An Ultra-Fast and Precise Automatic Design Framework for Predicting and Constructing High-Performance Shallow-Trench-Isolation LDMOS Device

An Ultra-Fast and Precise Automatic Design Framework for Predicting and Constructing High-Performance Shallow-Trench-Isolation LDMOS Device | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article An Ultra-Fast and Precise Automatic Design Framework for Predicting and Constructing High-Performance Shallow-Trench-Isolation LDMOS Device Chenggang Xu, Hongyu Tang, Yuxuan Zhu, Yue Cheng, Xuanzhi Jin, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4696885/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 09 Dec, 2024 Read the published version in Journal of Computational Electronics → Version 1 posted 8 You are reading this latest preprint version Abstract Shallow Trench Isolation laterally diffused metal oxide semiconductor (STI LDMOS) is a crucial device for power integrated circuits. In this article, a novel framework that integrates an optimal objective function, Bayesian Optimization (BO) algorithm and Deep Neural Network (DNN) model is proposed to fully realize automatic and optimal design of STI LDMOS devices. On the one hand, given the structure of device, the DNN model in the proposed method can provide the ultra-fast and high-accurate performance estimation including breakdown voltage (BV) and specific on-resistance (R onsp ). The experimental results demonstrate 98.68% prediction accuracy in average for both BV and R onsp , higher than that of other machine learning (ML) algorithms. On the other hand, to target the specified value of BV and R onsp , the proposed framework can fully automatically and optimally design the precise device structure that simultaneously achieves the target performance with the optimal figure-of-merit (FOM) of device. Compared to Technology Computer Aided Design (TCAD), there is only 0.002% error in FOM and 2.83% average error in BV and R onsp . Moreover, the proposed framework is 4000 times more efficient than other conventional frameworks. Thus, this research provides experimental groundwork for constructing an automatic design framework for LDMOS device and opens up new opportunities for accelerating the development of LDMOS device in the future. Laterally diffused metal oxide semiconductor Machine learning Bayesian optimization Deep neural networks Automatic design Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 1 Introduction Laterally diffused metal oxide semiconductor (LDMOS) devices have been widely adopted in power integrated circuits due to its high Breakdown Voltage (BV) and low specific on-resistance (R onsp ) [ 1 – 5 ]. It is the key determinant of the performance, cost, and integration level of power integrated circuits [ 6 , 7 ]. Currently, the conventional device design approach relies on simulation tools such as Sentaurus, Medici, Silvaco and so on. These simulation tools acquire the device electrical characteristics by solving the physical equations such as Poisson equation, Continuity equation and Transport equation of electrons and holes at the set mesh point [ 8 ]. However, the simulation results do not meet the expectations to some extent, it must require significant human intervention and configuration that spend great efforts on the remodeling and optimization. It is time-consuming and cumbersome. On the other hand, in the development of LDMOS devices, the most crucial performance metrics are BV and R onsp . There exists a ‘silicon limit’ constraint relationship between these two electrical performances, which increases the difficulty and cost of development [ 9 – 13 ]. In consequence, multiple parameter adjustments and iterations are essential for optimizing device performance, which in turn substantially raise manufacturing costs. Besides, capturing the influence of multiple processes on the performance of variable devices through manual methodologies presents significant challenges. Therefore, the traditional development method cannot satisfy the requirements of the widely applied LDMOS devices. Recently, Machine Learning (ML) algorithms exhibit great ability to efficiently accelerate device simulation and design. For example, Carrillo-Nunez et al. investigated the possibility to replace numerical time-consuming device simulations with a multi-layer neural network [ 14 ]. Mehta et al. demonstrated the possibility of predicting full transistor current-voltage and capacitance-voltage curves using trained prediction model based on Deep Neural Network (DNN) [ 15 ]. Han et al. proposed to use a neural network to learn an approximate solution for desired bias conditions to accelerate the simulation [ 16 ]. Wang et al. present a novel method of predicting and optimizing the performance of the existing TFETs by using deep learning to accelerate the device design [ 17 ]. Chen et al. proposed an automated structural design method for SOI lateral power device based on optimization algorithm [ 18 ]. These research firstly demonstrate the significant advantage of machine learning methods in device simulation, while also proving the possibility of using optimization algorithms to automatically design devices. However, there is no research that designs an optimal objective function to drive the optimization algorithm to iterate more diligently, to construct devices that better meet the design specifications. In the traditional device development process, device structure adjustments are performed not only to ensure the device satisfies fundamental performance requirements, but also to iteratively optimize the device to attain the optimal figure of merit (FOM). Hence, for an automated design framework, designing devices that can simultaneously exhibit target performance and optimal FOM is the most desired outcome after applying ML algorithms. Furthermore, there is also no research utilizing ML algorithms to accelerate and automate the design of Shallow Trench Isolation (STI) LDMOS device. This research proposes an ultra-fast and extremely precise framework to design STI LDMOS device automatically and optimally by the integration of an optimal objective function, Bayesian Optimization (BO) algorithm and DNN model. Firstly, a higher prediction accuracy model for STI LDMOS based on DNN algorithm. By inputting the structure parameters of device, the DNN model can effectively output BV and R onsp with precision of 98.68%. Then, an optimal objective function is defined, which includes two parts: (1) Optimal Function (OF): driving the device structure to attain the optimal FOM; (2) Target Function (TF): driving the device structure that exhibits target performance. By integrating this objective function, not only can the designed device meet the specified device performance, but also achieve the optimal FOM. Compared to TCAD, there is only 0.002% error on FOM and 2.83% average error on BV and R onsp performances. The entire processing time of the proposed framework for the automated design is less than 4 minutes. 2 Methods 2.1 A TCAD Simulation and Electrical Characteristics of Device Device Structure and TCAD Simulation Figure 1 shows a schematic diagram of the device structure of STI LDMOS. It includes five electrodes on the device. The constant doping profiles and Gaussian doping profiles are simultaneously defined in the device. The constant p-type doping background is used in the substrate. There is n + Gaussian doping profiles of source/drain and p + Gaussian doping profiles of bulk/psub placing on the device surface. Besides these Gaussian doping profiles, it exists two more extensive distributed doping profiles: n + Gaussian doping profiles of n-type drift region and p + Gaussian doping profiles of p-type body (pbody) region. There are two STI regions by deposit process to enhance BV. In Table 1 , nine parameters listed are used as the input parameters for TCAD simulations. They include: (1) the peak doping concentration of the pbody Gaussian doping (Npbody.p), (2) the doping concentration in specific depth of the pbody Gaussian doping (Npbody.s), (3) the length of the overlap region of pbody to gate (Lpog), (4) the peak doping concentration of the ndrift Gaussian doping (Nndrift.p), (5) the doping concentration in specific depth of the ndrift Gaussian doping (Nndrift.s), (6) the length of the extension region of ndrift beyond STI (Lnes), (7) the width of STI (Lsti.w), (8) the depth of STI (Lsti.d), (9) the length of the overlap region of STI to gate (Lsog). These structure parameters determine the doping distribution and the size of the pbody region, ndrift region, and STI region. The parameter sets were randomly generated by Python script, which size is 2578. Next, by inputting parameter sets, TCAD simulation tool can output performance sets. The commercial device simulator Sentaurus is used for device modeling and performance simulation [ 8 ]. Electrical Characteristics of Device BV represents the maximum voltage between the source and drain that the device can sustain without experiencing avalanche breakdown when it is in off state. The \(\:{I}_{DS}-{V}_{DS}\) measurement is performed and \(\:{V}_{DS}\) is ramped up to extract the maximum \(\:{V}_{DS}\) when the TCAD no longer converges: $$\:\begin{array}{c}BV={max}\left({V}_{DS}\right),\:{V}_{GS}={V}_{BS}={V}_{SS}=0V\#\left(1\right)\end{array}$$ We calculate the specific on-state resistance by $$\:\begin{array}{c}{R}_{onsp}={R}_{onds}\times\:AREA\#\left(2\right)\#\#\end{array}$$ Where AREA is half-pitch times a unit length (default value is 1 \(\:\mu\:m\) on the z-direction since 2D simulations is performed) and $$\:\begin{array}{c}{R}_{onds}=\frac{{V}_{DS}}{{I}_{DS}}\:({when\:V}_{GS}=5V,{V}_{DS}=0.1V)\#\left(3\right)\#\#\end{array}$$ Finally, the FOM is the most important metric in this study, equaling $$\:\begin{array}{c}FOM=\:\frac{{BV}^{2}}{{R}_{on,sp}}\#\left(4\right)\end{array}$$ The FOM is one of the most well-known metrics for evaluating the performance of power devices. A higher FOM indicates that the device has characteristics closer to an ideal switch. Researchers can use this FOM to gauge the performance of a power device. Table 1 The description and bound of device structure parameters Symbol(units) Description Bound N pbody.p (cm − 3 ) The peak value of the pbody Gaussian doping [1.4e17, 2.6e17] N pbody.s (cm − 3 ) The value of the pbody Gaussian doping in specific depth [0.7e15, 1.3e15] L pog (um) The length of the overlap region of pbody to gate [0.07, 0.13] N ndrift.p (cm − 3 ) The peak value of the ndrift Gaussian doping [0.7e17, 1.3e17] N ndrift.s (cm − 3 ) The value of the ndrift Gaussian doping in specific depth [1.4e16, 2.6e16] L nes (um) The length of the extension region of ndrift beyond STI [0.375, 0.715] L sti.w (um) The width of STI [1.4, 2.6] L sti.d (um) The depth of STI [0.14, 0.26] L sog (um) The length of the overlap region of STI to gate [0.7, 1.3] 2.2 Automatic Design Framework Deep Neural Network Algorithm Firstly, a total of 2578 samples in the dataset prepared for training the DNN model is obtained from the commercial device simulator Sentaurus which is presented in above session. The input features contain nine structural parameters listed in Table 1 . The output features contain the BV and R onsp , whose density distributions are illustrated in Fig. 2 . The dataset is divided into 8:2 for training dataset and testing dataset, respectively. It is obviously that there are different ranges and magnitudes of different input features. Note that the length Lpog is only tenth of micron, while the concentration Npbody.p is more than 1e17, which greatly affects the accuracy and generalization ability of the DNN model. Thus, the dataset needs to be normalized before training so that the values of each input feature will be scaled to the range of 0 to 1. Secondly, the DNN algorithm is inspired by structure of mammalian visual system that contains many layers of neural network [ 19 ]. Different numbers and weights of neurons and diverse activation functions will result in different relationship functions between input and output. The construction of the proposed DNN prediction model can be divided into two parts: the network design and the model training. In fact, continuous adjustment of the neural network structure and training strategy based on the training and validation results are required for the construction of neural networks. Figure 3 shows the overview of the proposed DNN model. The model is a regression network for BV and R onsp prediction with five hidden layers, and the neurons in each layer are 8, 32, 24, 16, 12, 8 and 2 respectively. This layer structure is verified for achieving highest accuracy and well optimized for STI LDMOS design to minimize the computational cost. Comparing among all these activation functions, the Relu function is selected and used for the input and hidden layers of all networks. During the training process, regression task used the mean absolute percentage error (MAPE) as the loss function, which is presented in Eq. (5). $$\:\begin{array}{c}Loss\:Function=\frac{1}{2n}{\sum\:}_{i=1}^{n}\left(\left|\frac{Bvdss-\widehat{Bvdss}}{\widehat{Bvdss}}\right|+\left|\frac{Ronsp-\widehat{Ronsp}}{\widehat{Ronsp}}\right|\right)\times\:100\%\#\left(5\right)\end{array}$$ Bayesian Optimization Algorithm The two critical modules (surrogate model and acquisition function) constitute BO algorithm. The surrogate model is a statistical model attempting to replicate the objective function and the acquisition function is used to decide where to sample the next data point [ 20 ]. In the proposed framework, the Gaussian Process Regression (GPR) algorithm is used as surrogate model and the Expected Improvement (EI), Probability of Improvement (PI) and Bayesian Confidence Bound (UCB) are utilized in acquisition function. Optimal Objective Function An optimal objective function, which includes two parts: OF(x) and TF(x), is defined in Eq. (6). OF(x) represents the optimal term of the optimal objective function, TF(x) denotes the target term of the optimal objective function. As shown in Eq. (7), the above nine structure parameters of STI LDMOS device are defined as independent variable. $$\:\begin{array}{c}O\left(x\right)=OF\left(x\right)+\:TF\left(x\right)\#\left(6\right)\end{array}$$ $$\:\begin{array}{c}x={\left\{{N}_{pbody.p},{N}_{pbody.s},\dots\:,Lsti.d,{L}_{sog}\right\}}^{T}\#\left(7\right)\end{array}$$ As defined in Eq. (8), the optimal term OF(x) represents the FOM, where BV(x) and R onsp (x) denote the corresponding performance values of the device constructed in each iteration of the automatic design framework. This function measures the comprehensive performance of the designed device. A higher value indicates that the device can achieve a higher BV under a lower R onsp condition. Therefore, OF(x) will drive the automatic design framework to further iterate and produce the optimal result when current performance of constructed device meets the target performance. $$\:\begin{array}{c}OF\left(x\right)=FOM\left(x\right)=\frac{{BV\left(x\right)}^{2}}{{R}_{onsp}\left(x\right)}\#\left(8\right)\end{array}$$ The target term TF(x), defined in Eq. (9), consists of two parts: P 1 (x) and P 2 (x). P 1 (x) is the performance target function for BV, while P 2 (x) is the performance target function for R onsp . The constant terms \(\:{\text{B}\text{V}}^{\text{t}}\) and \(\:{\text{R}}_{\text{o}\text{n}\text{s}\text{p}}^{\text{t}}\) are included in these functions, respectively, which represent the target performance values that the designed device should achieve. By substituting Eqs. (10) and (11) into Eq. (9), the expanded form of TF(x) is shown in Eq. (12). This function indicates whether the designed device has reached the basic target performance values. The P 1 (x) term being greater than zero indicates that the target BV has been achieved, while the P 2 (x) term being greater than zero indicates the target R onsp has been reached. Consequently, TF(x) drives the automatic design framework to construct devices that meet the target performance. $$\:\begin{array}{c}TF\left(x\right)=\:{P}_{1}\left(x\right)+{P}_{2}\left(x\right)\#\left(9\right)\end{array}$$ $$\:\begin{array}{c}{P}_{1}\left(x\right)=\left(BV\left(x\right)-{BV}^{t}\right)\#\left(10\right)\end{array}$$ $$\:\begin{array}{c}{P}_{2}\left(x\right)=\left({\:R}_{onsp}^{t}-{R}_{onsp}\left(x\right)\right)\#\left(11\right)\end{array}$$ $$\:\begin{array}{c}TF\left(x\right)=\:\left(BV\left(x\right)-{BV}^{t}\right)+\left({\:R}_{onsp}^{t}-{R}_{onsp}\left(x\right)\right)\#\left(12\right)\end{array}$$ Architecture of proposed Automatic Design Framework Figure 4 shows the flow diagram of automatic design flow. Firstly, the target values of BV and R onsp are specified to automatic design framework. Meanwhile, the two constants in the target term TF(x) of the objective function are determined. This objective function represents the goal of the automatic design framework, which can be expressed mathematically as follows: $$\:\begin{array}{c}O\left(x\right)=\frac{{BV\left(x\right)}^{2}}{{R}_{onsp}\left(x\right)}+\left(BV\left(x\right)-{BV}^{t}\right)+\left({\:R}_{onsp}^{t}-{R}_{onsp}\left(x\right)\right)\#\left(13\right)\end{array}$$ $$\:\begin{array}{c}Goal=argmax\left(Objective\:Function\right)\#\left(14\right)\end{array}$$ The automatic design framework will iterate to find maximum of the objective function. Hence, the goal of this automatic design framework will enable to ultimately obtain a device structure whose achievable performance can even surpass the target performance, while also exhibiting the optimal overall performance. This framework will start from a device with nine initial random parameters. The FOM, BV and R onsp of device are calculated by using the trained DNN model for each iteration. It run five hundred iterations optimization in BO process, which is experimentally proved to be enough to achieve high accuracy with the training dataset. After each iteration, the optimal objective function will drive the optimization algorithm generates new nine structure parameters \(\:{\varvec{x}}_{\varvec{i}+1}\) , and the DNN model calculates the FOM, BV and R onsp for the next device. When the iteration counter equal five hundred, the automatic design framework will output the maximum of FOM in specified target boundary of BV and R onsp and corresponding structure parameters. 3 Experimental Results and Discussions 3.1 Performance analysis of proposed DNN Model Model performance in dataset Figure 5 and Fig. 6 a shows MAPE of the BV and R onsp prediction for the training and test sets during the model training process. The train loss and test loss represent the model performance of different epoch. Especially, test error can be applied to assess the application quality of the trained model. The prediction error gradually decreases with the training epoch until convergence. Besides, the DNN model prediction performance of BV and R onsp is illustrated in Fig. 6 (a) and (b). The x-axis represents the BV or R onsp obtained by TCAD simulation, and the y-axis represents the BV or R onsp value predicted by the model. The distance of the dots from the diagonal line illustrates the accuracy of the prediction results. As shown in the figure clearly, most of the dots are focused on the diagonal attachment. In fact, there is only an average prediction error of 2.21% on BV and 0.43% on R onsp , which means an average performance prediction error of 1.32%. Compared to the previous work [ 21 ], the proposed DNN model use less than 20% of their neuron count, and the performance prediction error decreased from 3.81–1.32%. The results indicate the proposed DNN model for device predication owns higher accuracy with less computational cost. Table 2 Experimental results comparison about DNN with different ML algorithms (Corresponding Calculation Equations listed in Eq. (15) and Eq. (16)) Algorithm DNN Linear Regression Gradient Boosting SVR Random Forest MAPE 1.32 10.83 6.36 7.89 7.62 PA 98.68 89.17 93.64 92.11 92.38 Performance comparisons: proposed DNN vs. traditional ML algorithms As shown in Table 2 and Fig. 7 , other ML algorithms for BV and R onsp prediction and the comparison of these algorithms are illustrated. It is obvious that the error of the proposed DNN algorithm (with an error of 1.32%) is significantly lower than that of other traditional ML algorithms. The DNN algorithm has an excellent ability to predict BV and R onsp precisely. $$\:\begin{array}{c}Mean\:Absolute\:Percentage\:Error\left(MAPE\right)=\left|\frac{{Y}_{pred}-{Y}_{true}}{{Y}_{true}}\right|\times\:100\%\#\left(15\right)\end{array}$$ $$\:\begin{array}{c}Prediction\:Accuary\left(PA\right)=1-MAPE\#\left(16\right)\end{array}$$ Performance comparisons: proposed DNN vs. TCAD Our proposed model is implemented in Python on a Linux server with 3.5GHz CPU. We use Pytorch library for the DNN model. TCAD simulation also run in this server. The contrast of TCAD simulation and DNN calculation results using randomly selected structure parameters are illustrated in Fig. 8 .The comparison of the executed time for performance prediction between DNN model and TCAD is listed in Table 3 . The DNN model only takes 0.0039 seconds to execute, while the TCAD tool requires 1500 seconds. The DNN model runs several hundred thousand times faster than TCAD simulation. Therefore, for the development of STI LDMOS devices, using DNN model instead of TCAD simulation can significantly enhance research efficiency and greatly reduce development costs. Table 3 Executed time comparison between DNN model and TCAD Algorithm DNN Linear Regression MAPE 1.32 10.83 PA 98.68 89.17 3.2 Performance analysis of proposed design framework In this section, the automatic design framework is constructed to automatically design device structure of STI LDMOS, which significantly accelerates the development process. The framework focuses on optimizing device structures using an optimal objective function. BO algorithm is utilized to iteratively generate new structures, which are used by DNN model to evaluate the optimal FOM, BV and R onsp values. In all, the automatic design framework is used to search for the optimal device structure. Table 4 Executed time comparison of different frameworks Method BO + DNN BO + TCAD Time 190s At least 750000s Different operation modes of proposed automatic design framework Figure 9 illustrates different automatic design frameworks. In Fig. 9 (a), the proposed automatic design framework that integrates BO with DNN model, while in Fig. 9 (b), it’s traditional BO coupled with TCAD simulation tool [ 22 ]. The central advantage of proposed framework lies in the speed improvement. As shown in Table 4 , after iterating 500 times, the former takes only 190 seconds, whereas the latter requires at least 750,000 seconds. The automatic design speed of the former is nearly 4,000 times faster. Therefore, there is a significant advantage in ultra-fast speed for our proposed automatic design framework. This advantage mainly comes from using ML algorithms with DNN performance prediction model to replace TCAD Simulation Tool. It allows for much faster exploration of the device structure parameter space and optimization of STI LDMOS devices. The effectivity of target function with TF(x) The target value of BV is specified to be 50V, while the target value of R onsp is specified to be 25 \(\:m{\Omega\:}\bullet\:{mm}^{2}\) , the optimal FOM, BV and R onsp with the correspond structure parameters are eventually generated by the proposed framework. In Table 5 , the results with the optimal objective function integrating both OF(x) and TF(x) are compared to those with only OF(x). It’s illustrated that the desired results are better obtained through the proposed automatic design framework with optimal objective function integrated OF(x) and TF(x) in Fig. 10 . Although the automatic design framework is 2x slower after adding target term TF(x), it still cost only 190 seconds. This framework can also output optimal FOM, BV, and R onsp when the objective function only integrates OF(x). Nonetheless, the BV and R onsp with optimal FOM of this case cannot satisfy the target requirement of STI LDMOS. Hence, when the objective function integrated not only optimal term OF(x) but also target term TF(x), the automatic design framework will get another constraint to drive it to optimize device structures. As shown in Fig. 9 . a), the space below the two yellow dotted lines is constrained space defined by OF(x). And the automatic design framework will spare no effort to construct device performance located in this space. Therefore, device design requirements can only be met if the objective function integrates target term TF(x). Table 5 Outcome of different objective function Objective Function OF(x) + TF(x) OF(x) Time(s) 190 82 FOM (kW/mm2) 145.8 145.08 BV(V) 59.88 75.95 R onsp ( \(\:m{\Omega\:}\bullet\:{mm}^{2}\) ) 24.60 39.76 Table 6 Outcome of different objective function. Objective Function OF(x) + TF(x) Eq. (17) Time(s) 190 82 FOM (kW/mm2) 145.8 145.08 BV(V) 59.88 75.95 R onsp ( \(\:m{\Omega\:}\bullet\:{mm}^{2}\) ) 24.60 39.76 The effectivity of objective function with OF(x) Uniformly, the target value of BV is specified to be 50V, while the target value of R onsp is specified to be 25 \(\:m{\Omega\:}\bullet\:{mm}^{2}\) . In Table 6 and Fig. 11 , the results are compared between proposed optimal objective function and Eq. (17) in previous research [ 18 ]. The devices constructed by the automatic design framework that integrates the proposed optimal objective function demonstrate superior performance. Not only do they achieve the target performance values, but they consistently surpass these targets. Furthermore, the overall performance of constructed devices, considering FOM, is optimal. The automatic design framework integrating Eq. (17) can only generate approximately approach target performance. In the objective function of Eq. (17), this function also specifies the target values of BV and R onsp , similar to the target term TF(x) in the proposed optimal objective function, which aims to drive the automatic design framework to construct devices that meet the target performance values. However, for Eq. (17), its gradients in the BV and R onsp directions are shown in Eqs. (18) and (19). As illustrated in Fig. 11 .b), when BV is greater than \(\:{\text{B}\text{V}}^{\text{t}}\) , Eq. (18) is negative, its gradient direction is the arrow direction of the yellow dashed line 2. This direction is the iterative update direction of the automatic design framework, indicating that the automatic design framework needs to iteratively construct devices with smaller BV performance values. When BV is less than \(\:{\text{B}\text{V}}^{\text{t}}\) , i.e., Eq. (18) is positive, its gradient direction is the direction of the yellow dashed line 4. This direction is the iterative update direction of the automatic design framework, indicating that the automatic design framework needs to iteratively construct devices with larger BV performance values. The same applies to R onsp . In summary, from the perspective of gradient direction, Eq. (17) will cause the automatic design framework to iteratively move towards the point (50, 25), and the best outcome it can iterate out can only meet the target performance values. $$\:\begin{array}{c}r\left(x\right)=-\left\{\begin{array}{c}{\:\:\left(\frac{\left|{BV}^{t}-BV\left(x\right)\right|\times\:100}{{BV}^{t}}\right)}^{2}\:\\\:{+\left(\frac{\left|{R}_{onsp}^{t}-{R}_{onsp}\left(x\right)\right|\times\:100}{{R}_{onsp}^{t}}\right)}^{2}\end{array}\right\}\#\left(17\right)\end{array}$$ $$\:\begin{array}{c}\frac{\partial\:r\left(x\right)}{\partial\:BV\left(x\right)}=\frac{\left({BV}^{t}-BV\left(x\right)\right)\times\:\left(20000\right)}{{\left({BV}^{t}\right)}^{2}}\#\left(18\right)\end{array}$$ $$\:\begin{array}{c}\frac{\partial\:r\left(x\right)}{\partial\:{R}_{onsp}\left(x\right)}=\frac{\left({R}_{onsp}^{t}-{R}_{onsp}\left(x\right)\right)\times\:\left(20000\right)}{{\left({R}_{onsp}^{t}\right)}^{2}}\#\left(19\right)\end{array}$$ The gradient of the proposed optimal objective function, as shown in Eq. (20) and Fig. 10 a), is always positive in the BV direction, corresponding to the yellow dashed line 1, and always negative in the R onsp direction, corresponding to the yellow dashed line 2. As shown in Eq. (22), it is the sum of the gradient vectors of Eq. (20) and Eq. (21), which is also the same direction as the yellow dashed line 3. And it also represents the overall iterative optimization direction of the automatic design framework. Hence, the proposed objective function will drive the automatic design framework to iteratively optimize the device structure to achieve BV higher than the target value and R onsp lower than the target value. When the performance of the constructed device reaches the target performance, the optimization does not stop. The optimal term OF(x) will drive the automatic design framework to continue iterating, optimizing the device structure towards the direction of obtaining larger FOM values. $$\:\begin{array}{c}\frac{\partial\:O\left(x\right)}{\partial\:BV\left(x\right)}=\frac{2BV\left(x\right)}{{R}_{onsp}\left(x\right)}+1\#\left(20\right)\end{array}$$ $$\:\begin{array}{c}\frac{\partial\:O\left(x\right)}{\partial\:{R}_{onsp}\left(x\right)}=-\frac{{BV\left(x\right)}^{2}}{{{R}_{onsp}\left(x\right)}^{2}}-1\#\left(21\right)\end{array}$$ $$\:\begin{array}{c}g\left(x\right)=\sqrt{{\left(\frac{\partial\:O\left(x\right)}{\partial\:BV\left(x\right)}\right)}^{2}+{\left(\frac{\partial\:O\left(x\right)}{\partial\:{R}_{onsp}\left(x\right)}\right)}^{2}}\#\left(22\right)\end{array}$$ TCAD-based Verification of design results using the proposed framework Firstly, the boundary of BV was specified to be greater than 50V and the boundary of R onsp was specified to be less than 25 \(\:m{\Omega\:}\bullet\:{mm}^{2}\) . The framework output optimal FOM, BV and R onsp listed in Table 8 with corresponding structure parameters listed in Table 7 . And the correspond structure parameters are input back to TCAD simulation tool. Figure 12 and Fig. 13 is illustrated the STI LDMOS device simulation diagram in TCAD using the correspond structure parameters generated by automatic design framework. Table 8 also compare the results between automatic design framework and TCAD simulation tool. It is obvious that the results of the framework are extremely close to TCAD simulation tool, which are only 0.002% error of FOM, 1.98% error of BV and 3.68% error of R onsp . Therefore, the device designed by proposed automatic design framework is extremely precise. Table 7 The optimal device structure parameters. Structure parameters N pbody.p (cm − 3 ) N pbody.s (cm − 3 ) L pog (um) N ndrift.p (cm − 3 ) N ndrift.s (cm − 3 ) L nes (um) L sti.w (um) L sti.d (um) L sog (um) 2.314e17 7.838e14 7.606e-1 7.412e16 2.459e16 3.886e-1 1.856 1.829e-1 9.962e-1 Table 8 The comparison of Automatic Design Framework and TCAD. Method Automatic Design Framework TCAD Error FOM 145.8 146.12 0.002% BV 59.88 61.09 1.98% R onsp 24.60 25.54 3.68% 4 Conclusion In this article, an ultra-fast and precise automatic design framework of STI LDMOS device is proposed. It combines an optimal objective function, BO algorithm and DNN prediction model. Given the device structure parameters, the DNN prediction model can ultra-fast output the high accuracy performance including BV and R onsp . The first experimental results show that the DNN model achieves average 98.68% performance prediction accuracy. Specified the target values of BV and R onsp , the framework can fully automatically design the device structure that can satisfy the design constraints. The second experimental results demonstrate that the proposed framework is capable of optimizing the STI LDMOS device structure to obtain extremely precise designs. Moreover, the proposed framework is 4000 times more efficient than other frameworks. Thus, the proposed automatic design framework can significantly accelerate the development of STI LDMOS device compared to the traditional manual design flow. Declarations Funding This work was supported in part by the National Key R&D Program of China under Grant 2022YFF0605800, in part by the Zhejiang Provincial “Jianbing” “Lingyan” Research and Development Program of China under Grant 2024C01002 and 2022C01063, and in part by the National Natural Science Foundation of China under Grant 62204217. (Corresponding authors: Yitao Ma; Kai Xu) Competing Interests The authors have no relevant financial or non-financial interests to disclose. Author Contributes Chenggang Xu led the study and was responsible for the overall conceptualization and design of the research. Hongyu Tang, Yuxuan Zhu, Yue Cheng, Xuanzhi Jin, and Dawei Gao contributed to data collection, analysis, and interpretation of the results. Chenggang Xu, Yitao Ma and Kai Xu drafted the initial manuscript. All authors reviewed and approved the final manuscript. Yitao Ma and Kai Xu provided critical revisions and supervised the project. Data Availability Enquiries about data availability should be directed to the authors. References Dong, Z., Duan, B., Fu, C., Guo, H., Cao, Z., & Yang, Y. (2018). Novel LDMOS Optimizing Lateral and Vertical Electric Field to Improve Breakdown Voltage by Multi-Ring Technology. 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In 2016 IEEE 8th International Power Electronics and Motion Control Conference (IPEMC-ECCE Asia) (pp. 3116–3119). Presented at the 2016 IEEE 8th International Power Electronics and Motion Control Conference (IPEMC 2016 - ECCE Asia), Hefei, China: IEEE. https://doi.org/10.1109/IPEMC.2016.7512793 Su, R. Y., Yang, F. J., Tsay, J. L., Cheng, C. C., Liou, R. S., & Tuan, H. C. (2010). State-of-the-art device in high voltage power ICs with lowest on-state resistance. In 2010 International Electron Devices Meeting (p. 20.8.1-20.8.4). Presented at the 2010 IEEE International Electron Devices Meeting (IEDM), San Francisco, CA, USA: IEEE. https://doi.org/10.1109/IEDM.2010.5703403 Yang, F.-J., Gong, J., Su, R.-Y., Huo, K.-H., Tsai, C.-L., Cheng, C.-C., et al. (2013). A 700-V Device in High-Voltage Power ICs With Low On-State Resistance and Enhanced SOA. IEEE Transactions on Electron Devices, 60(9), 2847–2853. https://doi.org/10.1109/TED.2013.2273573 Synopsys, Sentaurus Device User Guide:Version T-2022.03, March 2022. Moens, P., Bauwens, F., Baele, J., Vershinin, K., De Backer, E., Sankara Narayanan, E. M., & Tack, M. (2006). XtreMOS : The First Integrated Power Transistor Breaking the Silicon Limit. In 2006 International Electron Devices Meeting (pp. 1–4). Presented at the 2006 International Electron Devices Meeting, San Francisco, CA: IEEE. https://doi.org/10.1109/IEDM.2006.346933 Xia, C., Cheng, X., Wang, Z., Xu, D., Cao, D., Zheng, L., et al. (2014). Improvement of SOI Trench LDMOS Performance With Double Vertical Metal Field Plate. IEEE TRANSACTIONS ON ELECTRON DEVICES, 61(10). Wei, J., Luo, X., Zhang, Y., Li, P., Zhou, K., Zhang, B., & Li, Z. (2016). High-Voltage Thin-SOI LDMOS With Ultralow ON-Resistance and Even Temperature Characteristic. IEEE Transactions on Electron Devices, 63(4), 1637–1643. https://doi.org/10.1109/TED.2016.2533022 Guo, Y., Yang, K., Chen, J., Li, M., Jiang, Z., Yao, J., et al. (2023). Tradeoff Between the Breakdown Voltage and Specific On-Resistance of SOI RESURF LDMOS. In 2023 IEEE 15th International Conference on ASIC (ASICON) (pp. 1–4). Presented at the 2023 IEEE 15th International Conference on ASIC (ASICON), Nanjing, China: IEEE. https://doi.org/10.1109/ASICON58565.2023.10396435 Wei, J., Ma, Z., Luo, X., Li, C., Deng, G., Song, H., et al. (2021). Experimental Study of Ultralow On-resistance Power LDMOS with Convex-shape Field Plate Structure. In 2021 33rd International Symposium on Power Semiconductor Devices and ICs (ISPSD) (pp. 87–90). Presented at the 2021 33rd International Symposium on Power Semiconductor Devices and ICs (ISPSD), Nagoya, Japan: IEEE. https://doi.org/10.23919/ISPSD 50666.2021.9452231 Carrillo-Nunez, H., Dimitrova, N., Asenov, A., & Georgiev, V. (2019). Machine Learning Approach for Predicting the Effect of Statistical Variability in Si Junctionless Nanowire Transistors. IEEE Electron Device Letters, 40(9), 1366–1369. https://doi.org/10.1109/LED.2019.2931839 Mehta, K., & Wong, H.-Y. (2021). Prediction of FinFET Current-Voltage and Capacitance-Voltage Curves Using Machine Learning With Autoencoder. IEEE Electron Device Lett., Article vol. 42, no. 2, pp. 136-139, Feb 2021, doi: 10.1109/led.2020.3045064. Han, S.-C., Choi, J., & Hong, S.-M. (2021). Acceleration of Semiconductor Device Simulation With Approximate Solutions Predicted by Trained Neural Networks. IEEE Transactions on Electron Devices, 68(11), 5483–5489. https://doi.org/10.1109/TED.2021.3075192 Wang G., Wang S., Ma L., Wang G., Wu J., Duan X., Chen S., & Liu H. (2022) Optimization and Performance Prediction of Tunnel Field-Effect Transistors Based on Deep Learning. Adv. Mater. Technol. 2022, 7, 2100682. https://doi.org/10.1002/admt.202100682 Chen, J., Alawieh, M. B., Lin, Y., Zhang, M., Zhang, J., Guo, Y., & Pan, D. Z. (2020). Automatic Selection of Structure Parameters of Silicon on Insulator Lateral Power Device Using Bayesian Optimization. IEEE Electron Device Letters, 41(9), 1288–1291. https://doi.org/10.1109/LED.2020.3013571 Huang Yi, Sun Shiyu, Duan Xiusheng, & Chen Zhigang. (2016). A study on Deep Neural Networks framework. In 2016 IEEE Advanced Information Management, Communicates, Electronic and Automation Control Conference (IMCEC) (pp. 1519–1522). Presented at the 2016 IEEE Advanced Information Management, Communicates, Electronic and Automation Control Conference (IMCEC), Xi’an, China: IEEE. https://doi.org/10.1109/IMCEC.2016.7867471 Shahriari, B., Swersky, K., Wang, Z., Adams, R. P., & De Freitas, N. (2016). Taking the Human Out of the Loop: A Review of Bayesian Optimization. Proceedings of the IEEE, 104(1), 148–175. https://doi.org/10.1109/JPROC.2015.2494218 Chen, J., Guo, X., Guo, Y., Zhang, J., Zhang, M., Yao, Q., & Yao, J. (2021). Deep neural network-based approach for breakdown voltage and specific on-resistance prediction of SOI LDMOS with field plate. Japanese Journal of Applied Physics, 60(7), 077002. https://doi.org/10.35848/1347-4065/ac06da Chuang, P.-J., Saadat, A., Van De Put, M. L., Edwards, H., & Vandenberghe, W. G. (2023). Algorithmic Optimization of Transistors Applied to Silicon LDMOS. IEEE Access, 11, 64160–64169. https://doi.org/10.1109/ACCESS.2023.3287204 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 09 Dec, 2024 Read the published version in Journal of Computational Electronics → Version 1 posted Editorial decision: Revision requested 30 Aug, 2024 Reviews received at journal 10 Aug, 2024 Reviewers agreed at journal 01 Aug, 2024 Reviewers agreed at journal 01 Aug, 2024 Reviewers invited by journal 27 Jul, 2024 Editor assigned by journal 07 Jul, 2024 Submission checks completed at journal 07 Jul, 2024 First submitted to journal 06 Jul, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4696885","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":333199596,"identity":"ad19a206-48b3-4897-99d7-01b18fd5401f","order_by":0,"name":"Chenggang Xu","email":"","orcid":"","institution":"Zhejiang University","correspondingAuthor":false,"prefix":"","firstName":"Chenggang","middleName":"","lastName":"Xu","suffix":""},{"id":333199599,"identity":"34490a92-de2b-4fd5-9f65-3aa1d67c5f2d","order_by":1,"name":"Hongyu Tang","email":"","orcid":"","institution":"Zhejiang 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13:09:55","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4696885/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4696885/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10825-024-02244-8","type":"published","date":"2024-12-09T15:56:57+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":61527805,"identity":"b249567f-43da-4cd6-b577-86cd0405c0ce","added_by":"auto","created_at":"2024-07-31 21:01:18","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":92126,"visible":true,"origin":"","legend":"\u003cp\u003eThe cross-section of device structure\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-4696885/v1/53e1d5dddc743d7c8da2cd1e.png"},{"id":61527807,"identity":"5a95d8c1-2978-4a8e-b91a-8c9ba290ad11","added_by":"auto","created_at":"2024-07-31 21:01:18","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":82127,"visible":true,"origin":"","legend":"\u003cp\u003eThe density distributions of performance: (a) BV and (b) R\u003csub\u003eonsp\u003c/sub\u003e\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-4696885/v1/3dc4323d74d2abbf5a305e1c.png"},{"id":61527809,"identity":"862048a2-aaa2-44c3-91d3-f8dde05fbc02","added_by":"auto","created_at":"2024-07-31 21:01:18","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":460534,"visible":true,"origin":"","legend":"\u003cp\u003eThe detailed diagram of the DNN model, which has five hidden layers, shows the neurons in each layer as 8, 32, 24, 16, 12, 8, and 2 respectively\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-4696885/v1/436a006bf8081aa3c780ae16.png"},{"id":61527811,"identity":"b6e8a231-807b-42ca-9156-9bed75f66197","added_by":"auto","created_at":"2024-07-31 21:01:18","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":183795,"visible":true,"origin":"","legend":"\u003cp\u003eThe automatic design framework\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-4696885/v1/04bacbf165ad177b2f481c96.png"},{"id":61527806,"identity":"fa0d9c37-d9ab-4d04-a950-b2d5cb692a73","added_by":"auto","created_at":"2024-07-31 21:01:18","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":82300,"visible":true,"origin":"","legend":"\u003cp\u003eThe train and test loss in each epoch, with the blue solid line representing the train loss and the red solid line representing the test loss\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-4696885/v1/53debcf50193ddedbb5c5768.png"},{"id":61527900,"identity":"c138571c-cec1-49f5-88b1-87929c5dacf9","added_by":"auto","created_at":"2024-07-31 21:09:18","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":105194,"visible":true,"origin":"","legend":"\u003cp\u003eThe model performance in dataset: (a) BV average prediction error and (b) R\u003csub\u003eonsp\u003c/sub\u003e average prediction error\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-4696885/v1/ca4eba4c45c3c19b11b892b7.png"},{"id":61527901,"identity":"009f715e-f0a4-4ec3-984c-121b0466e120","added_by":"auto","created_at":"2024-07-31 21:09:18","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":96047,"visible":true,"origin":"","legend":"\u003cp\u003eMAPE comparison of DNN model and different ML algorithms\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-4696885/v1/22c8a9dbb900a67abae92ac8.png"},{"id":61527813,"identity":"b5bedf87-d4e8-4b2b-8e97-3f50b3913004","added_by":"auto","created_at":"2024-07-31 21:01:18","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":93598,"visible":true,"origin":"","legend":"\u003cp\u003eRandom test of DNN model and TCAD: (a) BV and (b) R\u003csub\u003eonsp\u003c/sub\u003e comparison of DNN model with TCAD simulation\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-4696885/v1/6f6856a9b5b95ea37e2540eb.png"},{"id":61527815,"identity":"17c7f430-e9d2-4427-9dbd-447269fd9c04","added_by":"auto","created_at":"2024-07-31 21:01:18","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":136340,"visible":true,"origin":"","legend":"\u003cp\u003eThe flow diagram of framework integrated BO with (a) DNN model and (b) TCAD simulation\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-4696885/v1/aa8f94e0bd9f0d299146a9cf.png"},{"id":61527816,"identity":"36c5e762-b4a6-4368-ad8c-bf0e7fd9a118","added_by":"auto","created_at":"2024-07-31 21:01:18","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":229072,"visible":true,"origin":"","legend":"\u003cp\u003eThe iteration process of different objective function: (a) proposed optimal objective function and (b) objective function only integrated OF(x).\u003c/p\u003e","description":"","filename":"floatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-4696885/v1/de44374acea029526649f8f4.png"},{"id":61527903,"identity":"23f3ec92-e5ed-4928-9acf-0b8f2bc5ddfe","added_by":"auto","created_at":"2024-07-31 21:09:18","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":236989,"visible":true,"origin":"","legend":"\u003cp\u003eThe iteration process of different methods: (a) proposed optimal objective function and (b) objective function from previous article [18]\u003c/p\u003e","description":"","filename":"floatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-4696885/v1/9a26e1759ad6779166df05e5.png"},{"id":61527817,"identity":"06971ed2-cd83-476e-93c9-9b7607be08f5","added_by":"auto","created_at":"2024-07-31 21:01:19","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":50800,"visible":true,"origin":"","legend":"\u003cp\u003eThe outcome of TCAD simulation tool using the device structure parameters generated by automatic design framework: (a) the device structure from TCAD and (b) the breakdown process from TCAD\u003c/p\u003e","description":"","filename":"floatimage12.png","url":"https://assets-eu.researchsquare.com/files/rs-4696885/v1/bba59ec16f604d7901c5ae14.png"},{"id":61527902,"identity":"c1e88274-0ab8-41d1-a045-7f430b193189","added_by":"auto","created_at":"2024-07-31 21:09:18","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":76483,"visible":true,"origin":"","legend":"\u003cp\u003eThe performance outcome of TCAD simulation tool using the device structure parameters generated by automatic design framework: (a) the Id-Vd curve and (b) Id-Vg curve.\u003c/p\u003e","description":"","filename":"floatimage13.png","url":"https://assets-eu.researchsquare.com/files/rs-4696885/v1/5f982d19f66d8175d46275d6.png"},{"id":71552384,"identity":"59bac5e7-c5d4-462c-a373-245f5756d742","added_by":"auto","created_at":"2024-12-16 16:05:43","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2334790,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4696885/v1/130674be-210b-4d67-bc32-3b19a65fe05c.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"An Ultra-Fast and Precise Automatic Design Framework for Predicting and Constructing High-Performance Shallow-Trench-Isolation LDMOS Device","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eLaterally diffused metal oxide semiconductor (LDMOS) devices have been widely adopted in power integrated circuits due to its high Breakdown Voltage (BV) and low specific on-resistance (R\u003csub\u003eonsp\u003c/sub\u003e) [\u003cspan additionalcitationids=\"CR2 CR3 CR4\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. It is the key determinant of the performance, cost, and integration level of power integrated circuits [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Currently, the conventional device design approach relies on simulation tools such as Sentaurus, Medici, Silvaco and so on. These simulation tools acquire the device electrical characteristics by solving the physical equations such as Poisson equation, Continuity equation and Transport equation of electrons and holes at the set mesh point [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. However, the simulation results do not meet the expectations to some extent, it must require significant human intervention and configuration that spend great efforts on the remodeling and optimization. It is time-consuming and cumbersome.\u003c/p\u003e \u003cp\u003eOn the other hand, in the development of LDMOS devices, the most crucial performance metrics are BV and R\u003csub\u003eonsp\u003c/sub\u003e. There exists a \u0026lsquo;silicon limit\u0026rsquo; constraint relationship between these two electrical performances, which increases the difficulty and cost of development [\u003cspan additionalcitationids=\"CR10 CR11 CR12\" citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. In consequence, multiple parameter adjustments and iterations are essential for optimizing device performance, which in turn substantially raise manufacturing costs. Besides, capturing the influence of multiple processes on the performance of variable devices through manual methodologies presents significant challenges. Therefore, the traditional development method cannot satisfy the requirements of the widely applied LDMOS devices.\u003c/p\u003e \u003cp\u003eRecently, Machine Learning (ML) algorithms exhibit great ability to efficiently accelerate device simulation and design. For example, Carrillo-Nunez et al. investigated the possibility to replace numerical time-consuming device simulations with a multi-layer neural network [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. Mehta et al. demonstrated the possibility of predicting full transistor current-voltage and capacitance-voltage curves using trained prediction model based on Deep Neural Network (DNN) [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Han et al. proposed to use a neural network to learn an approximate solution for desired bias conditions to accelerate the simulation [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Wang et al. present a novel method of predicting and optimizing the performance of the existing TFETs by using deep learning to accelerate the device design [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. Chen et al. proposed an automated structural design method for SOI lateral power device based on optimization algorithm [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. These research firstly demonstrate the significant advantage of machine learning methods in device simulation, while also proving the possibility of using optimization algorithms to automatically design devices. However, there is no research that designs an optimal objective function to drive the optimization algorithm to iterate more diligently, to construct devices that better meet the design specifications. In the traditional device development process, device structure adjustments are performed not only to ensure the device satisfies fundamental performance requirements, but also to iteratively optimize the device to attain the optimal figure of merit (FOM). Hence, for an automated design framework, designing devices that can simultaneously exhibit target performance and optimal FOM is the most desired outcome after applying ML algorithms. Furthermore, there is also no research utilizing ML algorithms to accelerate and automate the design of Shallow Trench Isolation (STI) LDMOS device.\u003c/p\u003e \u003cp\u003eThis research proposes an ultra-fast and extremely precise framework to design STI LDMOS device automatically and optimally by the integration of an optimal objective function, Bayesian Optimization (BO) algorithm and DNN model. Firstly, a higher prediction accuracy model for STI LDMOS based on DNN algorithm. By inputting the structure parameters of device, the DNN model can effectively output BV and R\u003csub\u003eonsp\u003c/sub\u003e with precision of 98.68%. Then, an optimal objective function is defined, which includes two parts: (1) Optimal Function (OF): driving the device structure to attain the optimal FOM; (2) Target Function (TF): driving the device structure that exhibits target performance. By integrating this objective function, not only can the designed device meet the specified device performance, but also achieve the optimal FOM. Compared to TCAD, there is only 0.002% error on FOM and 2.83% average error on BV and R\u003csub\u003eonsp\u003c/sub\u003e performances. The entire processing time of the proposed framework for the automated design is less than 4 minutes.\u003c/p\u003e"},{"header":"2 Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 A TCAD Simulation and Electrical Characteristics of Device\u003c/h2\u003e \u003cp\u003e \u003cb\u003eDevice Structure and TCAD Simulation\u003c/b\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows a schematic diagram of the device structure of STI LDMOS. It includes five electrodes on the device. The constant doping profiles and Gaussian doping profiles are simultaneously defined in the device. The constant p-type doping background is used in the substrate. There is n\u0026thinsp;+\u0026thinsp;Gaussian doping profiles of source/drain and p\u0026thinsp;+\u0026thinsp;Gaussian doping profiles of bulk/psub placing on the device surface. Besides these Gaussian doping profiles, it exists two more extensive distributed doping profiles: n\u0026thinsp;+\u0026thinsp;Gaussian doping profiles of n-type drift region and p\u0026thinsp;+\u0026thinsp;Gaussian doping profiles of p-type body (pbody) region. There are two STI regions by deposit process to enhance BV.\u003c/p\u003e \u003cp\u003eIn Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, nine parameters listed are used as the input parameters for TCAD simulations. They include: (1) the peak doping concentration of the pbody Gaussian doping (Npbody.p), (2) the doping concentration in specific depth of the pbody Gaussian doping (Npbody.s), (3) the length of the overlap region of pbody to gate (Lpog), (4) the peak doping concentration of the ndrift Gaussian doping (Nndrift.p), (5) the doping concentration in specific depth of the ndrift Gaussian doping (Nndrift.s), (6) the length of the extension region of ndrift beyond STI (Lnes), (7) the width of STI (Lsti.w), (8) the depth of STI (Lsti.d), (9) the length of the overlap region of STI to gate (Lsog). These structure parameters determine the doping distribution and the size of the pbody region, ndrift region, and STI region. The parameter sets were randomly generated by Python script, which size is 2578. Next, by inputting parameter sets, TCAD simulation tool can output performance sets. The commercial device simulator Sentaurus is used for device modeling and performance simulation [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003cb\u003eElectrical Characteristics of Device\u003c/b\u003e \u003c/p\u003e \u003cp\u003eBV represents the maximum voltage between the source and drain that the device can sustain without experiencing avalanche breakdown when it is in off state. The \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{I}_{DS}-{V}_{DS}\\)\u003c/span\u003e\u003c/span\u003e measurement is performed and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{V}_{DS}\\)\u003c/span\u003e\u003c/span\u003e is ramped up to extract the maximum \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{V}_{DS}\\)\u003c/span\u003e\u003c/span\u003e when the TCAD no longer converges:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}BV={max}\\left({V}_{DS}\\right),\\:{V}_{GS}={V}_{BS}={V}_{SS}=0V\\#\\left(1\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWe calculate the specific on-state resistance by\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}{R}_{onsp}={R}_{onds}\\times\\:AREA\\#\\left(2\\right)\\#\\#\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere AREA is half-pitch times a unit length (default value is 1 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\mu\\:m\\)\u003c/span\u003e\u003c/span\u003e on the z-direction since 2D simulations is performed) and\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}{R}_{onds}=\\frac{{V}_{DS}}{{I}_{DS}}\\:({when\\:V}_{GS}=5V,{V}_{DS}=0.1V)\\#\\left(3\\right)\\#\\#\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eFinally, the FOM is the most important metric in this study, equaling\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equd\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}FOM=\\:\\frac{{BV}^{2}}{{R}_{on,sp}}\\#\\left(4\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe FOM is one of the most well-known metrics for evaluating the performance of power devices. A higher FOM indicates that the device has characteristics closer to an ideal switch. Researchers can use this FOM to gauge the performance of a power device.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe description and bound of device structure parameters\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSymbol(units)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDescription\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBound\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003epbody.p\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e(cm\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u0026minus;\u0026thinsp;3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003e)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eThe peak value of the pbody Gaussian doping\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e[1.4e17, 2.6e17]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003epbody.s\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e(cm\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u0026minus;\u0026thinsp;3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003e)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eThe value of the pbody Gaussian doping in specific depth\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e[0.7e15, 1.3e15]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eL\u003c/em\u003e\u003csub\u003e\u003cem\u003epog\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e(um)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eThe length of the overlap region of pbody to gate\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e[0.07, 0.13]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003endrift.p\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e(cm\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u0026minus;\u0026thinsp;3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003e)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eThe peak value of the ndrift Gaussian doping\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e[0.7e17, 1.3e17]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003endrift.s\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e(cm\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u0026minus;\u0026thinsp;3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003e)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eThe value of the ndrift Gaussian doping in specific depth\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e[1.4e16, 2.6e16]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eL\u003c/em\u003e\u003csub\u003e\u003cem\u003enes\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e(um)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eThe length of the extension region of ndrift beyond STI\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e[0.375, 0.715]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eL\u003c/em\u003e\u003csub\u003e\u003cem\u003esti.w\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e(um)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eThe width of STI\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e[1.4, 2.6]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eL\u003c/em\u003e\u003csub\u003e\u003cem\u003esti.d\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e(um)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eThe depth of STI\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e[0.14, 0.26]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eL\u003c/em\u003e\u003csub\u003e\u003cem\u003esog\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e(um)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eThe length of the overlap region of STI to gate\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e[0.7, 1.3]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Automatic Design Framework\u003c/h2\u003e \u003cp\u003e \u003cb\u003eDeep Neural Network Algorithm\u003c/b\u003e \u003c/p\u003e \u003cp\u003eFirstly, a total of 2578 samples in the dataset prepared for training the DNN model is obtained from the commercial device simulator Sentaurus which is presented in above session. The input features contain nine structural parameters listed in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The output features contain the BV and R\u003csub\u003eonsp\u003c/sub\u003e, whose density distributions are illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The dataset is divided into 8:2 for training dataset and testing dataset, respectively. It is obviously that there are different ranges and magnitudes of different input features. Note that the length Lpog is only tenth of micron, while the concentration Npbody.p is more than 1e17, which greatly affects the accuracy and generalization ability of the DNN model. Thus, the dataset needs to be normalized before training so that the values of each input feature will be scaled to the range of 0 to 1.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eSecondly, the DNN algorithm is inspired by structure of mammalian visual system that contains many layers of neural network [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Different numbers and weights of neurons and diverse activation functions will result in different relationship functions between input and output. The construction of the proposed DNN prediction model can be divided into two parts: the network design and the model training. In fact, continuous adjustment of the neural network structure and training strategy based on the training and validation results are required for the construction of neural networks. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows the overview of the proposed DNN model. The model is a regression network for BV and R\u003csub\u003eonsp\u003c/sub\u003e prediction with five hidden layers, and the neurons in each layer are 8, 32, 24, 16, 12, 8 and 2 respectively. This layer structure is verified for achieving highest accuracy and well optimized for STI LDMOS design to minimize the computational cost. Comparing among all these activation functions, the Relu function is selected and used for the input and hidden layers of all networks. During the training process, regression task used the mean absolute percentage error (MAPE) as the loss function, which is presented in Eq.\u0026nbsp;(5).\u003cdiv id=\"Eque\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Eque\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}Loss\\:Function=\\frac{1}{2n}{\\sum\\:}_{i=1}^{n}\\left(\\left|\\frac{Bvdss-\\widehat{Bvdss}}{\\widehat{Bvdss}}\\right|+\\left|\\frac{Ronsp-\\widehat{Ronsp}}{\\widehat{Ronsp}}\\right|\\right)\\times\\:100\\%\\#\\left(5\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cb\u003eBayesian Optimization Algorithm\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThe two critical modules (surrogate model and acquisition function) constitute BO algorithm. The surrogate model is a statistical model attempting to replicate the objective function and the acquisition function is used to decide where to sample the next data point [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. In the proposed framework, the Gaussian Process Regression (GPR) algorithm is used as surrogate model and the Expected Improvement (EI), Probability of Improvement (PI) and Bayesian Confidence Bound (UCB) are utilized in acquisition function.\u003c/p\u003e \u003cp\u003e \u003cb\u003eOptimal Objective Function\u003c/b\u003e \u003c/p\u003e \u003cp\u003eAn optimal objective function, which includes two parts: OF(x) and TF(x), is defined in Eq.\u0026nbsp;(6). OF(x) represents the optimal term of the optimal objective function, TF(x) denotes the target term of the optimal objective function. As shown in Eq.\u0026nbsp;(7), the above nine structure parameters of STI LDMOS device are defined as independent variable.\u003cdiv id=\"Equf\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equf\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}O\\left(x\\right)=OF\\left(x\\right)+\\:TF\\left(x\\right)\\#\\left(6\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equg\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equg\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}x={\\left\\{{N}_{pbody.p},{N}_{pbody.s},\\dots\\:,Lsti.d,{L}_{sog}\\right\\}}^{T}\\#\\left(7\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eAs defined in Eq.\u0026nbsp;(8), the optimal term OF(x) represents the FOM, where BV(x) and R\u003csub\u003eonsp\u003c/sub\u003e(x) denote the corresponding performance values of the device constructed in each iteration of the automatic design framework. This function measures the comprehensive performance of the designed device. A higher value indicates that the device can achieve a higher BV under a lower R\u003csub\u003eonsp\u003c/sub\u003e condition. Therefore, OF(x) will drive the automatic design framework to further iterate and produce the optimal result when current performance of constructed device meets the target performance.\u003cdiv id=\"Equh\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equh\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}OF\\left(x\\right)=FOM\\left(x\\right)=\\frac{{BV\\left(x\\right)}^{2}}{{R}_{onsp}\\left(x\\right)}\\#\\left(8\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe target term TF(x), defined in Eq.\u0026nbsp;(9), consists of two parts: P\u003csub\u003e1\u003c/sub\u003e(x) and P\u003csub\u003e2\u003c/sub\u003e(x). P\u003csub\u003e1\u003c/sub\u003e(x) is the performance target function for BV, while P\u003csub\u003e2\u003c/sub\u003e(x) is the performance target function for R\u003csub\u003eonsp\u003c/sub\u003e. The constant terms \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{B}\\text{V}}^{\\text{t}}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{R}}_{\\text{o}\\text{n}\\text{s}\\text{p}}^{\\text{t}}\\)\u003c/span\u003e\u003c/span\u003e are included in these functions, respectively, which represent the target performance values that the designed device should achieve. By substituting Eqs.\u0026nbsp;(10) and (11) into Eq.\u0026nbsp;(9), the expanded form of TF(x) is shown in Eq.\u0026nbsp;(12). This function indicates whether the designed device has reached the basic target performance values. The P\u003csub\u003e1\u003c/sub\u003e(x) term being greater than zero indicates that the target BV has been achieved, while the P\u003csub\u003e2\u003c/sub\u003e(x) term being greater than zero indicates the target R\u003csub\u003eonsp\u003c/sub\u003e has been reached. Consequently, TF(x) drives the automatic design framework to construct devices that meet the target performance.\u003cdiv id=\"Equi\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equi\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}TF\\left(x\\right)=\\:{P}_{1}\\left(x\\right)+{P}_{2}\\left(x\\right)\\#\\left(9\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equj\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equj\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}{P}_{1}\\left(x\\right)=\\left(BV\\left(x\\right)-{BV}^{t}\\right)\\#\\left(10\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equk\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equk\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}{P}_{2}\\left(x\\right)=\\left({\\:R}_{onsp}^{t}-{R}_{onsp}\\left(x\\right)\\right)\\#\\left(11\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equl\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equl\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}TF\\left(x\\right)=\\:\\left(BV\\left(x\\right)-{BV}^{t}\\right)+\\left({\\:R}_{onsp}^{t}-{R}_{onsp}\\left(x\\right)\\right)\\#\\left(12\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eArchitecture of proposed Automatic Design Framework\u003c/b\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows the flow diagram of automatic design flow. Firstly, the target values of BV and R\u003csub\u003eonsp\u003c/sub\u003e are specified to automatic design framework. Meanwhile, the two constants in the target term TF(x) of the objective function are determined. This objective function represents the goal of the automatic design framework, which can be expressed mathematically as follows:\u003cdiv id=\"Equm\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equm\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}O\\left(x\\right)=\\frac{{BV\\left(x\\right)}^{2}}{{R}_{onsp}\\left(x\\right)}+\\left(BV\\left(x\\right)-{BV}^{t}\\right)+\\left({\\:R}_{onsp}^{t}-{R}_{onsp}\\left(x\\right)\\right)\\#\\left(13\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equn\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equn\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}Goal=argmax\\left(Objective\\:Function\\right)\\#\\left(14\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe automatic design framework will iterate to find maximum of the objective function. Hence, the goal of this automatic design framework will enable to ultimately obtain a device structure whose achievable performance can even surpass the target performance, while also exhibiting the optimal overall performance. This framework will start from a device with nine initial random parameters. The FOM, BV and R\u003csub\u003eonsp\u003c/sub\u003e of device are calculated by using the trained DNN model for each iteration. It run five hundred iterations optimization in BO process, which is experimentally proved to be enough to achieve high accuracy with the training dataset. After each iteration, the optimal objective function will drive the optimization algorithm generates new nine structure parameters \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{x}}_{\\varvec{i}+1}\\)\u003c/span\u003e\u003c/span\u003e, and the DNN model calculates the FOM, BV and R\u003csub\u003eonsp\u003c/sub\u003e for the next device. When the iteration counter equal five hundred, the automatic design framework will output the maximum of FOM in specified target boundary of BV and R\u003csub\u003eonsp\u003c/sub\u003e and corresponding structure parameters.\u003c/p\u003e \u003c/div\u003e"},{"header":"3 Experimental Results and Discussions","content":"\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Performance analysis of proposed DNN Model\u003c/h2\u003e \u003cp\u003e \u003cb\u003eModel performance in dataset\u003c/b\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea shows MAPE of the BV and R\u003csub\u003eonsp\u003c/sub\u003e prediction for the training and test sets during the model training process. The train loss and test loss represent the model performance of different epoch. Especially, test error can be applied to assess the application quality of the trained model. The prediction error gradually decreases with the training epoch until convergence. Besides, the DNN model prediction performance of BV and R\u003csub\u003eonsp\u003c/sub\u003e is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e (a) and (b). The x-axis represents the BV or R\u003csub\u003eonsp\u003c/sub\u003e obtained by TCAD simulation, and the y-axis represents the BV or R\u003csub\u003eonsp\u003c/sub\u003e value predicted by the model. The distance of the dots from the diagonal line illustrates the accuracy of the prediction results. As shown in the figure clearly, most of the dots are focused on the diagonal attachment. In fact, there is only an average prediction error of 2.21% on BV and 0.43% on R\u003csub\u003eonsp\u003c/sub\u003e, which means an average performance prediction error of 1.32%. Compared to the previous work [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e], the proposed DNN model use less than 20% of their neuron count, and the performance prediction error decreased from 3.81\u0026ndash;1.32%. The results indicate the proposed DNN model for device predication owns higher accuracy with less computational cost.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eExperimental results comparison about DNN with different ML algorithms (Corresponding Calculation Equations listed in Eq.\u0026nbsp;(15) and Eq.\u0026nbsp;(16))\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAlgorithm\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDNN\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLinear Regression\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eGradient Boosting\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSVR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eRandom Forest\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMAPE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e7.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e7.62\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e98.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e89.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e93.64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e92.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e92.38\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003ePerformance comparisons: proposed DNN vs. traditional ML algorithms\u003c/b\u003e \u003c/p\u003e \u003cp\u003eAs shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e, other ML algorithms for BV and R\u003csub\u003eonsp\u003c/sub\u003e prediction and the comparison of these algorithms are illustrated. It is obvious that the error of the proposed DNN algorithm (with an error of 1.32%) is significantly lower than that of other traditional ML algorithms. The DNN algorithm has an excellent ability to predict BV and R\u003csub\u003eonsp\u003c/sub\u003e precisely.\u003cdiv id=\"Equo\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equo\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}Mean\\:Absolute\\:Percentage\\:Error\\left(MAPE\\right)=\\left|\\frac{{Y}_{pred}-{Y}_{true}}{{Y}_{true}}\\right|\\times\\:100\\%\\#\\left(15\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equp\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equp\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}Prediction\\:Accuary\\left(PA\\right)=1-MAPE\\#\\left(16\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cb\u003ePerformance comparisons: proposed DNN vs. TCAD\u003c/b\u003e \u003c/p\u003e \u003cp\u003eOur proposed model is implemented in Python on a Linux server with 3.5GHz CPU. We use Pytorch library for the DNN model. TCAD simulation also run in this server. The contrast of TCAD simulation and DNN calculation results using randomly selected structure parameters are illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e.The comparison of the executed time for performance prediction between DNN model and TCAD is listed in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The DNN model only takes 0.0039 seconds to execute, while the TCAD tool requires 1500 seconds. The DNN model runs several hundred thousand times faster than TCAD simulation. Therefore, for the development of STI LDMOS devices, using DNN model instead of TCAD simulation can significantly enhance research efficiency and greatly reduce development costs.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eExecuted time comparison between DNN model and TCAD\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAlgorithm\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDNN\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLinear Regression\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMAPE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10.83\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e98.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e89.17\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Performance analysis of proposed design framework\u003c/h2\u003e \u003cp\u003eIn this section, the automatic design framework is constructed to automatically design device structure of STI LDMOS, which significantly accelerates the development process. The framework focuses on optimizing device structures using an optimal objective function. BO algorithm is utilized to iteratively generate new structures, which are used by DNN model to evaluate the optimal FOM, BV and R\u003csub\u003eonsp\u003c/sub\u003e values. In all, the automatic design framework is used to search for the optimal device structure.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eExecuted time comparison of different frameworks\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMethod\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBO\u0026thinsp;+\u0026thinsp;DNN\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBO\u0026thinsp;+\u0026thinsp;TCAD\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTime\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e190s\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAt least 750000s\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eDifferent operation modes of proposed automatic design framework\u003c/b\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e illustrates different automatic design frameworks. In Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e (a), the proposed automatic design framework that integrates BO with DNN model, while in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e (b), it\u0026rsquo;s traditional BO coupled with TCAD simulation tool [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. The central advantage of proposed framework lies in the speed improvement. As shown in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, after iterating 500 times, the former takes only 190 seconds, whereas the latter requires at least 750,000 seconds. The automatic design speed of the former is nearly 4,000 times faster. Therefore, there is a significant advantage in ultra-fast speed for our proposed automatic design framework. This advantage mainly comes from using ML algorithms with DNN performance prediction model to replace TCAD Simulation Tool. It allows for much faster exploration of the device structure parameter space and optimization of STI LDMOS devices.\u003c/p\u003e \u003cp\u003e \u003cb\u003eThe effectivity of target function with TF(x)\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThe target value of BV is specified to be 50V, while the target value of R\u003csub\u003eonsp\u003c/sub\u003e is specified to be 25 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:m{\\Omega\\:}\\bullet\\:{mm}^{2}\\)\u003c/span\u003e\u003c/span\u003e, the optimal FOM, BV and R\u003csub\u003eonsp\u003c/sub\u003e with the correspond structure parameters are eventually generated by the proposed framework. In Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, the results with the optimal objective function integrating both OF(x) and TF(x) are compared to those with only OF(x). It\u0026rsquo;s illustrated that the desired results are better obtained through the proposed automatic design framework with optimal objective function integrated OF(x) and TF(x) in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e. Although the automatic design framework is 2x slower after adding target term TF(x), it still cost only 190 seconds. This framework can also output optimal FOM, BV, and R\u003csub\u003eonsp\u003c/sub\u003e when the objective function only integrates OF(x). Nonetheless, the BV and R\u003csub\u003eonsp\u003c/sub\u003e with optimal FOM of this case cannot satisfy the target requirement of STI LDMOS. Hence, when the objective function integrated not only optimal term OF(x) but also target term TF(x), the automatic design framework will get another constraint to drive it to optimize device structures. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e. a), the space below the two yellow dotted lines is constrained space defined by OF(x). And the automatic design framework will spare no effort to construct device performance located in this space. Therefore, device design requirements can only be met if the objective function integrates target term TF(x).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eOutcome of different objective function\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eObjective Function\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eOF(x)\u0026thinsp;+\u0026thinsp;TF(x)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eOF(x)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTime(s)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e190\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e82\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFOM (kW/mm2)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e145.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e145.08\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBV(V)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e59.88\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e75.95\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eR\u003csub\u003eonsp\u003c/sub\u003e (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:m{\\Omega\\:}\\bullet\\:{mm}^{2}\\)\u003c/span\u003e\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e24.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e39.76\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eOutcome of different objective function.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eObjective Function\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eOF(x)\u0026thinsp;+\u0026thinsp;TF(x)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eEq.\u0026nbsp;(17)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTime(s)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e190\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e82\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFOM (kW/mm2)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e145.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e145.08\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBV(V)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e59.88\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e75.95\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eR\u003csub\u003eonsp\u003c/sub\u003e (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:m{\\Omega\\:}\\bullet\\:{mm}^{2}\\)\u003c/span\u003e\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e24.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e39.76\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eThe effectivity of objective function with OF(x)\u003c/b\u003e \u003c/p\u003e \u003cp\u003eUniformly, the target value of BV is specified to be 50V, while the target value of R\u003csub\u003eonsp\u003c/sub\u003e is specified to be 25 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:m{\\Omega\\:}\\bullet\\:{mm}^{2}\\)\u003c/span\u003e\u003c/span\u003e. In Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e, the results are compared between proposed optimal objective function and Eq.\u0026nbsp;(17) in previous research [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. The devices constructed by the automatic design framework that integrates the proposed optimal objective function demonstrate superior performance. Not only do they achieve the target performance values, but they consistently surpass these targets. Furthermore, the overall performance of constructed devices, considering FOM, is optimal. The automatic design framework integrating Eq.\u0026nbsp;(17) can only generate approximately approach target performance.\u003c/p\u003e \u003cp\u003eIn the objective function of Eq.\u0026nbsp;(17), this function also specifies the target values of BV and R\u003csub\u003eonsp\u003c/sub\u003e, similar to the target term TF(x) in the proposed optimal objective function, which aims to drive the automatic design framework to construct devices that meet the target performance values. However, for Eq.\u0026nbsp;(17), its gradients in the BV and R\u003csub\u003eonsp\u003c/sub\u003e directions are shown in Eqs.\u0026nbsp;(18) and (19). As illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e.b), when BV is greater than \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{B}\\text{V}}^{\\text{t}}\\)\u003c/span\u003e\u003c/span\u003e, Eq.\u0026nbsp;(18) is negative, its gradient direction is the arrow direction of the yellow dashed line 2. This direction is the iterative update direction of the automatic design framework, indicating that the automatic design framework needs to iteratively construct devices with smaller BV performance values. When BV is less than \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{B}\\text{V}}^{\\text{t}}\\)\u003c/span\u003e\u003c/span\u003e, i.e., Eq.\u0026nbsp;(18) is positive, its gradient direction is the direction of the yellow dashed line 4. This direction is the iterative update direction of the automatic design framework, indicating that the automatic design framework needs to iteratively construct devices with larger BV performance values. The same applies to R\u003csub\u003eonsp\u003c/sub\u003e. In summary, from the perspective of gradient direction, Eq.\u0026nbsp;(17) will cause the automatic design framework to iteratively move towards the point (50, 25), and the best outcome it can iterate out can only meet the target performance values.\u003cdiv id=\"Equq\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equq\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}r\\left(x\\right)=-\\left\\{\\begin{array}{c}{\\:\\:\\left(\\frac{\\left|{BV}^{t}-BV\\left(x\\right)\\right|\\times\\:100}{{BV}^{t}}\\right)}^{2}\\:\\\\\\:{+\\left(\\frac{\\left|{R}_{onsp}^{t}-{R}_{onsp}\\left(x\\right)\\right|\\times\\:100}{{R}_{onsp}^{t}}\\right)}^{2}\\end{array}\\right\\}\\#\\left(17\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equr\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equr\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}\\frac{\\partial\\:r\\left(x\\right)}{\\partial\\:BV\\left(x\\right)}=\\frac{\\left({BV}^{t}-BV\\left(x\\right)\\right)\\times\\:\\left(20000\\right)}{{\\left({BV}^{t}\\right)}^{2}}\\#\\left(18\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equs\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equs\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}\\frac{\\partial\\:r\\left(x\\right)}{\\partial\\:{R}_{onsp}\\left(x\\right)}=\\frac{\\left({R}_{onsp}^{t}-{R}_{onsp}\\left(x\\right)\\right)\\times\\:\\left(20000\\right)}{{\\left({R}_{onsp}^{t}\\right)}^{2}}\\#\\left(19\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe gradient of the proposed optimal objective function, as shown in Eq.\u0026nbsp;(20) and Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003ea), is always positive in the BV direction, corresponding to the yellow dashed line 1, and always negative in the R\u003csub\u003eonsp\u003c/sub\u003e direction, corresponding to the yellow dashed line 2. As shown in Eq.\u0026nbsp;(22), it is the sum of the gradient vectors of Eq.\u0026nbsp;(20) and Eq.\u0026nbsp;(21), which is also the same direction as the yellow dashed line 3. And it also represents the overall iterative optimization direction of the automatic design framework. Hence, the proposed objective function will drive the automatic design framework to iteratively optimize the device structure to achieve BV higher than the target value and R\u003csub\u003eonsp\u003c/sub\u003e lower than the target value. When the performance of the constructed device reaches the target performance, the optimization does not stop. The optimal term OF(x) will drive the automatic design framework to continue iterating, optimizing the device structure towards the direction of obtaining larger FOM values.\u003cdiv id=\"Equt\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equt\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}\\frac{\\partial\\:O\\left(x\\right)}{\\partial\\:BV\\left(x\\right)}=\\frac{2BV\\left(x\\right)}{{R}_{onsp}\\left(x\\right)}+1\\#\\left(20\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equu\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equu\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}\\frac{\\partial\\:O\\left(x\\right)}{\\partial\\:{R}_{onsp}\\left(x\\right)}=-\\frac{{BV\\left(x\\right)}^{2}}{{{R}_{onsp}\\left(x\\right)}^{2}}-1\\#\\left(21\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equv\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equv\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}g\\left(x\\right)=\\sqrt{{\\left(\\frac{\\partial\\:O\\left(x\\right)}{\\partial\\:BV\\left(x\\right)}\\right)}^{2}+{\\left(\\frac{\\partial\\:O\\left(x\\right)}{\\partial\\:{R}_{onsp}\\left(x\\right)}\\right)}^{2}}\\#\\left(22\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cb\u003eTCAD-based Verification of design results using the proposed framework\u003c/b\u003e \u003c/p\u003e \u003cp\u003eFirstly, the boundary of BV was specified to be greater than 50V and the boundary of R\u003csub\u003eonsp\u003c/sub\u003e was specified to be less than 25 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:m{\\Omega\\:}\\bullet\\:{mm}^{2}\\)\u003c/span\u003e\u003c/span\u003e. The framework output optimal FOM, BV and R\u003csub\u003eonsp\u003c/sub\u003e listed in Table\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e8\u003c/span\u003e with corresponding structure parameters listed in Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. And the correspond structure parameters are input back to TCAD simulation tool. Figure\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e is illustrated the STI LDMOS device simulation diagram in TCAD using the correspond structure parameters generated by automatic design framework. Table\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e8\u003c/span\u003e also compare the results between automatic design framework and TCAD simulation tool. It is obvious that the results of the framework are extremely close to TCAD simulation tool, which are only 0.002% error of FOM, 1.98% error of BV and 3.68% error of R\u003csub\u003eonsp\u003c/sub\u003e. Therefore, the device designed by proposed automatic design framework is extremely precise.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe optimal device structure parameters.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"9\" nameend=\"c9\" namest=\"c1\"\u003e \u003cp\u003eStructure parameters\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003epbody.p\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(cm\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u0026minus;\u0026thinsp;3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003e)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003epbody.s\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(cm\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u0026minus;\u0026thinsp;3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003e)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eL\u003c/em\u003e\u003csub\u003e\u003cem\u003epog\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(um)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003endrift.p\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(cm\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u0026minus;\u0026thinsp;3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003e)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003endrift.s\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(cm\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u0026minus;\u0026thinsp;3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003e)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003eL\u003c/em\u003e\u003csub\u003e\u003cem\u003enes\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(um)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003eL\u003c/em\u003e\u003csub\u003e\u003cem\u003esti.w\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(um)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003eL\u003c/em\u003e\u003csub\u003e\u003cem\u003esti.d\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(um)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cem\u003eL\u003c/em\u003e\u003csub\u003e\u003cem\u003esog\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(um)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2.314e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e7.838e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e7.606e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e7.412e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.459e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e3.886e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.856\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.829e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e9.962e-1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab8\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 8\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe comparison of Automatic Design Framework and TCAD.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMethod\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAutomatic Design Framework\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTCAD\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eError\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFOM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e145.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e146.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.002%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e59.88\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e61.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.98%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eR\u003csub\u003eonsp\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e24.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e25.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.68%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4 Conclusion","content":"\u003cp\u003eIn this article, an ultra-fast and precise automatic design framework of STI LDMOS device is proposed. It combines an optimal objective function, BO algorithm and DNN prediction model. Given the device structure parameters, the DNN prediction model can ultra-fast output the high accuracy performance including BV and R\u003csub\u003eonsp\u003c/sub\u003e. The first experimental results show that the DNN model achieves average 98.68% performance prediction accuracy. Specified the target values of BV and R\u003csub\u003eonsp\u003c/sub\u003e, the framework can fully automatically design the device structure that can satisfy the design constraints. The second experimental results demonstrate that the proposed framework is capable of optimizing the STI LDMOS device structure to obtain extremely precise designs. Moreover, the proposed framework is 4000 times more efficient than other frameworks. Thus, the proposed automatic design framework can significantly accelerate the development of STI LDMOS device compared to the traditional manual design flow.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eFunding\u003c/p\u003e\n\u003cp\u003eThis work was supported in part by the National Key R\u0026amp;D Program of China under Grant 2022YFF0605800, in part by the Zhejiang Provincial \u0026ldquo;Jianbing\u0026rdquo; \u0026ldquo;Lingyan\u0026rdquo; Research and Development Program of China under Grant 2024C01002 and 2022C01063, and in part by the National Natural Science Foundation of China under Grant 62204217.\u0026nbsp;(Corresponding authors: Yitao Ma; Kai Xu)\u003c/p\u003e\n\u003cp\u003eCompeting Interests\u003c/p\u003e\n\u003cp\u003eThe authors have no relevant financial or non-financial interests to disclose.\u003c/p\u003e\n\u003cp\u003eAuthor Contributes\u003c/p\u003e\n\u003cp\u003eChenggang Xu led the study and was responsible for the overall conceptualization and design of the research. Hongyu Tang, Yuxuan Zhu, Yue Cheng, Xuanzhi Jin, and Dawei Gao contributed to data collection, analysis, and interpretation of the results. Chenggang Xu, Yitao Ma and Kai Xu drafted the initial manuscript. All authors reviewed and approved the final manuscript. Yitao Ma and Kai Xu provided critical revisions and supervised the project.\u003c/p\u003e\n\u003cp\u003eData Availability\u003c/p\u003e\n\u003cp\u003eEnquiries about data availability should be directed to the authors.\u003c/p\u003e\n"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eDong, Z., Duan, B., Fu, C., Guo, H., Cao, Z., \u0026amp; Yang, Y. (2018). Novel LDMOS Optimizing Lateral and Vertical Electric Field to Improve Breakdown Voltage by Multi-Ring Technology. IEEE Electron Device Letters, 39(9), 1358\u0026ndash;1361. https://doi.org/10.1109/LED.2018.2854417\u003c/li\u003e\n\u003cli\u003eYao, J., Sun, M., Xu, T., Liu, X., Li, M., Chen, J., et al. (2023). SOI LDMOS With High-k Multi-Fingers to Modulate the Electric Field Distributions. IEEE Transactions on Electron Devices, 70(5), 2204\u0026ndash;2209. https://doi.org/10.1109/TED.2023.3262224\u003c/li\u003e\n\u003cli\u003eErlbacher, T. (2014). Lateral Power Transistors in Integrated Circuits. Cham: Springer International Publishing. https://doi.org/10.1007/978-3-319-00500-3\u003c/li\u003e\n\u003cli\u003eQiao, M., Hu, X., Wen, H., Wang, M., Luo, B., Luo, X., et al. (2011). A novel substrate-assisted RESURF technology for small curvature radius junction. In 2011 IEEE 23rd International Symposium on Power Semiconductor Devices and ICs (pp. 16\u0026ndash;19). Presented at the IC\u0026rsquo;s (ISPSD), San Diego, CA, USA: IEEE. https://doi.org/10.1109/ISPSD.2011.5890779\u003c/li\u003e\n\u003cli\u003eTao Liang, Yitao He, Lu Lu, Ming Qiao, \u0026amp; Bo Zhang. (2016). 200-V high-side thick-layer-SOI field PLDMOS for HV switching IC. In 2016 IEEE 8th International Power Electronics and Motion Control Conference (IPEMC-ECCE Asia) (pp. 3116\u0026ndash;3119). Presented at the 2016 IEEE 8th International Power Electronics and Motion Control Conference (IPEMC 2016 - ECCE Asia), Hefei, China: IEEE. https://doi.org/10.1109/IPEMC.2016.7512793\u003c/li\u003e\n\u003cli\u003eSu, R. Y., Yang, F. J., Tsay, J. L., Cheng, C. C., Liou, R. S., \u0026amp; Tuan, H. C. (2010). State-of-the-art device in high voltage power ICs with lowest on-state resistance. In 2010 International Electron Devices Meeting (p. 20.8.1-20.8.4). Presented at the 2010 IEEE International Electron Devices Meeting (IEDM), San Francisco, CA, USA: IEEE. https://doi.org/10.1109/IEDM.2010.5703403\u003c/li\u003e\n\u003cli\u003eYang, F.-J., Gong, J., Su, R.-Y., Huo, K.-H., Tsai, C.-L., Cheng, C.-C., et al. (2013). A 700-V Device in High-Voltage Power ICs With Low On-State Resistance and Enhanced SOA. IEEE Transactions on Electron Devices, 60(9), 2847\u0026ndash;2853. https://doi.org/10.1109/TED.2013.2273573\u003c/li\u003e\n\u003cli\u003eSynopsys, Sentaurus Device User Guide:Version T-2022.03, March 2022.\u003c/li\u003e\n\u003cli\u003eMoens, P., Bauwens, F., Baele, J., Vershinin, K., De Backer, E., Sankara Narayanan, E. M., \u0026amp; Tack, M. (2006). XtreMOS : The First Integrated Power Transistor Breaking the Silicon Limit. In 2006 International Electron Devices Meeting (pp. 1\u0026ndash;4). Presented at the 2006 International Electron Devices Meeting, San Francisco, CA: IEEE. https://doi.org/10.1109/IEDM.2006.346933\u003c/li\u003e\n\u003cli\u003eXia, C., Cheng, X., Wang, Z., Xu, D., Cao, D., Zheng, L., et al. (2014). Improvement of SOI Trench LDMOS Performance With Double Vertical Metal Field Plate. IEEE TRANSACTIONS ON ELECTRON DEVICES, 61(10).\u003c/li\u003e\n\u003cli\u003eWei, J., Luo, X., Zhang, Y., Li, P., Zhou, K., Zhang, B., \u0026amp; Li, Z. (2016). High-Voltage Thin-SOI LDMOS With Ultralow ON-Resistance and Even Temperature Characteristic. IEEE Transactions on Electron Devices, 63(4), 1637\u0026ndash;1643. https://doi.org/10.1109/TED.2016.2533022\u003c/li\u003e\n\u003cli\u003eGuo, Y., Yang, K., Chen, J., Li, M., Jiang, Z., Yao, J., et al. (2023). Tradeoff Between the Breakdown Voltage and Specific On-Resistance of SOI RESURF LDMOS. In 2023 IEEE 15th International Conference on ASIC (ASICON) (pp. 1\u0026ndash;4). Presented at the 2023 IEEE 15th International Conference on ASIC (ASICON), Nanjing, China: IEEE. https://doi.org/10.1109/ASICON58565.2023.10396435\u003c/li\u003e\n\u003cli\u003eWei, J., Ma, Z., Luo, X., Li, C., Deng, G., Song, H., et al. (2021). Experimental Study of Ultralow On-resistance Power LDMOS with Convex-shape Field Plate Structure. In 2021 33rd International Symposium on Power Semiconductor Devices and ICs (ISPSD) (pp. 87\u0026ndash;90). Presented at the 2021 33rd International Symposium on Power Semiconductor Devices and ICs (ISPSD), Nagoya, Japan: IEEE. https://doi.org/10.23919/ISPSD 50666.2021.9452231\u003c/li\u003e\n\u003cli\u003eCarrillo-Nunez, H., Dimitrova, N., Asenov, A., \u0026amp; Georgiev, V. (2019). Machine Learning Approach for Predicting the Effect of Statistical Variability in Si Junctionless Nanowire Transistors. IEEE Electron Device Letters, 40(9), 1366\u0026ndash;1369. https://doi.org/10.1109/LED.2019.2931839\u003c/li\u003e\n\u003cli\u003eMehta, K., \u0026amp; Wong, H.-Y. (2021). Prediction of FinFET Current-Voltage and Capacitance-Voltage Curves Using Machine Learning With Autoencoder. IEEE Electron Device Lett., Article vol. 42, no. 2, pp. 136-139, Feb 2021, doi: 10.1109/led.2020.3045064.\u003c/li\u003e\n\u003cli\u003eHan, S.-C., Choi, J., \u0026amp; Hong, S.-M. (2021). Acceleration of Semiconductor Device Simulation With Approximate Solutions Predicted by Trained Neural Networks. IEEE Transactions on Electron Devices, 68(11), 5483\u0026ndash;5489. https://doi.org/10.1109/TED.2021.3075192\u003c/li\u003e\n\u003cli\u003eWang G., Wang S., Ma L., Wang G., Wu J., Duan X., Chen S., \u0026amp; Liu H. (2022) Optimization and Performance Prediction of Tunnel Field-Effect Transistors Based on Deep Learning. Adv. Mater. Technol. 2022, 7, 2100682. https://doi.org/10.1002/admt.202100682\u003c/li\u003e\n\u003cli\u003eChen, J., Alawieh, M. B., Lin, Y., Zhang, M., Zhang, J., Guo, Y., \u0026amp; Pan, D. Z. (2020). Automatic Selection of Structure Parameters of Silicon on Insulator Lateral Power Device Using Bayesian Optimization. IEEE Electron Device Letters, 41(9), 1288\u0026ndash;1291. https://doi.org/10.1109/LED.2020.3013571\u003c/li\u003e\n\u003cli\u003eHuang Yi, Sun Shiyu, Duan Xiusheng, \u0026amp; Chen Zhigang. (2016). A study on Deep Neural Networks framework. In 2016 IEEE Advanced Information Management, Communicates, Electronic and Automation Control Conference (IMCEC) (pp. 1519\u0026ndash;1522). Presented at the 2016 IEEE Advanced Information Management, Communicates, Electronic and Automation Control Conference (IMCEC), Xi\u0026rsquo;an, China: IEEE. https://doi.org/10.1109/IMCEC.2016.7867471\u003c/li\u003e\n\u003cli\u003eShahriari, B., Swersky, K., Wang, Z., Adams, R. P., \u0026amp; De Freitas, N. (2016). Taking the Human Out of the Loop: A Review of Bayesian Optimization. Proceedings of the IEEE, 104(1), 148\u0026ndash;175. https://doi.org/10.1109/JPROC.2015.2494218\u003c/li\u003e\n\u003cli\u003eChen, J., Guo, X., Guo, Y., Zhang, J., Zhang, M., Yao, Q., \u0026amp; Yao, J. (2021). Deep neural network-based approach for breakdown voltage and specific on-resistance prediction of SOI LDMOS with field plate. Japanese Journal of Applied Physics, 60(7), 077002. https://doi.org/10.35848/1347-4065/ac06da\u003c/li\u003e\n\u003cli\u003eChuang, P.-J., Saadat, A., Van De Put, M. L., Edwards, H., \u0026amp; Vandenberghe, W. G. (2023). Algorithmic Optimization of Transistors Applied to Silicon LDMOS. IEEE Access, 11, 64160\u0026ndash;64169. https://doi.org/10.1109/ACCESS.2023.3287204\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-computational-electronics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jcel","sideBox":"Learn more about [Journal of Computational Electronics](https://www.springer.com/journal/10825)","snPcode":"10825","submissionUrl":"https://submission.nature.com/new-submission/10825/3","title":"Journal of Computational Electronics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Laterally diffused metal oxide semiconductor, Machine learning, Bayesian optimization, Deep neural networks, Automatic design","lastPublishedDoi":"10.21203/rs.3.rs-4696885/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4696885/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eShallow Trench Isolation laterally diffused metal oxide semiconductor (STI LDMOS) is a crucial device for power integrated circuits. In this article, a novel framework that integrates an optimal objective function, Bayesian Optimization (BO) algorithm and Deep Neural Network (DNN) model is proposed to fully realize automatic and optimal design of STI LDMOS devices. On the one hand, given the structure of device, the DNN model in the proposed method can provide the ultra-fast and high-accurate performance estimation including breakdown voltage (BV) and specific on-resistance (R\u003csub\u003eonsp\u003c/sub\u003e). The experimental results demonstrate 98.68% prediction accuracy in average for both BV and R\u003csub\u003eonsp\u003c/sub\u003e, higher than that of other machine learning (ML) algorithms. On the other hand, to target the specified value of BV and R\u003csub\u003eonsp\u003c/sub\u003e, the proposed framework can fully automatically and optimally design the precise device structure that simultaneously achieves the target performance with the optimal figure-of-merit (FOM) of device. Compared to Technology Computer Aided Design (TCAD), there is only 0.002% error in FOM and 2.83% average error in BV and R\u003csub\u003eonsp\u003c/sub\u003e. Moreover, the proposed framework is 4000 times more efficient than other conventional frameworks. Thus, this research provides experimental groundwork for constructing an automatic design framework for LDMOS device and opens up new opportunities for accelerating the development of LDMOS device in the future.\u003c/p\u003e","manuscriptTitle":"An Ultra-Fast and Precise Automatic Design Framework for Predicting and Constructing High-Performance Shallow-Trench-Isolation LDMOS Device","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-07-31 21:01:13","doi":"10.21203/rs.3.rs-4696885/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-08-30T12:12:22+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-08-10T22:08:56+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"88070586589270762390437680591464256295","date":"2024-08-02T01:27:42+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"97708305234017657522878486801529764342","date":"2024-08-02T01:24:49+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-07-27T12:47:20+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-07-08T03:51:28+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-07-08T03:51:21+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Computational Electronics","date":"2024-07-06T13:08:27+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-computational-electronics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jcel","sideBox":"Learn more about [Journal of Computational Electronics](https://www.springer.com/journal/10825)","snPcode":"10825","submissionUrl":"https://submission.nature.com/new-submission/10825/3","title":"Journal of Computational Electronics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"fa6d26b8-4fe3-42c0-8ee0-5403cae8bc02","owner":[],"postedDate":"July 31st, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2024-12-16T16:00:14+00:00","versionOfRecord":{"articleIdentity":"rs-4696885","link":"https://doi.org/10.1007/s10825-024-02244-8","journal":{"identity":"journal-of-computational-electronics","isVorOnly":false,"title":"Journal of Computational Electronics"},"publishedOn":"2024-12-09 15:56:57","publishedOnDateReadable":"December 9th, 2024"},"versionCreatedAt":"2024-07-31 21:01:13","video":"","vorDoi":"10.1007/s10825-024-02244-8","vorDoiUrl":"https://doi.org/10.1007/s10825-024-02244-8","workflowStages":[]},"version":"v1","identity":"rs-4696885","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4696885","identity":"rs-4696885","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}