3D reflection ptychography using multi-layer Born approach

Abstract

Because of the growing demand for more advanced electric devices, an exponential growth of the number of transistors are supposed to be integrated into a single chip. To manufacture devices in the scale of nanometer cost-effectively, an accurate measurement for lithography process calibrating is necessary. Ptychography is a computational imaging technique which has the potential to serve as a metrology solution for semiconductor devices. It can reconstruct complex-valued permittivity function of an object from an extensive set of measured intensities of the diffraction patterns in the far field. It should be noted that also 2D and 3D a-periodic objects can be measured with this technique. Currently, this technique has been widely used in reconstructing thin and weakly scattering (satisfying the first Born approximation) objects in a transmission geometry (detectors and sources are placed on different sides of the objects).We propose an accurate 3D ptychography multi-layer Born model, and apply it to reconstruct refractive index distributions of semi-conductors. This model slices the sample into thin layers and first Born approximations are applied to each layer sequentially. For a transmission geometry, this model considers both forward scattering effects and backward scattering effects \cite{Chen2020Multi-layerMicroscopy}, as opposed to normal beam propagation models. For reflection geometry (detectors and sources are placed on the same side of the object), this model collects reflected fields on each layer of the sample and these fields will interact with the object again later together with other upwards fields. This procedure enables detectors arranged in a reflection geometry to gather complete information about the object. We implement the model on the existing ptychography platform based on the auto-differentiation (AD) solvers and manage to reconstruct high-resolution images of 3D objects.