High resolution profile measurement based on a trained parameter conditioned measurement model
Methods and systems for measurements of semiconductor structures based on a trained parameter conditioned measurement model are described herein. The shape of a measured structure is characterized by a geometric model parameterized by one or more conditioning parameters and one or more non-conditioning parameters. A trained parameter conditioned measurement model predicts a set of values of each non-conditioning parameter based on measurement data and a corresponding set of predetermined values for each conditioning parameter. In this manner, the trained parameter conditioned measurement model predicts the shape of a measured structure. Although a parameter conditioned measurement model is trained at discrete geometric points of a structure, the trained model predicts values of non-conditioning parameters for any corresponding conditioning parameter value. In some examples, training data is augmented by interpolation of conditioning parameters and corresponding non-conditioning parameters that lie between discrete DOE points. This improves prediction accuracy of the trained model.
1 . A system comprising:
one or more metrology systems including an illumination source configured to direct an amount of illumination electromagnetic radiation onto one or more structures disposed on a first wafer and a detector configured to detect an amount of electromagnetic radiation from the one or more structures in response to the amount of incident illumination electromagnetic radiation as an amount of measurement data, a geometric shape of the one or more structures characterized by a geometric model parameterized by one or more conditioning parameters and one or more non-conditioning parameters; and
a computing system configured to:
receive the amount of measurement data from the measurements of the one or more structures disposed on the first wafer;
generate a set of input values of each of the one or more conditioning parameters of the geometric model characterizing the geometric shape of the one or more structures; and
determine an estimated value of each of the one or more non-conditioning parameters corresponding to each of the set of input values of the one or more conditioning parameters from a trained parameter conditioned measurement model, wherein each of the set of input values of the one or more conditioning parameters and the amount of measurement data are provided as input to the trained parameter conditioned measurement model.
2 . The system of claim 1 , the computing system further configured to:
receive an amount of Design of Experiments (DOE) measurement data associated with measurements of one or more DOE structures;
receive known, reference values of one or more conditioning parameters and one or more non-conditioning parameters corresponding to the one or more conditioning parameters at a plurality of discrete locations of the one or more DOE structures, the one or more conditioning parameters and the one or more non-conditioning parameters characterizing a geometric shape of the one or more DOE structures; and
iteratively train the parameter conditioned measurement model based on the amount of DOE measurement data and the known, reference values of the one or more conditioning parameters and the one or more non-conditioning parameters, wherein the training involves a minimization of an optimization function including one or more measurement performance metrics.
3 . The system of claim 2 , wherein the optimization function includes a regularization term associated with each of the one or more measurement performance metrics, and wherein a weighting value associated with each of the regularization terms is dynamically controlled during iteration of the parameter conditioned measurement model.
4 . The system of claim 2 , wherein at least a portion of the amount of DOE measurement data associated with measurements of one or more DOE structures is generated by a simulation.
5 . The system of claim 4 , wherein the reference values of one or more parameters of interest associated with the one or more DOE structures are programmed values associated with the simulation.
6 . The system of claim 2 , wherein the known, reference values of the one or more conditioning parameters and the one or more non-conditioning parameters associated with the one or more DOE metrology targets are measured by a trusted, reference metrology system.
7 . The system of claim 2 , wherein at least a portion of the amount of DOE measurement data is collected from actual measurements of the one or more DOE structures disposed on a second wafer.
8 . The system of claim 7 , wherein the first wafer and the second wafer are the same wafer.
9 . The system of claim 2 , the computing system further configured to:
determine additional reference values of one or more conditioning parameters and one or more non-conditioning parameters corresponding to the one or more conditioning parameters at one or more locations between the plurality of discrete locations of the one or more DOE structures by interpolation.
10 . The system of claim 1 , wherein the trained parameter conditioned measurement model is a machine learning based model.
11 . The system of claim 1 , wherein the geometric shape of the one or more structures characterized by the geometric model parameterized by one or more conditioning parameters and one or more non-conditioning parameters is two dimensional or three dimensional.
12 . The system of claim 1 , wherein the amount of measurement data includes measurements of the one or more structures by at least one optical based metrology system, at least one x-ray based metrology system, or any combination thereof.
13 . The system of claim 1 , wherein the one or more conditioning parameters is a height parameter, and wherein the one or more non-conditioning parameters includes any of a critical dimension, a tilt, an ellipticity, and a helix.
14 . A method comprising:
illuminating one or more structures disposed on a first wafer with an amount of illumination electromagnetic radiation;
detecting an amount of electromagnetic radiation from the one or more structures in response to the amount of incident illumination electromagnetic radiation as an amount of measurement data, a geometric shape of the one or more structures characterized by a geometric model parameterized by one or more conditioning parameters and one or more non-conditioning parameters;
generating a set of input values of each of the one or more conditioning parameters of the geometric model characterizing the geometric shape of the one or more structures; and
determining an estimated value of each of the one or more non-conditioning parameters corresponding to each of the set of input values of the one or more conditioning parameters from a trained parameter conditioned measurement model, wherein each of the set of input values of the one or more conditioning parameters and the amount of measurement data are provided as input to the trained parameter conditioned measurement model.
15 . The method of claim 14 , further comprising:
receiving an amount of Design of Experiments (DOE) measurement data associated with measurements of one or more DOE structures;
receiving known, reference values of one or more conditioning parameters and one or more non-conditioning parameters corresponding to the one or more conditioning parameters at a plurality of discrete locations of the one or more DOE structures, the one or more conditioning parameters and the one or more non-conditioning parameters characterizing a geometric shape of the one or more DOE structures; and
iteratively training the parameter conditioned measurement model based on the amount of DOE measurement data and the known, reference values of the one or more conditioning parameters and the one or more non-conditioning parameters, wherein the training involves a minimization of an optimization function including one or more measurement performance metrics.
16 . The method of claim 15 , further comprising:
dynamically controlling a weighting value associated with each regularization term during iteration of the parameter conditioned measurement model, wherein the optimization function includes a regularization term associated with each of the one or more measurement performance metrics.
17 . The method of claim 15 , further comprising:
determining additional reference values of one or more conditioning parameters and one or more non-conditioning parameters corresponding to the one or more conditioning parameters at one or more locations between the plurality of discrete locations of the one or more DOE structures by interpolation.
18 . The method of claim 14 , wherein the amount of measurement data includes measurements of the one or more structures by at least one optical based metrology system, at least one x-ray based metrology system, or any combination thereof.
19 . A system comprising:
one or more metrology systems including an illumination source configured to direct an amount of illumination electromagnetic radiation onto one or more structures disposed on a first wafer and a detector configured to detect an amount of electromagnetic radiation from the one or more structures in response to the amount of incident illumination electromagnetic radiation as an amount of measurement data, a geometric shape of the one or more structures characterized by a geometric model parameterized by one or more conditioning parameters and one or more non-conditioning parameters; and
a non-transitory, computer-readable medium including instructions that when executed by one or more processors of a computing system cause the computing system to:
receive the amount of measurement data from the measurements of the one or more structures disposed on the first wafer;
generate a set of input values of each of the one or more conditioning parameters of the geometric model characterizing the geometric shape of the one or more structures; and
determine an estimated value of each of the one or more non-conditioning parameters corresponding to each of the set of input values of the one or more conditioning parameters from a trained parameter conditioned measurement model, wherein each of the set of input values of the one or more conditioning parameters and the amount of measurement data are provided as input to the trained parameter conditioned measurement model.
20 . The system of claim 19 , the non-transitory, computer-readable medium further including instructions that when executed by one or more processors of the computing system cause the computing system to:
receive an amount of Design of Experiments (DOE) measurement data associated with measurements of one or more DOE structures;
receive known, reference values of one or more conditioning parameters and one or more non-conditioning parameters corresponding to the one or more conditioning parameters at a plurality of discrete locations of the one or more DOE structures, the one or more conditioning parameters and the one or more non-conditioning parameters characterizing a geometric shape of the one or more DOE structures; and
iteratively train the parameter conditioned measurement model based on the amount of DOE measurement data and the known, reference values of the one or more conditioning parameters and the one or more non-conditioning parameters, wherein the training involves a minimization of an optimization function including one or more measurement performance metrics.