Si-compatible candidates for high-$\kappa$ dielectrics with the $Pbnm$ perovskite structure

We analyze both experimentally (where possible) and theoretically from first principles the dielectric tensor components and crystal structure of five classes of $Pbnm$ perovskites. All of these materials are believed to be stable on silicon and are therefore promising candidates for high-$\kappa$ dielectrics. We also analyze the structure of these materials with various simple models, decompose the lattice contribution to the dielectric tensor into force constant matrix eigenmode contributions, explore a peculiar correlation between structural and dielectric anisotropies in these compounds and give phonon frequencies and infrared activities of those modes that are infrared active. We find that ${\text{CaZrO}}_3$, ${\text{SrZrO}}_3$, ${\text{LaHoO}}_3$, and ${\text{LaYO}}_3$ are among the most promising candidates for high-$\kappa$ dielectrics among the compounds we considered.

Figure 1

(Color online) Photographs of single-crystal rare-earth scandates grown along the [110] direction by the Czochralski method. (a) ${\text{PrScO}}_3$ with a diameter of 12 mm, (b) ${\text{NdScO}}_3$ with a diameter of 16 mm, (c) ${\text{SmScO}}_3$ with a diameter of 18 mm, (d) ${\text{GdScO}}_3$ with a diameter of 32 mm, (e) ${\text{TbScO}}_3$ with a diameter of 18 mm, and (f) ${\text{DyScO}}_3$ with a diameter of 32 mm.

Figure 2

(Color online) 20-atom primitive cell of a $Pbnm$-distorted $AB{\text{O}}_3$ perovskite. $A$-site atoms are shown in black, $B$-site atoms in blue (at the centers of the octahedra), and oxygen atoms in red (at the vertices of the octahedra). Orthorhombic unit-cell vectors ($a$, $b$, and $c$) are also indicated.

Figure 3

(Color online) (a) Projection on the $a\text{−}c$ plane of the structure with ${\theta }_{\text{R}}>0$ and ${\theta }_{\text{M}}=0$. (b) Projection on the $a\text{−}b$ plane for ${\theta }_{\text{R}}=0$ and ${\theta }_{\text{M}}>0$. Color coding of atoms and positions of axes labels are the same as in Fig. 2. In (a), a darker shading is used to indicate the two octahedra that are further away along the $y$ coordinate; in (b), the two bottom octahedra are exactly below the two top octahedra.

Figure 4

Unit-cell volumes of all rocksalt rare-earth nitrides, in ${\text{Å}}^3$. Empty squares are the results obtained using our optimized ultrasoft pseudopotentials for rare-earth atoms; solid circles are experimental (Ref. 51) results. The solid line is a fit to the experimental values excluding CeN, PrN, and GdN.

Figure 5

(Color online) Structural information for all systems we considered. Bottom pane shows volume in cubic angstrom per formula unit (f.u.) of $AB{\text{O}}_3$. Calculated values are shown as red circles and experimental values as blue plus symbols, if available. Top pane shows oxygen octahedra rotation angles in degrees. Theoretical values are shown with red circles and squares and experimental values with blue plus and cross symbols. ${\theta }_{\text{R}}$ angles are shown with circles and plus symbols while ${\theta }_{\text{M}}$ angles with squares and cross symbols. For ${\text{La}}_{2}B{B}^{\prime }{\text{O}}_6$ systems the average of ${\theta }_{\text{M}}$ and ${\theta }_{\text{M}}^{\prime }$ is given. For numerical values see Tables .

Figure 6

(Color online) Measured temperature dependence at 10 kHz of the dielectric tensor components (top panel) and dielectric loss (bottom panel) of ${\text{GdScO}}_3$ (blue) and ${\text{DyScO}}_3$ (red). Downward-pointing triangles denote ${ϵ}_{xx}$ and $\text{tan}{\delta }_{xx}$; upward-pointing triangles denote ${ϵ}_{yy}$ and $\text{tan}{\delta }_{yy}$; circles denote ${ϵ}_{zz}$ and $\text{tan}{\delta }_{zz}$.

Figure 7

(Color online) Dielectric information for all systems we considered. Bottom pane shows average dielectric tensor $\overline{ϵ}$, middle pane shows $x\text{−}y$ anisotropy of the dielectric tensor, $\Delta {ϵ}_{\parallel }$, and $z$ anisotropy of the dielectric tensor $\Delta {ϵ}_{\perp }$ is given in top pane. Calculated values are shown with red circles and experimental values with blue cross symbols, if available. See Table for numerical values.

Figure 8

Eigenvalues of a force constant matrix ${\Phi }_{i\alpha ,j\beta }$ of modes that contribute to ${ϵ}_{xx}^{\text{ion}}$ (first horizontal pane from bottom), ${ϵ}_{yy}^{\text{ion}}$ (second pane), or ${ϵ}_{zz}^{\text{ion}}$ (third) by more than 1.5. For each mode the area of the circle is proportional to its contribution to ${ϵ}_{ii}^{\text{ion}}$. Eigenvalues are in electron volt per angstrom squared.

Figure 9

(Color online) Correlation between the dielectric tensor $z$ anisotropy $\left(\Delta {ϵ}_{\perp }\right)$ and the mismatch in the oxygen octahedra rotation angle. Only some perovskites are labeled. Perovskites where both $A$ and $B$ ions are III-valent are indicated with blue square symbols and those where $A$ ions are II-valent and $B$ are IV-valent are indicated with red circles.