柔性电子器件元件阵列的热脉冲响应分析

卞纯燕; 杨文成; 缪馥星

doi:10.21656/1000-0887.460035

柔性电子器件元件阵列的热脉冲响应分析

doi: 10.21656/1000-0887.460035

宁波大学冲击与安全工程教育部重点实验室, 浙江宁波 315211

基金项目:

国家自然科学基金 11572161

国家自然科学基金 11872218

浙江省自然科学基金重点项目 LZ23A020001

详细信息

作者简介:
卞纯燕(1997—)，女，硕士生(E-mail: 2211090002@nbu.edu.cn)

通讯作者:
缪馥星(1980—)，女，教授(通讯作者. E-mail: miaofuxing@nbu.edu.cn)

中图分类号: O347.1
计量
- 文章访问数: 53
- HTML全文浏览量: 16
- PDF下载量: 10
- 被引次数: 0
出版历程
- 收稿日期: 2025-02-27
- 修回日期: 2025-04-14
- 刊出日期: 2025-05-01

Thermal Impulse Response Analysis of Element Arrays in Flexible Electronic Devices

MOE Key Laboratory of Impact and Safety Engineering, Ningbo University, Ningbo, Zhejiang 315211, P.R.China

摘要

摘要: 柔性电子器件在工作时产生的热量，导致元件发生变形，极易影响其功能性. 本研究建立了柔性电子器件元件阵列热脉冲响应的有限元分析模型，探讨了柔性电子器件元件封装层与基底层的层厚比对整体结构热稳定性的影响，以及柔性电子器件元件的热脉冲响应. 初步得到：当热脉冲载荷从50 W/m²增大至150 W/m²时，功能层中心单元温度上升约0.47%，热应力增大约25.87%；若封装层与基底层的层厚比从0.2增大到5.0，功能层中心单元的热应力降低约92%，热应变降低约99%，沿层厚方向的位移降低约86%. 初步结果可为柔性电子器件元件热脉冲载荷的优化设计和防护提供基础数据.
- 柔性电子器件元件阵列 /
- 热脉冲响应 /
- 温度场 /
- 热应力 /
- 有限元分析
Abstract: The heat generated by flexible electronic devices during operation leads to deformation of the components, which is highly likely to affect their functionality. A finite element analysis model for the thermal impulse responses of the flexible electronic device element arrays were established, and the effects of the layer thickness ratio of the encapsulation layer to the substrate layer of the flexible electronic device element on the thermal stability of the overall structure, as well as the thermal impulse responses of the flexible electronic device components, were investigated. The results show that, the temperature of the functional layer center element rises by about 0.47% and the thermal stress increases by about 25.87% with the thermal impulse load increasing from 50 W/m² to 150 W/m². With the layer thickness ratio of the encapsulation layer to the substrate layer increasing from 0.2 to 5.0, the thermal stress of the functional layer center unit decreases by about 92%, the thermal strain decreases by about 99%, and the displacement along the layer thickness decreases by about 86%. The work provides basic data for the optimization design and protection against thermal impulse loading on flexible electronic device components.
- flexible electronic device element array /
- thermal impulse response /
- temperature field /
- thermal stress /
- finite element analysis

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图 1 柔性电子器件元件示意图

Figure 1. Diagram of flexible electronic components

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图 2 柔性电子器件元件有限元网格

Figure 2. Finite element grid diagram of flexible electronic components

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图 3 热脉冲载荷历程

Figure 3. The thermal impulse loading history

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图 4 本文热力耦合有限元模型的能量响应

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 4. Energy responses of the presented finite element model

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图 5 不同单元数下元件功能层中心单元热应力响应

Figure 5. Thermal stress responses of the central element in the functional layer with different numbers of elements

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图 6 不同热脉冲载荷下柔性电子器件元件各层的温度场

Figure 6. Temperature fields in various layers of flexible electronic device elements under different thermal impulse loads

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图 7 不同热脉冲载荷下元件功能层中心单元的热通量和温度响应

Figure 7. Heat flux and temperature responses of the central element of the functional layer under different thermal impulse loads

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图 8 n=3工况下，热力耦合模型的热应力分布图

Figure 8. Thermal stress distributions with the thermal coupling model in the case of n=3

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图 9 n=3工况下，热力耦合模型沿层厚方向的位移分布

Figure 9. Distributions of thickness direction displacements with the thermal coupling model in the case of n=3

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图 10 功能层中心单元温度随不同层厚比的变化曲线

Figure 10. The variation curve of the temperature of the functional layer central element with different thickness ratios

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图 11 功能层中心单元的热应力、热应变、沿层厚方向的位移随不同层厚比的变化曲线

Figure 11. Variation curves of the functional layer central element with different thickness ratios

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图 12 功能层中心单元温度的有限元结果与文献[30]结果的比较

Figure 12. Comparison of the finite element results of the temperature of the functional layer central element with the results of ref. [30]

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表 1 材料属性

Table 1. Material properties

material	elastic modulus /GPa	Poisson’s ratio	density /(kg·m^-3)	coefficient of thermal expansion /℃^-1	conductivity /(W·m^-1·℃^-1)	heat capacity /(J·℃^-1)
SU-8	2	0.17	1 200	5.20×10^-5	0.2	1.20×10⁹
Si	130	0.28	2 330	2.60×10^-6	160	7.00×10⁸
Cu	110	0.34	8 960	1.67×10^-5	401	3.84×10⁸
PDMS	0.002	0.49	965	3.10×10^-4	0.17	1.46×10⁹

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表 2 柔性电子器件元件的几何参数

Table 2. Geometric parameters of flexible electronic device components

parameter	a	b	h_SU-8	h_PDMS	a_Si	b_Si	h_Si	l	R_Cu	h_Cu	b_Cu
value /mm	25	25	0.5	2.5	2.5	2.5	0.5	5	1	0.05	0.5

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表 3 超弹性材料参数

Table 3. Hyperelastic material parameters

material	C₁₀/Pa	C₀₁/Pa	d/Pa^-1
SU-8^[19]	6.757 00×10⁴	-1.689 00×10⁴	4.800 00×10⁵
PDMS^[20]	1.288 68×10⁷	-3.126 97×10⁶	2.062 96×10^-9

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表 4 本文热力耦合有限元模型的不同单元数算例

Table 4. Cases of different meshes for the presented thermally coupled finite element model

example	SU-8	Si	Cu	PDMS	total
mesh 1	38 400	400	1 588	38 400	99 456
mesh 2	44 800	400	1 588	44 800	112 256
mesh 3	64 800	720	1 921	64 800	159 132
mesh 4	80 000	720	1 921	80 000	189 532

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表 5 封装层与基底层不同层厚比下的算例

Table 5. The cases with different thickness ratios of the encapsulation layer to the substrate layer

example	h_SU-8/mm	h_Si/mm	h_PDMS/mm	η
type 1	0.5	0.5	2.5	0.2
type 2	1.0	0.5	2.0	0.5
type 3	1.5	0.5	1.5	1.0
type 4	2.0	0.5	1.0	2.0
type 5	2.5	0.5	0.5	5.0

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