Method and apparatus for covering a multilayer process space during at-speed testing

1. A method for selecting a set of paths with which to test a process space, the method comprising:

determining a number N of paths to be included in the set of paths, where each of the N paths has an associated path slack;

determining a least number M of paths in N for which testing of the process space will fail;

computing a metric that ensures that the set of paths satisfies the requirements of N and M; and

outputting the metric for use in selecting the set of paths.

2. The method of claim 1 , wherein N, M, and a required path slack S M for the set of paths are user defined.

3. The method of claim 1 , wherein the computing comprises:

calculating a first value as an M−1 th smallest path slack among N−1 of the N paths;

calculating a second value as an M th smallest path slack among the N−1 of the N paths;

calculating a third value as a maximum of the first value and a last path slack among the N paths;

calculating a fourth value as a minimum of the first value and the third value; and

computing the metric as a probability that the fourth value is less than or equal to a required path slack S M for the set of paths.

4. The method of claim 1 , wherein the metric is substantially equal to a probability that the set of paths will fail testing.

5. The method of claim 1 , wherein M is greater than one.

6. The method of claim 1 , further comprising:

recursively updating the metric; and

outputting the metric, as updated.

7. The method of claim 6 , wherein the metric is recursively updated in accordance with a binary tree data structure.

8. The method of claim 6 , wherein the recursively updating includes two min/max operations.

9. The method of claim 1 , wherein the set of paths is used to test a batch of integrated circuit chips at-speed.

10. A method for defining multilayer coverage of a process space for a given set of N path slacks, the method comprising:

receiving a least number M of paths in N for which testing of the process space will fail;

defining the multilayer coverage as a probability that a set of paths associated with the set of N path slacks will fail testing; and

outputting the metric.

11. The method of claim 10 , wherein N, M, and a required path slack S M for the set of paths are user defined.

12. The method of claim 10 , further comprising:

applying the metric for use in selecting a set of paths with which to test the process space.

13. The method of claim 10 , wherein the computing comprises:

calculating a first value as an M−1 th smallest path slack among N−1 of the set of paths;

calculating a second value as an M th smallest path slack among the N−1 of the set of paths;

calculating a third value as a maximum of the first value and a last path slack among the set of paths;

calculating a fourth value as a minimum of the first value and the third value; and

computing the probability that the set of paths associated with the set of N path slacks will fail testing as a probability that the fourth value is less than or equal to a required path slack S M for the set of paths.

14. The method of claim 10 , wherein M is greater than one.

15. The method of claim 10 , further comprising:

recursively updating the metric; and

outputting the metric, as updated.

16. The method of claim 15 , wherein the metric is recursively updated in accordance with a binary tree data structure.

17. The method of claim 15 , wherein the recursively updating includes two min/max operations.

18. The method of claim 10 , wherein the metric is used to select a set of paths for testing a batch of integrated circuit chips at-speed.

19. A method for computing a metric to define a process space covered M times by a set of N path slacks {S 1 , . . . , S N }, the method comprising:

computing a first value as a first portion process space covered M times by a subset of the set of N path slacks {S 1 , . . . , S N−1 };

computing a second value as a joint space of a second portion process space covered by a last path slack S N of the set of N path slacks and a third portion of the process space covered M−1 times by the subset of the set of N path slacks {S 1 , . . . , S N };

summing the first value and the second value to produce the metric; and

outputting the metric.

20. The method of claim 19 , wherein M is a least number of paths in N for which testing of the process space will fail.

21. The method of claim 19 , further comprising:

recursively updating the metric; and

outputting the metric, as updated.

22. The method of claim 19 , wherein N, M, and a required path slack S M for the set of paths are user defined.

23. A method for computing a metric to define a process space covered M times by a set of N path slacks {S 1 , . . . , S N }, the method comprising:

recursively computing a function f N,k (·) as a k th smallest path slack in the set of N path slacks;

computing the metric as a probability that the function f N,k (·) is less than or equal to a minimum allowable path slack; and

outputting the metric.

24. The method of claim 23 , wherein M is a least number of paths in N for which testing of the process space will fail.

25. The method of claim 23 , wherein N, M, and a required path slack S M for the set of paths are user defined.