Visualization of three-dimensional semiconductor structures

1. A non-transitory computer-readable storage medium storing one or more programs for execution by one or more processors of a computer system, the one or more programs including instructions for:

based on inspection by a semiconductor metrology tool of an area of a semiconductor wafer that includes a plurality of instances of a three-dimensional (3D) semiconductor structure arranged periodically, generating a model of a respective instance of the 3D semiconductor structure;

rendering an image of the model that shows a 3D shape of the model, the image comprising:

at least one of a top surface or a bottom surface of the respective instance of the 3D semiconductor structure, and

a user-selectable translucent cross-section of the respective instance of the 3D semiconductor structure between the top and bottom surfaces; and

providing the image to a device for display.

2. The computer-readable storage medium of claim 1 , wherein the image comprises a projection of the model to be displayed in two dimensions.

3. The computer-readable storage medium of claim 1 , wherein the image shows uncertainty for the 3D shape in the model.

4. The computer-readable storage medium of claim 1 , wherein the image indicates deviation of the 3D shape or a cross-section of the 3D shape from a nominal shape.

5. The computer-readable storage medium of claim 1 , wherein the image comprises an animation that successively shows successive portions of the 3D shape.

6. The computer-readable storage medium of claim 1 , wherein:

the image is a 3D stereographic image; and

providing the image comprises sending the image to a 3D stereographic viewer.

7. The computer-readable storage medium of claim 1 , wherein:

the plurality of instances of the 3D semiconductor structure comprises a periodic arrangement of memory holes in a 3D memory; and

the respective instance of the 3D semiconductor structure comprises a respective memory hole.

8. The computer-readable storage medium of claim 7 , wherein the image shows an elliptical shape of the respective memory hole for multiple cross-sections of the respective memory hole.

9. The computer-readable storage medium of claim 8 , wherein the image shows the helicity of the respective memory hole for the multiple cross-sections, wherein the helicity indicates change in orientation of the elliptical shape.

10. The computer-readable storage medium of claim 7 , wherein the image indicates deviation from an elliptical shape for the multiple cross-sections.

11. The computer-readable storage medium of claim 7 , wherein the image shows tilt of the respective memory hole.

12. The computer-readable storage medium of claim 1 , wherein:

the plurality of instances of the 3D semiconductor structure comprises a periodic arrangement of finFETs; and

the respective instance of the 3D semiconductor structure comprises a respective finFET or a portion of a respective finFET.

13. The computer-readable storage medium of claim 1 , wherein:

the plurality of instances of the 3D semiconductor structure comprises an array of DRAM cells; and

the respective instance of the 3D semiconductor structure comprises a respective DRAM cell or a portion of a respective DRAM cell.

14. The computer-readable storage medium of claim 1 , wherein generating the model of the respective instance of the 3D semiconductor structure comprises:

obtaining a geometric model of the 3D semiconductor structure with parameterized dimensions; and

using measurements collected during the inspecting to determine values of the parameterized dimensions.

15. The computer-readable storage medium of claim 1 , wherein generating the model of the respective instance of the 3D semiconductor structure comprises:

obtaining sets of measurements for varying instances of the 3D semiconductor structure, the sets being labeled with respective values of dimensions; and

performing machine learning, using the sets and measurements collected during the inspecting, to determine values of the dimensions for the respective instance,

wherein the generating is performed without using a parameterized geometric model of the 3D semiconductor structure.

16. The computer-readable storage medium of claim 1 , wherein inspecting the area of the semiconductor wafer comprises performing an optical metrology technique selected from the group consisting of spectroscopic ellipsometry, single-wavelength ellipsometry, beam-profile ellipsometry, beam-profile reflectometry, single-wavelength reflectometry, angle-resolved reflectometry, spectroscopic reflectometry, scatterometry, and Raman spectroscopy.

17. The computer-readable storage medium of claim 1 , wherein inspecting the area of the semiconductor wafer comprises performing small-angle x-ray scattering.

18. A non-transitory computer-readable storage medium storing one or more programs for execution by one or more processors of a computer system, the one or more programs including instructions for:

based on inspection by a semiconductor metrology tool of an area of a semiconductor wafer that includes a plurality of instances of a three-dimensional (3D) semiconductor structure arranged periodically, generating a model of a respective instance of the 3D semiconductor structure;

rendering from a first perspective a first augmented-reality or virtual-reality (AR/VR) image of the model that shows a 3D shape of the model;

providing the first AR/VR image to an AR/VR viewing device for display;

after providing the first AR/VR image to the AR/VR viewing device for display, receiving user input requesting a change in perspective;

in response to the user input, rendering a second AR/VR image of the model from a second perspective; and

providing the second AR/VR image to the AR/VR viewing device for display.

19. A non-transitory computer-readable storage medium storing one or more programs for execution by one or more processors of a computer system, the one or more programs including instructions for:

based on inspection by a semiconductor metrology tool of an area of a semiconductor wafer that includes a plurality of instances of a three-dimensional (3D) semiconductor structure arranged periodically, generating a model of a respective instance of the 3D semiconductor structure;

rendering a first augmented-reality or virtual-reality (AR/VR) image of the model that shows a 3D shape of the model with an appearance that corresponds to values of a parameter of the model as determined based on measurements collected during the inspection;

providing the first AR/VR image to an AR/VR viewing device for display;

after providing the first AR/VR image to the AR/VR viewing device for display, receiving user input requesting a change to the values of the parameter;

in response to the user input, changing the values of the parameter for the model;

rendering a second AR/VR image of the model with an appearance that corresponds to the changed values; and

providing the second AR/VR image to the AR/VR viewing device for display.

20. A non-transitory computer-readable storage medium storing one or more programs for execution by one or more processors of a computer system, the one or more programs including instructions for:

based on inspection by a semiconductor metrology tool of an area of a semiconductor wafer that includes a periodic arrangement of memory holes in a three-dimensional (3D) semiconductor memory, generating a model of a respective memory hole;

rendering an image of the model that shows a 3D shape of the model, wherein the image shows an elliptical shape of the respective memory hole for multiple cross-sections of the respective memory hole and shows the helicity of the respective memory hole for the multiple cross-sections, wherein the helicity indicates change in orientation of the elliptical shape; and

providing the image to a device for display.

21. A non-transitory computer-readable storage medium storing one or more programs for execution by one or more processors of a computer system, the one or more programs including instructions for:

based on inspection by a semiconductor metrology tool of an area of a semiconductor wafer that includes a plurality of instances of a three-dimensional (3D) semiconductor structure arranged periodically, generating a model of a respective instance of the 3D semiconductor structure, comprising:

obtaining sets of measurements for varying instances of the 3D semiconductor structure, the sets being labeled with respective values of dimensions; and

performing machine learning, using the sets and measurements collected during the inspecting, to determine values of the dimensions for the respective instance,

wherein the generating is performed without using a parameterized geometric model of the 3D semiconductor structure;

rendering an image of the model that shows a 3D shape of the model; and

providing the image to a device for display.