Reconfiguring the position of semiconductor components 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 said method. [Background technology]

[0002] Prior Art In the packaging process of semiconductor components (especially PowerMOS), the traceability of the semiconductor components to their original wafer and to their original position on the wafer is lost. In concrete terms, this means that as soon as the wafer is cut or diced and packed, the position of each semiconductor component on the wafer is no longer available. The packaging process operator is in a position to provide at least a rough match between the loose semiconductor components at the Final Test and the semiconductor components on the wafer at the Wafer Level Test. However, this still leads to the fact that thousands of semiconductor components cannot be allocated to multiple wafers. Since this is effectively a combinatorial problem, the complexity of the solution to this problem is factorial, since there are n-factorially many different ways of arranging the 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 testing, although for semiconductor components such as PowerMOS this is not possible due to lack of memory. 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 using a greedy algorithm, potential allocations between semiconductor components are determined particularly efficiently, depending on the results of the wafer level test and the packaged semiconductor components and depending on the results of the Final Test, without the need for subsequently added metadata such as unique identifiers. Because a significantly lower computational and memory complexity is achieved based on the greedy algorithm, the allocation can be determined in a fraction of the computation time without the need for expensive hardware. This allows application to a significantly larger number of semiconductor components, in particular without increasing the error rate. The invention thereby widens the field of application, because the increased computational efficiency allows the allocation of more 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 has the further advantage of allowing a one-to-one assignment between semiconductor components and their original location on the wafer, thus allowing better process control (eg, root cause analysis of defective components, etc.).

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

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

[0009] The method starts with a step of initializing an allocation rule and providing a first and a second set. The initial allocation rule can be selected randomly or as a discriminatory allocation. Alternatively, other initial allocation rules are also envisaged, for example allocations that are pre-set and already partially correct.

[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 the iterations are interrupted if the interruption criterion is met, for example a minimal change in the allocation rules.

[0011] a) creating a data set with first variables and second variables assigned according to their respective assignment rules. This data set can also be called a training data set, 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 data set essentially only require the knowledge of the current assignment rules between the first and second variables, which can be provided by the data set or by the current assignment rules. The current assignment rules are the assignment rules present for the current iteration of steps a) to d), i.e. the assignment rules used during the most recent creation of the data set.

[0012] b) training the machine learning system so that it determines the respective assigned second variables of the data set in dependence on 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 in as close as possible to the second variables ("labels") of the data set. The 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. The optimization is preferably performed using a gradient descent method. The machine learning system can be one or more decision trees, neural networks, support vector machines, etc. This 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 predictions of the machine learning system and the second variables. The calculation of the distances can be performed sequentially, where each distance between the predictions of the machine learning system and the second variables is characterized according to an assignment rule, in particular between each variable of the second set for all predictions of the machine learning system. The determination of distances is preferably performed in the form of a cost matrix, where the entries of the cost matrix characterize the distances between the predictions of the machine learning system and the second variables according to an assignment rule, in particular between the predictions 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 envisaged. The cost matrix may be structured such that rows and columns are assigned to the first variable or to the predictions of the machine learning system depending 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. Entries that are not on the diagonal of the cost matrix can be thought of as the transportation costs that must be expended to assign a first variable to the second variable in the corresponding row / column, respectively, in violation of the assignment rule.

[0014] d) optimizing the allocation rule in dependence on the cost matrix, whereby the allocation rule generates a minimum total cost, in particular a 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 carry out 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 in dependence on the allocation rule is optimized, in particular minimized. It should be noted here that the entries are selected in dependence on the allocation rule, such that the entries of the respective columns and rows of the cost matrix are selected that are assigned to the first and second variables in dependence on the allocation rule and that are assigned to each other in dependence on 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 carrying out the following steps for all predictions of the machine learning system: i) randomly sampling a predicted value of the machine learning system and searching for a second variable having a shortest distance to the sampled predicted value of the machine learning system according to a cost matrix, in other words, based on the cost matrix, a second variable is selected whose entry in the cost matrix characterizes the shortest distance to the aforementioned predicted value; ii) modifying the assignment rule such that the assignment rule assigns the selected second variable to a first variable for which the extracted prediction 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 is dependent on the first variables, and entries assigned to the selected second variables.

[0016] At each iteration for the optimization of the allocation rule, the above method selects the shortest distance between the prediction of the machine learning system and the second variable. Since the method only considers a single target observation, the problem is optimized locally or greedily. Therefore, one can mention the existence of greedy implementations. The removal of selected variables after the modification of the allocation rule has the advantageous effect of being able to enforce a one-to-one allocation.

[0017] In the proposed approach, the cost is minimized locally rather than globally, which turns out to be much more computationally efficient and surprisingly does not degrade the quality of the assignment rules, since a greedy implementation leads to similar results: 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 over the cost matrix is ​​more or less unique.

[0018] The allocation rule determined 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, in particular sensor data captured or indirectly determined by a sensor. Preferably, the first and second variables are one or more measurement results, respectively, of one or more different measurements performed on one object of the plurality of objects. That is to say, each variable is assigned to one of the objects. It is also possible to use only a preconfigurable number of measurements of the plurality of measurements for the second variable in the step of creating the data set. The assignment rules 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 was performed at a first time point and the measurement for the second variable was performed at a second time point, where the second time point is after the first time point. The second time point may therefore be given after the object has undergone a modification or change.

[0020] It is proposed here that a batch size is preset, where during the step of determining the cost matrix a number of randomly selected predictors of the machine learning system are selected, where the number of randomly selected predictors of the machine learning system corresponds to the batch size, and where further during the step of determining the cost matrix a distance between the number of randomly selected predictors of the machine learning system for a second variable is determined. An advantage is that 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 here 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, a selection is made whether the optimization of the allocation rule is performed using steps i) to iii) or using the Hungarian algorithm, whereby it is advantageous that a flexible change of 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 method, also known as the Kuhn-Munkrös algorithm, is an algorithm for solving the weighted assignment problem.

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

[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 explanatory 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, the ordinary least squares method calculates 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, where Tikhonov regularization is used during the learning step. Linear regression aims to minimize the squared regression loss, so it is preferred 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 may here be given when one manufacturing process step is finished. The product may be any product manufactured in a manufacturing plant. Advantageously, 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, for example a screw (so-called "bulk material"). It is envisaged that the first variable characterizes a component (in particular a part) and the second variable characterizes a final product, where the allocation rules describe which component has been processed for which product or which part has been attached to which product. The invention thus makes it possible to assign a manufacturing batch of parts based on the measurements of the product, for example when it is no longer possible to remove parts from a product without destruction, for example to read out the serial number.

[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 the wafer, and the second variable is a second test result or measurement result of the semiconductor component after it has been cut out 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 results may also relate to the entire semiconductor component. Here, linear regression has proven to be particularly effective for machine learning systems to find the best allocation rules, since it starts from a linear relationship, which here represents a meaningful assumption for the allocation of test results. Linear regression is a special case of regression. In linear regression, a linear function is assumed here, i.e. 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 the method can find an appropriate allocation rule across multiple wafers even within a reasonable computation time.

[0031] It is further proposed to determine which second test result belongs to which first test result depending on the allocation rule, and then determine in which position the semiconductor component was located in the wafer depending on the associated first test result, which allows a position reconstruction that 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 position, further variables characterizing the wafer and / or semiconductor components on the wafer and the respectively assigned test results, whereby these data are integrated into a further training data set, whereby a further machine learning system is trained depending 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 further training data sets and to train further machine learning systems to predict the properties of packed semiconductor components at earlier stages 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 conserving process resources and reducing waste.

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

[0036] In the following, embodiments of the invention are explained in more detail with reference to the accompanying drawings. [Brief description of the drawings]

[0037] [Figure 1] FIG. 2 shows a schematic diagram of the packaging process. [Diagram 2] FIG. 2 is a schematic diagram illustrating an embodiment of a flow chart of the present invention. [Diagram 3] FIG. 1 is a schematic diagram of a training device. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0038] Description of the embodiment In the packaging process of semiconductor components or semiconductor components, the traceability of the semiconductor components to their original wafer and to their original position on the respective wafer is usually lost, because after the semiconductor components are cut out, a mixture of the individual semiconductor components can result, which leads to the loss of their position on the wafer without a unique marking of the components. This is shown diagrammatically in FIG. 1. The wafer 10 has a number of semiconductor components or semiconductor components 11, respectively. At this stage, each semiconductor component 11 has a known position on the wafer 10. Usually, the semiconductor components 11 undergo a number of tests, also referred to as wafer-level tests, at this stage. This is followed by cutting of the wafer 10, whereby the semiconductor components 11 are separated from one another. This cutting can be carried out by a saw 12 or a laser. Finally, the cut semiconductor components are packed and attached, for example, to a microcontroller 13. Then, at the latest at this stage, the information on which wafer 10 and in which position within the wafer 10 the semiconductor components were originally located is lost. Usually, the microcontroller 13 with the semiconductor components 11 is again subjected to a number of tests, also called final tests. However, due to the mixing caused by the sawing of the wafer 10, it is not easy to unambiguously associate on which wafer 10 the respective semiconductor components 11 of the microcontroller 13 are located and which wafer-level tests correspond to which final tests, i.e. the test results of the same semiconductor components. These semiconductor components may be, for example, microelectronic assemblies such as integrated circuits (hereinafter also called chips), sensors, etc.

[0039] The object of the present invention is to recover traceability according to the packaging method in the semiconductor manufacturing method. Such an assignment allows further contributions such as better process control or early prediction of final chip characteristics. Furthermore, the cause analysis of the deviations measured in the chip plane in the final inspection can be extended to the process in the wafer production. This also allows 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 the regression parameters (when regressing from wafer-level tests to the test data of the final test) followed by optimizing the assignment of test partners. 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 a suitable cost matrix, the regression error is used by calculating a suitable distance measure (e.g., L2 norm) between the final test prediction value of the trained regressor to 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 dependency).

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

[0043] The method starts 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, which is respectively assigned 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 in a known manner, for example, via minimizing the regression error on the training data set by adapting the parameters of the regressor f.

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

[0047] After step S24 is completed, the optimization of the allocation rules continues in step S25, 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 WLT test results can be determined retroactively starting from the FT test results based on the allocation rules. Typically, the WLT test results are additionally stored with respect to which position on the wafer the respective test was performed, so that it is possible to reconstruct exactly where on the wafer the corresponding semiconductor components were manufactured.

[0051] Depending on the positional reconfiguration after step S25, it is envisaged that a physical system, for example a computer-controlled machine such as a manufacturing machine, in particular a processing machine for wafers, may be driven by a control signal for controlling the physical system, for example a computer-controlled machine such as a manufacturing machine, in particular a processing machine for wafers, etc. 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 therefrom output variables. The output variables and the training data are provided to an evaluator 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 evaluator 53 is adapted to carry out 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, 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), namely: a) training a machine learning system so that the machine learning system determines the second variables, each of which is assigned according to an assignment rule, depending on the first variables (S23); b) determining a set of distances between predictions of the machine learning system depending on the first and second variables (S24); and c) optimizing the allocation rule in dependence on the set of determined distances (S25), 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 (S25); and 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 a shortest distance to the sampled predicted value of the machine learning system; ii) modifying the assignment rules such that the assignment rules assign selected second variables to first variables for which the extracted prediction value of the machine learning system is dependent on the first variables; iii) removing from the set of distances that the extracted prediction values ​​of the machine learning system are determined based on a first variable determined in dependence on the first variable and that are determined based on the selected second variable; is executed multiple times sequentially.

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

3. 3. The method according to claim 1 or 2, 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 according to any one of claims 1 to 3, wherein the machine learning system is a regression model (53) for determining the second variable depending on the first variable and parameters of a regression model.

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. 6. 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. 7. The method according to 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 out 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 1, wherein the semiconductor components are fabricated on different wafers, in particular the semiconductor components are power MOSFETs.

9. 9. The method according to claim 7, further comprising determining, depending on the allocation rule, which second test result belongs to which first test result, and then determining, depending on the associated first test result, in which position within the wafer the semiconductor component is located.

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

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

12. A computer program comprising instructions for causing a computer to carry out a method according to any one of claims 1 to 10, when the program is executed by the computer.

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

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