Acta Mechanica

, Volume 230, Issue 5, pp 1825–1841 | Cite as

Nonlinear solutions of PN junctions of piezoelectric semiconductors

  • MingKai Guo
  • Yuan Li
  • GuoShuai Qin
  • MingHao ZhaoEmail author
Original Paper


A PN junction between two types of piezoelectric semiconductors (PSCs) is analyzed based on the fully coupled nonlinear equations of PSCs without any assumptions. A perturbation theory is employed to obtain the analytical solution of the considered nonlinear problem. A general solution to one-dimensional problems for PSCs is represented by a sum of a series of perturbation solutions. Typical properties including the electromechanical fields, built-in potential and the current–voltage characteristics of the piezoelectric PN junction are investigated for conditions of mechanical loading combined with a bias. The results reveal that the simplified linear (i.e., first-order perturbation) solution reported in the literature fails to describe the nonlinear characteristics, such as current–voltage characteristics of the piezoelectric PN junction, although it can give the electromechanical fields as well as concentrations of the electrons and holes near the interface of the PN junction for small carrier concentration perturbations. The presented nonlinear solution is valid and corresponds closely with the numerical solutions based on the commercial software COMSOL.


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This work was supported by the National Natural Science Foundation of China (Nos. 11702252 and 11572289).


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mechanics and Engineering ScienceZhengzhou UniversityZhengzhouPeople’s Republic of China
  2. 2.School of Mechanical EngineeringZhengzhou UniversityZhengzhouPeople’s Republic of China
  3. 3.Henan Key Engineering Laboratory for Anti-fatigue Manufacturing TechnologyZhengzhou UniversityZhengzhouPeople’s Republic of China

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