@Article{icces.2023.09073,
AUTHOR = {Qiufeng Yang, Xudong Li, Zhaowei Liu, Feng Jin, Yilin Qu},
TITLE = {Mixed	Finite	Element	Approach	for	Semiconductor	Structures},
JOURNAL = {The International Conference on Computational \& Experimental Engineering and Sciences},
VOLUME = {26},
YEAR = {2023},
NUMBER = {3},
PAGES = {1--2},
URL = {http://www.techscience.com/icces/v26n3/54055},
ISSN = {1933-2815},
ABSTRACT = {Compared	 to	 piezoelectric	 effects	 restricted	 to	 noncentrosymmetric	 crystalline	 structures,	 flexoelectric	
effects	exist	 universally	in	all	 crystalline	 structures	 [1,2].	Meanwhile,	 some	 crystals,	 say	 silicon,	are	also	
semiconductive,	which	raises	interest	in	studying	 the	interactions	between	mechanical	 fields	and	mobile	
charges	in	semiconductors	with	consideration	of piezoelectricity	or	flexoelectricity	[3,4].	In	order	to	explain	
these	 coupling	 effects,	 macroscopic	 theories	 on	 elastic	 semiconductors	 considering piezoelectricity	 or	
flexoelectricity	 were	 proposed	 by	 Yang	 and	 co-authors	 [5,6].	 For	 piezoelectric	 semiconductors,	 the	
formulation	of	finite	elements	is	relatively	straightforward	since	the	governing	partial	derivative	equation	
(PDE)	 is	 twice-order.	 As	 for	 elastic	 semiconductors	 with	 consideration	 of	 flexoelectricity,	 it	 is	 more	
challenging	to	formulate	its	finite	element	due	to	the	strain	gradients	in	the	constitutive	relations	making	
the	governing	PDE	fourth-order.	For the fourth-order	PDE,	<i>C<sup>1</sup></i> continuity is	required	for	the	displacement	
tensor	when	we	use	traditional	finite	elements	(FEs)	for	the	numerical	solution,	which	brings	difficulties	in	
the	FE	implementation	[7,8].	In	the	present	work,	instead	of	using	<i>C<sup>1</sup></i> elements,	we	develop	an	alternative	
mixed	 finite	 element	 with	 <i>C<sup>0</sup></i> continuity	 for	 solving	 the	 problem.	 The	 convergency	 and	 accuracy	 of	 the	
developed	 element	 are	 verified,	 respectively. The validated mixed	 FE	method	is	 then used	 to	 study	 the	
problem	of	an	infinite-length	tube	with	an	axisymmetric	cross section.	Our	FE	methods	provide	a	tool	for	
exploring	the	coupling	effects	in	elastic	semiconductors.	},
DOI = {10.32604/icces.2023.09073}
}