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A Model for Resolution Dependent Roughness Values Measured by an Optical Profiler for Specific Surfaces

The rms roughness value obtained using an optical profiler depends on the horizontal resolution which is determined mainly by the objective magnification, especially when the surface grain or peak diameters are less than the resolution. A model is proposed to determine the dependency of the rms roughness value on the resolution. The optical height in an area of horizontal resolution is defined the an average of the surface profiles. A large area inspected by a small magnification (SX) objective is adjusted to R2-times the size of small areas inspected by a large magnification (LX) objective, where R2 is the ratio of a large cell area defined by the horizontal resolution of the SX objective to a small cell area defined by a horizontal resolution of the LX objective. It is shown that the ratio of the rms roughness value in the small area to that in the large area is equal to R, since the optical height of a grain in the small cell area is R2-times as large as that in the large cell area. The calculated value from the present model agrees with the average of experimental results.