Letter pubs.acs.org/JPCL
Cite This: J. Phys. Chem. Lett. 2019, 10, 2745−2752
Role of Quantum Confinement in 10 nm Scale Perovskite Optoelectronics Hoon Ryu,*,† Seokmin Hong,‡ Han Seul Kim,† and Ki-Ha Hong*,¶ †
J. Phys. Chem. Lett. Downloaded from pubs.acs.org by UNIV OF TECHNOLOGY SYDNEY on 05/13/19. For personal use only.
National Institute of Supercomputing and Networking, Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea ‡ Center for Spintronics, Korea Institute of Science and Technology, Seoul 02792, Republic of Korea ¶ Department of Materials Science and Engineering, Hanbat National University, Daejeon 34158, Republic of Korea ABSTRACT: Quantum confinement-driven band structure engineering of metal halide perovskites (MHPs) is examined for realistically sized structures that consist of up to 105 atoms. The structural and compositional effects on band gap energies are simulated for crystalline CH3NH3PbX3 (X = I/Br/Cl) with a tight-binding approach that has been well-established for electronic structure calculations of multimillion atomic systems. Solid maps of band gap energies achievable with quantum dots, nanowires, and nanoplatelets concerning sizes, shapes, and halide compositions are presented, which should be informative to experimentalists for band gap designs. The pathway to suppress band gap instability that appeared in mixed halide perovskites is proposed, revealing that the red shift induced by halide phase separation can be hugely diminished by reducing sizes and adopting halides of lower electronegativity. Our modeling results on finite MHP structures of over 10 nm dimensions show a blueprint for designs of stable lightemitting sources with precisely controlled wavelengths.
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compositions of halide mixtures,20,22−25,32,33 opening the possibility for band gap tuning to wavelengths in a visible spectrum. Band gap tunability coupled to structural and compositional variations, however, is still one of the focal research topics for MHPs because experimental efforts have explored either only box-shaped colloid quantum dots (QDs)20 or a few selected cases of bulk halide mixtures in terms of composition ratios and halide types.22,23,25 There is no doubt that the reported DFT studies27−31,34 presented distinguishing theoretical backgrounds for MHPs. Their modeling scopes however are not broad enough to cover structural and compositional variations due to the size limit of simulations. Solid understanding of band energy fluctuations driven by structural and compositional variations can be accelerated with simulation-based studies that can consider realistic conditions of physical samples because they can explore a wide range of supercell geometries and materials that is hard to completely cover with experimental efforts. An atomistic tight-binding (TB) approach, which is well-established to extend the scope of electronic structure simulations to solid structures of physically realizable dimensions that include up to several million atoms,35−37 has been extensively adopted to explain experimentally observed effects of structural and atomic variations on material properties.38−43 Boyer-Richard et al. proposed a set of TB parameters that reasonably match a DFT-
etal halide perovskites (MHPs) have attracted tremendous interest since they were successfully used to implement cost-efficient solar light absorbers for photovoltaic cells.1−4 Recently, MHPs were adopted in various optoelectronic applications such as light-emitting diodes (LEDs),5−8 lasers,9,10 and photodetectors11,12 due to their excellent photoelectronic properties. MHP-based optoelectronic devices have shown promising behavior even though they can be made with cheap processes due to the unique characteristics of MHPs such as defect immunities13−15 and strong Rashba spin−orbit couplings.16−18 Since Friend group has reported MHP LEDs operating at room temperature (RT) using 3D organic−inorganic hybrid lead halide perovskites,8 there has been rapid progress in both efficiency and stability.19 MHP has several advantages as a light-generating material, including flexible band gap tunabilities (400−800 nm), high quantum yields, and narrow emission bands (20%) is mixed.49,50 As such, a cubic phase is assumed for all of the supercells, which have 76−108 000 atoms depending on their shapes and dimensions. A TB theory normally needs a set of parameters to describe electronic structures of atomic systems, which have to be fit to reflect critical properties of band structures understood by experiments or ab initio theories. Adopting an sp3 TB model that employs eight localized orbital bases to represent a single atom with spin− orbit couplings, we model MAPbI3 with the parameters reported by Boyer-Richard et al.37 For X = Br/Cl, we tune the parameters proposed by Ashhab et al.44 to match bulk band gaps and offsets that are known experimentally.25 Figure 1b shows band gaps and offsets of bulk MAPbX3 that are obtained with the parameters used in this work. For those who are interested in the methodological details of TB simulations, we note that the work of Boyer-Richard et al.37 presents details of the atomistic representation of a single MAPbX3 cubic uc based on an eight-band sp3 TB model. Details of the atomic representation of Hamiltonian matrices of nanostructures, which in principle can be done with block matrices that represent a single uc and its coupling to neighboring ucs, can be found in the work of Rahman.51 The size of a TB Hamiltonian matrix describing a supercell that we want to model is proportional to the number of atoms included in the supercell. The computing load required to diagonalize largescale Hamiltonian matrices is efficiently distributed into multiple processors with parallel computing in our in-house code,52,53 which this work uses to solve large-scale Schrödinger equations that represent over 10 nm scale finite MHP supercells. Confinement effects on band gap energies are explored with MAPbX3 supercells consisting of homogeneous halide atoms. In Figure 2a, we present maps of band gap energies as a function of halide types and confinement sizes, where energies are represented as wavelengths (in a nm unit) to easily correlate them with the color spectrum of visible light that is included as an inset in each subfigure. Confinement sizes are
calculated bulk band structure of methylammonium lead iodide (MAPbI3) near band edges,37 opening the possibility to use a TB theory for large-scale electronic structure simulations of MHPs. Ashhab et al. extended the scope of TB simulations to methylammonium lead bromide (MAPbBr3),44 where the effects of atomic disorders in mixed halides (MAPbIxBr3−x) on band structures are explored for supercells consisting of up to 8 × 8 × 8 cubic unit cells (ucs) (2048 atoms). Most recently, Marronnier et al. studied the Rashba effect in black phases of bulk cesium lead iodide (CsPbI3) by computing band structures of small supercells with periodic boundary conditions.45 This work uses TB simulations to uncover band gap behaviors of realistically sized, confined MAPbX3 (X = I/Br/Cl) structures that have not been well-understood yet. We rigorously investigate the effects of structure and composition engineering on band gap energies and validate our modeling approach by presenting sound connections to the experimental works20,22−24 done for bulk-size samples. Band gap instability, a well-known issue that appears in mixed halide perovskites due to phase separation,22,23,33,46−48 is also studied, and strategies to increase the stability are elaborately proposed. To our knowledge, this is the first modeling study that focuses on optical properties of over 10 nm scale finite MHP structures. Figure 1a illustrates physical structures of supercells that are considered in this work. To explore the effects of structural engineering on band gap energies, we choose the four supercell geometries, i.e., cube- and sphere-shaped QD supercells, nanowire (NW) supercells of a square cross section that are assumed to be periodic along the transport direction ([100]), and nanoplatelet (NP) supercells that are assumed to be periodic along nonconfined directions ([100]/[010]). The confinement size (indicated with L in the insets of Figure 1a) is varied from 3 to 30 ucs. NW/NP supercells are 3 ucs thick along periodic directions. MAPbX3 MHPs tend to be in a cubic Pm3m phase at RT when X = Br/Cl.49 Though MAPbI3 is in a tetragonal phase at RT, the phase changes to Pm3m when Br 2746
DOI: 10.1021/acs.jpclett.9b00645 J. Phys. Chem. Lett. 2019, 10, 2745−2752
Letter
The Journal of Physical Chemistry Letters
Figure 2. Band gap energies of MAPbX3 supercells. (a) Band gap energies are plotted as a function of confinement sizes of the four types of supercells, where energies and sizes are shown with an unit of wavelengths (nm) and a number of ucs, respectively. A color spectrum of visible wavelengths is included as an inset of each subfigure to show the range of colors that is achievable with size and structural engineering. For MAPbI3 QDs, the entire range of visible wavelengths is achievable with size engineering. MAPbBr3 QDs are considerable to design violet-to-green light sources. As sphere QDs are most severely affected by structural confinements, they show smaller wavelengths compared to supercells of other shapes. (b) Using bulk band gaps as baselines, we see that sphere QDs invoke wavelength shifts comparable to or larger than a ballpark value (∼20 nm) of experimentally observed emission bands (refs 21 and 24) even at a 30 ucs confinement size (18−20 nm). For MAPbBr3, which generally shows smaller band gap shifts than other materials, cube QDs and NWs show over 20 nm band gap shifts at confinement sizes smaller than 19 and 15 ucs (11 and 9 nm), respectively.
supercells of other geometries, already show band gap shifts of 19−47 nm at a confinement size of 30 ucs (18−20 nm). Cube QDs and NWs generally exhibit smaller shifts than sphere QDs due to weaker confinements, such that for MAPbBr3, which shows smaller band gap shifts than other materials, cube QDs and NWs lose bulk characteristics (exhibiting over 20 nm shifts) at confinement sizes smaller than 19 and 15 ucs (11 and 9 nm), respectively. To understand how compositional variations of halide mixtures affect band gap energies of confined supercells, we perform another set of simulations for cube QDs with the three possible binary mixtures, i.e., I−Br, Br−Cl, and I−Cl, where the effects of random placements of halide atoms at the same composition ratio are explored as follows: (1) 100 cases of random placements are simulated per every combination of a single composition ratio and confinement size. To configure random atomic placements in halide mixtures for simulations, we first fill the simulation domain with ucs of a single type of halide atom. The second halide atoms are then incorporated into the domain by replacing the first atoms with a probability that is equal to the composition ratio given as one of the input
described with a number of ucs because the literature presents different constants for MAPbX3 cubic lattices.27,34 The bulk band gaps for X = I, Br, and Cl are 774, 539, and 401 nm, respectively, and they are shown as baselines with red dotted lines in the three subfigures of Figure 2a. Confinements reduce wavelengths (increase energies) such that band gaps of MAPbI3 supercells can be controlled to 375−773 nm with size engineering, covering the entire range of a visible spectrum. MAPbBr3 supercells have band gaps of 313−539 nm; therefore, they could be considered for designs of violetto-green light sources. MAPbCl3 supercells show band gaps of 196−400 nm, and achievable wavelengths are almost out of the visible spectrum. Confinement effects on band gaps can be looked into in more detail with Figure 2b, where we quantified confinement-driven wavelength shifts with respect to bulk band gaps. Taking 20 nm, which is a ballpark value of physically demonstrated emission bands,21,24 as a criterion to determine whether confinement effects can be ignored, we see that bulk-like characteristics cannot be found even from supercells of over 10 nm confinement sizes. Sphere QDs, which are more severely affected by confinements than 2747
DOI: 10.1021/acs.jpclett.9b00645 J. Phys. Chem. Lett. 2019, 10, 2745−2752
Letter
The Journal of Physical Chemistry Letters
Figure 3. Effects of halide mixtures on band gap energies. Band gap energies of (a) MAPbI3Br3−x, (b) MAPbBr3Cl3−x, and (c) MAPbI3Cl3−x cube QDs are presented as a function of composition ratios and confinement sizes (ucs). Each subfigure has two curves. The one with blue circles shows the result obtained when halides are completely segregated. The other with red circles shows the result of uniformly mixed cases, where the error bar placed on top of each circle indicates wavelength variations stemming from random placements of halide atoms (100 cases of random atomic configurations are simulated per each composition ratio). With no consideration of extremely segregated cases, random atomic placements in mixtures do not drive remarkable fluctuations in band gap energies when QDs are large, while fluctuations increase up to ∼20 nm as QDs become smaller. Considering extremely segregated cases together, however, we find that size miniaturization of QDs remarkably reduces the red shift caused by halide segregations regardless of halide types. When the QD size is fixed, the red shift can be reduced further if QDs have more halide atoms of lower electronegativity.
parameters. Though simulations here should be able to describe the effects of random atomic placements to a certain extent, 100 cases may not be large enough to cover the cases where two halide atoms are remarkably segregated unless supercells are extremely small. (2) We thus perform another single simulation to cover the extreme case where two halide atoms are completely segregated, forming a heterojunction-like structure. Simulation results of I−Br, Br−Cl, and I−Cl mixtures are shown in Figure 3a−c, respectively, where lines with red and blue empty circles in each subfigure show the result of 100 random cases and a completely segregated case, respectively. A vertical error bar is placed on top of each red circle to indicate wavelength fluctuations caused by random placements of halide atoms. If we focus on 100 random cases, which show the effects of random placements of halide atoms when the uniformity of halide mixtures is not significantly broken, the band gap sensitivity is not quite remarkable in large QDs. It however becomes stronger in smaller supercells; therefore, band gap energies fluctuate up to ∼20 nm regardless of halide atomic species when the confinement size reaches 5 ucs. In reality, the uniformity of halide mixtures is hardly maintained because halides tend to be strongly segregated,
causing a non-negligible red shift particularly when samples are exposed to light. The dashed lines with blue empty circles in Figure 3a−c, combined with the results of random halide distributions, confirm that segregation of halide atoms reduces band gap energies regardless of supercell sizes and halide species. In particular, the results of 30 × 30 × 30 uc QDs of I− Br mixtures (the rightmost subfigure of Figure 3a) are wellconnected in a qualitative manner to the experimental works that also reported light-induced phase separation in bulk-size MHP samples of I−Br mixtures.22,23,33,46 In addition, our results reveal two more messages that can be used as nice strategies to suppress the red shift. First, the red shift caused by halide segregations can be hugely reduced with size miniaturization of supercells; therefore, the segregated case shows a 0.04−7.63% red shift against the average value of the uniform cases at the same composition ratio in 3 × 3 × 3 uc QDs, while the amount of this shift jumps to 3.95−22.62% in 30 × 30 × 30 uc QDs. Next, even at the same confinement size, the red shift reduces as QDs contain more halide atoms of lower electronegativity. It should be noted that suppression of phase separation, which is also a critical research topic and has been experimentally demonstrated by controlling defect densities and grain sizes in MHP films,47,48 is not the reason 2748
DOI: 10.1021/acs.jpclett.9b00645 J. Phys. Chem. Lett. 2019, 10, 2745−2752
Letter
The Journal of Physical Chemistry Letters
electronic states close to band edges of APbBr3 do not have a significant dependency on the species of an A cation.29,37 Here we carefully want to mention that the result in Figure 5a could serve as a minimal clue to show the possibility that exchange interactions may not hugely affect band gaps of confined nanostructures as the connection to experiment is strong even though the calculated band gap energies do not take into account the effects of exchange energies. Solid connections between modeling and experiments can be also found for halide mixtures. Figure 5b-i,ii shows the photoluminescence (PL) spectra that are reported for the bulksize MAPbI0.3Br2.7 (I = 10%) and MAPbI1.3Br2.7 (I = 43%) samples, respectively, by previous experimental works.22,23 Light-induced phase separation affects both samples; therefore, PL peaks move to lower energies as time elapses upon illumination. In Figure 5b-iii, experimental data are compared to the band gap energies calculated for 30 × 30 × 30 uc cube QDs (the rightmost subfigure of Figure 3a), where it is assumed that energetic positions of PL peaks would not be hugely different from band gap energies. Green and magenta boxes indicate the two PL peak positions when I = 10 and 43%, respectively. Error bars show the full width at halfmaximum (FWHM) of each PL peak. Here, the deviation between measured and simulated PL peak position is less than 50 nm for both samples and becomes even smaller if FWHM’s are taken into consideration. Because the measured PL peaks appear at 535/683 nm (I = 10%) and 656/757 nm (I = 43%), our results can be regarded to be quite accurate, giving inaccuracy less than 10% for the measured data. Figure 5c-i shows the PL spectra that are experimentally obtained for the bulk-size MAPbIxBr3−x and MAPbIxCl3−x samples,24 where the composition x’s are unknown in both cases. By comparing experimental data to our results (in Figure 5c-ii,iii, which correspond to the rightmost subfigures of Figure 3a,c, respectively), we find that MAPbIxBr3−x and MAPbIxCl3−x samples include ∼35 and ∼70% of I, respectively, and that the experimental PL peaks would not be obtainable unless halides are segregated in both cases. We can therefore conclude that the MAPbIxBr3−x sample in ref 24 already experiences halide segregation. It is however worthwhile to note the I−Cl segregation in the sample could be due to its chemical nature rather than phase separation because it was reported that I−Cl tends to be hardly mixed.54,55 In summary, the role of quantum confinement in band gap energies of 10 nm scale MHP structures has been investigated with confined MAPbX3 supercells (X = I/Br/Cl). An eightband sp3 TB model has been used to set the target of electronic structure calculations to realistically sized supercells that are in principle hard to handle with DFT simulations. Taking sizes and shapes as the engineering factor, we have presented maps of theoretically achievable band gap energies for confined structures of various geometries. The effects of halide mixtures on band gap energies, an issue of huge interest due to the possibility for fine control of the characteristic wavelength of light-emitting devices, has been also rigorously examined. Simulation results deliver the range of band gap energies that can be achieved with confined structures and, more remarkably, reveal a pathway to suppress the red shift induced by halide phase separation with size and composition engineering, proposing the possibility to synthesize MHPs that are robust to the red shift induced by phase separation. Finally, our modeling approach has been validated with solid
for the two above-mentioned messages. The nontriviality of these messages is that they propose a pathway to increase the band gap stability with aids of size and composition engineering under the existing phase separation. The advantage of our messages in view of material designs can be explained more clearly with an example given in Figure 4, which shows
Figure 4. Driving robustness to the red shift with size and composition engineering. Robustness to the red shift induced by halide phase separation can be increased with size and composition engineering. An example case used for explanation is a 580 nm band gap MAPbIxBr3−x cube QD. At a confinement size of 30 ucs, the target can be designed with ∼25% of I (B1). However, the red shift induced by phase separation (B1 → B2) is ∼115 nm, which is almost 20% of the desired band gap. Another way to get the target QD would be to increase the composition of I to 60% with a size reduction to 10 ucs (A1), and this case shows a ∼30 nm red shift (A1 → A2) that is ∼4× smaller than the previous result.
band gap fluctuations in MAPbIxBr3−x cube QDs whose confinement sizes are 10 (left) and 30 ucs (right). Here, a 580 nm band gap energy, the target wavelength of interest, can be achieved with ∼25% of I at a confinement size of 30 ucs (marked as B1 in Figure 4). The red shift induced by phase separation (B1 → B2), however, becomes ∼115 nm, which is almost 20% of the desired band gap. Another way to get the target wavelength would be to increase the composition of I to 60% with a QD size reduction to 10 ucs (A1), and the red shift in this case is just ∼30 nm (A1 → A2), which is about 4× smaller than the previous case. Now we move the point of discussion to validation of modeling results with detailed analyses coupled with recent experimental studies.20,22−24 The first connection is presented in Figure 5a, where we compare the dependency of band gap energies on confinement sizes of MAPbBr3 cube QDs to the experimental result reported for CsPbBr3 colloid QDs.20 Here, the modeling (solid line with red empty circles) and experimental (black filled square) results show almost identical behaviors, where the maximal deviation of wavelengths at the same confinement size turns out to be just ∼3.5 nm, which is
