Apparatus and method for production process diagnosis using dynamic time warping

• US 4,861,419 A
• Filed: 08/15/1988
• Issued: 08/29/1989
• Est. Priority Date: 08/04/1987
• Status: Expired due to Term

• Current Assignee: Texas Instruments, Inc.
• Original Assignee: Texas Instruments, Inc.
• Inventors: Reese, Jon, Flinchbaugh, Bruce E., Srivastava, Aditya, Dolins, Steven B.
• Primary Examiner(s): Powell, William A.
• Application Number:
  US07/233,878
• Time in Patent Office: 379 Days
• Field of Search: 156/626, 156/627, 156/643, 156/646, 156/662, 156/345, 204/192.33, 204/298, 437/8, 118/712
• US Class Current: 216/59
• CPC Class Codes: H01J 37/32935 Monitoring and controlling tubes by information coming from the object and/or discharge

Abstract

Operations of a plasma etch reactor (10) are monitored to detect aberrations in etching operations. A reference end point trace is defined (62) for the etch process. Regions are defined in the reference end point trace (70) with aid of a dynamic time warping matching function (84) and characteristics and tolerances for each region are defined (72-80). The etcher is run and an actual end point trace is obtained (82) from the running of the etcher. A warping function is constructed (88) between the actual trace and the reference trace. In building the warping function, candidate path segments (100) are constructed according to a minimum cumulative cost function (96). Once the regions of the reference trace and the actual trace has been matched according to an optimum dynamic time warping function path (106), characteristics of the matched regions are compared (66) to determine whether aberrations have occurred during the etch process. In an alternative embodiment, the actual trace (164) is matched to each of a library of reference traces (162,182) by dynamic time warping (166). By determining the best match, a determination can be made whether the actual trace is abnormal (174) or normal (176), and the type of abnormality.

Claims

1. A process monitoring apparatus comprising:

a former for forming a variable signal reference curve corresponding to a predetermined process;

an acquirer for acquiring actual data forming a variable signal actual curve corresponding to an actual operation of said predetermined process;

a processor for dividing the reference data into reference regions at critical points based on characteristics of the reference data;

a matcher for matching the critical points on the reference curve with corresponding critical points on the actual curve using a dynamic time warping function;

a divider for dividing the actual curve into actual regions at said critical points of the actual curve;

a comparer for comparing characteristics of at least one actualr egion with characteristics of a reference region with which the actual region has been matched; and

a generator that generates a signal indicative of the variance of a characteristic of the actual region beyond a predefined limit from a corresponding characteristic of the reference region that has been matched with the actual region.

2. The apparatus of claim 1, wherein said matcher further comprises:

an initiator operable to match a beginning point of the reference trace to a beginning point of the actual trace to initiate a beginning point of an optimal time warping function path, said initiator further operable to match an end point of the reference trace to an end point of the actual trace to initiate an end point of the path; and

an optimal warping function path generator operable to generate an optimal time warping function path between the initiated beginning point and the initiated end point, said path consisting of a plurality of points correlating a compared point on the reference trace to a compared point on the actual trace.

3. The apparatus of claim 2, wherein said path generator further comprises:

a cumulative cost calculator operable to select path segments between points on the optimal time warping function path that each represent a minimum cumulative cost for advancing from one connected point to another connected point, said calculator calculating the value of the cumulative cost of ech point on said path as a function of the dissimilarity between the reference trace up to the compared point thereon and the actual trace up to the compared point thereon.

4. The apparatus of claim 3, wherein said cumulative cost calculator is operable to calculate a minimum cumulative cost for each of a plurality of taken points in each of a plurality of successive warping function stages, said cumulative cost calculator comprising:

an incremental cost calculator for calculating an incremental cost for a taken point;

a cumulative cost module for storing a maximum cumulative cost associated with each of a plurality of prior points adjacent the taken piont and in a preceding stage, a plurality of candidate cumulative costs calculated, one for each prior point, as equal to the cumulative cost obtained at the prior point plus the incremental cost for the taken point; and

a selector for selecting a minimum cumulative cost for the taken candidate point from the candidate cumulative costs.

5. The apparatus of claim 4, wherein said incremental cost calculator comprises an amplitude comparator operable to determine the dissimilarity of:

the amplitude at the comapred reference trace point; and

the amplitude at the compared actual trace point.

6. The apparatus of claim 5, wherein said incremental cost calculator further comprises a slope angle calculator operable to calculate the difference between:

the change in slope angle at the compared point on the reference trace from a prior point on the reference trace; and

the change in the slope angle at the compared point on the actual trace from a prior point on the actual trace.

7. The apparatus of claim 4, wherein said incremental cost calculator comprises a curve angle change calculator for calculating the difference between:

the change in slope angle at the compared point on the reference trace from a prior point on the reference trace; and

the change in slope angle at the compared point on the actual trace from a prior point on the actual trace.

8. The apparatus of claim 3, wherein said cumulative cost calculator further comprises a constrainor for constraining the taken points in each stage such that the compared point on the reference trace correlated by the candidate point is within a predetermined value in a time dimension of the point on the actual trace correlated by the candidate point.

55. The apparatus of claims 1 or 9 in which said predetermined process is a plasma etch process conducted in a plasma etch reactor.

56. The apparatus of claim 1 in which said reference curve indicates an intended operation for said predetermined process.

9. Apparatus for monitoring operations in process equipment which carries out a predetermined process, comprising:

a storer for storing a plurality of reference signal curves, each corresponding to the progress of a process conducted in said process equipment, said reference signal curves including at least one predefined normal reference signal curve corresponding to an acceptable operaiton of the process and a plurality of predefined abnormal reference signal curves, each corresponding to an unacceptable operation of the process;

a detector for generating an actual signal curve based on an actual operation of the process;

a warping function calculator for deriving a dynamic time warping function for each of said reference curves, each warping function resulting from a matching of the actual curve to a reference curve;

a cost calculator for calculating a cost related to the dissimilarity between the respective reference curve and said actual curve; and

a matcher for matching said actual curve with a selected reference curve, said reference curve associated with a minimum cost of the calculated costs.

10. The apparatus of claim 9, wherein said storer is operable to store a plurality of predefined normal reference signal curves, each corresponding to an acceptable operation of the process.

11. The apparatus of claim 9, wherein said warping function calculator comprises:

a matcher for matching a beginning point of a considered reference curve to a beginning point of said actual curve to originate a beginning point of an optimal time warping function path, said matcher further operable to match an end point of the considered reference curve to an end point of said actual curve to originate an end point of said path; and

a warping function path generator for generating a monotonic optimal time warping function path between said beginning point and said end point, points on said path each correlating a compared point on the considered reference curve to a compared point on said actual curve.

12. The apparatus of claim 11, wherein said warping function path generator comprises:

a matrix storer for storing a matrix of warping function points, each warping function point correlating a selected point on a reference curve to a selected point on said actual curve;

a generator for generating a tree of candidate path segments between stages of the warping function points, a beginning stage of said stages comprising said beginning point of said warping function path, a final stage of said matrix comprising said end point of said path, each stage comprising at least one warping function point that is adjacent to at least one warping function point in another stage, said tree generator comprising;

an incremental cost calculator for calculating an incremental cost for a taken warping function point;

a cumulative cost storer for storing a minimum cumulative cost associated with each of a plurality of candidate prodecessor points adjacent the taken point and in a preceding stage;

a selector for selecting a minimum cumulative costs from the stored cumulative costs associated with the candidate predecessor points, said selector selecting a predecessor point from the candidate predecessor points which is associated with said minimum; and

an adder for adding the incremental cost to the minimum of the cumulative costs associated with the prior points to derive a cumulative cost for the taken point.

13. The apparatus of claim 12, wherein said matrix storer further comprises a constrainer for constraining the stored warping function points in each stage such that the point on the reference curve correlated by a warping function point is within a predetermined value in a time dimension of the point on the actual curve correlated by the candidate point.

14. The apparatus of claim 12, wherein incremental cost calculator further comprises:

a differential curve amplitude detector for calculating each incremental cost as a function of the dissimilarity of;

the curve amplitude at a point on the reference curve correlated by the taken warping function point; and

the curve amplitude at a point on the actual curve correlated by the warping function point.

15. The apparatus of claim 14, wherein said incremental cost calculator further comprises:

a differential angle detector for calculating a factor for the incremental cost that is a function of the dissimilarity of;

the change in curve angle between the point on the reference curve correlated by the taken warping function point, and a prior point on the reference curve; and

the change in curve angle between a point on the actual curve correlated by the taken warping function point, and a prior point on the actual curve associated with the predecessor point.

16. The apparatus of claim 12, wherein said incremental cost calculator further comprises:

differential angle detector for calculating a factor for the incremental cost that is a function of the dissimilarity of;

the change in curve angle between the point on the reference curve correlated by the taken warping function point, and a prior point on the reference curve; and

the change in curve angle between a point on the actual curve correlated by the taken warping function point and a prior point on the actual curve.

17. A method for monitoring end point traces of a plasma etch reactor comprising:

establishing a reference end point trace for a predetermined etch process;

dividing the reference end point trace at critical points thereof into predetermined regions;

conducting the predetermined etch process on a semiconductor device;

obtaining an actual end point trace for the etch of the semiconductor device;

matching the critical points on the reference trace with corresponding critical points on the actual trace using a dynamic time warping function;

dividing the actual trace at the critical points thereof to define regions of the actual trace; and

comparing characteristics of regions of the actual end point trace with corresponding characteristics of matched regions of the reference end point trace.

18. The method of claim 17, and further comprising:

generating a signal indicative of the variance of characteristics of the regions of the actual end point trace beyond predefined limits from corresponding characteristics of matched regions of the reference end point trace.

19. The method of claim 17, wherein said step of comparing characteristics of regions of the actual end point trace with corresponding characteristics of matched regions of the reference end point trace comprise applying a set of rules to at least one of the regions of the actual end point trace.

20. The method of claim 19, wherein the set of rules comprises a set of process-independent rules and a set of process-specific rules.

21. The method of claim 20, wherein the application of the set of process-independent rules comprises comparing, between a region of the actual end point trace and a matched region of the reference end point trace, at least one of:

the value;

the slope; and

the time of at least one predefined point in the respective regions.

22. The method of claim 17, further comprising:

determing whether a deviation between a characteristic of the actual end point trace and a corresponding characteristic of the reference end point trace exceeds a predefined value;

attributing such deviation to at least one predefined cause;

generating a signal identifying said at least one predefined cause to which the deviation has been attributed.

23. The method of claim 17, wherein said step of matching the critical points comprises the further steps of:

matching a beginning point of the reference trace to a beginning point of the actual trace to originate a beginning poit of an optimal time warping function path;

matching an end point of the reference trace to an end point of the actual trace to originate an end point of the path;

generating an optimal time warping function path between the beginning point and the end piont thereof, points on the path each correlating a compared point on the reference trace to a compared point on the actual trace; and

correlating the critical points on the reference trace to critical points on the actual trace using the optimum time warping function path.

24. The method of claim 23, wherein said step of generating the optimal time warping function path comprises the further steps of:

using a minimum cumulative cost function in selecting path segments between points on the optimal time warping function path, the value of the cumulative cost function related to the dissimilarity between the reference trace up to the compared point thereon and the actual trace up to the compared point thereon.

25. The method of claim 24, and further including the step of calculating a minimum cumulative cost for each of a plurality of warping function points in each of a plurality of successive warping function stages, said step of calculating including, for any taken warping function point, the further steps of:

calculating an incremental cost for the taken point;

storing a cumulative cost associated with each of a plurality of candidate predecessor points adjacent the taken point and in a preceding stage;

selecting a minimum of the stored cumulative costs for the candidate predecessor points; and

adding the minimum stored cumulative cost to the incremental cost to derive a minimum cumulative cost for the taken point.

26. The method of claim 25, wherein said step of generating the optimal time warping function path further includes the steps of:

for each taken point constructing a candidate path segment between the predecessor point and the taken point; and

back-tracing an optimal time warping function path from the end point thereof to the beginning point thereof using connected candidate path segments.

27. The method of claim 26, wherein said incremental cost is calculated as a function of the dissimilarity of:

the amplitude at the compared reference trace point; and

the amplitude at the compared actual trace point.

28. The method of claim 27, wherein said incremental cost is further a function of the dissimilarity of:

the change in slope angle at the compared point on the reference trace from a prior point on the reference trace; and

the change in the slope angle at the compared point on the actual trce from a prior point on the actual trace.

29. The method of claim 26, and further including the steps of calculating the incremental cost as a function of the difference between:

the change in slope angle at the compared point on the reference trace from a prior point on the reference trace; and

the change in slope angle at the compared point on the actual trce from a prior point on the actual trace.

30. The method of claim 25, and further including the step of:

constraining the taken warping function points such that a compared point on the reference trace first pointer in the pair of pointers is within a predetermined value in time from the compared point on the actual trace.

63. The method of claim 17 in which said establishing a reference curve includes establishing a reference curve indicating an intended operation for said predetermined process.

31. A method for monitoring operations in process equipment which carries out a predetermined process, comprising:

monitoring a process by a detector that provides a variable actual signal curve corresponding to the progress of the process;

defining a variable reference signal curve corresponding to a predefined acceptable operation of the predetermined process;

dividing the reference curve into regions on the basis of shared characteristics of the points on the curve within the region, said step of dividing performed at a plurality of critical points on the reference curve;

matching the critical points on the reference curve with corresponding critical points on the actual curve using a dynamic time warping function;

dividing the actual curve into regions at the critical points thereof; and

comparing characteristics of at least one of the regions of the actual curve with the characteristics of a matched region in the reference curve.

32. The method of claim 31, wherein said step of matching the critical points comprises the further steps of:

matching a beginning point of the reference curve to a beginning point of the actual curve to formulate a beginning point of an optimal time warping function path;

matching an end point of the reference curve to an end point of the actual curve to originate an end point of the optimal time warping function path;

generating a monotonic optimal time warping function path between the beginning point and the end point thereof, points on the path each correlating a point on the reference curve to a point on the actual curve; and

correlating the critical points on the reference curve to critical points on the actual curve using the optimum time warping function path.

33. The method of claim 32, wherein said step of generating the monotonic optimal time warping function path comprises the further step of using a minimum cumulative cost function in determing path segments between points on the optimal time warping function path, the value of the cumulative cost function at any point on the path being related to the dissimilarity between the reference curve up to a correlated point thereon and the actual curve up to a correlated point thereon.

34. The method of claim 33, and further including the step of calculating a minimum cumulative cost for each of a plurality of taken warping function points in each of a plurality of successive warping function stages, said step of calculating including, for any taken warping function point, the further steps of:

calculating an incremental cost for the taken point;

storing a cumulative cost associated with each of a plurality of candidate predecessor points adjacent the taken point and in a preceding stage;

selecting a minimum of the cumulative costs associated with the candidate predecessor points, a predecessor point associated with the minimum being chosen from the candidate predecessor points; and

adding the incremental cost of the taken point to the cumulative cost of the predecessor point to derive the minimum cumulative cost for the taken point.

35. The method of claim 34, wherein said step of generating a monotonic optimal time warping function path includes the steps of:

for each taken warping function point, constructing a candidate path segment from the taken point to the predecessor point therefor; and

back-tracing a monotonic optimal warping path from the end point thereof to the beginning point thereof using connected candidate path segments.

36. The method of claim 35, and further including the step of calculating the incremental cost for a taken point as a function of the dissimilarity of:

the amplitude at the correlated point on the reference curve; and

the change in amplitude at the correlated point on the actual curve.

37. The method of claim 36, and further including the step of calculating the incremental cost as a further function of the dissimilarity of:

the change in curve angle between a correlated point on the reference curve and a prior point on the reference curve; and

the change in curve angle between a correlated point on the actual curve and a prior point on the actual curve.

38. The method of claim 35, and further including the step of calculating the incremental cost for the taken point as a function of the dissimilarity of:

the change in curve angle between a correlated point on the refrence curve and a prior point on the reference curve; and

the change in curve angle between a correlated poit on the actual curve and a prior point on the actual curve.

39. The method of claim 35, and further including the step of:

constraining the taken warping function points in each stage such that the point on the reference curve correlated by the taken warping function point is within a predetermined value in a time dimension of the point on the actual curve correlated by the taken point.

40. The method of claim 31, wherein said critical points are identified on the basis of changes in slope angle of the reference curve.

41. The method of claim 31, wherein said predetermined process comprises a plasma etch.

64. The method of claim 31 in which said defining a reference curve includes defining a reference curve indicating an intended operation for said predetermined process.

42. A method for monitoring operations in process equipment which carries out a predetermined process, comprising the steps of:

storing a plurality of reference signal curves each corresponding to the progress of a process, the reference signal curves including at least one predefined normal reference signal curve corresponding to an acceptable operation of the process and a plurality of predefined abnormal reference signal curves, each corresponding to an unacceptable operation of the process;

generating an actual signal curve by a detector, the actual curve corresponding to an actual operation of the process;

deriving a dynamic time warping function for each of the reference curves, each warping function resulting from a matching of the actual curve to a reference curve;

for each derived warping function, determining a cost related to the dissimilarity between the respective reference curve and the actual curve;

finding a minimum cost function of the determined cost functions; and

declaring a match between the actual curve and the reference curve associated with the minimum cost function.

43. The method of claim 42, wherein said step of deriving a dynamic time warping function for each of the reference curves comprises, for each reference curve, the steps of:

matching a beginning point of the reference curve to a beginning point of the actual curve to originate a beginning point of an optimal time warping function path;

matching an end point of the reference curve to an end point of the actual curve to originate an end point of the path; and

generating a monotonic optimal time warping function path between the beginning point and the end point thereof, points on the path each correlating a compared point on the reference curve to a compared point on the actual curve.

44. The method of claim 43, wherein said step of generating a monotonic optimal time warping function path comprises the further steps of:

defining a matrix of warping function points, each point correlating a compared point on the reference curve to a compared point on the actual curve;

generating a tree of candidate path segments, between warping function points in successive stages of the matrix, each warping function point in one stage adjacent at least one warping function point in a next preceding stage, a first stage containing the beginning point of the path, a last stage containing the end point of the path said step of generating the tree comprising, for each of a plurality of taken warping function points, the further steps of;

calculating an incremental cost for the taken warping function point;

storing a cumulative cost associated with each of a plurality of candidate predecessor points adjacent the taken poit and in a next preceding stage;

finding a minimum of the cumulative costs associated with the candidate predecessor points;

selecting a predecessor point from the candidate predecessor points, the predecessor point associated with the minimum of the last said cumulative costs;

constructing a candidate path segment from the taken point to the predecessor point therefor; and

back-tracing an optimum, monotonic warping function path from the end point thereof to the beginning point thereof using connected path segments.

45. The method of claim 44, and further including the step of calculating the incremental cost as a further function of the dissimilarity of:

the change in curve angle between a correlated point on the reference curve and a next preceding point on the reference curve; and

the change in curve angle between a correlated point on the actual curve and a next preceding point on the actual curve.

46. The method of claim 45, and further including the step of calculating the incremental cost as a function of the dissimilarity of:

the amplitude at a correlated point on the reference curve; and

the amplitude at a correlated point on the actual curve.

47. The method of claim 44, and further including the step of calculating the incremental cost as a function of the dissimilarity of:

the amplitude at a correlated point on the reference curve; and

the amplitude at a correlated point on the actual curve.

48. The method of claim 44, and further including the steps of:

constraining the taken points in each stage of the warping function matrix to those candidate points that match a point on the actual curve at a selected time to a point on the reference curve within a predetermined period from the selected time.

65. The method of claim 42 in which said predetermined process is a plasma etch process conducted in a plasma etch reactor.

49. An apparatus for monitoring a plasma etch process on a semiconductor device in a plasma etch reactor, said apparatus comprising:

a former for forming at least one variable signal reference curve from reference data corresponding to said plasma etch process;

an acquirer for acquiring actual data forming a variable signal actual curve corresponding to an actual operation of said plasma etch process; and

a warping function calculator for deriving a dynamic time warping function resulting from comparing said actual curve to said at least one reference curve.

50. The apparatus of claim 49 in which said reference curve indicates an intended operation for said predetermined process.

51. The apparatus of claim 49 in which said warping function calculator includes an initiator for matching a beginning point of said at least one reference curve to a beginning point of said actual curve to originate a beginning point of an optimal time warping path, said initiator further operable to match an end point of the considered reference curve to an end point of said actual curve to originate an end point of said path, and a warping function path generator for generating a monotonic optimal time warping function path between said beginning point and said end point, points on said path each correlating a compared point on said at least one reference curve to a compared point on said actual curve.

52. The apparatus of claim 49 further including a processor for dividing the reference data into reference regions at critical points based on critical characteristics of the reference data, said warping function calculator matching critical points on the reference curve with corresponding critical points on the actual curve using said dynamic time warping function, and further including a divider for dividing the actual curve into actual regions at said critical points of the actual curve, a comparer for comparing characteristics of at least one actual region with characteristics of a reference region with which the actual region has been matched, and a generator that generates a signal indicative of the variance of a characteristic of the actual region beyond a defined limit from a corresponding characteristic of the reference region that has been matched with the actual region.

53. The apparatus of claim 49 in which said former forms plural reference curves including at least one reference curve corresponding to an acceptable operation of the process and a plurality of predetermined reference curves each corresponding to an unacceptable operation of the process, and said calculator derives a dynamic time warping function for each of said reference curves resulting from a matching of the actual curve to a reference curve.

54. The apparatus of claim 53 including a cost calculator or calculating a cost related to the dissimilarity between the respective reference curve and said actual curve;

and a matcher for matching said actual curve with a selected reference curve, said reference curve associated with a minimum cost of the calculated costs.

57. A method of monitoring a plasma etch process on a semiconductor device in a plasma etch reactor, said method comprising:

defining at least one variable signal reference curve from reference data corresponding to said plasma etch process;

obtaining actual data forming a variable signal actual curve corresponding to an actual etching of said semiconductor device by said plasma etch process; and

deriving a dynamic time warping function resulting from comparing said actual curve to said at least one reference curve.

58. The method of claim 57 in which said defining includes defining at least one reference curve indicating an intended operation for said predetermined process.

59. The method of claim 57 in which said deriving includes matching a beginning point of said at least one reference curve to a beginning point of said actual curve to originate a beginning point of an optimal time warping path, and further matching an an end point of the considered reference curve to an end point of said actual curve to originate an end point of said path, and said deriving further including generating a monotonic optimal time warping function path between said beginning point and said end point, points on said path each correlating a compared point on said at least one reference curve to a compared point on said actual curve.

60. The method of claim 57 further including dividing the reference data into reference regions at critical points based on critical characteristics of the reference data, said deriving including matching ctitical points on the reference curve with corresponding critical points on the actual curve using said dynamic time warping function, and further including dividing the actual curve into actual regions at said critical points of the actual curve, comparing characteristics of at least one actual region with characteristics of a reference region with which the actual region has been matched, and generating a signal indicative of the variance of a characteristic of the actual region beyond a defined limit from a corresponding characteristic of the reference region that has been matched with the actual region.

61. The method of claim 57 in which said defining defines plural reference curves including at least one reference curve corresponding to an acceptable operation of the process and a plurality of predetermined reference curves each corresponding to an unacceptable operation of the process, and said deriving derives a dynamic time warping function for each of said reference curves resulting from a matching of the actual curve to a reference curve.

62. The method of claim 61 including calculating a cost related to the dissimilarity between the respective reference curve and said actual curve, and matching said actual curve with a selected reference curve, said reference curve associated with a minimum cost of the calculated costs.