First-principles study of codoping in lanthanum bromide

Codoping of Ce-doped ${\text{LaBr}}_3$ with Ba, Ca, or Sr improves the energy resolution that can be achieved by radiation detectors based on these materials. Here, we present a mechanism that rationalizes this enhancement on the basis of first-principles electronic structure calculations and point defect thermodynamics. It is shown that incorporation of Sr creates neutral $V_{\text{Br}}\text{−}{\text{Sr}}_{\text{La}}$ complexes that can temporarily trap electrons. As a result, Auger quenching of free carriers is reduced, allowing for a more linear, albeit slower, scintillation light yield response. Experimental Stokes shifts can be related to different ${\text{Ce}}_{\text{La}}\text{−}{\text{Sr}}_{\text{La}}\text{−}{V}_{\text{Br}}$ triple complex configurations. Codoping with other alkaline as well as alkaline-earth metals is considered as well. Alkaline elements are found to have extremely small solubilities on the order of 0.1 ppm and below at 1000 K. Among the alkaline-earth metals the lighter dopant atoms prefer interstitial-like positions and create strong scattering centers, which has a detrimental impact on carrier mobilities. Only the heavier alkaline-earth elements (Ca, Sr, Ba) combine matching ionic radii with sufficiently high solubilities. This provides a rationale for the experimental finding that improved scintillator performance is exclusively achieved using Sr, Ca, or Ba. The present mechanism demonstrates that codoping of wide-gap materials can provide an efficient means for managing charge carrier populations under out-of-equilibrium conditions. In the present case dopants are introduced that manipulate not only the concentrations but also the electronic properties of intrinsic defects without introducing additional gap levels. This leads to the availability of shallow electron traps that can temporarily localize charge carriers, effectively deactivating carrier-carrier recombination channels. The principles of this mechanism are therefore not specific to the material considered here but can be adapted for controlling charge carrier populations and recombination in other wide-gap materials.

Figure 1

Defect formation energies for (a), (b) intrinsic defects including $V_K$ centers as well as (c), (d) Sr. Formation energies for Sr-related defects were computed assuming equilibrium with ${\text{SrBr}}_2$ (compare Sec. 3e).

Figure 2

Equilibrium transition in red (left-hand columns) and trapping levels in blue (right-hand columns) obtained in the fashion indicated in Fig. 3.

Figure 3

(a) Configuration coordinate diagram illustrating the relation between neutral and charged Br vacancies. For convenience the electron chemical potential was assumed to coincide with the CBM $\left({\mu }_e={\epsilon }_{\text{CBM}}\right)$ such that the energy differences indicated by the vertical arrows correspond directly to the transition levels indicated in the middle panel. (b) Formation energy of Br vacancy configurations for La-rich conditions as a function of the electron chemical potential in the vicinity of the conduction band edge; compare Fig. 1. The solid and dotted lines are based on fully relaxed configurations, corresponding to minima in panel (a). Dashed lines indicate formation energies representing vertical transitions in panel (a). The horizontal blue and orange arrows thus correspond to the vertical arrows in panel (a). The red horizontal arrow is equivalent to the energy difference between the minima in panel (a). (c), (d) Quasiparticle spectra from DFT and $G_0{W}_0$ calculations for both (c) the isolated Br vacancy and (d) a ${\text{Sr}}_{\text{La}}\text{−}{V}_{\text{Br}}$ complex. The position of the defect level relative to the CBM changes by less than 0.1 eV when comparing the two types of calculations. Note that in both cases the defect level is unoccupied in equilibrium.

Figure 4

Structure of lanthanum bromide and defect configurations therein. (a) Projection onto the (0001) basal plane. Large blue and small red spheres represent La and Br sites, respectively. The shaded triangles correspond to atomic layers containing both atom types (green) and Br ions only (purple), respectively. (b) Perspective view. A representative Br vacancy site is indicated by the cube and Sr as well as Ce substitutional sites are shown by large green and light gray spheres, respectively. (c) Isosurface of localized vacancy level illustrating that it is composed of $5d$ states derived from the three nearest cations. (d) Isosurface of localized hole level for lowest energy $V_K$ center. (e)–(g) Configurations of the ${\text{Ce}}_{\text{La}}\text{−}{\text{Sr}}_{\text{La}}\text{−}{V}_{\text{Br}}$ triple complex, in which both Sr and Ce are within the first-neighbor shell of the Br vacancy. (e) In-plane ${\text{Ce}}_{\text{La}}\text{−}{V}_{\text{Br}}$ and out-of-plane ${\text{Sr}}_{\text{La}}\text{−}{V}_{\text{Br}}$. (f) Out-of-plane ${\text{Ce}}_{\text{La}}\text{−}{V}_{\text{Br}}$ and out-of-plane ${\text{Sr}}_{\text{La}}\text{−}{V}_{\text{Br}}$. (g) Out-of-plane ${\text{Ce}}_{\text{La}}\text{−}{V}_{\text{Br}}$ and in-plane ${\text{Sr}}_{\text{La}}\text{−}{V}_{\text{Br}}$.

Figure 5

Defect and free charge carrier concentrations in (a) pure and (b) Sr-doped ${\text{LaBr}}_3$ as a function of chemical potential assuming full equilibrium at 600 K (also compare Ref. [14]). (c) Concentrations of Br (solid lines) and La (dashed lines) vacancies as a function of temperature for different levels of Sr doping and assuming defect freezing at 600 K. Note that incorporation of Sr leads to an increase in the Br vacancy concentration by several orders of magnitude.

Figure 6

(a) Binding energies of Sr with various defects as a function of separation. The ${\text{Sr}}_{\text{La}}\text{−}{V}_{\text{Br}}\text{−}{\text{Ce}}_{\text{La}}$ triple complex is composed of a nearest-neighbor in-plane ${\text{Sr}}_{\text{La}}\text{−}{V}_{\text{Br}}$ defect and ${\text{Ce}}_{\text{La}}$ at various distances. (b) Position of equilibrium transition and trapping levels of Br vacancy as a function of separation from ${\text{Sr}}_{\text{La}}$ (also compare Ref. [14]). The arrows on the right-hand side indicate the levels obtained for the free Br vacancy; compare Fig. 3. The data points marked (A) and (B) correspond to first-nearest-neighbor out-of-plane and in-plane configurations, respectively; compare Fig. 4. (c) Potential induced by ${\text{Ce}}_{\text{La}}^{\times }$ and ${\text{Sr}}_{\text{La}}^{\prime }$ calculated by spherically averaging the difference in local potential between defect and ideal cell. The orange line is a fit to $1/r$.

Figure 7

(a) Configuration coordinate diagram illustrating the relation between ground and excited state of ${\text{Ce}}_{\text{La}}$ in its neutral charge state. The ground and excited state PES correspond to the electronic configurations ${\text{Ce}}^{3+}\text{−}4f^{1}5d^0$ and ${\text{Ce}}^{3+}\text{−}4f^{0}5d^1$, respectively. The spin-orbit splitting of the ground state PES is represented by filled and open circles. (b) Schematic representation of the displacements associated with the configurational coordinate. The primary change pertains to the six out-of-plane Br neighbors of the Ce site, which relax inward by about 0.1 Å going from the ground to the excited state ionic configuration while the in-plane neighbor positions are almost unaffected.

Figure 8

Solubility of selected dopants computed using Eq. (A1) and the formation energies for substitution on La. Li and Cs demark the upper and lower limit of solubilities for alkaline doping.

Figure 9

Lowest deviations from a cubic shape obtained for different cell sizes via Eqs. (C4) and (C2).

Figure 10

Finite-size scaling of formation energies of La vacancies in different charge states. Open symbols refer to formation energies calculated via Eq. (A2) whereas filled symbols belong to formation energies subjected to potential alignment and image charge corrections according to Eq. (C5). Solid lines are fits to Eq. (C6) and dashed lines indicate the average over the corrected formation energies. The numbers next to the lines indicate the formation energies obtained by extrapolation of the uncorrected data. In the case of the neutral vacancy $\left(q=0\right)$ there are no potential alignment and image charge corrections. Formation energies have been computed for Br-rich conditions and an electron chemical potential ${\mu }_e=0.6\text{eV}$, which was chosen to obtain a visual separation of the different charge states.