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Applications of SEM Monte Carlo Modeling to Geometry Determination in Single-Crystal Silicon Test Patterns



John S. Villarrubia, Andras Vladar, J R. Lowney, Samuel N. Jones, Michael T. Postek


Width measurements pose a particularly problematic calibration problem. The measurement entails determining the distance between inherently dissimilar edges. Even in the simplest imaginable case, an ideal line of rectangular cross section, the left and right edges are not identical but are, rather, mirror images of one another. Any error, Dx, in the assignment of one edge is mirrored (-Dx) on the other edge, resulting in twice the error when the positions are subtracted to determine the width. In the scanning electron microscope (SEM), this makes modeling of the instrument response, for example by using Monte Carlo tracing of electron trajectories, critical to an accurate measurement. As part of a project to test the accuracy of NIST's MONSEL 1 Monte Carlo model, we have performed measurements on the (110) face of single-crystal Si test structures fabricated in SIMOX and BESOI.2-4 These are two technologies for producing a 200 nm to 1000 nm layer of crystalline Si on top of an insulating oxide of similar thickness. Structures containing lines in the [112] and [112] directions were etched into this material. Along these directions the (110) top surface of the line is intersected at 90¿ by {111} sidewalls that are slow-etch planes for the KOH etchant. Because of preferential etching, the structures are expected to have low edge and wall roughness and nearly vertical sidewalls. We collected several series of SEM images of these structures and compared the profiles to the MONSEL result for Si lines of rectangular cross section. For the SIMOX structures, agreement was good. The SEM profiles on BESOI differed from those predicted in these significant respects: 1) The observed profiles were often asymmetrical, with one edge brighter than the other. 2) The extent of the asymmetry varied with position on the sample. 3) Even in locations where there was left-right symmetry, the observed edges were brighter than predicted. These differences necessitated revisiting the geometrical assumptions. By allowing the line to have a skewed trapezoidal cross section, with the extent of skew varying with position, we were better able to fit the observed intensities. The extent of deviations from the expected 90? that produces the best fit to the observations is quite small, typically 0.2¿ of trapezoidal splay skewed to left or right by amounts ranging from -0.2¿ to 0.2¿. Even though these are small angles, Monte Carlo results indicate very high sensitivity of the SEM profiles to angular changes of this magnitude. This high sensitivity is confirmed experimentally by tilting the sample by comparable amounts.
No. 2


scanning electron microscope Monte Carlo modeling, single-crystal silicon test patterns single-crystal silicon linewidth metrology electrical critical dimension (ECD) critical dimension manufacturing control


Villarrubia, J. , Vladar, A. , Lowney, J. , Jones, S. and Postek, M. (2000), Applications of SEM Monte Carlo Modeling to Geometry Determination in Single-Crystal Silicon Test Patterns, Scanning (Accessed July 25, 2024)


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Created May 1, 2000, Updated February 19, 2017