Chapter 18
On Converse Piezoelectricity
Michael Springborg, Bernard Kirtman, and Jorge Vargas
Abstract We review theoretical treatments of large regular non-conducting systems exposed to an electrostatic field. The field will induce a structural change (our
primary focus) that depends noticeably upon the surfaces no matter how large the
system. Interestingly, the surface effect can be determined by treating the system as
infinite and periodic, even though no surfaces are present in that case. Accurate results are presented for a simple model that verify and illustrate our infinite periodic
treatment. Approximate calculations are also carried out for a couple of real materials. The breakdown of our treatment for metals is analyzed and, on the basis of
that analysis, our approach is extended to account for the strain induced by a metal
short-circuiting the opposite surfaces of a semiconductor/insulator.
18.1 Introduction
Piezoelectricity describes the ability of materials (most often, crystals) to produce
an electric potential under the influence of an externally applied mechanical stress.
For a material that is not short-circuited, the mechanical stress will lead to a separation of opposite electrical charges at opposite crystal surfaces which results in
an electric voltage across the material. This effect is reversible in the sense that
materials exhibiting the so called direct piezoelectric effect, i.e., the production of
electricity when a stress is applied, also exhibit the converse piezoelectric effect,
i.e., the production of stress and/or strain when an electric field is applied.
In the present contribution we concentrate on the converse piezoelectric effect.
Specifically, we study how the spatial dimensions of a sample exposed to an electrostatic field change as a function of the externally applied voltage, as shown schematically in Fig. 18.1. The materials of interest to us are taken to be macroscopic so
that the thermodynamic limit has been reached. This assumption has two interesting
consequences that are discussed in this presentation.
Firstly, for a large macroscopic material the surfaces constitute an almost vanishingly small part of the complete system. This would suggest that their contribution
M. Springborg (B)
Physical and Theoretical Chemistry, University of Saarland, 66123 Saarbrücken, Germany
e-mail: m.springborg@mx.uni-saarland.de
M. Hotokka et al. (eds.), Advances in Quantum Methods and Applications in
Chemistry, Physics, and Biology, Progress in Theoretical Chemistry and Physics 27,
DOI 10.1007/978-3-319-01529-3_18,
© Springer International Publishing Switzerland 2013
331
On Converse Piezoelectricity
Michael Springborg, Bernard Kirtman, and Jorge Vargas
Abstract We review theoretical treatments of large regular non-conducting systems exposed to an electrostatic field. The field will induce a structural change (our
primary focus) that depends noticeably upon the surfaces no matter how large the
system. Interestingly, the surface effect can be determined by treating the system as
infinite and periodic, even though no surfaces are present in that case. Accurate results are presented for a simple model that verify and illustrate our infinite periodic
treatment. Approximate calculations are also carried out for a couple of real materials. The breakdown of our treatment for metals is analyzed and, on the basis of
that analysis, our approach is extended to account for the strain induced by a metal
short-circuiting the opposite surfaces of a semiconductor/insulator.
18.1 Introduction
Piezoelectricity describes the ability of materials (most often, crystals) to produce
an electric potential under the influence of an externally applied mechanical stress.
For a material that is not short-circuited, the mechanical stress will lead to a separation of opposite electrical charges at opposite crystal surfaces which results in
an electric voltage across the material. This effect is reversible in the sense that
materials exhibiting the so called direct piezoelectric effect, i.e., the production of
electricity when a stress is applied, also exhibit the converse piezoelectric effect,
i.e., the production of stress and/or strain when an electric field is applied.
In the present contribution we concentrate on the converse piezoelectric effect.
Specifically, we study how the spatial dimensions of a sample exposed to an electrostatic field change as a function of the externally applied voltage, as shown schematically in Fig. 18.1. The materials of interest to us are taken to be macroscopic so
that the thermodynamic limit has been reached. This assumption has two interesting
consequences that are discussed in this presentation.
Firstly, for a large macroscopic material the surfaces constitute an almost vanishingly small part of the complete system. This would suggest that their contribution
M. Springborg (B)
Physical and Theoretical Chemistry, University of Saarland, 66123 Saarbrücken, Germany
e-mail: m.springborg@mx.uni-saarland.de
M. Hotokka et al. (eds.), Advances in Quantum Methods and Applications in
Chemistry, Physics, and Biology, Progress in Theoretical Chemistry and Physics 27,
DOI 10.1007/978-3-319-01529-3_18,
© Springer International Publishing Switzerland 2013
331