Estimation of Uncertainty in Position Reconstruction of Semiconductor Components on a Wafer

Abstract

The present invention relates to a method for estimating the uncertainty of 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 steps of: determining an uncertainty of a machine learning system trained using the assignment rule, the uncertainty being determined using a difference between the first variable and the second variable predicted by the machine learning system depending on the first variable and the second variable assigned to the first variable according to the assignment rule; determining a covariance matrix depending on the determined uncertainty; determining a likelihood matrix; and normalizing the likelihood matrix by dividing the values ​​of the likelihood matrix by the corresponding column sums.

Description

[Technical field]

[0001] The invention relates to a method for estimating the uncertainty of an allocation rule for the reconstruction of the positions of semiconductor components on a wafer on which the semiconductor components are deposited after the semiconductor components have been cut from the wafer, and to an apparatus configured to implement the 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.

[0004] The not yet published German patent application No. 102021209343 discloses a method for determining allocation rules between semiconductor components depending on the results of a wafer-level test and for determining allocation rules between packed semiconductor components depending on the results of a final test. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] German Patent Application No. 102021209343 Summary of the Invention [Problem to be solved by the invention]

[0006] Advantages of the invention According to the invention having the features of independent claim 1, it is possible to output a probabilistic testimony regarding the reliability of this allocation rule, with the advantage that no additional metadata such as univocal identifiers is required.

[0007] Furthermore, the present invention has the advantage that better process control of production (eg, analysis of the causes of defective parts, etc.) is possible based on this required reliability.

[0008] 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]

[0009] Disclosure of the Invention In a first aspect, the invention relates to a method, particularly computer-implemented, for estimating the uncertainty of 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, said assignment rule being able to assign a first variable to a second variable in an univocal 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 an 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 an 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.

[0010] The method starts with a step of providing a machine learning system trained with an assignment rule for assigning a first variable to a second variable according to the assignment rule. This machine learning system may be one or more decision trees, neural networks, support vector machines, etc. It should be noted that preferably the assignment rule and the machine learning system are created and trained alternately to each other. Particularly preferably, the method of German patent application no. 102021209343 is used here.

[0011] This is followed by a step of determining the inaccuracies of the machine learning system, where the inaccuracies are determined by the machine learning system using a difference between the predicted second variables depending on the first variables and the second variables assigned to the first variables according to the assignment rule. The difference is preferably a residual between the prediction of the machine learning system and the assigned second variables. This is followed by a step of determining a covariance matrix depending on the determined inaccuracies. This is followed by a step of determining a likelihood matrix, where for this purpose the determined inaccuracies are grouped into vectors, where the vectors are transposed and multiplied with an inverse covariance matrix, and the result is multiplied with a vector. This is followed by a step of normalizing the likelihood matrix by dividing the values / entries of the likelihood matrix by the corresponding column sums. In an optional step, an output of the normalized likelihood matrix can be performed. The entries of the likelihood matrix preferably indicate the probability as to how certain or with what confidence the jth first variable assigned to the entry [i,j] and the ith second variable assigned to this entry are likely to have been assigned by the machine learning system, in particular by the assignment rule.

[0012] This method allows to essentially probabilistically quantify the (alleatory) uncertainty inherent in the machine learning system, since even a perfect model may have difficulty distinguishing between very similar components / chips. Thus, it is now possible to obtain an estimate of the uncertainty or reliability of the allocation rule via the aleatory uncertainty of the machine learning system.

[0013] The first and / or second variables may be scalars or vectors, such as time series captured in particular by a sensor or indirectly determined sensor data. Preferably, the first and second variables are respectively one or several measurement results of one or several different measurements performed on one object of the plurality of objects, i.e. each variable is assigned to one of the objects. 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 was performed at a first time point and the measurement for the second variable was performed at a second time point, the second time point being after the first time point. The second time point may therefore be given after the object has been modified or changed.

[0014] In the step of determining the likelihood matrix, it is additionally proposed to scale the vector-matrix-vector multiplication result by a preset value, whereby an exponential function is applied to this scaled result, preferably the preset value is less than 1, particularly preferably this value is 0.5.

[0015] This has the advantage that it allows for a probabilistic consideration of the uncertainty. Mathematically, this can be expressed as follows:

number

[0016] 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, whereby during learning, the parameters of the regression model are adapted. Preferably, the regression model is a linear regression model.

[0017] 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.

[0018] 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.

[0019] 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.

[0020] 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).

[0021] 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.

[0022] Preferably, there are fewer final test results than wafer level test results, such as voltage tests and / or contact connection tests.

[0023] It is further proposed that the semiconductor components are manufactured on several different wafers.

[0024] It is further proposed to determine which second test result belongs to which first test result depending on the allocation rule and the likelihood matrix, and then determine in which position the semiconductor component is located in the wafer depending on the associated first test result. This 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 to the preceding process step. Preferably, the position reconstruction is visualized together with the respectively associated entry of the likelihood matrix. This has the advantage that the user can quickly visually access which position reconstructions are unreliable.

[0025] Based on the allocation rules and the likelihood matrix, more accurate traceability can be achieved during the restoration of traceability between wafer level and final test values. Because the likelihood matrix contains a quantification of the uncertainty of the allocation rules, for example, only certain allocations can be used for tracing. For example, an allocation is certain if the corresponding entry of the likelihood matrix for each allocation is greater than a preset value.

[0026] Advantageously, the likelihood matrix can also be used to answer probabilistic queries, for example, based on the likelihood matrix, it can be estimated how many similar second variables (e.g., FT test results) exist given similar probability distributions along the columns of the likelihood matrix, or with what probability chip A is assigned to chip B, or with what probability the WLT value range given the FT test result is measured.

[0027] For example, based on the likelihood matrix, it can be estimated how likely it is that a particular chip will be marked as missing; for this, the row sum of the likelihood matrix is ​​calculated. Since this can be greater than 1, a cutoff is made at 1. The lower the sum for the first variable (e.g. chip) of the associated row, the higher the probability that it will be marked as "missing".

[0028] For example, based on the likelihood matrix it is also possible to estimate how reliable the assignments are, especially between wafer-level and final test results. Each column of the likelihood matrix shows a probability distribution of the assignments of FT test results. The more "concentrated" these distributions are, the lower the uncertainty. For example, to obtain a measure of reliability, the quantile with the highest value (= highest probability) of 95 can be calculated.

[0029] This kind of probabilistic testimony based on the likelihood matrix contributes to a deeper understanding of the model and the production process, which may lead to better process control. Additionally, a threshold can be defined for using certain assignments for the preceding task (e.g., selecting only assignments with high probability).

[0030] 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.

[0031] 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.

[0032] 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.

[0033] It is further proposed that the semiconductor component element is a power MOSFET (English spelling: "power MOSFET").

[0034] 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.

[0035] In the following, embodiments of the invention are explained in more detail with reference to the accompanying drawings. [Brief description of the drawings]

[0036] [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

[0037] 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.

[0038] In semiconductor manufacturing processes, it is important to enable traceability after the packing process. Such an 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 at final inspection can be extended to the process in wafer production. This also allows a deeper understanding of the process, leading to better process control and therefore better quality.

[0039] From German patent application DE 102021209343 A1 an allocation algorithm for determining an allocation rule is known, which consists of an alternating sequence of optimization of regression parameters (when regressing from wafer-level tests to the final test data) followed by optimization of the allocation of test partners. The current allocation of the final test chips is used as "regression label" in each iteration.

[0040] 2 shows a schematic flow chart 20 of a method for estimating, in particular determining, the uncertainty of an allocation rule, which can allocate test results of a final test to respective corresponding wafer-level test results. After the method is completed, an allocation rule for allocating associated test results of a wafer-level test to a final test and an estimate of the uncertainty of the allocation rule should exist.

[0041] The method begins with step S21, in which a machine learning system trained on an assignment rule is provided for assigning a first variable to a second variable according to the assignment rule.

[0042] This is followed by a step (S22) of determining an inaccuracy Δ of the machine learning system, where the inaccuracy is determined using the difference between a second variable predicted by the machine learning system in dependence on the first variable and the second variable assigned to the first variable according to the assignment rule.

[0043] This is followed by a step (S23) of determining the covariance matrix Σ depending on the determined inaccuracy.

[0044] This is followed by a step (S24) of determining the likelihood matrix L, which is given by the following formula:

number

[0045] Finally, this is followed by a step of normalizing the likelihood matrix L (S25).

[0046] In a step that optionally follows step S25, the positions of the semiconductor components 11 on the wafer 10 are reconstructed using the assignment rule and the likelihood matrix. Based on the assignment rule, the WLT test results can now be determined starting from the FT test results and working backwards, depending on the likelihood matrix, whether the assignment according to the assignment rule is reliable or not. Usually, 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.

[0047] It is envisaged that depending on the positional reconfiguration, a physical system, e.g. 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, e.g. if the FT test result is not optimal, the control signal may accordingly adapt the preceding manufacturing steps in order to obtain a better FT test result later.

[0048] The apparatus steps for performing the method according to FIG. 2 may be implemented as a computer program, which may be stored on a machine-readable storage medium 54 and executed by the processor 55 .

Claims

1. 1. A method for estimating uncertainty of an assignment rule that assigns 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: providing a machine learning system trained on the assignment rules for assigning the first variables to the second variables according to the assignment rules (S21); A step (S22) of calculating an inaccuracy of the machine learning system, the inaccuracy being calculated using a difference between a second variable predicted by the machine learning system depending on the first variable and a second variable assigned to the first variable according to the assignment rule; A step (S23) of determining a covariance matrix depending on the determined inaccuracy; a step (S24) of determining a likelihood matrix of the uncertainty of the allocation rule, the determined imprecisions being grouped into a vector, the vector being transposed and multiplied by an inverse covariance matrix, and the result being multiplied by the vector; normalizing the likelihood matrix (S25); A method comprising:

2. 2. The method of claim 1, wherein in the step (S24) of obtaining the likelihood matrix, the result of the vector-matrix-vector multiplication is additionally scaled by a preset value and an exponential function is applied to the scaled result.

3. The method according to claim 1 or 2, 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.

4. 4. The method of claim 1, wherein the first and second variables characterize products being 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.

5. 5. 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.

6. The method of claim 5 , wherein the first test result is a wafer level test result and the second test result is a final test result.

7. 7. The method according to claim 1, wherein the semiconductor components are manufactured on a plurality of different wafers.

8. 8. The method according to claim 5, further comprising determining which second test result belongs to which first test result depending on the assignment rule and the normalized likelihood matrix, and then determining in which position within a wafer the semiconductor component is located depending in particular on the associated first test result.

9. Apparatus configured to carry out the method according to any one of claims 1 to 8.

10. A computer program comprising instructions for causing a computer to carry out a method according to any one of claims 1 to 8, when the program is executed by the computer.

11. A machine-readable storage medium (55) having stored thereon a computer program according to claim 10.

Images