Assessment and optimization for metrology instrument including uncertainty of total measurement uncertainty
AssigneeInternational Business Machines Corporation
InventorsCharles N. Archie, G. William Banke, Jr., Matthew J. Sendelbach
Life of this patent
Estimating the term…
Abstract
Methods and related program product for assessing and optimizing metrology instruments by determining a total measurement uncertainty (TMU) based on precision and accuracy. The TMU is calculated based on a linear regression analysis and removing a reference measuring system uncertainty (URMS) from a net residual error. The TMU provides an objective and more accurate representation of whether a measurement system under test has an ability to sense true product variation. The invention also includes a method for determining an uncertainty of the TMU.
Claims25
A program product stored on a computer-readable medium, which when executed, assesses a measurement system under test (MSUT) that measures a substrate having a plurality of structures, the program product comprising program code for performing the following:
- measuring a dimension of the plurality of structures using a reference measurement system (RMS) to generate a first data set, and calculating an RMS uncertainty (URMS) from the first data set, where the RMS uncertainty (URMS) is defined as one of
- (i) an RMS precision;
- (ii) an independently determined RMS total measurement uncertainty (TMURMS);
- and
- (iii) VURMS=VST+VAG, wherein VURMS is URMS expressed as a variance, VST is a
- short term precision variance, and VAG is an across grating variance;
- measuring the dimension of the plurality of structures using the MSUT to generate a second data set, and calculating a precision of the MSUT from the second data set;
- conducting a linear regression analysis of the first and second data sets to determine a corrected precision of the MSUT and a net residual error;
- determining a total measurement uncertainty (TMU) for the MSUT by removing the RMS uncertainty (URMS) from the net residual error;
- and
- outputting the TMU to a system capable of optimizing the MSUT.
A program product stored on a computer-readable medium, which when executed, assesses a measurement system under test (MSUT) that measures a substrate having a plurality of structures, the program product comprising program code for performing the following:
- measuring a dimension of the plurality of structures according to a measurement parameter using a reference measurement system (RMS) to generate a first data set, and calculating an RMS uncertainty (URMS) from the first data set, where the RMS uncertainty (URMS) is defined as one of
- (i) an RMS precision;
- (ii) an independently determined RMS total measurement uncertainty (TMURMS);
- and
- (iii) VURMS=VST+VAG, wherein VURMS is URMS expressed as a variance, VST is a short term precision variance, and VAG is an across grating variance;
- measuring the dimension of the plurality of structures according to the measurement parameter using the MSUT to generate a second data set, and calculating a precision of the MSUT from the second data set;
- conducting a linear regression analysis of the first and second data sets to determine a corrected precision of the MSUT and a net residual error;
- determining a total measurement uncertainty (TMU) for the MSUT by removing the RMS uncertainty (URMS) from the net residual error;
- repeating the measuring, the conducting and the determining for at least one other measurement parameter;
- optimizing the MSUT by determining an optimal measurement parameter based on a minimal total measurement uncertainty;
- and outputting the TMU to a system capable of optimizing the MSUT.
A program product stored on a computer-readable medium, which when executed, estimates an uncertainty in an estimated total measurement uncertainty (TMU), the program product comprising program code for performing the following:
- making a plurality of measurements;
- calculating a Mandel net residual error (DM) and a reference measurement system uncertainty (σRMS) for each measurement;
- calculating a variance for each DM and σRMS;
- constructing a Chi-squared probability distribution function (X2−pdf) for the DM variances and the σRMS variances;
- calculating a X2−pdf for the TMU according to the equation
- pdfTMU=χDm22χσRMS22,
- wherein pdfTMU is the TMU X2−pdf, χDM22 is the DM variance X2−Pdf, χσRMS22 is the σRMS variance X2−pdf, and is a convolution operation;
- determining a TMU range from pdfTMU, wherein the TMU range determines the uncertainty in the estimated TMU;
- outputting the TMU range to a system capable of optimizing a measurement system under test.
A program product stored on a computer-readable medium, which when executed, determines an uncertainty in a total measurement uncertainty (TMU), the program product comprising program code for performing the following:
- determining a confidence limit for a net residual error from a Mandel analysis (DM) using chi-squared distribution tables;
- determining a confidence limit for a total measurement uncertainty (σTMU) according to the equation
- σTMU=√{square root over (DM2−URMS2)}, where URMS is a measurement uncertainty of a reference measurement system;
- and
- outputting the σTMU.
Dependencies are inferred from the claim text.