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

Recently, layered hybrid perovskites have been attracting huge interest due to a wide range of possible chemical compositions and the resulting tunability of the materials properties. In this study, we investigate the effect of the chain length of the organic ligands on the optical properties of stacks of two dimensional perovskite layers consisting of alkylammonium lead iodide (CnH2n+1NH3)2PbI4 with n=4-18. Photoluminescence and absorption spectroscopy reveal a blueshift with increasing chain length n including a jump of 110 meV between the n=10 and n=12 ligands due to a change in octahedral tilting. Using Xray diffraction (XRD) we determine the crystal structure and find the octahedral tilting to be the main cause of this blueshift. However, for very short chain lengths additional effects further reduce the transition energy. Results of effective mass approximation model calculations show good agreement between the expected reduction of transition energy and measured photoluminescence emission wavelength for these samples. This highlights how octahedral tilting plays a major role in determining the optical bandgap and suggests that miniband formation plays only a minor role in this material.


Introduction:
Perovskites possess an intriguing crystal structure showing many interesting properties and effects such as strong optical absorption, ferroelectricity and superconductivity. [1][2][3][4] For the threedimensional (3D) halide variant of the perovskites the general formula of the crystal structure is ABX 3 , where A and B are monovalent and divalent cations, respectively, and X is a monovalent anion. The B 2+ and Xions 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 cornersharing [BX] 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][8][9] In addition to the 3D perovskites there are several other classes of perovskites, amongst them organic-inorganic layered two-dimensional (2D) perovskites. [10][11][12][13][14][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 A2BX4. 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 (CnH2n+1NH3)2PbI4 will hereafter be abbreviated as CnPbI4 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 1a illustrates the chemical structures of these organic-based perovskite multi-layers. The cornersharing PbI 6 form 2Dmonolayers 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][22][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 PL emission wavelength shows a consistent blueshift with increasing chain length interrupted by a large jump in the blueshift between the C 10 and C 12 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, LB is short enough to allow electronic coupling between layers. The resulting miniband formation leads to the observed decrease of the PL energy.
Results and discussion: For the sample preparation a 1.0 molar C n -ammonium iodide solution in dimethylformamide (DMF) and 0.25 molar 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 materials and methods section. For a first structural analysis X-ray diffraction (XRD) measurements were carried out ( Figure 1b). The analysis of the peaks showed that all samples crystallized in an orthorhombic crystal configuration at room temperature with dominant peaks in the 002 direction where 1,2,3 … . [24][25][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.Åfor C 4 PbI 4 to 31.5Åfor C 18 PbI 4 , in excellent agreement with previously reported values ( Figure 1c). [24][25][26] Using the width of the perovskite layer 6.0Å, the thickness of the organic ligand layer separating the individual perovskite layers lies between 7.6Å(C 4 PbI 4 ) and 25.5Å(C 18 PbI 4 ).
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 Table S1 in the supporting information. 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 ( Figure 1b), 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 n PbI 4 with n varying between 4 and 18 was observed by Billing and Lemmerer [24][25][26] in single crystal X-ray diffraction experiments at the same position as the here observed jump in EPL. This can be seen by plotting both the octahedral tilt angles, which were obtained from these publications [24][25][26] , and EPL against the organic ligand chain length (Figure 2c). 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 EPL (Figure 3a). 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 ( Figure 3b). 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 C8PbI4 and C10PbI4 are above the fit.
Already in the 1990s Mitzi and coworkers 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 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, 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 to 4 times) than in the bulk case, 44 where the effective masses for holes are likely quite similar and approximated to be between 0.1 and 0.2 . 45 Hence, we have chosen mQW* = 0.5me and mB* = 1me, which should constitute a good approximation of the situation found in our case.
The modified band gap energy is given by the formula:

Materials:
First, the precursor salts were obtained by reacting the long-chain amine with HI in slight access to ensure full protonation (ratio of 1.1:1.0). Subsequently, the ammonium salts were dried in the rotary evaporator and washed three times with ethanol. The product were light yellow to white precursor salts. These precursors were dissolved in DMF such that a 1 molar solution was obtained. PbI2 was dissolved in DMF that a 0.25 molar solution was obtained.
Small amounts of the precursor stock solution were mixed in a stoichiometric ratio PbI2 to nammonium iodide 1:2. This mixture was heated to 70°C in an oil bath and drop casted on a glass substrate. The samples were placed on a heat plate at 70°C to ensure full evaporation of the solvent.

Structural analysis:
XRD analysis were performed on a Bruker D8 Advance A25 diffractometer using Cu-Kα (λ=1.52 Å) radiation. The powder diffraction pattern was scanned over the angular range of 2 to 60 (2θ) with a step size of 0.05, at room temperature. The database Mercury 10 with entries from references [24][25][26] was used for data analysis.
For SEM measurements, a Gemini Ultra Plus field emission scanning electron microscope with a nominal resolution of ~2 nm (Zeiss, Germany) was used. The images were collected by the in-lens detector at an electron accelerating voltage of 0.5 kV and a working distance of 1 mm.

Optical characterization:
UV-vis absorption was measured with a Varian Cary 5000 UV-vis-NIR spectrometer. For photoluminescence (PL) measurements the samples were excited with a monochromated Xelamp. PL spectra were taken with a Fluorolog-3 FL3-22 (Horiba Jobin Yvon GmbH) spectrometer equipped with a water-cooled R928 PMT photomultiplier tube mounted at a 90° angle. The excitation wavelength was set to 400nm, excitation and emission slits to 2 nm, and the step size to 0.5 nm. Comparison with other measurements with slit size 1 nm let us conclude that the error is less than +/-1nm, i.e. less than 6 meV.   [24][25][26] in dependence on the hydrocarbon chain length. There is a large jump for both E PL and θ between n10 and n12.