Predicting IC manufacturing yield by considering both systematic and random intra-die process variations

• US 20070174797A1
• Filed: 01/24/2006
• Published: 07/26/2007
• Est. Priority Date: 01/24/2006
• Status: Active Grant

• Current Assignee: Synopsys Incorporated
• Original Assignee: Synopsys Incorporated
• Inventors: Luo, Jianfeng, Su, Qing, Sinha, Subarnarekha, Chiang, Charles
• Granted Patent: US 8,000,826 B2
• Time in Patent Office: Days
• US Class Current: 716/56
• CPC Class Codes: G05B 19/41875 characterised by quality surveillance of production
• CPC Class Codes: G05B 2219/32204 Performance assurance; assure certain level of non-defective products
• CPC Class Codes: G05B 2219/35142 Generate tile patterns, mosaic
• CPC Class Codes: G05B 2219/45031 Manufacturing semiconductor wafers
• CPC Class Codes: Y02P 90/02 Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

Abstract

One embodiment of the present invention provides a system that predicts manufacturing yield for a die within a semiconductor wafer. During operation, the system first receives a physical layout of the die. Next, the system partitions the die into an array of tiles. The system then computes systematic variations for a quality indicative value to describe a process parameter across the array of tiles based on the physical layout of the die. Next, the system applies a random variation for the quality indicative parameter to each tile in the array of tiles. Finally, the system obtains the manufacturing yield for the die based on both the systematic variations and the random variations.

Claims

1. A method for predicting a manufacturing yield for a die within a semiconductor wafer, the method comprising:

receiving a physical layout of the die;

partitioning the die into an array of tiles;

computing systematic variations for a quality indicative parameter across the array of tiles based on the physical layout of the die;

applying a random variation for the quality indicative parameter to each tile in the array of tiles; and

obtaining the manufacturing yield for the die based on both the systematic variations and the random variations.

2. The method of claim 1, wherein obtaining the manufacturing yield for the die based on both the systematic variations and the random variations involves:

receiving specification limits for the quality indicative parameter;

computing probability values for all of the tiles in the die indicating whether the die satisfies the specification limits based on both the systematic variations and the random variations; and

obtaining the manufacturing yield for the die from the probability values.

3. The method of claim 1, wherein computing the systematic variations involves:

performing a physical layout extraction across the array of tiles; and

obtaining a nominal value for the quality indicative parameter for each tile based on the physical layout extraction.

4. The method of claim 1, wherein applying a random variation to each tile involves applying a random distribution around the nominal value of the quality indicative parameter for each tile to represent random fluctuations of the quality indicative parameter for the tile.

5. The method of claim 1, further comprising:

obtaining spatial correlations for the random variations between the tiles; and

wherein obtaining the manufacturing yield additionally involves spatial correlations of the random variations.

6. The method of claim 5, wherein obtaining the spatial correlation, for the random variations between the tiles involves:

obtaining measurement data from test structures; and

extracting correlation coefficients as a function of a distance between the tiles from the measurement data.

7. The method of claim 6, wherein the correlation coefficients are used to construct a covariance matrix for the array of tiles, wherein the covariance matrix contains data which indicates spatial correlations between the tiles.

8. The method of claim 5, further comprising:

selecting a window with a specific geometry and size which is larger than a single tile;

selecting a first tile from the array of tiles which satisfies a criterion;

placing a first instance of the window around the first tile and iteratively,

selecting a tile from the array of tiles which satisfies the criterion and is not covered by an instance of the window;

placing a new instance of the window around the tile; and

repeating the above process until the entire die is covered by instances of the window;

computing spatial correlations for the random variations between only the selected tiles; and

obtaining the manufacturing yield for the die based on the systematic variations, the random variations and the spatial correlation of the random variations between the selected tiles.

9. The method of claim 8, wherein the criterion is either a maximum nominal value or a minimum nominal value for the quality indicative parameter.

10. The method of claim 8, wherein the window size is determined such that any two locations within the window have a spatial correlation coefficient that is sufficiently close to unity.

11. A computer-readable storage medium storing instructions that when executed by a computer cause the computer to perform a method for predicting a manufacturing yield for a die within a semiconductor wafer, the method comprising:

receiving a physical layout of the die;

partitioning the die into an array of tiles;

computing systematic variations for a quality indicative parameter across the array of tiles based on the physical layout of the die;

applying a random variation for the quality indicative parameter to each tile in the array of tiles; and

obtaining the manufacturing yield for the die based on both the systematic variations and the random variations.

12. The computer-readable storage medium of claim 11, wherein obtaining the manufacturing yield for the die based on both the systematic variations and the random variations involves:

receiving specification limits for the quality indicative parameter;

computing probability values for all of the tiles in the die indicating whether the die satisfies the specification limits based on both the systematic variations and the random variations; and

obtaining the manufacturing yield for the die from the probability values.

13. The computer-readable storage medium of claim 11, wherein computing the systematic variations involves:

performing a physical layout extraction across the array of tiles; and

obtaining a nominal value for the quality indicative parameter for each tile based on the physical layout extraction.

14. The computer-readable storage medium of claim 11, wherein applying a random variation to each tile involves applying a random distribution around the nominal value of the quality indicative parameter for each tile to represent random fluctuations of the quality indicative parameter for the tile.

15. The computer-readable storage medium of claim 11, wherein the method further comprises:

obtaining spatial correlations for the random variations between the tiles; and

wherein obtaining the manufacturing yield additionally involves spatial correlations of the random variations.

16. The computer-readable storage medium of claim 15, wherein obtaining the spatial correlation for the random variations between the tiles involves:

obtaining measurement data from test structures; and

extracting correlation coefficients as a function of a distance between the tiles from the measurement data.

17. The computer-readable storage medium of claim 16, wherein the correlation coefficients are used to construct a covariance matrix for the array of tiles, wherein the covariance matrix contains data which indicates spatial correlations between the tiles.

18. The computer-readable storage medium of claim 15, wherein the method further comprises:

selecting a window with a specific geometry and size which is larger than a single tile;

selecting a first tile from the array of tiles which satisfies a criterion;

placing a first instance of the window around the first tile and iteratively,

selecting a tile from the array of tiles which satisfies the criterion and is not covered by an instance of the window;

placing a new instance of the window around the tile; and

repeating the above process until the entire die is covered by instances of the window;

computing spatial correlations for the random variations between only the selected tiles; and

obtaining the manufacturing yield for the die based on the systematic variations, the random variations and the spatial correlation of the random variations between the selected tiles.

19. The computer-readable storage medium of claim 18, wherein the criterion is either a maximum nominal value or a minimum nominal value for the quality indicative parameter.

20. The computer-readable storage medium of claim 18, wherein the window size is determined such that any two locations within the window have a spatial correlation coefficient that is sufficiently close to unity.

21. An apparatus for predicting a manufacturing yield for a die within a semiconductor wafer, the apparatus comprising:

a receiving mechanism configured to receive a physical layout of the die;

a partitioning mechanism configured to partition the die into an array of tiles;

a computing mechanism configured to compute systematic variations for a quality indicative parameter across the array of tiles based on the physical layout of the die;

an applying mechanism configured to apply a random variation for the quality indicative parameter to each tile in the array of tiles; and

an obtaining mechanism configured to obtain the manufacturing yield for the die based on both the systematic variations and the random variations.

22. The apparatus of claim 21, wherein the obtaining mechanism is configured to:

receive specification limits for the quality indicative parameter;

computing probability values for all of the tiles in the die indicating whether the die satisfies the specification limits based on both the systematic variations and the random variations; and

to

obtain the manufacturing yield for the die from the probability values.

23. The apparatus of claim 21, wherein the computing mechanism is configured to:

perform a physical layout extraction across the array of tiles; and

to

obtain a nominal value for the quality indicative parameter for each tile based on the physical layout extraction.

24. The apparatus of claim 21, wherein the applying mechanism is configured to apply a random distribution around the nominal value of the quality indicative parameter for each tile to represent random fluctuations of the quality indicative parameter for the tile.

25. The apparatus of claim 21:

wherein the obtaining mechanism is additionally configured to compute spatial correlations for the random variations between the tiles; and

wherein the obtaining mechanism is configured to obtain the manufacturing yield for the die based on the systematic variations, the random variations and the spatial correlation of the random variations.

26. The apparatus of claim 25, wherein the obtaining mechanism is configured to obtain the spatial correlation for the random variations between the tiles by:

obtaining measurement data from test structures; and

extracting correlation coefficients as a function of a distance between the tiles from the measurement data.

27. The apparatus of claim 26, wherein the correlation coefficients are used to construct a covariance matrix for the array of tiles, wherein the covariance matrix contains data which indicates spatial correlations between the tiles.