# Detachment Energy Evaluation in Nano-Particle Cleaning Using Lateral Force Microscopy
## 1 Introduction  
In recent years, abrasive particles smaller than 50 nm have been applied in Chemical Mechanical Polishing (CMP) techniques to achieve a surface with nanoscale flatness within the depth of focus in a lithography process in each layer. This advancement is crucial for realizing multilayer wiring structures and reducing wiring widths down to 7 nm in high-performance large-scale ICs [1; 2; 3]. Due to this, the presence of residual particles on the polished film surface can be a killer defect (short or opens in electric circuits, etc.) as a mask in the lithography process [4], causing partial convexity in the subsequent film deposition process [5], etc., and then leading to lower LSI chip yields. In particular, the oxide films that serve as interlayer insulators and are polished with smaller silica nano-particles are used in the process. Hence, detaching smaller nano-particles (abrasive particles, cleaning waste/dust, etc.) from polished surfaces has indeed posed a significant challenge in post-CMP wet cleaning processes.  
In general, contact cleaning by polyvinyl alcohol (PVA) brush scrubbing and non-contact cleaning by enforcing MHz waves were applied to detach nano-particles from the surface. Although the cleaning process is being reconsidered to realize optimal and efficient cleaning [2; 6], the cleaning phenomenon has not yet been clearly understood because the residual contamination on the wafer surface is typically inspected only after the cleaning process in dry conditions, rather than wet conditions using the surface scanning methods (e.g., scanning electron microscopy). Consequently, it is essential to investigate the cleaning mechanisms, which involve the detachment of the nano-particle from the surface to be cleaned, and the occasional reattachment to the surface.  
Thus, we have established a direct observation method for studying the cleaning phenomena that occurred in a range of a few hundred nanometers from the surface by employing an evanescent light which generated a few hundred nanometers from the surface to be cleaned [7; 8; 9; 10; 11; 12; 13]. By using this observing method, size-dependent particle behaviors during cleaning were evaluated in the cleaning phenomenon [14; 15; 16; 17], especially in the presence of inevitable shear flow [18]. As a result, the smaller particles required considerably more time to detach. This size-dependent detachability of the nano-particle is considered involvement with the physicochemical energy between the nano-particle and the substrate in the shear flow. However, the potential energy of the physicochemical interactions has not been investigated quantitatively.  
Various research groups have evaluated the vertical force to pull the particle with a diameter of a few micrometers at the smallest size from the substrate surface by the force curve mode of AFM [19] or by numerically calculating the interaction (van der Waals force, repulsive forces by the electric double layer, etc.) of the nano-particle and the substrate under theoretical models [20]. Hence, the energy evaluation of the nano-particle detachment in the action shear force (lateral force) was indispensable.  
In this article, we proposed an evaluation method of energy required to detach various-sized nano-particles from the substrate by using Lateral Force Microscopy (LFM) in order to investigate the dominant interactions. Distinctively, the energy quantity is not a vector quantity like the interacting force, but a scalar quantity at the nanoscale. Therefore, the phenomenon could be evaluated in terms of its scalar quantity as the physicochemical energy, and not only evaluated in terms of the acting behavior to nano-particles in one or two directions and at a certain moment.  
As an example, the detachment energy of the silica nano-particle from the oxide film (SiO\({}_{2}\) film on a silicon wafer) surface was measured such as in post-CMP cleaning as shown in Figure 1. The dominant energy to detach the particle which involves breaking the bond was discovered.