Effect of alloying on the dynamics of coherent
acoustic phonons in bismuth double perovskite
single crystals
X
IHONGL
IN,
1,5B
OW
U,
1,5,6W
EIHUAN
ING,
2M
INJUNF
ENG,
3Q
IANGX
U,
3F
ENGG
AO,
2T
ZEC
HIENS
UM,
3,7 ANDG
UOFUZ
HOU1,41Guangdong Provincial Key Laboratory of Optical Information Materials and Technology & Institute of
Electronic Paper Displays, South China Academy of Advanced Optoelectronics, South China Normal University, Guangzhou 510006, China
2Department of Physics, Chemistry, and Biology (IFM), Linköping University, Linköping SE-581 83,
Sweden
3Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang
Technological University, 21 Nanyang Link, 637371, Singapore
4Shenzhen Guohua Optoelectronics Tech. Co. Ltd., Shenzhen 518110, China 5These authors contributed equally to this work
6bowu@m.scnu.edu.cn 7tzechien@ntu.edu.sg
Abstract: The bismuth double perovskite Cs2AgBiBr6has been regarded as a potential candidate for lead-free perovskite photovoltaics. A detailed study on the coherent acoustic phonon dynamics in the pure, Sb- and Tl-alloyed Cs2AgBiBr6single crystals is performed to understand the effects
of alloying on the phonon dynamics and band edge characteristics. The coherent acoustic phonon frequencies are found to be independent of the alloying, while the damping rates are highly dependent on the alloying. Based on the mechanism of coherent acoustic phonon damping, a technique has been successfully developed that can accurately extract the absorption spectra near the indirect band gap for these single crystals with coefficients on the order of 102cm−1.
© 2021 Optical Society of America under the terms of theOSA Open Access Publishing Agreement 1. Introduction
In the last decade, solution-processed lead halide perovskites have shown great promise for high-efficiency solar cells with efficiencies exceeding 25% [1,2]. However, there remains toxicity and stability problems for these lead based perovskites. On the other hand, the recently emerged bismuth based double perovskites (DPs) with Bi3+and a monovalent metal cation (e.g., Ag+)
substituting two Pb2+cations possess merits such as low-toxicity and high stability, yet their
performance is far from satisfactory (structure shown in Fig.1(a)). The ultimate performance of a semiconductor for solar cell application is related to some key optoelectronic properties such as the band gap energy (Eg), carrier mobility, carrier lifetime and light absorption coefficients,
etc. Till now, these optoelectronic properties are still poorly understood, or under dispute for
bismuth based DPs. For example, although Sb or Tl alloying reduces the band gap that is beneficial for solar light harvesting, the effects of alloying on other optoelectronic properties such as the phonon dynamics have never been investigated. Furthermore, for the most-frequently used DP: Cs2AgBiBr6, the measured band gap fluctuates in the range of 1.80-2.25 eV, [3–6]
which is partially attributed to it possessing an indirect band gap with the band edge absorption characteristics difficult to measure. In this Letter, we present a comprehensive study on the coherent acoustic phonon (CAP) dynamics of the pure, Sb- and Tl-alloyed Cs2AgBiBr6single
crystals, not only to investigate the effects of alloying on phonon dynamics, but also to probe
#414857 https://doi.org/10.1364/OE.414857
the band edge absorption characteristics of these DPs. We found that Sb or Tl alloying does not alter the CAP frequencies, but accelerates the CAP damping rates which is attributed to the increased weak absorption below the original indirect band gap of the pure DP. The increased sub-gap absorption may originate from the redshift of the indirect band gap and/or the increased density of band tail states by alloying. More importantly, we have developed a method based on the CAP damping mechanism to accurately extract the absorption spectrum on the absolute scale near the band edge for the DPs, which is too weak to be measured using conventional UV-vis spectrometer.
Fig. 1.(a) Crystal structure of Cs2AgBiBr6DP. Typical images of as grown (b)Cs2AgBiBr6, (c) Cs2AgBi0.625Sb0.375Br6and (d) Cs2Ag1−aBi1−bTlxBr6(x = a + b=0.075) single crystals. 2. Experimental design
Following previous reports, [7,8] the Cs2AgBiBr6single crystals were fabricated by dissolving
CsBr (213 mg, 1.00 mmol), BiBr3(225 mg, 0.5 mmol), and AgBr (94 mg, 0.5 mmol) in 3 mL
of 47% HBr and reacting at 120 °C for 24 h. Large single crystals showing red color were then precipitated after slow cooling the precursor solution to room temperature. The Sb-alloyed Cs2AgBiBr6(Cs2AgBi0.625Sb0.375Br6) single crystals were prepared via the same procedures
for the pure Cs2AgBiBr6, except that the 0.5 mmol BiBr3 was replaced by 0.5 mmol mixture
of BiBr3 and SbBr3 at a molar ratio of 3:2. For the growth of the Tl-alloyed Cs2AgBiBr6
(Cs2Ag1−aBi1−bTlxBr6(x = a + b=0.075)) single crystals, we followed the previous report by A.
D. Slavney et al: [9] aqueous solution of TlBr in HBr (3.6 (1) mM), TlBr beads (∼50.0 mg, 0.176 mmol) were dissolved in 48 weight% HBr at 80° C for 2 h. The undissolved residues were removed by filtering through glass microfiber filter paper. The solution (2 mL) was then mixed with BiBr3(57 mg, 0.13 mmol), AgBr (24 mg, 0.13 mmol), and CsBr (53 mg, 0.25 mmol)
and heated at 100 °C to yield a clear yellow solution. The solution was then cooled to room temperature over 3 days at a rate of 1 °C/hr and black crystals appear after the cooling and further storage. All the processes were done in a sealed vial to prevent any contact with the toxic Tl. Typical as-grown pure, Sb- and Tl-alloyed Cs2AgBiBr6single crystals with sizes on the order of
mm × mm × mm are shown in Fig.1(b)-(d). For the calculations of the electron structure and mechanical properties of Cs2AgBiBr6, we employed the all-electron-like projector augmented
wave (PAW) method [10] and the Perdew-Burke-Ernserhof revised for solids (PBEsol) exchange correlation potential [11] as implemented in the VASP code [12].
We implemented pump-probe technique in reflection mode to characterize the CAP in the DP single crystals. In our measurements, a commercial white-light pump-probe setup (Helios, Ultrafast Systems LLC) was used. The 400 nm pump pulses were generated from a Ti-sapphire regenerative amplifier (Coherent Libra, 800 nm, 50 fs, 4 mJ, 1 kHz) that passed through a frequency-doubling barium borate (BBO) crystal. The probe pulses were generated by passing a small fraction of the 800 nm pulses from the regenerative amplifier through a 1 mm thick sapphire crystal. Both the pump and probe pulses have an incident angle < 10° and the incident direction is along the (111) orientation.
3. Results and discussion
Figure2(a) shows the pseudo-color map of the transient reflectivity for a pure Cs2AgBiBr6
single crystal upon 400 nm photoexcitation (200 µJ cm−2). Clearly it is found that for all the
probe wavelengths larger than ∼480 nm, strong oscillations can be observed. Figure2(b) depicts the transient reflectivity dynamics of Cs2AgBiBr6bulk crystals at selected probe wavelengths
(520 nm, 600 nm, 690 nm). After the fast initial decay within a few ps, the transient reflectivity is dominated by these strong oscillations. The fast initial decay is attributed to the electronic relaxation via optical and acoustic phonons. These strong oscillations with periods on the order of tens of ps, are attributed to CAPs, i.e., the photoexcitation induces lattice strain through mechanisms such as deformation potential, thermoelasticity, inverse piezoelectricity and electrostriction and the strain modifies the refractive index through the photoelastic effect [13]. The reflected probe beam by the surface of the sample and by the propagating CAP in the bulk then interfere with each other resulting in an oscillation.
Fig. 2.(a) Pseudo-color map of the transient reflectivity for Cs2AgBiBr6single crystal. (b) Transient reflectivity of Cs2AgBiBr6single crystal probed at 690 nm, 600 nm and 520 nm showing strong CAP oscillations. Black lines are the fitted curves using Eq. (3).
According to Thomsen et al and Wu et al, in the opaque bulk crystals with thickness L >> 1/α that can be treated as a semi-infinite medium, the CAP oscillation in transient reflectivity is
expressed by:[14,15]
∆R(t) ∝sin(2πft − ϕ)e−t/τd
f = 2nvscos θ/λ (1)
where ϕ is the oscillation phase, f is the oscillation frequency, θ is the incident angle, vsdenotes
dephasing time of CAP. The dephasing of CAP can be attributed to the intrinsic phonon decay and the finite penetration depth of the probe light into the crystal, which is expressed by:[16]
1 τd =
1
τphonon + vsαprobe (2)
where αprobeis the absorption coefficient at the probe wavelength.
We then fitted the transient reflectivity signals using the model given by: ∆R(t)= A sin(2πft − ϕ)e−t/τd+∑︂
i
Aie−kit (3)
where the first term at the right side represents the CAP oscillation as shown in Eq. (1), and the second term, the multi-exponential decay accounts for the electronic decays. In practice, by fitting the data at the probe wavelengths with negligible CAP oscillations, we found that tri-exponential decay model is sufficient to fit the electronic dynamics.
Figure3(a) shows the CAP oscillation frequency as a function of the probe energy for the pure, Sb- and Tl-alloyed Cs2AgBiBr6single crystals. It is found that the CAP frequency increases
linearly with the probe energy for E < Eg. However, when E > Eg, the linear relation does not
hold. From Eq. (1), we know that the CAP frequency is related to the refractive index. The nonlinear relation above the band gap is therefore attributed to the significant contribution by interband transitions on the dielectric constants. The solid line is the linear fitting using Eq. (1) for the data below the band gap of Cs2AgBiBr6, which yields a fitted nvs= 6660 m/s. J. Steele et
alcalculated the high-frequency optical dielectric constant εo=5.4 [17]. We used it to calculate
the refractive index far below the band gap and obtained a sound velocity vs= 2.87 ×103m/s.
The extracted sound velocity is then compared with the theoretical prediction. With the aid of first-principle calculations, we obtained the stiffness coefficients of Cs2AgBiBr6: c11=52.06 GPa,
c12=18.08 GPa, and c44=7.57 GPa. The elastic constant along the (111) direction is expressed
by: C(111)=1/3(c11+2 c12+4 c44) = 39.5 GPa. We then obtained the theoretical sound velocity
of 2.83 ×103 m/s along the (111) direction using v
s = √︁C/ρ, where ρ is the material mass
density, which is in excellent consistency with the experimental values. We found Sb or Tl alloying have negligible effect on the CAP oscillation frequency. This means the refractive indices are less affected by the alloying in the probe wavelength range. In linear response theory, the dielectric function of a semiconductor is contributed by different types of oscillators with different resonance frequencies and strength, e.g., excitons, phonons, etc [18]. Near the band gap, the dielectric constant is strongly affected by absorption via interband or sub-gap defect transitions. For the pure, Sb- and Tl-alloyed Cs2AgBiBr6, it was shown that they all possess
indirect band gaps, with the direct absorption bands a few hundred meV above the indirect band gaps. Alloying Sb or Tl reduces the indirect band gap of the pure Cs2AgBiBr6as observed in
diffuse reflectance and predicted by the density function theory calculations. [6,9] Furthermore, alloying may also introduce lattice disorder which increases the band tail absorpion below the band gap as discussed later. We note that both the indirect absorption and the band tail absorption are much weaker than the direct absorption. Therefore, we speculate that the alloying only alters the weak indirect or band tail transition energies/strength, while those direct transitions with strong oscillator strength above the indirect band gap are little affected by Sb or Tl alloying. As a result, the real part of the dielectric constant does not change much as inferred from the Kramers-Kronig relation due to the fact that only the weak transitions are modified by the alloying. Our speculation is consistent with the results that when we fabricated thin films using the black Tl-alloyed single crystals, the absorption spectrum is almost the same with the films prepared by the pure single crystals (Supplement 1, Fig. S1). In a thin film with the thickness of ∼100 nm, the indirect absorption is too weak to be measured. Therefore, it proves that the direct transitions above the indirect band gap are less affected by the alloying. The difference in color in single
crystals (red versus black) for the pure and Tl-alloyed DPs arises from the change of absorption by weak transitions which become apparent when light passes through these thick crystals.
Fig. 3.(a) The CAP frequency and (b) damping rate as a function of the probe energy for the pure and alloyed Cs2AgBiBr6DPs.
Figure3(b) shows the CAP damping rate (kd=1/τd) as a function of the probe energy for the
pure and alloyed DP single crystals. At the low energy side far below the band gap, the damping rates for all the crystals have little dependence on the probe energy and approaches the order of 10−1ns−1. According to Eq. (2), this corresponds to an intrinsic acoustic phonon lifetime on
the order of 10 ns, regardless of the alloying. The similarly ultra-long acoustic phonon lifetime implies that in all the three types of single crystals the interaction between defects and the low frequency acoustic phonons is weak. As the increase of the probe energy, the damping rates for all the crystals rapidly soar by orders and reaches 15 ns−1when E is around 2.5 eV. We cannot
further extract the damping rate for E > 2.6 eV due to the dominance of the electronic signal and the diminishing CAP oscillations. The increase of the damping rates corresponds to a decreased penetration depth of the probe light according to Eq. (2). Compared to the pure DP, The CAP damping of Sb- and Tl-alloyed DPs shows similar contribution from the intrinsic phonon as observed at the low energy side. However, as the increase of the probe energy, it is found the damping rate is: kpure<kSb<kTl, until the energy reaches ∼2.5 eV. Since the intrinsic phonon
lifetime is little affected by the alloying, the increased damping rate is most probably due to different absorption above the indirect band gap by Sb or Tl alloying. Therefore, the rate of CAP damping may provide us important information on the absorption characteristics near the band edge for these indirect band gap semiconductors.
After subtracting the intrinsic phonon contribution and using the sound velocity derived above, we are able to provide absorption spectra on the absolute scale for the pure and alloyed Cs2AgBiBr6 single crystals near the band edge (1.7-2.5 eV) as shown in Fig. 4. We found
the absorption coefficients of the pure DP show excellent consistency with those measured using UV-vis spectrometer for a polycrystalline thin film (∼ 100 nm thick) for E >2.3 eV. The spectrum in this region is mainly attributed to the direct exciton absorption located at X and Γ points of the band structure [19,20]. Below E∼2.3 eV, the steady-state absorption spectroscopy cannot provide accurate measurement for weak absorption in the thin film, and the signal is immersed in noise. On the other hand, the method used in this work can still yield good results for absorption coefficient on the order of 102 cm−1. The indirect band gap determined by
Tauc plot is around 2.25 eV (Fig.4inset), consistent with reports using diffused reflectance spectroscopy, photothermal deflection spectroscopy etc [20,21]. Below the indirect band gap, there is still a long tail of weak absorption extending to ∼1.6 eV, which is attributed to the band
tail states by thermal fluctuation or impurities/defects. The light absorption coefficients for the Sb- and Tl- alloyed single crystals are increased in the energy region of 1.7-2.5 eV. This is consistent with the color change and the reduced indirect band gap for the alloyed single crystals. Above E > 2.5 eV, the absorption shows little difference (Fig.3(b) & Fig.4), which is congruent with our speculation above that the direct transitions are little affected by the alloying. In previous reports, using diffuse reflectance spectroscopy, it is determined the indirect band gap for Cs2AgBi0.625Sb0.375Br6is around 1.86 eV, and for Cs2Ag1−aBi1−bTlxBr6(x = a + b=0.075) is
around 1.4 eV [6,9]. For the latter, we could not determine the band gap in our measurements due to the spectral limitation of our spectrometer (λ < 800 nm). However, Tauc plot also does not show band gap like characteristics at around 1.86 eV for the former. We propose that it possibly arises from an overlapping of the absorption by the original band tail states and the reduced indirect band gap by Sb alloying. On one hand, the alloying tunes the lattice parameters and shrinks the band gap; on the other hand, the incorporation of foreign atoms may increase the lattice disorder and the density of sub-gap band tail states. The absorption arising from the former has a square-like dependence on the photon energy between the original and new band gaps, while the absorption from the latter shows an exponential decay with the decrease of photon energy (Supplement 1, Fig. S2). Both of them are comparably weak which leads to the complex absorption characteristics when adding together. Therefore, inferred from our measurements, those band gaps determined by the diffuse reflectance spectroscopy in previous reports may beg the question as the band tail absorption may also contribute. This may also explain why the band gaps predicted by theoretical calculations and determined by different experimental techniques show large discrepancies.
Fig. 4. Near-band gap absorption spectrum measured using the CAP damping method. Inset: The indirect band gap determined using the CAP damping method for the pure Cs2AgBiBr6single crystal.
4. Conclusion
In summary, we have performed a comprehensive study on the dynamics of CAPs in pure, Sb-and Tl-alloyed Cs2AgBiBr6DP single crystals. We found Sb or Tl alloying increases the weak
absorption below the original band gap of the pure DP by red-shifting the band gap and/or increasing the band tail states, which has negligible effect on the CAP frequency due to these weak transitions contributing insignificantly to the real part of the dielectric constant. However, the increased weak absorption can drastically accelerate the CAP damping rate which is highly sensitive to the light penetration depth. Based on the mechanism of CAP damping, we developed a method to measure the weak absorption near the indirect band gap of the pure and alloyed Cs2AgBiBr6DP single crystals with coefficients on the order of 102cm−1, which can be hardly
measured using existing techniques. The method may be further applied to many other materials showing CAPs such as Si, III-V compounds, superlattice, etc, which is a promising complement to the existing optical absorption measurement techniques.
Funding.National Natural Science Foundation of China (51802331); Program for Chang Jiang Scholars and Innovative Research Teams in Universities (IRT_17R40); Science and Technology Program of Guangzhou (2019050001); Guangdong Provincial Key Laboratory of Optical Information Materials and Technology (2017B030301007); Higher Education Discipline Innovation Project; Ministry of Education - Singapore (AcRF Tier 2 grant MOE2019-T2-1-006); National Research Foundation Singapore (NRF Investigatorship (NRF-NRFI-2018-04)); Knut och Alice Wallenbergs Stiftelse (Dnr KAW 2019.0082).
Acknowledgments. The computational work for this article was (fully/partially) performed on resources of the National Supercomputing Centre (NSCC), Singapore (https://www.nscc.sg). F.G. acknowledges the financial support from the Knut och Alice Wallenbergs Stiftelse (Dnr KAW 2019.0082).
Disclosures.The authors declare no conflicts of interest.
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