Electronic Impurity Doping of a 2D Hybrid Lead Iodide Perovskite by $\mathrm{Bi}$ and $\mathrm{Sn}$

Control over conductivity and carrier type (electrons and holes) defines semiconductors. A primary approach to target carrier concentrations involves introducing a small population of aliovalent impurity dopant atoms. In a combined synthetic and computational study, we assess impurity doping by introducing $\mathrm{Bi}$ and $\mathrm{Sn}$ into the prototype 2D Ruddlesden-Popper hybrid perovskite phenylethylammonium lead iodide (${\mathrm{PEA}}_2{\mathrm{Pb}\mathrm{I}}_4$). Experimentally, we demonstrate that $\mathrm{Bi}$ and $\mathrm{Sn}$ can achieve n- and p-type doping, respectively, but the doping efficiency is low. Simulations show that $\mathrm{Bi}$ introduces a deep defect energy level (∼0.5 eV below the conduction band minimum) that contributes to the low doping efficiency, but, to reproduce the low doping efficiency observed experimentally, an acceptor level must also be present that limits n-type doping. Experiments find that $\mathrm{Sn}$ achieves p-dopant behavior and simulations suggest that this occurs through the additional oxidation of $\mathrm{Sn}$ defects. We also study how substitutional $\mathrm{Bi}$ incorporation can be controlled by tuning the electrochemical environment during synthesis. First-principles impurity doping simulations can be challenging; typical dopant concentrations constitute less than 0.01% of the atoms, necessitating large supercells, while a high level of theory is needed to capture the electronic levels. We demonstrate simulations of complex defect-containing unit cells that include up to 3383 atoms, employing spin-orbit coupled hybrid density functional theory. While p- and n-type behavior can be achieved with $\mathrm{Sn}$ and $\mathrm{Bi}$, simulations and experiments provide concrete directions where future efforts must be focused to achieve higher doping efficiency.

Popular Summary

Metal-halide perovskites are at the center of immense attention as economically processable tunable semiconductors. Electronic doping is key to enabling semiconductor technologies, but it is not completely understood or addressed. Here, the authors combine experimental results with high-fidelity band structure calculations to demonstrate that 2D lead-halide perovskite semiconductors can be fabricated as n- or p-type when ${\mathrm{Bi}}^{3+}$or ${\mathrm{Sn}}^{2+}$, respectively, replace ${\mathrm{Pb}}^{2+}$ in the lattice. Simulations show that aliovalent n-type doping by bismuth is facilitated during synthesis under reducing conditions. Hybrid density functional theory simulations of complex defect-containing unit cells with up to 3383 atoms properly capture the physicochemical behavior of isolated impurity dopants. The combination of (i) experimentally tracked Fermi levels as a function of impurity incorporation, (ii) a conceptual model of Fermi level evolution, and (iii) hybrid DFT simulations enables the authors to shed light on the doping mechanism. They show that any n-type doping will be limited by a fairly large concentration of defects that trap the electrons donated by n-type dopant incorporation, while p-type doping by ${\mathrm{Sn}}^{2+}$ is limited by the necessarily indirect nature of the doping process.

Figure 1

(a) Crystal structure of ${\mathrm{PEA}}_2{\mathrm{Pb}\mathrm{I}}_4$ and illustrative doping effects by impurity atoms. (b) Summary of ICPMS data showing the ratio of incorporated dopants relative to $\mathrm{Pb}$ for input dopants $\mathrm{Bi}$ and $\mathrm{Sn}$. Dotted lines indicate estimated linear approximations of the dopant incorporation levels as a guide to the eye. (c) UV-vis absorption spectra of undoped, ${\mathrm{Bi}}^{3+}$-doped, and ${\mathrm{Sn}}^{2+}$-doped ${\mathrm{PEA}}_2{\mathrm{Pb}\mathrm{I}}_4$. x% corresponds to the input atomic ratio of ${\mathrm{Bi}}^{3+}$ or ${\mathrm{Sn}}^{2+}$ relative to ${\mathrm{Pb}}^{2+}$; inset shows optical images of as-grown doped crystals. (d) PXRD spectra of undoped, $5\mathrm{\%}{\mathrm{Bi}}^{3+}$-doped, and $3\mathrm{\%}{\mathrm{Sn}}^{2+}$-doped ${\mathrm{PEA}}_2{\mathrm{Pb}\mathrm{I}}_4$ crystals.

Figure 2

(4 × 4)-${\mathrm{Sn}}_{\mathrm{Pb}}$ and (4 × 4)-${\mathrm{Sn}}_{\mathrm{Pb}}$+ V${}_{\mathrm{Pb}}$ structural models. (a) Full geometry of (4 × 4)-${\mathrm{Sn}}_{\mathrm{Pb}}$; $\mathrm{Pb}$ in green, $\mathrm{Sn}$ in blue (atom in center), $\mathrm{I}$ in purple; wire models indicate PEA molecules. The orbital associated with the highest occupied ${\mathrm{Sn}}_{\mathrm{Pb}}$-derived state at the Γ point is shown by the yellow isosurface (of isosurface level 0.03, corresponding to |Ψ|), showing that this is an extended state, essentially hybridized with the host (${\mathrm{PEA}}_2{\mathrm{Pb}\mathrm{I}}_4$) valence band. (b) Defect-containing layer of (4 × 4)-${\mathrm{Sn}}_{\mathrm{Pb}}$, showing only the B-site atoms ($\mathrm{Pb}$ or $\mathrm{Sn}$) for clarity. (c) Computed DFT-HSE06 + SOC electronic band structure of (4 × 4)-${\mathrm{Sn}}_{\mathrm{Pb}}$, Brillouin zone definition shown in (i). Contribution of B-site atoms to different bands; $\mathrm{Pb}$ is green and $\mathrm{Sn}$ is blue. Species contributions of $\mathrm{Sn}$ (blue) are layered on top of contributions from $\mathrm{Pb}$ (green). The dashed black horizontal line labeled E_H indicates the energy above which states are unoccupied in the computation. (Note that this is not a Fermi level, since the calculations do not include a formal temperature.) (d) Tabulated fractions of species contributions to the VBM and the electronic state directly below the VBM (VBM-1) at the Γ point. Values are listed as total fractions and (in brackets) fractions per atom. Note the high $\mathrm{Sn}$ contribution (per atom) to the VBM. Analogous results are given for the (4 × 4)-${\mathrm{Sn}}_{\mathrm{Pb}}+$V${}_{\mathrm{Pb}}$ structure in (e)–(h).

Figure 3

Structural models, DFT-HSE06 + SOC predicted band structures, and orbitals for the reduced and nonreduced $\mathrm{Bi}$-incorporated structures (4 × 4)-${\mathrm{Bi}}_{\mathrm{Pb}}$ and (4 × 4)-${\mathrm{Bi}}_2$□, respectively (see text). (a) Brillouin zone. (b) Impurity-containing layers of the substitutional defect and the vacancy-forming defect models, showing only B-site positions—Pb (green), Bi (cyan), or vacancy—for clarity. Computed DFT-HSE06 + SOC electronic band structures of (c) substitutionally doped (4 × 4)-${\mathrm{Bi}}_{\mathrm{Pb}}$ (spin-polarized) and (d) vacancy structure (4 × 4)-${\mathrm{Bi}}_2$□. Bands highlighted in green are predominantly derived from $\mathrm{Pb}$; bands highlighted in cyan are predominantly derived from $\mathrm{Bi}$. Highest occupied level in (c) is the band around 1.5 eV. (e) Orbital associated with the occupied $\mathrm{Bi}$-derived defect band at the Γ point of (4 × 4)-${\mathrm{Bi}}_{\mathrm{Pb}}$ shown for an isosurface value (corresponding to |Ψ|) of 0.03. (f) Analogous to (e), but for (4 × 4)-${\mathrm{Bi}}_2$□. $\mathrm{Pb}$, green; $\mathrm{Bi}$, cyan; $\mathrm{I}$, purple; wireframe, PEA. Dashed black horizontal lines labeled E_H in (c),(d) indicate the energy above which states are unoccupied in the computation. (Note that this is not a Fermi level, since the calculations do not include a formal temperature.)

Figure 4

(a) Sheet resistance of ${\mathrm{PEA}}_2{\mathrm{Pb}\mathrm{I}}_4$ films versus dopant concentration. (b),(c) HRXPS spectra of the valence band edge region as a function of dopant concentration for $\mathrm{Bi}$ and $\mathrm{Sn}$, respectively. (d) E_VBM with respect to E_F (E_F − E_VBM) as a function of dopant concentration; CBM is plotted as unfilled rectangles and is determined as the VBM plus the electronic band gap, taken here to be 2.67 eV. (e) Extracted band edge energies of undoped, $\mathrm{Sn}$-doped, and $\mathrm{Bi}$-doped ${\mathrm{PEA}}_2{\mathrm{Pb}\mathrm{I}}_4$ films with respect to the Fermi level (set to zero here). To extract E_VBM with respect to E_F (E_F − E_VBM), a linear fit of the photoelectron intensity onset is performed, and the intersection with the baseline is extracted. (f) Fermi level with respect to VBM (VBM is set to zero here) as a function of incorporated $\mathrm{Bi}$ dopant fraction. Blue dots, experimental data extracted from XPS results. Red line, model including a compensating trap level (Sec. XI within the Supplemental Material [49]). Black solid line, model without compensation.