The adhesive interlayer effect on the thermoelectric structure with multiple electrodes

doi:10.1007/s10483-026-3363-9

Abstract

Abstract:

Driven by the trend of device miniaturization and high-density integration, the interaction between adjacent electrodes has become a critical factor affecting the interfacial reliability of thermoelectric (TE) structures. This study investigates the influence of adjoining electrode interactions on the interfacial response of a multi-electrode/TE substrate structure, including interfacial stresses and stress intensity factors at the electrode ends. To solve the corresponding boundary-value problem, the Fourier transforms are adopted to derive a governing integro-differential equation for the interfacial shear stress in multi-electrode systems, incorporating the TE effects as generalized forces on the right-hand side. The results show that both the interfacial tension and transverse stress in the electrodes are significantly affected by the presence of adjacent electrodes. The interaction between neighboring electrodes diminishes as their spacing increases or when an adhesive interlayer is introduced. Furthermore, the softer and thinner electrodes, the softer and thicker adhesive interlayer, and the smaller TE loads are found to be beneficial for improving the interfacial performance. These findings may contribute to the accurate measurement in surface sensors and layout design of multi-point health monitoring systems for TE structures.

Key words: thermoelectric (TE) material, multiple electrodes, adhesive interlayer, interface behavior

2010 MSC Number:

O343.3

Xiaojuan TIAN, Yueting ZHOU. The adhesive interlayer effect on the thermoelectric structure with multiple electrodes. Applied Mathematics and Mechanics (English Edition), 2026, 47(3): 573-598.

TrendMD

Figures/Tables 22

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Fig. 11

Table 1

Shear stress intensity factors near the ends of the left electrode (x=a1, x=b1) for different distances between the two adjacent electrodes d/w1 with the following fixed parameters: w2/w1=1, hf1/w1=hf2/w1=0.04, Gf1/Gs=Gf2/Gs=3, Je1=Je2=6 A/m, and Ju1=Ju2=0.01 W/m"

Shear stress intensity factor	$d / w 1$
Shear stress intensity factor	0.001	0.01	0.1	0.4	1
$K II (a 1)$	7 908.39	7 894.02	7 825.05	7 743.94	7 691.31
$K II (b 1)$	$− 10 916$	$− 10 067$	$− 8 489.85$	$− 7 903.8$	$− 7 730.7$

Table 1

Table 2

Shear stress intensity factors near the ends of both electrodes for different widths of the right electrode w2/w1 with the following fixed parameters: d/w1=0.1, hf1/w1=hf2/w1=0.04, Gf1/Gs=Gf2/Gs=3, Je1=Je2=6 A/m, and Ju1=Ju2=0.01 W/m"

Shear stress intensity factor	$w 2 / w 1$
Shear stress intensity factor	0.1	0.3	0.6	1	2
$K II (a 1)$	7 835.84	7 801.43	7 803.79	7 825.05	7 888.13
$K II (b 1)$	$− 8 014.8$	$− 8 278.8$	$− 8 432.4$	$− 8 489.9$	$− 8 499.6$
$K II (a 2)$	18 855.3	13 921	10 629	8 489.85	6 145.76
$K II (b 2)$	$− 18 257$	$− 13 125$	$− 9 871$	$− 7 825$	$− 5 635$

Table 2

Table 3

Shear stress intensity factors near the ends of the left electrode (x=a1, x=b1) for different total electric current loads Je1 and Je2 with the following fixed parameters: d/w1=0.1, w2/w1=1, hf1/w1=hf2/w1=0.04, Gf1/Gs=Gf2/Gs=3, and Ju1=Ju2=0.01 W/m"

Shear stress intensity factor	$J e1, J e2 / (A ⋅ m − 1)$
Shear stress intensity factor	0	6	12	15	18
$K II (a 1)$	6 834.94	7 825.05	10 795.4	13 023.1	15 745.9
$K II (b 1)$	$− 7 415.6$	$− 8 489.9$	$− 11 713$	$− 14 130$	$− 17 084$

Table 3

Table 4

Shear stress intensity factors near the ends of the left electrode (x=a1, x=b1) for different total energy flux loads Ju1 and Ju2 with the following fixed parameters: d/w1=0.1, w2/w1=1, hf1/w1=hf2/w1=0.04, Gf1/Gs=Gf2/Gs=3, and Je1=Je2=6 A/m"

Shear stress intensity factor	$J u1, J u2 / (W ⋅ m − 1)$
Shear stress intensity factor	0	0.01	0.03	0.05	0.09
$K II (a 1)$	990.109	7 825.05	21 494.9	35 164.8	62 504.6
$K II (b 1)$	$− 1 074.2$	$− 8 489.9$	$− 23 321$	$− 38 152$	$− 67 815$

Table 4

Table 5

Shear stress intensity factors near the ends of both electrodes for different thicknesses of the left electrode hf1/w1 with the following fixed parameters: d/w1=0.1, w2/w1=1, hf2/w1=0.04, Gf1/Gs=Gf2/Gs=3, Je1=6 A/m, Je2=0 A/m, Ju1=0.01 W/m, and Ju2=0 W/m"

Shear stress intensity factor	$h f1 / w 1$
Shear stress intensity factor	0.001	0.004	0.04	0.1	0.2
$K II (a 1)$	500.464	1 155.01	3 665.04	5 379.27	6 758.02
$K II (b 1)$	$− 559.85$	$− 1 283.8$	$− 3 976.4$	$− 5 768.5$	$− 7 195.5$
$K II (a 2)$	3 629.07	3 653.76	3 976.41	4 299.7	4 582.82
$K II (b 2)$	$− 3 627$	$− 3 629.3$	$− 3 665$	$− 3 703.9$	$− 3 738.8$

Table 5

Fig. 12

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