Method and system for wafer quality predictive modeling based on multi-source information with heterogeneous relatedness
The present invention generally relates to the monitoring and controlling of a semiconductor manufacturing environment and, more particularly, to methods and systems for virtual meteorology (VM) applications based on data from multiple tools having heterogeneous relatedness. The methods and systems leverage the natural relationship of the multiple tools and take advantage of the relationship embedded in process variables to improve the prediction performance of the VM predictive wafer quality modeling. The prediction results of the methods and systems can be used as a substitute for or in conjunction with actual metrology samples in order to monitor and control a semiconductor manufacturing environment, and thus reduce delays and costs associated with obtaining actual physical measurements.
1. A method for predicting quality of wafers produced by production equipment that includes multiple chambers in each of which multiple wafers are simultaneously processed, comprising:
measuring process variables of each of the wafers;
sending the process variables to a central database;
receiving the process variables of each of the wafers and historical measurements;
representing respective sides of the multiple chambers as wafer quality predictive modeling tasks based on the historical measurements;
grouping the wafer quality predictive modeling tasks according to heterogeneous relatedness of the production equipment, said grouping step including, for each chamber in which multiple wafers are simultaneously processed, grouping wafer quality predictive modeling tasks for all of the respective sides of the each chamber, each chamber of the multiple chambers being treated as a group of one or more wafers quality predictive modeling tasks;
partitioning the process variables into two sets;
generating a prediction model that accommodates the grouping of the wafer quality predictive modeling tasks from the grouping step and the partitioned process variables from the partitioning step;
predicting a quality of each of the wafers produced in individuals sides of the multiple chambers based on the prediction model generated in the generating step;
sending the predicted quality of each of the wafers to an advanced process controller and the central database;
measuring an actual quality of at least one sample of the wafers;
sending the actual quality of at least one sample of the wafers to the advanced process controller and a virtual metrology machine;
updating the virtual metrology machine with the actual quality of at least one sample of the wafers;
determining a feedback control by the advanced process controller; and
processing the wafers by the production equipment in accordance with the feedback control,
wherein the receiving, representing, grouping, partitioning, generating, and predicting steps are executed by a virtual metrology machine implemented on a computer, and
wherein for each chamber in which multiple wafers are simultaneously processed, each side of the each chamber processes only one wafer at a time.
2. The method of claim 1 , wherein a first set of the two sets of the process variables represents independent variables and a second set of the two sets of the process variables represents dependent variables.
3. The method of claim 2 , wherein the prediction model is generated as a function of coefficient vectors for the independent variables and the dependent variables.
4. The method of claim 3 , wherein the prediction model accommodates the grouping of the wafers by connecting the coefficient vectors for the independent variables and the dependent variables through a transformation matrix and imposing similarity on the coefficient vectors for one or more of the independent variables and the dependent variables.
5. The method of claim 1 further comprising:
optimizing the prediction model by implementing a block coordinate descent.
6. The method of claim 5 , wherein the block coordinate descent includes an accelerated update.
7. The method of claim 1 , wherein the process variables are indicative of production of each of the wafers processed by the production equipment.
8. The method of claim 1 , wherein the historical measurements are examples of actual wafer quality measurements.
9. The method of claim 2 , wherein the independent variables are selected from the group consisting of pressure, power, temperature, and gas flows, each member of the group being subject to an advanced process controller.
10. The method of claim 2 , wherein the dependent variables are selected from the group consisting of impedance, electric bias, and throttle valve positions, and have an impact on the quality of the wafers being heavily dependent on the independent variables.
11. The method of claim 1 , wherein the feedback control is determined based on the predicted quality.
12. The method of claim 1 , wherein the feedback control is determined based on the predicted quality and the actual quality.
13. The method of claim 1 , wherein the quality of the wafers is measured in terms selected from the group consisting of deposition thickness, resistance, stress, and refractive index.