Ind. Eng. Chem. Res. 2000, 39, 4481-4486
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Effect of Pressure on the Static Forces of Micron-Scale Particle Adhesion Michael A. Matthews* and James Becnel Department of Chemical Engineering, University of South Carolina, Columbia, South Carolina 29208
Supercritical or liquid carbon dioxide has been proposed as an environmentally benign solvent for precision cleaning. In this work, a model is presented that describes the static forces responsible for adhesion of microscopic particles to solid surfaces with a fluid layer present on the surface. This model is descriptive of particle adhesion in precision cleaning applications, such as cleaning of microelectronic devices. Predictions are made for the effects of high pressure on an idealized particle/fluid/surface system. The idealized system is a 1 µm graphite particle on a metal surface that is contaminated with a thin layer of n-dodecane. Calculations predict that the high pressures (as would be required for liquid or supercritical CO2 cleaning) can increase the particle-surface separation distance in some regions of temperature-pressure space and that this effect may be coupled with a decrease in the total adhesion force. This model is useful as a first approximation to the design and analysis of dense-phase CO2-based precision cleaning systems. 1. Introduction The removal of micron-scale particles is important in numerous processes, including precision parts machining and silicon wafer production.1 As the features of such products become ever smaller in size, very fine particles can increasingly interfere with surface details and affect the final product performance. For example, the features of DRAM chips are predicted to drop from 180 nm in 1999 to 35 nm by 2014.2 Current particle removal technology employs a variety of methods including detergent washing, high solvent velocities, sonication, and wiping.3 The most common method of removing adhered particles is the use of high solvent velocities near the surface to be cleaned.3 High solvent velocities impart high drag and shear forces that, if great enough, will overcome the particle adhesion. Micron-scale particles adhered to a surface will typically reside in a laminar sublayer. Within this sublayer, the solvent velocity is near zero close to the surface and quickly approaches the bulk solvent velocity as the distance from the surface increases. This implies that the particle-surface separation distance can be crucial in systems that rely on solvent shear and drag forces for particle removal. Of particular interest in this study is the use of dense gas (supercritial fluid or slightly subcritical liquid) solvents for particle removal, especially dense carbon dioxide (CO2). The numerous environmental and process design benefits of dense CO2 cleaning systems have been described previously.4-8 However, the microscopic physics of particle removal in dense gas solvents has not been studied. The use of dense gases or any elevated-pressure system in particle cleaning applications can significantly alter the static force balance on adhered particles. The influence of elevated pressures can manifest when a second fluid phase (e.g., a polishing oil) forms a bridge between the particle and the surface. This second fluid phase forms a well-defined phase interface with the bulk * To whom correspondence should be addressed. E-mail:
[email protected]. Fax: (803) 777-8265.
solvent. Because of the curvature of this phase interface, there is a pressure rise within the entrapped fluid bridge, which can be estimated with the Kelvin equation.9 This pressure rise within the fluid bridge produces a force on the particle which acts to push it away from the surface. This study focuses on the description of the static forces in an idealized system with a separate fluid phase entrapped between the particle and the surface. It is hypothesized that, for certain conditions, an increase in pressure will increase the particle-surface separation distance for these systems. This paper reviews the relevant forces and provides a framework for predictive calculations. To obtain realistic solvent and entrapped fluid properties, the carbon dioxide/n-tetradecane system10 is used to illustrate the effect of pressure on static forces. This system was chosen as an approximate representation of carbon dioxide cleaning of machined parts. Although high-speed cutting additives have wide chemical variety, n-tetradecane (n-C14) has a representative molecular weight and the necessary fundamental data are readily available.10 2. Description of Static Forces Particles adhere to surfaces because of a combination of forces. These forces range from short-range van der Waals forces to long-range electrostatic interactions. Four adhesion forces are considered: van der Waals, bulk electrostatic charge, electron-level interactions, and gravity. Surface tension effects are important in systems such as the one studied where a small amount of fluid is entrapped between the particle and the surface and forms a bridge between them. The interface created between the entrapped fluid and the solvent generates two opposing forces: (1) the interface’s surface tension adds to the total adhesion force and (2) the capillary pressure effect due to the curvature of the interface acts against the adhesion forces. This investigation is based on an idealized model of a particle and a surface. The particle is taken to be a
10.1021/ie000204o CCC: $19.00 © 2000 American Chemical Society Published on Web 10/21/2000
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Figure 1. Graphical description of particle and static forces. A 1.0 × 10-6 m diameter particle at static equilibrium in CO2/n-C14 (1600 psi, 344.3 K):. (1) particle; (2) entrapped fluid; (3) solvent; (4) vdW force, 1.17 × 10-11 N; (5) electrostatic image force, 4.01 × 10-9 N; (6) electrostatic potential force, 1.30 × 10-10 N; (7) gravitational force, 1.00 × 10-14 N; (8) capillary force, 2.55 × 10-9 N; (9) capillary pressure effect force, -6.70 × 10-9 N.
perfect sphere close to a perfectly flat surface. Both the particle and the surface have homogeneous physical properties. No deformation of the particle is considered. Refer to Figure 1 for a visualization of the model system. 2.1. van der Waals Force. The van der Waals force arises from weak molecular interactions: dipole, induced dipole, and instantaneous dipole. These interactions are only significant over relatively short distances of ∼
