Introduction

Gallium nitride high electron mobility transistors (GaN HEMTs) are attractive due to two-dimensional electron gas (2DEG), large breakdown E-field, and the wide bandgap. Recently, thanks for the insulator under the gate metal, high performance power metal–insulator-semiconductor high electron mobility transistors (MIS-HEMTs) have been demonstrated1,2,3, which is promising for the power switching applications. However, the high electrical filed in the access region during an off-state drain bias stress can lead to the earlier breakdown, defect generations and trapping effects, limiting the performance and stability of these GaN HEMTs4,5. To address these issues, field plates (FPs) have been designed to optimize the electrostatic potential6,7; this is crucial for performance and reliability, particularly in GaN HEMTs for high-power applications. Numerical simulation techniques, such as technology computer-aided design (TCAD) simulations, have been widely used for modeling electrostatic potentials8,9. However, these simulations are time-consuming because of the complexity of the heterojunction and underlying physics. Moreover, although analytical models are often used to model device electrical characteristics10,11, analytical models cannot be efficiently applied to devices with different materials and structures.

Recently, high-performance computing has enabled the use of deep learning techniques to predict the electrical properties of devices from the input parameters12,13,14,15,16,17. However, since fully connected neural networks are not designed for image-related tasks, electrostatic potential modeling in previous studies has been limited to one-dimensional devices12. On the other hand, the convolutional neural network (CNN) based approach18,19,20,21,22,23,24,25,26,27 is also attractive for pixel-based image prediction and segmentation, which has been widely used in the biomedical sciences21,22,24,25 due to local connection and weight-sharing advantages. Still, the applications of CNN-based approach are limited in the semiconductor research. Recently, one study reported that the pixels of the two-dimensional landscape of low-voltage Si devices could be modeled by a CNN with a U-Net architecture26. Note that the advantage of using a U-Net CNN is that, in general, U-Net CNN requires only few images to have a relatively good results23,24,25,26,27. The network of U-Net is structured with a contracting path and an expansive path, forming its distinctive U-shaped architecture. The contracting path embodies a conventional convolutional network, utilizing a series of convolution applications, each paired with a rectified linear unit (ReLU) and a subsequent max pooling operation. This phase systematically diminishes spatial information while amplifying feature data. Conversely, the expansive pathway unites feature and spatial information by employing up-convolutions and merging them with high-resolution features obtained from the contracting path through concatenation. However, this work26 is limited to the dimensional variation with only considering the impact of on-state voltage that directly applied at the surface of the semiconductor with simplified symmetric device design that is not practical for the real device fabrication, which results from the relative compact and shallow network constructed by only 4 layers of contracting path and the expanding path. Furthermore, the impacts of the external dimensional variations, e.g., field plate variations on top of the semiconductor, on the potential distribution inside the semiconductor are not discussed26, which is more practical for the consideration of the semiconductor design.

In this work, we demonstrate U-Net CNN approach to model the pixel-based electrostatic potential image in GaN power MIS-HEMTs considering the different gate and source field plates and drain voltages, showing that the electrostatic potential can be accurately and effectively modeling by using the U-Net CNN approach. Our modified U-Net is consisted of 7 layers of the contracting path and 7 layers of the expanding path. Each contracting path is consisted of 2 convolutions with ReLU followed by a maxpooling function. Last two layers of the contracting path even followed by a dropout function in order to avoid the overfitting problem. On the other hand, each layer of the expanding path is consisted of a upsampling with ReLU, the concatenation with the data from the counterpart of the contracting path, and 2 convolutions with ReLU.

Device schematic and typical electrical property

Schematic of a GaN MIS-HEMT is shown in Fig. 1. The electrostatic potentials in this work are generated by Sentaurus TCAD for various gate and source field plate designs and different applied drain biases ranged from 100 to 500 V with a step of 100 V. The gate and source field plates are designed by considering the ratio compared to the gate-to-drain distance (LGD) as shown in Eq. (1) & (2). Please note that the ratio of the gate and source field plates ranges from 0 to 1. The field plate designs used in this work are shown in Table 1.

$$Gate\;field\;plate\;ratio = \frac{{L_{{FP_{Gate} }} }}{{L_{GD} }}$$
(1)
$$Source\;field\;plate\;ratio = \frac{{L_{{FP_{Source.extra} }} }}{{L_{Source.extra} }}$$
(2)
Figure 1
figure 1

Schematic of the GaN MIS-HEMTs with the gate and drain field plate designs.

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Table 1 The field plate designs used in this work.
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A total of 80 images representing the electrostatic potential distribution were generated through TCAD simulations that ran for over 640 h. Figure 2 presents an example of the pixel-based images of electrostatic potential distribution generated from TCAD simulation with consideration of the gate FP ratio, source FP ratio, and drain voltage of 0.8, 0.8,and 500 V, respectively.

Figure 2
figure 2

An example of the pixel-based images of electrostatic potential distribution generated from TCAD simulation.

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Methodology

Figure 3a presents the workflow for predicting the pixel-based electrostatic potential of the GaN MIS-HEMTs using a U-Net CNN model and schematics of the input layers. The images of device structures are divided into 6 layers to form the matrix representing the material information and applied voltage: (1) GaN, (2) AlGaN, (3) AlN, (4) source/gate/drain metal, (5) nitride, and (6) the applied bias (Fig. 3b). For layers 1–5 in the one-hot matrix, if the pixel location is the targeted materials, it will be recorded as “1” or “0” for not the targeted materials. Forthe 6th layer, the voltage was linearly normalized to a range of 0–1.

Figure 3
figure 3

(a) An example of the electrostatic potential modeled by U-Net CNN and (b) the schematics of the 6 input layers.

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The U-Net CNN consists of two segments: the down-sampling side and the up-sampling side as shown in Fig. 4. The down-sampling side contains eight rows of convolution and maxpooling. The up-sampling side contains eight rows of up-sampling, convolution, and concatenation. The model is trained and evaluated by the mean-squared error (MSE) loss function, which measures the error between the output electrostatic potentials from the developed U-Net CNN and the reference electrostatic potential from the TCAD simulations. The goal of the training process is to minimize the loss function by adjusting its parameters, resulting in the better modeling. The optimizer for the iterations is Adam algorithm with an initial learning rate of 5 × 10−6. After the model is constructed, the images of the electrostatic potential distribution can be visualized for further verification.

Figure 4
figure 4

The simplified schematic of a U-Net model.

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The TCAD generated datasets are randomly divided into two groups: (1) the images for the training (72 images) and (2) the image for the verifications (8 images). The images for the verification purpose are not shown to the model during the training. Hence, they are suitable to verify the performance of the trained model.

Results and discussions

Figure 5 shows the decreases of the mean square error (MSE) during the training process, suggesting that developed U-Net CNN is efficient to minimize the error between the output electrostatic potentials from the developed U-Net model and the reference electrostatic potential from the TCAD simulations. Note that the TCAD computational environment is equipped with an 8 core Intel Xeon CPU, 47GiB of RAM, while the machine learning environment is equipped with a GPU of an Nvidia Tesla V100. Also, the training time of the U-Net CNN model is about 21.8 h.

Figure 5
figure 5

MSE records during the training process.

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Figure 6 shows the side-by-side comparison of the simulation results from the TCAD and the modeling results (output) from the trained U-Net model in the dataset of the image for verifications. Furthermore, a less than 1% error of the electrostatic potential distribution in AlGaN/GaN interface can be obtained, indicating the excellent consistent results (Fig. 7). Furthermore, the modeling time of potential distributions by U-Net takes about 80 ms.

Figure 6
figure 6

Comparison of electrostatic potential distributions from (a) the TCAD simulation and (b) the developed U-Net model.

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Figure 7
figure 7

Comparison of electrostatic potential in AlGaN/GaN interface from the TCAD simulation and the developed U-Net model.

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Conclusion

In this work, the modeling of the electrostatic potential distributions is successfully demonstrated for the first time by considering the pixel-base images using the U-Net CNN with the different gate and source field plate designs and applied drain voltages in GaN power MIS-HEMTs. The different gate and source field plate designs and drain voltages are generated by TCAD simulation as references in this study, and the corresponding pixel-based electrostatic potential distribution images are modeled by the U-Net CNN. Less than 1% error of a 500 V electrostatic potential modeling in the AlGaN/GaN interface between the developed U-Net model and the reference electrostatic potential from the TCAD simulations can be achieved (error equation = (Usimulation—UU-Net)/Usimulation), indicating a successful modeling using developed U-Net CNN approach. Note that the modeling by the U-Net CNN requires only 80 ms, which is a huge speed improvement compared to the TCAD simulations. In sum, the U-Net CNN approach is promising for the accurate and efficient methodology in modeling the distribution-based characteristics, e.g., electrostatic potential, electric filed, current density, etc., in GaN power devices.