Keywords

1 Introduction

Halide perovskites are exciting materials for light-harvesting [1,2,3] and light-emitting [4,5,6] applications. Their success foots on the large absorption coefficient, high charge-carrier mobility, high photoluminescence (PL) quantum yield (QY), and cost-effective synthesis [1,2,3,4,5,6]. Further, the emission color from halide perovskites can cover the entire UV-visible-near infrared spectrum, which emanates from different band-gaps induced by changing the halogen compositions in the material [4,5,6]. Interestingly, these properties of halide perovskite are maintained irrespective of their size. Such attributes make halide perovskites highly promising semiconductor materials that can compete with the existing silicon technology for solar cells and quantum dot (QD) technology for light-emitting devices and displays. In addition to the chemical and physical stability of perovskites, the generation, stabilization, and binding energy of charge-carriers in these materials are also fundamental aspects to be considered for such device applications.

Charge-carrier dynamics in halide perovskites are complicated by the coexistence of bound electron-hole pairs (excitons) and free charge-carriers [7,8,9,10,11]. The coulombic binding between an electron and a hole in an exciton can be strong or weak, depending upon the exciton binding energy (Eb). Weakly and strongly bound excitons in semiconductors are shown schematically in Fig. 11.1. Weakly bound excitons are called Mott-Wannier excitons (Fig. 11.1a), where low Eb results in the larger delocalization of electron-hole pair, resulting in exciton Bohr radius (RB) much greater than the lattice constant (a) of the material. On the other hand, strongly bound exciton with high Eb is called Frenkel exciton whose RB is much smaller than the a of the material (Fig. 11.1b). In halide perovskites, Eb lies in between those of Mott-Wannier and Frenkel excitons and is either less than or comparable to the thermal energy. Hence, free charge-carriers dominate in the films and bulk single crystals of these materials. Studies have shown that the free charge-carriers are the consequence of dissociation of excitons when the associated binding energy is overcome by the thermal energy [8,9,10,11,12]. The free charge-carrier property of halide perovskites is associated with long carrier diffusion lengths and lifetimes, as observed in the case of bulk films and single crystals [2, 3]. Nevertheless, the carrier lifetime varies in the range of sub-nanoseconds to microseconds in different types of halide perovskites, depending upon their size, dimensionality, and composition [2, 3, 8,9,10,11,12,13,14,15].

Fig. 11.1
figure 1

Weakly and strongly bound excitons in semiconductors. a Mott-Wannier type and b Frenkel type excitons, where RB is exciton Bohr radius, a is lattice constant, and Eb is exciton binding energy

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Exciton binding energies in perovskite nanocrystals (PNCs) are higher than the corresponding bulk crystal. For example, Eb of 320 meV is reported for MAPbBr3 (MA = methylammonium, CH3NH3+) nanocrystals, which is more than three times higher (84 meV) than that for the corresponding bulk crystal [16]. Therefore, quantum confinement effects are observed in PNCs as well, when their physical size becomes smaller than the corresponding RB values [13, 15]. Additionally, the quantum confinement effects in PNCs are depended upon not only the size but also the dimensionality. For instance, blue-shift in absorption and PL spectra, which is associated with the increase in optical band-gap, is observed in the case of perovskite nanoplatelets when the layer thickness decreases below RB [15]. Despite the quantum confinement effects in PNCs, when compared to the conventional chalcogenide QDs, slow cooling and efficient extraction of hot carriers are reported in their colloidal solutions [17]. The intrinsic phonon bottleneck and Auger heating effects at low and high carrier densities, respectively, in PNCs account for such observations. Apart from this, the excellent optoelectronic properties of PNCs, which are comparable to the conventional QDs, are maintained even at the weak quantum confinement regime. While RB in lead halide perovskites lies in the range of 2–7 nm [13, 15, 16, 18, 19], most of the studies demonstrating the light-emitting [4, 6] and photovoltaic [17, 18] applications of PNCs show the nanocrystal size either only slightly smaller or larger than the corresponding RB value. This suggests that, compared to the chalcogenide QDs, the application of PNCs in light-harvesting and light-emitting device is diverse and immense.

2 Photoluminescence Blinking

In quantum-confined semiconductor nanocrystals or QDs, the photogenerated electrons and holes are strongly correlated. Carrier dynamics in such strongly confined QDs is governed by the discrete energy states showing sharp excitonic band in the absorption spectrum, fast radiative recombination of charge-carriers, carrier multiplication or multi-exciton generation, and increased Auger recombination [20]. Moreover, the PL properties of these semiconductor nanocrystals at their single particle level are often intricated by the stochastic emission behavior with a sequence of bright ‘ON’ and dark ‘OFF’ events known as PL intermittency or blinking. This is attributed to the random charging by photoionization and neutralization or discharging of the QD. The blinking behavior in QDs is often described as A-type and B-type [21]. In A-type blinking, the ‘OFF’ state is associated with the decrease in PL lifetime, whereas the carrier-recombination rates are not affected by the ‘OFF’ or the ‘ON’ states in B-type blinking. The short PL lifetime observed during the ‘OFF’ state in A-type blinking is attributed to the formation of a charged excitonic state called a trion (X−) which promotes the mono-exponential nonradiative Auger-type carrier recombination in QDs. On the other hand, B-type blinking mostly depends on the activation and deactivation of the traps or its recombination centers which leads to the ‘ON’ and ‘OFF’ states, respectively.

Apart from the QDs, diverse stochastic emission behavior has been observed in the case of perovskite single nanocrystals, microcrystals, and thin films [22,23,24,25,26,27]. Some perovskite single-emitters have shown blinking with two-state fluctuations between ‘ON’ and ‘OFF’ events [24, 25, 27], which is similar to the case of chalcogenide QD and is ascribed to the process of photocharging and neutralization. Semiconductor nanocrystals or QDs show various interesting optoelectronic properties in the isolated forms. On the other hand, multi-state PL blinking has also been reported from the nanocrystals, microcrystals, and films of lead halide perovskite [22, 23, 26]. An early report on PL blinking in MAPbI3 PNCs and microcrystals has shown that the chemical and structural properties of material are responsible for the multi-state stochastic emission behavior [22]. This is explained through two mechanisms, namely the quenching-site and the emitting-site model, which is shown in Fig. 11.2. In emitting-site model, as shown in Fig. 11.2a, the emitters are at the either end of the nanocrystal which randomly get charged and discharged leading to the ‘ON’ and ‘OFF’ states, respectively. Quenching-site model (Fig. 11.2b) considers the whole nanocrystal as an emissive site, where the emission localization position and center of the nanocrystals lie at the same point. Quenchers in quenching-site model act as traps which are present at the either end of the nanocrystal and deactivate the electrons and holes during the diffusion, resulting in the ‘OFF’ state. An interesting behavior of PL blinking in lead halide perovskites is that, unlike lead chalcogenide QDs, the multi-state PL fluctuations in these semiconductor materials is suppressed under high-intensity of excitation, which on the other hand becomes more intense at low-intensity of excitation. Figure 11.3a shows the excitation laser intensity-dependent PL blinking in MAPbI3 PNCs at the ambient environment. The suppression of PL blinking in such perovskite samples at high-intensity excitation is attributed to the decrease in efficiency of active quenchers to trap large number of charges. Alternately, more emitting sites are generated at high-intensity excitation, resulting in the averaged PL intensity over many emitting sites. Nevertheless, as shown in Fig. 11.3a(i) and b(i), photobleaching cannot be ruled out at high-intensity excitation under the ambient atmosphere [22, 25, 27].

Fig. 11.2
figure 2

Reproduced with permission from Ref. [22]. Copyright 2015, American Chemical Society

Models of PL blinking in lead halide perovskites: a Quenching-site model and b emitting-site model.

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Fig. 11.3
figure 3

Reproduced with permission: (a) from Ref. [22]. Copyright 2015, American Chemical Society. (b) From Ref. [25]. Copyright 2019, Wiley-VCH

Excitation intensity- and local environment-dependent PL blinking in lead halide perovskites. a PL blinking in MAPbI3 PNCs under increasing intensity of the excitation laser: (bottom) 0.01 to (top) 0.5 Wcm−2. b PL blinking in MAPbI3 PNCs (i, iv) in air (ii) under continuous argon purging, and (iii) in polymer matrix

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3 External Factors Affecting the Photoluminescence

Importantly, different environmental factors such as moisture, nitrogen, oxygen, polymer, and light have shown variable results on the PL properties of perovskites at their single particle level [24, 27]. The PL blinking trajectories of MAPbI3 nanocrystals at different local environment are shown in Fig. 11.3b. For example, different roles of oxygen on the PL properties of lead halide perovskites have been reported for different types of perovskite samples [22, 25, 27]. While PL brightening was observed as the consequence of photoinduced trap-filling in the case of MAPbI3 PNCs in presence of oxygen [22], PL bleaching was reported in CsPbI3 perovskite QDs under the similar environment [27]. Recently, a study carried out at the single particle level in MAPbI3 PNCs under air, argon, and polymer matrix (Fig. 11.3b) reveals its PL degradation mechanism [25]. The PNCs degrade or photobleach under the air atmosphere, whereas the PL intensity remains constant under the argon and the polymer atmosphere. The photostability of a PNC under the argon or the polymer atmosphere is the result of low reactivity of oxygen with the nanocrystal during its ‘ON’ state. Interestingly, as shown in Fig. 11.3b(iv), a recovery of PL intensity level is observed even at the air atmosphere after the long ‘OFF’ event, suggesting that there was no degradation of PNCs during the long ‘OFF’ duration that involves nonradiative recombination. Alternately, the PL degradation at the air atmosphere when the PNCs were more frequently in the ‘ON’ state or with the long-living ‘ON’ duration can be ascribed to the oxidation of nanocrystals by the generation of superoxide, which is discussed schematically in Fig. 11.4. Here, the neutral and ionized states are responsible for the ‘ON’ and ‘OFF’ events in the PL blinking trajectories of PNCs. When the nanocrystal is in excited state, it can either oxidize and transfer electron to the oxygen present in the atmosphere generating superoxide or get ionized. The generated superoxide can take the vacancies of the anion and deprotonate the methyl ammonium cation, thereby slowly degrading the PNCs. On the other hand, when the nanocrystal is in the ionized state, nonradiative recombination becomes faster than the electron transfer, and the reactivity of oxygen is suppressed during the long ‘OFF’ duration. In such ON-OFF dynamics and oxidation/antioxidation processes, the excitation light intensity plays a crucial role on the density and fate of charge-carriers. Apart from this, the confinement or diffusion of locally generated multiple charge-carriers depends upon the particle-particle interaction.

Fig. 11.4
figure 4

Reproduced with permission from Ref. [25]. Copyright 2019, Wiley-VCH

Oxidation in perovskite. Schematic representation of the PL blinking and the degradation of the MAPbI3 PNCs.

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4 Carrier Migration in Perovskite Assemblies

When semiconductor nanocrystals or QDs are assembled into a superlattice, their individual properties transform to produce more unique optical, electronic, and thermal properties. This arises from the interaction between the individual particles in the assembly [28,29,30]. In a superlattice, when the QDs are very close to each other, the interaction between their electronic wavefunctions increases. At a point, when the inter-particle spacing is too short, the discrete energy states of individual nanocrystals or QDs split to form minibands. As the result, long-range energy and charge transport in these superlattices through these bands become possible [30]. Strong electronic coupling and the formation of minibands as a function of inter-particle distance in semiconductor nanocrystal superlattice is shown schematically in Fig. 11.5. Such properties of QD superlattice are highly applicable in electronic, optoelectronic and thermoelectric devices [30, 31]. Since the pioneering work of Bawendi and coworkers on chalcogenide QD superlattices [28], many researchers have carried out a successful coupling of QDs and migration of energy or excitons among them in their two- or three-dimensional superlattice structures [31,32,33]. Exciton diffusion is observed in a highly ordered CdSe QD superlattice with center-to-center distance less than 7 nm between the adjacent QDs [32]. In such QD superlattices, the exciton diffusion length as longer as 125 nm is reported. A faster exciton diffusion among highly interacting QDs can result in a faster exciton decay, which is attributed to the larger number of traps or defect sites on different QDs that the excitons may encounter within their lifetime. Besides, a highly ordered QD superlattice can result lower PLQY when compared to the disordered films and colloidal QD samples. This is ascribed to the faster energy transfer among closely-packed QDs. Similarly, directional transport of excitons is observed in long-range ordered and strongly coupled binary nanocrystal superlattice of PbSe consisting of two different sizes [33]. The surface-to-surface inter-particle spacing in such QD array can be reduced further by ligand exchange which results in the ultrafast exciton decay within few picoseconds, showing strong electronic coupling between QDs.

Fig. 11.5
figure 5

Scheme showing strong electronic coupling and the formation of minibands in semiconductor nanocrystal superlattice

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In a QD superlattice, the coupling energy between the individual QDs is much smaller than the exciton binding energy. Therefore, the excitons do not dissociate into free charge-carriers in the superlattice, rather they diffuse or hop and undergo ultrafast recombination, or the nonradiative energy transfer takes place among the closely-packed QDs. On the other hand, if the inter-particle distance between the QDs is very small (for example, center-to-center distance <1 nm), it induces sintering and straining of QDs, leading to increased disorder [29, 32]. Owing to these limitations of QD solids, a superlattice of semiconductor nanocrystals where long-range diffusion of free charge-carriers, which is associated with delayed recombination, is largely required for their efficient applications in solar cells; and the organic-inorganic hybrid lead halide perovskites are promising candidates for this purpose.

Organic-inorganic hybrid PNCs (Fig. 11.6a) when assembled into close-packed film (Fig. 11.1c inset) show unexpectedly delayed PL (Fig. 11.6b, c, and d) under low-intensity excitation [34, 35], which are comparable to the free carrier recombination in single microcrystals and bulk films of perovskites [2, 3, 7, 14]. For instance, a PL lifetime >900 ns is observed for MAPbBr3 PNC film [34], which becomes much longer (>4 μs) in the case of FAPbBr3 (FA = formamidinium,CHN2H3+) perovskite nanocrystal PNC film [35]. Under the increasing excitation intensity, the radiative recombination becomes extremely fast, resulting in amplified emission. The excitation intensity-dependent PL decay profiles of MAPbBr3 PNC film and the temporally and spectrally resolved photocount maps of FAPbBr3 PNC film are shown in Fig. 11.6b, and d–g, respectively. The fast PL lifetimes at higher intensities of excitation are associated with the exponential rise in the number of photons emitted by the PNC film, which is discussed in Fig. 11.6c. On the other hand, a fast PL is obvious in the case of isolated PNCs in their colloidal solution, irrespective of the intensity of excitation. These observations point toward the long-range migration of excitonically unbound charge-carriers at low-intensity excitation and spatial confinement of these charge-carriers at higher intensities in PNC films. The amplified emission can be assigned to the radiative recombination of high-density electrons and holes that are generated and spatially confined among the close-packed PNCs in the film [34, 35].

Fig. 11.6
figure 6

Reproduced with permission from Ref. [34]. Copyright 2019, American Chemical Society

Excitation intensity-dependent PL and charge-carrier properties of PNC films. a TEM image of MAPbBr3 PNCs. The scale bar is 20 nm. b PL decay profiles of a MAPbBr3 PNC film under increasing intensity of excitation laser: (top) 0.0175 to (bottom) 170 MWcm−2. c Plots of the PL lifetime and the number of photons emitted as a function of excitation laser power for a MAPbBr3 PNC film. Inset: MAPbBr3 PNC film under UV light. d–g Temporally and spectrally resolved photocount maps of a FAPbBr3 PNC film with an increase in excitation laser power: d 0.17, e 1.7, f 17, g 170 MWcm−2.

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The dynamics of charge-carriers generated in a PNC film at low- and high-intensity excitations is shown schematically in Fig. 11.7a and b, respectively. At high-intensity excitation, manifold charge-carriers are generated among different PNCs in the irradiated area (Fig. 11.7b). On the other hand, the concentration of photogenerated charge-carriers is less at low-intensity excitation, which reduces the carrier-carrier interactions and allows for the long-range diffusion in the film (Fig. 11.7a). Owing to such a long-range carrier diffusion, PNC films excited with low-intensity laser show unexpectedly delayed PL. On the other hand, the diffusion of photogenerated charge-carriers is spatially confined by increasing the intensity of excitation laser, which is the result of an increase in the carrier concentration. Accordingly, the rate of radiative recombination within the irradiated area controls over the diffusion, providing amplified emission.

Fig. 11.7
figure 7

Reproduced with permission from Ref. [34]. Copyright 2019, American Chemical Society

Diffusion and recombination of charge-carriers in a PNC film a, b Scheme of charge-carrier diffusion and recombination in a PNC film under a low-intensity and b high-intensity excitations. c PL spectra of FAPbBr3 PNC films with different PNC density. The corresponding PL lifetime values are shown in the line-symbol plot. d PL decay profiles of FAPbBr3 PNC films with different PNC density.

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The degree of charge-carrier migration across PNCs in their close-packed assembly (or film) depends upon their packing density [34]. As seen in Fig. 11.7c, the PL spectra of a loose-packed PNC film is blue-shifted, whereas that of a close-packed film is red-shifted. Additionally, as shown in Fig. 11.7c and d, a red-shifted PL spectrum is associated with long PL lifetime. The low-energy photons which are associated with the delayed emission in PNC film point toward the diffusion of charge-carriers through closely-spaced energy states during which some energy is lost, resulting in long-lived low-energy photons. Such delayed PL, as a result of long-range migration of photogenerated charge-carriers, in close-packed assembly of PNCs is a promising property for the harvesting of charge-carriers in high-efficiency solar cells. Indeed, an appreciable rate of electron transfer (3.3 × 106 s−1) is achieved from the photoexcited close-packed assembly of PNCs to fullerene (C60), revealed by the fast PL decay of the PNC film doped with C60, when compared to a pristine film without C60, as shown in Fig. 11.8 [35].

Fig. 11.8
figure 8

Reproduced with permission from Ref. [35]. Copyright 2019, Royal Society of Chemistry

PL decay profiles of a PNC film excited with low-intensity laser (0.0175 µJ/pulse) (red) before and (blue) after doping with C60.

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5 Conclusions

The optical and electronic properties of individual QDs modify when they are arranged into superlattices. The overlapping of QDs electronic wavefunctions in the lattice facilitates the long-range diffusion or hopping of excitons. Due to the high exciton binding energy in strongly quantum-confined systems, the diffusing excitons do not dissociate into free charge-carriers. Thus, the exciton recombination becomes ultrafast, and the isolated semiconductor nanocrystals or QDs show PL blinking. In contrast, metal halide perovskite nanocrystals and QDs arranged into superlattices exhibit long-range carrier migration and delayed radiative recombination. This is analogous to the long-range diffusion of free charge-carriers in bulk perovskites, suggesting a weak confinement of photogenerated electron-hole pairs. The formation of new inter-particle energy states in superlattices of PNCs assist in the diffusion of coulombically uncorrelated electrons and holes. Such freely diffusing electrons are effectively harvested using C60. Therefore, superlattices of PNCs are promising structures for the development of high-efficiency solar cells.