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Energy transport in plasma etching of nanoporous dielectric materials
Superlattices and Microstructures 35 (2004) 195–204 www.elsevier.com/locate/superlattices
Energy transport in plasma etching of nanoporous dielectric materials Joel Plawskya,∗, Shom Ponotha, George Dalakosa, Kourosh Malekb, Marc-Olivier Coppensb a Rensselaer Polytechnic Institute, Troy, NY, USA b DelftChemTech, Faculty of Applied Sciences, Delft University of Technology, Julianalaan 136, 2628BL Delft,
The Netherlands Received 18 May 2003; accepted 30 October 2003 Available online 19 May 2004
Abstract A Monte Carlo routine was developed to simulate the motion and energetics of ions in the pores of a xerogel material under plasma etching conditions. The simulation included the effects of an applied electric field and input conditions for the pore as a function of pressure and applied voltage in the plasma reactor. We were interested in the ion energy in a pore, the ion penetration depth and the effect of ion energy on etching. At low pressures the nanoporous material etches faster than dense silicon dioxide. This is to be expected given the decrease in density and increase in surface area that arises due to the porosity. However, as the pressure is increased, the etch rate decreases dramatically and, eventually, the dense oxide may etch faster than the porous material. CHF3 was used as the etchant gas and, for this gas, we believe this behavior to be controlled by the ion energy and energy transport in the pores of the xerogel material. As the pressure in the plasma reactor is increased, the incoming ions switch over from etching activation to polymerisation activation. This agrees with the observed crossover in etch rate seen experimentally and with the cessation in etching as pressure is increased. The switch is affected by pore roughness and correlates with the average ion energy in the pore. © 2004 Elsevier Ltd. All rights reserved. Keywords: Plasma etching; Nanoporous solids; Diffusion and reaction
∗ Corresponding author. Tel.: +1-518-276-6049; fax: +1-518-276-4030.
E-mail address: [email protected] (J. Plawsky). 0749-6036/$ - see front matter © 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.spmi.2003.10.001
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Fig. 1. Rate of etching of xerogel as a function of porosity and pressure.
1. Introduction Traditionally, nanoporous materials have been used in heterogeneous catalysis, fuel cells, membranes, and insulation, but, increasingly, nanoporous materials are being investigated for use as interlayer dielectrics in integrated circuits [1–5]. An understanding of diffusion and reaction in these materials under microelectronics processing conditions is fundamentally important if these materials are to be qualified for IC fabrication. In plasma processing, pressures are generally low, <1 Torr, and so Knudsen diffusion [6] is the dominant mechanism for movement of species inside xerogel pores. Malek and Coppens [7, 8] used Monte Carlo methods to investigate the effect of pore roughness on Knudsen self-diffusion, transport diffusion, and chemical reaction in rough nanopores. There is an extremely limited amount of experimental data on the reactive ion etching of nanoporous materials [9, 10]. Fig. 1 shows the results of some work we have performed using nanoporous silica xerogels. There are two significant features. At low pressures the porous material etches faster than dense silicon dioxide. This is to be expected given the decrease in density and increase in surface area that arises due to the porosity. However, as the pressure is increased, the etch rate decreases dramatically and, eventually, the dense oxide may etch faster than the porous material. The etch system in this work was CHF3 diluted in N2 . CHF3 is an etching gas normally used for controlled etching of oxide materials. This gas produces ions that undergo two different types of chemical reaction. In the first reaction, the fluoride containing ions etch the silicon dioxide [11]. In the second,
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Fig. 2. The xerogel etch rate with oxygen in the plasma.
the carbon containing ions can polymerise to form a fluorocarbon layer [12]. This polymerisation normally occurs on the walls of a trench or via and allows one to preferentially etch the base, leading to deep trenches or vias with very straight sidewalls. Such a process can occur in the pores of a nanoporous material and this is what is believed to be happening here [9, 13]. As pressure or porosity is increased, polymerisation may overtake etching, which can be verified by adding some oxygen to the etching plasma. When oxygen is added, the fluorocarbon film is removed and the etch rates for the materials approach one another as shown in Fig. 2. The etch rate is also a function of time. This is clearly shown in Fig. 3 where we plot the etch rates for several xerogel materials compared with that for solid SiO2 as a function of time. Here one can see that several of the lower porosity xerogel materials are etched more slowly than the solid SiO2 but that as time progresses the etch rates at this pressure (120 mTorr) eventually approach one another and are asymptotically approaching zero. In all cases, we are forming polymer inside the pores and eventually this polymer deposition chokes off the etching of the silicate material. This data also shows that the etch rate is affected by the pore size since pore size in these materials generally increases with porosity. That is one reason the 55% porous material appears to always etch faster than the solid. We should note that the etch rate is defined by following the signature of the “pure” xerogel material that we obtain from ellipsometry. Since the fluorocarbon layer and its build-up within the xerogel changes with time, the optical properties of the mixed layer also change with time. As yet, we have not developed a procedure for defining the exact composition of that layer. Thus the etch rates that we report should be considered as maximum etch rates since there are most likely remnants of xerogel remaining in the mixed layer. Figs. 4–6 show high resolution field emission scanning electron micrographs of the surface of a 55% porous xerogel material at etch times of 0, 2, and 10 min. One can clearly
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Fig. 3. Etch rates for xerogel and SiO2 films as a function of time. The etch pressure was 120 mTorr.
Fig. 4. A surface image of a 55% porous xerogel film prior to etching. The dark areas represent larger pores in the material that are rough and tortuous.
see from the featureless image of Fig. 6 how the pores of the material become filled as the etching process proceeds. In this paper we perform some preliminary, dynamic Monte Carlo simulations to investigate how plasma processing affects and is affected by the porosity and roughness of a nanoporous material such as a xerogel.
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Fig. 5. The surface of a 55% porous xerogel film after etching for 2 min. Rough tortuous pores are still distinct.
Fig. 6. The surface of a 55% porous xerogel material after etching for 10 min. Only remnants of the largest pores are still visible. Smaller pores have been filled with polymer.
2. Model development In developing the model we assumed that a Knudsen diffusion regime exists inside the pore. The particle adsorbs or slams into the pore wall and is emitted at angles that obey a cosine distribution. This presumes some interaction between the particle and the wall so that the particle does not remember the angle at which it struck the wall. The particle transfers energy to the pore wall molecules upon each collision. This energy transfer depends upon the particle energy, the particle and target molecular weights, and the angle of collision with the wall. The pore wall dissipates the deposited energy instantaneously and remains at a constant temperature. The overall etching process involves a trade-off between
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Fig. 7. Successive generations of (pre)fractal pore walls.
Fig. 8. Single-charged particle trajectories inside a 1st-generation pore. (a) V = 0; (b) V = 10.
fluorocarbon polymerisation and etching, both of which are activated by the incoming ions. Etching is facilitated if a particle transfers enough energy to exceed a threshold energy for sputtering the fluorocarbon film. A much lower threshold energy on the order of 1.5 eV is sufficient to activate polymerisation. The equilibrium energy corresponding to the pore wall temperature was taken as 0.04 eV (298 K). 2.1. Pore geometry The pore wall was generated using a randomised fractal iteration algorithm to yield a 2D Koch pore [7, 8]. The pores were labelled as 0th, 1st, 2nd, etc. generations with the 0th generation being a straight pore. Fig. 7 shows the first three generations of pore wall showing how the roughness is increased with each successive generation. 2.2. Ion motion If a field is applied along the length of a pore, then ion motion is no longer perfectly random but takes on a set of preferred directions that depend upon the charge on the ion and the strength of the field. A Glauber criterion was used to choose and bias the random walk. The effect this has on particle trajectories can be seen in Fig. 8. Once the field is applied, particles take fewer steps within a pore and their steps going against the field direction (right to left) are much smaller.
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2.3. Ion/particle energy A particle’s energy in the pore depends upon the particle’s molecular weight, the target molecule’s molecular weight, and the angle at which the two particles collide. In a centerof-mass coordinate system, Eq. (1) describes the fraction of energy left in the molecule following a collision with the wall. This formula applies at the energies used in this study. 4m 1 m 2 2 θ Energy left = 1.0 − . (1) sin 2 (m 1 + m 2 )2 Here m 1 and m 2 are the masses of the particles and θ is the angle of the collision. In this model we assume that the ion mass is that of N2 (28) and the target is Si(28) or O(16) (these are the two constituents of the xerogel material). 2.4. Reaction Two reactions were assumed to take place simultaneously: etching and polymerisation. The ions colliding with the pore wall were assumed to facilitate or activate these reactions. The actual reaction and reaction rate depend upon reactive molecules adsorbing on the surface and products diffusing away. Thus, the rate of reaction is a complicated function that requires a more sophisticated Monte Carlo simulation than what was undertaken here. Our goal is to just see whether some features of what we observe experimentally can be understood on the basis of a much simpler, equilibrium-like activation mechanism. 2.5. Input conditions To accurately simulate the angular and energy distributions of ions entering a pore we needed to simulate what was occurring in the plasma sheath. Building on earlier work by Sawin [14], Kushner [15–17] and co-workers, we wrote a plasma sheath routine that simulated the motion and collisions of the ions. Fig. 9 shows a comparison of that simulation with some older experimental data [14]. Since plasmas are very complex, the data are very hard to take, and details of the plasma were not reported in the original paper, the agreement between simulation and data is reasonable. 3. Results and discussion We were interested in how far dangerous ions, i.e. ions that could activate reactions, could penetrate into a pore. In Fig. 10 we chart the distance it takes for an ion to reach equilibrium in the pore. Once equilibrated, the ions no longer have enough energy to activate etching or polymerisation and hence are harmless. The penetration depth for the ions is important for semiconductor manufacturers who are worried that open pore materials such as xerogels could allow dangerous ions to penetrate all they way through the material and to the substrate below. As the pore roughness increases, the penetration depth decreases significantly. The average depth in combination with an exit fraction of ions gives a clue as to how “dangerous” a pore would be. Rougher pores appear to be preferred from a device stability and protection standpoint.
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Fig. 9. Comparison of experimental Ar plasma energy with simulated plasma energy distributions. (a) P = 30 mTorr; (b) P = 50 mTorr.
Fig. 10. The average distance a particle penetrated into the pore while delivering enough energy to sputter.
Fig. 11 shows the average energy of particles in the pore. We see a sharp decrease in average energy with pressure that follows the decrease in etch rate observed experimentally. This has also been seen in simulations by Sankaran and Kushner [13] who varied the average energy by changing the plasma bias voltage. There is also a substantial decrease in the average energy as the pore gets rougher, though that change reaches an asymptote. The decrease in average energy is much steeper than for a flat plate scenario, indicating the
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Fig. 11. The average energy of particles inside the pore.
effect of roughness. Energies all seem to converge at high pressure, which also follows the etch rate data. The results seem to indicate that facilitation of etching versus polymerisation may depend upon a threshold average energy inside the pore itself, rather than a specific threshold that we set for each individual process. For example, if we use a 5 eV average ion energy in the pore as the threshold for determining when etching will dominate over polymerisation, we can see from the horizontal dashed line that there is a clear pressure at which the various generations of pores switch over from mostly etching to polymerisation. As the pores get rougher, the pressure at which the switch takes place becomes less. This also agrees qualitatively with the data in Fig. 1 where we correlate an increase in porosity of the open pore material with the roughness increase in the simulation. Since our surface area and tortuosity increase with porosity, this is not necessarily a bad approximation. Much more experimental data is needed to confirm that the simulation is representing reality and that the threshold pressures do indeed change in a systematic manner. 4. Conclusions A Monte Carlo simulation program was developed to show how ions would diffuse and behave inside the rough pores of a xerogel material. The energy transfer from a particle to the pore wall was calculated and depends on the molecular weights of the colliding species, the incoming energy statistics, and the angle of collision. By accurately simulating the incoming energetic conditions, we were able to simulate how the ions behave inside a rough pore as a function of pressure and how they would activate etching or polymerisation reactions in the pore. As pressure is increased, the activation switches over from mostly etching activation to mostly polymerisation activation. This agrees well with what is observed experimentally where a crossover is seen and as pressure is increased, etching stops. The switch seems to correlate with an average threshold ion energy in the pore indicating that as the pores get rougher or the porosity increases the switch occurs at lower and lower pressures. Activation of either polymerisation or etching becomes more effective as the pore roughness increases.
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Acknowledgements This material is based on work that was supported by Delft University of Technology who graciously supported the first author’s sabbatical leave. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the view of Delft University of Technology. References [1] J.-K. Hong, H.-S. Yang, M.-H. Jo, H.-H. Park, S.-Y. Choi, Thin Solid Films 308–309 (1997) 495. [2] S.V. Nitta, V. Pisupatti, A. Jain, P.C. Wayner Jr., W.N. Gill, J.L. Plawsky, J. Vac. Sci. Tech. B 17 (1999) 205. [3] A. Jain, S. Rogojevic, S. Ponoth, J.L. Plawsky, W.N. Gill, E. Simonyi, S.-T. Chen, J. Appl. Phys. 91 (2002) 3275. [4] A. Jain, S. Rogojevic, W.N. Gill, J.L. Plawsky, J. Appl. Phys. 90 (2001) 5832–5834. [5] A. Jain, S. Rogojevic, S. Ponoth, N. Agarwal, I. Matthew, W.N. Gill, P. Persans, M. Tomozawa, J.L. Plawsky, E. Simonyi, Thin Solid Films 389–399 (2001) 513. [6] M.A. Lieberman, A.J. Lichtenberg, Principles of Plasma Discharges and Materials Processing, John Wiley & Sons, New York, 1994. [7] K. Malek, M.-O. Coppens, Phys. Rev. Lett. 87 (2001) 125505. [8] K. Malek, M.-O. Coppens, Coll. Surf. A 206 (2002) 335. [9] T.E.F.M. Standaert, E.A. Joseph, G.S. Oehrlein, A. Jain, W.N. Gill, P.C. Wayner Jr., J.L. Plawsky, J. Vac. Sci. Tech. A 18 (2000) 2742. [10] A.J. Bariya, C.W. Frank, J.P. McVittie, J. Electrochem. Soc. 137 (1990) 2575. [11] T.E.F.M. Standaert, M. Schaepkens, N.R. Rueger, P.G.M. Sebel, G.S. Oehrlein, J.M. Cook, J. Vac. Sci. Tech. A 15 (1997) 1881. [12] K. Miyata, M. Hori, T. Goto, J. Vac. Sci. Tech. A 14 (1996) 2083. [13] A. Sankaran, M.J. Kushner, Appl. Phys. Lett. 82 (2003) 1824. [14] B.E. Thompson, H.H. Sawin, D.A. Fisher, J. Appl. Phys. 63 (1988) 2241. [15] M.J. Grapperhaus, M.J. Kushner, J. Appl. Phys. 81 (1997) 569. [16] D. Zhang, M.J. Kushner, J. Appl. Phys. 87 (2000) 1060. [17] D. Zhang, M.J. Kushner, J. Vac. Sci. Tech. A 19 (2001) 524.
Energy transport in plasma etching of nanoporous dielectric materials Joel Plawskya,∗, Shom Ponotha, George Dalakosa, Kourosh Malekb, Marc-Olivier Coppensb a Rensselaer Polytechnic Institute, Troy, NY, USA b DelftChemTech, Faculty of Applied Sciences, Delft University of Technology, Julianalaan 136, 2628BL Delft,
The Netherlands Received 18 May 2003; accepted 30 October 2003 Available online 19 May 2004
Abstract A Monte Carlo routine was developed to simulate the motion and energetics of ions in the pores of a xerogel material under plasma etching conditions. The simulation included the effects of an applied electric field and input conditions for the pore as a function of pressure and applied voltage in the plasma reactor. We were interested in the ion energy in a pore, the ion penetration depth and the effect of ion energy on etching. At low pressures the nanoporous material etches faster than dense silicon dioxide. This is to be expected given the decrease in density and increase in surface area that arises due to the porosity. However, as the pressure is increased, the etch rate decreases dramatically and, eventually, the dense oxide may etch faster than the porous material. CHF3 was used as the etchant gas and, for this gas, we believe this behavior to be controlled by the ion energy and energy transport in the pores of the xerogel material. As the pressure in the plasma reactor is increased, the incoming ions switch over from etching activation to polymerisation activation. This agrees with the observed crossover in etch rate seen experimentally and with the cessation in etching as pressure is increased. The switch is affected by pore roughness and correlates with the average ion energy in the pore. © 2004 Elsevier Ltd. All rights reserved. Keywords: Plasma etching; Nanoporous solids; Diffusion and reaction
∗ Corresponding author. Tel.: +1-518-276-6049; fax: +1-518-276-4030.
E-mail address: [email protected] (J. Plawsky). 0749-6036/$ - see front matter © 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.spmi.2003.10.001
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J. Plawsky et al. / Superlattices and Microstructures 35 (2004) 195–204
Fig. 1. Rate of etching of xerogel as a function of porosity and pressure.
1. Introduction Traditionally, nanoporous materials have been used in heterogeneous catalysis, fuel cells, membranes, and insulation, but, increasingly, nanoporous materials are being investigated for use as interlayer dielectrics in integrated circuits [1–5]. An understanding of diffusion and reaction in these materials under microelectronics processing conditions is fundamentally important if these materials are to be qualified for IC fabrication. In plasma processing, pressures are generally low, <1 Torr, and so Knudsen diffusion [6] is the dominant mechanism for movement of species inside xerogel pores. Malek and Coppens [7, 8] used Monte Carlo methods to investigate the effect of pore roughness on Knudsen self-diffusion, transport diffusion, and chemical reaction in rough nanopores. There is an extremely limited amount of experimental data on the reactive ion etching of nanoporous materials [9, 10]. Fig. 1 shows the results of some work we have performed using nanoporous silica xerogels. There are two significant features. At low pressures the porous material etches faster than dense silicon dioxide. This is to be expected given the decrease in density and increase in surface area that arises due to the porosity. However, as the pressure is increased, the etch rate decreases dramatically and, eventually, the dense oxide may etch faster than the porous material. The etch system in this work was CHF3 diluted in N2 . CHF3 is an etching gas normally used for controlled etching of oxide materials. This gas produces ions that undergo two different types of chemical reaction. In the first reaction, the fluoride containing ions etch the silicon dioxide [11]. In the second,
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Fig. 2. The xerogel etch rate with oxygen in the plasma.
the carbon containing ions can polymerise to form a fluorocarbon layer [12]. This polymerisation normally occurs on the walls of a trench or via and allows one to preferentially etch the base, leading to deep trenches or vias with very straight sidewalls. Such a process can occur in the pores of a nanoporous material and this is what is believed to be happening here [9, 13]. As pressure or porosity is increased, polymerisation may overtake etching, which can be verified by adding some oxygen to the etching plasma. When oxygen is added, the fluorocarbon film is removed and the etch rates for the materials approach one another as shown in Fig. 2. The etch rate is also a function of time. This is clearly shown in Fig. 3 where we plot the etch rates for several xerogel materials compared with that for solid SiO2 as a function of time. Here one can see that several of the lower porosity xerogel materials are etched more slowly than the solid SiO2 but that as time progresses the etch rates at this pressure (120 mTorr) eventually approach one another and are asymptotically approaching zero. In all cases, we are forming polymer inside the pores and eventually this polymer deposition chokes off the etching of the silicate material. This data also shows that the etch rate is affected by the pore size since pore size in these materials generally increases with porosity. That is one reason the 55% porous material appears to always etch faster than the solid. We should note that the etch rate is defined by following the signature of the “pure” xerogel material that we obtain from ellipsometry. Since the fluorocarbon layer and its build-up within the xerogel changes with time, the optical properties of the mixed layer also change with time. As yet, we have not developed a procedure for defining the exact composition of that layer. Thus the etch rates that we report should be considered as maximum etch rates since there are most likely remnants of xerogel remaining in the mixed layer. Figs. 4–6 show high resolution field emission scanning electron micrographs of the surface of a 55% porous xerogel material at etch times of 0, 2, and 10 min. One can clearly
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Fig. 3. Etch rates for xerogel and SiO2 films as a function of time. The etch pressure was 120 mTorr.
Fig. 4. A surface image of a 55% porous xerogel film prior to etching. The dark areas represent larger pores in the material that are rough and tortuous.
see from the featureless image of Fig. 6 how the pores of the material become filled as the etching process proceeds. In this paper we perform some preliminary, dynamic Monte Carlo simulations to investigate how plasma processing affects and is affected by the porosity and roughness of a nanoporous material such as a xerogel.
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Fig. 5. The surface of a 55% porous xerogel film after etching for 2 min. Rough tortuous pores are still distinct.
Fig. 6. The surface of a 55% porous xerogel material after etching for 10 min. Only remnants of the largest pores are still visible. Smaller pores have been filled with polymer.
2. Model development In developing the model we assumed that a Knudsen diffusion regime exists inside the pore. The particle adsorbs or slams into the pore wall and is emitted at angles that obey a cosine distribution. This presumes some interaction between the particle and the wall so that the particle does not remember the angle at which it struck the wall. The particle transfers energy to the pore wall molecules upon each collision. This energy transfer depends upon the particle energy, the particle and target molecular weights, and the angle of collision with the wall. The pore wall dissipates the deposited energy instantaneously and remains at a constant temperature. The overall etching process involves a trade-off between
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Fig. 7. Successive generations of (pre)fractal pore walls.
Fig. 8. Single-charged particle trajectories inside a 1st-generation pore. (a) V = 0; (b) V = 10.
fluorocarbon polymerisation and etching, both of which are activated by the incoming ions. Etching is facilitated if a particle transfers enough energy to exceed a threshold energy for sputtering the fluorocarbon film. A much lower threshold energy on the order of 1.5 eV is sufficient to activate polymerisation. The equilibrium energy corresponding to the pore wall temperature was taken as 0.04 eV (298 K). 2.1. Pore geometry The pore wall was generated using a randomised fractal iteration algorithm to yield a 2D Koch pore [7, 8]. The pores were labelled as 0th, 1st, 2nd, etc. generations with the 0th generation being a straight pore. Fig. 7 shows the first three generations of pore wall showing how the roughness is increased with each successive generation. 2.2. Ion motion If a field is applied along the length of a pore, then ion motion is no longer perfectly random but takes on a set of preferred directions that depend upon the charge on the ion and the strength of the field. A Glauber criterion was used to choose and bias the random walk. The effect this has on particle trajectories can be seen in Fig. 8. Once the field is applied, particles take fewer steps within a pore and their steps going against the field direction (right to left) are much smaller.
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2.3. Ion/particle energy A particle’s energy in the pore depends upon the particle’s molecular weight, the target molecule’s molecular weight, and the angle at which the two particles collide. In a centerof-mass coordinate system, Eq. (1) describes the fraction of energy left in the molecule following a collision with the wall. This formula applies at the energies used in this study. 4m 1 m 2 2 θ Energy left = 1.0 − . (1) sin 2 (m 1 + m 2 )2 Here m 1 and m 2 are the masses of the particles and θ is the angle of the collision. In this model we assume that the ion mass is that of N2 (28) and the target is Si(28) or O(16) (these are the two constituents of the xerogel material). 2.4. Reaction Two reactions were assumed to take place simultaneously: etching and polymerisation. The ions colliding with the pore wall were assumed to facilitate or activate these reactions. The actual reaction and reaction rate depend upon reactive molecules adsorbing on the surface and products diffusing away. Thus, the rate of reaction is a complicated function that requires a more sophisticated Monte Carlo simulation than what was undertaken here. Our goal is to just see whether some features of what we observe experimentally can be understood on the basis of a much simpler, equilibrium-like activation mechanism. 2.5. Input conditions To accurately simulate the angular and energy distributions of ions entering a pore we needed to simulate what was occurring in the plasma sheath. Building on earlier work by Sawin [14], Kushner [15–17] and co-workers, we wrote a plasma sheath routine that simulated the motion and collisions of the ions. Fig. 9 shows a comparison of that simulation with some older experimental data [14]. Since plasmas are very complex, the data are very hard to take, and details of the plasma were not reported in the original paper, the agreement between simulation and data is reasonable. 3. Results and discussion We were interested in how far dangerous ions, i.e. ions that could activate reactions, could penetrate into a pore. In Fig. 10 we chart the distance it takes for an ion to reach equilibrium in the pore. Once equilibrated, the ions no longer have enough energy to activate etching or polymerisation and hence are harmless. The penetration depth for the ions is important for semiconductor manufacturers who are worried that open pore materials such as xerogels could allow dangerous ions to penetrate all they way through the material and to the substrate below. As the pore roughness increases, the penetration depth decreases significantly. The average depth in combination with an exit fraction of ions gives a clue as to how “dangerous” a pore would be. Rougher pores appear to be preferred from a device stability and protection standpoint.
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Fig. 9. Comparison of experimental Ar plasma energy with simulated plasma energy distributions. (a) P = 30 mTorr; (b) P = 50 mTorr.
Fig. 10. The average distance a particle penetrated into the pore while delivering enough energy to sputter.
Fig. 11 shows the average energy of particles in the pore. We see a sharp decrease in average energy with pressure that follows the decrease in etch rate observed experimentally. This has also been seen in simulations by Sankaran and Kushner [13] who varied the average energy by changing the plasma bias voltage. There is also a substantial decrease in the average energy as the pore gets rougher, though that change reaches an asymptote. The decrease in average energy is much steeper than for a flat plate scenario, indicating the
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203
Fig. 11. The average energy of particles inside the pore.
effect of roughness. Energies all seem to converge at high pressure, which also follows the etch rate data. The results seem to indicate that facilitation of etching versus polymerisation may depend upon a threshold average energy inside the pore itself, rather than a specific threshold that we set for each individual process. For example, if we use a 5 eV average ion energy in the pore as the threshold for determining when etching will dominate over polymerisation, we can see from the horizontal dashed line that there is a clear pressure at which the various generations of pores switch over from mostly etching to polymerisation. As the pores get rougher, the pressure at which the switch takes place becomes less. This also agrees qualitatively with the data in Fig. 1 where we correlate an increase in porosity of the open pore material with the roughness increase in the simulation. Since our surface area and tortuosity increase with porosity, this is not necessarily a bad approximation. Much more experimental data is needed to confirm that the simulation is representing reality and that the threshold pressures do indeed change in a systematic manner. 4. Conclusions A Monte Carlo simulation program was developed to show how ions would diffuse and behave inside the rough pores of a xerogel material. The energy transfer from a particle to the pore wall was calculated and depends on the molecular weights of the colliding species, the incoming energy statistics, and the angle of collision. By accurately simulating the incoming energetic conditions, we were able to simulate how the ions behave inside a rough pore as a function of pressure and how they would activate etching or polymerisation reactions in the pore. As pressure is increased, the activation switches over from mostly etching activation to mostly polymerisation activation. This agrees well with what is observed experimentally where a crossover is seen and as pressure is increased, etching stops. The switch seems to correlate with an average threshold ion energy in the pore indicating that as the pores get rougher or the porosity increases the switch occurs at lower and lower pressures. Activation of either polymerisation or etching becomes more effective as the pore roughness increases.
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