Distributed force probe bending model of critical dimension atomic force microscopy bias

Abstract. Critical dimension atomic force microscopy (CD-AFM) is a widely used reference metrology technique. To characterize modern semiconductor devices, small and flexible probes, often 15 to 20 nm in diameter, are used. Recent studies have reported uncontrolled and significant probe-to-probe bias variation during linewidth and sidewall angle measurements. To understand the source of these variations, tip-sample interactions between high aspect ratio features and small flexible probes, and their influence on measurement bias, should be carefully studied. Using theoretical and experimental procedures, one-dimensional (1-D) and two-dimensional (2-D) models of cylindrical probe bending relevant to carbon nanotube (CNT) AFM probes were developed and tested. An earlier 1-D bending model was refined, and a new 2-D distributed force (DF) model was developed. Contributions from several factors were considered, including: probe misalignment, CNT tip apex diameter variation, probe bending before snapping, and distributed van der Waals-London force. A method for extracting Hamaker probe-surface interaction energy from experimental probe-bending data was developed. Comparison of the new 2-D model with 1-D single point force (SPF) model revealed a difference of about 28% in probe bending. A simple linear relation between biases predicted by the 1-D SPF and 2-D DF models was found. The results suggest that probe bending can be on the order of several nanometers and can partially explain the observed CD-AFM probe-to-probe variation. New 2-D and three-dimensional CD-AFM data analysis software is needed to take full advantage of the new bias correction modeling capabilities.