Tuning the optical bandgap in layered hybrid perovskites through variation of alkyl chain length

Perovskites possess an intriguing crystal structure showing many interesting properties and effects such as strong optical absorption, ferroelectricity, and superconductivity.^1–4 For the three-dimensional (3D) halide variant of the perovskites, the general formula of the crystal structure is ABX₃, where A and B are monovalent and divalent cations, respectively, and X is a monovalent anion. The B²⁺ and X⁻ ions form octahedra, with neighboring octahedra sharing corners, consequently spanning a 3D network.^5,6 The A⁺ ion is located in the gaps between 8 such corner-sharing [B₆X]⁴⁻ octahedra. The crystal structure allows for phase transitions, cation displacement, distortions, and octahedral tilt that alter the properties of the material.^1,5,7–9 In addition to the 3D perovskites, there are several other classes of perovskites, amongst them two-dimensional (2D) layered hybrid perovskites.^10–15 In this group, the organic A⁺ ion is too big to fit inside the interoctahedral space, thus prohibiting the formation of the 3D structure. Instead, these perovskites form sheets of corner-sharing octahedra separated by an organic moiety comprised of the organic ligand. The corresponding crystal structure is then given by the chemical formula A₂BX_4. Already in the 1990s, layered perovskites were used for thin-film field effect transistors.^16,17 Recently, layered perovskites have received significant attention, for example, due to their ability to shield and thus increase the stability of 3D perovskite films for solar photovoltaic applications.^18,19

In this study, the general formula of the investigated 2D perovskites is [(R-NH₃)₂PbI₄], where R is an organic alkyl chain. The correct chemical formula (C_nH_2n+1NH₃)₂PbI₄ will hereafter be abbreviated as C_nPbI₄ where n is the number of C-atoms. These structures have long been known to naturally form electronic potentials as known for multiple quantum wells.^11,12,20 Figure 1(a) illustrates the chemical structures of these organic-based perovskite multi-layers. The corner-sharing PbI₆ octahedra form 2D monolayers constituting the quantum wells with the organic ligands forming barriers, separating the quantum wells. In the past, several studies have shown experimentally and theoretically that, in 2D perovskites, the quantum confinement of the electron and hole and thus the emission wavelength can be tuned by varying the thickness of the inorganic part, so effectively the quantum well thickness.^21–23 In contrast, the present study focuses on the systematic variation of the “barrier” length (L_B) achieved through variation of the organic ligand length and its effect on the optical properties of these layered organic-based perovskites. Herein, we synthesize films of such multiple stacked quantum wells. The photoluminescence (PL) emission wavelength shows a consistent blueshift with increasing chain length interrupted by a large jump in the blueshift between the C₁₀ and C₁₂ ligand-based samples. As all samples are found in an orthorhombic crystal configuration, structural phase transitions can be excluded and octahedral tilting can be isolated as a crucial factor determining the emission wavelength. Additionally, remaining discrepancies of optical measurements and tilting angles indicate that, for short ligands, additional effects further lower the PL energy. Effective mass approximation (EMA) model calculations suggest that, for short ligands, n < 12, L_B is short enough to allow electronic coupling between layers. The resulting miniband formation leads to the observed decrease of the PL energy.

For the sample preparation, a 1.0 M C_n-ammonium iodide solution in dimethylformamide (DMF) and 0.25 M lead iodide solution in DMF were mixed in a stoichiometric ratio of 2:1 and were drop casted on a glass substrate. The perovskite crystals formed upon evaporation of the organic solvent. Details can be found in the subsequent paragraphs. For a first structural analysis, X-ray diffraction (XRD) measurements were carried out [Fig. 1(b)]. The analysis of the peaks showed that all samples crystallized in an orthorhombic crystal configuration at room temperature with dominant peaks in the (002l) direction where l = (1, 2, 3, …).^24–26 As can be seen in the figure, the peak to peak distance decreased with increasing organic molecule length. Using Bragg’s law, we determined the octahedron-to-octahedron center-to-center distance between neighboring layers, hereafter referred to as d_Bragg. It was found to increase linearly from 13 Å for C₄PbI₄ to 31.5 Å for C₁₈PbI₄, in excellent agreement with previously reported values [Fig. 1(c)].^24–26 Using the width of the perovskite layer d = 6.0 Å, the thickness of the organic ligand layer separating the individual perovskite layers lies between 7.6 Å (C₄PbI₄) and 25.5 Å (C₁₈PbI₄).

The color of all films was yellow to orange under ambient illumination at room temperature in agreement with previous reports on perovskite monolayers and nanoplatelets.^23–26 To determine whether the ligand had an effect on the optical properties, we recorded absorption and PL spectra for all samples [Fig. 2(a)]. All absorption spectra show the characteristic features of a 2D semiconductor, with a prominent 1s exciton peak and a step-like continuum absorption at shorter wavelengths. The PL spectra of all samples show a single emission peak, with a small Stokes shift of 14–33 meV, indicating excitonic recombination. The PL maximum lies around 521 nm for the films with the shorter hydrocarbon chains (n = 4-10), with a slight blueshift of 2 nm (9 meV) total occurring with increasing ligand length. The PL emission exhibits a blueshift jump of 23 nm (110 meV) between the C₁₀PbI₄ and C₁₂PbI₄ samples, followed by a further gradual blueshift of 5 nm (25 meV) up to the C₁₈PbI₄ perovskite sample. For detailed values, see Table S1 in the supplementary material. Similar jumps in PL and absorption are known from layered hybrid perovskites, which is however induced by a phase transition at high temperatures.²⁷ As shown through the XRD analysis [Fig. 1(b)], all samples here crystallize in the orthorhombic structure, and so a crystal phase transition cannot explain the observed blueshift. However, there can also be structural changes that do not require a phase change, e.g., through a change in the bond angles within the crystal. A correlation between the photoluminescence energy maxima E_PL and bond angles was experimentally observed for related layered perovskite structures.^28–34 Indeed, a jump in Pb–I–Pb bridging angles, hereafter referred to as octahedral tilting, for C_nPbI₄ with n varying between 4 and 18 was observed by Billing and Lemmerer^24–26 in single crystal XRD experiments at the same position as the here observed jump in E_PL. This can be seen by plotting both the octahedral tilt angles, which were obtained from these publications,^24–26 and E_PL against the organic ligand chain length [Fig. 2(c)]. While the jump aligns nicely and a similar trend can be observed for the longer ligands, the shorter ligands deviate considerably. This can be visualized more effectively by plotting the tilt angle directly versus E_PL [Fig. 3(a)]. A linear fit is applied to this graph, with a general correlation between the two parameters: the larger the octahedral tilt, the higher the emission energy [Fig. 3(b)]. Again, for longer chain lengths, the data points arrange nicely on the line, while the shorter ones deviate further from it, indicating an additional effect taking place when the perovskite layers come closer together. The data points of C₄PbI₄ and C₆PbI₄ lie below the fit, while those of C₈PbI₄ and C₁₀PbI₄ are above the fit.

Already in the 1990s, Mitzi and co-workers proposed that the inorganic perovskite layers can be seen as semiconductor quantum wells, with potential wells for both electrons and holes, as confirmed by the absorption spectra. However, one must consider that these quantum wells are extremely thin, at only approximately 6 Å. This leads to a strong blueshift of the energetic bandgap and also to higher exciton binding energies.^21,22,36 These latter values turn out to be larger than that can be expected simply through reduction in dimension. As the exciton is confined in the 2D inorganic layer, the dimension is reduced which leads to an increase of the exciton binding energy of four times the values of the bulk counterpart.²² In addition to this reduction in dimension, dielectric confinement, caused by a significantly lower dielectric constant of the organic moiety compared to the inorganic layer, results in a further increase of the exciton binding energy as not all of the Coulomb interaction is strongly screened by the perovskite layer.¹¹ This leads to binding energies of more than 10 times those of the bulk materials.^11,23 However, if the perovskite quantum wells are brought close enough together, according to the multiple quantum well picture, one can expect an electronic coupling between neighboring quantum wells and can no longer consider them as isolated. In classic semiconductor systems, such as GaAs/AlAs, electronic coupling between quantum wells or superlattice formation is a well-known effect.^37–39 In contrast to an isolated semiconductor quantum well where the energy eigenvalues are discrete and the density of states are step-function like [Fig. 4(a)], in a superlattice, electronic coupling between the quantum wells leads to the formation of a miniband of width 2Δ [Fig. 4(b)], which increases with decreasing quantum well separation. Although the density of states is continuous in the range of the miniband, the charge carriers recombine between the miniband edges. This leads to a transition energy which is smaller than that of an isolated quantum well. In the limit of an infinitely long barrier, the energy levels of the isolated quantum well are recovered. The occurrence of coupling depends on the quantum well potential, effective masses of carriers, quantum well thickness, and barrier length.^40–42 Scanning electron microscopy (SEM) images of the films used in this work confirmed the formation of continuous films with lateral grain sizes varying between several hundreds of nanometers up to micrometers (Fig. S1).

In the aforementioned model, the separate dispersion for electrons and holes can be written as

with

and with the quantization of electron and hole energies E_e(h), the width of the QW and barrier L_QW and L_B, $me(h)QW$ and $me(h)B$⁠, and δ a real parameter, equal to q(L_QW + L_B), where q = ((2πn)/L) with L the length of the lattice. Parameters were set as L_QW = 6 Å, V_CB = 0.9 eV, and V_VB = 2.9 eV.²² L_B, as mentioned before, is calculated by subtracting L_QW from the Bragg distance, d_Bragg − L_QW. The choice of effective masses is difficult due to a lack of experimental values, especially for the 2D case.⁴³ Yet, one can expect the values to be significantly larger (up to 3–4 times) than in the bulk case,⁴⁴ where the effective masses for holes are likely quite similar and approximated to be between 0.1m_e and 0.2m_e.⁴⁵ Hence, we have chosen $mQW*$ = 0.5 m_e and $mB*$ = 1.0 m_e, which should constitute a good approximation of the situation found in our case.

The modified band gap energy $EgSL$ is given by the formula

where E_g^3D is the bandgap energy of the 3D material. The calculated values for $EgSL$ versus the ligand length are depicted in Fig. 4(c). The energy assumes a constant value $EgSL$ = 2.68 eV for all barrier widths L_B from an infinite length down to the equivalent of a ligand length of n = 12. For shorter ligand lengths, we start to see a decrease in the energy, with an exponential dependence down to a value of 2.65 eV for the lowest ligand length applied (n = 4). For infinite barrier spacings, the Kronig-Penney model yields the energy $EgQW$ of an isolated quantum well

The model calculations thus show that for long ligands (n > 11), there is no miniband formation. For shorter ligands, miniband formation occurs, lowering the energy by $ΔE(n)=EgQW−EgSL(n)$ between 2 meV and 28 meV for the ligand lengths of n = 10 and n = 4, respectively. For detailed values, see Table S2 of the supplementary material. These results agree with the findings by Even et al.,⁴³ who predicted miniband formation for n < 12 using lower effective masses (0.3 m_e and 0.75 m_e) and of Ahmad et al. who reported no interlayer coupling for ligand lengths of n = 12.⁴⁶ 

While the trend of our values agrees well with predicted values, the absolute values are still off by a significant margin (2.65 eV–2.68 eV for our values compared with 2.38 eV–2.52 eV for E_PL as obtained in our experiments). This total discrepancy of between 160 meV and 270 meV can be explained by the fact that we are comparing transition energies from PL measurements, for which one also has to consider the exciton binding energy which can reach values in the hundreds of meVs, far greater than the bulk values.^22,23,47 Experimentally, a value of 220 meV for E_B in C₁₀PbI₄ was found, in good agreement with our data and proposed model.²⁰ 

These calculations show that for all samples with ligands shorter than n = 12, the transition energies do not only depend on the tilting angle, but additional effects do play a role. According to effective mass approximation (EMA) model calculations, miniband formation could explain these effects. In order to see the sole dependence of the tilting angle on the PL emission energy, we added the calculated energy drop due to miniband formation ΔE(n) to the experimentally determined energies for the excitonic PL. These artificially decoupled PL energy values are replotted as a function of the octahedral tilt [Fig. 4(d)]. Taking this into consideration, nearly all points lie on a straight line nicely showing a linear dependence of the tilting angle on the transition energy and at the same time strongly suggesting that the observed deviations from this linearity as seen in Fig. 3(a) for n < 12 are due to miniband formation. One must note that Even et al. suggest that the EMA approach might be invalid for ultrathin perovskite layers due to the non-parabolicity of the VB and CB.⁴³ Accordingly, it was suggested that density functional theory (DFT) calculations would be necessary to accurately describe these systems. However, in a recent publication by Traore et al.,³⁵ the data obtained from DFT calculations still show a mismatch with the optical data for the shortest ligands used. Thus, the tilting angle does not seem sufficient to explain the observed shift in the PL emission data. Consequently, we conclude that the transition energies of monolayer perovskites are determined by two factors, the octahedral tilt angle and the degree of miniband formation resulting from electronic coupling between the quantum wells. While only a small effect due to the high effective masses of the charge carriers, it is currently the only proposed model that can explain the deviations observed for the systems comprising the shortest alkyl chains.

In summary, we have investigated the optical transition energies in thin films of inorganic-organic multiple perovskite layers based on (C_nH_2n+1NH₃)₂PbI₄ with the length of the C_nPbI₄ varying from C₄ to C₁₈. All samples were found in an orthorhombic crystal structure conformation, with only a variation in the octahedral tilt angle occurring, dependent on the organic chain length. UV-Vis and PL spectroscopy revealed a blueshift of the optical transition energies with increasing ligand length, with a large jump occurring between the C₁₀PbI₄ and C₁₂PbI₄ samples. Through structure-function analysis, we could identify the octahedral tilt as the dominant factor in this observed shift. Interestingly, for shorter ligands (n < 12), electronic coupling between the perovskite layers likely occurs. The resulting miniband formation is suggested to be the cause of a further reduction of the transition energy by values of up to 28 meV for the C₄PbI₄ sample. These experimental findings highlight the intricate and exciting nature of layered halide perovskite structures and suggest that more studies are necessary to fully understand and apply these highly-complex systems.

See supplementary material for the complete data for PL measurements, crystal structures, octahedral tilt angles, and observed energy shifts from the expected linear trend, and scanning electron microscopy (SEM) images of C₁₀PbI₄ and C₁₂PbI₄ samples.

We would like to thank Dr. Bert Nickel and Janina Römer for helpful discussions regarding X-ray diffraction (XRD). This research was supported by the Bavarian State Ministry of Science, Research, and Arts through the grant “Solar Technologies go Hybrid (SolTech),” by the German Research Foundation (DFG) through the Excellence Cluster “e-conversion,” by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programm (Grant Agreement No. 759744 - PINNACLE), and by LMU Munich’s Institutional Strategy LMU excellent within the framework of the German Excellence Initiative.