US-20260127739-A1 - METHOD FOR ADAPTING DEPTH STRUCTURE MODEL DATA TO COHERENCE TOMOGRAPHY MEASUREMENT DATA AND COHERENCE TOMOGRAPHY METHOD

US20260127739A1US 20260127739 A1US20260127739 A1US 20260127739A1US-20260127739-A1

Abstract

A method for adapting depth structure model data to coherence tomography measurement data of a sample having a plurality of layers composed of layer materials in a layer construction in a depth direction. A plurality of layers having layer thicknesses and a plurality of layer transitions upstream of the respective layers in the depth direction are derived from the depth structure. Furthermore, model reflectivity coefficients are adapted to the respective layer-transition-specific, spectrally resolved reflectivity coefficients by way of a value that optimizes the adaptation being calculated in each case for the at least one parameter of one of the model layer transitions. On the basis of the value calculated for the at least one parameter, depth structure model data can be obtained, the resolution of which in the depth direction goes beyond the resolution predefined by a CT measurement on which the spectral complex field reflectivity is based.

Inventors

Felix Wiesner
Silvio Fuchs
Gerhard G. Paulus
Johann Jakob ABEL

Assignees

FRIEDRICH-SCHILLER-UNIVERSITAET JENA

Dates

Publication Date: 20260507
Application Date: 20251106
Priority Date: 20230508

Claims (12)

1 . Computer-implemented method for adapting depth structure model data to coherence tomography measurement data of a sample, which has a plurality of layers of layer materials in a depth direction in a layer structure, comprising the steps: providing CT measurement data in a processor, wherein the CT measurement data comprise a depth structure unambiguously derived from a spectral complex field reflectivity, wherein the depth structure is based on a resolution in the depth direction, which is predetermined by a CT measurement on which the spectral complex field reflectivity is based; deriving from the depth structure a plurality of layers having layer thicknesses and a plurality of layer transitions, which are arranged upstream of the respective layers in the depth direction; extracting layer transition-specific, spectrally resolved reflectivity coefficients from the depth structure for the plurality of layer transitions; providing depth structure model data in the processor, wherein the depth structure model data model the layer structure of the sample and are initialized for the plurality of derived layers based on the layer thicknesses and the layer materials belonging to the layers; and a plurality of model layer transitions, the spectrally resolved model reflectivity coefficients of which can be modeled in a layer transition-specific manner based on at least one parameter; adapting the model reflectivity coefficients to the respective layer transition-specific, spectrally resolved reflectivity coefficients by calculating a value optimizing the adaptation in each case for the at least one parameter of one of the model layer transitions; and adapting the depth structure model data on the basis of the value calculated for the at least one parameter.
2 . The computer-implemented method according to claim 1 , wherein, before adapting a model reflectivity coefficient of a layer transition, the model reflectivity coefficients preceding in each case in the depth direction are adapted to the layer transition-specific, spectrally resolved reflectivity coefficients.
3 . The computer-implemented method according to claim 1 , wherein the depth structure model data are adapted layer by layer in the depth direction with respect to the layer transitions; and/or wherein the value calculated for the at least one parameter is below the resolution in the depth direction predetermined by the CT measurement data.
4 . The computer-implemented method according to claim 1 , wherein, for adapting the depth structure model data to the CT measurement data, the model reflectivity coefficients are recursively optimized in a plurality of steps with respect to layer transitions located deeper in the sample, wherein, in particular, starting from the surface of the sample, the layer structure is reconstructed and the depth structure model data are updated layer by layer by in a first step, parameters of a surface layer such as a roughness and a thickness of the surface layer are optimized by minimizing a deviation between measured and modeled reflectivity coefficients of the surface layer by varying the parameters, the values of the parameters of the surface layer are fixed in the depth structure model data for the further optimization; in a second step, parameters of the second layer transition in the depth direction such as a roughness and a thickness of a buried oxide layer are optimized by minimizing a deviation function between measured and modeled reflectivity coefficients of the second layer transition by varying the parameters while the parameter of the surface layer being fixed; the values of the parameters of the second layer transition are fixed in the depth structure model data for the further optimization; in further steps, the parameters of the layer transition respectively closest in the depth direction are successively optimized; and optionally, the sum of the thicknesses determined for the surface layer and the subsequent layer transitions and the thicknesses of the layers determined from the depth structure is kept constant with respect to the depth structure.
5 . The computer-implemented method according to claim 1 , wherein layer transition-specific, spectrally resolved reflectivity coefficients are extracted by identifying a depth region in the depth structure assigned to a layer transition, in particular by sequential spatial filtering of the depth structure; and calculating the layer transition-specific, spectrally resolved reflectivity coefficients by a Fourier transformation of the field reflectivity limited to the respective layer transition.
6 . The computer-implemented method according to claim 1 , wherein the at least one parameter of a model reflectivity coefficient of a layer transition is selected from the group of parameters comprising a layer transition thickness; a roughness; a spectral reflection or transmission value; a material density; a material type; a material composition; a stoichiometric ratio of a material composition; and/or a material transition gradient of a material composition.
7 . The computer-implemented method according to claim 1 , wherein the layer transition comprises an interface or an intermediate layer delimited by two interfaces between two layers of the same material; or an interface or an intermediate layer delimited by two interfaces between two layers of different materials.
8 . The computer-implemented method according to claim 1 , further comprising: a first step of adapting the initialized depth structure model data to the coherence tomography measurement data, comprising: optimizing a model reflectivity coefficient, which is assigned to an input-side interface of the sample and represents a first modelable layer transition, in particular a modelable surface layer, by matching with a reflectivity coefficient; and/or an output step, in which the adapted depth structure model data and in particular the set values of the at least one parameter for the layer transitions are output by the processor on an input and output device.
9 . The computer-implemented method according to claim 1 , wherein the value optimizing the adaptation is calculated for a layer transition by, within the scope of a parameter scan, minimizing a deviation function, which is dependent on the at least one parameter, between layer transition-specific, spectrally resolved reflectivity coefficients assigned to the layer transition and the model reflectivity coefficient assigned to the layer, in particular iteratively.
10 . Method for examining a sample, which has a plurality of layers in a layer structure in a depth direction, using optical coherence tomography, comprising the steps: performing a CT measurement on the sample, wherein a spectral complex field reflectivity is generated as CT measurement data by a phase-sensitive measurement and evaluation of an optical coherence signal or a spectrally resolved measurement, performed in particular within the scope of an artifact-free coherence tomography data analysis, of an intensity reflectivity of the sample and a derivation of phase information by an iterative phase retrieval method; deriving an unambiguous depth structure by Fourier transforming the spectral complex field reflectivity using a processor, wherein the depth structure is based on a resolution in the depth direction, which is predetermined by the CT measurement; deriving layers and layer thicknesses of the sample taking into account a dispersion correction based on known layer materials of the sample; generating depth structure model data using the processor, wherein the depth structure model data model the layer structure of the sample and are initialized for the plurality of derived layers based on the layer thicknesses and the layer materials belonging to the layers; and a plurality of model layer transitions, the spectrally resolved model reflectivity coefficients of which can be modeled in a layer transition-specific manner based on at least one parameter; and performing the computer-implemented method of claim 1 for adapting the depth structure model data to the CT measurement data of the sample, whereby the depth structure model data are expanded in particular by parameters of model layer transitions.
11 . The method according to claim 10 , wherein the CT measurement on the sample is performed using XUV radiation; and in particular, the spectral width of the XUV radiation limits a resolution of the CT measurement in the depth direction to a range of a few 10 nanometers, and the computer-implemented method identifies structures assigned to the transition layers with a resolution in the nanometer range.
12 . The method according to claim 10 , wherein the CT measurement on the sample is performed for a plurality of lateral regions, in particular in order to detect lateral inhomogeneities, present in a layer, of parameters of the layer structure; and wherein, in particular, radiation is irradiated successively onto the lateral regions, such that a spectral complex field reflectivity is respectively generated for the lateral regions of the plurality of lateral regions for performing the computer-implemented method for adapting the depth structure model data to the CT measurement data of the sample.

Description

CROSS REFERENCE TO RELATED APPLICATIONS This application is a continuation under 35 U.S.C. § 120 of International Application PCT/EP2024/062672, filed May 8, 2024, which claims priority to German Application No. 10 2023 111 920.6, filed May 8, 2023, the contents of each of which are incorporated by reference herein. The present invention relates to a computer-implemented method for adapting depth structure model data to coherence tomography measurement data of a sample and to a method for examining a sample by means of optical coherence tomography. Optical coherence tomography (OCT) has become established as an optical microscopy method for diffraction-free three-dimensional imaging. OCT is based on backscattering of incident light at an interface of a sample to be examined. The interface is also referred to herein as a layer transition. Information about the sample to be examined can be obtained, for example, by evaluating the interference of the light (back)scattered at different interfaces. In addition to the spatial superposition, a low temporal coherence of the superimposed light is a precondition. See “Optical coherence tomography—principles and applications”, A F. Fercher et al., Rep. Prog. Phys. 66 239 (2003) for a fundamental introduction into OCT. The spectral range for OCT investigations was extended to the spectral range from 30 eV to 530 eV within the scope of the so-called XCT (optical coherence tomography in the XUV range) using extreme ultraviolet (XUV) sources (e.g. synchrotron-based or laser-based). Siee, for example, U.S. Pat. No. 7,656,538 B2 (“short-wave-length coherence tomography”) for a laser-based XCT. Due to the large usable frequency bandwidths in the XUV, XCT enables an axial resolution in the range of, e.g., a few tens of nanometers. This results in new applications in the non-destructive examination of, e.g., (multilayer) coatings such as optical or XUV mirrors, functional axial structures in solar cells or axially structured semiconductors (graphene-based electronics) and of biological membrane layer structures. In particular, XCT enables a three-dimensional imaging of near-surface structures of thick samples. In the examination of structured semiconductors, XCT represents, for example, an interesting alternative to scanning electron microscopy (SEM) or transmission electron microscopy (TEM) as the latter usually require a preparation of the sample which often destroys the sample. In the scientific publication “Laboratory setup for extreme ultraviolet coherence tomography driven by a high-harmonic source”, J. Nathanael et al., Rev. Sci. Instrum. 90, 113702 (2019), an exemplary setup for the detection of XCT spectra using the example of a nanostructured sample and an exemplary data processing of the XCT spectra are described. Further introductory explanations for spectroscopic XCT are furthermore disclosed in “Coherence tomography with broad bandwidth extreme ultraviolet and soft X-ray radiation”, S. Skruszewicz et al., Applied Physics B (2021) 127:55. How an exemplary XCT algorithm in combination with a one-dimensional phase retrieval (PR) algorithm can derive the depth structure of a sample from the autocorrelation signal is explained in detail in the scientific publication “Optical coherence tomography with nanoscale axial resolution using a laser-driven high-harmonic source”, S. Fuchs et al., Vol. 4, No. 8/August 2017/Optica and the associated supplementary information. In the scientific publication “Characterization of encapsulated graphene layers using extreme ultraviolet coherence tomography”, F. Wiesner et al., Vol. 30, No. 18/29 Aug. 2022/OpticsExpress 32267, it is furthermore disclosed how ratios of reflectivities following an XCT depth structure analysis can be used for model-based acquisition of boundary layer parameters. The inventors have recognized that OCT is limited in its resolution in the depth direction by the bandwidth of the incident light, wherein, however, structures, which cause the backscattering of the incident light, can have a size in the depth direction that is below the OCT resolution given by the bandwidth. An aspect of this disclosure is based on the object of providing a method that can resolve structures of a sample within the scope of a coherence tomography (CT), which are below the resolution of the coherence tomography given by the bandwidth. A further object is to derive parameters of such structures and to adapt a depth structure model of the sample based thereon. Furthermore, aspects of the disclosure can be based on the object of characterizing layer transitions in a sample having a layer structure in more detail. At least one of these objects is achieved by a method according to claim 1 or by a method according to claim 10. Developments are provided in the dependent claims. In one aspect, a computer-implemented method for adapting depth structure model data to coherence tomography (CT) measurement data of a sample, which—in a depth dir