Optimization-based image processing for metrology

Patent metadata

Field	Value
Publication number	US-12050408-B2
Application number	US-202017416329-A
Country	US
Kind code	B2
Filing date	Nov 24, 2020
Priority date	Nov 24, 2020
Publication date	Jul 30, 2024
Grant date	Jul 30, 2024

Abstract

One or more images of a device feature are acquired using an imaging tool. A geometrical shape is defined encompassing the relevant pixels of each image, where the geometrical shape is represented in terms of one or more parameters. A cost function is defined whose variables comprise the one or more parameters of the geometrical shape. For each image, numerical optimization is applied to obtain optimal values of the one or more parameters for which the cost function is minimized. The optimal values of the one or more parameters are reported as metrology data pertaining to the device feature.

First claim

What is claimed is:

1. A method comprising:
acquiring one or more images of a device feature using an imaging tool, wherein the one or more images are top-down images;
defining a geometrical shape encompassing relevant pixels of each image of the one or more images, wherein the geometrical shape is represented in terms of one or more parameters;
defining a cost function whose variables comprise the one or more parameters of the geometrical shape;
for each image, applying numerical optimization to obtain optimal values of the one or more parameters for which a value of the cost function is minimum; and
providing the optimal values of the one or more parameters as metrology data pertaining to the device feature.

2. The method of claim 1 , further comprising:
prior to acquiring the one or more images, tuning imaging tool parameters to maximize signal to noise ratio of the one or more images.

3. The method of claim 1 , wherein the geometrical shape comprises an ellipse, wherein the one or more parameters representing the ellipse comprises a major axis diameter of the ellipse, a minor axis diameter of the ellipse, coordinates of a center of the ellipse, and angular direction of the ellipse.

4. The method of claim 3 , wherein the cost function is defined as:
cost( x,y,a,b ,θ)=Values( x,y,a,b ,θ)−λ Area( a,b )

where, a=major axis diameter of the ellipse,
b=minor axis diameter of the ellipse,
(x, y) are coordinates of a center of the ellipse,

θ is an angle between a horizontal axis and the major axis of the ellipse, indicating an angular direction of the ellipse,
Area=area of the ellipse; and
λ is a tuning parameter for optimizing the cost function.

5. The method of claim 4 , wherein the tuning parameter λ controls tradeoff between the first term of the cost function (Values (x, y, a, b, θ)) and the second term of the cost function (λ Area(a, b)).

6. The method of claim 4 , wherein the optimal values of the parameters of the ellipse for which the cost function is minimized represent the largest and the darkest ellipse that encompasses the relevant pixels in a relatively brighter background.

7. The method of claim 3 , further comprising:
detecting an annulus of relatively brighter pixels in a relatively dark background in an image with low signal to noise ratio;
defining an inner ellipse and an outer ellipse that collectively constitute an elliptical ring that encompasses the annulus of the relatively brighter pixels; and
tailoring the cost function such that the numerical optimization yields one or more parameters of the elliptical ring.

8. The method of claim 3 , wherein the device feature comprises a hole having a top opening, and a bottom surface that is partially obscured from being directly imaged by the imaging tool, wherein the top opening and the bottom surface are connected by sloped sidewalls.

9. The method of claim 8 , further comprising:
obtaining known dimensions of the bottom surface of the hole from prior measurements;
defining a top ellipse and a bottom ellipse that respectively encompass a first set of pixels representing the top opening and a second set of pixels representing the bottom surface, wherein the bottom ellipse incorporates the known dimensions of the bottom surface obtained from the prior measurements; and
tailoring the cost function, such that the numerical optimization yields an offset value between the top ellipse and the bottom ellipse.

10. The method of claim 9 , wherein incorporating the known dimensions to define the bottom ellipse compensates for the bottom surface being obscured from being directly imaged due to the sloped sidewalls.

11. A non-transitory machine-readable storage medium storing instructions which, when executed, cause a processing device to perform operations comprising:
defining a geometrical shape encompassing relevant pixels of each image of one or more images of a device feature acquired using an imaging tool, wherein the one or more images are top-down images, and wherein the geometrical shape is represented in terms of one or more parameters;
defining a cost function whose variables comprise the one or more parameters of the geometrical shape;
for each image, applying numerical optimization to obtain optimal values of the one or more parameters for which a value of the cost function is minimum; and
providing the optimal values of the one or more parameters as metrology data pertaining to the device feature.

12. The non-transitory machine-readable storage medium of claim 11 , wherein the geometrical shape comprises an ellipse, wherein the one or more parameters representing the ellipse comprises a major axis diameter of the ellipse, a minor axis diameter of the ellipse, coordinates of a center of the ellipse, and angular direction of the ellipse.

13. The non-transitory machine-readable storage medium of claim 12 , wherein the cost function is defined as:
cost( x,y,a,b ,θ)=Values( x,y,a,b ,θ)−λ Area( a,b )

where, a=major axis diameter of the ellipse,
b=minor axis diameter of the ellipse,
(x, y) are coordinates of a center of the ellipse,

θ is an angle between a horizontal axis and the major axis of the ellipse, indicating the angular direction of the ellipse,
Area=area of the ellipse; and
λ is a tuning parameter for optimizing the cost function.

14. The non-transitory machine-readable storage medium of claim 12 , wherein the optimal values of the parameters of the ellipse for which the cost function is minimized represent the largest and the darkest ellipse that encompasses the relevant pixels in a relatively brighter background.

15. The non-transitory machine-readable storage medium of claim 12 , wherein the processing device further performs:
detecting an annulus of relatively brighter pixels in a relatively dark background in an image with low signal to noise ratio;
defining an inner ellipse and an outer ellipse that collectively constitute an elliptical ring that encompasses the annulus of the relatively brighter pixels; and
tailoring the cost function such that the numerical optimization yields one or more parameters of the elliptical ring.

16. The non-transitory machine-readable storage medium of claim 12 , wherein the processing device further performs:
obtaining known dimensions of a bottom surface of a device feature from prior measurements, wherein the device feature comprises a hole having a top opening, and the bottom surface that is partially obscured from being directly imaged by the imaging tool, wherein the top opening and the bottom surface are connected by sloped sidewalls;
defining a top ellipse and a bottom ellipse that respectively encompass a first set of pixels representing the top opening and a second set of pixels representing the bottom surface, wherein the bottom ellipse incorporates the known dimensions of the bottom surface obtained from the prior measurements; and
tailoring the cost function, such that the numerical optimization yields an offset value between the top ellipse and the bottom ellipse.

17. A system comprising a memory and a processing device coupled to the memory, wherein the processing device performs the following operations:
obtaining one or more images of a device feature, wherein the one or more images are top-down images;
defining a geometrical shape encompassing relevant pixels of each image of the one or more images, wherein the geometrical shape is represented in terms of one or more parameters;
defining a cost function whose variables comprise the one or more parameters of the geometrical shape;
for each image,

Assignees

• Applied Materials Inc

Inventors

• Bishara Waheb
• Chen Stephanie W
• Lin Bin
• Xiao Xinhuo

Classifications

• G03F7/706837

  Data analysis, e.g. filtering, weighting, flyer removal, fingerprints or root cause analysis · CPC title

• G01B2210/56

  Measuring geometric parameters of semiconductor structures, e.g. profile, critical dimensions or trench depth · CPC title

• G06T2207/30148

  Semiconductor; IC; Wafer · CPC title

• G03F7/70625 Primary

  Dimensions, e.g. line width, critical dimension [CD], profile, sidewall angle or edge roughness · CPC title