Measurement of Nanometric Heights by Modal Decomposition

Measuring the height of steplike features in samples has become important in many scientific and industrial applications. It is routinely done using both tactile and optical methods, the latter being preferable due to their noncontact nature and improved speed capabilities. Nevertheless, techniques less sensitive to instabilities or without calibration or reference sample requirements would be advantageous. Here, we propose a method to measure nanometric step heights based on a modal analysis of the reflected or transmitted field. Our approach requires a minimum of four single-point measurements by detectors with no spatial resolution (photodiodes) and yet can reconstruct spatial structure with nanometric resolution. It has the benefits of not requiring a reference measurement or calibration and it is completely digital, thus offering high reliability and real-time measurement. As proof of principle, we perform measurements on reflective samples, finding excellent agreement between the set and measured values, with uncertainties comparable to those of scanning-force microscopes.