Reconfiguration of semiconductor component positions on a wafer

Abstract

The invention relates to a method for determining an allocation rule for combining test results of different tests of the same semiconductor component, the method comprising the steps of fitting a model, for example a linear regression model, and using the model for predicting test data (S23), calculating a cost matrix based on the prediction (S24), and applying a greedy implementation to the cost matrix to obtain new allocation rules (S25), repeating these steps multiple times.

Description

[Technical Field]

[0001] The present invention relates to a method for reconstructing the positions of semiconductor components on a wafer on which they are deposited after they have been cut from the wafer, and to an apparatus configured to carry out this method. [Background technology]

[0002] Prior art During the packaging process for semiconductor components (especially PowerMOS), traceability of semiconductor components to their original wafers and their original location on the wafer is lost. Specifically, this means that once the wafer is cut or diced and packed, the location of each semiconductor component on the wafer is no longer available. Packaging process operators are able to provide at least a rough match between the loose semiconductor components at final test and the semiconductor components on the wafer at wafer-level test. However, this still results in thousands of semiconductor components being unable to be allocated to multiple wafers. Because this is essentially a combinatorial problem, the complexity of the solution to this problem is factorial. This is because there are n-factorially many different ways to arrange multiple semiconductor components so that they correspond to the correct order, where n is the number of semiconductor components.

[0003] For ASIC semiconductor components, a solution to this combination problem exists: for this purpose, a unique identifier is stored in the memory of the ASIC semiconductor component during wafer-level testing, which makes it possible to assign the final inspection after packaging to the wafer-level test. However, for semiconductor components such as PowerMOS, this is not possible due to memory limitations. Summary of the Invention [Problem to be solved by the invention]

[0004] Advantages of the invention The invention having the features of independent claim 1 has the advantage that potential allocations between semiconductor components are determined particularly efficiently using a greedy algorithm, depending on the results of wafer-level tests and packaged semiconductor components, and on the results of final tests, without the need for additional metadata such as unique identifiers. Because the greedy algorithm achieves significantly lower computational and memory complexity, the allocations can be determined in a fraction of the computation time, without the need for expensive hardware. This allows for application to a significantly larger number of semiconductor components, particularly without increasing the error rate. The invention thereby broadens the scope of application, since the increased computational efficiency allows for the allocation of a larger number of semiconductor components than ever before.

[0005] One objective of the present invention is to increase the amount of semiconductor components that can be processed by at least an order of magnitude.

[0006] The present invention also has the advantage of allowing for a one-to-one assignment between semiconductor components and their original location on the wafer, thus allowing for better process control (eg, root cause analysis of defective components).

[0007] Further aspects of the invention are the subject of the parallel independent claims. Preferred developments are the subject of the dependent claims. [Means for solving the problem]

[0008] DISCLOSURE OF THE INVENTION In a first aspect, the present invention relates to a particularly computer-implemented method for determining assignment rules for assigning variables from a first set of first variables to variables from a second set of second variables, respectively, such that the assignment rules can assign first variables to second variables in an unambiguous manner, i.e., each first variable is assigned at most one second variable by the assignment rule, and preferably vice versa. A set can be understood to mean a unified form of individual variables. Preferably, the first and second sets are different sets that have no variables in common. Preferably, variables in the first and second sets are assigned one index each. All indexes in the first and second sets can be considered as an index set, i.e., as a set, their elements are indexed over the variables of the first or second set. The assignment rule then assigns one index from the second index set to each of the first index set. An assignment rule therefore describes which first variable belongs to which second variable, and preferably vice versa. The assignment rule can exist as a list or a table, etc.

[0009] The method begins with the step of initializing an allocation rule and providing a first and a second set. The initialized allocation rule can be selected randomly or as a discriminatory allocation. Alternatively, other initialized allocation rules are also contemplated, such as preset and already partially correct allocations.

[0010] This is followed by repeatedly performing steps a) to d) as described below, which can be performed for a preset maximum number of iterations or an interruption criterion can be defined, in which case the iterations are interrupted if the interruption criterion is met, e.g., a minimal change in the allocation rules.

[0011] a) creating a dataset having first variables and second variables assigned according to their respective assignment rules. This dataset can also be called a training dataset, in which case the assigned second variables are so-called "labels" of the first variables. It should be noted that this step may be optional, since the following steps using this dataset essentially only require information of 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 iteration of steps a) to d), i.e., the assignment rule that was used when the dataset was most recently created.

[0012] b) training the machine learning system to determine the second variables of the dataset assigned to each of the first variables. Training can be understood to mean that the parameters of the machine learning system are adapted so that the predictions of the machine learning system determined thereby are as close as possible to the second variables ("labels") of the dataset. Optimization can be performed with respect to a cost function. The cost function preferably characterizes the mathematical difference between the output of the machine learning system and the labels. Optimization is preferably performed using gradient descent. The machine learning system can be one or more decision trees, neural networks, support vector machines, etc. Training can be performed until further improvement of the machine learning system during training becomes negligible, i.e., until a second interruption criterion is met.

[0013] c) determining a set of distances between the predicted values ​​of the machine learning system and the second variable. The distance calculations can be performed sequentially, where each distance between the predicted values ​​of the machine learning system and the second variable is characterized according to an assignment rule, in particular between each variable of the second set for all predicted values ​​of the machine learning system. Preferably, the distances are determined in the form of a cost matrix, where the entries of the cost matrix characterize the distances between the predicted values ​​of the machine learning system and the second variable according to the assignment rule, in particular between the predicted values ​​of the machine learning system and all variables of the second set. The distances can be determined using the L2 norm. Other distance measures are also contemplated. The cost matrix can be structured such that rows and columns are assigned to the first variable or to the predicted values ​​of the machine learning system that depend on the first variable and the second variable, respectively, where the entries characterize the distances between the variables assigned to the rows and columns, respectively. The entries that are not on the diagonal of the cost matrix can be understood as the transportation costs that must be incurred to assign the first variable to the second variable in the corresponding row / column, respectively, in violation of the assignment rule.

[0014] d) optimizing the allocation rule depending on the cost matrix, so that the allocation rule generates the minimum total cost, in particular the minimum total distance, based on the entries of the cost matrix. The total cost corresponds to the sum of the entries of the cost matrix required to perform the allocation of the variables of the first set to the second set according to the current allocation rule from the cost matrix. In other words, the sum over the entries selected from the cost matrix depending on the allocation rule is optimized, in particular minimized. It should be noted here that the entries are selected depending on the allocation rule so that the entries of the respective columns and rows of the cost matrix are selected to be assigned to the first and second variables according to the allocation rule and to each other according to the allocation rule.

[0015] The optimization of the allocation rule is carried out by the following steps, which are repeated iteratively until, in particular, a stopping criterion is met, which may be defined, for example, by performing the following steps for all predictions of the machine learning system: i) randomly sampling predicted values ​​of the machine learning system and searching for a second variable that has the shortest distance to the sampled predicted values ​​of the machine learning system according to a cost matrix, in other words, based on the cost matrix, a second variable whose entry in the cost matrix characterizes the shortest distance to the above-mentioned predicted values ​​is selected; ii) modifying the assignment rule so that the assignment rule assigns the selected second variable to a first variable for which the extracted predicted value of the machine learning system is dependent on the first variable; iii) removing from the cost matrix entries assigned to the first variables for which the extracted prediction value of the machine learning system was determined depending on the first variables, and entries assigned to the selected second variables.

[0016] At each iteration of optimizing the allocation rule, the method selects the shortest distance between the prediction of the machine learning system and the second variable. Since the method considers only a single target observation, the problem is locally or greedily optimized. Therefore, one can refer to the existence of a greedy implementation. The removal of selected variables after modifying the allocation rule has the advantageous effect of forcing a one-to-one allocation.

[0017] In the proposed approach, costs are minimized locally rather than globally, which is much more computationally efficient and surprisingly turns out not to degrade the quality of the assignment rules, since a greedy implementation would lead to similar results. This means that, presumptively, a greedy implementation finds an assignment rule independent of all other entries in the cost matrix, where the row index of the column minimum across the cost matrix is ​​more or less unique.

[0018] The allocation rule found in the last iteration of step d) is the final allocation rule that is output in an optional step.

[0019] These variables may be scalars or vectors, such as time series, and in particular may be sensor data captured by a sensor or indirectly determined. Preferably, the first and second variables are one or more measurement results, respectively, of one measurement or multiple different measurements performed on one object of the multiple objects. That is, each variable is assigned to one of the objects. In the step of creating the dataset, it is also possible to use only a preconfigurable number of measurements from the multiple measurements for the second variable. The assignment rule may indicate 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 a first time point, and the measurement for the second variable is performed at a second time point, where the second time point occurs after the first time point. Thus, the second time point may be given after the object has been modified or changed.

[0020] It is proposed here that a batch size is preset, wherein during the step of determining the cost matrix, a plurality of randomly selected predicted values ​​of the machine learning system are selected, wherein the plurality of randomly selected predicted values ​​of the machine learning system corresponds to the batch size, and wherein further during the step of determining the cost matrix, a distance between the plurality of randomly selected predicted values ​​of the machine learning system with respect to a second variable is determined. Advantageously, the complexity is significantly reduced (compared to previous implementations of the Hungarian algorithm). Previously, the complexity was O(n 3 ), but here it is O(n * batch_size 3 )=O(n).

[0021] It is further proposed that during the step of optimizing the allocation rule, depending on the bit flags set on the basis of the entries of the cost matrix, the optimization of the allocation rule is selected either by steps i) to iii) or by the Hungarian algorithm, which is advantageous in that a flexible change of the optimization can be performed, for example if the Hungarian algorithm remains in a local minimum and subsequently the bit flags are set accordingly.

[0022] The Hungarian algorithm, also known as the Kuhn-Munkles algorithm, is an algorithm for solving weighted assignment problems.

[0023] It is further proposed that the machine learning system is a regression model that determines a second variable depending on a first variable and parameters of the regression model, where the parameters of the regression model are adapted during learning.

[0024] Regression is used to model the relationship between one dependent variable (often also the explained variable) and one or more independent variables (often also the explaining variables). Regression is in the context of parameterizing more complex functions so that they best reproduce these data according to certain mathematical criteria. For example, ordinary least squares methods calculate a unique line (or hyperplane) that minimizes the sum of squares of deviations between the true data and the line (or hyperplane), i.e., the sum of squares of residuals.

[0025] Preferably, the regression model is a linear regression model, in which case Tikhonov regularization is used during the training step. Linear regression aims to minimize the squared regression loss, so it is preferable to choose the squared Euclidean distance as the distance measure for the cost matrix.

[0026] It is further proposed that the first and second variables characterize a product being manufactured according to different manufacturing process steps. For example, the second point in time here may be the end of one manufacturing process step. The product may be any product manufactured in a manufacturing plant. Preferably, during the manufacture of a product, traceability to its preceding process steps is lost when it is no longer possible to directly assign a manufacturing batch to a product made of bulk material, such as a screw (so-called "bulk material"). It is assumed that the first variable characterizes a component (especially a part) and the second variable characterizes the final product, where the assignment rule describes which component was processed for which product or which part was attached to which product. Thus, the present invention makes it possible to assign a manufacturing batch of parts based on product measurements, for example, when it is no longer possible to remove parts from a product without destruction in order to read their serial numbers.

[0027] The first and second variables may be measurement / test results or other characteristics of a product, component, etc. The first and second variables preferably vary slightly from one another based on, for example, manufacturing tolerances, but describe the same measurement / characteristic of the product, component, etc.

[0028] It is further proposed that the first variable is a first test result or measurement result of a semiconductor component on a wafer, and the second variable is a second test result or measurement result of the semiconductor component after it has been cut from the wafer. The semiconductor component may be part of an electrical component grown on the wafer, for example, a group of transistors of an integrated circuit. The test result may also relate to the entire semiconductor component. Here, linear regression has proven particularly effective for machine learning systems to find the best allocation rule, since it starts from a linear relationship, which represents a meaningful assumption here for the allocation of test results. Linear regression is a special case of regression. In linear regression, a linear function is assumed here. That is, only relationships are used in which the dependent variable is a linear combination of the regression coefficients (but not necessarily the independent variables).

[0029] It is further 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 than wafer-level test results. These tests are, for example, voltage tests and / or contact connection tests.

[0030] It is further proposed that semiconductor component devices are fabricated on multiple different wafers, since this method can find a reasonable allocation rule across multiple wafers even within a reasonable computing time.

[0031] Furthermore, it is proposed that depending on the assignment rule, it is determined which second test result belongs to which first test result, and then in this case it is determined in which position the semiconductor component was located within the wafer depending on the associated first test result, which makes it possible for the first time to unambiguously trace the semiconductor component from the last manufacturing process step of semiconductor manufacturing back to the preceding process step.

[0032] Furthermore, it is proposed to determine, in addition to the location, further variables characterizing the wafer and / or semiconductor components on the wafer and the respective assigned test results, wherein these data are integrated into a further training data set, and wherein a further machine learning system is trained based on the further training data set to predict a second test result.

[0033] The advantage here is that the assignments can be used to create additional training data sets, train additional machine learning systems, and predict the properties of packed semiconductor components earlier in the manufacturing process, significantly reducing the time to identify deviations in process parameters, especially for parameters (e.g., RDSon) that can only be properly evaluated during final inspection.

[0034] An additional benefit here is that this allocation can also be used to train additional machine learning systems that proactively identify defective semiconductor chips, thereby saving process resources and reducing waste.

[0035] In further aspects, the present invention relates to an apparatus and a computer program respectively configured to carry out the above method, and to a machine-readable storage medium having stored thereon said computer program.

[0036] In the following, embodiments of the invention will be described in more detail with reference to the accompanying drawings. [Brief explanation of the drawings]

[0037] [Figure 1] FIG. 1 shows a schematic diagram of a packaging process. [Figure 2] FIG. 1 is a diagram illustrating an example of a flowchart of the present invention. [Figure 3] 1 is a schematic diagram of a training device. DETAILED DESCRIPTION OF THE INVENTION

[0038] Description of the Examples During the packaging process of semiconductor components or semiconductor elements, the traceability of the semiconductor elements to their original wafer and their original position on the wafer is usually lost. This is because, after the semiconductor elements are cut out, a mixture of the individual semiconductor elements can result, which means that the positions of the elements on the wafer are lost without their unique marking. This is shown diagrammatically in FIG. 1. Each wafer 10 contains a number of semiconductor components or semiconductor elements 11. At this stage, each semiconductor element 11 has a known position on the wafer 10. Typically, the semiconductor elements 11 undergo several tests, also referred to as wafer-level tests, at this stage. This is followed by sawing of the wafer 10, whereby the semiconductor elements 11 are separated from one another. This cutting can be performed with a saw 12 or a laser. Finally, the cut semiconductor elements are packaged and attached, for example, to a microcontroller 13. At this stage at the latest, information about which wafer 10 and in which position within the wafer 10 the semiconductor components were originally located is then lost. Typically, the microcontroller 13 with its semiconductor components 11 undergoes a number of tests, also referred to as final tests, again. However, due to the mixing caused by the cutting of the wafer 10, it is not easy to unambiguously determine on which wafer 10 each semiconductor component 11 of the microcontroller 13 is located and which wafer-level test corresponds to which final test, i.e., the test results of the same semiconductor component. These semiconductor components may be, for example, microelectronic assemblies such as integrated circuits (hereinafter also referred to as chips), sensors, etc.

[0039] The object of the present invention is to restore traceability along the packaging method in semiconductor manufacturing processes. Such assignment allows further contributions such as better process control or early prediction of final chip characteristics. Furthermore, the analysis of the causes of deviations measured in the chip plane during final inspection can be extended to processes in wafer production. This also allows for a deeper understanding of the process, leading to better process control and therefore better quality.

[0040] An assignment algorithm is proposed that consists of an alternating sequence of optimizing regression parameters (when regressing from wafer-level tests to final test data) followed by optimizing test partner assignments. The current assignment of the final test chips is used as the "regression label" in each iteration.

[0041] The present invention further uses a cost minimization algorithm, which can find the optimal one-to-one assignment under a preset cost matrix. To construct an appropriate cost matrix, the regression error is used by calculating an appropriate distance measure (e.g., L2 norm) between the final test prediction value of the trained regressor and the regression label. Based on this cost matrix, the algorithm sorts the final test chips so that the regression loss is minimized. Depending on the characteristics of the data, the regressor or regression model can be freely selected (e.g., linear regression for linear dependence).

[0042] 2 shows a schematic flow chart 20 of a method for determining an allocation rule, which allocates test results from a final test to each test result from a corresponding wafer-level test. After the method is completed, there should be an allocation rule that allocates commonly attributed test results from the wafer-level test to a final test, i.e., describes commonly attributed test results that originate from the same semiconductor component.

[0043] The method begins with step S21, in which allocation rules are initialized, and in which test results of wafer level test (WLT) and final test (FT) are provided.

[0044] This is followed by step S22, where a training data set is created, which comprises the WLT test results and the FT test results assigned according to their respective assignment rules.

[0045] After step S22 is completed, step S23 follows. In this step, a regressor f is trained, so that the regressor determines the final test assigned respectively according to the training data set depending on the wafer level test (WLT): f(WLT)=FT. The regressor f may be a linear regression model. The regressor is trained by known methods, for example, by minimizing the regression error on the training data set by adapting the parameters of the regressor f.

[0046] After the regressor has been trained, step S24 follows, where a cost matrix is ​​created. Rows and columns are assigned to wafer-level tests and final tests, respectively. The cost matrix entries are calculated, for example, using the L2 norm between the regressor's predictions, which depend on the corresponding WFT test results for each row and the corresponding FT test results for each column from the training data, and stored in the cost matrix.

[0047] After step S24 is completed, the allocation rules are optimized in step S25, either by applying the greedy implementation described above and / or by applying the Hungarian algorithm to the cost matrix to obtain improved allocation rules based on the cost matrix.

[0048] If the interruption criterion is not met, steps S22 to S25 are executed again, which may be a preset maximum number of iterations.

[0049] If the interruption criteria are met, the method ends and an allocation rule can be output.

[0050] In a step that optionally follows step S25, the allocation rules are used to reconstruct the positions of the semiconductor components 11 on the wafer 10. Here, the allocation rules can be used to determine the WLT test results starting from the FT test results and working backward. Typically, the WLT test results are additionally stored with the location on the wafer at which each test was performed, so that it is possible to reconstruct exactly where on the wafer the corresponding semiconductor components were manufactured.

[0051] It is envisaged that depending on the positional reconfiguration after step S25, a physical system, for example a computer-controlled machine such as a manufacturing machine, in particular a processing machine for wafers, may be driven and controlled by a control signal, for example, if the FT test result is not optimal, the control signal may adapt the preceding manufacturing steps accordingly in order to obtain a better FT test result later.

[0052] FIG. 3 shows diagrammatically an apparatus 30 for carrying out the method according to FIG.

[0053] The apparatus comprises a provider 51 which provides a training data set according to step S22. These training data are then provided to a regressor 52 which determines output variables therefrom. The output variables and the training data are provided to an estimator 53 which determines therefrom updated parameters for the regressor 52 which are transmitted to a parameter memory P where they replace the current parameters. The estimator 53 is configured to perform step S23.

[0054] The steps performed by the apparatus 30 may be implemented as a computer program stored on a machine-readable storage medium 54 and executed by a processor 55 .

[0055] The term "computer" includes any device for processing preconfigurable computational rules, which may exist in the form of software, hardware, or a mixture of software and hardware.

Claims

1. 1. A method for determining an assignment rule for assigning a first variable from a first set of first variables to a second variable from a second set of second variables, the method comprising: The method comprises the following steps: Initializing an allocation rule (S21) and providing said first and second sets (S21); The following steps a) to c) are performed: a) training a machine learning system so that the machine learning system determines the second variables respectively assigned according to an assignment rule depending on the first variables (S23); b) determining a set of distances between the predictions of the machine learning system depending on the first variable and the second variable (S24); and c) optimizing the allocation rule (S25) in dependence on the set of determined distances, whereby the allocation of the first variables to the second variables according to the allocation rule produces a minimum total distance in dependence on the determined distances; repeatedly executing Including, Here, for the step of optimizing the allocation rule (S25), the following steps are performed: i) randomly sampling a predicted value of the machine learning system, and searching for the second variable having the shortest distance to the sampled predicted value of the machine learning system; ii) modifying the assignment rules so that the assignment rules assign selected second variables to first variables on which the extracted predicted values ​​of the machine learning system depend; iii) removing distances in which the extracted predicted values ​​of the machine learning system are determined based on first variables that are determined depending on the first variables and that are determined based on the selected second variables from the set of determined distances; is executed multiple times sequentially.

2. 2. The method of claim 1, wherein a batch size is set in advance, a plurality of randomly selected predicted values ​​of the machine learning system are selected in the step (S24) of obtaining the set of distances, the number of the plurality of randomly selected predicted values ​​of the machine learning system corresponds to the batch size, and further wherein a distance between the plurality of randomly selected predicted values ​​of the machine learning system for the second variable is obtained in the step (S24).

3. 2. The method according to claim 1, wherein during the step (S25) of optimizing the allocation rule, depending on a set bit flag, it is selected whether the optimization of the allocation rule is performed using steps i) to iii) or using the Hungarian algorithm.

4. The method of claim 1 , wherein the machine learning system is a regression model (53) that determines the second variable depending on the first variable and parameters of a regression model.

5. 5. The method of claim 4, wherein the regression model (53) is a linear regression model and Tikhonov regularization is used during the training step (S23).

6. 2. The method of claim 1 , wherein the first and second variables characterize products as manufactured according to different manufacturing process steps, and the allocation rule characterizes which of the first and second sets of variables characterize the same product.

7. 2. The method of claim 1, wherein the first variable is a first test result of a semiconductor component on a wafer and the second variable is a second test result of the semiconductor component after it has been cut from the wafer, and the allocation rule characterizes which first and second test results originate from the same semiconductor component, in particular the first test result is a wafer-level test result and the second test result is a final test result.

8. 8. The method according to claim 7, wherein the semiconductor components are fabricated on different wafers, in particular the semiconductor components are power MOSFETs.

9. 8. The method according to claim 7, wherein depending on the assignment rule, it is determined which second test result belongs to which first test result, and then depending on the associated first test result, it is determined in which position within the wafer the semiconductor component is located.

10. 10. The method of claim 9, further variables characterizing the wafer and / or the semiconductor components on the wafer and second test results assigned to each of them are determined in addition to the positions, these data are combined into a training data set, and a further machine learning system is trained to predict the second test results depending on the training data set.

11. An apparatus (30) configured to perform the method of claim 1.

12. A computer program comprising instructions for causing a computer to carry out the method of claim 1 when said program is run by said computer.

13. A machine-readable storage medium having stored thereon the computer program of claim 12.

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