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
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(我刊青年编委张春利、编委陈伟球来稿)edited-by
详细信息
Analysis of Nonlinear Multi-Field Coupling Mechanics of Piezoelectric Semiconductor Beams via PINNs
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(Contributed by ZHANG Chunli, M.AMM Youth Editorial Board & CHEN Weiqiu, M.AMM Editorial Board)-
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.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.
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Key words:
- PS beam /
- multi-field coupling /
- nonlinearity /
- PINNs
edited-byedited-by1) (我刊青年编委张春利、编委陈伟球来稿) -
图 2 PINNs的训练和预测过程
注 为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.
Figure 2. The training and prediction process of PINNs
图 4 压电半导体悬臂梁的位移、电势和电子浓度分布
Figure 4. Distributions of displacements, electric potentials and electron concentrations of the PS cantilever
图 5 两端固支压电半导体梁的位移、电势和电子浓度分布
Figure 5. Distributions of displacements, electric potentials and electron concentrations of the PS beam with CC boundary conditions
图 6 压电悬臂梁位移和电势分布
Figure 6. Distributions of displacements and electric potentials of the piezoelectric cantilever
图 7 纯弹性悬臂梁的位移分布
Figure 7. Distributions of displacements of the pure elastic cantilever
表 1 压电半导体悬臂梁的位移、电势和电子浓度最大值
Table 1. Maximum displacements, electric potentials and electron concentrations of the PS cantilever
displacement u/(10-11·m) displacement w/(10-10 ·m) electric potential φ/V electron concentration n/(1021 ·m3) COMSOL -8.430 0 -6.690 0 -1.237 1 1.200 0 PINNs -8.864 2 -6.715 2 -1.234 5 1.198 1 relative error ε/% 5.15 0.36 0.21 0.15 
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表 2 两端固支压电半导体梁的位移、电势和电子浓度最大值
Table 2. Maximum displacements, electric potentials and electron concentrations of the PS beam with CC boundary conditions
displacement u/(10-12·m) displacement w/(10-11 ·m) electricpotential φ/V electron concentration n/(1021 ·m3) COMSOL -8.540 0 -4.310 0 0.055 1 1.260 0 PINNs -8.419 6 -4.286 3 0.055 4 1.232 4 relative error ε/% 1.41 0.55 0.54 2.19
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表 3 压电悬臂梁的位移和电势最大值
Table 3. Maximum displacements and electric potentials of the piezoelectric cantilever
displacement u/(10-11·m) displacement w/(10-10 ·m) electric potential φ/V COMSOL -7.940 0 -6.310 0 -0.164 8 PINNs -7.949 8 -6.301 3 -0.165 5 relative error ε/% 0.12 0.14 0.42
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表 4 纯弹性悬臂梁的位移最大值
Table 4. Maximum displacements of the pure elastic cantilever
displacement u/(10-11·m) displacement w/(10-10 ·m) COMSOL -8.840 0 -7.000 8 PINNs -8.832 0 -7.000 6 relative error ε/% 0.090 0.002
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