Moment-Based Method and System for Evaluation of Metal Layer Transient Currents in an Integrated Circuit

• US 20080222579A1
• Filed: 03/06/2007
• Published: 09/11/2008
• Est. Priority Date: 03/06/2007
• Status: Active Grant

• Current Assignee: International Business Machines Corporation
• Original Assignee: International Business Machines Corporation
• Inventors: Liu, Ying, Agarwal, Kanak B.
• Granted Patent: US 7,716,620 B2
• Time in Patent Office: Days
• US Class Current: 716/4
• CPC Class Codes: G06F 30/367 Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods

Abstract

A moment-based method and system for evaluation of metal layer transient currents in an integrated circuit provides a computationally efficient evaluation of transient current magnitudes through each interconnect in the metal layer. The determinable magnitudes include peak, rms and average current, which can be used in subsequent reliability analyses. Interconnect path nodes are traversed and circuit moments are either retrieved from a previous interconnect delay analysis or are computed. For each pair of nodes, current moments are computed from the circuit moments. The average current is computed from the zero-order circuit moment and the peak and rms currents are obtained from expressions according to a lognormal or other distribution shape assumption for the current waveform at each node.

Claims

1. A computer-performed method for calculating a transient current magnitude in a metal layer of an integrated circuit, said method comprising:

selecting an interconnect path segment of said metal layer;

obtaining circuit moments for nodes corresponding to endpoints of said segment;

specifying an input voltage waveshape;

computing current moments from said circuit moments and said waveshape;

calculating a current value for said segment from at least one of said current moments; and

storing a result of said calculating in a memory of a computer system.

2. The computer-performed method of claim 1, wherein said computing current moments further computes said current moments from an overlap resistance of said segment.

3. The method of claim 2, wherein said computing current moments comprises:

subtracting first circuit moments corresponding to a first one of said nodes from second circuit moments corresponding to a second one of said nodes to obtain current moment differences;

collecting terms of an expansion corresponding to a predetermined voltage waveshape, wherein said terms are products of said current moment differences and coefficients determined in accordance with said predetermined voltage waveshape; and

dividing a result of said collecting by said overlap resistance.

4. The method of claim 1, wherein said calculating a current value for said segment comprises computing an average value of said transient current magnitude from a lowest-order one of said current moments.

5. The method of claim 1, wherein said calculating a current value calculates said current value from an analytical expression corresponding to a predetermined function having characteristics according to a probability density function.

6. The method of claim 5, wherein said calculating a current value calculates an rms current value.

7. The method of claim 5, wherein said calculating a current value calculates a peak current value.

8. The method of claim 5, wherein said predetermined function is a lognormal distribution function.

9. A computer system, comprising a processor coupled to a memory for storing program instructions for execution by said processor for calculating a transient current magnitude in a metal layer of an integrated circuit, wherein said program instructions comprise program instructions for:

selecting an interconnect path segment of said metal layer;

obtaining circuit moments for nodes corresponding to endpoints of said segment;

specifying an input voltage waveshape;

computing current moments from said circuit moments and said waveshape;

calculating a current value for said segment from at least one of said current moments; and

storing a result of said calculating in a memory of a computer system.

10. The computer system of claim 9, wherein said program instructions for computing current moments further compute said current moments from an overlap resistance of said segment.

11. The computer system of claim 10, wherein said program instructions for computing current moments comprise program instructions for:

subtracting first circuit moments corresponding to a first one of said nodes from second circuit moments corresponding to a second one of said nodes to obtain current moment differences;

collecting terms of an expansion corresponding to a predetermined voltage waveshape, wherein said terms are products of said current moment differences and coefficients determined in accordance with said predetermined voltage waveshape; and

dividing a result of said collecting by said overlap resistance.

12. The computer system of claim 9, wherein said program instructions for calculating a current value for said segment compute an average value of said transient current magnitude from a lowest-order one of said current moments.

13. The computer system of claim 9, wherein said program instructions for calculating a current value calculate said current value from an analytical expression corresponding to a predetermined function having characteristics according to a probability density function.

14. The computer program product of claim 13, wherein said program instructions for calculating a current value calculate an rms current value.

15. The computer system of claim 13, wherein said program instructions for calculating a current value calculate a peak current value.

16. The computer system of claim 13, wherein said predetermined function is a lognormal distribution function.

17. A computer program product comprising storage media containing program instructions for execution by a processor for calculating a transient current magnitude in a metal layer of an integrated circuit, said program instructions comprising program instructions for:

selecting an interconnect path segment of said metal layer;

obtaining circuit moments for nodes corresponding to endpoints of said segment;

specifying an input voltage waveshape;

computing current moments from said circuit moments and said waveshape;

calculating a current value for said segment from at least one of said current moments; and

storing a result of said calculating in a memory of a computer system.

18. The computer program product of claim 17, wherein said program instructions for computing current moments further compute said current moments from an overlap resistance of said segment.

19. The computer program product of claim 18, wherein said program instructions for computing current moments comprise program instructions for:

subtracting first circuit moments corresponding to a first one of said nodes from second circuit moments corresponding to a second one of said nodes to obtain current moment differences;

collecting terms of an expansion corresponding to a predetermined voltage waveshape, wherein said terms are products of said current moment differences and coefficients determined in accordance with said predetermined voltage waveshape; and

dividing a result of said collecting by said overlap resistance.

20. The computer program product of claim 17, wherein said program instructions for calculating a current value for said segment compute an average value of said transient current magnitude from a lowest-order one of said current moments.

21. The computer program product of claim 17, wherein said program instructions for calculating a current value calculate said current value from an analytical expression corresponding to a predetermined function having characteristics according to a probability density function.

22. The computer program product of claim 21, wherein said program instructions for calculating a current value calculate an rms current value.

23. The computer system of claim 21, wherein said program instructions for calculating a current value calculate a peak current value.

24. The computer system of claim 21, wherein said predetermined function is a lognormal distribution function.

25. A computer system for calculating a transient current magnitude in a metal layer of an integrated circuit, comprising:

a processor; and

program means for calculating and storing at least one current value computed from current moments along segments of an interconnect path of said metal layer.

26. The computer system of claim 25, further comprising program means for computing said current moments in conformity with a predetermined transient voltage waveshape.

27. The computer system of claim 25, further comprising program means for analytically calculating said current value from said current moments.

28. The computer system of claim 27, wherein said program means for analytically calculating said current value calculate said current value in accordance with a function having characteristics according to a probability density function.

29. The computer system of claim 28, wherein said probability density function is a lognormal distribution function.

30. The computer system of claim 25, wherein said program means calculate an rms current value.

31. The computer system of claim 25, wherein said program means calculate a peak current value.