System and method using x-rays for depth-resolving metrology and analysis

A method for analyzing a three-dimensional structure of a sample, the method comprising:

• generating a first x-ray beam, the first x-ray beam having a first energy bandwidth less than 20 eV at full-width-at-half maximum and a first mean x-ray energy that is in a range of 1 eV to 1 keV higher than a first absorption edge energy of a first atomic element of interest, the first x-ray beam collimated to have a first collimation angular range less than 7 mrad in at least one direction perpendicular to a first propagation direction of the first x-ray beam;
• irradiating the sample with the first x-ray beam at a plurality of incidence angles relative to a substantially flat surface of the sample, the incidence angles of the plurality of incidence angles in a range of 3 mrad to 400 mrad, and the plurality of incidence angles comprise less than 100 incidence angles and at least 20% of the incidence angles are separated from one another by at least 3 mrad;
• simultaneously detecting a reflected portion of the first x-ray beam from the sample and detecting x-ray fluorescence x-rays and/or photoelectrons from the sample;
• and
• selecting at least some of the incidence angles of the plurality of incidence angles to correspond to expected extrema in the detected reflected portion of the first x-ray beam from the sample and/or expected extrema in the detected x-ray fluorescence x-rays from the sample.

A method for analyzing a layered structure comprising substantially parallel interfaces, the method comprising:

• irradiating the layered structure with an incident x-ray beam at one or more incidence angles in a range of 3 mrad to 400 mrad relative to the substantially parallel interfaces, the incident x-ray beam having an energy bandwidth less than 20 eV at full-width-at-half maximum and a mean x-ray energy that is in a range of 1 eV to 1 keV higher than an absorption edge energy of an atomic element of interest, the incident x-ray beam having sufficient coherence to produce a standing x-ray wave having x-ray intensity modulation in a direction normal to the substantially parallel interfaces and inside the layered structure through constructive and destructive interference of the incident x-ray beam and x-rays of the incident x-ray beam reflected by the substantially parallel interfaces of the layered structure;
• tuning an incidence angle of the x-ray beam relative to the substantially parallel interfaces to position nodes and antinodes of the standing x-ray wave along the direction at predetermined positions relative to the substantially parallel interfaces and within the layered structure;
• and
• simultaneously detecting at least some of the x-rays reflected by the substantially parallel interfaces and detecting x-ray fluorescence x-rays and/or photoelectrons from the layered structure.

A system for analyzing a three-dimensional structure of a sample, the system comprising:

• at least one x-ray source configured to generate at least one x-ray beam having an energy bandwidth less than 20 eV at full-width-at-half maximum and a mean x-ray energy that is in a range of 1 eV to 1 keV higher than an absorption edge energy of an atomic element of interest, the at least one x-ray beam collimated to have a collimation angular range less than 7 mrad in at least one direction perpendicular to a propagation direction of the at least one x-ray beam, the at least one x-ray source further configured to direct the at least one x-ray beam to irradiate the sample at an incidence angle relative to a substantially flat surface of the sample, the sample having a layered structure comprising a plurality of layers and a plurality of substantially parallel interfaces between the plurality of layers, the incidence angle in a range of 3 mrad to 400 mrad, the at least one x-ray beam having sufficient coherence to produce a standing x-ray wave having x-ray intensity modulation in a direction normal to the surface and inside the layered structure through constructive and destructive interference of the at least one x-ray beam and x-rays of the at least one x-ray beam reflected by the plurality of substantially parallel interfaces of the layered structure;
• at least one stage configured to adjust and set the incidence angle of the at least one x-ray beam relative to the surface at specific predetermined values such that positions of nodes and antinodes of the standing x-ray wave are adjusted and set at predetermined positions relative to the plurality of layers and the plurality of substantially parallel interfaces along the direction normal to the surface and within the layered structure;
• at least one first detector configured to detect a reflected portion of the at least one x-ray beam from the sample;
• and
• at least one second detector configured to detect x-ray fluorescence x-rays and/or photoelectrons from the sample simultaneously with the at least one first detector detecting the reflected portion of the at least one x-ray beam.