Specification window violation identification with application in semiconductor device design

1. A method for identifying specification window violations for an integrated circuit, the method comprising:

generating a pseudo-random sample set of input parameters for the integrated circuit;

simulating the integrated circuit using the pseudo-random sample set of input parameters to generate an output set;

fitting a mathematical model to the output set;

optimizing the mathematical model by identifying areas where the mathematical model does not fit the output set, and re-fitting the mathematical model after removing a least statistically significant term;

defining a set of desirability functions to an out-of-spec condition, the desirability functions are set based on an analysis of the output set;

searching the mathematical model using the desirability functions to identify a worst-case data point;

determining whether the worst-case data point is within specification or out of specification; and

implementing the worst-case data point for defining an integrated circuit design to be used to make the integrated circuit when the worst-case data point is within specification.

2. The method of claim 1 , further comprising confirming the worst-case data point by simulating the integrated circuit using input parameters defined by the worst-case data point.

3. The method of claim 1 , wherein generating the pseudo-random sample set of input parameters comprises generating a Latin hypercube sample set, wherein the Latin hypercube sample set has uniform factors.

4. The method of claim 1 wherein the simulating is performed using a SPICE tool.

5. The method of claim 1 wherein the fitting is performed using a second order Taylor series expansion.

6. The method of claim 5 wherein the fitting further comprises optimizing the second order Taylor series expansion by analyzing and reducing residuals.

7. A non-transitory machine readable medium embodying program instructions for identifying specification window violations for an integrated circuit, the machine readable medium comprising:

program instructions for generating a pseudo-random sample set of input parameters for the integrated circuit;

program instructions for simulating the integrated circuit using the pseudo-random sample set of input parameters to generate an output set;

program instructions for fitting a mathematical model to the output set;

program instructions for identifying areas where the mathematical model does not fit the output set;

program instructions for re-fitting the mathematical model after removing a least statistically significant term;

program instructions for searching the model using desirability functions to identify a worst-case data point, the desirability functions are set based on an analysis of the output set;

program instructions for determining whether the worst-case data point is within specification or out of specification; and

program instructions for implementing the worst-case data point for defining an integrated circuit design to be used to make the integrated circuit when the worst-case data point is within specification.

8. The machine readable medium of claim 7 , further comprising program instructions for confirming whether the worst-case data point is within specification by simulating the integrated circuit using input parameters defined by the worst-case data point.

9. The machine readable medium of claim 7 , wherein the program instructions for generating the pseudo-random sample set of input parameters comprises program instructions for generating a Latin hypercube sample set, wherein the Latin hypercube sample set has uniform in factors.

10. The machine readable medium of claim 7 , wherein the program instructions for simulating is a SPICE tool.

11. The machine readable medium of claim 7 , wherein the program instructions for fitting generate a second order Taylor series expansion.

12. The machine readable medium of claim 11 , wherein the program instructions for fitting further comprise program instructions for optimizing the second order Taylor series expansion by analyzing and reducing residuals.