Method for analyzing local thermal expansion behavior of heterostructure

Abstract

This invention discloses a method for analyzing the local thermal expansion behavior of heterostructures, comprising providing substrate samples of a first material and a second material with different coefficients of thermal expansion; performing surface scanning of the substrate samples at a first temperature using a scanning probe microscopy system to obtain first surface height data including a first height numerical matrix; heating the substrate samples to a second temperature higher than the first temperature, and performing surface scanning of the substrate samples again to obtain second surface height data including a second height numerical matrix; performing alignment processing on the first height numerical matrix and the second height numerical matrix; and performing a difference operation on the second height numerical matrix and the first height numerical matrix to obtain a three-dimensional expansion numerical matrix.

Claims

1. A method for analyzing the local thermal expansion behavior of heterostructures, comprising: A substrate sample is provided, comprising a first material and a second material surrounding the first material; The first thermal expansion coefficient of the first material is higher than the second thermal expansion coefficient of the second material; First scanning operation: a scanning probe microscopy system is used to scan a test area of ​​the substrate sample at a first temperature to obtain a first surface height data containing a first height value matrix, and the test area covers the surface of the first material and the surface of the second material; Second scanning operation: the substrate sample is heated to a second temperature higher than the first temperature, and the test area is scanned again using the scanning probe microscopy system to obtain a second surface height data containing a second height value matrix; Alignment operation: the surface of the second material is set as a reference plane, and alignment processing is performed on the first height value matrix and the second height value matrix to establish the spatial correspondence between corresponding pixels of the two matrices; and Analysis operation: the second height value matrix and the first height value matrix are subjected to a difference operation to obtain a three-dimensional expansion value matrix.

2. The method as described in request item 1, wherein, After obtaining the three-dimensional expansion numerical matrix, the analysis task further includes: outputting the three-dimensional expansion numerical matrix as a visualized three-dimensional expansion map to characterize the local thermal expansion behavior of the first material during the heating process.

3. The method as described in request item 1, wherein, The first material is a metallic material, and the second material is a dielectric material.

4. The method as described in request item 3, wherein, The metal material is a copper pad, the dielectric material is a silicon dioxide dielectric layer, and the copper pad is embedded in an opening in the silicon dioxide dielectric layer; wherein the substrate sample further comprises a third material, the third material is a semiconductor substrate, and the copper pad and the silicon dioxide dielectric layer are disposed on the semiconductor substrate.

5. The method as described in request item 1, wherein, In the alignment operation, the alignment process includes using at least one repeatably identifiable feature point on the surface of the first material as an alignment reference feature for alignment.

6. The method of claim 1, wherein the alignment operation further comprises: automatically identifying repeatable feature points on the surface of the first material using an image feature detection algorithm, the feature points being one of grains, grain boundaries or surface micro-defects, and performing alignment correction by translation or rotation accordingly.

7. The method as described in request item 1, wherein, The value of each element in the three-dimensional expansion numerical matrix represents the height difference of that location before and after heating.

8. The method as described in request item 1, wherein, The scanning probe microscopy system is a system that includes an atomic force microscope (AFM).

9. The method as described in claim 1, wherein, The first temperature is between 20°C and 30°C, and the second temperature is between 100°C and 500°C.

10. The method as described in claim 1, wherein, The alignment operation further includes: dividing the first height numerical matrix and the second height numerical matrix into multiple sub-analysis regions; independently finding at least one reproducibly identifiable feature point within each sub-analysis region to perform local alignment of the sub-region; wherein the analysis operation further includes: after completing local alignment in each sub-analysis region, obtaining multiple local three-dimensional dilatation numerical matrices through pixel-by-pixel difference operations; and reassembling the multiple local three-dimensional dilatation numerical matrices into a global three-dimensional dilatation numerical matrix.

11. The method of claim 1, wherein the analysis operation further comprises: after obtaining the three-dimensional dilatation numerical matrix, applying a numerical mask to the three-dimensional dilatation numerical matrix to mark or replace edge region values, negative values, or values ​​outside a reasonable range in the three-dimensional dilatation numerical matrix.

12. The method as described in claim 1, wherein, The analysis task further includes: after obtaining the three-dimensional expansion numerical matrix, setting a height threshold value, and calculating the percentage of expansion heights in the three-dimensional expansion numerical matrix that are greater than or equal to the height threshold value, in order to evaluate the proportion of the bondable area of ​​the first material.

13. The method of claim 1, further comprising a third scanning operation: after the second scanning operation, cooling the substrate sample from the second temperature back to the first temperature, and scanning the area to be measured again with the scanning probe microscopy system to obtain a third surface height data including a third height numerical matrix; and performing a difference operation between the third height numerical matrix and the first height numerical matrix to form a plastic deformation numerical matrix characterizing the irreversible deformation distribution of the first material.

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