Unraveling the ${\text{LiNbO}}_3$ X-cut surface by atomic force microscopy and density functional theory

The ${\text{LiNbO}}_3$(2$\overline{1}\overline{1}0$) surface, commonly referred to as X-cut, is investigated by means of atomic force microscopy and first-principles calculations. Atomically resolved atomic force microscopy images show geometrical patterns not compatible with truncated bulk terminations. Fast Fourier transformation of the real-space images shows an oblique surface unit cell with lattice parameters of $a=0.75\pm 0.02$ nm, $b=0.54\pm 0.02$ nm, and $\alpha =94.8^{\circ }$. Comparing these experimental results with the theoretical models of stable surface terminations provides clear evidence for the formation of a -${\text{Li}}_{12}$ termination. The LN X-cut is, thus, characterized by a nonstoichiometric and Li-enriched composition. An analysis of the surface electronic charge indicates that the atomic force microscopy contrast is governed by the charge accumulation at the oxygen ions.

Figure 1

Tapping mode AFM images of the positive (left-hand side) and negative (right-hand side) LN X-cut at the μm scale. Images were taken in air after cleaning in acetone and isopropanol in an ultrasonic bath and annealing at ${700}^{\circ }$C [(a) and (b)], ${800}^{\circ }$C [(c) and (d)], and ${900}^{\circ }$C [(e) and (f)].

Figure 2

Height distribution plot at the LN(2$\overline{11}$0) surface. The distribution originates from an area of 1 $\mu {\mathrm{m}}^2$. The corresponding sample was cleaned in acetone and isopropanol in an ultrasonic bath for 15 min each, dried in a nitrogen flow, and annealed at 1000${}^{\circ }$C for 10 h.

Figure 3

Perspective view of (a) the unrelaxed truncated-bulk X-cut and (b) the -${\text{Li}}_{12}$ terminated X-cut. Distances between the atomic layers are indicated. White atoms represent Nb, gray atoms Li, and small atoms O.

Figure 4

High-resolution FM-AFM images of the positive X-cut sample shown in Fig. 1.

Figure 5

Atomic models of the truncated bulk terminations of the LN X-cut. Two nonequivalent cuts with (a) cationic and (b) anionic terminations can be discriminated. White atoms represent Nb, gray atoms Li, and small atoms O. The unit cells of arbitrarily chosen surface atoms are highlighted. Note that all the Li and Nb ions, as well as all the oxygen ions, are located at the same height.

Figure 6

Calculated atomic models of the (a) -${\text{Li}}_6$, (b) -${\text{Li}}_9$, (c) -${\text{Li}}_{12}$, and (d) ${\text{Li}}_6$${\text{Nb}}_6$${\text{O}}_9$ terminations. Atomic patterns compatible with the AFM pictures are highlighted. Color coding as in previous pictures. (e)–(h) Corresponding electronic charge distribution calculated 0.25 Å above the highest atom. The dimensions and the character of the surface unit cells as they would appear in AFM measurements are indicated.

Figure 7

Comparison of the atomically resolved FM-AFM image of the LN X-cut (left-hand side) with the surface electronic charge density of the -${\text{Li}}_{12}$ terminated X-cut model calculated within the DFT (right-hand side). The bright spots in the pictures correspond to oxygen ions.