Magnetically Induced Carrier Distribution in a Composite Rod of Piezoelectric Semiconductors and Piezomagnetics

Abstract

In this work, we study the behavior of a composite rod consisting of a piezoelectric semiconductor layer and two piezomagnetic layers under an applied axial magnetic field. Based on the phenomenological theories of piezoelectric semiconductors and piezomagnetics, a one-dimensional model is developed from which an analytical solution is obtained. The explicit expressions of the coupled fields and the numerical results show that an axially applied magnetic field produces extensional deformation through piezomagnetic coupling, the extension then produces polarization through piezoelectric coupling, and the polarization then causes the redistribution of mobile charges. Thus, the composite rod exhibits a coupling between the applied magnetic field and carrier distribution through combined piezomagnetic and piezoelectric effects. The results have potential applications in piezotronics when magnetic fields are relevant.

Keywords: applied magnetic field; carrier tuning; piezoelectric semiconductor; piezomagnetic.

Figure 1

A composite rod of a piezoelectric semiconductor and piezomagnetics.

Figure 2

A differential element of the composite rod under mechanical loads.

Figure 3

Magnetic potential and piezomagnetically induced mechanical fields under different ${\psi }_0$ when $n_0=1\times {10}^{21}/{\mathrm{m}}^3$. (a) $\mathsf{\Delta }\psi =\psi -{\psi }_0{x}_3/L$, (b) mechanical displacement, (c) strain.

Figure 3

Magnetic potential and piezomagnetically induced mechanical fields under different ${\psi }_0$ when $n_0=1\times {10}^{21}/{\mathrm{m}}^3$. (a) $\mathsf{\Delta }\psi =\psi -{\psi }_0{x}_3/L$, (b) mechanical displacement, (c) strain.

Figure 4

Piezoelectrically induced electric fields under different ${\psi }_0$ when $n_0=1\times {10}^{21}/{\mathrm{m}}^3$. (a) Electric potential, (b) electric field, (c) electric displacement.

Figure 4

Piezoelectrically induced electric fields under different ${\psi }_0$ when $n_0=1\times {10}^{21}/{\mathrm{m}}^3$. (a) Electric potential, (b) electric field, (c) electric displacement.

Figure 5

Polarization-induced charge distributions under different ${\psi }_0$ when $n_0=1\times {10}^{21}/{\mathrm{m}}^3$. (a) Effective polarization charge and (b) electron concentration perturbation.

Figure 5

Polarization-induced charge distributions under different ${\psi }_0$ when $n_0=1\times {10}^{21}/{\mathrm{m}}^3$. (a) Effective polarization charge and (b) electron concentration perturbation.

Figure 6

Magnetic potential and piezomagnetically induced mechanical fields for different n₀ when ${\psi }_0={10}^{-4}\mathrm{AT}$. (a) $\mathsf{\Delta }\psi =\psi -{\psi }_0{x}_3/L$, (b) mechanical displacement, (c) strain.

Figure 6

Magnetic potential and piezomagnetically induced mechanical fields for different n₀ when ${\psi }_0={10}^{-4}\mathrm{AT}$. (a) $\mathsf{\Delta }\psi =\psi -{\psi }_0{x}_3/L$, (b) mechanical displacement, (c) strain.

Figure 7

Piezoelectrically induced electric fields for different n₀ when ${\psi }_0={10}^{-4}\mathrm{AT}$. (a) Electric potential, (b) electric field, (c) electric displacement.

Figure 7

Piezoelectrically induced electric fields for different n₀ when ${\psi }_0={10}^{-4}\mathrm{AT}$. (a) Electric potential, (b) electric field, (c) electric displacement.

Figure 8

Polarization-induced charge distributions for different n₀ when ${\psi }_0={10}^{-4}\mathrm{AT}$. (a) Effective polarization charge, (b) electron concentration perturbation.

Figure 8

Polarization-induced charge distributions for different n₀ when ${\psi }_0={10}^{-4}\mathrm{AT}$. (a) Effective polarization charge, (b) electron concentration perturbation.

Figure 9

$\mathsf{\Delta }n/n_0$ versus h/c at different locations along the rod.