CN-122020354-A - Depth profile inversion method based on soft constraint for surface analysis

CN122020354ACN 122020354 ACN122020354 ACN 122020354ACN-122020354-A

Abstract

The invention discloses a depth analysis inversion method based on soft constraint, which is used for material surface analysis. The method comprises the steps of S1, obtaining the measured apparent concentration distribution of elements in a material based on the obtained X-ray photoelectron spectrum peak angle distribution, S2, presetting the depth distribution of the element concentration in the material, calculating the photoelectron spectrum peak angle distribution, S3, obtaining the calculated apparent concentration distribution of the elements in the material based on the calculated photoelectron spectrum peak angle distribution, S4, determining a residual error item based on the measured apparent concentration distribution and the calculated apparent concentration distribution, introducing a regularization item and a soft constraint item, and establishing a joint probability function, and S5, carrying out iterative calculation by taking the function value of the joint probability function as a criterion, and finally determining the depth distribution of the element concentration in the material. According to the invention, soft constraint terms are introduced into the algorithm, so that the hard dependence of the algorithm on accurate physical priori is reduced, and the accuracy and stability of the depth analysis algorithm are improved.

Inventors

CHEN HAONAN
CHEN XIANGJUN
XU CHUNKAI
SHAN XU
WANG ENLIANG

Assignees

中国科学技术大学

Dates

Publication Date: 20260512
Application Date: 20251215

Claims (7)

1. A soft constraint-based depth profile inversion method for surface analysis, comprising: s1, obtaining the measured apparent concentration distribution of elements in a material based on the obtained X-ray photoelectron spectrum peak angle distribution; s2, presetting the depth distribution of element concentration in a material, and calculating the peak angle distribution of photoelectron spectroscopy; s3, obtaining calculated apparent concentration distribution of elements in the material based on the calculated photoelectron spectrum peak angle distribution; S4, determining residual error terms based on the measured apparent concentration distribution and the calculated apparent concentration distribution, introducing regularization terms and soft constraint terms to establish a joint probability function, and And S5, performing iterative calculation by taking the function value of the joint probability function as a criterion, and finally determining the depth distribution of the element concentration in the material.
2. The soft constraint based depth profile inversion method for surface analysis of claim 1 wherein said X-ray photoelectron spectrum peak angle distribution is : Wherein, theta is the photoelectron emergence angle, Is the depth distribution of element concentration in the material, z is the depth of the material, lambda is the mean free path of electrons, Is a constant comprising the instrument transfer function, geometry factor, and atomic photoionization section.
3. The soft constraint based depth profile inversion method for surface analysis of claim 1 wherein the joint probability function is: Wherein the method comprises the steps of Is a residual term; in order to regularize the term(s), Is a regularization parameter; In the case of a soft constraint term, Is a weight factor.
4. A soft constraint based depth profile inversion method for surface analysis according to claim 1 or 3, wherein the residual term is: Wherein, the In order to measure the apparent concentration profile, To calculate the apparent concentration distribution, j represents the element species in the material, k represents the different exit angles, Representing the data variance.
5. The soft constraint-based depth profile inversion method for surface analysis according to claim 1, wherein the depth profile of the element concentration is accurately obtained by measuring the obtained peak angle profiles of the X-ray photoelectron spectra of different elements.
6. The soft constraint based depth profile inversion method of claim 1 wherein the soft constraint term can be any physically significant prior.
7. The soft constraint based depth profile inversion method for surface analysis of claim 1 wherein the depth distribution of element concentration in the material is determined by iterative calculation using the function value of the joint probability function as a criterion such that the function value is minimized.

Description

Depth profile inversion method based on soft constraint for surface analysis Technical Field The disclosure relates to the technical field of surface analysis, in particular to a depth profile inversion method based on soft constraint for surface analysis. Background The surface analysis technology is an important means for acquiring the surface composition, chemical state and structural information of materials, and is widely applied to the fields of semiconductors, films, catalysis and the like. Among the numerous surface analysis techniques, X-ray photoelectron spectroscopy (XPS) is one of the more common. The technology utilizes X-rays to excite inner-layer electrons of atoms on the surface of a sample and analyzes the energy distribution of escaped photoelectrons, so that the element types and the chemical valence states thereof are quantitatively analyzed. In XPS, element information of different depths of a sample is obtained by measuring photoelectron signals of different emission angles, angle distribution of emitted electrons is fitted by a least square method, and depth information is obtained by residual analysis. The angle-depth mapping is essentially a pathological inverse laplace transform process, and must rely on depth profile inversion algorithms. In the conventional least squares method, if only the residual term is used as a criterion, signal noise may be infinitely amplified in the algorithm, resulting in serious overfitting. For this purpose, regularization terms (smooth prior) can be introduced to constitute, together with residual terms, a joint probability function, by minimizing which overfitting is effectively suppressed. However, only introducing a smooth prior still has difficulty in ensuring the accuracy and stability of the analysis results in many cases. To further enhance the accuracy and stability of the algorithm, a priori constraints with physical significance may also be introduced into the algorithm. Stringent conditional constraints are usually applied with physical priors, which are called hard constraints. But may lead to deviations in the analysis results when the physical priors are not perfectly accurate. In order to solve the problems, the method introduces soft constraint terms into the regularized inversion algorithm, namely introduces physical priori in the form of punishment terms into the joint probability function, reduces the hard dependence on accurate physical priori, and improves the accuracy and stability of the depth analysis algorithm. Disclosure of Invention In view of the above, in order to solve the above-mentioned technical problems, the present disclosure provides a depth profile inversion method based on soft constraint for surface analysis, which comprises the following steps: the invention provides a depth analysis inversion method based on soft constraint for surface analysis, which comprises the following operations: s1, obtaining the measured apparent concentration distribution of elements in a material based on the obtained X-ray photoelectron spectrum peak angle distribution; s2, presetting the depth distribution of element concentration in a material, and calculating the peak angle distribution of photoelectron spectroscopy; s3, obtaining calculated apparent concentration distribution of elements in the material based on the calculated photoelectron spectrum peak angle distribution; S4, determining residual error terms based on the measured apparent concentration distribution and the calculated apparent concentration distribution, introducing regularization terms and soft constraint terms to establish a joint probability function, and And S5, performing iterative calculation by taking the function value of the joint probability function as a criterion, and finally determining the depth distribution of the element concentration in the material. According to an embodiment of the present disclosure, the photoelectron spectrum peak angle distribution is: Wherein, theta is the photoelectron emergence angle,Is the depth distribution of element concentration in the material, z is the depth of the material, lambda is the mean free path of electrons,Is a constant comprising the instrument transfer function, geometry factor, and atomic photoionization section. According to an embodiment of the present disclosure, the joint probability function is: Wherein the method comprises the steps of Is a residual term; in order to regularize the term(s), Is a regularization parameter; In the case of a soft constraint term, Is a weight factor. The residual term is: Wherein, the In order to measure the apparent concentration profile,To calculate the apparent concentration distribution, j represents the element species in the material, k represents the different exit angles,Representing the data variance. According to the embodiment of the disclosure, the soft constraint term is a priori with physical meaning, optionally the soft constraint term is concentrat