Kernel based cluster fault analysis

1. A method for performing fault analysis, the method comprising:

receiving fault data from wafer level testing, wherein

the fault data identifies locations of a plurality of die on a wafer, and

the fault data identifies test results of the plurality of die from the wafer level testing;

applying a kernel transform to the fault data to produce cluster data, wherein

the kernel transform defines a fault impact distribution for a failed die,

the fault impact distribution extends radially out from the failed die and has an outer radial boundary at a terminating distance from the failed die,

the fault impact distribution defines fault contribution from the failed die to local die that fall within the outer radial boundary, and

the applying the kernel transform comprises:

for each die that failed wafer level testing, centering the fault impact distribution at a location of the die that failed wafer level testing,

associating each local die that falls within the outer radial boundary with a respective fault contribution value according to the fault impact distribution, and

for each respective die of the plurality of die, accruing fault contribution values associated with the respective die to produce a cluster value for the respective die, wherein

the cluster value correlates to a probability of failure of the respective die at a future time.

2. The method of claim 1 , wherein the fault data comprises a binary wafer map indicating either a pass status or a fail status for each of the plurality of die.

3. The method of claim 1 , wherein the fault impact distribution comprises a Gaussian distribution.

4. The method of claim 3 , wherein the Gaussian distribution is scalable to different pluralities of die by changing a bandwidth value of the Gaussian distribution.

5. The method of claim 1 , wherein

the fault impact distribution is normalized,

the failed die is associated with a fault contribution value of 1, according to the normalized fault impact distribution, and

remaining local die that fall within the outer radial boundary are associated with respective contribution values of less than 1, according to the normalized fault impact distribution.

6. The method of claim 1 , further comprising:

comparing each cluster value of the plurality of die to a threshold cluster value; and

identifying a failure cluster of predicted likely-to-fail die where at least one cluster value is greater than or equal to the threshold cluster value.

7. The method of claim 6 , wherein a magnitude of the at least one cluster value greater than or equal to the threshold cluster value correlates to a size and a density of the failure cluster.

8. The method of claim 6 , wherein

a cluster value having a magnitude of zero indicates no failure,

a cluster value having a magnitude less than the threshold cluster value and greater than zero indicates a random non-clustering failure, and

a cluster value having a magnitude greater than or equal to the threshold cluster value indicates a systemic clustering failure.

9. The method of claim 1 , further comprising:

identifying a maximum cluster value from among a plurality of cluster values for the plurality of die, wherein the maximum cluster value correlates to a largest or most dense failure cluster on the wafer, and the maximum cluster value is used as a metric to compare failures across a plurality of wafers.

10. The method of claim 1 , wherein

the fault impact distribution has a first concentric radial portion around the first failed die and a second concentric radial portion around the first concentric radial portion,

a first set of the plurality of die that fall within the first concentric radial portion are each associated with a first fault contribution value,

a second set of the plurality of die that fall within the second concentric radial portion are each associated with a second fault contribution value, and

the second fault contribution value is less than the first fault contribution value.

11. The method of claim 10 , wherein

the first concentric radial portion has a boundary at a first radial distance from the failed die,

the second concentric radial portion has a boundary at a second radial distance from the failed die, and

the second radial distance is greater than the first radial distance.

12. A method for performing fault analysis, the method comprising:

receiving fault data from wafer level testing, wherein

the fault data identifies locations of a plurality of die on a wafer, and

the fault data identifies a subset of failed die of the plurality of die;

applying a fault impact distribution to a location of a first failed die, wherein

the fault impact distribution extends radially out from the first failed die and defines a first outer radial boundary at a terminating distance from the first failed die;

associating a first local die that falls within the first outer radial boundary with a first fault contribution value according to the fault impact distribution;

applying the fault impact distribution to a location of a second failed die, wherein

the fault impact distribution extends radially out from the second failed die and defines a second outer radial boundary at a terminating distance from the second failed die;

associating the first local die that also falls within the second outer radial boundary with a second fault contribution value according to the fault impact distribution; and

summing the first fault contribution value and the second fault contribution value to produce a cluster value for the first local die, wherein

the cluster value correlates to a probability of failure of the first local die at a future time.

13. The method of claim 12 , wherein

the first local die is not immediately adjacent to the first failed die, and

the first local die is not immediately adjacent to the second failed die.

14. The method of claim 12 , wherein the fault impact distribution defines fault contribution values that decrease from a center of the fault impact distribution toward the outer radial boundary.

15. The method of claim 12 , further comprising:

comparing the cluster value of the first local die to a threshold cluster value; and

identifying that the first local die is part of a failure cluster in response to the cluster value being greater than or equal to the threshold cluster value.

16. The method of claim 12 , further comprising:

growing the failure cluster by increasing a bandwidth value of the fault impact distribution to produce an extended outer radial boundary of the fault impact distribution that correlates with the bandwidth value, wherein

the fault impact distribution defines fault contribution from the failed die to local die that fall within the extended outer radial boundary.

17. A method for performing fault analysis, the method comprising:

receiving fault data comprising a binary wafer pattern of wafer level testing results for a plurality of die; and

applying a kernel transform to the fault data to produce a continuous value wafer pattern, wherein

the kernel transform defines a fault impact distribution that is applied to each failed die of the fault data,

the fault impact distribution defines fault contribution of each failed die to a local set of die comprising one or more die that fall within an outer radial boundary of the fault impact distribution,

each respective die of the fault data accumulates a cluster value indicating an amount of fault contributed to the respective die from surrounding failed die,

the cluster value correlates to a probability of failure of the respective die at a future time.

18. The method of claim 17 , wherein

the outer radial boundary is defined by a terminating distance from a center failed die, and

the fault impact distribution is scalable by adjusting a bandwidth value to produce a corresponding change in the terminating distance that defines the outer radial boundary.

19. The method of claim 17 , further comprising:

comparing each cluster value of the continuous value wafer pattern to a threshold cluster value; and

identifying a failure cluster where at least one cluster value is greater than or equal to the threshold cluster value.

20. The method of claim 19 , further comprising one of:

discarding predicted likely-to-fail die in the failure cluster, or

performing burn-in stress testing on the predicted likely-to-fail die in the failure cluster while skipping burn-in stress testing on remaining ones of the plurality of die.