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

• US 8,000,826 B2
• Filed: 01/24/2006
• Issued: 08/16/2011
• Est. Priority Date: 01/24/2006
• Status: Active Grant

• Current Assignee: Synopsys Incorporated
• Original Assignee: Synopsys Incorporated
• Inventors: Luo, Jianfeng, Chiang, Charles C., Su, Qing, Sinha, Subarnarekha
• Primary Examiner(s): Decady; Albert
• Assistant Examiner(s): STEVENS, THOMAS H
• Application Number:
  US11/339,184
• Publication Number:
  US 20070174797A1
• Time in Patent Office: 2,030 Days
• Field of Search: 700/95, 700/21, 257/48, 382/141, 382/149, 382/151, 382/154, 714/30
• US Class Current: 700/95
• 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, which includes;

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

determining values for the quality indicative parameter based at least on results of the physical layout extraction;

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

iteratively placing instances of a window in the die until the die is covered with instances of the window, wherein each iteration includes,

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

placing an instance of the window around the selected tile;

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

computing the manufacturing yield for the die based at least on the systematic variations, the random variations, and the spatial correlations for the random variations.

2. The method of claim 1, wherein computing the manufacturing yield for the die includes:

receiving specification limits for the quality indicative parameter;

computing a joint probability distribution for the selected tiles which indicate whether the selected tiles satisfy the specification limits; and

obtaining the manufacturing yield for the die from the joint probability distribution.

3. The method of claim 1, wherein computing the spatial correlations for the random variations between the selected tiles includes:

obtaining measurement data from test structures; and

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

4. The method of claim 3, wherein computing the spatial correlations for the random variations between the selected tiles includes using the correlation coefficients to construct a covariance matrix for the instances of the window.

5. The method of claim 1, wherein the criterion is either a maximum value or a minimum value for the quality indicative parameter.

6. The method of claim 1, wherein a size of the window is such that any two tiles within a window have a spatial correlation coefficient that is substantially equal to unity.

7. A non-transitory 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, which includes;

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

determining values for the quality indicative parameter based at least on results of the physical layout extraction;

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

iteratively placing instances of a window in the die until the die is covered with instances of the window, wherein each iteration includes,

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

placing an instance of the window around the selected tile;

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

computing the manufacturing yield for the die based at least on the systematic variations, the random variations, and the spatial correlations for the random variations.

8. The non-transitory computer-readable storage medium of claim 7, wherein computing the manufacturing yield for the die includes:

receiving specification limits for the quality indicative parameter;

computing a joint probability distribution for the selected tiles which indicate whether the selected tiles satisfy the specification limits; and

obtaining the manufacturing yield for the die from the joint probability distribution.

9. The non-transitory computer-readable storage medium of claim 7, wherein computing the spatial correlations for the random variations between the selected tiles includes:

obtaining measurement data from test structures; and

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

10. The non-transitory computer-readable storage medium of claim 9, wherein computing the spatial correlations for the random variations between the selected tiles includes using the correlation coefficients to construct a covariance matrix for the instances of the window.

11. The non-transitory computer-readable storage medium of claim 7, wherein the criterion is either a maximum value or a minimum value for the quality indicative parameter.

12. The non-transitory computer-readable storage medium of claim 7, wherein a size of the window is such that any two tiles within a window have a spatial correlation coefficient that is substantially equal to unity.

13. 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 first 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, wherein the first computing mechanism is configured to;

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

determine values for the quality indicative parameter based at least on results of the physical layout extraction;

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

a placing mechanism configured to iteratively place instances of a window in the die until the entire die is covered with instances of the window, wherein each iteration includes,

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

placing an instance of the window around the selected tile;

a second computing mechanism configured to compute spatial correlations for the random variations between the selected tiles; and

a third computing mechanism configured to compute the manufacturing yield for the die based at least on the systematic variations, the random variations, and the spatial correlations for the random variations.

14. The apparatus of claim 13, wherein the third computing mechanism is configured to:

receive specification limits for the quality indicative parameter;

compute a joint probability distribution for the selected tiles which indicate whether the selected tiles satisfy the specification limits; and

obtain the manufacturing yield for the die from the joint probability distribution.

15. The apparatus of claim 13, wherein the second computing mechanism is configured to:

obtain measurement data from test structures; and

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

16. The apparatus of claim 15, wherein the second computing mechanism is configured to use the correlation coefficients to construct a covariance matrix for the instances of the window.

17. The apparatus of claim 13, wherein the criterion is either a maximum value or a minimum value for the quality indicative parameter.

18. The apparatus of claim 13, wherein a size of the window is such that any two tiles within a window have a spatial correlation coefficient that is substantially equal to unity.