Methods and systems for measuring semiconductor structures based on a trained scanning conditional measurement model are described herein. A scanning conditional model is trained based on Design Of Experiments (DOE) measurement data associated with known values of one or more parameters of interest and a set of perturbed values of the one or more parameters of interest. The trained conditional model minimizes the output of an error function characterizing the error between the known values of the perturbed values of the one or more parameters of interest for the given DOE measurement data. During inference, an error value associated with each candidate value of one or more parameters of interest is determined by the trained scanning conditional measurement model. The estimated value of the parameter of interest is the candidate value of the parameter of interest associated with the minimum error value.

An apparatus for X-ray inspection is provided. The apparatus includes: a stage on which an inspection target is loaded, the stage including a first surface and an opposite second surface; an X-ray generator disposed on or over the first surface of the inspection target and configured to irradiate the inspection target with incident X-rays; and a detection system disposed on or under the second surface of the inspection target and configured to detect first transmitted X-rays transmitted through the inspection target. The detection unit includes a first lens system and a second lens system. The first transmitted X-rays pass through one of the first lens system and the second lens system. The second lens system includes a micro zone plate.

An apparatus for X-ray inspection is provided. The apparatus includes: a stage on which an inspection target is loaded, the stage including a first surface and an opposite second surface; an X-ray generator disposed on or over the first surface of the inspection target and configured to irradiate the inspection target with incident X-rays; and a detection system disposed on or under the second surface of the inspection target and configured to detect first transmitted X-rays transmitted through the inspection target. The detection unit includes a first lens system and a second lens system. The first transmitted X-rays pass through one of the first lens system and the second lens system. The second lens system includes a micro zone plate.