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Colloids and Surfaces A: Physicochem. Eng. Aspects 300 (2007) 111–116

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Diffusion of solvents in thin porous films D. Shamiryan ∗ , M.R. Baklanov, P. Lyons 1 , S. Beckx, W. Boullart, K. Maex IMEC, Kapledreef 75, Belgium

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Received 16 June 2006; received in revised form 12 October 2006; accepted 23 October 2006 Available online 29 October 2006

Abstract

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Porous films are used nowadays as dielectrics with low dielectric constant (so-called low-k dielectrics). Knowing the porous structure of such films is important for successful integration in the semiconductor manufacturing technology. We developed a simple characterization method based on diffusion of solvents inside a porous film. In our experiments toluene as a non-polar solvent and ethanol as a polar solvent were used. A porous film is covered with a barrier impermeable for solvent so the solvent only can enter the film from the side. The barrier is transparent that allows observation of diffusion as a color change of the film. Measuring diffused distance as a function of diffusion time, diffusion coefficients can be calculated. It was found that the diffusion coefficients strongly depend on the porous structure of the films. Small pores (with the size comparable with the solvent molecule size) show low diffusion coefficients with high activation energies comparable with the enthalpy of evaporation. Bigger pores exhibit high diffusion coefficients with low activation energies corresponding to the activation energy of the solvent viscosity. Measuring diffusion coefficients as functions of porosity/pore size it is possible to evaluate the interconnectivity of the porous structure of a film in question. © 2006 Elsevier B.V. All rights reserved.

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Keywords: Low-k dielectric; Porosity; Diffusion; Pore interconnectivity

1. Introduction

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The performance of integrated circuits (IC) has been increasing for several decades. The most direct way to increase working speed of an integrated circuit is to pack more faster and smaller transistors into an IC. For the last two decades device feature sizes have decreased from 1 ␮m down to 90 nm increasing the working frequency of microprocessors from 66 MHz to 4 GHz. However, not all IC components work faster as their sizes decrease. While continuous shrinking makes transistors work faster it makes interconnections between transistors work slower. A good figure of merit to characterize interconnects is RC, which is a unit of time. A signal propagating through the interconnection experiences resistance–capacitance (RC) delay. Shrinking the cross-section of a wire increases its resistance and bringing wires closer together increases capacitance between wires. As a result, RC delay increases with device shrinkage and limits performance improvements resulting from device scaling.

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Corresponding author. Tel.: +32 16288029; fax: +32 16281214. E-mail address: [email protected] (D. Shamiryan). Also at University of Dublin, Trinity College, Ireland.

0927-7757/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2006.10.055

The RC delay must be reduced as size reduction continues. It is predicted that soon RC delay will exceed transistor speed becoming a serious limitation to performance improvement. Since scaling down dimensions works against RC delay, the only way to bring down resistance and capacitance is to use other metals (with lower resistivity) and dielectrics (with lower dielectric constant) instead of conventional aluminium/SiO2 . The obvious candidate to replace Al is Cu (36% decrease in resistivity). Copper has been successfully integrated into IC manufacturing after considerable effort. Replacing SiO2 as a dielectric has not been a straightforward process. In principle, any material with a dielectric constant k lower than 4.2 (so-called low-k dielectric) are of interest, but k-value is only one of many required properties. One of the possible ways to reduce k-value of a material is reduction of its density. The density of a material can be decreased by increasing its free volume by rearranging the material structure or by the introduction of porosity. Porosity can be related in two different ways: constitutive and subtractive. Constitutive porosity refers to self-organization of a material. After manufacturing, such a material is porous without any additional treatment. Constitutive porosity is relatively low (usually less than 15%) and pore sizes are around 1 nm in diameter. According to IUPAC classification [1], pores with sizes less than 2 nm are called “micropores”.

D. Shamiryan et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 300 (2007) 111–116

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plenty of techniques that are able to characterize total porosity and pore size distribution of a porous film: positron annihilation lifetime spectroscopy (PALS) [2,3]; small-angle neutron scattering (SANS) and small-angle X-ray scattering (SAXS) combined with specular X-ray reflectivity (XRR) [4]; and ellipsometric porosimetry [5,6]. However, characterization of pore interconnectivity is less obvious. EP is able to measure only interconnected pores since it is based on penetration of solvent into a porous film, and therefore, can provide an answer whether the pores interconnected or not. However, if pores are interconnected, the interconnection structure cannot be revealed. Another technique that is claimed to reveal interconnectivity is PALS where movement of a positronium through a porous film is studied. There is a concern, however, about ability of positronium to travel through the narrow channels since they may represent too high energetic barriers for such a quantum particle [7]. In this work, we present a simple and effective method for studying interconnectivity of a porous film. The method is based on diffusion of solvent inside the porous film in the lateral direction and does not require any special equipment. 2. Experimental technique The studying of interconnectivity is based on lateral solvent diffusion in a porous film. The porous film is capped at the top surface by any film that would prevent solvent from penetration through the top surface (e.g. rather thick SiO2 , Si3 N4 or SiC). The capping layer should not penetrate into the porous film itself in order not to disturb the porous structure of the studied film. In that respect the best deposition technique would be plasmaenhanced chemical vapour deposition (PECVD) as it is known that such type of deposition result in penetration of the capping layer into the porous film no more than 3–5 nm [8,9]. Taking into account that our films were of 400 nm thickness the limited penetration of the barrier should not have a significant influence on the results. It should be noted that the capping film should be transparent in order to allow observation of the solvent diffusion. Thus prepared, the samples were cleaved and introduced

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Subtractive porosity, on the other hand, implies selective removal of part of the material. The removable part can be an artificially added ingredient (e.g. a thermally degradable substance called “porogen” which is removed by an anneal leaving behind pores) or just part of the material that is removed by selective etching (e.g. Si–O bonds in SiOCH materials could be removed by HF). Subtractive porosity can be as high as 90% and pore sizes vary from 2 nm to tens of nanometers (pores with sizes larger than 2 nm are called “mesopores” according to IUPAC classification). Although beneficial for k-value reduction, porosity creates number of challenges when porous dielectrics are to be integrated in IC manufacturing. Among other issues (e.g. mechanical instability or low thermal conductivity), porosity allows unwanted diffusion through the film. It could be, for example, diffusion of chemicals used in processing or diffusion of copper. Copper readily degrades the dielectric properties of the insulator increasing leakage currents and decreasing the breakdown voltage. As a result, reliability of the devices significantly decreases making their lifetimes unacceptably short. Copper diffusivity drastically increases with porosity of the dielectric. Copper diffusion must be stopped by a diffusion barrier between copper and a porous film. Due to technological reasons that will not be covered in this work, the diffusion barrier cannot be deposited on copper but must be deposited on a porous film instead. The barrier must be thin (nm scale) and fully dense (contain no pinholes). Covering a porous material with such a barrier is non-trivial. If the material is highly porous with large pores connected to each other, the barrier may be unacceptably thick in order to bridge all the exposed pores (see Fig. 1). It should be noted that the barrier itself should not penetrate into the porous material, which is possibility with some deposition techniques. In some approaches, porous surface is first sealed to prevent barrier penetration and then a diffusion barrier is deposited on the sealed surface. Deposition of a rigorous barrier tends to be easiest when pores are small and porosity is low. From the above consideration we can conclude that not only porosity and pore size are important for characterization of a porous film, but also pore interconnectivity. There are

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Fig. 1. A schematic representation of a thin film deposited on a porous material with (a) separated mesopores connected by microchannels and (b) interconnected mesopores. As porosity increases, the mesopore connections make the deposition of a continuous film more difficult. It should be noted that the pore size is the same in both cases.

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Fig. 2. Schematic representation of solvent diffusion experiments. Diffusion distance l is measured as colour change by optical microscope.

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Fig. 4. Diffused distances of toluene in different low-k materials (MSQs with 40% porosity, SiOCH with 7% porosity) as functions of square root of exposure time. Diffusion coefficients were calculated from the line slopes using Eq. (1).

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The films are quite uniform in terms in porosity and pore size from top to bottom. First, the density of the film (and, therefore, porosity) was found to be uniform by X-ray reflection (XRR) measurements. Second, uniformity of pore size distribution was indirectly shown by ellipsometric porosimetry. During porosimetry measurements when the film is subjected to toluene at different pressures, condensation in pores observed depending on the pore size. At every pressure, when the toluene is condensed in the pores of particular size, it was possible to fit a simple single-layer model with uniform optical properties to the ellipsometric measurements. Therefore, as the film is filled with toluene uniformly we can presume that the porosity and pore size distribution is uniform throughout the film thickness.

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in liquid solvent. The solvent penetrates the porous film through the edges and diffuses laterally as schematically shown in Fig. 2. The diffusion distance l is measured as a colour variation in topdown view by optical microscope, a typical observation of such colour variation is shown in Fig. 3. The main measure of diffusion is a diffusion coefficient. It is known from diffusion theory [10] that the mean distance l travelled by a diffusion front is described (in a simplified form) by the following equation: √ l = 2 Dt (1)

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D. Shamiryan et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 300 (2007) 111–116

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where D is a diffusion coefficient (in our case the diffusion coefficient of solvent in the porous film) and t is diffusion time. Therefore, measuring diffusion distance as a function of time it is possible to calculate a diffusion coefficient of the solvent in a particular porous film. In our experiments, we used toluene and ethanol as solvents and four different low-k materials: two porous MSQs (methylsilsesquioxane, varied porosity from 15% to 40%) deposited by spin-on technique, one SiOCH (silicon oxycarbide, initial porosity of 7%, increase up to 40% porosity achieved by HF treatment [11]) deposited by PECVD and a low porosity polymer deposited by spin-on technique. Porosity and pore size distribution of the films were measured by ellipsometric porosimetry.

Fig. 3. Example of colour variation of a porous film due to solvent diffusion as observed by optical microscope.

3. Results and discussion The diffusion coefficients are calculated from the slopes of the curves representing penetration distances as functions of square root of the exposure time. Such curves for four studied materials (MSQs with 40% porosity, SiOCH with 7% porosity and the polymer) are shown in Fig. 4. One can see that diffusion strongly depends on porosity. Let us now see how diffusion changes when porosity of a film is gradually increases. For this observation we selected one of the MSQs with varied porosity. A few words should be said about preparation of such material. Pristine as deposited MSQ has constitutive porosity of about 15% consisting of micropores of about 1 nm in size. The porosity, however, can be increased by adding so-called porogen – thermally unstable organic molecules of about 3 nm in size – during MSQ deposition. After thermal decomposition, the porogen leaves behind mesopores of about 3 nm size. Obviously, the higher porogen content is, the higher total porosity of the film will be. The results of characterization of such a film with varied porogen content by EP is shown in Fig. 5, where total porosity is divided between microporous and

D. Shamiryan et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 300 (2007) 111–116

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Fig. 5. Porosity as a function of porogen load of MSQ. Relative volume of micro- and mesoporosity is indicated by different bar fill.

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The following explanation can be proposed for the diffusion coefficient behaviour. When amount of mesopores is small they are connected to each other only by micropores and, therefore, diffusion is limited by movement of solvent through micropores resulting in rather low diffusion coefficient. Slight increase in diffusion coefficient with increase of amount of mesopores can be explained by the fact that distance between mesopores (where solvents travels through micropores) becomes smaller. This situation is described by the scheme represented by Fig. 1(a). As amount of mesopores increases further and passes a certain threshold, mesopores overlap creating rather large paths for diffusion. At this moment diffusion coefficient abruptly increases as micropores are not the limiting paths for diffusion anymore. The scheme represented by Fig. 1(b) is realized. One can conclude that low diffusion coefficient indicating the fact that mesopores are connected by micropores should predict easier diffusion barrier deposition (or, in other words, easier sealing of the porous surface). Indeed, such an effect was observed in experiments of sealing of the porous surface by plasma treatment [12]. The exposure of porous surface to plasma led in some cases to the conversion of the top porous surface to a dense sealing layer impermeable for solvents. It was found that a porous film can be sealed by plasma when the toluene diffusion coefficient does not exceed 100 ␮m2 /s. From the presented results one can suggest that diffusion in micro- and mesopores occurs through different mechanisms. It is known that diffusion of a substance through a porous medium can be described by at least three different mechanisms: Knudsen diffusion, viscous flow and surface diffusion [13]. Knudsen diffusion is mostly applicable to the diffusion of gases in porous media when diffusing molecules collide with pore walls and not with each other. As obvious from the designation, the viscous flow model is applicable to a flow of liquid through a porous medium. In this mode of transport, a diffusion coefficient is proportional to the specific permeability coefficient B of a porous

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mesoporous fractions. One can see that total porosity gradually increases as porogen content increases. It should be noted that the mean size of micro- and mesopores remains almost constant. The diffusion coefficient, however, shows a remarkably different behaviour. When porogen load is low (less than 10%), the diffusion coefficient increases gradually. However, as porogen load exceeds 10% an abrupt increase of the diffusion coefficient is observed, as shown in Fig. 6. Other material with varied porosity show similar behaviour to the one described above—diffusion drastically increases as porosity exceeds a certain threshold (see Fig. 7). Steeper increase of the diffusion coefficient in the case of SiOCH can be attributed to the fact that not only porosity but also mean pore size increases as this material is treated with HF, while both MSQs have constant pore size with only porosity increased.

Fig. 7. Diffusion coefficient as a function of porosity for all studied materials with varied porosity.

Fig. 6. Diffusion coefficient of the porous MSQ with different porogen load as a function of total porosity.

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D. Shamiryan et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 300 (2007) 111–116

Fig. 9. Dependence of porosity (filled squares) and pore size (open circles) of SiOCH film on the HF treatment time.

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varied porosity (variation in porosity/pore size is obtained by HF treatment, the dependence of porosity and pore size on the treatment time is shown in Fig. 9). The activation energies were calculated from the Arrhenius plots (logarithm of D versus 1/T, the plot for toluene is shown in Fig. 10). The activation energies of ethanol and toluene diffusion coefficients in SiOCH versus HF treatment are shown in Fig. 11. One can see that there are two different diffusion modes with different activation energies depending on HF treatment time (meaning dependence on porosity/pore size). The activation energies are higher for the films with low porosity/small pores and lower for the films with higher porosity/bigger pores. The measured activation energies can be compared with the known values [15] for these two solvents. When the pores are big, the activation energy of diffusion are close to those of the viscos-

(2)

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where p is porosity, r the pore radius and q is tortuosity factor. Tortuosity can be approximated by the Maxwell relation [14]:

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B=

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Fig. 8. Diffusion coefficients of toluene and ethanol as functions of the specific permeability B (see text) of the SiOCH with varied porosity.

1 q = 1 + (1 − p) 2

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(3)

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Substituting Eqs. (2) and (3), one can see that B depends only on porosity and pore size. The diffusion coefficients of toluene and ethanol as a function of the specific permeability of SiOCH with varied porosity (see Fig. 8) reveal proportionality between D and B for higher porosity/mesopores. In the region of lower porosity/micropores the dependencies deviate from the linear law implying the viscous flow model is not valid. Indeed, the size of micropores (<2 nm) is comparable with the size of diffusing molecules (0.6 nm for toluene and 0.4 nm for ethanol) and conception of a viscous flow becomes meaningless. Moreover, the model is developed for single pore size and apparently is not valid for bi-modal pore size distribution (as in the case of SiOCH after 2 HF treatment). We can conclude, however, that the viscous flow diffusion model could be used for description of solvent diffusion in porous low-k containing mesopores with single-modal distribution. Another distinction between different diffusion modes can be made based on activation energy of solvent diffusion in films with different porosity. If the viscous flow model is valid then the diffusion should be determined by the solvent viscosity and its temperature dependence. In the case of the surface diffusion the process is determined by removing a molecule from one surface site (desorption) and attaching it to another one. In that case the temperature dependence should be governed by enthalpy of desorption. To measure activation energies, we measured diffusion coefficients of toluene and ethanol at several different temperatures (ranging from 18 to 40 ◦ C) in SiOCH films with

Fig. 10. Diffusion coefficient of toluene in SiOCH with varied HF treatment (varied porosity/pore size) versus reciprocal temperature. The lines are exponential fits.

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D. Shamiryan et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 300 (2007) 111–116

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be described by a viscous flow model. The diffusion depends on porosity and pore size as predicted by the model and, moreover, the activation energy of the diffusion corresponds to that of the viscosity temperature dependence. Diffusion in small pores (comparable with the size of the diffusing molecules) is likely to be described by the surface diffusion model when a diffusing molecule hops from one site in a pore to another. The diffusion activation energy in that case is higher and comparable with the enthalpy of evaporation of the diffusing substance. Therefore, observing diffusion in a porous film that contains both micropores and mesopores it is possible to reveal its pore structure interconnections. If the diffusion is slow and described by the surface diffusion model, then the mesopores are connected only through narrow micropores. If the diffusion is high and described by the viscous flow model, then mesopores are percolated and connected directly to each other.

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[1] J. Rouquerol, D. Avnir, C.W. Fairbridge, D.H. Everett, J.H. Haynes, N. Pernicone, J.D.F. Ramsay, K.S.W. Sing, K.K. Unger, Pure Appl. Chem. 66 (1994) 1739. [2] D.W. Gidley, W.E. Frieze, T.L. Dull, J. Sun, A.F. Yee, C.V. Nguen, D.Y. Yoon, Appl. Phys. Lett. 76 (2000) 1272. [3] M.P. Petkov, M.H. Weber, K.G. Lynn, K.P. Rodbell, A. Cohen, Appl. Phys. Lett. 74 (1999) 2546. [4] W. Wu, W.E. Wallace, E. Lin, G.W. Lynn, C.J. Glinka, R.T. Ryan, H. Ho, J. Appl. Phys. 87 (2000) 1193. [5] F.N. Dultsev, M.R. Baklanov, Electrochem. Solid State Lett. 2 (1999) 192. [6] M.R. Baklanov, K.P. Mogilnikov, V.G. Polovinkin, F.N. Dultsev, J. Vac. Sci. Technol. B 18 (2000) 1385. [7] K.P. Mogilnikov, M.R. Baklanov, D. Shamiryan, M. Petkov, Jpn. J. Appl. Phys. 43 (2004) 247. [8] Y.W. Koh, K.P. Loh, L. Rong, A.T.S. Wee, L. Huang, J. Sudijono, J. Appl. Phys. 93 (2003) 1241. [9] V. Jousseaume, M. Fayolle, C. Guedj, P.H. Haumesser, C. Huguet, F. Pierre, R. Pantel, H. Feldis, G. Passemard, J. Electrochem. Soc. 152 (2005) F156. [10] P.W. Atkins, Physical Chemistry, 6th ed., Oxford University Press, 1998, p. 753. [11] D. Shamiryan, M.R. Baklanov, S. Vanhaelemeersch, K. Maex, Electrochem. Solid State Lett. 4 (2001) F3. [12] T. Abell, D. Shamiryan, M. Patz, K. Maex, in: G.W. Ray, T. Smy, T. Ohta, M. Tsujimura (Eds.), Proceedings of the Advanced Metallization Conference (AMC 2003), 2003, p. 549. [13] D.D. Do, Adsorption analysis: equilibria and kinetics Series on Chemical Engineering, vol. 2, Imperial College Press, London, 1998, p. 374. [14] D.D. Do, Adsorption analysis: equilibria and kinetics Series on Chemical Engineering, vol. 2, Imperial College Press, London, 1998, p. 398. [15] D.R. Lide (Ed.), CRC Handbook of Chemistry and Physics, 85th ed., CRC Press, 2005.

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ity change and we can conclude that the diffusion of solvents in films with big pores indeed can be described by the viscous flow model. In the region of small pores/low porosity the measured activation energies can be compared with the enthalpy of evaporation of the solvents. There are discrepancies between the measured activation energies and the enthalpies of evaporation that might be attributed to the fact that evaporation is removing a molecule from an ensemble of same molecules in the liquid which is not the same as removing a molecule in a pore where curvature of the meniscus plays a role. However, the tendency to higher activation energy in small pores (evaporation/desorption) as compared to lower activation energy in big pores (viscosity) is clearly observed.

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Fig. 11. Toluene and ethanol diffusion activation energies in SiOCH as functions of HF treatment. The enthalpies of evaporation and viscosity activation energies are shown for comparison.

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4. Conclusions

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We propose a simple and effective method for studying the porous structure of a thin film. The method is based on observation of lateral diffusion of solvents inside a porous film using optical microscope. The diffusion coefficients of solvents calculated from such observations can be used for revealing the pore interconnection structure of the porous film in question. There are two different type of diffusion depending on pore size and, perhaps, porosity. When pores are big (several times bigger than the size of a diffusing molecule) the diffusion can

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