Phonon Influence on Bulk Photovoltaic Effect in the Ferroelectric Semiconductor GeTe

The shift current (SHC) has been accepted as the primary mechanism of the bulk photovoltaic effect (BPVE) in ferroelectrics, which is much different from the typical $p\text{−}n$ junction-based photovoltaic mechanism in heterogeneous materials. In the present work, we use first-principles calculations to investigate the SHC response in the ferroelectric semiconductor GeTe, which is found possess a large SHC response due to its intrinsic narrow band gap and high covalency. We explore the changes of SHC response induced by phonon vibrations, and analytically fit current versus vibrational amplitude to reveal the quantitative relationships between vibrations and the SHC response. Furthermore, we demonstrate the temperature dependence of the SHC response by averaging the phonon vibration influence in the Brillouin zone. Our investigation provides an explicit experimental prediction about the temperature dependence of BPVE and can be extended to other classes of noncentrosymmetric materials.

Figure 1

(a) The rhombohedral unit cell of GeTe (green dotted lines) and the first Brillouin zone (black solid lines), with the ferroelectric polarization along the $\widehat{z}$ direction. (b) The band structure of ferroelectric GeTe, with the conduction-band minimum at the $L$ point and valence-band maximum at the $Z$ point.

Figure 2

Three kinds of phonon vibrations: the phonon vibration along the (a) $\widehat{x}$ and (b) $\widehat{z}$ direction in the primitive unit cell, and (c) the antiferroelectric vibration mode in the $2\times 2\times 2$ supercell.

Figure 3

(a) The shift current response (${\sigma }_{zzZ}$) of GeTe versus photon energy, and its dependence on the ferroelectric vibrational amplitude. (b) The change of the shift current response versus the vibrational amplitude, with the photon energy $\hslash \omega =0.9$ and 1.1 eV, respectively. The squares and triangles in (b) are the results from the first-principles calculations, and the lines in black and red are the fitting curves from the polynomial $C_1(\omega )\lambda +C_2(\omega ){\lambda }^2$.

Figure 4

(a) The shift current response (${\sigma }_{zzZ}$) versus the photon energy, and its dependence on the perpendicular phonon vibrational amplitude. (b) The change of the shift current response versus the amplitude $\lambda$, with the photon energy $\hslash \omega =1.0$ and 1.2 eV, respectively. The squares and triangles in (b) are the results from the first principles calculations, and the lines in black and red are the fitting curves from the polynomial $C_2(\omega ){\lambda }^2$.

Figure 5

(a) The shift current response (${\sigma }_{zzZ}$) versus the photon energy, and its dependence on the antiferroelectric phonon vibrational amplitude. (b) The change of the shift current response versus the amplitude $\lambda$, with the photon energy $\hslash \omega =0.9$ and 1.1 eV, respectively. The squares and circles in (b) are the results from the first-principles calculations, and the lines in black and red are the fitting curves from the parabola $C_2(\omega ){\lambda }^2$.

Figure 6

(a) The shift current response (${\sigma }_{zzZ}$) versus the photon energy for different temperatures. (b) Temperature dependence of the shift current response (${\sigma }_{zzZ}$) with the photon energy $\hslash \omega =0.8$, 0.9, 1.0, and 1.1 eV.