Patent Publication Number: US-2023142936-A1

Title: Modelling and prediction system with auto machine learning in the production of memory devices

Description:
CLAIM OF PRIORITY 
     The present application is a Continuation-in-Part of U.S. patent application Ser. No. 17/979,142, entitled “Modelling and Prediction of Virtual Inline Quality Control in the Production of Memory Devices” by Sendoda et al., filed Nov. 2, 2022, which is a Continuation-in-Part of U.S. patent application Ser. No. 17/725,695, entitled “Virtual Metrology for Feature Profile Prediction in the Production of Memory Devices” by Chu et al., filed Apr. 21, 2022, which is a Continuation-in-Part of U.S. patent application Ser. No. 17/360,573, entitled “Virtual Quality Control Interpolation and Process Feedback in the Production of Memory Devices” by Ikawa et al., filed Jun. 28, 2021, all of which are hereby incorporated by reference in their entireties. 
    
    
     BACKGROUND 
     In the course of manufacturing of memory devices or, more generally other integrated circuits and electronic devices, many testing and inspection operations are typically performed. The testing can occur at many stages during manufacturing and also afterwards to determine defects and process variations. The test results can be used to determine defective, or potentially defective, devices, sort devices according to their characteristics, or to adjust processing parameters. The more testing that is done, the more data that is available for quality control; however, testing can be expensive and time consuming, and in some cases involves preparing of test sample in ways that make them subsequently unusable. Because of this, the number of test samples and the types of tests that can be performed are limited. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWING 
         FIG.  1    is a drawing of a three dimensional non-volatile memory device of the BiCS type. 
         FIG.  2    represents a side view cross-section of a BiCS structure and its memory holes. 
         FIG.  3    is the top view of the layers formed within the memory hole to provide the memory cells of the NAND structure. 
         FIG.  4    is a side view of an actual 3D NAND memory device, similar to lower portion of the drawing of  FIG.  2   , to illustrate some examples of processing problems in the fabrication of such a device. 
         FIG.  5    shows a top view of an actual 3D NAND structure, similar to  FIG.  3   , but showing more memory hole structures. 
         FIG.  6    is a flowchart for one embodiment of the application of test data feedback to the fabrication of a non-volatile memory circuit. 
         FIG.  7    is a plot illustrating the data relationship between the number of bad blocks on a memory chip versus early failure rate for sampled memory dies. 
         FIG.  8    is a plot illustrating the data relationship between the photo inspection related defect data of a memory chip versus early failure rate for sampled memory dies. 
         FIG.  9    is a schematic representation of the use of virtual PLY interpolation and process feedback. 
         FIG.  10    illustrates the improvement in correlation between bad block count and PLY data obtained by applying interpolation using a generalized linear model embodiment. 
         FIGS.  11 A and  11 B  illustrate utilizing a machine learning study to provide different type of virtual PLY data. 
         FIGS.  12 A and  12 B  respectively illustrate a point analysis of PLY data by only measured data and with interpolated PLY data at the lot level. 
         FIGS.  13 A and  13 B  respectively present conventional sampling for quality control and the use of virtual quality control by machine learning to illustrate the advantage of incorporating virtual quality control data. 
         FIG.  13 C  represents an embodiment for the different physical facilities in which the processes of  FIG.  13 B  would be performed. 
         FIG.  14    present an embodiment for a sequence schematically representing virtual critical dimension interpolation at the chip level. 
         FIGS.  15 A and  15 B  respectively present conventional sampling for quality control and the use of virtual quality control by machine learning to illustrate the advantage of incorporating virtual quality control data for the critical dimension example. 
         FIGS.  16  and  17    are flowcharts for embodiments of virtual PLY interpolation and virtual CD interpolation, respectively corresponding the schematic representations of  FIGS.  13 B and  15 B . 
         FIG.  18    illustrates some of the components of an embodiment of a virtual metrology approach for use of die sort and inline test data. 
         FIG.  19    is a virtual metrology platform diagram for an embodiment based on word line RC values. 
         FIG.  20    is a plot of the predicted versus actual word line resistance values that can be used in model auto-calibration. 
         FIG.  21    illustrates an example to show predicted total word line RC values versus die sort measured word line RC values. 
         FIG.  22    illustrates inputs, predictions, and, for comparison, actual data for virtual metrology RC prediction of wafer level average memory hole profiles. 
         FIG.  23    illustrates die level memory hole profile data from virtual metrology RC prediction. 
         FIG.  24    is a flowchart for an embodiment of the virtual metrology techniques described with respect to  FIGS.  18 - 23   . 
         FIG.  25    presents the incorporation of virtual inline quality control data (IQC) into the process of  FIG.  15 B . 
         FIG.  26    is a flowchart of an embodiment for calculating virtual inline quality control data using a two step modelling approach. 
         FIG.  27    is a detail system flow for a system B embodiment of the model and prediction system for virtual inline quality control with the lot/wafer report. 
         FIG.  28    is a flowchart for an embodiment of the fabrication of an integrated circuit incorporating modelling and prediction of virtual inline quality control as described with respect to  FIGS.  25 - 27   . 
         FIG.  29    is a detail system flow for a system A and system B embodiment of the model and prediction system for virtual inline quality control with the lot/wafer report to highlight modelling evaluation and selection. 
         FIGS.  30  and  31    are embodiments for the portion of the system flow related to choosing the best model for wither of system A or system B without and with hyperparameter tuning, respectively. 
         FIG.  32    is a flowchart for an embodiment for the evaluation and selection of the models that incorporates parameter tuning. 
         FIG.  33    is a screenshot of an example of a leader board for tunings of several models for one embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     In the course of manufacturing non-volatile memory circuits or other integrated circuits, testing is performed at many stages during manufacturing and afterwards to determine defects and process variations. The testing results can be used to determine defective, or potentially defective, devices, sort devices according to their characteristics, or to adjust processing parameters. Although testing a higher proportion of the devices can lead to more accurate and representative test data, testing is expensive in terms of both time and cost and can also reduce yields, as some tests render the samples subsequently unusable. To improve on this situation, the following introduces the use of machine learning to generate virtual values for one set of tests, by interpolating the virtual test results for devices on which the test is not performed, based on correlations with other sets of tests. 
     One set of embodiments uses an example of sacrificial layer wet-etch photo inspection, or photo-limited yield (PLY), data for a machine learning correlation study between bad block values or other circuit characteristics (e.g., resistance, current, threshold voltages) determined at die sort and PLY values determined inline during processing. The correlation can be applied to interpolate virtual inline PLY data for all of the memory dies, allowing for more rapid feedback on the processing parameters for manufacturing the memory dies and making the manufacturing process more efficient and accurate. In another set of embodiments, the machine learning is used to extrapolate limited critical dimension or other metrology test data to all of the memory dies through interpolated virtual metrology test values. In further embodiments, virtual metrology is used to interpolate memory hole profiles in a three dimensional (3D) NAND memory structure based on the electrical properties (e.g., RC values) of the word lines of the layers of the memory structure. 
     To provide some context for the primary example of a non-volatile integrated memory circuit to which the techniques presented here are applied in the following discussion,  FIG.  1    is a drawing of a three dimensional non-volatile memory device of the Bit Cost Scalable (BiCS) type. In  FIG.  1   , a number of memory holes, such as marked at  101 , extend down from bit lines to a substrate, passing through silicon layers (Si) corresponding to the word lines that form the control gates layers surrounding the memory holes. In between the control gate layers are dielectric layers (e.g., SiO 2 ). The BiCS structure of  FIG.  1    is of the U type, where a memory hole extends downward to a pipe connection, such as marked at  103 , in the substrate that connects it to another memory hole that then extends upward to a source line. Together, the two sections form a NAND string between a bit line and a source line, where a select gate line is formed on the ends of the NAND strings between the memory cells and the bit lines on one end and the source lines on the other end. The memory cells are formed in the memory holes in the regions where the holes pass through the control gate layers. 
     In the illustration of  FIG.  1   , only a few control gate layers are shown and a U-type structure is used. A typical BiCS structure will have many more such layers and will often not use the U-type structure, but will have the source lines connected along the bottom of the memory hole/NAND string at the substrate end, as illustrated in  FIG.  2   . 
       FIG.  2    represents a side view cross-section of a (non-U-type) BiCS structure and its memory holes. In the processing to fabricate the structures of  FIGS.  1  and  2   , a large number of alternating control gate layers and dielectric layers are formed, connected between bit lines at top (top circled region,  201 ) and a source line at the bottom (bottom circuit region,  205 ). In the embodiment of  FIG.  2   , at a central circled region  203  is a joint region that divides the select gates into an upper half and a lower half. The formation of the memory holes through the control gate layers, dielectric layers, and other layers is a delicate and complex processing operation, which can be particularly delicate at the circled regions  201 ,  203 , and  205  of  FIG.  2   . These regions comprise a bottom, “dimple” region formed under the memory holes in the substrate at the region  205 ; a central, joint region in  203  in central portion of the memory array structure; and a “shoulder” region at  201 , where the memory hole opens up and connects to the bit lines. To form the memory cells, a number of concentric ring-like layers are formed within the memory holes. 
       FIG.  3    is a top view of the layers formed within the memory hole to provide the memory cells of the NAND structure, showing a view from above horizontal cross-section taken at A-A part way down the structure of  FIG.  2   . The view of  FIG.  3    can be prepared from a fully fabricated device that is pared back after processing is complete, or from an intermediate state of processing during the fabrication operation.  FIG.  3    illustrates a Metal Oxide Nitride Oxide Silicon (MONOS) of, starting at the outside of the memory hole and working inward for this particular embodiment, a blocking layer followed by a dielectric layer. Next is a charge trap layer, in which the memory device stores electrons to determine the data state of a memory cell. The charge trap layer is separated by a tunnel layer from the channel layer of the NAND string, with an inner core oxide formed inside of the channel layers. 
     In forming such a memory structure, the memory holes and the layers within them are formed to have generally circular cross-sections, with each of the layers meant to have a specified and uniform thickness. Due to process variations, the actual shapes and thicknesses of these layer will vary. Because of this, processing samples can be collected and analyzed to determine the quality of the integrated circuits. As the number of memory holes in a given device is extremely large, and the number of devices produced is also large, visual or photo inspection tests by a person is very labor intensive process and, as a practical matter, only a small percentage of the memory holes on a given device, and only a small number of devices, can be inspected.  FIGS.  4  and  5    illustrate some examples of defects that man occur in the fabrication of such complex structures. 
       FIG.  4    is a side view cross-section image of an actual 3D NAND memory device, similar to lower portion of the drawing of  FIG.  2   , to illustrate some examples of processing problems in the fabrication of such a device. The view of  FIG.  4    shows three memory holes,  401 ,  403 ,  405 , and several word lines (e.g.,  411 ) separated by dielectric layers (e.g.,  413 ) at an intermediate processing stage, where the alternating word line-dielectric layers have been formed, but the MONOS regions, that serve as a memory film, have not been completed. The middle memory hole  403  has some problems. A first is that, in forming the stack of word line-layers, the memory holes through the layers, and the various lining layers of  FIG.  3   , at certain stages sacrificial silicon layers are formed with the memory holes as part of the processing process. These sacrificial silicon layers need to be cleaned out of the memory holes so that the desired layers can be formed within the memory holes. The middle memory hole has a sacrificial silicon residue (SAC Si residue) that was not sufficiently cleaned out, so that the MONOS layers of the lower few layers (including any source side select gates for the NAND string) cannot be properly formed and the resultant NAND string will be unusable. Another processing defect illustrated in  FIG.  4   , as highlighted by the broken oval where vertical layers of the MONOS structure are not properly formed, in which case the memory cells in this region are also unusable. 
       FIG.  5    shows a top view of an actual 3D NAND structure, similar to  FIG.  3   , but showing more memory hole structures. More specifically,  FIG.  5    illustrates when memory holes “bow”, so that they are not evenly spaced and not of circular cross-section resulting in layers of the different memory holes are not well-formed and distinct. As illustrated in the portion of the structure within the broken box outline, the layers of several of the memory holes are not distinct, so that the memory cells of these memory holes are unusable. 
     For quality control (QC) purposes, many tests are performed on memory devices, and integrated circuits more generally, at various points in the manufacture to test for defects, including those illustrated with respect to  FIGS.  4  and  5   . This test information can be used to prevent the shipping of defective parts, but can also be used to adjust the parameters of the fabrication process reduce the number of defects. The more devices that are tested, the more representative that the test data will be and the more accurately that the processing parameters can be updated; however, testing is expensive in terms of time and cost and, for some tests, results in the tested device being unusable.  FIG.  6    illustrates the incorporation of test data feedback into the fabrication process, where, as discussed in more detail below, quality control data can be interpolated to provide more extensive test data values. 
       FIG.  6    is a flowchart for one embodiment of the application of test data feedback, such as related to the memory hole example illustrated with respect to  FIGS.  1 - 5   , to the fabrication of a non-volatile memory circuit. This testing can be done as part of a normal test process during fabrication or in response to the occurrence of failed devices as part of failure analysis. The testing can also be done as part of a sorting or binning process (separating devices into lots of good/bad, good/bad/marginal, and or so) or monitor processing, where the results can be used to go back and adjust processing parameters. 
     Beginning at step  601 , samples of an integrated circuit are prepared for imaging. Depending on the embodiment, this can involve the fabrication of samples of the integrated circuit, such as by a sequence of processing steps to build up the circuit on a substrate, or receiving samples of the circuit. Depending on the features of interest, completed samples of the integrated circuit may be used, or the integrated circuits may be at some earlier stage of the fabrication process. For checking on some features, such as the memory hole structures of a three dimensional non-volatile memory circuit, a completed or partially completed circuit can be pared back through one or more layers to reach the layer of interest. The preparing of the integrated circuits for imaging can also include cleaning of the circuits and any needed mounting for generating the images. 
     At step  603 , a set of images are produced, such as by using an electron microscope (a scanning electron microscope, or SEM, for example), on a set of memory chips or other integrated circuits. As noted, to prepare the images, in some embodiments, a finished memory chip can be pared down to a desire level (such as the circled regions in  FIG.  2   ) of the structure, or the device can be only partially completed (such as just the initial stages in order to consider the “dimple” regions where the lower end of the memory hole extends into the substrate). At step  605 , additional test data can be generated by applying machine learning to interpolate test data values to extend to additional, or even all, of the devices being fabricated, as in embodiments presented below. For example, as is discussed in more detail below, in order to obtain critical dimension (CD) data for all a group of chips, generalized linear model (GLM), gradient boosting machine (GBM), or other machine learning techniques is performed by measured CD value and its die/sort (D/S) characteristics and, by using the correlation, all virtual CD is interpolated. 
     At step  607  the expanded test data (both directly measured and interpolated) can be analyzed and used to generate data, including statistics such as expected Circular Memory holes per image vs. Expected Data. At step  609 , the statistics can be fed back into the processing operation to adjust the processing for fabricating the integrated circuit based upon the analysis of step  607 . At step  611 , the devices can then be fabricated with the updated processing parameter(s). For example, the time or parameters (such as temperatures or concentration levels) for various process steps can be changed. Referring back to  FIGS.  3  and  5   , if, for example, memory holes are too small or too large the time for performing the etch to form the memory holes can be increased or decreased. If some of the layers within a memory hole are too thick or too thin, the time for depositing such a layer can be adjusted. If a layer is too non-circular, the rate at which it is formed could be slowed to obtain more uniformity by, for example, altering the temperature for the processing step or the concentration of the reactants. 
     The feedback of step  609  can be performed in an iterative process in some embodiments, by including a loop of steps  611 ,  613 ,  617 ,  617 ,  619 , and  621 . At step  611 , the processing feedback of step  609  is used in a new processing operation to manufacture one or more samples. At  613 , electron microscope images can then be generated (similarly to the process of step  603 ), with additional data being obtain in step  615  (as in step  605 ). Step  619  can, similarly to step  609 , analyze the data and determine whether another iteration is called for: if so, the flow can loop back to step  609 ; and if not, the process can end at step  621 . 
     In the flow of  FIG.  6   , the processing steps for the fabrication of the integrated circuits at steps  601  and  611  can be performed by any of the processing methods used in fabricating the integrated circuits being analyzed. The application of machine learning to obtain additional data in steps  605  and  615  can be computationally intensive operations and can be implemented using hardware, firmware, software, or a combination of these. The software used can be stored on one or more processor readable storage devices described above to program one or more of the processors to perform the functions described herein. The processor readable storage devices can include computer readable media such as volatile and non-volatile media, removable and non-removable media. By way of example, and not limitation, computer readable media may comprise computer readable storage media and communication media. Computer readable storage media may be implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data. Examples of computer readable storage media include RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can be accessed by a computer. A computer readable medium or media does (do) not include propagated, modulated or transitory signals. The training phase is typically more computationally intensive and can be performed in the cloud, for example, while inferencing may be performed more locally, such as on computational facilities at the fabrication facility. Examples of the processing units that can be used for the machine learning can include one or more of CPU (central processing unit), GPU (graphic processing unit), TPU (tensorflow processing unit), and NPU (neural processing unit) devices, among others. 
     The following discussion will mainly be described in the context of the errors described above in  FIGS.  4  and  5   . As discussed above,  FIG.  4    illustrates an example of sacrificial layer wet-etch photo inspection, or photo-limited yield (PLY), related defects for the lower portions (i.e., below region  203  of  FIG.  2   ) of the memory holes, which are often expressed as defective parts per million (DPPM) issues reported in early failure rate (EFR) results. This sort of PLY data can be a key piece of information to detect device failure and to study process improvements from both a yield and a DPPM point of view; but such directly obtained sacrificial layer wet-etch photo inspection PLY data is very limited data since the measurement is not done for all chips and all wafers. As also discussed above,  FIG.  5    illustrates upper memory hole (i.e., above region  203  of  FIG.  2   ) bow related DPPM issues reported in early failure rate results, where upper memory hole bow related critical dimension (CD) data can be a key parameter to screen for failure by the cherry picking of samples to study process improvements from both a yield and a DPPM point of view; but, again, upper memory hole CD data is very limited data since the measurement is not done for all chip and all wafers. 
     Considering the sacrificial layer wet-etch photo inspection PLY related defect data for the lower portions of the memory holes, for defect determination a bad block index or other circuit characteristics (e.g., resistance, current, threshold voltages) determination can be performed to determine cherry picking criteria, but as illustrated with respect to  FIGS.  7  and  8   , it can be insufficient to screen for all defects for a sample set due to poor correlation at lower defect regions. 
       FIG.  7    is a plot illustrating the data relationship between the number of bad blocks on a memory chip versus early failure rate for sampled memory dies, such as can be performed during backend (i.e., post-processing). The vertical axis in  FIG.  7    is the early fail rate (EFR) due to defective lower memory holes, such as can be expressed in terms of defective parts per million and the horizontal axis is the number of bad blocks as determined from die sort data, where a linear scale is used on both axes. The correlation between the early fail rate and bad block count is high for the data of  FIG.  7    is high, with an R 2  value of 0.97, where R 2  (or sometimes written r2) is the “coefficient of determination” and represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s) and ranges from 0, for no correlation, to 1, for full correlation. The data of  FIG.  7    can be used determine criteria for cherry picking of samples, where, in the example  FIG.  7    the criteria of a bad block count (BBK) of BBK=3 is used. 
       FIG.  8    is a plot illustrating the data relationship between inline photo inspection related defect data of a memory chip versus early failure rate for sampled memory dies. The vertical axis in  FIG.  8    is the sacrificial layer wet-etch photo inspection (PLY) determined related defect data for the lower portions of the memory holes in logarithmic scale and the horizontal axis is again the number of bad blocks as determined from die sort data in a linear scale. The vast majority of data points are clumped at low bad block count values, so that there is poor correlation (R 2 =0.621) between the PLY values and the bad block count based on the limited amount of measured PLY values. To improve upon this situation, the embodiments presented here apply machine learning interpolate the test data in order generate more accurate processing feedback, as represented in  FIG.  9   . 
       FIG.  9    is a schematic representation of the use of virtual PLY interpolation and process feedback. The process begins with performing a detailed correlation study of, in this embodiment, die sort bad block data (D/S BBK) and PLY data by machine learning based on measured values for several lots of memory dies or, more generally, other integrated circuit chips, which is then used to interpolate the PLY data for all of the lots being processed. (In the case of other types of integrated circuitry, a metric other than bad block count can be used.) The result is illustrated at left in  FIG.  9   , where the measured PLY values (that can again be in a log scale as in  FIG.  8   ) are used to construct the die sort bad block function values as represented by the line  901 . 
     The interpolation of values is illustrated by the table at the center of  FIG.  9   . The table includes the lower memory hole sacrificial layer wet-etch PLY defect values (LMH SAC WET PLY) and the number of bad blocks (BBK index) for a number of lots (lots A-G) of memory dies. In this example, for lots A, E, and G, both bad block count from die sort and the PLY values determined, where these sets of directly measured values are underlined. For the other lots, the numbers of bad blocks are also measured at die sort, but the PLY values are determined by interpolation based on the correlation as shown at left as determined by the machine learning process. 
     The impact of different processing items can be checked at different points during fabrication to allow for PLY data to be interpolated for these different processing items, where the PLY data can be interpolated by both die sort items and process items. This can allow the tracking and monitoring of different sources of error across time and the adjusting of processing parameters according, as illustrated at right of  FIG.  9   . In the bar graph, the horizontal axis is time, each set of bars are the PLY date of a time interval (e.g., a week) showing the contributions of, in this example, three different PLY error contributions. For example, the upper region  911  can correspond to a lower memory hole critical dimension value, the central region  913  could correspond to leakage times for charge from the charge trap layer across the tunnel layer to the channel region, and  915  could correspond to charge trap layer&#39;s thickness (see  FIG.  3   ). This sort of data allows for different possible source of defects to be tracked and parameters adjusted accordingly over time. 
     Considering the machine learning used, one of several techniques, or a combination of such techniques, can be applied depending on the embodiment, including: deep neural networks (DNNs); distributed random forest (DRF), extremely randomized trees (XRT); generalized linear models (GLMs); and/or gradient boosting machine (GBM). Generalized linear models are an extension of traditional linear models for statistical data analysis, having a flexibility of the model structure unifying regression methods (such a linear regression and logistical regression for binary classification), availability of model-fitting techniques, and the ability to scale well with large datasets. 
     Gradient boosting machine is an ensemble of either regression or classification tree models, both of which are forward-learning ensemble methods that obtain predictive results using gradually improved estimations. Boosting is a flexible nonlinear regression procedure that helps improve the accuracy of trees, where weak classification algorithms are sequentially applied to the incrementally changed data to create a series of decision trees, producing an ensemble of weak prediction models. While boosting of the trees increases their accuracy, it also decreases speed and user interpretability, whereas the gradient boosting method generalizes tree boosting to minimize these drawbacks. 
       FIG.  10    illustrates the improvement in correlation between bad block count and PLY data obtained by applying interpolation using, in this embodiment, a generalized linear model embodiment. At left,  FIG.  10    repeats for comparison the PLY measured data (in a log scale) versus bad block count graph of  FIG.  8    based on a conventional single bad block count correlation, while at right  FIG.  10    illustrates the PLY measured data (in a log scale) versus predicted PLY values (in a log scale) using four items as interpolated using a generalized linear model. As illustrated in the right side of  FIG.  10   , by use of the generalized technique, the correlation is improved to R 2 =0.70 from the R 2 =0.62 of the conventional single bad block index correlation at left. Once a correlation study of die sort bad block values and PLY data is completed by machine learning, interpolation can be performed, as illustrated with respect to the examples of  FIGS.  11 A and  11 B . 
       FIGS.  11 A and  11 B  illustrate utilizing a machine learning study to provide different types of virtual PLY data.  FIG.  11 A  is a plot of PLY data from inline testing data, where inline data is data gathered on the memory dies during the course of the fabrication process. The vertical axis is for the virtual PLY values and the horizontal axis is the inline data function, with the line  1101  corresponding to the correlation determined based on actual data. The interpolated data points can then be generated by point analysis based on the die sort bad block values. 
       FIG.  11 B  is a plot of PLY data from die sort testing data, gathered on the memory dies as part of the post-fabrication process testing. The vertical axis is the virtual PLY values and the horizontal axis is the die sort (D/S) data function, with the line  1103  corresponding to the correlation determined based on actual data. The PLY data can be determined by the die sort data, and the interpolation by related multiple die sort index values. The correlation data can be confirmed for both inline and die sort data and, if the correlation is good, interpolated data can be used for various studies, such as defective parts per million, yield, and process improvement, to provide data volume, as illustrated by  FIGS.  12 A and  12 B . 
       FIGS.  12 A and  12 B  respectively illustrate a point analysis of PLY data by only measured data and with interpolated PLY data at the lot level. In conventional point analysis using only measured data of  FIG.  12 A , the vertical axis is the measured PLY values in a log scale and the horizontal axis is the defect points summed over a set of several measured defect values. The number of data points is relatively sparse, compared to the total number of memory dies, and correlation is relatively low, with R 2 =0.485. 
       FIG.  12 B  presents a point analysis using virtual quality control data and illustrates the increase in data points through use of interpolated PLY data. (The black rectangle in both  FIGS.  12 A and  12 B  is redacted specific numeral information that does not enter into the discussion here.) The horizontal axis is again the defect point data summed over a set of several measured defect values, but not including the virtual data points, and the vertical axis is the predicted PLY values in a log scale. As can be seen by comparing  FIG.  12 A  to  FIG.  12 B , the number of data points increased is greatly increased by the use of virtual quality control data. By using interpolated volume data, the correlation accuracy improved from R 2 =0.485 (without interpolated data) to R 2 =0.537. This allows for a clear correlation to be obtained for key process steps by interpolating inline data by big data analyses to contribute to processing improvements and die sort/early failure rate correlation studies. 
     The incorporation of virtual quality control data at inline (i.e., during the fabrication process) can be particularly useful as it can provide faster feedback for adjusting processing parameters to decrease the number of defects, such as measured by defective parts per million (DPPM). Quality control data collected inline during production is fastest way to detect device failures, but data volumes are traditionally limited; however, by interpolating all data by inline data, the volume can be increased and analysis accuracy will be improved, providing a faster feedback speed for adjusting processing parameters during the fabrication process. This can be illustrated with respect to  FIGS.  13 A and  13 B . 
       FIGS.  13 A and  13 B  respectively present conventional sampling for quality control and the use of virtual quality control by machine learning to illustrate the advantage of incorporating virtual quality control data. In the sequences of  FIGS.  13 A and  13 B , the same sequence is shown, but the amount and location of testing and resultant incorporation of processing feedback is different. 
     In the conventional processing sequence of  FIG.  13 A , the cleanroom operations are the fabrication and inline testing processes, and including cleanroom in at block  1301 , followed by various proceeding steps to fabricate and prepare a sample for imaging at block  1303 , corresponding to step  601  of  FIG.  6    in which the samples of the integrated circuits are prepared for imaging. Block  1305  is the inline photo inspection, corresponding to step  603  of  FIG.  6   , such as lower memory hole sacrificial silicon PLY data. In the conventional flow of  FIG.  13 A , only a relatively small amount of testing is performed, due to time and cost limitations and also due to resultant yield loss for tests that render the device subsequently unusable. For example, only a small percentage of the wafer lots (e.g., 20%), and only perhaps a single wafer per lot, are tested. Due to the limited data volume, the correlation between the collected PLY data and bad block count is low, as discussed above with respect to  FIG.  8   , so that that amount of feedback and advanced process control that can provided to earlier processing steps is consequently limited. The memory dies leave the clean room at block  1307 , after which subsequent testing can be performed on the completed die. 
     Die sort follows at  1309 , which can include bad block determination and other testing, followed by additionally early fail rate (EFR) and other backend testing at block  1311  to determine defect rates (DPPM), where the following uses the bad block value as the main example. At both the die sort and backend testing, there is again weak correlation or a lack of data due to the low proportion of samples used in some tests. This again results limited feedback for the processing operations. Additionally, the backend tests of block  1311  and, in some cases, die sort in block  1309  are often performed at different physical locations, involves shipping of devices and consequent delays for even what feedback is available. 
       FIG.  13 B  illustrates the incorporation of quality control data by machine learning and is arranged in blocks similar to those of  FIG.  13 A , where blocks  1351  and  1353  can be as described for blocks  1301  and  1303 . The inline inspection of block  1355  is similar to the inline inspection of block  1305 , except now, by use the virtual quality control data obtain by interpolation as illustrated in  FIG.  9   , feedback/advanced process control data for all (or at least the majority) of wafers of all lots can be provided back to the earlier processing steps of block  1353 . In addition to the increased amount of feedback available, this feedback is also provided as part of the inline processing and is consequently much faster that feedback from the die sort or backend tests. The memory dies leave the clean room at block  1357 , after which subsequent testing can be performed on the completed die. 
     Die sort again follows at  1359 , which can be bad block and other testing (e.g., resistance, current, threshold voltages), followed by additionally early fail rate (EFR) and other backend testing at block  1361  to determine defect rates (DPPM). The testing and samples of blocks  1359  and  1361  can be the same or similar as for blocks  1309  and  1311  of  FIG.  13 A , but now the machine learning techniques described above are applied to perform a prediction fail model and cherry picking criteria that are applied at block  1355  to interpolate the virtual quality control data that is used to generate the feedback to block  1353  to adjust the processing parameters for subsequently produced memory die. The prediction fail model study and determination of cherry picking criteria can be performed at regular intervals (weekly, for example) to update the feedback/advanced process control interpolation used between blocks  1353  and  1355 . As illustrated conceptually in  FIGS.  9  and  11 A , this relation between blocks  1353  and  1355  has the merit of allowing the interpolation of inline data (block  1355 ) by the previous steps (block  1353 ) by interpolating a 100% of the die sort data (block  1359 ) after certain process steps are completed. By using virtual quality control data, a clear correlation and detail study can be done by 100% data volume; and by optimizing quality control measurement volume with the virtual PLY method, quality control steps can be minimized and improvement cycle times and virtual fabrication concept feasibility. 
       FIG.  13 C  represents an embodiment for the different physical facilities in which the processes of  FIG.  13 B  can be performed. The fabrication facility  1391  is the manufacturing facility, including cleanrooms, in which the memory dies or other integrated circuits are manufactured. Inline testing, such as for PLY values, is performed at the fabrication facility  1391 . After being manufactured, the integrated circuits are transferred to a die sort facility  1393 . The die sort facility  1393  may be part of or located near by the fabrication facility  1391 , or at a different location that would require shipping. Following die sort, the integrated circuits are typically shipped to any backend facilities  1395  as part of the further quality control and customer distribution. 
     To perform inline tests (such as for PLY data), the die sort testing (such as bad block count data), and additional bad end testing (such as EFR) requires any operations at one location to be finished before the integrated circuits can transferred to the next location for the subsequent set to tests to be done there. These various data sets for a set of memory circuits or other integrated circuits can then be provided to a processing facility  1397 , where this can be one or more locations, including the fabrication facility  1391 , die sort facility  1393 , and backend facility, or other locations, such as in the cloud. Under the arrangement of  FIG.  13 A , in addition to the relative lack of data, all of these different data sets would be provided to the processing  1397  to determine updates to processing parameters, with the resultant delays in feedback due to the transfers between the different facilities. In contrast, under the arrangement of  FIG.  13 B , the different data sets can be used to perform the machine learning (e.g., generalized linear models, gradient boosting machine, neural networks, randomized trees) study to generate the interpolation functionality, such as interpolation algorithms for use in advanced process control software, that can be used within the fabrication process for feedback and automated process control based on the inline testing. 
     With respect to the processing  1397 , including the application of machine learning, this can be implemented by one or more processors using hardware, firmware, software, or a combination of these. The software used can be stored on one or more processor readable storage devices described above to program one or more of the processors to perform the functions described herein. The processor readable storage devices can include computer readable media such as volatile and non-volatile media, removable and non-removable media. By way of example, and not limitation, computer readable media may comprise computer readable storage media and communication media. Computer readable storage media may be implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data. Examples of computer readable storage media include RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can be accessed by a computer. A computer readable medium or media does (do) not include propagated, modulated or transitory signals. The training phase is typically more computationally intensive and can be performed in the cloud, for example, while inferencing may be performed more locally, such as on computational facilities at the fabrication facility. Examples of the processing units that can be used for the machine learning can include one or more of CPU (central processing unit), GPU (graphic processing unit), TPU (tensorflow processing unit), and NPU (neural processing unit) devices, among others. 
     The discussion so far has mainly focused on virtual PLY data interpolation, but the techniques can also be applied to metrology, such as critical dimension data for the memory hole bowing as illustrated in  FIG.  5   . To obtain all chip metrology data virtually, machine learning (such as gradient boosting machine and generalized linear model techniques) is performed by measured wafer CD values and its die sort characteristics and then, by using the correlation, all virtual CD data can be interpolated. This can be illustrated with respect to  FIG.  14   . 
     The following focusses on the critical dimension example, and more specifically to its application to upper memory holes, but can be extended to other metrological data inspection steps. In addition to the critical dimension measurement of line widths and hole diameters at specified locations on a semiconductor wafer that can be performed by a scanning electron microscope, for example, other examples of metrology inspection can include overly and thicknesses of films. In forming a semiconductor wafer, thin films are often applied on the surface of the wafer and their thickness can be measure by use of an ellipsometer, for example. With respect to overlays, a metrology system can check the accuracy of a shot overlay (such as by an overlay tool) of layer patterns as transferred on to the wafer. 
       FIG.  14    present an embodiment for a sequence schematically representing virtual critical dimension interpolation at the wafer level. To screen with better accuracy, chip level interpolation and virtual upper memory hole CD values are generated for data wafers and chips without directly measured CD data. A correlation of die sort data (such as bad block count or other circuit characteristics like resistance, current, or threshold voltages) with CD measured data is obtained, and then, by using the reference correlation, data can be interpolated for chips and wafers for which the data was not directly measured. All CD related values can then be interpolated, and the correlation to early failure rate DPPM data (such as in term of block failure rate) checked at chip level to decide upon wafer/chip rejection criteria for all samples. 
     The sequence of  FIG.  14    is similar to that described above with respect to  FIG.  9   . At far left,  FIG.  14    illustrates the measurement of chip level CD data from a subset of the memory die or other integrated circuits on a wafer. In the example, for a sample wafer a subset of around a quarter of the chips are selected for testing, where these include a series of chips running both vertically and horizontally, as illustrated by the darker squares, and series of diagonal chips, as represented by the intermediate gray squares. As represented at center left, machine learning is applied to perform universal line fitting of  1401  from the measured data points to generate a correlation between CD values and the die sort index. As described above, the machine learning used can be one of several techniques, or a combination of such techniques, depending on the embodiment, including: deep neural networks (DNNs); distributed random forest (DRF), extremely randomized trees (XRT); generalized linear models (GLMs); and/or gradient boosting machine (GBM). 
     As represented schematically at center right by the darkening of the whole wafer, virtual CD interpolation can be applied to all, or at least a majority of, chips and wafers of a lot. At far right, the relationship of the all-chip interpolated virtual CD data to block failure rate can then be used for studying the early failure rate (i.e., block failure rate). As illustrated at the far right of  FIG.  14   , different ranges of virtual CD values correspond to different block failure rates, with rejection criteria determined as represented by the broken line. 
     By using the process illustrated by the sequence of  FIG.  14    the ratio of the number of chips with CD data can become 100%, whereas the percentage of memory dies that are actually measure by scanning electron microscope is typically, depending on the feature being measured, in the range of 1% to a few hundredths of a percent. This increase in chip level data can be used to detect grown bad block (i.e., bad blocks that occur one a device is in use) failures that, previously, could not be readily detected due limited CD data and, more generally, be used for cherry picking of test samples and studies of process improvement. 
       FIGS.  15 A and  15 B  respectively present conventional sampling for quality control and the use of virtual quality control by machine learning to illustrate the advantage of incorporating virtual quality control data for the critical dimension example. In the sequences of  FIGS.  15 A and  15 B , the same sequence is shown, but the amount and location of testing and resultant incorporation of processing feedback is different. Relative to  FIGS.  13 A  and  13 B, block  1505 / 1555  differ in that they now relate to CD or other metrology data rather than PLY data. 
     In the conventional sampling of quality control values sequence of  FIG.  15 A , the cleanroom operations are the fabrication and inline testing processes and include cleanroom in at block  1501 , followed by various proceeding steps to fabricate and prepare a sample for imaging at block  1503 , corresponding to step  601  of  FIG.  6    in which the samples of the integrated circuits are prepared for imaging. Block  1505  is the metrology data collection (e.g., CD for upper memory hole scanning electron microscope), corresponding to step  603  of  FIG.  6   . In the conventional sampling of  FIG.  15 A , only a relatively small amount of testing is performed, due to time and cost limitation and also due to resultant yield loss for tests that render the device subsequently unusable. For example, only a small percentage of the wafer (e.g., ˜2-5 per lot) are tested. Due to the limited data volume, the correlation between the collected CD data and bad block count is low, so that that amount of feedback and advanced process control that can provided to earlier processing steps is consequently limited. The memory dies leave the clean room at block  1507 , after which subsequent testing can be performed on the completed die. 
     Die sort follows at  1509 , including bad block and other testing (e.g., resistance, current, threshold voltages), followed by additionally early fail rate (EFR) and other backend testing at block  1511  to determine defect rates (DPPM). At both the die sort and backend testing, there is again weak correlation or a lack of data due to the low proportion of samples used in some tests. This again results limited feedback for the processing operations. Additionally, the backend tests of block  1511  and, in some cases, die sort in block  1509  are often performed at different physical locations, involves shipping of devices and consequent delays for even what feedback is available. 
       FIG.  15 B  illustrates the incorporation of quality control data by machine learning and is arranged in blocks similar to those of  FIG.  15 A , where blocks  1551  and  1553  can be as described for blocks  1501  and  1503 . The CD SEM or other metrology data of block  1555  is similar to the CD SEM or other metrology data of block  1505 , except now, by use the virtual quality control data obtain by interpolation as illustrated in  FIG.  14   , feedback/advanced process control data for all (or at least the majority) of wafers of all lots can be generated. The memory dies leave the clean room at block  1557 , after which subsequent testing can be performed on the completed die. 
     Die sort again follows at  1559 , at which can be performed by bad block and other testing, followed by additionally early fail rate (EFR) and other backend testing at block  1561  to determine defect rates (DPPM). The testing and samples of blocks  1559  and  1561  can be the same or similar as for blocks  1509  and  1511  of  FIG.  15 A , but now the machine learning techniques described above are applied to perform a prediction fail model and cherry picking criteria that are applied at block  1555  to interpolate the virtual quality control data. The prediction fail model study and determination of cherry picking criteria can be performed at regular intervals (weekly, for example). By using machine learning, such as generalized linear models or gradient boosting machine embodiments, for limited die sort characteristics, all production chip data can be interpolated from the limited measured data, which can then be used for cherry picking and prediction of failure issues. By optimizing quality control measurement volume with virtual critical dimension methods, other quality control steps can be minimized, improving cycle times and virtual fabrication concept feasibility. In terms of the physical facilities for the processes of  FIG.  15 B , these can be as described above with respect to  FIG.  13 C . 
       FIGS.  16  and  17    are flowcharts for embodiments of virtual PLY interpolation and virtual CD interpolation, respectively corresponding to the schematic representations of  FIGS.  13 B and  15 B . The flow of  FIG.  16    begins at step  1601  with the manufacturing of a non-volatile memory device or other integrated circuit at a fabrication facility according to a first set of processing parameter values. This can be any of the processing processes used, for the main embodiments here, to form non-volatile memory circuits, such as for the 3D NAND memory described above, as well other architectures and other non-volatile memory technologies (e.g., NRAM, ReRAM). A subset of the integrated circuits are selected during the manufacturing process as test samples for a first set of tests at step  1603 , with the one or more first test done at step  1605 . As discussed above, the number of die selected for this inline testing is typically a small percentage of the production. The inline test data of step  1605  can be generated by a scanning electron microscope and can include both the PLY data related to a sacrificial etch and the lower memory holes, as in the primary example above, also other inline test data. At step  1607  one or more second tests on the integrate circuits are performed after completing the manufacturing process, where this can include one or both of die sort stage testing (such as bad block counts) and other backend testing (such as early failure rate data). 
     Based on the results of the first tests and the second tests, one or more processors can then apply machine learning to determine a correlation between the two sets of tests for the integrated circuit at step  1609 , where the machine learning can use one or more of generalized linear models, gradient boosting machine, deep neural networks, distributed random forest, or extremely randomized trees, for example. Once the correlation is established, additional examples of the integrated circuit can be manufactured at step  1611  and the second test performed on these additional examples at step  1613 . Based on the correlation from step  1609  and test results from step  1613 , at step  1615  results for the first tests (e.g., PLY data) can interpolated as described above with respect to  FIGS.  9  and  13 B , for example. The interpolated results of step  1615  can be used part of the feedback/advanced process control for adjusting the processing parameter values at step  1617 . The results of the second test values can then also be used for cherry picking of test samples at step  1619 . 
     The flow of  FIG.  17    is for the example of virtual CD interpolation, corresponding the schematic representations of  FIG.  15 B , and begins at step  1701  with the manufacturing of a non-volatile memory device or other integrated circuit at a fabrication facility. This can be any of the processing processes used, for the main embodiments here, used to form non-volatile memory circuits, such as for the 3D NAND memory described above, as well other architectures and other non-volatile memory technologies (e.g., NRAM, ReRAM). A subset of the integrated circuits are selected as test samples at step  1703 , where, as discussed above, the number of die selected is typically a small percentage of the production. At step  1705  one or more first tests are performed on the first test samples to determine a corresponding one or more critical dimension or other metrology values for each of the first test samples. At step  1707  one or more second tests on the integrate circuits are performed for the first plurality of the integrated circuit, where this can include one or both of die sort stage testing (such as bad block counts) and other backend testing (such as early failure rate data). 
     Based on the metrology values and the results of the second tests, one or more processors can then apply machine learning to determine a correlation between the two sets of test results for the integrated circuit at step  1709 , where machine learning can use one or more of generalized linear models, gradient boosting machine, deep neural networks, distributed random forest, or extremely randomized trees, for example. Once the correlation is established, additional examples of the integrated circuit can be manufactured at step  1711  and the second test performed on these additional examples at step  1713 . Based on the correlation from step  1709  and test results from step  1713 , at step  1715  results for the virtual critical dimension or other metrology values can interpolated as described above with respect to  FIGS.  14  and  15 B , for example. 
     Consequently, the techniques described above for virtual quality control interpolation and process feedback can significantly improve costs and efficiencies in the manufacture of non-volatile memories and other integrated circuits by generating more extensive test data and more rapid feedback. In addition to the specific examples and embodiments presented, the techniques can also be applied to selective testing, where if correlations between die sort and inline data are determined, it can be known whether or not a chip or wafer can pass die sort testing without the die sort testing with it having to be performed, allowing the die sort testing to be fully or partially skipped, contributing to die sort test cost reductions. 
     In an additional set of embodiments, further use is made of data that is often obtained as part of the die sort or inline testing process of integrated circuits, such as the multi-layer memory structures described above. In such a complex structure, composed of multiple complex circuitry layers, although it would be highly useful to have information on the features of each of the layers, such as CD values for memory holes, it is impractical to directly measure such values for more than a small subset of the wafers, chips, and layers due to the time and expense of such testing and also since many of these test are destructive to the device. However, it is common to perform tests of other properties of the circuit for many, even all, of the circuit elements of a circuit for their electoral properties. For example, during die sort or inline testing of a multi-layer memory circuit it is common to test many or all of elements such as the word lines for capacitance and resistance values. By applying techniques such as those presented above, based on testing of a subset of the devices for features such as memory hole CD values, the electrical data from die sort and/or inline test data can be used to provide virtual metrology data for features such as memory hole profiles and other features of the circuit. 
     Although the following discussion will again be presented in the context of a multi-layer non-volatile memory structure and focus on the feature of memory hole CD of the layers, it can be more generally applied to other circuit features that can be modelled and predicted based upon measured electrical or other data determined as part of the inline, die sort, or other test data collected for the device. 
     As discussed above, memory hole CD control is an example of an important feature in the fabrication of the 3D memory structures illustrated in  FIGS.  1  and  2    as it is directly related to yield and reliability. As such, it would be highly useful to be able to obtain memory hole CD profiles for all wafers and dies. However, it is not practical to obtain such information as part of inline or die sort testing for all layers of all dies and wafers, due to the time and expense this would involve, but also as such tests are often destructive to the device. In a typical arrangement, inline or die sort testing will only perform SEM or optical CD measurements for selected features and then for only a small percentage of the chips, such as performing optical CD testing on only a few selected word line layers for only a few tenths or hundredths of a percent of the memory dies and making SEM CD measurements on the top of a similarly small percentage of the memory dies. There are, however, other inline and die sort test that are performed on most or even all of the layers of the memory die. 
     As part of one or both of the inline and die sort testing, it is common the make electrical measurements of the die&#39;s circuitry to determine defective memory devices or defective portions, such as bad memory blocks. For example, the word lines of each layer of each die may be measured for its resistance and capacitance as part of die sort and device characterization, as are the electrical properties of other elements. This information on the electrical properties of the word lines running in one direction (the “X” direction) of a layer can then be used to predict the CD values of features in the other direction (the “Y” direction) of the layer through machine learning. The following discussion develops a model and prediction system for memory hole profiles based on a machine learning data set for such memory hole profiles that can be used to estimate the memory hole profiles for all wafers and chips. 
       FIG.  18    illustrates some of the components of an embodiment of a virtual metrology approach for use of die sort and inline test data. The process includes a virtual methodology resistance/capacitance (VMRC) model creation  1801  for the creation of an RC correlation model and memory hole profile prediction  1803  to fit the memory hole value for each word line to match the word line resistance/capacitance (WLRC) data. One set of the inputs to the VMRC model creation can include inline testing data  1811  including CD values for features such as memory holes, trenches (e.g., silica trenches etched into the structure such as used to separate regions), and other feature as determined by SEM and optical testing as determined for a subset of the layers of a subset of the memory on a subset of the wafers. The inline testing data  1811  for these subsets can also include thickness measurements for layers of the memory structure of  FIGS.  1  and  2    such as dielectric layers and the various layers of the word line/control gate structures. The die sort data testing data  1813  inputs for the virtual methodology resistance/capacitance model creation can include electrical measurements such as word line resistance/capacitance data. In additional to resistance and capacitance values for word lines, electrical data for other circuit elements, such as select lines, bit lines, source lines, logic lines, or other features appropriate to a given circuit design from die sort can similarly be used depending on the embodiment. In addition to the inline data  1811  and die sort data  1813 , input to the model creation can also include electric design rule (EDR) and design data  1815 , such as word line hook-up (WLHU) resistance. Based on these inputs, a virtual methodology RC (or other electrical data) correlation model  1821  can be created. 
     Once the virtual methodology correlation model  1821  is created based the input of sample data from a subset of devices, it can then be used for memory hole profile or other feature prediction  1803 . On the profile prediction side, the inputs can include the die sort data  1833 , such as the word line RC values for all of the word lines or other electrical data for which the correlation model  1821  was trained. Other inputs can include data such transmission electron microscope data or use OCD data (e.g., scatterometry OCD metrology)  1831  on features such as trench CD profiles, which can be a one-time, general measurement for a device. The correlation model then uses these inputs  1821  to fit, in this example, the memory hole CD value for each word line to match the die sort word line RC data to generate the output  1835  for the memory hole CD profile. 
     Consequently, as illustrated in  FIG.  18   , the virtual methodology approach to modelling and prediction allows for creation of a correlation model based on one or more of inline, die sort, and EDR and design inputs automatically. EDR and design inputs can be fixed for a given technology and the inline and die sort inputs can be used to create a unique model parameter for a batch of lots. In the example embodiment, this can provide die level memory hole profile through the correlation model and the inputs of die sort word line RC values from all of the tested word lines. 
       FIG.  19    is a virtual metrology platform diagram for an embodiment based on word line RC values, where the testing and processing facilities can again be as described above with respect  FIG.  13 C , although the inline and die sort data can now include the examples discussed here (e.g., word line RC data from die sort testing). The data preparation process has a training data processing component, that can include a data query, data assembly, and data filtering and a prediction data processing component, that can include data query and data assembly. The data query for the training data processing can include retrieving geometry information from an inline database, such as memory hole (MH) and silica trench (ST) SEM data and optical CD data such as thicknesses of the circuitry structure&#39;s layers. The data query for the training data processing can also include retrieving electrical measurement from a die sort database, such as word line resistance and RC values. Data assembly in the training data processing can include categorizing data according to different word line metal processing and the version of die sort testing used and performing a data concatenation based on processing lot/wafer IDs. The data filtering can determine key correlation parameters and perform multivariate outlier detection, such as by using a Mahalanobis distance method, for example. 
     With respect to the prediction data processing, in the data query phase trench SEM information is retrieved for the lots for memory profile prediction from inline database, corresponding to  1831  of  FIG.  18   , and the die sort data for all word line level RC information is retrieved for interested lot/wafer/dies from a die sort database, corresponding to  1833  of  FIG.  18   . At data assembly, data concatenation is performed based on lot/wafer/die ID. 
     Once the training data has been processed, it can be used in the creation of the virtual methodology RC correlation model, corresponding to  1821  of  FIG.  18   . The model creation includes a word line RC model, an array word line resistance/capacitance calibration, and determination of a correlation model. The word line RC model can be a physics-based word line RC model that is established outside of the platform. As this process uses an analytical model, it is not software dependent. Auto-calibration with training data can be modelled using, for example, least-square fitting. The array word line resistance and capacitance correlation process can use the geometry information from training data set and calibrated word line RC model to calculate array portion word line resistance and word line capacitance. To construct the correlation model, the word line hook-up resistance can be calculated from EDR and layout information, where this can be a one time operation for a given technology, independent of training data set. Machine learning can then be used to create correlations between die sort RC data, calculated word line resistance and capacitance values, and word line hook-up resistance values. As described above, the machine learning can be based on one or more techniques such as generalized liner models (GLM) including lasso regulation, random forest models, gradient boosting machine (GBM) models, and neural networks. 
     Once a correlation model is created, this can be used with the concatenated data assembled in the prediction data processing for wafer/die level memory hole profile prediction. In a profile prediction phase, silica trench CD for each word line can be generated based on a general silica trench profile and inline silica trench SEM correction. The created virtual metrology RC model, prediction data set, and silica trench profile are then used to calculate MH profiles for each wafer and die. Analysis and visualization (A &amp; V) then follows, where this can include generating memory hole CD across-wafer distribution map for each word line level, calculating CD variation, plotting memory hole profiles for all dies on a wafer, and calculating average profile. 
     Considering some of the components or modules of  FIG.  19    in more detail, with respect to the word line RC model calibration, the word line RC model can be a physics-based model established based on technology computer-aided design (TCAD) leanings, which can incorporate effects such as current from word lines seeping through memory holes, fringing field effects between word lines and surrounding layers, and other effects that can be properly included. Within word line RC model input parameters, geometry information can be obtained from an inline database. The word line resistivity information depends on process used for word line metal and can be automatically extracted based on each inline geometry/die sort word line resistance data set. 
     With respect to auto-calibration of the word line RC model, the word line resistance can be calculated based on the word line RC model with geometry inputs from inline testing. Least square fitting can then be used to search for the best word line resistivity model formula and parameter values based on the predicted versus actual word line resistance, such as illustrated in  FIG.  20   , in order to have calculated word line resistance matching to the die sort testing measured word line resistance. In this way, the resistivity parameters can be automatically calibrated. 
     With respect to virtual metrology RC model creation, the die sort measured word line RC values can be determined based on number of counts of clock numbers needed to rise a word line signal to certain voltage. It includes the contribution from array properties such as word line resistance, word line capacitance, word line hook-up resistance (including contributions such as wiring resistance, transistor resistance, etc.), and system shift. The machine learning method is used here to create correlation between die sort measured word line RC, calculated array portion word line resistance and capacitance component, and word line hook-up resistance.  FIG.  21    illustrates an example to show predicted total word line RC versus die sort measured word line RC values, showing good correlation of R2˜0.73. 
     As noted above, one of several machine learning model techniques, or a combination of such techniques, can be applied depending on the embodiment, including: deep neural networks; distributed random forest, extremely randomized trees; generalized linear regression models; and/or gradient boosting machine. The results from the different techniques can have different levels of accuracy and relative advantages. For example, generalized linear regression models might provide good correlation between layers but with a relatively large difference between predicted and actual values, while a gradient boosted machine may have poorer correlation of each layer but with a smaller difference between predicted and actual values. 
       FIG.  22    illustrates inputs, predictions, and, for comparison, actual data for virtual metrology RC prediction of wafer level average memory hole profiles for a circuit structure such as illustrated in  FIG.  2   . The vertical axis in each of the individual figures is the depth into the structure and includes data for the upper tier of the memory holes (though layers above the joint region circled at  203 ) and the lower tier of the memory holes (through layers below the joint region circled at  203 ). The inputs in this embodiment include the mean die sort RC values from the die sort database, the word line hook-up resistance values calculated based on EDR and layout, and the general profile of the silica trenches from optical CD data. From these inputs, the virtual RC model can predict a mean memory hole CD profile as illustrated to the right of the inputs. For comparison, at far right is actual transmission electron microscope (TEM) and/or OCD data for memory hole CD values obtained by cutting wafer samples. As illustrated, the memory hole CD values predicted by the model match the actual TEM and/or OCD data well. 
       FIG.  23    illustrates die level memory hole profile data from virtual metrology RC prediction. At left, the memory holes profiles for all dies on a wafer are plotted as memory hole CD versus depth to show the overall shape. At right the memory hole CD variation for each word line level is calculated as the sigma values of the memory hole CD values versus depth. 
       FIG.  24    is a flowchart for an embodiment of the virtual metrology techniques described above with respect to  FIGS.  18 - 23   . The flow of  FIG.  24    is similar to that of  FIGS.  16  and  17    and can again be performed in the context of  FIG.  13   , but where the tests and data are now for the generation of a virtual metrology based on the electrical properties of the layers of a multi-later circuit structure, such as, for example, determining memory hole profiles of a 3D memory circuit based on word line RC values. Beginning at step  2401 , integrated circuits having multiple layers of circuitry, such as the 3D NAND memory example, are fabricated according to a set of processing parameters at a fabrication facility  1391 . 
     The test samples for the integrated circuit are selected or received at step  2403  and one or more first tests are performed on the test sample to determine corresponding metrology data values for the test samples at step  2405 . The tests at step  2405  can include one or more of inline testing at the fabrication facility, die sort testing at the die sort facility  1393  (which may or may not be at the same location as the fabrication facility  1391 ), or other testing and testing locations, such as backend testing. Examples of such tests can include SEM CD data, optical CD data, and TEM data, as described above with respect to  FIGS.  18  and  19   . A second set of tests are performed on the samples at step  2407 , where these second tests include determining values for electrical properties of a subset of the circuitry layers for test samples. In the example embodiment, these tests can be die sort testing to determine word line RC values of selected layers by applying a voltage to the word lines and determine the time for voltage level on the word line to reach a specified voltage level in response. 
     The results of the first tests and second tests can then supplied to the processing facility  1397  to performing a machine learning process at step  2409  to determine a correlation between the metrology data values and results of the second tests, as described with respect to  FIGS.  18  and  19   . This process can also include physics-based models for features such as word line RC values. The processing at the processing facility  1397  can be as described above with respect to  FIG.  13 C  and can also include selection of the machine learning model used. Once the machine learning process determines the correlation between metrology (e.g., features such memory hole profiles) and the electrical properties of the layers (e.g., word line RC values), the virtual metrology can be applied to other examples of the integrated circuit. The additional examples are received at step  2411  and at step  2413  values for the electrical properties of a first plurality of the circuitry layers, such as word line RC values for all of the word lines of all layers being determined at the die sort facility  1393 . The data from step  2415  can be provided to the processing facility  1397 , where at step  2415  metrology data values can be interpolated for the circuitry layers of the second plurality of the integrated circuit from the correlation and results of the values for the electrical properties of the first plurality of the circuitry layers. Based on the interpolated metrology data values from step  2415 , at step  2417  the processing parameters for the integrated circuit can be adjusted and provided to the fabrication facility  1391 . At step  2419 , the integrated circuit can then be fabricated using the adjusted processing parameters. 
     As described above, the virtual metrology RC approach can provide a fast virtual metrology method (e.g., minutes) for physical dimension measurement compared to traditional TEM methods (e.g., days). This approach is able to use existing limited inline data and rich die sort word line RC data to predict entire memory hole profiles at each word line level for each wafer and each die. This allows further die sort yield/reliability analysis for all dies. The virtual metrology RC prediction can be automated without engineer interaction and the model build is independent of the die sort version used, such that it need not be rebuilt for each one. 
       FIG.  15 B  illustrates the incorporation of quality control data by machine learning with die sort characteristic data to be able to obtain a clear correlation and detail study for all of the memory die and wafers. The following discussion presents embodiments to further include inline quality control data to generate virtual inline quality control data. This can be illustrated with respect to  FIG.  25   . 
       FIG.  25    presents the incorporation of virtual inline quality control data (IQC) into the process of  FIG.  15 B  to develop the modelling and prediction system of the virtual inline quality control data using by die sort characteristic data and measure inline quality control report data, where examples of inline quality control that can be measured in the clean room at step  2553  can include gate thicknesses, critical dimension (CD) data from memory holes, and overlay of photolithography, among others as discussed above. The inline quality control data can reported as a large data table and include information from the fabrication facility including not just die sort and inline quality control data, but also history for different fabrication lots, where this file is used for yield analysis with machine learning and/or statistical methods. 
       FIG.  25    is laid out similarly to  FIG.  15 B  and is similarly numbered, where blocks  2551 ,  2553 ,  2555 ,  2557 ,  2559 , and  2561  can be as described with respect to  1551 ,  1553 ,  1555 ,  1557 ,  1559 , and  1561 , but where blocks  2553  and  2555  will now also include virtual quality control using machine learning with inline quality control report data to provide feedback and advanced process control prediction to provide a clear correlation detail study for all of the memory dies/wafers. More specifically, the embodiment of  FIG.  25    incorporates two step modelling using a “System A”, for virtual quality control using machine learning with die sort characteristic data, and a “System B”, for virtual quality control using machine learning with the inline report data. By optimizing quality control measurement volume with a virtual PLY (photo-limited yield) method, the quality control steps can be minimized, contributing to cycle time improvements. 
       FIG.  26    is a flowchart of an embodiment for calculating virtual inline quality control data using the two step approach. In the first modelling stage of system A, at step  2601  the system creates a virtual inline quality control interpolation model by using the inline quality control data from block  2553  with the die sort characteristic data from block  2559 , where the model can be created since the die sort data is not sampling data. Although  FIG.  26    is for an embodiment using die sort characteristic data, other post-manufacturing test data (such as backend testing from block  2561 ) can alternately or additional be used. At step  2603  the interpolation of the virtual inline quality control data is calculated by using the die sort characteristic data. The system A steps can be much as described above with respect to  FIGS.  15 B- 24   . 
     The second modelling of system B then follows at steps  2605  and  2607 . Step  2605  creates a virtual inline quality control model through interpolation of inline quality control data and the inline data report from the clean room of block  2553 . Using the model and the inline data report for the lots and wafers from the clean room, the virtual inline quality control values can then be calculated in the clean room at step  2607 . In some embodiments, the second modelling of system B can done with multiple machine learning models and, if so, at step  2609 , the different machine learning models are then evaluated to determine which provides the most accurate predictions. As before, the models can include a generalized linear model (GLM) based on linear regression or non-linear regression models such as gradient boosting machine (GBM) or a random forest (RF) model, where the particular model available for determination at step  2609  can be dependent on the embodiment. As noted above, linear regression models provide simple modelling that is easier to understand, whereas the non-linear models are more complex but can provide good prediction values. Finally at step  2611 , the virtual inline quality control data can be calculated in the clean room with the inline report data. 
     The two step modelling process allows for the system to have no missing values that are not covered by the virtual inline quality control data. Both of systems A and B use a similar flow, but with differing input data and output data. More specifically, system A uses die sort characteristic data and actual inline quality control data as inputs, with virtual inline quality control output data to interpolate sampling data. System B uses virtual inline quality control and fabrication facility data to establish a clear correlation of fabrication facility data and predict the inline quality control data from fabrication facility data. 
     In the conventional approach of  FIG.  15 A , only a relatively small percentage of the inline quality control data is used, although much of the inline quality control sampling data exists in the clean room. Consequently, it difficult to determine a clear relationship between the inline quality control data and processing paraments and to create a machine learning based prediction model as the low data volume results in low accuracy prediction or that machine learning may not even be executable. The two step modelling process of  FIGS.  25  and  26    can exchange the missing inline quality control data for virtual inline quality control data through interpolation provide data from all, or a large majority, of the inline quality control data. The interpolation of the virtual inline quality control data is generated by using die sort characteristic data and then creating a prediction model from the inline processing data report. A detail flow of the system A model and prediction system for virtual inline quality control with die sort characteristic data was presented above with respect to  FIGS.  18  and  19   .  FIG.  27    presents an embodiment for the system B case. 
       FIG.  27    is a detail system flow for a system B embodiment of the model and prediction system for virtual inline quality control with the lot/wafer report. The information of  FIG.  27    is similar to that presented in the flowchart of  FIG.  26   , but helps to illustrate the relationship of the different operations. In block  2701  cleanroom lot/wafer report data is received. This can include processing history, such as the equipment used, and the processing recipe, processing times, as well as inline quality control data, such as critical dimension values. The virtual inline quality control data from system A is retrieved in step  2703 , where this can include virtual critical dimension data, including that obtained by interpolation, from die sort modelling. 
     Data pre-processing follows at step  2705  based on the retrieved lot/wafer data from  2701  and virtual IQC data from  2703 . The pre-processing can join the lot wafer report data with the virtual inline quality control data table values. From these data, categorical data encoding can be performed, where missing (or redundant) data values can be excluded. Following pre-processing, modelling and evaluation can follow at block  2707 . Various machine learning models, including generalized linear models (GLM) with LASSO regulation, random forest (RF) models, and gradient boosting (GBM) models, among others, where the results can be evaluated and confirmed based on R-squared, variable importance, and scatter plot results to determine the relative accuracy of the models. Prediction then can follow at  2709 , with new lot/wafer data reports from the clean room, with categorical data encoded. Based on results of block  2707 , a user can choose a model that can then be used to calculate the predicted value by using the selected model with the new lot/wafer data report from the clean room to provide the virtual critical dimension data from the lot/wafer modelling. As with the earlier embodiments, processing for the modelling and prediction system for the virtual inline quality control data can done as described above with respect to  FIG.  13 C  in the processing facility  1397 . 
     As described with respect to  FIGS.  25 - 27   , modelling and prediction of virtual inline quality control data can be done using die sort characteristic data and inline quality control report data. The system can calculate the virtual inline quality control data such as gate thickness, critical dimension data for memory holes, and photolithography overlay values, for example, from die sort characteristic data to interpolate the inline quality control data in the clean room for the inline quality control report data. 
       FIG.  28    is a flowchart for an embodiment of the fabrication of an integrated circuit incorporating modelling and prediction of virtual inline quality control as described above with respect to  FIGS.  25 - 27   . The flow of  FIG.  28    is similar to that of  FIGS.  16 ,  17   , and  24  and can again be performed in the context of  FIG.  13 C , but where the tests and data are now for the modelling and prediction of virtual inline quality control. Beginning at step  2801 , integrated circuits are fabricated according to a set of processing parameters at a fabrication facility  1391 . 
     The first virtual inline quality control data model for the fabrication of the integrated circuits is created in the processing facility  1397  at step  2803  using inline quality control data of test samples of the integrated circuit from the fabrication facility  1391  and post-fabrication test data of the test samples from the die sort testing in the die sort facility  1393 , backend testing from the backend facilities  1395 , or a combination of these. At step  2805  the processing facility can then interpolate virtual inline quality control data for the fabrication of the integrated circuits using the first set of processing parameters from the first virtual inline quality control data model and the post-fabrication test data. The test data can be various inline, die sort, and backend testing as described above. 
     In step  2807 , the processing facility  1397  can create the second virtual inline quality control data model for the fabrication of the integrated circuit using the first set of processing parameters from the interpolated virtual inline quality control data and an inline data report for the fabrication of the integrated circuits using the first set of processing parameters. The second virtual inline quality control data model can then be provided to the fabrication facility  1391  and be used, in the clean room, for interpolating virtual inline quality control data for the fabrication of the integrated circuit using the first set of processing parameters from the second virtual inline quality control data model and the inline data report at step  2809 . Based on the interpolated virtual inline quality control data from step  2809 , at step  2811  the processing parameters for the integrated circuit can be adjusted and, at step  2813 , the integrated circuit can then be fabricated using the adjusted processing parameters. 
     As noted above with respect to blocks  2707  and  2709  of  FIG.  27   , for example, a number of different machine learning models can be used for modeling and evaluation, with the user selecting from these models. The more accurate the model that is determined, the higher the accuracy of the predictions that the systems will provide. The following considers the application of autotuned machine learning to determine the best choice of model. 
     More specifically, it is important to find the best model to predict the virtual inline quality control data accurately in the system A and system B presented above with respect to  FIGS.  25 - 28   . As presented above, system A and system B can execute several models (e.g., GLM, GBM, RF), but do not include either the fine tuning of the hyperparameters for each model or Deep Learning (DL). Autotune machine learning (AutoML) can be used to find the best model of several models, such as GBM, GLM, RF, and DL, and then execute hyperparameter tuning by using a random grid search technique or other optimization techniques. 
     In machine learning, a hyperparameter is a parameter whose value is used to control the learning process, as opposed to other parameters (e.g., node weights) that are determined as part of the training process. Hyperparameter tuning is an optimization problem of determining a set of optimal hyperparameters for the learning algorithm of a model. For a given application, the same type of machine learning model can require different constraints or learning rates to generalize to different applications and different data patterns. These hyperparameters can be tuned so that the model can optimally solve the machine learning problem by finding a set of values for hyperparameters that yields an optimal model by minimizing a cost or lost function on given independent data. 
     Consequently, an important consideration in machine learning is the optimization of the hyperparameters, where these can be local minima and global minima. The number and specifics of hyperparameters vary from model to model. In the embodiments presented above, models such as GLM, GBM, and RF have been used in the modelling and prediction system of virtual inline quality control, but did not include hyperparameter tuning within of the system. Prediction accuracies can be improved through hyperparameter tuning to further optimize the models and then select between the optimized models; however, this can be difficult to perform manually for each of the multiple models, but can be addressed by introducing automated machine learning for the tuning into the flows presented above. For example, grid search across a multiple hyperparameter space can be used. To take one example embodiment, for a 2 hyperparameter optimization considering 10 different values each, a total of 100 different combinations can be considered to determine the global minimum of discretized hyperparameter values. 
       FIG.  29    is a detail system flow for a system A and system B embodiment of the modelling and prediction system for virtual inline quality control with the lot/wafer report to highlight modelling evaluation and selection.  FIG.  29    is similar to  FIG.  27   , but highlights some of the features relevant to the incorporation of hyperparameter tuning. The flow of system A runs across the top of  FIG.  29    above the broken line, with the flow of system B below. In system A, data is retrieved at block  2901 , where this can include die sort characteristic data and actual upper memory hole wet-etch optical critical dimension or other critical dimension data. At block  2911  during pre-processing, the die sort characteristic data can be joined with the optical critical dimension or other critical dimension data to create pre-ranking (i.e., variable importance) for a selected first one of the models (e.g., with a gradient boosting machine model), which can presented as a table of values. The pre-ranking for the selected model can then be used, as described below with respect to  FIG.  31   , for the autotuned machine learning process. 
     In system B, at block  2903  the received data can include process history of the fabrication process, such as the equipment used, recipe, timings, and other processing related data, and also virtual memory hole wet etch critical dimension data and other data interpolated from system A as described above. At block  2913  during pre-processing the fab data can be joined with the virtual inline quality control data to create pre-ranking (i.e., variable importance) for a selected one of the models that can be the same as for system A (e.g., with a gradient boosting machine model) or another model, which can presented as a table of values. The pre-ranking for the selected model can then be used, as described below with respect to  FIG.  31   , for the autotuned machine learning process. 
     For both of system A and system B, modelling and recommendation follows at step  2921 , where, in the approaches presented so far, hyperparameter tuning is not used. As discussed with respect to embodiments presented above (i.e., with respect to  FIG.  27    and earlier figures), the different models (generalized linear models with LASSO regulation, random forest models, gradient boosting models, and so on) can them be evaluated and selected based on metrics such as R 2 , the coefficient of determination that is the proportion of the variation of a dependent variable that is predictable from the independent variables. Based on the recommendations of block  2921 , the best model for system A can then be selected in block  2931  and the best model for system B can be selected in block  2933 . On the system A side at block  2931 , the chosen model can be applied to retrieved new die sort characteristic data to determine interpolated virtual quality control data, such as the upper memory hole wet etch layer optical critical data values for all die and wafers. On the system B side at block  2933 , the chosen model can be applied to new data retrieved from the fabrication facility to generate interpolated virtual quality control data, such as the upper memory hole wet etch layer optical critical data values for all die and wafers, within the clean room of the fabrication facility. 
       FIGS.  30  and  31    are embodiments for the portion of the system flow related to choosing the best model for system A without and with hyperparameter tuning, respectively. The system flow for system B will be similar and can be independently determined. When hyperparameter tuning is not used, the receiving and preprocessing of data is at block  3001 , which can correspond to the receive data ( 2901 ) and data pre-processing ( 2911 ) blocks of  FIG.  29   . In the system A example this can again be the die sort characteristic data and actual optical critical dimension data as discussed above, with their data tables then joined in preprocessing. For this system B case, block  3001  would similarly correspond to the blocks  2903  and  2913  of  FIG.  29   . At block  3003  the models are evaluated and then selected, such as described above with respect to  2921  of  FIG.  29  or  2707    of  FIG.  27    with respect to parameters such as R 2 , the coefficient of determination, as described above in detail with respect to  FIG.  7    and subsequent figures. In the process of  FIG.  30   , the evaluation and recommendation is made without hyperparameter tuning for the models, so that for each of the models the user would evaluate R 2  or other metrics to select the model to use for the prediction phase of block  3005 , such as for calculating virtual critical dimension data from new die sort characteristic data, as in block  2931  of  FIG.  29    for system A. For system B, the prediction could correspond to block  2933 . 
       FIG.  31    illustrates the incorporation of hyperparameter tuning into the processes of  FIG.  29   . The retrieving and pre-processing of data at block  3101  can be as described with respect to  3001  of  FIG.  30   . Unlike the preceding processing flows, at block  3103  a pre-ranking of the importance of variables can be performed using a selected one of the models without hyperparameter tuning, such as the gradient boosting machine model for example, to determine the relative importance of the data variables. A common data set for use in the auto machine learning process can then be generated for use in block  3105 . Using the common data set, autotune machine learning is then used to evaluate the selected set of models and corresponding sets of hyperparameter values, such as deep learning, generalized linear, random forest, and gradient boosting models using grid search or other techniques to evaluate the model and hyperparameter values, such as by a leader board. Once the model and corresponding set of hyperparameter values are selected, prediction can then follow at block  3107  as at block  3105 , but using the selected hyperparameter-tuned model. An embodiment of the process of block  3105  is consider in more detail with respect to  FIG.  32   . 
       FIG.  32    is a flowchart for an embodiment for the evaluation and selection of the models that incorporates parameter tuning presented in the context of system A, where the process can be similarly and independently applied to system B. Starting at step  3201 , a common data set is created for the evaluation of the evaluation of the different models when hyperparameter tuning is included. Using the common data set, the different models are executed including autotuned machine learning at step  3203 . To select the best models, at  3205  the different models being used with different hyperparameter tunings can be ranked on an auto ML leaderboard for comparison. In step  3207  the prediction data (e.g., virtual upper memory hole wet etch optical critical dimension data) for the different models and autotuned hyperparameter values can be generated from the new die sort data over a number of time periods or production intervals, such as on a weekly basis. The prediction data from step  3207  can then be compared with the actual data, such as for optical critical data, at step  3209  by of data analysis such as scatter plots to confirm the coefficient of determination (R 2 ), for example, over several of the time periods, such as for several weeks, to track the relative accuracy of the tuned models over time. Depending on the tracking, the model and/or hyperparameters values can be reselected for one or both of the systems. 
     The different models will have different corresponding sets of hyperparameters. The auto ML process can execute to tune these different sets of hyperparameters automatically based on a random grid search, a Bayesian optimization, or other optimization techniques. For example, the gradient boosting machine model has relatively few hyperparameters, which can make it a good model choice for the pre-ranking of the importance of variables. At step  3205  of  FIG.  32   , the accuracy of the different modes with different tuning can be ranked on a leader board as illustrated in  FIG.  33   . 
       FIG.  33    is a screenshot of an example of a leader board for tunings of several models for one embodiment. Among the models, this example includes deep leaning, generalized linear model, and gradient boosting model with auto ML executed for different hyperparameter values with the top 15 model/hyperparameter combination results shown for this evaluation. The left column of  FIG.  33    (“model_id”) lists the model and a set of hyperparameter value designation. The second column lists the corresponding measurements of error, in the case the root mean squared error (“rmse”). In this example, the highest ranking model (highlighted at “1”) is a deep learning model with a set of hyperparameters determined in the auto ML process. The highest position of another model is the fifth row for a GLM model and the highest ranking of a third model is a GBM model at 9 th . In this example, a random forest model was also considered, but its error values were too large to make the top 15. These top ranking auto ML tuned versions for each of the three models can be compared against the non-tuned versions to further check that they are more accurate than the standard (i.e., non-tuned) versions. Scatter plots with virtual and actual optical critical dimension data and coefficient of determination values (R 2 ) for each model can be used to further check the accuracy. Further comparing the autotuned models against the standard models over several time intervals, such as several weeks of production runs for the fabrication facility, can be used as a further check on model selection. 
     In a first set of embodiments, a method includes: receiving inline quality control data of test samples from manufacture of an integrated circuit; receiving post-manufacturing test data of the test samples; creating a first virtual inline quality control data model for the manufacture of the integrated circuit from the inline quality control data and the post-manufacturing test data; and interpolating virtual inline quality control data for the manufacture of the integrated circuit from the first virtual inline quality control data model and the post-manufacturing test data. The method also includes: receiving an inline data report for the manufacture of the integrated circuit and creating a second virtual inline quality control data model for the manufacture of the integrated circuit from the interpolated virtual inline quality control data and the inline data report. One or both of creating the first virtual inline quality control data model and creating the second virtual inline quality control data model includes selecting a machine learning model from a plurality of machine learning models including one or more versions of one or more of the machine learning models with different hyperparameter values. The virtual inline quality control data for the manufacture of the integrated circuit is then interpolated from the second virtual inline quality control data model and the inline data report. 
     In further embodiments, a method includes: fabricating a plurality of an integrated circuit using a first set of processing parameters; creating a first virtual inline quality control data model for the fabrication of the integrated circuits from inline quality control data of test samples of the integrated circuit and post-fabrication test data of the test samples; and interpolating virtual inline quality control data for the fabrication of the integrated circuits using the first set of processing parameters from the first virtual inline quality control data model and the post-fabrication test data. The method also includes creating a second virtual inline quality control data model for the fabrication of the integrated circuit using the first set of processing parameters from the interpolated virtual inline quality control data and an inline data report for the fabrication of the integrated circuits using the first set of processing parameters, where one or both of creating the first virtual inline quality control data model and creating the second virtual inline quality control data model includes selecting a machine learning model from a plurality of machine learning models including one or more versions of one or more of the machine learning models with different hyperparameter values. The method further includes: interpolating virtual inline quality control data for the fabrication of the integrated circuit using the first set of processing parameters from the second virtual inline quality control data model and the inline data report; based on the interpolated virtual inline quality control data for the fabrication of the integrated circuit using the first set of processing parameters from the second virtual inline quality control data model and the inline data report, adjusting the first set of processing parameters; and fabricating the integrated circuit using the adjusted first set of processing parameters. 
     In additional embodiments, a system includes one or more processors. The one or more processors are configured to: receive, from a fabrication facility, inline quality control data of test samples from manufacture of an integrated circuit; receive post-manufacturing test data of the test samples; create a first virtual inline quality control data model for the manufacture of the integrated circuit from the inline quality control data and the post-manufacturing test data; interpolate virtual inline quality control data for the manufacture of the integrated circuit from the first virtual inline quality control data model and the post-manufacturing test data; receive, from the fabrication facility, an inline data report for the manufacture of the integrated circuit; create a second virtual inline quality control data model for the manufacture of the integrated circuit from the interpolated virtual inline quality control data and the inline data report, where one or both of creating the first virtual inline quality control data model and creating the second virtual inline quality control data model includes selecting a machine learning model from a plurality of machine learning models including one or more versions of one or more of the machine learning models with different hyperparameter values; and provide the second virtual inline quality control data model to the fabrication facility. 
     For purposes of this document, reference in the specification to “an embodiment,” “one embodiment,” “some embodiments,” or “another embodiment” may be used to describe different embodiments or the same embodiment. 
     For purposes of this document, a connection may be a direct connection or an indirect connection (e.g., via one or more other parts). In some cases, when an element is referred to as being connected or coupled to another element, the element may be directly connected to the other element or indirectly connected to the other element via intervening elements. When an element is referred to as being directly connected to another element, then there are no intervening elements between the element and the other element. Two devices are “in communication” if they are directly or indirectly connected so that they can communicate electronic signals between them. 
     For purposes of this document, the term “based on” may be read as “based at least in part on.” 
     For purposes of this document, without additional context, use of numerical terms such as a “first” object, a “second” object, and a “third” object may not imply an ordering of objects, but may instead be used for identification purposes to identify different objects. 
     For purposes of this document, the term “set” of objects may refer to a “set” of one or more of the objects. 
     The foregoing detailed description has been presented for purposes of illustration and description. h It is not intended to be exhaustive or to limit to the precise form disclosed. Many modifications and variations are possible in light of the above teaching. The described embodiments were chosen in order to best explain the principles of the proposed technology and its practical application, to thereby enable others skilled in the art to best utilize it in various embodiments and with various modifications as are suited to the particular use contemplated. It is intended that the scope be defined by the claims appended hereto.