Systems and methods for determining specification limits in a semiconductor device virtual fabrication environment

1 . A non-transitory computer-readable medium holding computing device-executable instructions, the instructions when executed causing at least one computing device equipped with one or more processors to:

perform a Design of Experiments (DOE) simulation for a semiconductor device structure, the simulation including a plurality of virtual fabrication runs, the plurality of virtual fabrication runs building a plurality of 3D models of the semiconductor device structure;

receive a selection of one or more virtual metrology target parameters;

determine whether virtual metrology data for the selected virtual metrology target parameters is normally distributed;

compute an empirical distribution based on the virtual metrology data for one or more of the selected virtual metrology target parameters;

determine confidence bounds for points in the empirical distribution for the one or more of the selected virtual metrology target parameters;

determine an upper and lower specification limits for one or more of the selected virtual metrology target parameters based on the respective confidence bounds; and

output the upper and lower specification limits.

2 . The medium of claim 1 , wherein the instructions when executed further cause the at least one computing device to:

extrapolate, using one or more regression models, from the confidence bounds, the upper and lower specification limits.

3 . The medium of claim 2 wherein the one or more regression models include a linear regression model.

4 . The medium of claim 2 wherein the one or more regression models include a spline regression model.

5 . The medium of claim 1 , wherein the instructions when executed further cause the at least one computing device to:

output the upper and lower specification limits as export data.

6 . The medium of claim 1 , wherein the instructions when executed further cause the at least one computing device to:

output the upper and lower specification limits on a graphical user interface.

7 . The medium of claim 1 , wherein the instructions when executed further cause the at least one computing device to:

identify a first set of confidence bounds that contain a selected positive sigma probability;

identify a second set of confidence bounds that contain a selected negative sigma probability;

perform a first regression using the first set of confidence bounds to determine an upper specification limit for the target parameter; and

perform a second regression using the second set of confidence bounds to determine a lower specification limit for the target parameter.

8 . The medium of claim 7 wherein the first regression uses the lower confidence bound in the first set of confidence bounds as an independent variable and the second regression uses the upper confidence bound in the second set of confidence bounds as an independent variable.

9 . The medium of claim 1 wherein the instructions when executed further cause the at least one computing device to:

output analysis of the virtual metrology data for the selected virtual metrology target parameters; and

receive user input indicating that the virtual metrology data for the selected virtual metrology target parameters fails to follow a normal distribution.

10 . The medium of claim 1 , wherein the upper or lower specification limit is at least one of a standard deviation value or an extremum.

11 . The medium of claim 1 , wherein at least one set of confidence bounds is computed with an alpha value of at least 0.99.

12 . The medium of claim 1 wherein the instructions when executed further cause the at least one computing device to:

plot the empirical distribution and confidence bounds for the one or more selected virtual metrology target parameters; and

display the plots on a graphical user interface.

13 . A computing device-implemented method, the computing device including one or more processors, the method comprising:

performing a Design of Experiments (DOE) simulation for a semiconductor device structure, the simulation including a plurality of virtual fabrication runs, the plurality of virtual fabrication runs building a plurality of 3D models of the semiconductor device structure;

receiving a selection of one or more virtual metrology target parameters;

determining whether virtual metrology data for the selected virtual metrology target parameters is normally distributed;

computing an empirical distribution based on the virtual metrology data for one or more of the selected virtual metrology target parameters;

determining confidence bounds for points in the empirical distribution for the one or more of the selected virtual metrology target parameters;

determining an upper and lower specification limits for one or more of the selected virtual metrology target parameters based on the respective confidence bounds; and

outputting the upper and lower specification limits.

14 . The method of claim 13 , further comprising:

extrapolating, using one or more regression models, from the confidence bounds, the upper and lower specification limits.

15 . The method of claim 14 wherein the one or more regression models include a linear regression model.

16 . The method of claim 14 wherein the one or more regression models include a spline regression model.

17 . The method of claim 13 , further comprising:

outputting the upper and lower specification limits as export data.

18 . The method of claim 13 , further comprising:

outputting the upper and lower specification limits on a graphical user interface.

19 . The method of claim 13 , further comprising:

identifying a first set of confidence bounds that contain a selected positive sigma probability;

identifying a second set of confidence bounds that contain a selected negative sigma probability;

performing a first regression using the first set of confidence bounds to determine an upper specification limit for the target parameter; and

performing a second regression using the second set of confidence bounds to determine a lower specification limit for the target parameter.

20 . The method of claim 19 wherein the first regression uses the lower confidence bound in the first set of confidence bounds as an independent variable and the second regression uses the upper confidence bound in the second set of confidence bounds as an independent variable.

21 . The method of claim 13 , further comprising:

outputting analysis of the virtual metrology data for the selected virtual metrology target parameters; and

receiving user input indicating that the virtual metrology data for the selected virtual metrology target parameters fails to follow a normal distribution.

22 . The method of claim 13 , wherein the upper or lower specification limit is at least one of a standard deviation value or an extremum.

23 . The method of claim 13 , wherein at least one set of confidence bounds is computed with an alpha value of at least 0.99.

24 . The method of claim 13 further comprising:

plotting the empirical distribution and confidence bounds for the one or more selected virtual metrology target parameters; and

displaying the plots on a graphical user interface.

25 . A system, comprising:

at least one computing device equipped with one or more processors and configured to generate a virtual fabrication environment that is configured to:

perform a Design of Experiments (DOE) simulation for a semiconductor device structure, the simulation including a plurality of virtual fabrication runs, the plurality of virtual fabrication runs building a plurality of 3D models of the semiconductor device structure,

receive a selection of one or more virtual metrology target parameters,

determine whether virtual metrology data for the selected virtual metrology target parameters is normally distributed,

compute an empirical distribution based on the virtual metrology data for one or more of the selected virtual metrology target parameters,

determine confidence bounds for points in the empirical distribution for the one or more of the selected virtual metrology parameters;

determine an upper and lower specification limits for one or more of the selected virtual metrology target parameters based on the respective confidence bounds, and

output the upper and lower specification limits; and

a display surface in communication with the at least one computing device, the display surface configured to display data generated in the virtual fabrication environment.