Critical Dimension Atomic Force Microscopy (CD-AFM) is a primary means to measure the geometric shapes of walls and trenches on the nanometer scale in laboratories supporting the electronic industry. As the widths of commercially available CD-AFM probes have become as small as 50 nm, the deformation of the probe tip during measurement may not be negligible. To understand how the deformation might vary from one measurement configuration to another, it is necessary to develop a detailed computational model of tip-sample interaction and dynamic behaviors of the tip. In order to estimate the probe deflections due to surface intermittent contact and the resulting dimensional biases and uncertainties, we have developed finite element models for simulating dynamic behavior of AFM cantilevers with a CD tip attached. Probe tip and cantilever beam responses to intermittent contact between the probe tip and sample surface are computed using the finite element method. Using a commercially available software system, intermittent contacts with a wall and a horizontal surface are computed and modeled, respectively. The responses of the probe to interaction forces between the sample surface and the probe tip are shown in both time and frequency domains. In particular, interactions between a 75 nm CD tip and both a vertical wall and a horizontal surface of a silicon sample are modeled using Lennard-Jones theory. The Snap-in and snap-out of the probe tip in surface scanning are calculated and shown in the time domain. The calculation includes the compliance of the probe, the sample-tip interacting force model, and dynamic forces generated by vibration. Cantilever and probe tip deflections versus interaction forces in the time domain can be derived for both vertical contact with a plateau and horizontal contact with a side wall. Dynamic analysis using the finite element method and Lennard-Jones model provide a unique means to analyze the interaction of the probe and sample, including calculation of the deflection and the gap between the probe tip and the measured sample surface.
Citation: International Journal of Nanotechnology
Pub Type: Journals
Atomic force, Cantilever, Critical Dimension, Compliance, Microscopy, Nanometrology, Probe modeling, Scanned probe