Ravi Jaiswal

Modeling and Validation of the van der Waals Force During the Adhesion of Nanoscale Objects to Rough Surfaces: A Detailed Description

The interactions between nanoparticles and rough surfaces are of great scientific and engineering importance and have numerous applications in surface science and biotechnology. Surface geometry and roughness play crucial roles in observed particle adhesion forces. We previously developed a model and simulation approach to describe adhesion between microscale bodies. This work provides detailed descriptions of the modeling framework, with associated experimental validation, applied to nanoscale systems. The physical systems of interest include nanoscale silicon nitride adhering to different surfaces in both dry and aqueous environments. To perform the modeling work, precise descriptions of the geometry of the particle and the roughness of the particle and substrate were generated. By superimposing the roughness and geometry models for the particle and the substrate, it was possible to precisely describe the spatial configurations of the adhering surfaces. The interacting surfaces were then discretized, and the adhesion force between the two surfaces was calculated by using Hamakers additive approach, based on van der Waals interactions. In the experimental work, an atomic force microscope (AFM) was used to measure the adhesion force (pull-off force) between nanoscale silicon nitride cantilever tips and a range of substrates in different environments. The measured and predicted force distributions were compared, and good agreement was observed between theory and experiment.

Scaling of van der Waals and Electrostatic Adhesion Interactions from the Micro- to the Nano-Scale

Work performed to study the scalability of continuum force models to describe particle adhesion from the micro- to the nano-scale is described. This work employed silicon nitride particles with nominal diameters on the micrometer scale and silicon nitride atomic force microscope cantilevers with nanometer-scale radii of curvature to determine adhesion interaction forces to substrates relevant to advanced lithography applications in the semiconductor industry. The force required to dislodge the particles or cantilevers from the substrates was taken to be the adhesion force. For all systems studied, a distribution of adhesion forces was observed resulting from roughness on the particles and/or substrates and geometry variations on the particles. Previously developed adhesion models that included van der Waals (vdW) and electrostatic (ES) interactions, and that also included the geometry and morphology of the interacting surfaces, were used to describe the force distributions. In air, the ES forces were found to be insignificant compared to the vdW forces. In aqueous electrolytes, the ES forces may play an important role, even at the point of particle–substrate contact, due to the formation of electrical double layers under certain conditions. The predicted force distributions showed good agreement with the experimental data.

Approximate scheme for calculating van der Waals interactions between finite cylindrical volume elements.

A successful approach to calculating van der Waals (vdW) forces between irregular bodies is to divide the bodies into small cylindrical volume elements and integrate the vdW interactions between opposing elements. In this context it has been common to use Hamakers expression for parallel plates to approximate the vdW interactions between the opposing elements. This present study shows that Hamakers vdW expression for parallel plates does not accurately describe the vdW interactions for co-axial cylinders having a ratio of cylinder radius to separation distance (R/D) of 10 or less. This restricts the systems that can be simulated using this technique and explicitly excludes consideration of topographical or compositional variations at the nanoscale for surfaces that are in contact or within a few nm of contact. To address this limitation, approximate analytical expressions for nonretarded vdW forces between finite cylinders in different orientations are derived and are shown to produce a high level of agreement with forces calculated using full numerical solutions of the corresponding Hamakers equations. The expressions developed here allow accurate calculation of vdW forces in systems where particles are in contact or within a few nm of contact with surfaces and the particles and/or surfaces have heterogeneous nanoscale morphology or composition. These calculations can be performed at comparatively low computational cost compared to the full numerical solution of Hamakers equations.

Adhesion of Contaminant Particles to Advanced Photomask Materials

A challenge to the use of extreme ultraviolet lithography (EUVL) is contamination of the mask during its processing and storage since current techniques for contamination prevention, such as pellicles, cannot be used with the mask materials under EUVL conditions. This paper characterizes the adhesion forces between model contaminant particles and photomask and thin film surfaces relevant to extreme ultraviolet and deep ultraviolet lithography. Specifically, experimental studies of the adhesion of nanoscale and microscale silica and silicon nitride particles to surfaces such as chromium oxynitride, quartz, MoSi, tantalum oxynitride, and ruthenium in air are described. In addition, an adhesion force mapping scheme, the “force band diagram,” is presented. This method allows upper and lower limits to be imposed on the adhesion force between given particle-substrate pairs. Two extremes of behavior are considered in the force bands, a rough prolate spheroid (minimum adhesion force) and a smooth oblate spheroid (maximum adhesion force). Experimental data are compared with the force band models and in all cases the measured adhesion forces fall within the established boundaries for particle sizes ranging from the nanoscale to the microscale. This technique is general, and can be applied to other surfaces of interest to the microelectronics manufacturing community.

Particle Adhesion to Photomask Substrates

Semiconductor manufacturing technologies require strict control on the size and number of particulate contaminants that can be tolerated on wafers and photomasks. Most present cleaning protocols rely on a fluid mechanical force or a combination of a fluid mechanical force and a chemical reaction (such as undercutting) to remove contaminant particles from surfaces. Dislodged particles may then be stabilized away from a surface of interest using electrostatic interactions. For future photomask substrates, many of the mechanisms that are effective in current mask cleaning will not be acceptable. Specifically, any etch-based process will not be tolerated, as substrate layers are too thin and roughness limits are too strict to accept the consequences of etching. At the same time, the critical particle size will drop, and fluid-mechanical based cleans will be increasingly ineffective at imparting the required removal force on the particles due to boundary layer effects. The development of viable cleaning techniques for the I.C. industry requires detailed understanding of the forces of adhesion between particles and substrates. In this work, experimental and modeling studies of the adhesion between photomask substrates and model contaminants with different characteristic length scales are presented. The model substrates include CrOxNy, TaOxNy, quartz, MoSi, and Ru. Model contaminants include micro-scale glass spheres and Si3N4 particles, as well as Si3N4 atomic force microscope (AFM) cantilevers with nanoscale radii of curvature. The predicted force distribution showed a very good agreement with the measured one for micron scale particles and for cantilevers with nanoscale pyramidal tip in both dry and aqueous environment.