Method and apparatus for determining an assignment rule for reconstructing the position of semiconductor components on a wafer

Abstract

This invention relates to a method for determining an assignment rule to combine test results from different tests of the same semiconductor device, taking into account a yield loss during the production of the semiconductor devices. The method includes the following steps: (S23) fitting a model such as a linear regression model to predict test data; (S24) calculating a cost matrix based on the predictions; (S25) applying the Hungarian method to the cost matrix to obtain a new assignment rule, and repeating these steps multiple times.

Description

Technical Field

[0001] The present invention relates to a method for reconstructing the position of semiconductor elements mounted on a wafer, which are subsequently cut off from the wafer, and to an apparatus configured to perform the method. Prior Technology

[0002] In the packaging process of semiconductor devices (especially PowerMOS), traceability of the semiconductor device to its original wafer and its original position on the wafer is lost. Specifically, this means that once the wafer has been diced or split (a method of separating the semiconductor device from the wafer) and packaged, the position of each semiconductor device on the wafer is no longer available. Packaging providers can at least provide a rough match between the loose semiconductor devices in final testing (i.e., testing of the semiconductor device after packaging) and the semiconductor devices on the wafer in wafer-level testing (testing before packaging). However, this still results in thousands of semiconductor devices not being assigned to multiple wafers. Since this is essentially a combinatorial problem, the complexity of the solution is factorial, due to the existence of n-factorially different ways to arrange the semiconductor devices in the correct order, where n is the number of semiconductor devices.

[0003] For ASIC semiconductor devices, there is a solution to this combined problem. For this purpose, a unique identifier is stored in the ASIC semiconductor device's memory during wafer-level testing, which allows final testing to be assigned to wafer-level testing after packaging. However, due to the absence of memory, this is not possible for semiconductor devices such as PowerMOS.

[0004] Another challenge in matching final testing with wafer-level testing is that individual semiconductor devices are picked out after wafer-level testing, and information about which specific semiconductor device was picked out is lost here. Therefore, the combination problem is complex because there are now more potentially related wafer-level tests for the final test results, and it is also necessary to determine which wafer-level tests do not have corresponding final test results.

[0005] Advantages of this invention

[0006] The present invention, which features independent technical solution 1, has the following advantages: it enables the determination of a potential assignment between a semiconductor element that depends on the results of wafer-level testing and a packaged semiconductor element that depends on the results of final testing, without the need for retrospectively added metadata, such as unique identifiers or the like.

[0007] This invention also has the advantage of taking into account yield losses that can occur during manufacturing. This allows not all semiconductor components to be assigned to testing. Based on yield losses and the assignment of results, additional traceability information is available, making it possible to estimate where yield losses occur on the wafer. Depending on this, better process control (e.g., root cause analysis of defective portions) can be enabled.

[0008] Other aspects of the invention are the subject of the corresponding claims. Advantageous extensions are the subject of the subsidiary claims. Summary of the Invention

[0009] In the first embodiment, the present invention relates to a method for determining assignment rules, particularly a computer-implemented method, in which, in various situations, the assignment rule assigns a variable from a second set of second variables to a plurality of variables from a first set of first variables. The first set contains more variables than the second set. The assignment rule can assign the second variable to a plurality of first variables in a one-to-one manner, that is, assign the maximum value of a second variable to a first variable by the assignment rule, and preferably also assign the maximum value of a first variable to a second variable by the assignment rule. In other words, the assignment rule is configured to assign the second variable to a subset of the first variables. Preferably, the number of variables in the subset of the first variables is equal to the number of variables in the second set. Next, the assignment rule assigns the first variables to each second variable, wherein because the first set has more variables than the second set, some first variables are not assigned to any second variables. However, it is also possible to imagine that the subset is smaller than the second set.

[0010] A set can be understood as a combination of individual variables. Preferably, the first set and the second set are different sets that do not share common variables. Preferably, indices are assigned to the variables in the first set and the second set respectively. All indices in the first set and the second set can be interpreted as an index set, and thus, as a set, the elements of this index set are consecutively indexed for the variables of the first set or the second set. The assignment rule then assigns the indices from the second index set to the first index set. The assignment rule thus describes which first variable belongs to which second variable, and preferably also describes which second variable belongs to which first variable. The assignment rule can be a list, a table, or something similar.

[0011] This method begins by initializing an assignment rule and providing a first set and a second set, where the first set contains more variables than the second set. The initial assignment rule can be chosen randomly or selected as an identity mapping. Preferably, the assignment rule is initialized such that it considers all second variables in its assignments; that is, it assigns only as many first variables as there are second variables to the second variables, or it assigns the first variables to all second variables. Other initial assignment rules may be used as alternatives, such as predefined, partially correct assignments.

[0012] Subsequently, a number of first variables are randomly selected, the number of which is at least equal to the number of variables in the first set that exceed the number of variables in the second set. When this step is performed by a computer, the random selection can be performed by a pseudo-random generator. In other words, generally, random selection is performed without favoring any of the first variables. However, it is also conceivable to select certain variables with a higher probability, because, for example, such variables represent anomalies relative to the remaining variables in the first set.

[0013] Steps a) through e) are then repeated, as explained below. A maximum number of repetitions can be specified, or a termination criterion can be defined, where repetition is terminated if the criterion is met. For example, the termination criterion is the minimum modification to the assignment rule.

[0014] a) Create a dataset containing a first variable but not the currently selected first variable and its respective second variable as assigned according to the assignment rules. The currently selected variable is either the first variable previously selected to perform steps a) through e), or, when these steps are performed for the first time, a randomly selected first variable.

[0015] The dataset can also be referred to as the training dataset, where the second variable is assigned as the so-called "label" of the first variable. It should be noted that this step is optional, as subsequent steps using this dataset essentially only require information about the current assignment rule between the first and second variables, which can be provided by the dataset or by the current assignment rule. The current assignment rule is the assignment rule that exists for the current repetition of steps a) through e), that is, the assignment rule used when the most recent version of the dataset was created.

[0016] (b) Train the machine learning system such that it determines the assigned second variable of the dataset based on the first variable. The training procedure can be understood as adjusting the parameters of the machine learning system so that the predictions made by the system using its determinations are as close as possible to the second variable ("label") of the dataset. Optimization can be performed relative to a cost function. The cost function preferably characterizes the mathematical difference between the output of the machine learning system and the label. Gradient descent is preferably used to perform optimization. The machine learning system can be one or more of a decision tree, neural network, support vector machine, or similar. Training can be performed until any further improvement of the machine learning system during training is negligible, i.e., the second termination criterion is satisfied.

[0017] (c) Calculate the cost matrix, where each item in the cost matrix is ​​characterized by the distance between the machine learning system's prediction and the second variable, specifically the distance between the machine learning system's prediction and all variables in the second set, according to the assignment rules. The L2 norm can be used to determine the distance. Other distance measures can also be conceived. The cost matrix can be structured such that columns and rows are each assigned to the first variable, or to the machine learning system's prediction depending on the first variable, and the second variable, where each item in the column and row is characterized by the distance between the respective assigned variables.

[0018] d) Optimize the assignment rule based on the cost matrix such that the assignment rule produces the minimum total cost based on the cost matrix items. The total cost is the sum of the cost matrix items required to perform the assignment of variables of the first set from the cost matrix to the second set according to the current assignment rule. In other words, optimize (especially minimize) this sum on the items selected from the cost matrix according to the assignment rule. Note that the items are selected according to the assignment rule such that the items in each row and column of the cost matrix selected according to the assignment rule are the items assigned to the first and second variables, which are assigned to each other according to the assignment rule.

[0019] e) Select the first variable that has not been assigned to one of the second variables according to the optimized assignment rules. The selected first variable is preferably stored in a list and updated each time steps a) through e) are executed again.

[0020] The assignment rule determined in the final repetition of step d) is the final assignment rule, which is output in an optional step. Similarly, the first variable selected in the final repetition of step e) can be output, for example, to determine which first variables do not have corresponding second variables.

[0021] Variables can be scalars or vectors, such as time series, especially sensor data acquired or indirectly determined by sensors. Preferably, the first and second variables are one or more measurement results from a single measurement or from a plurality of different measurements, each of which has been performed on one of a plurality of objects. In other words, each variable is assigned to one of the objects. In the step of creating the dataset, only a predetermined number of measurement results from the plurality of measurement results are available for the second variable. Assignment rules can specify which first and second variables are measurement results of the same object. Particularly preferably, at least one measurement of the object for the first variable is performed at one time point, and a measurement of the second variable is performed at a second time point, which is after the first time point. The second time point can be defined after the object has been modified or changed. The difference in the number of different measurement results can be the loss of the object when it was measured, for example, by picking it out.

[0022] This paper proposes using a cost minimization algorithm to optimize assignment rules on a given cost matrix. For example, optimization can be achieved using the Hungarian method applied to the cost matrix. The Hungarian method (also known as the Kuhn-Munkres algorithm) is an algorithm for solving weighted mapping problems. Alternatively, a greedy implementation of the cost minimization algorithm can be used.

[0023] It also proposes that the machine learning system is a regression model, which determines the second variable based on the first variable and the parameters of the regression model, wherein the parameters of the regression model are adjusted during training.

[0024] Regression is used to model the relationship between strain variables (often also called response variables) and one or more independent variables (often also called explanatory variables). Regression can parameterize more complex functions so that the data is best represented according to a specific mathematical criterion. For example, the common least squares method calculates a unique straight line (or hyperplane) that minimizes the sum of the squares of the deviations between the true data and this line (or hyperplane), that is, the sum of the squares of the residuals.

[0025] The invention also proposes a first and a second variable to characterize the product during different production process steps. For example, the second point in time could be the time when a manufacturing process step has been completed. The product can be any product manufactured in the manufacturing facility. Preferably, when manufacturing a product, traceability to previous process steps is lost (the so-called "bulk material"), for example, if it is no longer possible to directly assign the product from a block of material (e.g., a screw) to a production batch. It is conceivable that the first variable characterizes components (especially parts), and the second variable characterizes the final product, where the assignment rules describe which component has been processed to produce which product, or which component has been installed in which product. An example of this is whether components in a product can no longer be non-destructively removed to read their serial numbers. In the present invention, it is possible to assign the production batch of components by measuring the product. The difference in the number of different variables in the two sets can represent the yield loss during production.

[0026] The first and second variables can be measurement / test results or other attributes of the product, component, etc. The first and second variables are usually slightly different from each other, for example, due to manufacturing tolerances, but describe the same measurement / attribute of the product, component, etc.

[0027] The first variable is proposed as the first test result or measurement result of the semiconductor component on the wafer, and the second variable is the second test result or measurement result after the semiconductor component has been cut off from the wafer. The semiconductor component can be a portion of an electrical component already grown on the wafer, such as a transistor group in an integrated circuit. The test result can also be related to the entire semiconductor component. Linear regression has proven particularly effective in finding optimal assignment rules for machine learning systems. This is based on a linear relationship, which is a reasonable assumption for assigning test results in this situation. Linear regression is a special case of regression. In linear regression, a linear function is assumed. It only uses the linear combination of strain coefficients (but not necessarily independent variables) to determine the relationship.

[0028] It is also proposed that the first test result is a wafer-level test result, and the second test result is a final test result. Preferably, there are fewer final test results compared to wafer-level test results. The tests are, for example, voltage tests and / or contact tests.

[0029] It also proposes manufacturing semiconductor components on multiple different wafers. This is because it has been demonstrated that this method can even traverse multiple wafers to find the correct assignment rule within a reasonable computational time.

[0030] The paper also proposes assignment rules to determine which second test result belongs to which first test result, and then, based on the associated first test result, to determine the location of the semiconductor device within the wafer. This allows for location reconstruction, making it possible for the first time to uniquely trace a semiconductor device from the final manufacturing process step to a previous processing step. The same procedure can also be performed for the selected first variable that was not assigned to one of the second variables according to the optimized assignment rules, in order to trace which semiconductor devices were picked up or removed. Therefore, the manufacturing process steps can be modified so that it is no longer necessary to pick up subsequently produced semiconductor devices at corresponding locations on the wafer.

[0031] In other respects, the present invention relates to an apparatus and a computer program, wherein each is configured to perform the above-described method; and the present invention relates to a machine-readable storage medium having the computer program stored thereon. Simple Explanation of the Diagram

[0032] In the following text, illustrative specific examples are described in more detail with reference to the accompanying drawings. In the drawings: [Figure 1] A schematic diagram illustrating the packaging process; [Figure 2] illustrates a specific example of the flowchart of the present invention; [Figure 3] Schematic diagram showing the training device. Implementation

[0033] During the packaging process of semiconductor components or devices, traceability of the components to their original wafers and their original locations on the wafer is lost. After the semiconductor component parts have been cut off, individual semiconductor components may sometimes be mixed together, meaning that the location of the components on the wafer is lost without uniquely marking them. This is schematically illustrated in Figure 1. Wafers 10 each have a plurality of semiconductor components or devices 11. At this stage, each semiconductor device 11 has a known location on wafer 10. Typically, semiconductor devices 11 undergo multiple tests at this stage, which is also known as wafer-level testing. Wafer 10 is then diced into several parts, separating the semiconductor devices 11 from each other. Dicing can be performed using a saw 12 or by laser. Finally, the semiconductor devices diced to the appropriate size are packaged, for example, mounted in a microcontroller 13. This is the latest stage, in which information about the wafer 10 where the semiconductor devices were originally located and their location within wafer 10 has been lost. Typically, the microcontroller 13 with semiconductor device 11 undergoes multiple tests, also known as final tests. However, due to the mixing caused by dicing wafer 10 into several parts, it is not easy to definitively determine which wafer 10 a given semiconductor device 11 of a microcontroller 13 is configured on, and which wafer-level test corresponds to which final test, i.e., whether it is the test result of the same semiconductor device. The semiconductor device may be a microelectronic module, such as an integrated circuit (also referred to as a chip below), a sensor, etc.

[0034] One objective of this invention is to restore traceability in semiconductor manufacturing after the packaging process. Such assignment achieves other benefits, such as better process control or earlier prediction of final wafer properties. Furthermore, root cause analysis of deviations measured at the wafer level in final testing can be extended to the wafer manufacturing process. This, in turn, enables a deeper understanding of these processes and leads to better process control, and thus improved quality.

[0035] An assignment algorithm is proposed, consisting of an alternating sequence of the following: optimizing regression parameters (when regressing from wafer-level testing to final test data), followed by optimizing the assignment of test partners. The current assignment of the final test chip is used as a "regression label" in each iteration.

[0036] This invention also employs a cost-minimization algorithm that determines the optimal one-to-one assignment under a given cost matrix. To construct a suitable cost matrix, regression error is applied by calculating an appropriate distance measure (e.g., L2 norm) between the final test prediction of the trained regression factors and the regression labels. Based on this cost matrix, the algorithm reconfigures the chips in the final test to minimize regression loss. The regression factors or regression model can be freely chosen depending on the characteristics of the data (e.g., linear regression for linear dependencies).

[0037] Figure 2 shows a schematic flowchart 20 of the method for assigning rules, which is used to determine the mapping of the final test results to the corresponding wafer-level test results.

[0038] When the method is completed, an assignment rule should be obtained that assigns the associated test results of the wafer-level tests to the final tests. Therefore, this rule describes the associated test results derived from the same semiconductor device.

[0039] The method begins at step S21a. This step initializes the assignment rules. Test results for both the wafer-level test (WLT) and the final test (FT) are also provided in this step. Due to yield losses, fewer FT test results may exist compared to WLT test results.

[0040] Step S21b follows step S21a. In this step, the yield loss is determined, which is, for example, the ratio of the WLT test result to the FT test result. A subset of the WLT test results is randomly selected based on the yield loss. For example, the subset corresponds to the amount of lost semiconductor devices.

[0041] The next step is step S22. In this step, a training dataset is created containing the WLT test results assigned according to the assignment rules and their respective FT test results, wherein the subset selected in step S21b is removed from the WLT test results.

[0042] It should be noted that, in this specific instance, the removal of test results was chosen so that the training dataset has an equal number of WLT and FT test results. However, it is also conceivable to add rather than remove FT test results. Addition could be performed, for example, using a trial-and-error approach.

[0043] After step S22 is completed, step S23 is then performed. In this step, depending on the wafer-level test (WLT), a regression factor f is trained such that the regression factor determines the assigned final test based on the training dataset: f(WLT) = FT. The regression factor f can be a linear regression model. The regression factor is trained in a known manner, for example, by adjusting the parameters of the regression factor f to minimize the regression error on the training dataset.

[0044] Once the regression factors have been trained, proceed to step S24. In this step, a cost matrix is ​​created. Columns and rows are assigned to wafer-level tests and final tests, respectively. Items in the cost matrix are determined from the training data using the L2 norm between regression predictions, depending on the corresponding WFT test results for each series and the corresponding FT test results for each row, and are stored in the cost matrix. Because the number of test results varies, the cost matrix has a rectangular shape.

[0045] After step S24 is completed, step S25 proceeds to optimize the assignment rules. Optimization is performed by applying the Hungarian method to the cost matrix to obtain an improved assignment rule based on the cost matrix.

[0046] Next, step S26 is performed, in which a first variable is selected that has not been assigned to one of the second variables according to the optimized assignment rules. These selected first variables then form a subset of the first variables that have not been assigned to the corresponding FT test results.

[0047] If the termination criterion is not met, steps S22 through S25 are executed again. Note that when repeating step S22, the subset selected in the repetitions of the immediately preceding step S26 is now removed from the training dataset. The termination criterion can be a specified number of submaximum repetitions.

[0048] If the termination criteria are met, the method is terminated and the assignment rules can be output.

[0049] In an optional step following step S25, assignment rules are used to reconstruct the location of semiconductor element 11 on wafer 10. The assignment rules can be used to determine the WLT test results in reverse order of the FT test results. Since the storage of WLT test results typically includes additional locations within the wafer where individual tests have been performed, it is possible to accurately reconstruct the locations on the wafer where the corresponding semiconductor devices were manufactured. Therefore, the locations of semiconductor elements whose WFT test results were not assigned to the FT test results according to the assignment rules can also be reconstructed. In other words, those semiconductor elements that were rejected after the WLT test and their individual locations are identified.

[0050] It is conceivable that, depending on the position reconstruction following step S25 and / or step 26, control signals can be initiated to control physical systems, such as computer-controlled machines, manufacturing machines, and especially wafer processing machines. For example, if the FT test results are not optimal, the control signals can adjust previous production steps accordingly to obtain better FT test results later.

[0051] Figure 3 shows a schematic diagram of the apparatus 30 used to perform the method according to Figure 2.

[0052] The apparatus includes a provider 51 that provides the training dataset as described in step S22. The training data is then fed to a regression factor 52, which uses this data to determine the output variable. The output variable and the training data are fed to an evaluator 53, which uses the output variable and the training data to determine updated parameters of the regression factor 52. These updated parameters are transferred to parameter memory P, where they replace the current parameters. The evaluator 53 is configured to perform step S23.

[0053] The steps performed by device 30 can be implemented as a computer program on machine-readable storage medium 54 and executed by processor 55.

[0054] The term "computer" encompasses any device used to process predefined computational rules. These computational rules may be provided in software form, hardware form, or a hybrid of software and hardware.

[0055] 10: Wafer 11: Semiconductor devices 12: Saw 13: Microcontroller 20: Flowchart 30: Device 51: Provider 52: Regression Factor 53: Evaluator 54: Machine-readable storage media 55: Processor S21a: Steps S21b: Steps S22: Steps S23: Steps S24: Steps S25: Steps S26: Steps P: Parameter memory

Claims

1. A method for determining an assignment rule for reconstructing the location of a semiconductor element on a wafer, the assignment rule assigning second variables from a second set of second variables to a plurality of first variables from a first set of first variables, the method comprising the steps of: initializing (S21a) the assignment rule and providing (S21a) the first set and the second set, wherein the first set contains more variables than the second set; randomly selecting (S21b) a number of first variables, wherein the number of selected first variables is at least equal to the number of variables in the first set that are greater than the number of variables in the second set; repeating steps a) to d): a) training (S23) a machine learning system such that the machine learning system determines the second variables assigned according to the assignment rule based on the first variables in the first set that do not contain the selected first variables; b) Calculate (S24) a cost matrix, wherein the cost matrix items characterize the distance between the predictions of the machine learning system based on the first variables of the first set and the second variables of the second set; c) Optimize (S25) the assignment rule based on the cost matrix such that the assignment from the first variables to the second variables according to the assignment rule produces the minimum total cost based on the items in the cost matrix; and d) Select (S26) the first variables that are not assigned to one of the second variables according to the optimized assignment rule.

2. The method of request item 1, wherein the optimization (S25) of the assignment rule is performed by means of a Hungarian algorithm or a greedy implementation.

3. The method of claim 2, wherein the number of rows and columns of the cost matrix is ​​equal to the number of the first variables and the number of the second variables, wherein when determining (S24) the cost matrix, the distances between the predictions of the machine learning system for all first variables and the predictions of the machine learning system for all second variables are determined respectively.

4. The method of any one of requests 1 to 3, wherein the machine learning system is a regression model (53) that determines the second variables based on the first variables and the parameters of the regression model (53).

5. The method of any one of claims 1 to 3, wherein the first variables and the second variables characterize the products during production according to different production process steps, wherein the assignment rule characterizes which of the variables in the first set and the second set characterizes an identical product, wherein the number of first variables randomly selected in the random selection (S21b) or selected in the selection (S26) corresponds to a yield loss in production.

6. The method of any one of claims 1 to 3, wherein the first variables are first test results of semiconductor components on the wafer, and the second variables are second test results of semiconductor components after the semiconductor components have been cut from the wafer, wherein the assignment rule specifies which first test results and second test results originate from the same semiconductor component.

7. The method of claim 6, wherein the first test results are wafer-level test results and the second test results are final test results.

8. The method of any one of claims 1 to 3, wherein the semiconductor components are manufactured on a plurality of different wafers.

9. The method of claim 6, wherein the assignment rule is used to determine which second test result belongs to which first test result, and then, depending on the associated first test result, to determine where the semiconductor device is located within a wafer, and where the semiconductor devices for which no second test result exists are located.

10. The method of claim 6, wherein the semiconductor components are power MOSFETs.

11. An apparatus (30) configured to perform the method of any one of claims 1 to 10.

12. A computer program product comprising commands that cause a computer to perform any one of the methods described in claims 1 to 10 during execution of the program.

13. A machine-readable storage medium having a computer program product as described in claim 12 stored thereon.

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