Binary pseudo-random patterned structures for modulation transfer function calibration and resolution characterization of a full-field transmission soft x-ray microscope

Abstract

We present a modulation transfer function (MTF) calibration method based on binary pseudo-random (BPR) one-dimensional sequences and two-dimensional arrays as an effective method for spectral characterization in the spatial frequency domain of a broad variety of metrology instrumentation, including interferometric microscopes, scatterometers, phase shifting Fizeau interferometers, scanning and transmission electron microscopes, and at this time, x-ray microscopes. The inherent power spectral density of BPR gratings and arrays, which has a deterministic white-noise-like character, allows a direct determination of the MTF with a uniform sensitivity over the entire spatial frequency range and field of view of an instrument. We demonstrate the MTF calibration and resolution characterization over the full field of a transmission soft x-ray microscope using a BPR multilayer (ML) test sample with 2.8 nm fundamental layer thickness. We show that beyond providing a direct measurement of the microscope’s MTF, tests with the BPRML sample can be used to fine tune the instrument’s focal distance. Our results confirm the universality of the method that makes it applicable to a large variety of metrology instrumentation with spatial wavelength bandwidths from a few nanometers to hundreds of millimeters.