# Stress, Strain, Piezoresistivity, and Piezoelectricity

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

Stress Tensor Shear Strain Strain Tensor Uniaxial Stress Biaxial Stress
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Authors and Affiliations

• Yongke Sun
• 1
Email author
• 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