As integrated circuits become smaller and faster, the measurement of line width must have less uncertainty and more versatility. The common requirement for uncertainty is less than 10 nanometers. The industrial need for versatility is three dimensional scanning in order to measure the geometric shapes of walls and trenches. Atomic Force Microscopes (AFMs) are commonly used in laboratories for a range of critical measurements of dimensions demanded by the electronic industry. However, it is difficult to predict the measurement bias arising from the compliance of the AFM probe. The issue becomes particularly important in this situation: nanometer uncertainties need to be quantified when flexible carbon nanotubes, having diameters of 1 to 10 nm and mounted on AFM cantilevers, are used as high resolution probes. In order to estimate the probe deflections due to surface contact and the resulting dimensional biases and uncertainties, we have developed a finite element model for simulating the mechanical behavior of AFM cantilevers with carbon nanotubes attached. The finite element model was developed using the commercially available software systems, Abaqus and Ansys. They provide simulations of both the static and dynamic behavior of the cantilever/nanotube assembly through video clips and graphs. Spring constants of both the nanotube and cantilever in two directions are calculated using the finite element method with known Young?s moduli of both silicon and multi-wall nanotube as input data. Compliance of the AFM probe tip may be calculated from the set of spring constants. Both static models for contact scanning and dynamic models for tapping mode AFM are working and are being applied to estimate uncertainties in linewidth measurement using nanotubes.
Proceedings Title: Abstract for Proceedings of the Eighth Annual International Scientific Meeting on Scanning Mircoscopies 2007
Conference Dates: March 15-19, 2007
Conference Location: Washington, DC
Pub Type: Conferences
Nanometrology, and Scanned probe, Atomic force, Cantilever, Carbon nanotube, Compliance, Microscopy, Probe modeling