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Published at November 19

MORE-Stress: Model Order Reduction based Efficient Numerical Algorithm for Thermal Stress Simulation of TSV Arrays in 2.5D/3D IC

cs.CE

Released Date: November 19, 2024

Authors: Tianxiang Zhu¹, Qipan Wang², Yibo Lin³, Runsheng Wang³, Ru Huang³

Aff.: ¹School of Integrated Circuits, Peking University; ²School of Integrated Circuits, Peking University; Academy for Advanced Interdisciplinary Studies, Peking University; ³School of Integrated Circuits, Peking University; Institute of Electronic Design Automation, Peking University; Beijing Advanced Innovation Center for Integrated Circuits

Arxiv: http://arxiv.org/abs/2411.12690v1

$p=15$ $\upmu$ m
array size		$10\times 10$	$20\times 20$	$30\times 30$	$40\times 40$	$50\times 50$
ANSYS	time	391 s	1296 s	2952 s	5392 s	8612 s
ANSYS	memory	12.2 G	53.1 G	119.7 G	212.7 G	330.1 G
Linear	time	2.4 s	3.9 s	9.6 s	13.4 s	20.5 s
superposition	memory	0.24 G	0.47 G	0.81 G	1.23 G	1.72 G
(jung2012chip, ; jung2014tsv, )	error	5.36 $\%$	6.57 $\%$	7.27 $\%$	7.69 $\%$	7.98 $\%$
Ours	time	2.5 s	4.4 s	9.5 s	13.1 s	17.1 s
	memory	0.31 G	0.67 G	1.23 G	1.85 G	2.91 G
	error	0.93 $\%$	0.87 $\%$	0.80 $\%$	0.72 $\%$	0.67 $\%$
Improve.	time	156 $\times$	295 $\times$	311 $\times$	412 $\times$	504 $\times$
over ANSYS	memory	39 $\times$	79 $\times$	97 $\times$	115 $\times$	113 $\times$
Improve.
over Linear	accuracy	5.8 $\times$	7.6 $\times$	9.1 $\times$	10.7 $\times$	12.0 $\times$
superposition
$p=10$ $\upmu$ m
array size		$10\times 10$	$20\times 20$	$30\times 30$	$40\times 40$	$50\times 50$
ANSYS	time	352 s	1201 s	2840 s	5304 s	8508 s
ANSYS	memory	12.6 G	48.0 G	108.2 G	196.8 G	312.9 G
Linear	time	2.3 s	4.0 s	9.6 s	13.3 s	20.7 s
superposition	memory	0.24 G	0.46 G	0.81 G	1.23 G	1.71 G
(jung2012chip, ; jung2014tsv, )	error	7.40 $\%$	10.33 $\%$	12.37 $\%$	13.60 $\%$	14.43 $\%$
Ours	time	2.3 s	4.5 s	11.4 s	13.9 s	18.5 s
	memory	0.31 G	0.67 G	1.22 G	1.86 G	2.90 G
	error	0.98 $\%$	0.92 $\%$	0.85 $\%$	0.79 $\%$	0.74 $\%$
Improve.	time	153 $\times$	267 $\times$	250 $\times$	382 $\times$	460 $\times$
over ANSYS	memory	41 $\times$	72 $\times$	87 $\times$	106 $\times$	108 $\times$
Improve.
over Linear	accuracy	7.6 $\times$	11.2 $\times$	14.6 $\times$	17.2 $\times$	19.5 $\times$
superposition