基于PINNs的压电半导体梁的非线性多场耦合力学分析

肖争光; 张春利; 陈伟球

doi:10.21656/1000-0887.450070

基于PINNs的压电半导体梁的非线性多场耦合力学分析

doi: 10.21656/1000-0887.450070

肖争光¹,
张春利^1,2, ,,
陈伟球^1,2

1. 浙江大学航空航天学院，杭州 310027;
2. 浣江实验室，浙江诸暨 311816

基金项目:

国家自然科学基金（面上项目）（12172326；11972319）；国家重点研发计划（2020YFA0711701；2020YFA0711700）

详细信息

作者简介:
肖争光（1995—），男，博士生 (E-mail: 12124091@zju.edu.cn)；张春利（1980—），男，教授，博士，博士生导师 (通讯作者. E-mail: zhangcl01@zju.edu.cn)；陈伟球（1969—），男，教授，博士，博士生导师，教育部长江学者特聘教授（E-mail: chenwq@zju.edu.cn）.

通讯作者:
张春利（1980—），男，教授，博士，博士生导师 (通讯作者. E-mail: zhangcl01@zju.edu.cn)

中图分类号: O343.5
计量
- 文章访问数: 89
- HTML全文浏览量: 22
- PDF下载量: 35
- 被引次数: 0
出版历程
- 收稿日期: 2024-03-19
- 修回日期: 2024-04-26
- 网络出版日期: 2024-10-31
- 刊出日期: 2024-10-01

Analysis of Nonlinear Multi-Field Coupling Mechanics of Piezoelectric Semiconductor Beams via PINNs

1. School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, P.R.China;
2. Huanjiang Laboratory, Zhuji, Zhejiang 311816, P.R.China

Funds:

The National Science Foundation of China(12172326；11972319)

摘要

摘要: 压电半导体(PS)具有压电性和半导体特性共存耦合的特征，在新型多功能电子/光电子学器件中有广阔应用前景.因此，理论分析压电半导体结构在外载作用下的多场耦合力学响应是十分重要的.然而，描述压电半导体多场耦合力学行为的控制方程中含有非线性的电流方程，属于物理非线性；而且很多半导体器件通常工作在大变形模式下，在力学上属于几何非线性问题.物理非线性和几何非线性给问题的求解带来了挑战.该文针对压电半导体梁结构，基于物理信息神经网络（physics informed neural networks，PINNs），构建了能高效求解其非线性多场耦合力学问题的PINNs方法.通过依次删除网络结构中载流子项和压电项，该方法即可退化到压电结构和纯弹性结构的情况.利用所构建的PINNs，分析了压电半导体梁在均布压力下的多场耦合力学响应.数值结果表明：该文所提出的基于PINNs的模型能有效求解压电半导体、压电以及纯弹性结构非线性多场耦合问题，相对而言，其在求解压电和纯弹性结构的力学响应时具有更高的精度.
- 压电半导体梁 /
- 多场耦合 /
- 非线性 /
- PINNs
Abstract: Piezoelectric semiconductors (PSs) possess the characteristics of coexistence of piezoelectric and semiconductor properties and have broad application prospects in new multifunctional electronic/optoelectronic devices. It is very important to theoretically analyze multi-field coupling mechanical responses of PS structures under external loads. However, the governing equations describing the multi-field coupling mechanical behaviors of PS structures contain physically nonlinear current equations. On the other hand, many semiconductor devices typically operate under large deformation, which raises a geometrically nonlinear problem. The presence of physical and geometric nonlinearity poses challenges to the solution of the problem. Herein, for PS beam structures, a method based on physics informed neural networks (PINNs) was established to efficiently solve their nonlinear multi-field coupling responses. Through successive elimination of carrier-related terms and piezoelectricity-related terms from the constructed PINNs, the proposed method can be reduced to the cases of piezoelectric and pure elastic structures, respectively. With the proposed PINNs, the multi-field coupling responses of a PS beam under static uniform pressure were predicted. Numerical results show that, the proposed method can effectively solve the nonlinear multi-field coupling problems of the PS, piezoelectric and pure elastic structures. Relatively, it exhibits higher accuracy in solving piezoelectric and pure elastic structures.
- PS beam /
- multi-field coupling /
- nonlinearity /
- PINNs

HTML全文

参考文献(37)

[2]QIN Y, WANG X D, WANG Z L. Microfibre-nanowire hybrid structure for energy scavenging[J].Nature,2008,451(7180): 809-813.

HICKERNELL F S. The piezoelectric semiconductor and acoustoelectronic device development in the sixties[J].IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control,2005,52(5): 737-745.

[3]LIU Y, YANG Q, ZHANG Y, et al. Nanowire piezo-phototronic photodetector: theory and experimental design[J].Advanced Materials,2012,24(11): 1410-1417.

[4]HAN W H, ZHOU Y S, ZHANG Y, et al. Strain-gated piezotronic transistors based on vertical zinc oxide nanowires[J].ACS Nano,2012,6(5): 3760-3766.

[5]WANG Z L. Piezopotential gated nanowire devices: piezotronics and piezo-phototronics[J].Nano Today,2010,5(6): 540-552.

[6]罗逸璕. 层状压电半导体结构的多场耦合力学行为分析[D].杭州: 浙江大学, 2019. (LUO Yixun. Analysis of multi-field coupling mechanical behavior of laminated piezoelectric semiconductor structures[D].Hangzhou: Zhejiang University, 2019. (in Chinese))

[7]梁超, 张春利. 恒磁场作用下压磁/压电半导体复合圆柱壳的耦合响应分析[J].固体力学学报, 2020,41(3): 206-215. (LIANG Chao, ZHANG Chunli. Analysis of multi-field coupling responses of piezomagnetic/piezoelectric semiconductor cylindrical shell under a constant magnetic field[J]. Chinese Journal of Solid Mechanics,2020,41(3): 206-215. (in Chinese))

[8]程若然, 张春利. 多个局部温度载荷下压电半导体纤维杆的压电电子学行为分析[J].力学学报, 2020,52(5): 1295-1303. (CHENG Ruoran, ZHANG Chunli. Analysis of the piezotronic effect of a piezoeletric semiconductor fiber under mutiple local temperature loadings[J]. Chinese Journal of Theoretical and Applied Mechanics,2020,52(5): 1295-1303. (in Chinese))

[9]李德志, 张春利. 弹性纵波在压电-压电半导体周期杆中的传播[J].哈尔滨工程大学学报, 2022,43(9): 1252-1257. (LI Dezhi, ZHANG Chunli. Propagation of elastic longitudinal waves in a periodic piezoelectric-piezosemiconductor rod[J]. Journal of Harbin Engineering University,2022,43(9): 1252-1257. (in Chinese))

[10]ZHANG C L, WANG X Y, CHEN W Q, et al. Carrier distribution and electromechanical fields in a free piezoelectric semiconductor rod[J]. Journal of Zhejiang University (Science A),2016,17(1): 37-44.

[11]王晓媛. 一维压电半导体杆的力学行为研究[D].杭州: 浙江大学, 2017. (WANG Xiaoyuan. Research on mechanical behaviors of one-dimensional piezoelectric semiconductor rods[D].Hangzhou: Zhejiang University, 2017. (in Chinese))

[12]CHENG R R, ZHANG C L, CHEN W Q, et al. Temperature effects on mobile charges in extension of composite fibers of piezoelectric dielectrics and non-piezoelectric semiconductors[J].International Journal of Applied Mechanics,2019,11(9): 1950088.

[13]LUO Y X, ZHANG C L, CHEN W Q, et al. Thermally induced electromechanical fields in unimorphs of piezoelectric dielectrics and nonpiezoelectric semiconductors[J].Integrated Ferroelectrics,2020,211(1): 117-131.

[14]ZHANG C L, WANG X Y, CHEN W Q, et al. An analysis of the extension of a ZnO piezoelectric semiconductor nanofiber under an axial force[J].Smart Materials and Structures,2017,26(2): 025030.

[15]FAN S Q, HU Y T, YANG J S. Stress-induced potential barriers and charge distributions in a piezoelectric semiconductor nanofiber[J].Applied Mathematics and Mechanics (English Edition),2019,40(5): 591-600.

[16]HUANG H Y, QIAN Z H, YANG J S. I-V characteristics of a piezoelectric semiconductor nanofiber under local tensile/compressive stress[J].Journal of Applied Physics,2019,126(16): 164902.

[17]ANCONA M G, BINARI S C, MEYER D J. Fully coupled thermoelectromechanical analysis of GaN high electron mobility transistor degradation[J].Journal of Applied Physics,2012,111(7): 074504.

[18]ANCONA M G. Fully coupled thermoelectroelastic simulations of GaN devices[C]//2012 International Electron Devices Meeting.San Francisco, CA, USA, 2012: 13.5.1-13.5.4.

[19]ANCONA M G. Nonlinear thermoelectroelastic simulation of Ⅲ-N devices[C]//2014 International Conference on Simulation of Semiconductor Processes and Devices (SISPAD).Yokohama, Japan, 2014: 121-124.

[20]ANCONA M G. Nonlinear thermoelectroelastic analysis of Ⅲ-N semiconductor devices[J].IEEE Journal of the Electron Devices Society,2017,5(5): 320-334.

[21]ZHAO M H, ZHANG Q Y, FAN C. An efficient iteration approach for nonlinear boundary value problems in 2D piezoelectric semiconductors[J].Applied Mathematical Modelling,2019,74: 170-183.

[22]ZHAO M H, MA Z L, LU C S, et al. Application of the homopoty analysis method to nonlinear characteristics of a piezoelectric semiconductor fiber[J].Applied Mathematics and Mechanics (English Edition),2021,42(5): 665-676.

[23]ZHAO M H, YANG C H, FAN C Y, et al. A shooting method for nonlinear boundary value problems in a thermal piezoelectric semiconductor plate[J].ZAMM Journal of Applied Mathematics and Mechanics,2020,100(12): e201900302.

[24]BAO G F, LI D Z, KONG D J, et. al. Analysis of axially loaded piezoelectric semiconductor rods with geometric nonlinearity[J]. International Journal of Applied Mechanics,2022,14(10): 2250104.

[25]PANG G, D’ELIA M, PARKS M, et al. nPINNs: nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications[J].Journal of Computational Physics,2020,422: 109760.

[26]HAGHIGHAT E, JUANES R. SciANN: a Keras/TensorFlow wrapper for scientific computations and physics-informed deep learning using artificial neural networks[J].Computer Methods in Applied Mechanics and Engineering,2021,373: 113552.

[27]MENG X, LI Z, ZHANG D, et al. PPINN: parareal physics-informed neural network for time-dependent PDEs[J].Computer Methods in Applied Mechanics and Engineering,2020,370: 113250.

[28]ZHAO Q K, YANG H Y, LIU J B, et al. Machine learning-assisted discovery of strong and conductive Cu alloys: data mining from discarded experiments and physical features[J]. Materials & Design,2021,197: 109248.

[29]LIU X, ATHANASIOU C E, PADTURE N P, et al. A machine learning approach to fracture mechanics problems[J].Acta Materialia,2020,190: 105-112.

[30]HENKES A, WESSELS H, MAHNKEN R. Physics informed neural networks for continuum micromechanics[J].Computer Methods in Applied Mechanics and Engineering,2022,393: 114790.

[31]ATHREYA A P, BRCKL T, BINDER E B, et al. Prediction of short-term antidepressant response using probabilistic graphical models with replication across multiple drugs and treatment settings[J].Neuropsychopharmacology,2021,46(7): 1272-1282.

[32]RAISSI M, PERDIKARIS P, KARNIADAKIS G E. Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations[J].Journal of Computational Physics,2019,378: 686-707.

[33]JAGTAP A D, KARNIADAKIS G E. Extended physics-informed neural networks (XPINNs): a generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations[J]. Communications in Computational Physics,2020,28(5): 2002-2041.

[34]RAISSI M, YAZDANI A, KARNIADAKIS G E. Hidden fluid mechanics: learning velocity and pressure fields from flow visualizations[J].Science,2020,367(6481): 1026-1030.

[35]HAGHIGHAT E, RAISSI M, MOURE A, et al. A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics[J].Computer Methods in Applied Mechanics and Engineering,2021,379: 113741.

[36]REDDY J N.Mechanics of Laminated Composite Plates and Shells[M].CRC Press, 2004.

[37]AULD B A.Acoustic Fields and Waves in Solids[M].Vol1. Wiley-Inter Science Publication, 1974.

施引文献

资源附件(0)

访问统计

计量

文章访问数: 89
HTML全文浏览量: 22
PDF下载量: 35
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

留言板

基于PINNs的压电半导体梁的非线性多场耦合力学分析

doi: 10.21656/1000-0887.450070

通讯作者:
张春利（1980—），男，教授，博士，博士生导师 (通讯作者. E-mail: zhangcl01@zju.edu.cn)

计量

Analysis of Nonlinear Multi-Field Coupling Mechanics of Piezoelectric Semiconductor Beams via PINNs

计量

目录

留言板

基于PINNs的压电半导体梁的非线性多场耦合力学分析

doi: 10.21656/1000-0887.450070

通讯作者: 张春利（1980—），男，教授，博士，博士生导师 (通讯作者. E-mail: zhangcl01@zju.edu.cn)

计量

出版历程

Analysis of Nonlinear Multi-Field Coupling Mechanics of Piezoelectric Semiconductor Beams via PINNs

计量

出版历程

目录

通讯作者:
张春利（1980—），男，教授，博士，博士生导师 (通讯作者. E-mail: zhangcl01@zju.edu.cn)