured at higher temperatures exhibit reduced thermal expansion, which we attribute to the more dense molecular packing and higher degree of cross-linking obtained at higher temperatures. Surprisingly, all PMSSQ films exhibit very strong anisotropic thermal expansion; depending on the curing temperature, R⊥ ranges from 140 to 329 ppm/°C, while R| ranges from 12 to 29 ppm/°C. We attribute this anisotropic thermal expansion in the PMSSQ thin films to the anisotropy of cross-link density in the films, which results from the preferential orientation of methyl groups toward the upper film surface and the preferential network formation in the film plane that occurs during curing. The R⊥ values of the PMSSQ thin films are much larger than that (2.8 ppm/°C) of silicon wafers and that (20 ppm/ °C) of copper metal that are used in the semiconductor industry, potentially causing large residual stress in the interfaces of the films with silicon wafers and metal lines in the out-of-plane direction of semiconductor devices with multilayer structures. The R| values of the films are only 4-10 times larger than those of silicon wafers but are comparable to that of copper metal and therefore relatively low residual stress is expected to arise at the interfaces of silicon wafer and metal lines with the films in semiconductor devices with multilayer structures. The film electron densities were also determined from the synchrotron X-ray reflectivity measurements, and the film biaxial moduli were measured using residual stress analysis; these densities and biaxial moduli were found to be always smaller than those of silicon oxide. Acknowledgment. This study was supported by the Korean Ministry of Commerce, Industry & Energy, and the Korean Ministry of Science & Technology (MOST) (Basic System IC Technology Project: M103BY01003503B2501-03550), by the Center for Integrated Molecular Systems (Korea Science & Engineering Foundation), and by the Korean Ministry of Education (BK21 Program). LA049581M