Intricate carrier dynamics of bismuth halide perovskites: localized excitons and polarons

Abstract

The interaction between carriers and photons in halide perovskites gives rise to intriguing phenomena in their excited states. In particular, bismuth halide perovskites exhibit behavior that extends beyond free carriers, involving excitons and polarons. Here, we report the steady state and excited state dynamics in the lead-free A₃Bi₂I₉ [A = FA (formamidinium), MA (methylammonium), Cs (cesium)] perovskite derivatives. The A₃Bi₂I₉ system exhibits strong excitonic peaks in the absorption spectra because of defect-related direct-bound excitons. The emission from self-trapped excitons influenced by carrier-phonon coupling and exciton–exciton interactions results in broad photoluminescence spectra. The low-energy photo-induced absorption (PIA-L) band below the bandgap energy is attributed to band gap renormalization (BGR) and the formation of self-trapped excitons (STSs) through electron-acoustic phonon coupling. Hot carrier cooling results in a transient absorption response and the occupation of modified band edge states. The interplay between BGR and polaron formation plays a crucial role in determining the amplitude of PIA-L during the cooling process. We observe that the carrier dynamics in the A₃Bi₂I₉ system are mostly dominated by localized excitons and small polarons. This study enhances our understanding of the fundamental processes governing their optoelectronic behavior and paves the way for their further utilization in advanced device applications.

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Introduction

Recently, bismuth halide lead-free perovskites have emerged as a promising category of materials for optoelectronics and photovoltaics. They present a viable alternative to lead-based counterparts, owing to their non-toxic properties and diverse structural characteristics.^1–4 Beyond photovoltaics, these materials are widely reported for radiation detection, supercapacitors, and photocatalysis applications.^5–8 Significant progress has been made in the material exploration and device engineering of bismuth halide perovskite to boost their performance. With the device engineering of semiconductors, the fundamental limitations of charge carriers and lattice dynamics should be known to unleash their maximum performance in optoelectronic applications.

Bismuth halide perovskites exhibit low dimensional lattice connectivity and quantum confinement effect, which can significantly influence their lattice dynamics and photophysical characteristics.^9,10 The relationship between the structural and photophysical properties of A₃Bi₂I₉ perovskites has spurred investigations into the dynamics of charge carriers in these materials after photoexcitation. The zero-dimensional lattice connectivity of A₃Bi₂I₉ leads to quantum confinement of charge carriers. Ghosh et al. examined the limitations of Cs₃Bi₂I₉ as a photovoltaic absorber material and identified weak interactions between [Bi₂I₉]³⁻ bioctahedra as a major barrier to achieving high solar cell efficiency.^11,12 Scholz et al. explored exciton dynamics in the MA₃Bi₂I₉ film deposited on mesoporous TiO₂.¹³ Earlier, we investigated the polaron-mediated photoconduction and phonon-mediated hot carrier cooling dynamics in the Cs₃Bi₂I₉ single crystalline system.^14,15 We also studied the hot carrier relaxation in A₃Bi₂I₉ polycrystalline films and found that the nature of the A-site cation significantly influences the hot carrier cooling time.¹⁶

Despite the considerable interest generated by bismuth halide perovskite materials and extensive theoretical and experimental research aimed at uncovering their photophysical processes, key aspects such as electron-lattice coupling, hot carrier cooling dynamics, and polaron formation are still not fully understood. Additionally, the origins of the observed photoinduced absorption at both the high-energy and low-energy sides of the bleaching band in transient absorption features remain elusive. Moreover, it is imperative to develop a comprehensive understanding of how different cation substitutions impact carrier relaxation dynamics and photoinduced effects.

In this work, we have explored the steady-state and excited-state dynamics in lead-free A₃Bi₂I₉ (A = FA, MA, Cs) perovskite nanocrystals using the steady state and transient optical spectroscopy technique and investigated how the nature of the A-site cation can influence these characteristics. These nanocrystals were synthesized using the antisolvent precipitation technique and characterized by X-ray diffraction (XRD), transmission electron microscopy (TEM), and steady-state optical spectroscopy techniques. Furthermore, we have excited the three perovskite NCs above the band edge (350 nm) with the same excitation power and observed that the relaxation of hot carriers occurs most slowly in the inorganic Cs₃Bi₂I₉ perovskite. The significant variation in hot carrier cooling with different cation compositions is due to the interactions between the various cations (A = FA, MA, Cs) and the Bi-I frameworks. Moreover, we observed distinct features in the form of high-energy positive bands (photoinduced absorption, PIA-H), negative bands (ground state bleaching, GSB), and low-energy broad positive bands (PIA-L) for all three nanocrystals. We found the bandgap renormalization in the presence of hot carriers, and polaron-mediated activation of forbidden transitions are mainly responsible for the observed transient absorption features. These findings enhance our understanding of the fundamental processes governing their optoelectronic behavior and pave the way for their potential utilization in advanced device applications.

Results and discussion

Fabrication and structure of A₃Bi₂I₉ nanocrystals

The A₃Bi₂I₉ NCs are synthesized by the ligand-assisted reprecipitation (LARP) method as previously reported.^17,18 The synthesized NCs and their image under UV illumination are shown in Fig. S1 (ESI†). The TEM images and diffraction pattern are shown in Fig. S2 (ESI†), which reveal the morphology and crystalline nature of the synthesized nanocrystals. The average size was found to be 3.6 ± 0.8 nm for Cs₃Bi₂I₉ NCs, 3.1 ± 0.5 nm for MA₃Bi₂I₉ NCs and 2.5 ± 0.5 nm for FA₃Bi₂I₉ NCs, as shown in Fig. S3 (ESI†). In the A₃Bi₂I₉ structure, the formation of hydrogen bonds (H-bonds) occurs between the H⁺ ion and I⁻ ions, resulting in the stretching of (Bi₂I₉)³⁻. The hydrogen-bonding interaction is more pronounced for the FA⁺ cation due to the presence of two NH₂ groups. The positive charge in the MA⁺ cation mainly resides in its –NH₃ moiety, whereas in the FA⁺ cation, it is distributed between the two –NH₂ groups. As a result, the FA⁺ cation exhibits a significantly smaller dipole moment compared to the MA⁺ cation.^16,19 In the case of A₃Bi₂I₉, a bioctahedra [Bi₂I₉]³⁻ is formed when a pair of [BiI₆]³⁻ octahedra share faces, which differs from the corner-sharing octahedra observed in perovskite structures like methylammonium lead iodide (MAPbI₃). This results in a 0D structure, as depicted in Fig. 1a–c. The voids between these bioctahedrons are occupied by A-cations. The organic FA and MA cations exhibit disordered orientations, and their dynamic rotational motion poses challenges in accurately determining their precise positions within the structure.²⁰ Furthermore, we have recorded the XRD pattern of A₃Bi₂I₉ NCs, as shown in Fig. 2d and Fig. S4 (ESI†). We observe that all three major peaks shift to higher values in the order of FA to MA to Cs, reflecting a decrease in lattice spacing. The ionic radii of FA, MA, and Cs cations are 2.79 Å, 2.7 Å, and 1.88 Å, respectively.^16,21–23 The larger size of the A-cation leads to an increased lattice constant. Moreover, the presence of an organic cation at the A-site results in increased distortion of the bioctahedrons, with FA₃Bi₂I₉ possessing more rotational distortion in comparison to MA₃Bi₂I₉. The A₃Bi₂I₉ system exhibits a hexagonal crystal structure with space group P6₃mmc at room temperature.

Fig. 1 Crystal structure of (a) Cs₃Bi₂I₉, (b) MA₃Bi₂I₉, and (c) FA₃Bi₂I₉ perovskite drawn by VESTA software. (d) X-ray diffraction pattern of the A₃Bi₂I₉ NCs powder. (e) Absorbance spectra of the synthesized A₃Bi₂I₉ NCs dispersed in chlorobenzene solvent.

Fig. 2 Electronic band structure with the contribution from spin–orbit coupling (SOC) and atom-projected partial density of states (pDOS) for (a) and (d) Cs₃Bi₂I₉; (b) and (e) MA₃Bi₂I₉; and (c) and (f) FA₃Bi₂I₉.

Optical properties and density functional theory results

To investigate the optical characteristics, we measured the absorbance spectra of the NCs. The steady-state absorption spectrum for Cs₃Bi₂I₉, MA₃Bi₂I₉, and FA₃Bi₂I₉ NCs is shown in Fig. 1e. The absorption spectrum shows an exciton peak at 495 nm for Cs₃Bi₂I₉ NCs, 504 nm for MA₃Bi₂I₉, and 510 nm for FA₃Bi₂I₉ NCs. Generally, the large-radii A-cation results in a red-shift in the absorption maxima, consistent with our results.^16,23–25 Earlier studies have demonstrated that bismuth halide perovskites inherently contain stable shallow defects, which are both significant and readily formed.^17,18 These shallow defects function as hole acceptors, resulting in the localization of holes. Consequently, these trapped holes exhibit infinite effective mass. A trapped hole can pair with a heavy electron to form a bound exciton with a high binding energy. Hence, we ascribe the prominent excitonic peak observed to defect-related direct bound excitons (localized excitons). The broad absorption band extending up to 350 nm contains at least two sub-bands around 365 nm and 420 nm, which has been ascribed to the electron transitions from the ground 1S₀ to the excited states of Bi³⁺ in the isolated Bi₂I₉³⁻ clusters. The calculated indirect and direct bandgaps using the Tauc plot are shown in Fig. S5a and b (ESI†), respectively. The indirect (direct) bandgap was estimated as 2.17 (2.30) eV for Cs₃Bi₂I₉, 2.15 (2.25) eV for MA₃Bi₂I₉, and 2.13 (2.21) eV for FA₃Bi₂I₉, which indicates that the bandgap is slightly decreased with increased A-cation size attributed to the geometrical effect of large cations on the band formation, which enhances the overlap in energy levels and reduces the energy between the VBM and CBM.^16,23–25

Furthermore, to gain detailed insights into the optical and electronic properties of these materials, we compute the electronic band structure and atom-projected partial density of states (pDOS) using density functional theory (DFT).^9,11,26 We find that all these materials are indirect band gap semiconductors, with indirect (direct) band gaps of 1.81 (1.92) eV, 1.79 (1.89) eV, and 1.78 (1.82) eV for Cs₃Bi₂I₉, MA₃Bi₂I₉, and FA₃Bi₂I₉, respectively (Fig. 2a–c).^{11,12,27–30} The difference between the indirect and direct band gaps is minimal, on the order of 0.1 eV. Additionally, we observe a decreasing trend in the band gap with increasing size of the A-site cation, consistent with experimental observations (Fig. S5, ESI†). From the pDOS plots, we observe that for all A₃Bi₂I₉ materials, the valence band edges are primarily contributed by the I (p) orbitals, while the conduction band edges are predominantly composed of hybridized Bi (p) and I (p) orbitals (Fig. 2d–f). We note that the A-site cation does not directly contribute to the band edges (Fig. S6, ESI†). However, it significantly affects the band dispersion. We estimate the effective mass of electrons for these perovskites by the parabolic fitting of the lowest conduction band edges. The effective masses are found to be 1.64 m_e, 4,55 m_e, and 2.02 m_e for Cs₃Bi₂I₉, MA₃Bi₂I₉, and FA₃Bi₂I₉, respectively. In the case of organic A-site cations, we observe a decrease in the band dispersion of the lowest lying conduction band, indicating smaller electron mobility in organic perovskites compared to inorganic Cs₃Bi₂I₉.

Moreover, we observe excitonic peaks in the optical spectra computed theoretically using many-body perturbation theory (G₀W₀/BSE). The first peak obtained through the G₀W₀ method represents the electronic band gap of a material, incorporating many-body effects. However, it does not account for the formation of electron–hole pairs (i.e., excitons). To include electron–hole interactions, we solved the model Bethe–Salpeter equation (mBSE) and determined the optical spectra (Fig. S7, ESI†). The shift in the optical spectra, resulting in a lower optical band gap compared to the electronic band gap, indicates the presence of excitons in these materials. The difference between the electronic (G₀W₀) and optical (mBSE) band gaps provides an estimate of the exciton binding energy (E_B). We observe that E_B (Cs₃Bi₂I₉) < E_B (MA₃Bi₂I₉) < E_B (FA₃Bi₂I₉). The larger dielectric screening of the Coulomb interaction between electrons and holes in the inorganic system results in smaller exciton binding energy compared to the organic systems. However, there is a very small difference in the static electronic dielectric contribution of these materials, with values of 4.0, 3.8, and 3.4 for Cs₃Bi₂I₉, MA₃Bi₂I₉, and FA₃Bi₂I₉, respectively, resulting in closely lying values of E_B.

Furthermore, we measured the photoluminescence (PL) spectrum of all three NCs with different excitation wavelengths as shown in Fig. 3. The Cs₃Bi₂I₉ NCs display emission peaks ∼405 nm (3.06 eV) and ∼455 nm (2.72 eV) accompanied by a broad emission spanning the range of 500 to 650 nm when excited within the wavelength range of 350 to 400 nm. Subsequent excitation at higher wavelengths only resulted in the observation of broad emission in the range of 500 to 650 nm. In the case of MA₃Bi₂I₉ and FA₃Bi₂I₉, emission peaks are observed at ∼408 nm (3.06 eV), ∼438 nm (2.72 eV), and ∼462 nm (with a small shift of 2–3 nm with changing MA to FA) with a broad emission from 500 to 650 nm in response to excitation wavelengths from 350 nm to 400 nm. The occurrence of emission peaks at ∼405 and ∼455 nm, at energies higher than the lowest-energy broad emission, is quite unusual. To confirm the origin of these high-energy peaks, we perform measurements of the excitation spectrum by analyzing the emission at all observed wavelengths. Remarkably, the obtained photoexcitation (PLE) spectrum matches well with the absorption spectrum. We find that these high energy emission peaks occur because of electron transitions from the ground 1S₀ to the excited states of Bi³⁺ in the isolated [Bi₂I₉]³⁻ clusters. The broad emission spanning from 500 nm to 650 nm can be attributed to excitonic emission. The broad emission profile displays a characteristic shape with a relatively sharp cutoff on the high-energy side, followed by a long exponential tail extending towards lower energies.³¹ This unique behavior clearly indicates photoluminescence associated with an exponential tail in the density of states.³² The extended low-energy tail in the PL spectrum corresponds to the emission of localized excitons (LE) and is broad, existing at lower energies.^32,33 Previous observations in bismuth halide systems have reported the presence of self-trapped exciton (STE) photoluminescence at room temperature.³⁴ The carrier-phonon coupling effect induced by phonon-assisted absorption and recombination processes is strong in these indirect-bandgap nanocrystals, leading to the formation of self-trapped excitons.^35–38 Consequently, due to the presence of an indirect band structure calculated from DFT calculations, intervalley scattering processes are expected in these systems.³⁹ Given these insights, a more comprehensive investigation into the interplay between the indirect band structure, phonon interactions, and self-trapped excitons is warranted in future studies to gain a deeper understanding of the fundamental photophysical properties of bismuth halide nanocrystals.

Fig. 3 Emission spectrum at excitation wavelengths from 350 nm to 400 nm, (a) Cs₃Bi₂I₉, (d) MA₃Bi₂I₉, and (g) FA₃Bi₂I₉. Emission spectrum at excitation wavelengths from 400 nm to 500 nm, (b) Cs₃Bi₂I₉, (e) MA₃Bi₂I₉, and (f) FA₃Bi₂I₉. The photoluminescence excitation (PLE) spectrum of (c) Cs₃Bi₂I₉, (f) MA₃Bi₂I₉, and (i) FA₃Bi₂I₉ at different emission wavelengths.

Excited state dynamics

To investigate the excited state dynamics of the photoexcited carriers, we conducted transient absorption (TA) spectroscopy on the A₃Bi₂I₉ NCs. In these studies, a pump pulse centered at 350 nm is used to excite all three samples (FA₃Bi₂I₉, MA₃Bi₂I₉, and Cs₃Bi₂I₉), followed by a broadband probe pulse with a variable time delay. Fig. 4a–c portrays a 2D color plot of the TA spectra of the Cs₃Bi₂I₉ (Fig. 4a), MA₃Bi₂I₉ (Fig. 4c), and FA₃Bi₂I₉ (Fig. 4e) NCs in response to excess energy excitation (λ_excitation = 350 nm). Here, we observe three bands as a (i) high energy positive band (ΔA > 0), (ii) negative band (ΔA < 0), and (iii) low energy broad positive band in the TA spectrum for all three NCs as shown in Fig. 4b (Cs₃Bi₂I₉), Fig. 4d (MA₃Bi₂I₉), and Fig. 4f (FA₃Bi₂I₉).¹² In the FA₃Bi₂I₉, we have obtained some fluctuations in the data because of the possibility of photodamage, it has been reported that FA-based systems are prone to experiencing significant photodamage.¹⁶ The early time spectra up to 50 ps are presented in Fig. S8 (ESI†). In Cs₃Bi₂I₉, the high energy positive band is centered at ∼2.61 eV, which is assigned as the photoinduced absorption (PIA-H) band. A negative band is observed between 2.4 to 2.55 eV centered at ∼2.49 eV, which is assigned as the ground state bleaching (GSB) band. At the lower energy side, a broad positive band (PIA-L) is observed, of which the intensity and broadness vary with the A-site cation. Similarly, these bands are assigned for MA₃Bi₂I₉ and FA₃Bi₂I₉. These spectral signatures of the PIA-H and GSB bands closely match the second derivative of the absorption spectra (Fig. S9, ESI†). Previously, Scholz et al. explained the derivative shape of the transient absorption spectra in MA₃Bi₂I₉.¹³ They proposed that the presence of significant local fields within the perovskite material leads to the emergence of a trapped-carrier-induced Stark effect.

Fig. 4 Femtosecond transient absorption (fs-TA) spectra in response to 350 nm optical excitation. The pseudo color plot of the TA spectrum (a) Cs₃Bi₂I₉, (c) MA₃Bi₂I₉, and (e) FA₃Bi₂I₉ NCs. TA spectra at the indicated delay time (b) Cs₃Bi₂I₉, (d) MA₃Bi₂I₉, and (f) FA₃Bi₂I₉ NCs.

In our systems, a large number of excitons are formed after photoexcitation. These excitons are primarily localized in nature, characteristic of Frenkel excitons, which possess high binding energy.^13,36,40 The GSB band position is located around the excitonic peak in the absorption spectra for all three systems, ∼2.49 eV for Cs₃Bi₂I₉ (∼0.15 eV width), ∼2.38 eV for MA₃Bi₂I₉ (∼0.19 eV width) and ∼2.43 eV for FA₃Bi₂I₉ (∼0.19 eV width) as presented in Fig. 4b, d and f, respectively. The origin of GSB is attributed to the band-filling effect and the width of GSB is determined by the hot carrier's distribution and exciton–exciton interaction.^41–43 Localization of excitons in this system can lead to exciton–exciton interaction and scattering, which results in the width of the GSB band at initial delays.^42,44 The excitons in A₃Bi₂I₉ perovskites exhibit strong confinement within the isolated 0D (Bi₂I₉)³⁻ dimers. The bleach observed near the exciton resonance, along with two PIA bands flanking the bleaching peak, is characteristic of exciton band broadening caused by carrier-exciton scattering following photoexcitation.^17,18,45 The observed shift in the GSB band at earlier delay is due to hot carrier occupancies in the density of states and then relaxation towards low energy levels of the conduction band. During the initial delay times following photoexcitation, the broadening of the exciton bands can be primarily attributed to the presence of non-relaxed hot carriers; after that, the carriers gradually relax towards the indirect band edge of the perovskite, and at this stage their contribution to the scattering effects becomes more significant.^21,45 In addition, coulombic interaction due to A-cation and rotational dynamics of organic MA and FA cations significantly alters the density of states distribution and band dispersion, which affects the width and position of the GSB band and decay kinetics.^46,47 We observe the GSB band broadness increase in the case of MA₃Bi₂I₉ and FA₃Bi₂I₉ cations because of the increased disorder in the density of states and enhanced exciton–exciton scattering. The vibrational modes of these organic cations enhance the involvement of lattice phonons and hence increase the contribution from the indirect band edge, which increases the broadness of the GSB band.^23,24

The GSB kinetics comparison is shown in Fig. 5a. By analyzing the GSB kinetics, we observe a slower initial decay in Cs₃Bi₂I₉, suggesting that the relaxation of hot carriers occurs at a slower rate. Conversely, in FA₃Bi₂I₉, the initial decay is found to be faster, indicating a rapid relaxation process for hot carriers. One contributing factor to this distinct kinetics can be attributed to the size disparity among the organic cations present in the nanostructures. The FA cation, being considerably larger than the MA and Cs cations, promotes a stronger interaction with the perovskite Bi-I framework. As a result, the motion of the FA cation induces larger changes in the wave functions, consequently leading to more significant couplings.^21,22,48 This increased interaction highlights a stronger distribution of excited states' charge on the FA cation compared to Cs and MA. Moreover, previous studies have demonstrated that FA-based perovskites exhibit a smaller bulk modulus, indicating a softer material, in contrast to MA and Cs-based perovskites.^21–23 This difference is primarily attributed to the interaction between the organic cations and the Bi-I framework, which can alter the lattice phonons within hybrid perovskites when compared to the purely inorganic Cs₃Bi₂I₉ structure. In the case of MA₃Bi₂I₉ and FA₃Bi₂I₉, the modes of libration and torsion of the organic cations can couple with the Bi-I modes, which are essential for nonadiabatic coupling, ultimately leading to relaxation. Specifically, the phonon modes associated with the organic cations exhibit significant overlap with the Bi-I modes, enabling their active participation in the relaxation of hot carriers via carrier-phonon interactions. Consequently, the bismuth halide perovskites based on organic cations (MA and FA) demonstrate faster hot carrier relaxation than their counterparts based on Cs cations.

Fig. 5 Kinetics at different probe wavelengths for all three systems. Comparable kinetics at the (a) GSB band, (b) PIA-L band, and (c) PIA-H band. Comparable kinetics of the GSB, PIA-L, and PIA-H band for the (d) Cs₃Bi₂I₉, (e) MA₃Bi₂I₉, and (f) FA₃Bi₂I₉ system.

Furthermore, the low energy PIA (PIA-L) is observed in all three systems. Previously, it is mentioned that in low-dimensional materials, the broad positive absorption below the bandgap energy is typically associated with STEs and polaron formation.^49–52 From the steady-state absorbance and photoluminescence features, we also observe the presence of self-trapped excitons in the A₃Bi₂I₉ system with large electron–phonon coupling. In lead-halide perovskites, large polaronic features typically emerge (Fröhlich polaron) due to long-range interactions within the 3D connected lattice structure. However, in our A₃Bi₂I₉ system, short-range interactions dominate, with electron-acoustic phonon coupling occurring through the deformation potential, a consequence of the spatial isolation between [Bi₂I₉]³⁻ bioctahedra (0D electronic connectivity).⁴² The deformation potential in the lattice facilitates the formation of small polarons, which act as self-trapped excitons and lead to charge carrier trapping. Additionally, band gap renormalization in the presence of hot carriers can also contribute to the rise of this PIA-L. It is understood that hot carriers occupy fewer states at the newly lowered band edge compared to cooler carriers, resulting in an initial TA signal at the renormalized band edge, caused by newly created optical transitions due to the altered band edge states. The observed bandgap renormalization is likely attributable to an amplified contribution from photo-induced lattice fluctuations.⁵³ Therefore, we attribute the occurrence of the PIA-L band to the simultaneous interplay of BGR and polaron formation features in the A₃Bi₂I₉ system.

The decay kinetics of this PIA-L band are presented in Fig. 5b, which shows faster decay in the case of MA₃Bi₂I₉ than FA₃Bi₂I₉ and Cs₃Bi₂I₉ exhibits slower decay of PIA-L kinetics, indicating that PIA-L decay is significantly influenced by the A-site cation size and nature. Previously, it was demonstrated in the case of lead-halide perovskite that the MA cation exhibits strong overall H-bonding because of a larger dipole on MA⁺ than FA⁺.^54,55 Similarly, in our case, we state that MA₃Bi₂I₉ has strong H-bonding capability and a large dipole moment.¹⁹ The Cs₃Bi₂I₉ has no H-bonding capability. Interestingly, the strength of hydrogen bonding (MA > FA > Cs) is found to be inversely correlated with the decay lifetime of PIA-L. This suggests that if the dominance of hydrogen bonding strength was to govern the kinetics of PIA-L, a clear anticorrelation would be observed, indicating that weaker hydrogen bonding would result in slower decay of the PIA-L signal. As we discussed above the disorder induced by the organic cation significantly influences the exciton–phonon coupling; hence polaron formation is altered by the nature of the organic cations. In addition, bandgap renormalization also depends on the occupied density of states and band dispersion, which is influenced by the orientational dynamics and disorder of the organic cations. Therefore, MA₃Bi₂I₉ exhibits faster decay of PIA-L. Furthermore, the dynamics of polaron formation and the kinetics of PIA-L can also be influenced by ionic migration. Ionic species, carrying charge, can significantly impact lattice fluctuations. Consequently, their migration within the material can have implications for the formation of polarons and affect the decay kinetics of PIA-L. In our previous study, it was demonstrated that FA₃Bi₂I₉ exhibits lower levels of ionic migration compared to MA₃Bi₂I₉.¹⁹ This difference in ionic migration suggests that the interference from polarons may be more pronounced in MA₃Bi₂I₉, leading to a faster decay of the PIA-L signal. However, it is important to note that since A₃Bi₂I₉ materials possess zero-dimensionality, the influence of ionic migration on excited state dynamics may not be as significant. This assumption requires further experimental and theoretical verification to confirm its validity.

Furthermore, we have observed PIA-H in all three-systems centered at ∼2.61 eV in Cs₃Bi₂I₉, ∼2.58 eV in MA₃Bi₂I₉, and ∼2.62 eV in FA₃Bi₂I₉. Previously, the origin of this high-energy PIA is attributed to the photoinduced refractive index change.⁵⁶ Scholz et al. proposed that this PIA-H could be associated with the Stark effect, which corresponds to the second derivate of the absorption spectra.¹³ In a report, Rosi et al. attributed the origin of the observed PIA-H in CsPbBr₃ QDs to the light-induced activation of parity-forbidden exciton transitions facilitated by the formation of symmetry-breaking polarons.⁵⁷ They elucidated that under photoexcitation, there is strong activation of the forbidden transitions, resulting in a distinct and well-defined induced absorption signal located between the two dipole-allowed excitonic transitions. This activation occurs due to a significant perturbation generated by the lattice-distorting polaron, which is formed when an exciton is excited. The strong perturbation can modify the selection rule for exciton transitions. The A₃Bi₂I₉ system exhibits strong quantum confinement due to isolated (Bi₂I₉)³⁻ dimers (0D lattice connectivity). Previously, we have demonstrated the polaron-mediated features and strong exciton–phonon coupling because of the large deformation potential.^14,15,58,59 Therefore, we attribute the origin of PIA-H in the A₃Bi₂I₉ system to the parity-forbidden exciton transitions mediated by the symmetry-breaking polarons. The cationic effect can alter the position and intensity of this band. The decay kinetics of this band are shown in Fig. 5c and Fig. S10 (ESI†) and extracted components are shown in Table 1. The first two components are shorter in the case of MA₃Bi₂I₉ because of the high orientation and strong dipole moment of the MA cation, which induces strong lattice deformation. All inorganic Cs₃Bi₂I₉ exhibit longer decay of this PIA-H band suggesting less lattice deformation.

Table 1 Estimated time constants from TA kinetics for all three NCs fitted at positive bands

Perovskite	Bands (eV)	A 1 (%)	τ 1 (ps)	A 2 (%)	τ 2 (ps)	A 3 (%)	τ 3 (ps)
Cs3Bi2I9	2.61 (PIA-H)	87	25.4	13	344
	2.18 (PIA-L)	89	26.8	11	724
MA3Bi2I9	2.58 (PIA-H)	88	0.26	10	136	2	>500
	2.10 (PIA-L)	47	0.49	17	13	36	133
FA3Bi2I9	2.62 (PIA-H)	56	0.48	36	20.7	8	>500
	2.14 (PIA-L)	16	1.24	62	30.3	22	1400

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Furthermore, we compare the GSB, PIA-L, and PIA-H kinetics for each system (Fig. 5d–f). By scrutinizing these kinetics, we observe that PIA-L and PIA-H exhibit similar patterns of decay kinetics patterns with variations in lifetime components. The observation of similar kinetics between PIA-L and PIA-H provides compelling evidence supporting the formation of small polarons and the occurrence of light-induced activated forbidden transitions mediated by polarons within these systems. The formation of small polarons, induced by lattice distortions caused by photoexcitation, plays a crucial role in facilitating the activation of forbidden transitions and subsequently contributes to the observed kinetics. Moreover, we found an intriguing relationship between the kinetics of GSB and PIA-L. The kinetics of GSB is found to reflect those of PIA-L, indicating a connection between these two phenomena. This correspondence lends support to the notion of bandgap renormalization, which involves a modification of the effective bandgap due to interactions between excited carriers and the surrounding lattice. Additionally, the kinetics of GSB provides insight into the relaxation of hot carriers, further emphasizing the interplay between electronic and lattice dynamics within the A₃Bi₂I₉ system.

Conclusions

Here, we have investigated the steady state and excited state behavior of A₃Bi₂I₉ perovskite nanocrystals. We observe strong localized excitonic features in the absorption spectra of these nanocrystals, attributed to defect-related direct-bound excitons. Besides, electron transitions from ground states to excited states of Bi³⁺ in isolated Bi₂I₉³⁻ clusters result in broad absorption towards lower wavelengths. The emission from self-trapped excitons influenced by carrier-phonon coupling and exciton–exciton interactions results in broad photoluminescence spectra. High energy peaks in the photoluminescence spectra are related to the emission from the excited states of Bi³⁺ in isolated Bi₂I₉³⁻ clusters as revealed by the PLE spectra. The transient absorption spectra exhibited PIA-H, GSB, and PIA-L for all three NCs. The low energy photoinduced absorption (PIA-L) can be attributed to the simultaneous contribution of band gap renormalization (BGR) and small polarons. The high energy photoinduced absorption band (PIA-H) occurs because of the parity-forbidden exciton transitions mediated by the symmetry-breaking polarons. The dynamics of these bands are significantly influenced by the size and nature of the A-site cation. From the TA kinetics analysis, we find slower hot carrier cooling in Cs₃Bi₂I₉ and faster cooling in the FA₃Bi₂I₉ and MA₃Bi₂I₉ systems, attributed to disorder and H-bonding strength of the A-site cation. Our results emphasize the significant roles played by localized excitons and small polarons in determining and influencing the carrier dynamics within these bismuth halide systems. These findings deepen our understanding of the optoelectronic properties of bismuth halide perovskites and contribute to the development of future applications in areas such as photovoltaics and optoelectronics.

Methods

Materials

Cesium iodide (CsI), methylammonium iodide (MAI), formamidinium iodide (FAI) and bismuth iodide anhydrous (BiI₃) were purchased from TCI chemicals. The extra pure DMF solvent was purchased from SRL. Oleic acid (OA, technical grade, 90%) was purchased from Alfa Aesar. All chemicals were used as received without further purification.

Synthesis of A₃Bi₂I₉ nanocrystals

We dissolved single crystals of A₃Bi₂I₉ for making the precursor solution. We used dimethyl sulfoxide (DMF) as the solvent to dissolve A₃Bi₂I₉ single crystals. Chlorobenzene was used as the antisolvent to precipitate NCs. In 5 mL of chlorobenzene, we mixed 0.5 mL oleic acid. Then 50 μL of precursor solution was added dropwise to this solution under stirring vigorously and left for 10 min after the addition. The NC solution was then centrifuged at 6000 rpm for 5 min to achieve size-dependent separation in the NC solution.

Characterizations

To measure the size and shape of the prepared nanocrystals, TEM images were taken with the help of FEI Tecnai G2 20 S-Twin Transmission Electron Microscope with an accelerating voltage of 200 kV. The samples were prepared in a copper made TEM grid for the characterization. The UV-vis absorption spectra of the NCs were measured in the solution phase with an Agilent Technologies UV-vis spectrophotometer. The photoluminescence (PL) and PLE measurement was done by a Shimadzu RF6000 Fluorescence spectrometer. XRD was performed using a Rigaku X-ray diffractometer with a 9 kW rotating anode copper K_α (λ = 0.15418 nm) X-ray source. The crystal structures were drawn using VESTA software. The femtosecond TA spectroscopy technique was used to measure excited state absorption and the associated lifetime of the materials. Details of the TA setup are reported in our previous studies.^15,59

Computational details

First-principles density functional theory (DFT) calculations were performed using the Vienna ab initio Simulation Package (VASP), which implements projector-augmented wave (PAW) pseudopotentials.^60–62 The atomic positions of the experimentally obtained structures were optimized using the Perdew–Burke–Ernzerhof (PBE) parameterized exchange–correlation (ε_xc) functional within the generalized gradient approximation (GGA) until the Hellmann–Feynman forces were smaller than 10⁻³ eV Å⁻¹.⁶¹ A total energy threshold of 10⁻⁵ eV and a kinetic energy cutoff of 550 eV were used in the self-consistent calculations. The electronic band structure and atom-projected partial density of states were estimated using the PBE ε_xc functional, including spin–orbit coupling effects. Single-shot GW (G₀W₀) calculations were performed on PBE as a starting point to account for many-body effects. A gamma-centered k-grid of 4 × 4 × 2 was used, with 240 unoccupied bands included in the GW self-energy correction.^63,64 To incorporate electron–hole interactions, we employed model Bethe–Salpeter Equation (mBSE) approach on top of PBE. The mBSE calculations were performed using a 4 × 4 × 2 k-grid, with 4 occupied and 4 unoccupied orbitals to construct the excitonic Hamiltonian.⁶⁵ Instead of using GW quasiparticle energies, mBSE calculations were performed using PBE eigenvalues with a scissor correction, determined as the difference between the GW and PBE band gaps. The dielectric screening in mBSE was modeled using a local model function:
where ε_∞ is the static high-frequency ion-clamped dielectric constant, and λ is the screening length obtained by fitting the GW calculated screening function at small wave vectors with respect to |q + G|. Here, q and G are the wave vectors and lattice vectors of the reciprocal cell, respectively. The exciton binding energy was computed as the difference between the optical (mBSE) and electronic (G₀W₀) band gaps. The values of inverse dielectric constant (ε_∞⁻¹) and screening length (λ) used for each material are provided in Table 2.

Table 2 Inverse dielectric constant and screening length for all A₃Bi₂I₉ materials

Material	ε ∞ ^−1	λ
Cs3Bi2I9	0.27	0.69
MA3Bi2I9	0.26	1.21
FA3Bi2I9	0.29	1.33

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Data availability

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

Conflicts of interest

The authors state that they have no financial conflicts of interest.

Acknowledgements

N. K. T. acknowledges the grant GAL-2370-PHY/24-25, the Fulbright-Nehru Postdoctoral Research Fellowship, and the Department of Chemistry, Northwestern University, USA (present affiliation of N. K. T.). We also acknowledge IIT Roorkee for providing the instrument facilities and express our gratitude to Amit Kumar Sharma for conducting TEM measurements at the Institute Instrumentation Center, IIT Roorkee. SS would like to acknowledge the SERB IRPHA Grant (IPA/2021/000096).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5tc00498e

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