Method for training a machine learning model to predict properties of semiconductor devices manufactured on semiconductor wafers

Abstract

According to various embodiments, a method for training a machine learning model to predict properties of semiconductor devices fabricated on wafers is described, comprising measuring, for each wafer of a training wafer set, the properties for a set of semiconductor devices on the wafer; training a machine learning model to predict the measured properties for the training wafer set; measuring, for a further wafer, the properties for a subset of the semiconductor devices on the further wafer; and adapting the machine learning model to reduce a loss that includes a prediction loss between the machine learning model's prediction for the properties of the subset of semiconductor devices on the further wafer and the properties measured for the subset of semiconductor devices on the further wafer.

Description

[0001] The present disclosure relates to methods for training a machine learning model to predict properties of semiconductor devices fabricated on semiconductor wafers.

[0002] During the fabrication of semiconductor devices on wafers, process variations typically occur that affect the parameters of the semiconductor devices. Knowledge of the parameters of the semiconductor devices is important because, through appropriate calibration, they can be adjusted to achieve good performance despite the fluctuations during their production. However, it is complex to perform corresponding measurements for all semiconductor devices, as they are often fabricated on wafers in high volumes. Therefore, effective approaches for estimating the properties of semiconductor devices manufactured on semiconductor wafers (possibly including test structures) are desirable.

[0003] According to various embodiments, a method is provided for training a machine learning model for predicting properties of semiconductor devices fabricated on (semiconductor) wafers, comprising measuring, for each wafer of a training wafer set, the (to be predicted) properties for a set of semiconductor devices on the wafer, training a machine learning model for predicting the measured properties for the training wafer set (i.e., the measured properties are used as ground truth (i.e., ground truth, i.e., labels for training)), measuring, for a further wafer, the properties for a portion of the semiconductor devices on the further wafer; and adapting the machine learning model for reducing (i.e., towards a reduction) a loss that (e.g.,as a loss term of a loss function) involves a prediction loss between the machine learning model's prediction for the properties of the portion of semiconductor devices on the further wafer and the properties measured for the portion of semiconductor devices on the further wafer (i.e., the machine learning model is adapted to the further wafer by further training the machine learning model to predict the properties measured for the further wafer).

[0004] The method described above enables improved parameter estimation (i.e., determination of properties) of sensors on a wafer, both in terms of accuracy and efficiency. The estimated parameters can be used for further process steps, such as sensor calibration. The increased efficiency (not all sensors need to be measured) can accelerate the manufacturing process. Nevertheless, calibration based on the (precise) estimate allows for high sensor accuracy and performance.

[0005] Various examples of implementation are given below.

[0006] Embodiment 1 is a method for training a machine learning model for predicting properties of semiconductor devices fabricated on (semiconductor) wafers as described above.

[0007] Embodiment 2 is a method according to embodiment 1, wherein the set of semiconductor components includes the majority of semiconductor elements of the wafer (e.g., all or at least almost all) and wherein the portion of the semiconductor components on the further wafer includes only a minority of the semiconductor components of the further wafer.

[0008] In other words, the wafers in the training wafer set are measured at least almost completely, while the additional wafer(s) for which the machine learning model is then adapted are only partially measured. This allows the properties of the additional wafer(s) to be determined with significantly less effort than with a full measurement.

[0009] Embodiment 3 is a method according to embodiment 1 or 2, wherein the loss includes an unsupervised training loss.

[0010] Thus, for adapting the machine learning model for the additional wafer, the supervised loss, which uses the measured properties as labels (ground truth), can be supplemented with a loss from unsupervised training. For example, a network parameter change loss can be used to prevent the adapted model from deviating too far from the trained model (e.g., due to outliers in the properties measured for the additional wafer).

[0011] Embodiment 4 is a method according to any one of embodiments 1 to 3, wherein training the machine learning model comprises: training, for each wafer of the training wafer set, a respective instance of the machine learning model for predicting the properties measured for a (true) subset of the set of semiconductor devices on the wafer; and adapting the machine learning model in the descending direction of a further loss (i.e., a loss used in the adaptation) that includes the prediction error of the instances of the machine learning model for (respectively) the set of semiconductor devices averaged over the wafers of the training wafer set (i.e.,in the direction of the descent of a loss which includes (as a loss term) a total error which is the average over errors, where each of the averaged errors is the prediction error of the respective instance for the set of semiconductor devices of the respective wafer).

[0012] Thus, the machine learning model forms a generalized model that can provide good predictions over a large class of wafers (as represented by the training wafer set) and can be efficiently adapted to specific wafers of this class.

[0013] To adapt the machine learning model in the descending direction of the further loss, a total error can first be determined, which is the average over errors, where each of the errors being averaged is the prediction error of the respective instance for the set of semiconductor components of the respective wafer, and a gradient can be determined from this, or a gradient of the respective prediction error is determined for each instance and averaged over these gradients.

[0014] Embodiment 5 is a method according to embodiment 4, wherein the further loss includes an unsupervised training loss.

[0015] Thus, the supervised loss, which uses the measured features as labels (ground truth), can be supplemented with an unsupervised training loss. For example, the use of augmentations can improve training without having to increase the number of training wafers.

[0016] Embodiment 6 is a method according to any one of embodiments 1 to 5, further comprising predicting properties of other semiconductor devices on the further wafer as the part of the semiconductor devices on the further wafer by means of the adapted machine learning model.

[0017] Embodiment 7 is a semiconductor device test arrangement configured to perform a method according to any one of embodiments 1 to 6.

[0018] Embodiment 8 is a computer program including instructions that, when executed by a processor, cause the processor to perform a method according to any one of embodiments 1 to 6.

[0019] Embodiment 9 is a computer-readable medium storing instructions that, when executed by a processor, cause the processor to perform a method according to any one of embodiments 1 to 6.

[0020] In the drawings, like reference characters generally refer to the same parts throughout the several views. The drawings are not necessarily to scale, emphasis instead generally being placed upon illustrating the principles of the invention. In the following description, various aspects are described with reference to the following drawings. Fig. 1 shows a semiconductor wafer. Fig. 2 illustrates the training of a meta-model according to one embodiment. Fig. 3 illustrates the adaptation of the meta-model to another wafer. Fig. 4 shows a flowchart illustrating a method for training a machine learning model to predict properties of semiconductor devices fabricated on semiconductor wafers according to one embodiment.

[0021] The following detailed description refers to the accompanying drawings, which, by way of illustration, show specific details and aspects of this disclosure in which the invention may be practiced. Other aspects may be utilized, and structural, logical, and electrical changes may be made without departing from the scope of the invention. The various aspects of this disclosure are not necessarily mutually exclusive, as some aspects of this disclosure may be combined with one or more other aspects of this disclosure to form new aspects.

[0022] Various examples are described in more detail below.

[0023] (Semiconductor) components that are manufactured on the basis of semiconductors are typically manufactured on semiconductor wafers.

[0024] Fig. 1 shows a semiconductor wafer 100.

[0025] A plurality of components 101 are formed on the semiconductor wafer 100. In the following examples, it is assumed that the components 101 are sensors (e.g., MEMS (Micro-Electro-Mechanical System) sensors), but they may also be other components 101, such as, for example, integrated electronic circuits.

[0026] During the production of sensors (or other components) on wafers, inaccuracies and fluctuations in the process parameters typically occur due to stochastic and deterministic variations in the manufacturing process. As a result, the individual sensors 101 on the wafer 100 differ in various parameters (i.e., properties), which affect their subsequent performance. In the case of MEMS gyroscope sensors 101, for example, they can differ in their resonance frequency, quality factor, damping, etc. This can depend on various factors, in particular the position on the wafer where a particular sensor 101 was formed.

[0027] Knowledge of the individual sensor parameters (such as resonance frequency) can be used to better calibrate the sensors later in the process, thereby increasing performance and compensating for variations between the individual sensors. For this reason, the individual sensors on the wafer are often measured after production in order to obtain knowledge of the parameters (e.g. resonance frequency for each sensor 101). However, this is a time-consuming and therefore costly process. Especially with sensors for consumer applications, which can be manufactured with little effort per sensor, the complex measurement can drive up the effort (and therefore price) per sensor 101. For this reason, in practice, it is often not necessary to measure all sensors 101 on the entire wafer and instead only measure a small number of them. Even with this amount, some manufacturing variations can be discovered.Using classical or simple interpolation methods or even neural networks, if only (parameter) measurements were performed for a portion of the sensors 101 on a wafer 100, the values ​​for the measured parameters for the other sensors 101 on the entire wafer 100 can be estimated, thus obtaining information about the individual sensors 101 of the entire wafer 100. However, approaches are desirable that enable an estimation of the parameter values ​​that is precise enough to support subsequent calibration (e.g., calibration to a specific resonance frequency) and thus achieve high sensor performance.

[0028] According to various embodiments, an adaptation method is used for this purpose, which makes it possible to adapt a machine learning model (e.g., a neural network) to new conditions (i.e., in the present application, to a specific wafer). For this purpose, for example, a (machine) meta-(learning) model is generated that is suitable for several different tasks (in the present application, wafers) simultaneously. This meta-model can then be adapted to specific individual tasks using various methods.

[0029] Such a meta-model can be trained (i.e., adapted) with as little training data as possible for a new task (predicting sensor parameters of a specific wafer), so that it can be adapted to a task-specific model (for a specific wafer) and used for many different wafers. One meta-adaptation method for training a machine learning model is the "Model-Agnostic Meta-Learning" (MAML) algorithm. This consists of two optimization steps that adapt the parameters of respective model instances using gradient training steps: the "inner" and the "outer" optimization. Inner optimization trains a model for a specific task (e.g., a specific wafer, for example, for each of a set of "training" wafers), while outer optimization determines a general meta-model.

[0030] An unsupervised training method can also be used to reduce the amount of training data needed to achieve a certain accuracy or to adapt a machine learning model to a new data domain after supervised training. This can be applied to a meta-learning method such as MAML by defining a fixed unsupervised loss function or even training in a meta-context.

[0031] In the following, an embodiment of the procedure described above (i.e. training a meta-model based on measurements of several wafers, which is then adapted for a new wafer (i.e. a wafer that is not completely measured)) is presented for the Fig. 1, where the components 101 are sensors, is described.

[0032] Each wafer of a certain (specified or pre-selected) set of wafers (hereinafter referred to as training wafer set) is completely measured (e.g. during sensor production and thus during wafer processing), i.e. for all sensors of the wafers of this set, the properties (i.e. parameter values) that are ultimately to be predicted for further ("new") wafers are measured (such as the resonance frequency for MEMS sensors).

[0033] The data obtained from these measurements represent a basic test data set D B (per wafer) (in Fig. 1 is shown as capturing all sensors of wafer 100). In addition, a decision is made as to which sensors will be measured later on a new wafer in order to adapt the meta-model for this new wafer based on this in order to estimate (predict) the properties of all sensors on this new wafer.

[0034] The measurement of these sensors, which are measured for each new wafer, represents the calibration data set D C (per wafer), where D C ⊂ D B (per wafer) to save time and therefore money in mass production.

[0035] Based on the measured data D BThe meta-model is trained using a meta-training algorithm (of all wafers in the training wafer set). The meta-model can be viewed as a general model for all wafers (assuming that the training wafer set is representative of all wafers, including the "new" wafers). It can be a neural network or, in general, any other doubly differentiable function (represented by a machine learning model). Its parameters are denoted by θ below. In the present application, the use of a graph-based neural network for the meta-model can be advantageous, as such a network can model the spatial relationship of the sensors on the wafer and also allows the inclusion of wafer-specific parameters. Even simpler functions are conceivable using other meta-learning algorithms.

[0036] Fig. 2 illustrates the training of a meta-model according to one embodiment.

[0037] The meta-model training includes an inner optimization step, which includes an inner training 201 per wafer of the training wafer set, and an outer optimization step.

[0038] In the inner optimization step, one instance (copy) of the (initially untrained) meta-model 202 is taken for each wafer of the training wafer set as a wafer-specific model 203 for this wafer. Each wafer-specific model 203 is individually optimized for the respective wafer using the respective calibration data D C to a wafer-specific trained model 204, ie, various wafer-specific optimized models 204 are determined. The parameters of the model instance 203 for the i-th wafer are denoted by ϕ i (ie, the index i indicates the wafers of the training wafer set). The parameters of the model instance 203 trained by the inner training are denoted by ϕ̂ iThe model instances are also denoted by f ϕi or f ϕ̂i and the meta-model 202 is also used with f θ or its trained version with f θ̂ designated.

[0039] The training of the inner optimization step consists of a forward pass for each wafer of the training wafer set. This involves passing the respective input data through the meta-model (or the respective instance thereof) to obtain the corresponding output data. For example, the input data for a wafer is a matrix with entries for each sensor on the wafer, an initial value for the sensor's resonant frequency (e.g., a nominal value for it), and a position of the sensor on the wafer (if necessary, by specifying its neighbors). The output data are the predictions of the resonant frequency for all sensors on the wafer.

[0040] The quality of the prediction is determined in the inner training step using the respective calibration data D C evaluated, e.g. using a loss function such as the mean-squared error of the estimation error (ie the error of the prediction) LTi,DCinner

[0041] Here T i for the i-th task (here, the prediction for the i-th wafer from the training wafer set). Based on this error and its dependence on the parameters ϕ i the model instance is adjusted using a gradient step (i.e., an adjustment in the direction of the error descent), i.e., the wafer-specific model parameters ϕ i are changed e.g. according to ϕi=ϕi−α∇ϕiLTi,DCinner(fϕi)

[0042] Here, α is a scaling parameter and corresponds to the learning rate of the inner training. It should be noted that for the inner optimization step, only (ground truth) data is used, which is also obtained from the measurement of new wafers in production, i.e., the calibration data D C .

[0043] After the inner optimization step, the performance (prediction quality) of the wafer-individual trained models 204 is determined using all data D B evaluated (baseline test data + calibration data) or only the baseline test data (ie D B without D C ), e.g. as the mean square error between the predictions and the ones given by D B or D B without D C given labels. The resulting evaluation loss value is LTi,DC+DBeval designated.

[0044] With the help of the outer optimization step, the meta-model 202 is now trained to a trained meta-model 205. This is done, for example, by the evaluation loss values LTi,DC+DBeval The trained wafer-individual models 204 are summed and averaged to form a total error, and this value is used to adjust the meta-model over a training step, i.e., the parameters θ of the meta-model 202 are adjusted in the direction of the decrease of the total error (given by the gradient of the total error). The resulting gradient values ​​are scaled using the parameter β, which corresponds to the outer learning rate. The model parameters of the meta-model are thus adjusted, for example, as follows. θ=θ−β1T∇∑iTLTi,DC+DBeval(fϕi)

[0045] The meta-model starts, for example, with randomly chosen parameters θ. The inner training step starts for the wafer-specific models 203, for example, by copying the randomly chosen start parameters θ to the ϕ i .

[0046] Alternatively, the gradients are determined for each model instance and then summed and averaged, e.g. the meta-model 202 is adapted according to: θ=θ−β1T∑iT∇LTi,DC+DBeval(fϕi)

[0047] It should be noted that, since the model instances 204 are instances of the meta-model, each parameter of a model instance 204 corresponds to a parameter of the meta-model (e.g., a weight of a model instance 204 corresponds to the weight at the same location in the meta-model 202).

[0048] During a training step of the outer optimization, a gradient for the total error is calculated (or gradients for the evaluation loss values, which are then averaged). Thus, the outer training aims to maximize the performance of the wafer-specific models. It should be noted that these wafer-specific models 204 can only be optimized using the calibration data D C Since the calibration data D C are usually significantly less than the base test data, the model learns to achieve good performance based on all data (base test data + calibration data) using a small amount of data.

[0049] The Fig. The training shown in Figure 2 follows the model-agnostic meta-learning algorithm. However, the meta-model 202 can also be trained using other meta-learning methods.

[0050] After training, the trained meta-model 202 can be used in sensor manufacturing to predict sensor properties for new wafers. The meta-model is adapted using the measured calibration data for each individual (new) wafer.

[0051] Fig. 3 illustrates the adaptation of the meta-model to a “new” wafer.

[0052] If a new wafer 100 is available for which the properties of the sensors 101 (e.g. the resonance frequency) are to be estimated for all sensors 101, these properties are first measured for a part of the sensors 101 in order to obtain the calibration data D C for this wafer

[0053] For the adaptation 301 of the meta-model 302 to the wafer (e.g. with index j), this is instantiated for the wafer and analogous to the inner training 201 of Fig. 2 the (trained) meta-model 302 using the calibration data D C(as ground truth, ie labels) adapted (ie further trained). This results in a wafer-specific model 303. The adaptation of the meta-model 302 thus occurs in the direction of the loss LTi,DCinner.

[0054] In a further embodiment, the training may be supplemented by an unsupervised training loss LTi,DCinner,unmonitored This can be a fixed loss, such as a "bootstrap your own latent" loss (e.g., a loss that measures the difference between the outputs for two augmented versions of a training input element) or a network parameter change loss, etc. The loss function can also be trained during the development process.

[0055] In all cases, the unsupervised training loss can be added to the supervised training loss LTi,DCinner be used for internal training, so that the internal training (for internal training 201 of Fig. 2 and / or for the adaptation of the meta-model 302 of Fig. 3) in the direction of the decline of a loss LTi,DCinner=λ1LTi,DCinner,unmonitored+λ2LTi,DCinner,monitored where λ1 and λ2 are weight values. The unsupervised training loss can also be used instead of the supervised training loss LTi,DCinner or represent another stage in the meta-model training and / or meta-model adaptation. For example, the inner

[0056] Training 201 in Fig. 2 training based on or precedes the unsupervised training loss.

[0057] In summary, according to various embodiments, a method is provided as described in Fig. 4 shown.

[0058] Fig. 4 shows a flowchart 400 illustrating a method for training a machine learning model for predicting properties of semiconductor devices fabricated on (semiconductor) wafers according to one embodiment.

[0059] In 401, for each wafer of a training wafer set, the (predicted) properties for a set of semiconductor devices on the wafer are measured.

[0060] In 402, a machine learning model (also referred to as a meta-model, see in particular the above embodiments) is trained to predict the measured properties for the training wafer set (i.e., the measured properties are used as ground truth, i.e., labels for training)).

[0061] In 403, the properties for a portion of the semiconductor components on a further wafer are measured for the further wafer.

[0062] In 404, the machine learning model is adapted to reduce (i.e., toward a reduction) a loss that includes (e.g., as a loss term of a loss function) a prediction loss between the prediction of the machine learning model for the properties of the portion of semiconductor devices on the further wafer and the properties measured for the portion of semiconductor devices on the further wafer (i.e., the machine learning model is adapted to the further wafer by further training the machine learning model to predict the properties measured for the further wafer).

[0063] In other words, according to various embodiments, a meta-learning algorithm is used, such as the "model-agnostic meta-learning" algorithm, to determine a meta-model. Here, an individual wafer and the estimation of the individual parameters are defined as a task. The meta-model learns from many wafers (i.e., for many tasks) and thus has knowledge about parameter distribution and relationships across many wafers. The meta-model can then be adapted to individual wafers (here, the "additional wafer") using an internal training step. This is possible by measuring some sensors on the additional wafer, thereby (further) training (i.e., adapting) the meta-model.

[0064] The semiconductor components can also be partially test structures (i.e., part of the semiconductor components are, for example, sensors and another part are test structures that are manufactured on the wafer).

[0065] The procedure of Fig.4 may be performed by one or more computers having one or more data processing units. The term “data processing unit” may be understood as any type of entity that enables the processing of data or signals. The data or signals may, for example, be handled according to at least one (i.e., one or more than one) specific function performed by the data processing unit. A data processing unit may include or be formed from an analog circuit, a digital circuit, a logic circuit, a microprocessor, a microcontroller, a central processing unit (CPU), a graphics processing unit (GPU), a digital signal processor (DSP), a programmable gate array (FPGA) integrated circuit, or any combination thereof.Any other way of implementing the respective functions described in more detail herein may also be understood as a data processing unit or logic circuit arrangement. One or more of the method steps described in detail herein may be performed (e.g., implemented) by a data processing unit through one or more specific functions performed by the data processing unit.

[0066] According to various embodiments, the method is therefore particularly computer-implemented.

Claims

[1] A method for training a machine learning model (303) for predicting properties of semiconductor devices (101) fabricated on wafers (100), comprising: Measuring, for each wafer (100) of a training wafer set, the properties for a set of semiconductor devices (101) on the wafer (100); Training a machine learning model (302, 202) to predict the measured properties for the training wafer set; Measuring, for a further wafer (100), the properties for a portion of the semiconductor components (101) on the further wafer (100); and Adapting the machine learning model (302, 202) to reduce a loss that includes a prediction loss between the prediction of the machine learning model (302, 202) for the properties of the portion of the semiconductor devices (101) on the further wafer (100) and the properties measured for the portion of the semiconductor devices (101) on the further wafer (100). [2] The method of claim 1, wherein the set of semiconductor devices (101) includes the majority of semiconductor devices of the wafer (100) and wherein the portion of the semiconductor devices (101) on the further wafer (100) includes only a minority of the semiconductor devices (101) of the further wafer (100). [3] The method of claim 1 or 2, wherein the loss includes an unsupervised training loss. [4] The method according to any one of claims 1 to 3, wherein training the machine learning model (303) comprises: Training, for each wafer (100) of the training wafer set, a respective instance of the machine learning model to predict the properties measured for a subset of the set of semiconductor devices (101) on the wafer (100); and Adapting the machine learning model (302, 202) in the downward direction of a further loss which includes the prediction error of the instances of the machine learning model for the set of semiconductor devices (101) averaged over the wafers (100) of the training wafer set. [5] The method of claim 4, wherein the further loss comprises an unsupervised training loss. [6] The method according to any one of claims 1 to 5, further comprising predicting properties of other semiconductor devices (101) on the further wafer (100) as the part of the semiconductor devices (101) on the further wafer (100) by means of the adapted machine learning model (303). [7] Semiconductor device test arrangement which is arranged to carry out a method according to one of claims 1 to 6. [8] A computer program comprising instructions which, when executed by a processor, cause the processor to perform a method according to any one of claims 1 to 6. [9] A computer-readable medium storing instructions which, when executed by a processor, cause the processor to perform a method according to any one of claims 1 to 6.

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