Deposition of Aerosol Particles on Surface Composed of Different Kinds of Materials t

Experimental and theoretical studies of particle deposition on a surface composed of different materials (copper and polyethylene) were conducted. Deposition of charged aerosol particles was affected by a localized electrostatic field created by the contact potential difference between the metal (copper) and the dielectric material (polyethylene), and the particles charged with positive polarity deposited mainly on the polyethylene surface, which was charged with negative polarity. This fact suggests that the deposition is caused by the Coulombic force between the surface and the particles. The deposition flux was larger for smaller particles because of the larger effect of the electrostatic field. Aerosol particles with negative polarity do not deposit on the polyethylene surface because the surface charge is negative. The deposition is, however, enhanced on the neighboring copper surface. This is explained by the fact that the electrostatic field vector directs to the main stream. It is found that the agreement between calculated results and experimental data is better for the case of assuming intrusion of the electric charge into the polyethylene than for that of assuming fixed interface charge.


Introduction
Recently, reliable techniques to prevent the deposition of fine particles on wafers in a superclean room have been in increasing demand to use in producing high-quality integrated circuits during the LSI manufacturing process.There are a number of dielectric (Si0 2 ) -metal (Cu or Al) contacts on a wafer constituting an LSI, and even fine particles less than 0.1 pm, when deposited on the wafer surface, may prove to be major cause of a defec-tive product.It is essential, therefore, to analyze the quantity and distribution of aerosol particles deposited on a surface consisting of different kinds of materials and the deposition mechanisms involved, in order to develop a method for electively preventing the particle deposition.Few studies, except for Rosinsky, et al. 6 ), Emi, et a!.z), and Ikumi, et al. 3 ), have discussed the effects of the wall surface materials on the deposition of fine particles.Rosinsky, et al. 6 ), and Ikumi, et al. 3 ), have investigated the distribution of fine particles deposited on dielectric surfaces, concluding that these particles are not distributed evenly, but instead form particle-islands, because the dielectric surfaces are not electrically uniform.Emi, et al., have passed charged and noncharged particles through pipes made of different materials to obtain the penetration efficiency.They concluded that the deposition of particles on the inner dielectric walls was main-ly determined by the amount of electrostatic force 2 ).
The above results are related to the deposition of particles on relatively large surfaces, and provide little information regarding deposition of a aerosol particles on surfaces composed of dissimilar materials of fine patterns, where the dissimilarity between the surface materials serves as a major driving force for the deposition of particles onto the surfaces.
In this study, the authors have attempted to numerically investigate and analyze where and to what extent the aerosol particles are deposited on a surface composed of different kinds of materials (copper and polyethylene).

. Experimental Equipment and Procedure
Figure 1 illustrates the experimental equip-

Pump
Heater ment used in this study.The monodisperse latex aerosol particles (Dp : 0.17 pm, 0.33 pm and 0.62 pm) were used as test particles, which were generated by a nebulizer.The aerosol particles generated by the nebulizer were electrically charged.In order to control the charge level of particle, the following three types of particles were used: (1) Particles which had not been controlled in charge level.(2) Particles which were neutralized, after passing through a charge neutralizer (using americium oxide) and a charged particle collector operating under a high voltage.
( The air rate was set to a low level ({Jx = 6 cm/s), simulating the conditions of a clean room or work room.The area of test space was 50 em long and 30 mm X 120 mm.The test piece was set on the upper wall 20 em downstream of the aerosol supply.
Figure 2 shows the test piece, which had a 0.3 mm thickness polyethylene sheet sandwiched by 1.5 mm thickness copper plates.The surface on which the particles were to be deposited was polished, and the copper plates were grounded for a long time before the test.The test period lasted from 15 to 20 hr, and the particle distribution on the test piece was determined by using a scanning electron microscope (JSM-5200) to count the deposited particles.

1 State of particle deposition
Figure 3 shows an SEM photograph of the latex particles (Dp: 0.33 pm) deposited on the dissimilar surface.The charge level of these particles was not controlled.They deposited more on the dielectric side than on the copper side.
In an attempt to clarify changes in the deposited quantity around the interface between these dissimilar materials, the deposition flux distributions were determined by counting the latex particles on the SEM photographs in different positions.Figure 4 shows the deposition flux distribution for the 0.33 11m particles.As shown, the deposition flux proved to be approximately 5 times greater on the dielectric than on copper, and attained a maximum level at the dielectric center while proving to be slightly lower on the interfaces.We also observed that the deposition flux was almost constant at a position about 1 mm or more from the dielectric.The positively charged particles were deposited on the polyethylene surface, because the polyethylene charged negatively due to the contact potential difference between the copper and polyethylene.It was therefore necessary to understand the degree of the contact potential difference between the polyethylene and copper.The contact potential difference between dissimilar materials is well known, but that between a dielectric and a metal is still relatively unknown.Tests were, therefore, performed, in which a polyethylene sheet was placed into contact with a variety of metals with different work functions.Thereafter, the charge level difference between them could be measured after they were separated, based on the concept that the work function which indicated zero charge transfer was equivalent work function of the dielectric 1).
Figure 5 shows the results.The very small charge generated was measured using a Faraday cage (Advantest, TR-8031) and a vibrationcapacity electrometer (Advantest, TR-8411) in a chamber in which temperature and humidity were kept at constant levels.The polyethylene sheet measured was 15 mm square.The results were scattered, unless the sheet's charge was eliminated as far as possible.As Fig. 5 shows, the equivalent work function of the dielectric was 4.6 eV, and the contact potential difference between copper and polyethylene was approximately 0.3 V. Thus, the polyethylene sheet would have a negative charge relative to the copper plate, when these two came into contact.
As a matter of course polyethylene will become positively charged relative to platinum, when these two come into contact, since the work function of the platinum is larger than the polyethylene.

2 Theoretical analysis
A numerical analysis was carried out to understand the contact potential difference created as a result of the contact between polyethylene and copper, and the resulting electrical field generated around the interfaces.The potential distribution in a space is provided by the following equation: where V represents the potential difference, p represents the space-charge density and E represents the dielectric constant.The equation ( 1) may be reduced to a dimensionless Laplace's differential equation ( 2) without dimensions by use of the contact potential difference between the dissimilar materials, and assuming that the aerosol concentration is sufficiently low to create only a negligibly small space where V = V/.Fig. 6 Calculated electric potential distribution contact potential difference, and R is the width of the rectangular area through which the aerosol particles pass.Equation ( 2) was solved numerically by applying the relaxation method, with the boundary conditions of the dimensionless potentials, V = -1 at the polyethylene surface and f7 = 0 at the grounded copper section.
Figure 6 shows the calculated equivalent potential distributions, including those around the polyethylene-copper interfacial area.It also shows the detailed boundary conditions applied in solving Equation (2).The results suggest that the equivalent potential is synmetrically distributed, and that the potential abruptly changes around the interfacial area, decreasing sharply with the distance from the polyethylene section.
Next, the potential distribution was used to estimate the deposition flux on the wall surfaces.The convective diffusion equation (3) could be applied, by neglecting the inertial force acting on the particles, since the particle size and flow rate were sufficiently small: ax ay ax 2 ay 2 where vx and vy represent the particle velocity components in the x.y directions, c is the concentration, and D is the Brownian diffusion coefficient.We considered the following three components of the electrostatic force applied to the particles: (1) Coulombic force (2) force generated by image charge (3) clielectric migration force The particle velocity components in the x andy directions can be obtained by the following equations, considering the electrostatic force, consisting of the above three components as well as gravity as the external forces applied to the particles: where Ex and Ey represent the strength of the electrical field in the x and y directions (Ex = -a V/ax, and Ey = -a Vjay), Ep and Eo represent the dielectric constants of the particles and the air, q represents the charge of the particle, C represents Canningham's slip correction factor, and ux and Uy represent the fluid velocity components in the x and y directions respectively.
The particle velocity components, calculated by Equation (4), were substituted into Equation (3 ), to determine the concentration field by applying a numerical analysis with the relaxation method.The concentration at the wall surface was assumed to be zero (perfect absorption wall), as the boundary condition.For the differential expression of Equation (3), it is desirable to use the central difference for assessing the convection term near the wall and the windward difference for assessing the convection term at the duct center.This will improve the calculation accuracy because the particle velocity components are sufficiently small in the vicinity of the wall surface indicating that the diffusion term is not longer negligible.The exponential methods), automatically taking the above into consideration, was used to carry out a numerical calculation.
The following equation was used to determine the particle deposition flux at the wall surface: The following is a discussion of the experimental results for the case in which the charge on the particles, generated by the nebulizer, is not controlled.
Figure 7 presents the results for 0.62 pm particles, in which the dimensionless deposition flux ratio represents the ratio of particles deposited by diffusion only to the particles deposited by both diffusion and electrostatic force.The following equation demonstrates this ratio: -JD+E J = --JD (6) The experimental data are well represented by the calculated results (solid line) developed by assuming that each particle is charged with electricity of q = 6e.As shown, the amount of particles deposited on the polyethylene surface is higher than the amount deposited on the copper surface.The figure also shows the calculated results by assuming that q = e (broken line); the deposited amount is smaller because of the reduced electrostatic effect.Figure 8 presents similar results for the 0.33 pm particles, the number of 0.33 pm particles deposited on the polyethylene surface greatly increases compared with the 0.62 pm particles.This results are due to the increased electrostatic effect for the smaller particles, and the experimental results are well represented by the calculated results developed by assuming q = 2e (solid line).-----.-------.=n------~------.,=; 7 Figure 9 provides the results for the 0.1 7 pm particles, the number of particles deposited on the polyethylene surface greatly increases in this case as well.The calculated results follow the same trend.The experimental results are well represented by the calculated results developed by assuming q = l.Se.This, however, is not true for those particles around the interfaces.The calculated flux ratio decreases in the copper section near the interface vicinity, which is conceivably the result of the electrical field vector being directed locally to the upstream side, as illustrated in the equivalent potential chart (Fig. 6 ).The sharp increase in deposition flux at the dielectric surface near the interfaces is the result of the sharply changing potential 44 of these areas.There is a discrepancy between the experimental and calculated results of the copper surface in the vicinity of the interfaces because the calculation assumes that all the particles are positively charged, while some particles are actually negatively charged.Surface roughness was considered to somewhat affect the deposition flux.The effects, however, are negligible, since the interface thickness is sufficiently greater than the surface roughness.The experimental results presented by Shimada, et a!.?), support this proposition.

b) Non-charged particles:
The results shown in Fig. 7 through 9 indicate that the electrostatic force, generated by the particles' electricity is the major cause forcing them to deposit on the dielectric surface.This means that the number of noncharged particles deposited onto a surface should be constant, irrespective of the surface material.In order to confirm this, we conducted experiments with non-charged particles, in which the aerosol particles generated by the nebulizer were passed through a charge neutralizer and a high-voltage (3 k V) field between two parallel plates, to remove the charged particles.The distance between the plates and the size of the plates were designed to remove the charged particles completely.
Figure 10 compares the results of the charged 0.1 7 pm particles with the same size noncharged particles.The deposition flux of the non-charged particles is constant, irrespective of the surface material.In principle, even the 8 I ,=; non-charged particles are affected by the dielectric migration force.This effect, however, proved to be very small under the conditions of this study (as indicated by the solid line representing the calculated results) because there was a very low contact potential difference of 0.3 V.These results have confirmed that the particles' electricity is the major cause of the differences in the extent of the deposits, depending on the surface material.

c) Particles with a known charge level:
When copper makes contact with polyethylene, the latter is negatively charged, as indicated by the work function relationship, which is shown in Fig. 5. Using particles of a known charge level, therefore, allows us to control the amount deposited on the polyethylene surface.In order to confirm the above proposition, we attempted to control the charge level of the particles by passing them through a differential mobility analyzer (DMA) 4 ). Figure 11 shows the results of the 0.17 ~m particles, whose charge level was controlled at q =e.This figure also presents the corresponding calculated results.The experimental results agree well with The next case considers the effect of the intrusion of an electrical charge into the dielectric material in the numerical calculation.The calculated deposition flux ratio shown in Fig. 11 increases sharply in the interfacial area on the polyethylene surface, while the experimental ratio attains its maximum at the polyethylene center.For the calculation, the potential on the dielectric surface was assumed to be constant, thus causing the potential to rapidly change in the vicinity of the interface.In actuality, however, some charge seemingly intrudes into the dielectric body 1 ), with the result that the potential is not evenly distributed over the dielectric surface.
Assuming that the potential distribution on the dielectric surface is represented by the following equation l), the particle deposition flux is calculated, where the intrusion of a charge into the dielectric body is considered: where x represents distance from the interface and o for the depth to which the charge intrudes.In the region of x >> o, the potential (contact potential difference) is constant.
Figure 13 compares the calculated results to the experimental ones, where the potential distribution determined by equation (7) in the case of q = e.The calculated results still show a maximum flux at the interface with a low o level of 0.02 mm, but the maximum appears at the dielectric center with a o level of 0.04 mm, thus showing the same trend as the experimental results.

Conclusion
The deposition of aerosol particles on a surface composed of different kinds of materials (copper and polyethylene) was investigated both experimentally and theoretically, in order to determine where and to what extent the particles were deposited.
( 1) The electrically charged particles are affected by the electrical field, which is spontaneously generated when the metal comes into contact with the dielectric; the positively charged particles are deposited extensively onto the polyethylene surface, which is charged negatively in the copperpolyethylene system.(2) The extensive deposition of positively charged particles onto the dielectric surface is mainly caused by the coulombic force generated as a result of the interaction between the particles and the electrical field.Smaller particles are more affected by the electrical field, and, therefore, deposited more extensively onto the surface.(3) The negatively charged particles are rarely deposited on a negatively charged dielectric, but are deposited extensively onto the copper section in the vicinity of the interfaces.This occurs because the electrical field vector is directed locally to the main stream flow in the vicinity of the interfaces.(4) The calculated results assuming that a charge intrudes into the dielectric body match better with the experimental results than in the case in which no charge intrusion is considered.

Acknowledgement
This study was financed in part by a grant from the Ministry of Education (General Research C, 62550703, 1987) in Japan.[kg/m•s] permittivities of air and particle, respectively [F /m] constants defined by Eq. (7) [ -] effective Debye length [m]

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Fig. I Experimental apparatus

XFig. 5
Fig. 5 Relation between amount of charge and work function

Fig. I 0
Fig. I 0 Effect of particle charge on the deposition flux distribution

Fig. 11 Deposition flux distribution with particle charge equal to e 2 theFig. 12
Fig. 11 Deposition flux distribution with particle charge equal to e

Fig. 13
Fig. 13 Deposition flux distribution compared with modified calculated result width of two-dimensional test section (3.0cm) distance from wall fluid velocity component of x and y directions, respectively average