Defect structure in quantum-cutting ${\mathrm{Yb}}^{3+}$-doped $\mathrm{CsPb}{\mathrm{Cl}}_3$ perovskites probed by x-ray absorption and atomic pair distribution function analysis

Ytterbium doping in all-inorganic lead-halide perovskites $\left[\mathrm{CsPb}{\left({\mathrm{Cl}}_{1-x}{\mathrm{Br}}_x\right)}_3\right]$ generates interesting properties including quantum cutting and narrow line emission, making these materials attractive spectral down converters for solar photovoltaics. The relationship between this optical efficiency and the defect structure(s) associated with ${\mathrm{Yb}}^{3+}$ dopants within perovskites is not well understood. Various charge-neutral doping motifs have previously been proposed and studied computationally, including clusters involving two substitutional ${\mathrm{Yb}}^{3+}$ ions charge compensated by a single local ${\mathrm{Pb}}^{2+}$ vacancy. Near-band-edge defect states associated with such motifs are believed to play an important mechanistic role in quantum cutting itself. Here, we report the results of x-ray absorption and x-ray total-scattering measurements on ytterbium-doped $\mathrm{CsPb}{\mathrm{Cl}}_3$. XANES shows that the dopant oxidation state is exclusively ${\mathrm{Yb}}^{3+}$, and a combination of $\mathrm{Yb}{L}_3$ and $\mathrm{Pb}{L}_3$ extended x-ray absorption fine structure (EXAFS) shows that this ${\mathrm{Yb}}^{3+}$ substitutes exclusively at ${\mathrm{Pb}}^{2+}$ sites, where it adopts a pseudo-octahedral ${\left[\mathrm{Yb}{\mathrm{Cl}}_6\right]}^{3-}$ coordination environment. Shell-by-shell fits to the data show a short Yb-Cl bond distance of 2.58 Å compared to the Pb-Cl bond distance of 2.83 Å. We confirm this finding by x-ray pair distribution function analysis, which also shows evidence of additional ${\mathrm{Pb}}^{2+}$ vacancy formation induced by ${\mathrm{Yb}}^{3+}$ doping. We evaluate whether this is the primary mechanism of charge compensation using simulated EXAFS and pair distribution function data for several computed defect structures. Together, these results resolve the local dopant structures and charge-compensation mechanisms in lanthanide-doped all-inorganic lead-halide perovskites, and, as such, significantly advance the understanding of structure-function relationships in this important class of materials.

Figure 1

$\mathrm{Yb}{L}_3$-edge XANES spectra for single-crystal and thin-film (TF) samples of ${\mathrm{Yb}}^{3+}$:$\mathrm{CsPb}{\mathrm{Cl}}_3$, compared with ${\mathrm{Yb}}^{3+}$ ($\mathrm{Yb}{\mathrm{Cl}}_3·6{\mathrm{H}}_2\mathrm{O}$) and ${\mathrm{Yb}}^{2+}$ ($\mathrm{Yb}{\mathrm{I}}_2$) standards. All ${\mathrm{Yb}}^{3+}$:$\mathrm{CsPb}{\mathrm{Cl}}_3$ samples show the same dominant peak coinciding with the ${\mathrm{Yb}}^{3+}$ standard peak (vertical dashed line). The second derivatives of the ${\mathrm{Yb}}^{3+}$:$\mathrm{CsPb}{\mathrm{Cl}}_3$ spectra (not shown) also show no detectable ${\mathrm{Yb}}^{2+}$.

Figure 2

Fourier transform (real space) EXAFS spectra from the $\mathrm{Yb}{L}_3$ (solid) and $\mathrm{Pb}{L}_3$ (dashed) edges for 7.4%- (blue) and 0.9%-doped (red) ${\mathrm{Yb}}^{3+}$:$\mathrm{CsPb}{\mathrm{Cl}}_3$ single crystals. The Pb data have been vertically scaled so the primary peak intensity matches that of the $\mathrm{Yb}{L}_3$ data for the same sample for comparison. Data have been phase-corrected to the primary peak for each edge, based on $M$-Cl single scattering paths, where $M=\mathrm{Yb}$ or Pb. A window of 1.0–2.8 Å was used for shell-by-shell fitting. The peak positions indicate a 0.2-Å contraction of ${\left[\mathrm{Yb}{\mathrm{Cl}}_6\right]}^{3-}$ octahedra relative to ${\left[\mathrm{Pb}{\mathrm{Cl}}_6\right]}^{4-}$ octahedra.

Figure 3

${\mathrm{Yb}}^{3+}$ dopant/defect $\mathrm{CsPb}{\mathrm{Cl}}_3$ structures (sliced along [110] plane) used in DFT calculations. Red: ${\mathrm{Yb}}^{3+}$; gray: ${\mathrm{Pb}}^{2+}$; blue: ${\mathrm{Cl}}^{-}$. ${\mathrm{Cs}}^{+}$ ions have been omitted for clarity. (a) ${\left[{\mathrm{Yb}}_{\mathrm{Pb}}-V_{\mathrm{Pb}}\right]}^{-}$: a substitutional ${\mathrm{Yb}}^{3+}$ adjacent to a ${\mathrm{Pb}}^{2+}$ vacancy. (b) ${\left[{\mathrm{Yb}}_{\mathrm{Pb}}\right]}^{+}$: a single substitutional ${\mathrm{Yb}}^{3+}$. (c),(d) ${\left[{\mathrm{Yb}}_{\mathrm{Pb}}-V_{\mathrm{Pb}}-{\mathrm{Yb}}_{\mathrm{Pb}}\right]}^0$: charge-neutral “dimer” structures involving two substitutional ${\mathrm{Yb}}^{3+}$ ions adjacent to a single ${\mathrm{Pb}}^{2+}$ vacancy in (c) a linear arrangement and (d) a bent or orthogonal arrangement.

Figure 4

EXAFS spectra calculated from AIMD trajectories (top) from each calculated structure of Fig. 3, compared with $\mathrm{Yb}{L}_3$-edge EXAFS data (purple, brown) in (a) $k$ space and (b) $R$ space for 7.4%- and 0.9%-doped ${\mathrm{Yb}}^{3+}$:$\mathrm{CsPb}{\mathrm{Cl}}_3$ single crystals. Dashed lines in (b) serve as a guide for the eye on minor peak positions.

Figure 5

(a) Experimental pair distribution function profiles [PDF, $G$($r$)] measured for $\mathrm{CsPb}{\mathrm{Cl}}_3$, 0.9% ${\mathrm{Yb}}^{3+}$:$\mathrm{CsPb}{\mathrm{Cl}}_3$, and 7.4% ${\mathrm{Yb}}^{3+}$:$\mathrm{CsPb}{\mathrm{Cl}}_3$ powdered single crystals. Primary short-range-order peaks are labeled. Inset: color-coordinated illustration of key atom pairs in the $\mathrm{CsPb}{\mathrm{Cl}}_3$ structure. Black dashed lines denote peaks with significant Pb-Pb pair contribution, the green dashed line denotes the Pb-Cl pair peak, and the red dashed line the Pb-Cs pair peak. (b) Differential PDFs [dPDFs, $D\left(r\right)$] obtained by subtracting the $\mathrm{CsPb}{\mathrm{Cl}}_3$ PDF from the PDFs of each of the ${\mathrm{Yb}}^{3+}$-doped samples. Note that the 0.9% ${\mathrm{Yb}}^{3+}$:$\mathrm{CsPb}{\mathrm{Cl}}_3 D\left(r\right)$ amplitudes are multiplied by 8 to allow representation on the same $y$ scale as the 7.4% ${\mathrm{Yb}}^{3+}$:$\mathrm{CsPb}{\mathrm{Cl}}_3$ data.

Figure 6

Pb-Cl peak region in the PDF of $\mathrm{CsPb}{\mathrm{Cl}}_3$ (black) and 7.4% ${\mathrm{Yb}}^{3+}$:$\mathrm{CsPb}{\mathrm{Cl}}_3$ (blue) and dPDF of 7.4% ${\mathrm{Yb}}^{3+}$:$\mathrm{CsPb}{\mathrm{Cl}}_3$ powdered single crystals. The 7.4% ${\mathrm{Yb}}^{3+}$:$\mathrm{CsPb}{\mathrm{Cl}}_3$ data show a decrease in the Pb-Cl peak intensity at 2.8 Å and an increase in intensity at $\sim 2.58\AA$, consistent with the loss of ${\mathrm{Pb}}^{2+}\text{−}{\mathrm{Cl}}^{-}$ bonds and the appearance of ${\mathrm{Yb}}^{3+}\text{−}{\mathrm{Cl}}^{-}$ bonds. A similar result is obtained for the 0.9% ${\mathrm{Yb}}^{3+}$:$\mathrm{CsPb}{\mathrm{Cl}}_3$ data, but with a diminished signal-to-noise ratio [Fig. 5]. Red markers indicate predicted changes in the peak intensity for ${\mathrm{Yb}}^{3+}$ substitution without any ${\mathrm{Pb}}^{2+}$ vacancies, and green markers indicate predicted changes with 0.5 ${\mathrm{Pb}}^{2+}$ vacancies per ${\mathrm{Yb}}^{3+}$.

Figure 7

Comparison of the experimental differential PDF (dPDF) for 7.4% ${\mathrm{Yb}}^{3+}$:$\mathrm{CsPb}{\mathrm{Cl}}_3$ (black) with simulated dPDFs for the various calculated defect structures depicted in Fig. 3. The bent dimer simulation was arbitrarily chosen for ${\left[{\mathrm{Yb}}_{\mathrm{Pb}}-V_{\mathrm{Pb}}-{\mathrm{Yb}}_{\mathrm{Pb}}\right]}^0$. Two additional dPDFs included to account for nonlocal charge compensation ($2{\left[{\mathrm{Yb}}_{\mathrm{Pb}}\right]}^{+}+{\left[V_{\mathrm{Pb}}\right]}^{2-}$, and ${\left[{\mathrm{Yb}}_{\mathrm{Pb}}-V_{\mathrm{Pb}}\right]}^{-}+{\left[{\mathrm{Yb}}_{\mathrm{Pb}}\right]}^{+}$) were obtained by averaging the PDFs of their specified components. The Pb-Cl peak has been marked with a blue dashed line, and several Pb-Pb peaks are marked with black dashed lines. The position of the Cs-Pb peak in the data, poorly reproduced by the simulations, is marked with a brown dashed line.