Nonlinear analysis of a crack in 2D piezoelectric semiconductors with exact electric boundary conditions

Abstract

In this paper, taking the exact electric boundary conditions into account, we propose a double iteration method to analyze a crack problem in a two-dimensional piezoelectric semiconductor. The method consists of a nested loop process with internal and outside circulations. In the former, the electric field and electron density in governing equations are constantly modified with the fixed boundary conditions on crack face and the crack opening displacement; while in the latter, the boundary conditions on crack face and the crack opening displacement are modified. Such a method is verified by numerically analyzing a crack with an impermeable electric boundary condition. It is shown that the electric boundary condition on crack face largely affects the electric displacement intensity factor near a crack tip in piezoelectric semiconductors. Under exact crack boundary conditions, the variation tendency of the electric displacement intensity factor versus crack size is quite different from that under an impermeable boundary condition. Thus, exact crack boundary conditions should be adopted in analysis of crack problems in a piezoelectric semiconductor.

Coupling of Pyro–Piezo-Phototronic Effects in a GaN Nanowire

“…Let us take the Schottky (Ag-GaN)-Ohmic contact as an example; the boundary conditions are given by [ 37 , 38 , 39 , 40 ] where V a is an applied bias voltage and the effective built-in voltage V b = V bi + V ph + V pizeo + V pyro . V bi is the built-in voltage without load.…”

“…Let us take the Schottky (Ag-GaN)-Ohmic contact as an example; the boundary conditions are given by [37][38][39][40]…”

Mathematical Model Optimization Techniques under Unreliable Electromagnetic Field for ECG Waves

“…The Equations governing the whole circulatory system could be written down as in the following with the boundary conditions taking into account [18,19]; QA(t)=QA1(t)+QM(t), ( 1) QM(t)= QB(t)+QC(t), ( 2) QM1(t)=QD1(t)+ QDO(t)+QX(t), ( 4) QC(t)= QC1(t)+QCO(t)+ QM2(t), ( 5) QM2(t)=QE1(t)+QEO(t)+QY(t), ( 6) QF(t)= QX(t)+ QY(t), ( 7)…”

Size effect in piezoelectric semiconductor nanostructures

“…The electric field and electron density in the governing equations were constantly modified with the fixed boundary conditions on the crack face. It was found that the electric boundary condition on the crack face could significantly affect the electric displacement intensity factor in the piezoelectric semiconductors (Zhao et al, 2020a).…”

“…Furthermore, fracture problem in PSCs has also received considerable attention in recent years (Hu et al, 2007;Sladek et al, 2014aSladek et al, , 2014bSladek et al, , 2015Zhao et al, 2016Zhao et al, , 2017Zhao et al, , 2018. More recently, a double iteration method was proposed to analyze the crack problem in a 2D piezoelectric semiconductor with more accurate and real electric boundary conditions (Zhao et al, 2020a). The electric field and electron density in the governing equations were constantly modified with the fixed boundary conditions on the crack face.…”