Stress, Strain, Piezoresistivity, and Piezoelectricity

  • Yongke Sun
  • Toshikazu Nishida
  • Scott E. Thompson
Chapter

Abstract

Strain in crystals is created by deformation and is defined as relative lattice displacement. For simplicity, we use a 2D lattice model in Fig.2.1 to illustrate this conception, but discuss the general conception in 3D cases. As shown in Fig. 2.1a, we may use two unit vectors \(\widehat{x}, \widehat{y}\) to represent the unstrained lattice, and in a simple square lattice, they correspond to the lattice basis vectors. Under a small uniform deformation of the lattice, the two vectors are distorted in both orientation and length, which is shown in Fig. 2.1b. The new vectors \(\widehat{{\rm x}}^{\prime}\) and \(\widehat{{\rm y}}^{\prime}\) may be written in terms of the old vectors:
$$\widehat{\mathbf{X}}^{\prime} = (1 + \varepsilon_{xx})\widehat{x} + \varepsilon_{xy}\widehat{y} + \varepsilon_{xz}\widehat{z},$$
(2.1)
$$\widehat{\mathbf{Y}}^{\prime} = \varepsilon_{yx}\widehat{x} + (1 + \varepsilon_{yy})\widehat{y} + \varepsilon_{yz}\widehat{z},$$
(2.2)
and in the 3D case, we also have
$$\widehat{\mathbf{Z}}^{\prime} = \varepsilon_{zx}\widehat{x} + \varepsilon_{zy}\widehat{y} + (1 + \varepsilon_{zz})\widehat{z}.$$
(2.3)

Keywords

Zinc Torque GaAs Wurtzite 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Yongke Sun
    • 1
  • Toshikazu Nishida
    • 2
  • Scott E. Thompson
    • 3
  1. 1.SanDisk CorporationMilpitasUSA
  2. 2.Department Electrical & Computer EngineeringUniversity of FloridaGainesvilleUSA
  3. 3.Department Electrical & Computer EngineeringUniversity of FloridaGainesvilleUSA

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