UNSAFETY ASSESSMENT OF A POSITION RECONSTRUCTION OF SEMICONDUCTOR COMPONENTS ON A WAFER

Description

[0001] The invention relates to a method for estimating the uncertainty of an assignment rule for reconstructing the positions of semiconductor components on a wafer on which they were deposited after the semiconductor components were cut out of the wafer, and to a device configured to carry out the method. State of the art

[0002] During the packaging process of semiconductor components (specifically PowerMOS), the traceability of the semiconductor components to their original wafer and their original position on the wafer is lost. Specifically, this means that the position of each semiconductor component on a wafer is no longer available once the wafer has been cut or diced (a process in which the semiconductor component is separated from the wafer) and packaged. Packaging process providers are able to offer at least a rough matching between loose semiconductor components in the final test (the inspection process for semiconductor components after packaging) and semiconductor components on the wafer in wafer-level tests (the inspection process before packaging). However, this still results in several thousand unassignable semiconductor components from multiple wafers.Since this is essentially a combinatorial problem, the complexity of the solution to this task is factorial, as there are n factorial many different ways to arrange the semiconductor components so that they correspond to the correct sequence, where n is the number of semiconductor components.

[0003] For ASIC semiconductor devices, there is a solution to this combinatorial problem. During wafer-level testing, a unique identifier is stored in the memory of the ASIC semiconductor device, allowing the final inspection to be linked to the wafer-level test after packaging. However, this is not possible for semiconductor devices like PowerMOS due to the lack of memory.

[0004] From the unpublished DE 10 2021 209 343 a method is known to determine an allocation rule between semiconductor components depending on the results of the wafer-level test and packaged semiconductor components depending on the results of the final test.

[0005] From US patent 7 868 474 B2, a method and structures for indexing chips are known.

[0006] An integral record of semiconductor wafers is known from US 5 256 578 A. Advantages of the invention

[0007] The invention with the features of independent claim 1 has the advantage that it makes it possible to output a probabilistic statement regarding the reliability of this assignment rule, and it does so without added metadata, such as unique identifiers or the like.

[0008] The invention also has the advantage that, based on this determined reliability, better process control of production (e.g. root cause analysis of defective parts) is enabled.

[0009] Further aspects of the invention are the subject of the dependent claims. Advantageous embodiments are the subject of the dependent claims. Disclosure of the invention

[0010] In a first aspect, the invention relates to a method, particularly a computer-implemented one, for estimating the uncertainty of an assignment rule that assigns first quantities from a first set of first quantities to second quantities from a second set of second quantities. The assignment rule can assign the first quantities to the second quantities in a unique way, i.e., that each first quantity is assigned at most one second quantity by the assignment rule, and preferably vice versa. A set can be understood as a form of a grouping of the individual quantities. Preferably, the first and second sets are distinct sets that do not have a common quantity. Preferably, each quantity in the first and second sets is assigned an index. All indices of the first and second sets could be considered index sets, i.e., sets whose elements index the quantities of the first or second set.The assignment rule then assigns each index from the second index set to the first. The assignment rule thus describes which first value belongs to which second value, and preferably vice versa. The assignment rule can be in the form of a list, table, or similar format.

[0011] The process begins with the provision of a machine learning system, which has been trained using the assignment rule to assign the first quantities to the second quantities according to the assignment rule. The machine learning system can be one or more decision trees, a neural network, a support vector machine, or similar. It should be noted that preferably the assignment rule and the machine learning system are created and trained alternately. The method described in DE 10 2021 209 343 is particularly preferred.

[0012] This is followed by the determination of inaccuracies of the machine learning system, whereby the inaccuracies are determined by the difference between the second quantities predicted by the machine learning system, depending on the first quantities, and the second quantities assigned to the first quantities according to the assignment rule. The difference is preferably a residual between the prediction of the machine learning system and the assigned second quantity. This is followed by the determination of a covariance matrix depending on the determined inaccuracies. This is followed by the determination of a likelihood matrix, whereby the determined inaccuracies are grouped into a vector, the vector is transposed, multiplied by the inverted covariance matrix, and the result is multiplied by the vector.This is followed by normalizing the likelihood matrix by dividing the values / entries of the likelihood matrix by the corresponding column sums. Optionally, the normalized likelihood matrix can be output. The entries of the likelihood matrix preferably indicate the probability of how reliably the machine learning system, specifically its assignment rule, would assign the j-th first quantity and the i-th second quantity to the entry [i,j].

[0013] This method makes it possible to quantify the inherent (aleatory) uncertainty in the machine learning system in a probabilistic way, since even a perfect model can have difficulty distinguishing between very similar components / chips. This makes it possible to determine an uncertainty or reliability estimate of the assignment rule based on the aleatory uncertainty of the machine learning system.

[0014] The first and / or second quantities can be scalars or vectors, such as a time series, and in particular can be sensor-acquired or indirectly determined sensor data. Preferably, the first and second quantities are each one or more measurement results from a single measurement or from multiple different measurements, each performed on one or more objects. That is, each quantity is assigned to one of the objects. The assignment rule can specify which first and second quantities are measurement results of the same object. It is particularly preferred that at least one measurement of the objects for the first quantities is performed at a first time point and the measurement for the second quantities is performed at a second time point, the second time point being after the first. The second time point can then be after the objects have been subjected to a modification or change.

[0015] It is proposed that, when determining the likelihood matrix, the result of the vector-matrix-vector multiplication is additionally scaled by a predetermined value, and an exponential function is applied to this scaled result. Preferably, the predetermined value is less than 1; more preferably, the value is 0.5.

[0016] This has the advantage that a probabilistic analysis of the uncertainties is now possible. Mathematically, this can be expressed as follows: L ij = exp − 1 2 y j − f x i T Σ − 1 y j − f x i where f ( xi ) the prediction of the machine learning system depends on the first quantity x and y the second size describes and Σ the covariance matrix.

[0017] Furthermore, it is proposed that the machine learning system be a regression model which determines the second variables based on the first variables and parameters of the regression model, whereby the parameters of the regression model are adjusted during training. Preferably, the regression model is a linear regression model.

[0018] Regression is used to model relationships between a dependent variable (often also called the explained variable) and one or more independent variables (often also called explanatory variables). Regression can parameterize a more complex function so that it best represents the data according to a specific mathematical criterion. For example, the ordinary least squares method calculates a unique line (or hyperplane) that minimizes the sum of squared deviations between the true data and this line (or hyperplane), i.e., the residual sum of squares.

[0019] Furthermore, it is proposed that the first and second parameters characterize a product during its manufacture, specifically at different stages of the manufacturing process. For example, the second parameter could be defined as the point in time when a manufacturing process step has been completed. The product can be any product manufactured at a production facility. Preferably, traceability to its preceding process steps is lost during the product's manufacture (so-called "bulk material"), for example, when it is no longer possible to directly assign the product from the bulk material, e.g., screws, to a production batch. It is conceivable that the first parameters characterize components, particularly parts, and the second parameters characterize finished products, with the assignment rule describing which component was processed into which product or which part was installed in which product.For example, if the component in the product can no longer be removed non-destructively in order to read its serial number. With this invention, it is then possible to assign the component's production batch based on measurements of the product.

[0020] The first and second values ​​can be measurement / test results or other properties of the products, components, etc. The first and second values ​​preferably differ slightly from each other, for example due to manufacturing tolerances, but describe the same measurements / properties of the products, components, etc.

[0021] Furthermore, it is proposed that the first values ​​represent initial test results or measurement results of semiconductor components on a wafer, and the second values ​​represent the second test results or measurement results of the semiconductor components after they have been removed from the wafer. Semiconductor components can be parts of grown electrical components on the wafer, such as a transistor group in an integrated circuit. The test results can also refer to the entire semiconductor component. For the machine learning system, linear regression has proven particularly effective in finding the optimal assignment rule. This is because it assumes a linear relationship, which is a sensible assumption for assigning the test results. Linear regression is a special case of regression. In linear regression, a linear function is assumed.Therefore, only those relationships are considered where the dependent variable is a linear combination of the regression coefficients (but not necessarily of the independent variables).

[0022] It is further proposed that the first test results be wafer-level test results and the second test results be final test results. Preferably, there should be fewer final test results than wafer-level test results. The tests include, for example, voltage tests and / or contact tests.

[0023] Furthermore, it is suggested that the semiconductor component elements were manufactured on a plurality of different wafers.

[0024] Furthermore, it is proposed that, depending on the assignment rule and the likelihood matrix, it is determined which second test result corresponds to which first test result. Then, based on the corresponding first test result, the position of the semiconductor component within a wafer is determined. This allows for position reconstruction, which for the first time makes it possible to unambiguously trace semiconductor components from the last manufacturing process steps of semiconductor production back to previous process steps. Preferably, the position reconstruction is visualized together with the respective entries of the likelihood matrix. This has the advantage that it allows a user to quickly see which position reconstructions might be less reliable.

[0025] Using the assignment rule and the likelihood matrix, more accurate traceability can be achieved when restoring traceability between wafer level and final test values, as the likelihood matrix quantifies the uncertainty of the assignment rule, allowing, for example, the use of only reliable assignments for traceability. An assignment is considered reliable if, for example, a corresponding entry in the likelihood matrix for the respective assignment is greater than a predefined value.

[0026] Advantageously, the likelihood matrix can also be used to answer probabilistic questions. For example, the likelihood matrix can be used to estimate how many similar second quantities (e.g., FT test results) exist given similar probability distributions along columns of the likelihood matrix, or with what probability chip A is assigned to chip B, or with what probability a WLT value range is measured given an FT test result.

[0027] For example, the likelihood matrix can be used to estimate the probability that a specific chip is marked as missing, by calculating the row sum of the likelihood matrix. Since this sum can also be higher than 1, a cutoff is applied at 1. The lower the sum for a first item (e.g., a chip) in the corresponding row, the higher the probability that it will be marked as "Missing".

[0028] For example, the likelihood matrix can also be used to estimate the reliability of the mapping, particularly between wafer levels and final test results. Each column in the likelihood matrix represents a probability distribution for the mapping of an FT test result. The more concentrated these distributions are, the lower the uncertainty. For instance, a highest value (the highest probability) can be calculated using the .95 quantile to determine a measure of reliability.

[0029] Such probabilistic statements based on the likelihood matrix contribute to a deeper understanding of the model and the production process and can lead to better process control. Furthermore, thresholds can be defined for the use of certain assignments for upstream tasks (e.g., selecting only assignments with a high probability).

[0030] Furthermore, it is proposed that, in addition to the positions, further parameters characterizing the wafer and / or the semiconductor components on the wafer and their respective associated test results are determined, with these data being combined into a further training data set, and with the further training data set being used to train another machine learning system to predict the second test results.

[0031] The advantage here is that the mapping can be used to create another training dataset to train another machine learning system to predict the properties of a packaged semiconductor device at an early stage of the manufacturing process. This significantly reduces the time to detect deviations in the process parameters, especially for parameters that can only be correctly evaluated during final tests (e.g., RDSon).

[0032] Another advantage is that the mapping can also be used to train another machine learning system that actively identifies defective semiconductor chips. This saves process resources and reduces waste.

[0033] Furthermore, it is proposed that the semiconductor component elements are power MOSFETs.

[0034] In further aspects, the invention relates to a device and a computer program, each configured to perform the above methods, and a machine-readable storage medium on which this computer program is stored.

[0035] Embodiments of the invention are explained in more detail below with reference to the accompanying drawings. The drawings show: Figure 1 schematically illustrates a packaging process; Figure 2 schematically illustrates an embodiment of a flowchart of the invention; Figure 3 schematically illustrates a training device. Description of the exemplary implementations

[0036] During the packaging process of semiconductor components, the traceability of the components to their original wafer and their original position on the respective wafer is typically lost. This is because, after the semiconductor components are cut out, they can become mixed up, and without a clear marking of the components, their position on the wafer is lost. This is shown schematically in Figure 1The wafers 10 each contain a plurality of semiconductor components 11. At this stage, each semiconductor component 11 has a known position on the wafers 10. Typically, the semiconductor components 11 are subjected to a plurality of tests at this stage, also known as wafer-level tests. This is followed by cutting the wafers 10 so that the semiconductor components 11 are separated from one another. Cutting can be done by saw 12 or by laser. Finally, the cut semiconductor components are packaged, e.g., installed in microcontrollers 13. At this stage, at the latest, the information about which wafer 10 and at which position within the wafer 10 the semiconductor component was originally located is lost.Typically, the microcontrollers 13, along with the semiconductor components 11, are subjected to a series of tests, also known as final tests. However, since the wafers 10 were cut and mixed, it is not readily possible to definitively trace back to which wafer 10 each semiconductor component 11 of the microcontroller 13 was located, nor to which wafer-level test corresponds to which final test—that is, to which test results are for the same semiconductor component. The semiconductor components can be microelectronic assemblies, such as integrated circuits (hereinafter also referred to as chips), sensors, or similar devices.

[0037] It is important to enable traceability after the packaging process in a semiconductor manufacturing process. Such tracking allows for further benefits such as improved process control and early prediction of final chip properties. Furthermore, the root cause analysis of deviations measured during final inspection at the chip level can be extended to the processes in wafer production. This, in turn, enables a much deeper understanding of the processes and leads to better process control and thus improved quality.

[0038] From DE 10 2021 209 343, an assignment algorithm for determining an assignment rule is known, which consists of an alternating sequence of optimizing regression parameters (when regressing from wafer-level test to final-test test data) and subsequent optimization of the assignment of test partners. The current assignment of the final test chips is used as the 'regression label' in each iteration.

[0039] Figure 2 Figure 20 schematically shows a flowchart of a procedure for estimating, in particular determining, the uncertainty of the assignment rule. The assignment rule can assign test results of the final test to the respective corresponding wafer-level test results. After completion of the procedure, an assignment rule and an estimate of the uncertainty of the assignment rule should be available, which assigns the corresponding test results of the wafer-level test to the final tests.

[0040] The procedure begins with step S21. In this step, a machine learning system is provided, which has been trained on the assignment rule to assign the first quantities to the second quantities according to the assignment rule.

[0041] This is followed by a determination (S22) of inaccuracies Δ of the machine learning system, whereby the inaccuracies are determined by the machine learning system by means of a difference between the predicted second quantities depending on the first quantities and the second quantities assigned to the first quantities according to the assignment rule.

[0042] Then follows the determination (S23) of a covariance matrix. Σ depending on the inaccuracies identified.

[0043] Next, a likelihood matrix L is determined (S24). This can be calculated using the following formula: L = exp − 1 2 Δ T Σ − 1 Δ

[0044] Finally, a normalization (S25) of the likelihood matrix L follows.

[0045] In an optional step following step S25, the position of the semiconductor components 11 on the wafer 10 is reconstructed using the assignment rule and the likelihood matrix. Here, the WLT test results can be determined backwards from the FT test results using the assignment rule, with the likelihood matrix determining whether the assignment is reliable. Since the position within the wafer where each test was performed is typically stored along with the WLT test results, it is possible to reconstruct precisely where the corresponding semiconductor component was manufactured on the wafer.

[0046] It is conceivable that, depending on a position reconstruction, a control signal could be triggered to control a physical system, such as a computer-controlled machine, like a manufacturing machine, especially wafer processing machines. For example, if the FT test results are not optimal, the control signal could adjust a previous manufacturing step accordingly to obtain better FT test results later.

[0047] The steps from a device to carrying out the procedure according to Fig. 2 can be implemented as a computer program, stored on a machine-readable storage medium 54, and executed by a processor 55.

Claims

1. Computer-implemented method for estimating an uncertainty of an assignment rule that assigns first variables from a first set of first variables to second variables from a second set of second variables, wherein the first variables are first test results of semiconductor components on a wafer, wherein, in relation to the first test results, the position within the wafer at which the respective test was carried out is additionally stored, and the second variables are second test results of the semiconductor components after they have been cut out from the wafer, wherein the assignment rule characterizes which first and second test results originate from the same semiconductor component, comprising the following steps: providing (S21) a machine learning system that has been trained, based on the assignment rule, to assign the first variables to the second variables in accordance with the assignment rule; determining (S22) inaccuracies of the machine learning system, wherein the inaccuracies are determined by way of a difference between second variables predicted by the machine learning system, which are predicted depending on the first variables, and the second variables assigned to the first variables in accordance with the assignment rule; determining (S23) a covariance matrix depending on the determined inaccuracies; determining (S24) a likelihood matrix (L) of the uncertainties of the assignment rule, wherein the determined inaccuracies are grouped into a vector, wherein the vector (Δ) is transpose-multiplied by the inverted covariance matrix (Σ) and the result thereof is multiplied by the vector (Δ) according to the formula L = exp − 1 2 Δ T Σ − 1 Δ , and normalizing (S25) the likelihood matrix (L), determining, depending on the assignment rule and the normalized likelihood matrix, which second test result belongs to which first test result, and determining, depending on the associated first test result, the position at which the semiconductor component was arranged within the wafer.

2. Method according to Claim 1, wherein, when determining (S24) the likelihood matrix (L), the result of the vector-matrix-vector multiplication is additionally scaled with a predefined value and wherein an exponential function is applied to this scaled result.

3. Method according to either of the preceding claims, wherein the machine learning system is a regression model (53) that determines the second variables depending on the first variables and parameters of the regression model.

4. Method according to Claims 1 to 3, wherein the first test results are wafer-level test results and the second test results are final test results.

5. Method according to one of the preceding claims, wherein the semiconductor components were produced on a plurality of different wafers.

6. Device configured to carry out the method according to one of the preceding claims.

7. Computer program comprising instructions that, when the program is executed by a computer, cause the latter to carry out the method according to Claims 1 to 5.

8. Machine-readable storage medium (55) on which the computer program according to Claim 7 is stored.