Functional Complex Point-Defect Structure in a Huge-Size-Mismatch System

Cubic boron nitride is a promising system for photonics and optoelectronics. Determining the inclusion mechanisms for dopants with a large size mismatch, such as luminous rare-earth elements, is prerequisite to understanding their functional properties and to effective doping control. Combining evidence from subangstrom resolution scanning transmission electron microscopy, imaging simulations, and first-principles calculations, we show that cationic ${\mathrm{Ce}}^{3+}$ single dopants are not located at cationic B sites but rather at anionic N sites surrounded by B-site vacancies.

Figure 1

(a) Blue luminous cathodoluminescence optical image obtained from a $c$-BN:Ce single crystal. Atomic-resolution ADF STEM images of $c$-BN viewed along the [110] direction: (b) as recorded and (c) averaged to reduce the scan noise and enhance the visibility (by simple summation of equivalent areas). The structure model (zinc-blende type) is overlaid on (b), with the B and N atoms shown in blue (right) and red (left), respectively. The specimen thickness is determined to be $\sim 12\mathrm{nm}$ by means of the EELS log-ratio method [28]. (d) Simulated image, obtained under the present microscope conditions: the probe-forming aperture half-angle is 24.5 mrad and the half-angle of the ADF detector spans from 68 to 280 mrad.

Figure 2

(a) ADF STEM image of $c$-BN:Ce viewed along the [110] direction (Gaussian filter is performed). High magnification ADF STEM images: (b) as recorded and (c) Gaussian filtered. The specimen thickness is $\sim 14\mathrm{nm}$, measured by EELS. (d) Intensity profiles along $X–X^{\prime }$ and $Y–Y^{\prime }$ in the simulated [inset of (b)] and experimental (c) images, respectively. The image simulation is based on the $({\mathrm{Ce}}_{\mathrm{N}}\mathrm{\text{−}}4V_{\mathrm{B}}{)}^{6-}$ complex point-defect structure [see Figs. 3c, 3d, 3e], and the Ce atom is assumed to be at a depth of 5 nm in the 14 nm thick specimen. The experimental intensity profile is well reproduced by the simulation. (e) Core-loss spectrum obtained from a single nitrogen atom column containing one Ce atom. The peaks are identified as the Ce $M_5$ and $M_4$ edges, respectively.

Figure 3

Formation energies of $\mathrm{Ce}_{\mathrm{B}}{}^q$, $\mathrm{Ce}_{\mathrm{N}}{}^q$, $({\mathrm{Ce}}_{\mathrm{B}}\mathrm{\text{−}}4V_{\mathrm{N}}{)}^q$, and $({\mathrm{Ce}}_{\mathrm{N}}{\mathrm{\text{−}}mV}_{\mathrm{B}}{)}^q$ ($m=1–4$) as a function of the Fermi level under two extreme chemical potential conditions: (a) the B-rich limit and (b) the N-rich limit. The range of the Fermi level is given by the valence band maximum (0 eV) and the conduction band minimum (5.8 eV). The slope corresponds to the charge state ($q=-6–+6$). (c) Relaxed $({\mathrm{Ce}}_{\mathrm{N}}\mathrm{\text{−}}4V_{\mathrm{B}}{)}^{6-}$ complex point-defect structure and (d) its [100] and (e) [110] views. The first ($V_{\mathrm{B}}$-tetrahedron) and second shells of the $({\mathrm{Ce}}_{\mathrm{N}}\mathrm{\text{−}}4V_{\mathrm{B}}{)}^{6-}$ structure model are shown in the inset of (a). A small amount of relaxation in the second shell of N atoms is evident in (c).