A set of temperature sensors are embedded in a hotplate to measure temperature to heat and keep temperature uniformity of the hotplate. For example, a hotplate for a bake module heats wafers to evaporate residual substances on wafer during semiconductor lithography which is a process to transfer a pattern from a photomask to the wafer [1]. Temperature sensors embedded in the hotplate is used for a closed loop feedback control system to control temperature uniformity required for uniform wafer thickness during the wafer heating. In detail, a resistance temperature detector (RTD) is usually used to measure high temperature of a hotplate accurately based on resistance increase of sensor material such as platinum depending on temperature increase. A hotplate is divided into multiple zones for efficient temperature control. During operation, heaters in the zones activate or deactivate to keep target temperature by multiple feedback control systems based on temperature measured the RTD embedded in each zone.

During operation of a hotplate, a thermal stress condition can cause oxidation to the sensor material, resulting in measurement error, determined as a sensor failure. When measurement error is occurred due to oxidized sensor material, specific zones of the hotplate can be overheated due to inaccurate temperature measurements, and the temperature uniformity is deteriorated. In the lithography process, when the partially overheated hotplate causes a variation of 1°C, it can yield a 10 nm disparity on wafer thickness [2,3], resulting in time and financial loss. However, it may be hard to detect the sensor failure when the failed sensor cannot measure actual temperature. Furthermore, the hotplate with failed sensors may be complex to detect incipient failures. The overheating is continuously relieved by temperature control systems for surrounding area affected by heat transfer. So, RTDs in a hotplate require a real-time diagnosis method which overcomes the measurement error.

Some researchers have studied to detect sensor failures by estimating sensor measurements with analytical models. Yuqing et al. [4] detected sensor failures in a spacecraft attitude control system by establishing mathematical models for multi sensors. The researchers defined failure thresholds for each sensor failure scenario based on an analytical relationship between multi sensors. Chi et al. [5] employed an analytical relation between oscillator frequency and temperature sensor. The sensor failure was detected by a statistical threshold for residuals between measured temperature and temperature estimated by the frequency. Xiong et al. [6] also employed residuals to detect voltage and current sensor failures in battery management system based on an estimated model for lithium-ion battery. Extended Kalman filter was used to compensate the model by sensor measurements. The sensor failures are diagnosed based on residuals between model-estimated capacity and calculated capacity. Park et al. [7] and Ai et al. [8] developed a method to monitor adhesion quality of piezoelectric sensors. The researchers investigated analytical relation between adhesion quality and admittance of the sensor. Adhesion quality was estimated based on admittance measured by a sensing device attached to the piezoelectric sensors. Some researchers have been developed machine learning methods instead of analytical models. Liu et al. [9] proposed an automatic failure detection method using support vector machines (SVM) for water quality monitoring devices. After other failures in the devices were isolated by rule-based decision tree, multiclass SVM models diagnosed various types of sensor failures using statistical features extracted from sensor measurements. Messai et al. [10] proposed a diagnosis method for a fuel rod temperature sensor in a nuclear reactor. Artificial neural networks (ANN) were employed to estimate temperature of the fuel rod based on inputs of control rods elevation and coolant flow rate data which are physically related with the temperature. The temperature sensor failure was detected by residuals between measured and estimated temperature. Salmasi et al. [11] introduced schemes for detection, isolation, and compensation of current and speed sensor failures for induction motor without a system model. Features for failure detection were extracted based on effects of each failure in closed-loop control system such as imbalance current flow. Experimental results identified successful failure detection, isolation, and compensation by the features extracted from sensor measurements. In summary, the conventional methods detect sensor failures by monitoring anomalous in measurements determined based on physical relation between the sensor of interest and other sensors.

However, the conventional methods may have limitation for real-time sensor diagnosis because they require complex analytical models or sensing data for measurement estimation with knowledge for effect of sensor failures on the system. A hotplate may be too complicate to analyze effect of sensor failures on the multiple temperature control systems. Furthermore, it may also be hard to install other sensors related with actual temperature for temperature estimation due to thermal stress during the hotplate operation.

A data-driven diagnostic method for RTDs in a hotplate would be developed to extract sensor failure information from only temperature measurements from whole RTDs in the hotplate. Since temperature difference due to overheating causes heat transfer on a hotplate, sensors surrounding a failed sensor can provide failure information such as a failure location based on temperature difference regarding to sensor locations. Since 1 dimensional temperature data measured by RTDs is hard to contain sensor location information, a 2-D image feature is developed by converting measurements to an image based on layout of RTDs on the hotplate. As a result, the image feature is expected to indicate thermal distribution on the hotplate although it is not perfectly same with actual thermal distribution. A convolution neural network (CNN), one of representative ANNs for image classification, was used to extract thermal distribution information involved in the image feature. While a convolution layer in the CNN analyzes measurements from a sensor and its surrounding sensors with kernels, the CNN helps to extract overheated area from the image feature and to monitor temperature uniformity. Finally, the sensor location-based diagnosis method can refer data-based relation of the sensor failure with only temperature measurements in real-time.

In this study, characteristics of the RTD failure mechanisms are analyzed in the background. A sensor location-based image is created to analysis thermal distribution on a hotplate. The CNN trained the created images, and classified failure conditions based on geometrical characteristics instead of demonstrating the thermal distribution exactly. The detailed processes are introduced in the method section.

A RTD usually consists of two parts: sensor and wires. The sensor part is made by a material such as platinum of which resistance increases linearly depending on temperature increase. The sensor in this study is made by Pt100 which is 100 Ω at 0°C with increase of 0.00385 Ω per 1°C [12]. The wire part, usually made by copper and nickel, is used to transmit electrical signals for resistance measured by the sensor part to a calculation instrument to avoid heat. While common sensors usually use 2 wires connected at each end of the sensor part, a hotplate of interest usually uses a 3-wire RTD which adds a wire to cancel out resistance of the wires for precise measurement. In the 3-wire RTD, an additional wire for measuring output voltage affected by the sensor resistance is connected to one end of the sensor part to prevent measurement error caused by resistance of the other wires. The added wire cancels the wire resistance using an electrical circuit called a Wheatstone bridge.

A circuit diagram of the RTD is shown with the Wheatstone bridge in Fig. 1. The sensor part resistance, R_g, can be estimated based on the output voltage, V_O, by following Wheatstone bridge equations,

while R′_g is an estimated resistance value of the sensor part R₁, R₂, and R₃ are known resistance values in the wheat stone bridge, V_S is a known input voltage value, and R_L1 and R_L2 are unknown resistance values in the part of wires.

The equation involves two failure modes: overestimated and underestimated temperature. Resistance both the sensor and wire parts are affected by oxidation due to heat from the hotplate. The oxidation reaction causes change of resistance estimation in the sensor part, resulting in change of temperature estimation. In this study two suppositions are determined to estimate the major failure mode based on the oxidation reaction. First, resistance is hard to decrease by oxidation. Second, wires are oxidized simultaneously by ambient temperature. Then two failure mechanisms are derived: increase of the sensor part resistance and increase of the wire part resistance. According to materials of each part, the wire material, nickel or copper, is usually oxidized earlier than the sensor part, platinum. Therefore, increase of wire part resistance is only focused. Eqs. (3) to estimate output voltage is newly defined based on (1), when R_o is determined resistance increase by oxidation.

In other words, the major failure mechanism can be determined as the wire resistance increase due to oxidation. According to Eq. (3), output voltage is underestimated due to the resistance increase, resulting in temperature underestimation. Thus, the major failure mode is determined as temperature underestimation due to resistance increase in wire parts.

The major failure mode by oxidized wires may require years to be occurred. So, a failure injection test is designed by adding a resistance in the wire to eliminate time to oxidize wires. The resistance is added at the location of R_L2 in Fig. 1 instead of two wires for convenience since the temperature underestimation can be conducted with only increase of R_L2. 0.4 and 0.2 Ω of resistances are used to generate 1 and 0.5°C of the measurement error based on the sensor failure mechanism.

In the case of the lithography processes, a cover of the hotplate repeats to be opened and closed to heat wafers sequentially. Then, one cycle of the heating process can be determined by 3 steps. First, open the cover to insert a wafer. Second, close the cover for heating. Third, open the cover again to take the wafer out of the hotplate. Repetition of the processes induces temperature cycling of the hotplate. While the hotplate installed in a bake module is usually operated with high ambient temperature with enclosed shells, a hotplate in the lab condition was operated without shells in room temperature. In the lab condition, the hotplate is repeatedly turned on for 30 minutes and turned off for 2 minutes as in Fig. 4 to imitate actual temperature cycling due to the lithography process.

An actual bake module was used for a test rig which usually uses to heat semiconductor wafer to 400°C for this study. The hotplate in the module has 15 RTDs with 15 zones of which layout is same with Fig. 2(a). Failure injected sensors were determined based on sensor location in Fig. 2(a) to imitate sensor failures at center or periphery, double sensor failures, and triple sensor failures. The bake module was controlled by an instrumental control program. The temperature data from the sensors was monitored every one second and transmitted to a computer using RS232 port. The test matrix is summarized in Table 1.

The measured data from 15 RTDs was converted to the sensor location-based image. Shape of the image was determined a 29 × 29 matrix based on the schematic of the hotplate. When creating the image feature, mean temperature of test 1 subtracted from all measurements for qualitative comparison by the feature. The CNN with two convolution layers was used for convenience and its parameters were determined for best accuracy to classify test data. In first convolution layer of CNN, the sensor location-based image was expanded to 32 channels by a zero-padding method with a 3 × 3 kernel matrix. The expanded feature was compressed by a max pooling method using a 2 × 2 matrix. In second convolution layer, it was expanded to 64 channels with a 3 × 3 kernel matrix and compressed by a 2 × 2 matrix for max pooling. Finally, a hidden layer had 100 nodes with a fully connected network. All the connections used the ReLu function for nonlinearity. Softmax function was employed to classify the condition in the final layer. The datasets split into 5 groups for the k-fold cross validation method. The training processes for 1-fold were repeated with 2,500 times iteration with Adam optimizer [24]. 5 test results derived by the 5-fold cross validation method were combined by one confusion matrix. In the other classification method, the random forest method used classification trees with depth of 10 which is determined for best classification accuracy. In SVMs, a linear function and an RBF were used for a kernel. An ANN used a same layer structure with the fully connected network of the CNN to identify effect of convolution layers in the CNN for sensor diagnosis. The ANN also used the ReLu function for nonlinear connections, the softmax function to classify the condition, and 2500 times iterative training with Adam optimizer. A 1-D CNN used same layers with the proposed CNN except 3 × 1 kernels and 2 × 1 pooling matrix for two convolution layers. All the methods for performance comparison except the 1-D CNN trained an input matrix consisting of 871 cells, which reconstructed from a 29 × 29 matrix, with the 5-fold cross validation method. The 1-D CNN trained an input matrix with 15 temperature data measured by 15 RTDs simultaneously.

The temperature of the hotplate was continuously measured by the 15 numbers of RTDs for a day. About 50 cycles of temperature were measured. Comparison between before and after failure injection is plotted in Fig. 5. In the case of the failure injected sensor of test 2 (Sensor 8), the measured temperature was slightly lower than the normal condition. Especially, the measurement error was the biggest at valley of the temperature cycle. In this study, the valley values of each cycle were used for efficient analysis.

As shown in Fig. 6, sensor location-based image features were created using temperature data at valley points. In test 3, temperature measured by the failure injected sensor (Sensor 8) was lower than temperature measured by the normal sensor in accordance features in Figs. 6 and valley points in 7. Temperature measured by surrounding sensors were slightly changed due to heat transfer after the failure injection. Based on the results, the proposed method can train thermal distribution by capturing both temperature change measured by the failure injected sensor and surrounding sensors.

A confusion matrix from the 5-fold cross validation results is shown in Fig. 8. According to the confusion matrix of the CNN, the proposed method perfectly predicted failure locations, but accuracy decreased when diagnosed extent of the failure at the center area of the hotplate. Based on the layout of the hotplate, the accuracy may decrease since multiple control systems, which relieve overheating, surround the center area. According to Table 2, the CNN with the image feature showed outperforming results with 96.88% accuracy. The other methods have lower accuracy than the proposed method. Furthermore, performance results show that the other methods except the 1-D CNN and the SVM with linear function cannot predict failure location perfectly. By a comparison between results with and without the image feature, accuracy usually decreases when sensors are with only raw measurements. Although accuracy in some methods is similar regardless of the feature, other parameters such as recall decreases. In summary, the sensor-location based image feature works effectively for sensor diagnosis. As the result, the proposed method can diagnose not only failure locations but also extent of the failure of temperature sensors with high performance.

The proposed method was developed to diagnose a set of temperature sensors embedded in a hotplate with only temperature measurements while multiple closed-loop feedback control systems interrupt the diagnosis. A sensor location-based image feature in accordance with a layout of the hotplate was created to observe thermal distribution indirectly. A CNN was employed to classify normal and failure injected sensors by extracting underlying failure information from the sensor location-based image. The results demonstrated that the proposed method performs sensor diagnosis with high performance compared to other machine learning methods.

The image feature was more effective for sensor diagnosis than raw measurements. Furthermore, the image feature creation only requires real-time measurements from the embedded sensors. While conventional image-based or spatial feature-based approaches, such as recurrence plot and Gramian angular field, mostly capture the changes in measurement over time, the proposed method contains both the temporal and the spatial information between the set of temperature sensors, resulting from the failure of a particular or more sensors. Thus, the proposed method allows the user to locate the faulty sensors, as well as to identify how much the sensor has degraded.

The proposed method can also detect the extent of failure in real-time. It can be improved for the sensor maintenance by compensating the error in the temperature control system. The real-time compensation can economize on time and expense to change failed sensors.

While the proposed method is of interest and promising, it still has limitation, requiring more development on the following areas: dataset acquisition and hotplate designs. The performance of the proposed method is dependent upon the training datasets collected under multiple sensor locations, i.e. zone 1, 4 and 7 in this study, as well as multiple degraded states, i.e. added resistance of 0.2 and 0.4 Ω. There is a tradeoff between the size of training datasets and the diagnosis performance. Also, the hotplate design is directly associated with both the sensor location and its failure mode. The training datasets may need to be obtained and trained again entirely when the hotplate design changes.

In future, the proposed method will be applied to other test conditions with various extent of the sensor failure, the sensor location-based image feature will be improved with a physical model for heat transfer on a hotplate for accurate diagnosis, and the proposed image feature will be used to diagnose sensors with fixed locations in other control system.