Observability in metrology measurements

• US 7,502,715 B1
• Filed: 09/21/2005
• Issued: 03/10/2009
• Est. Priority Date: 09/21/2004
• Status: Expired due to Fees

• Current Assignee: ASML Netherlands BV (ASML Holding NV)
• Original Assignee: ASML Netherlands BV (ASML Holding NV)
• Inventors: Middlebrooks, Scott A.
• Primary Examiner(s): Nghiem; Michael P.
• Assistant Examiner(s): Le; Toan M
• Application Number:
  US11/233,527
• Time in Patent Office: 1,266 Days
• Field of Search: 702/182, 702/196, 702/108, 702/179, 702188-190, 703/2, 703/22, 703/13, 700/108, 700/52, 700 28- 29, 700/31, 438/14
• US Class Current: 702/182
• CPC Class Codes: G05B 13/048 using a predictor
• CPC Class Codes: G05B 17/02 electric
• CPC Class Codes: G05B 23/0254 based on a quantitative model, e.g. mathematical relationships between inputs and outputs; functions: observer, Kalman filter, residual calculation, Neural Networks

Abstract

Evaluating the observability of a system includes determining an output measurement scheme, and based on the output measurement scheme, quantifying the ability of the output measurement scheme to provide information about a state of the system by producing an observability value that gauges the ability. In one embodiment, a matrix transformation of the observability matrix may be used to quantify the observability of the states.

Claims

1. A method of evaluating the observability of a system, comprising:

determining an output measurement scheme;

determining a mapping between a state of the system and a measured output of the system;

determining an observability matrix using a plurality of mappings between states of the system and measured outputs of the system;

performing singular value decomposition on the observability matrix to determine a right singular vector of the observability matrix;

determining a norm of the right singular vector;

quantifying an ability of the output measurement scheme to provide information about a state of the system by using the norm; and

conveying the ability of the output measurement scheme as an observability measurement.

2. A method as recited in claim 1, wherein determining the output measurement scheme includes providing a sensor model.

3. A method as recited in claim 1, wherein quantifying the ability of the output measurement scheme to provide information about a state of the system includes:

performing a threshold operation on the diagonal matrix.

4. A method as recited in claim 1, wherein the norm is a percentage value indicating the observability of the state.

5. A method as recited in claim 1, wherein the system includes a semiconductor processing system.

6. A method as recited in claim 1, wherein the output measurement is a first output measurement obtained via a first measurement scheme;

the method further comprising;

obtaining a second output measurement using a second measurement scheme;

placing the second output measurement scheme in context of the model;

based on the second output measurement and the model, quantifying the ability of the second output measurement to provide information about the state of the system; and

comparing the ability of the first output measurement scheme to provide information about the system with the ability of the second output measurement to provide information about the state of the system.

7. A method as recited in claim 1, wherein the system includes a nonlinear model.

8. A state estimator for evaluating the observability of a system, comprising:

a processor configured to;

determine an output measurement scheme;

determine a mapping between a state of the system and a measured output of the system;

determine an observability matrix using a plurality of mappings between states of the system and measured outputs of the system;

perform singular value decomposition on the observability matrix to determine a right singular vector of the observability matrix;

determine a norm of the right singular vector;

quantify an ability of the output measurement scheme to provide information about a state of the system by using the norm; and

convey the ability of the output measurement scheme as an observability measurement; and

a memory coupled to the processor, configured to provide the processor with instructions and to store the observability measurement.

9. A state estimator as recited in claim 8, wherein to determine the output measurement scheme comprises providing a sensor model.

10. A computer program product for evaluating the observability of a system, the computer program product being embodied in a computer readable medium and comprising computer instructions for:

determining an output measurement scheme;

determining a mapping between a state of the system and a measured output of the system;

determining an observability matrix using a plurality of mappings between states of the system and measured outputs of the system;

performing singular value decomposition on the observability matrix to determine a right singular vector of the observability matrix;

determining a norm of the right singular vector;

quantifying an ability of the output measurement scheme to provide information about a state of the system by using the norm; and

conveying the ability of the output measurement scheme as an observability measurement.

11. A computer program as recited in claim 10, wherein the output measurement is a first output measurement obtained via a first measurement scheme;

the method further comprising;

obtaining a second output measurement using a second measurement scheme;

placing the second output measurement scheme in context of the model;

based on the second output measurement and the model, quantifying the ability of the second output measurement to provide information about the state of the system; and

comparing the ability of the first output measurement scheme to provide information about the system with the ability of the second output measurement to provide information about the state of the system.