Correlation between electronic polarization and shift current in cubic and hexagonal semiconductors $\mathrm{LiZn}X$ $(X=\mathrm{P},\mathrm{As},\mathrm{Sb})$

The rectified bulk photovoltaic effect (BPVE) in noncentrosymmetric semiconductors, also called shift current, is considered promising for optoelectronic devices, terahertz emission, and possibly solar energy harvesting. A clear understanding of the shift current mechanism and search for materials with large shift current is, therefore, of immense interest. $ABC$ semiconductors $\mathrm{LiZn}X$ $(X=\mathrm{N}, \mathrm{P}, \mathrm{As}, \text{and} \mathrm{Sb})$ can be stabilized in cubic as well as hexagonal morphologies lacking inversion symmetry—an ideal platform to investigate the significant contributing factors to shift current, such as the role of structure and chemical species. Using density-functional calculations properly accounting for the electronic bandgaps, the shift current conductivities in $\mathrm{LiZn}X$ $(X=\mathrm{P}, \mathrm{As}, \mathrm{Sb})$ are found to be approximately an order of magnitude larger than the well-known counterparts and peak close to the maximum solar radiation intensity. Notably, hexagonal LiZnSb shows a peak shift current conductivity of about $-75\mu \mathrm{A}/{\mathrm{V}}^2$ and Glass coefficient of about $-20\times {10}^{-8} \mathrm{cm}/\mathrm{V}$, comparable to the highest predicted values in literature. Our comparative analysis reveals a quantitative relationship between the shift current response and the electronic polarization. These findings not only posit Li-Zn-based $ABC$ semiconductors as viable material candidates for potential applications but also elucidates key aspects of the structure-BPVE relationship.

Figure 1

Crystal structures of $\mathrm{LiZn}X$ ($X=\mathrm{N}$, P, As, and Sb) semiconductors in (a) cubic $F\overline{4}3m$ phase and (b) hexagonal $P{6}_{3}mc$ phase. (c) Elementary electronic properties in terms of selected partial density of states per formula unit for LiZnAs (as a representative for $X=\mathrm{P}$, As, Sb) and LiZnN calculated with TB-mBJ potential. The inset shows a zoom-in view of the conduction band edge in hexagonal LiZnN. SOC is included for LiZnAs.

Figure 2

(a) Linear optical conductivity and (b) nonlinear shift current conductivity of cubic $\mathrm{LiZn}X$ ($X=\mathrm{P}$, As, Sb) calculated with TB-mBJ potential. SOC is taken into account for the As and Sb compounds.

Figure 3

(a) $zz$ component of linear optical conductivity; (b), (c) $zzz$ and $zxx$ components of SCC calculated with TB-mBJ potential for hexagonal ferroelectric $\mathrm{LiZn}X$ ($X=\mathrm{P}$, As, Sb). SOC is considered for the As and Sb compounds.

Figure 4

Shift current response and degree of inversion symmetry breaking due to optical irradiation, defined in terms of ion-clamped piezoelectric coefficient $e_{14}^{\mathrm{el}}$ and electronic polarization $P_z^{\mathrm{el}}$ in cubic and hexagonal polymorphs, respectively. All the properties are calculated within TB-mBJ. SOC is included for LiZnAs and LiZnSb.

Figure 5

(a) Net shift current density per light intensity along $z$ in response to unpolarized light and (b), (c) nonvanishing independent components of Glass coefficient calculated for hexagonal ferroelectric $\mathrm{LiZn}X$ ($X=\mathrm{P}$, As, Sb) with TB-mBJ potential. SOC is considered for the As and Sb compounds.