Self-wavelength shifting in two-dimensional perovskite for sensitive and fast gamma-ray detection

Lead halide perovskites have recently emerged as promising X/γ-ray scintillators. However, the small Stokes shift of exciton luminescence in perovskite scintillators creates problems for the light extraction efficiency and severely impedes their applications in hard X/γ-ray detection. Dopants have been used to shift the emission wavelength, but the radioluminescence lifetime has also been unwantedly extended. Herein, we demonstrate the intrinsic strain in 2D perovskite crystals as a general phenomenon, which could be utilized as self-wavelength shifting to reduce the self-absorption effect without sacrificing the radiation response speed. Furthermore, we successfully demonstrated the first imaging reconstruction by perovskites for application of positron emission tomography. The coincidence time resolution for the optimized perovskite single crystals (4 × 4 × 0.8 mm3) reached 119 ± 3 ps. This work provides a new paradigm for suppressing the self-absorption effect in scintillators and may facilitate the application of perovskite scintillators in practical hard X/γ-ray detections.

where is the number density, is the classical electron radius of 2.818 × 10 -15 m, and the atomic scattering factors ( 1 and 2 ) of different elements can be obtained from the website  The 2θ was fixed and the instrument angles (ω, ψ, ϕ) were varied according to the calculated parameters in Supplementary Table 3 to obtain corresponding XRD patterns with penetration depth of 100 nm, 300 nm and 500 nm. The peak near 26.6° was chosen for further analysis. At each fixed depth, diffraction data were fitted with Gaussian distribution function to determine the peak location. The state of the residual stress and macroscopic residual strain can be judged by the slope k of 2θ-sin 2 φ (φ=arccos(cosψcos(ω-θ))) line. When k < 0, it is tensile strain/stress. When k > 0, it is compressive strain/stress, and the magnitude of strain/stress is determined by the value of the slope. As shown in Figure 4d, all fitting lines exhibited positive value in the slopes, and the slopes are 1.08 ± 0.045 @ 100nm, 0.09±0.013 @ 300nm and 0.07±0.084 @ 500nm respectively.

Supplementary Note 1. Definition of absorption efficiency and optical efficiency.
The absorption efficiency of high-energy photons is defined as where e is the natural log,  is the absorption coefficient for X/ photons and d is the thickness.
The optical efficiency represents the ratio of outgoing light to pristine light after passing through a specific distance within the scintillator, which is defined as where I0 is incident light intensity, I is outgoing light intensity, e is the natural log,  is the absorption coefficient and d is the thickness. 22

Supplementary Note 2. Electronic structure calculations of PEA2PbI4 and
PEA2PbBr4.
Density functional theory (DFT) suffers from a well-known problem in recovering the fundamental gap of semiconductors and insulators, at least under its local density approximation (LDA) or generalized gradient approximation (GGA) forms. One explanation is that these approximations only use local or semi-local forms for the electron exchange, and the incorrect exchange energy mainly leads to insufficient cancellation of the spurious electronic self-interaction.
Including these unphysical self-interactions tend to over-estimate the levels of the valence band, reducing the band gap. Hybrid functionals are indeed more reasonable approaches, but the high computational load forbids their applications in very large supercells such as PEA2PbI4 and PEA2PbBr4 surface models with a certain amount of organic cations and inorganic anions missing, especially considering that spin-orbit coupling has to be taken into account simultaneously. Hence, in this work the electronic structure calculations require an efficient method that is yet accurate in terms of the band gaps.
There is an efficient self-energy correction method named DFT-1/2, proposed in 2008 by Ferreira and coworkers. The method introduces some self-energy potentials, obtained from atomic calculations, onto those anions that contribute to the valence band. The self-energy potentials have to be trimmed by a spherical cutoff function, otherwise the overlapping of -1/r tails would render the total energy divergent. The selected cutoff radius should lead to a maximized band gap, thus it is not an empirical parameter, but rather should be obtained in a variational way. An improved form of DFT-1/2 was further given in 2018, named shell DFT-1/2, which aims at better fitting covalent semiconductor calculations. Yet, in the mean time, in certain cases it may improve the electronic structures for ionic insulators and semiconductors, especially when large anions are present. The shell DFT-1/2 method involves two cutoff radii for the self-energy potential, an outer cutoff radius (rout) as well as inner cutoff radius (rin), both should be optimized to maximize the band gap.
Whenever rin = 0, shell DFT-1/2 automatically reduces to conventional DFT-1/2, but for large anions one usually finds a fairly large rin. In this work, Brand Iare large anions. Hence, shell DFT-1/2 is adopted for electronic structure calculations, with non-collinear DFT runs that consider spin-orbit coupling.
In these perovskite materials, the only anion is the halogen elements (Br or I). However, their structures are quite complicated, and the same halogen element appears in very distinct chemical environments. For simple semiconductors, the optimization of rout/rin may be simultaneously done for all anions of a specific element just once. However, in a strict sense, the cutoff radii should be optimal for each anion individually, according to our previous work (RSC Advances 7, 21856 (2017)). Taking PEA2PbI4 as an example, the I anions can be roughly divided into equatorial ones (I (1) ) and polar ones (I (2) ). They are subject to quite different chemical environments. Hence, to obtain more accurate electronic structures, we optimize the self-energy potential cutoff radii for I (1) and I (2) separately. The optimized values are rin = 1 bohr, rout = 3.1 bohr for I (1) ; while rin = 1.5 bohr, rout = 2.9 bohr for I (2) . Shell DFT-1/2 band gap calculated at these optimal cutoff radii is 2.20 eV, with spin-orbit coupling considered.