The electronic properties of metal-organic frameworks (MOFs) are increasingly attracting the attention due to potential applications in sensor techniques and (micro-) electronic engineering, for instance, as low-k-dielectric in semiconductor technology. Here, the band gap and the band structure of MOFs of type HKUST-1 are studied in detail by means of spectroscopic ellipsometry applied to thin surface-mounted MOF films and by means of quantum chemical calculations. The analysis of the density of states, the band structure, and the excitation spectrum reveal the importance of the empty Cu-3d orbitals for the electronic properties of HKUST-1. This study shows that, in contrast to common belief, even in the case of this fairly “simple” MOF, the excitation spectra cannot be explained by a superposition of “intra-unit” excitations within the individual building blocks. Instead, “inter-unit” excitations also have to be considered.
Metal-organic Frameworks (MOFs)1 are one of the most intensively studied classes of nanoporous materials. Due to the crystalline MOF structure with very large surface areas2 and its very high diversity3 as well as due to the option of tuning the physical and chemical properties,4 many different applications seem possible, ranging from gas storage, molecular separation, catalysis, and molecular sensing1 to photovoltaics.5 In recent years, the electronic properties of these interesting framework materials have become a research focus.6 So far, the densities of the electronic states and the band structures were theoretically determined for different MOF structures, see, e.g., Refs. 7–13. However, the theoretical results are complemented by experimental data in a few cases only.14,15 The electronic structure of HKUST-1, also known as Cu3(BTC)2 or MOF-199—one of the most popular and most frequently used MOF structures16–19 —has not yet been thoroughly investigated by means of detailed (time-dependent) quantum chemical calculations which are combined with experimental data. HKUST-1 is composed of Cu(II) paddle-wheel-like clusters and BTC (1,3,5-benzene tricarboxylate) linkers and has a face-centered cubic structure. The size of the pore windows is about 0.9 nm.16 In recent studies, HKUST-1 attracted a lot of interest with regard to electronic applications. For instance, by loading the MOF pores with certain guest molecules, like ferrocene20,21 or TCNQ (tetracyanoquinodimethane),22 the conductivity of HKUST-1 can be tuned by many orders of magnitude. By loading the MOF pores with the europium complexes, the porous molecular framework has been shown to act as photonic antenna.23 For gaining a better understanding of the electronic structure in HKUST-1, thin, highly crystalline HKUST–1 films were studied by means of spectroscopic ellipsometry. For high-quality ellipsometry measurements, smooth and defect-free thin films are required. Therefore, thin and homogeneous HKUST-1 films were prepared by a dipping robot equipped with an ultrasonic bath in a layer-by-layer fashion. These thin MOF films are referred to as surface-mounted MOFs, SURMOFs,24,25 and can, e.g., be used as functional coatings26,27 or as a well-defined model for powder MOFs.28–30 The experimental investigations are complemented by quantum chemical calculations, mainly using density functional theory (DFT), which calculates the density of states, the band structure, and excitation energies.
The SURMOF substrates were silicon wafers with (100) orientation and a native SiO2 layer which were illuminated with an UV light for 30 min, resulting in a high density of functional OH groups on the surface. The SURMOFs of type HKUST-1 were synthesized in a layer-by-layer fashion using liquid-phase epitaxy by employing a dipping robot. Here, the main steps are explained briefly, more details can be found in Ref. 31. The functionalized substrate was consecutively immersed in ethanolic copper acetate solution (1 mM), pure ethanol, ethanolic 1,3,5-benzenetricarboxylate solution (BTC, 0.2 mM), and again pure ethanol for typically 10 min, 2 min, 15 min, and 2 min, respectively. Ultrasonication, which was switched on during the immersion of the sample in pure ethanol, improved the purging process.31 The SURMOF was prepared in 100 layer-by-layer cycles leading to a total thickness of roughly 400 nm. The out-of-plane X-ray diffraction (XRD) data (Figure 1) show the high crystallinity of the HKUST-1 SURMOF.
The ellipsometric measurements of the HKUST-1 SURMOFs on the silicon substrates were performed using a Woollam M-2000 T-Solar ellipsometer at three angles of incidence (AOIs—65°, 70°, and 75°) in a spectral range from 0.7 to 5 eV, i.e., from 250 nm to 1800 nm.
In order to obtain the density of states and the band structure, we performed the DFT calculations employing the plane wave code VASP,32–35 the projector augmented wave (PAW) method,36,37 and the PBE exchange-correlation functional38,39 of the HKUST-1 structure, including the treatment of the open Cu-3d shells (for technical details, see supplementary material 1, Ref. 40). It is well known that the band gap of semiconductors is systematically underestimated in the DFT calculations based on the local density approximation functionals or generalized gradient approximation functionals because of the self interaction error. Furthermore, such functionals fail to give a proper description of the strongly correlated Cu 3d orbitals. Therefore, DFT+U with an onsite Coulomb interaction of U = 5 eV for the 3d electrons is used in the calculations. In addition, the density of states was recalculated with the range separated hybrid functional HSE06.41,42 The latter contains 25% Fock exchange in the short range part.
The excitation spectra were obtained by time-dependent density functional theory (TD-DFT) calculations on two different cluster models using the program package TURBOMOLE49 (see supplementary material 2 and the inset of Figure 4, Ref. 40). One model comprises the BTC linker and six point charges, carrying +0.5 atomic charges each, to mimic the influence of the copper centers on the BTC ions (model 1). For this model, the results obtained with different density functionals are compared with the approximate coupled cluster calculations (CC2). The other model includes the BTC linker and one full Cu-paddle-wheel structure at one of the carboxylate groups (model 2). A similar model was successfully used for the calculation of oriented circular dichroism in MOFs,43 where it was shown that the TD-DFT calculations with a B3-LYP functional combined with 35% Hartree-Fock exchange (B3-LYP35) could reproduce the peak positions of the experimental spectrum. B3-LYP35 also performed best in our test calculations on model 1. Therefore, we used this functional for the calculations on model 2.
In ellipsometry, the changes in the polarization state of the light are measured after reflection at the sample surface (and interface). Usually, two ellipsometric parameters Ψ and Δ are recorded, which, in the case of the sample being isotropic and non-depolarizing, are sufficient to fully describe the change in the polarization state of the light.44 However, Ψ and Δ cannot be directly inverted to yield the dielectric function (also referred to as permittivity) of the sample, unless it can be approximated with a half infinite medium. For the samples studied, Ψ and Δ show an interference pattern resulting from the interference of the light reflected from the upper surface and from the interface to the Si substrate, clearly indicating that the sample does not absorb light with an energy of less than roughly 3.6 eV (i.e., wavelengths larger than 340 nm—see Figure 2). Therefore, for modeling the data, a Cauchy dispersion for the absorption-free range was used in a first approach. The Cauchy model assumes a refractive index n which varies slowly with the wavelength, like n(λ) = A + B/λ2 + C/λ4. During the fit, the thickness as well as A and B was the free parameters, while C was set to 0. After the thickness determination, a Kramers–Kronig consistent procedure was used to extract the dielectric function in the whole spectral range. Introducing a surface roughness (SR) layer in the model, consisting of an effective medium approximation with 50% voids,44 considerably improves the match between measured and simulated data (Figures 2(a) and 2(b)). The SR layer has the same effect like introducing a gradient in the layer which lowers the refractive index towards the surface. The imaginary part of the dielectric function is essentially 0 in the range from 0.7 to 3.6 eV, showing that no electronic states in the HKUST-1 can be excited with photon energies below 3.6 eV. Above 3.6 eV, the HKUST-1 starts to absorb light with a maximum at 4.6 eV. The sharp absorption band indicates a high combined density of states, which are very likely related to rather weak dispersion of the occupied and unoccupied bands in the electronic band structure.
The total density of states (DOS) as well as the contributions of the Cu-3d bands calculated by the DFT are shown in Figure 3. The gap between the highest occupied states below the Fermi level, which have contributions from the linker molecule as well as from the Cu-3d orbitals, and the lowest unoccupied states above the Fermi level, which stem from the empty Cu-3d orbitals, is determined to be approximately 2 eV. However, it has to be noted that the DFT calculations often fail in determining the exact value of the band gap. Furthermore, it depends on the value chosen for U in the DFT+U approach. Therefore, the density of states is also calculated with the HSE06 functional, see Fig. S1 and the supplementary material 1, Ref. 40. While the general structure of the DOS is very similar with both functionals, the band gap is significantly larger in the HSE06 calculations and amounts to 3.8 eV.
Although the absolute values of the energy are not precisely determined by the DFT, the character of the bands can be analyzed. The character of the bands close to the Fermi level indicates that the low lying excitations should belong to the Cu-3d orbitals. This is verified by a comparison with the DOS of a model where Cu was replaced by Zn, resulting in a significantly larger band gap (3.2 eV, see supplementary material 4, Ref. 40).
The band structure calculated along the high symmetry directions is shown in Fig. 3(b). The bands are rather flat. This should lead to a high combined density of states in agreement with the sharp peak in the imaginary part of the dielectric function. The total band width of the 12 empty Cu orbitals amounts to only 0.1 eV. (These 12 orbitals comprise 6 orbitals at the paddle-wheel unit with degenerate spin up and spin down bands. Due to the antiferromagnetic coupling, the spin up is located at one Cu atom, spin down at the other Cu atom.)
Excitation energies and HOMO-LUMO gaps, which were calculated for the BTC linker with point charges (model 1), are summarized in supplementary material 2, Ref. 40. These results show that the calculations on an isolated linker molecule are not sufficient to describe the electronic structure of HKUST–1.
Therefore, the influence of the Cu ions on the excitation spectrum was investigated with one BTC linker and one full Cu-paddle-wheel structure (model 2). In the Cu paddle wheels, both Cu centers are d9 systems with one unpaired electron each. The two Cu centers in the paddle wheel are coupled antiferromagnetically. All calculations on the excitation spectra of model 2 were performed starting from a broken symmetry wave function (see Fig. S3 for the ground state spin density and the LUMO orbitals), which is 0.0237 eV lower in energy than the triplet state. This value is in the range of typical coupling constants in the Cu paddle wheels.45
In the calculated excitation spectrum (Fig. 4), the peak with the lowest energy is at about 2 eV. This peak stems from the local d-d excitations at the individual Cu centers. Due to symmetry reasons (d-d transitions in centrosymmetric systems are actually forbidden by the Laporte rule47,48), these transitions have low intensities in the optical spectrum and cannot be experimentally observed by ellipsometry. This peak is also not observed in the complete active space self-consistent field (CASSCF) calculations on the d-d excitations (see supplementary material 3, Ref. 40).
The peaks with the next higher excitation energy start at an energy of 3.6 eV, which is in excellent agreement with the ellipsometry data. All calculated peaks between 3.6 eV and 4.8 eV are caused by transitions of the electron density from the BTC linker molecule (mainly from the carboxylate groups) to the empty 3d orbitals of the Cu centers (which are about 1.5 eV above the Fermi level), see Fig. 4. This is in agreement with the character of the band gap in the VASP calculations.
Due to conceivable applications as low-k-dielectric in semiconductor technology and other applications as coatings in electronic engineering, the electronic structure of the MOFs requires detailed investigations. Here, we focus on the electronic structure of HKUST-1. By applying spectroscopic ellipsometry to thin surface-mounted MOF films grown by using liquid-phase epitaxy, an optical gap of 3.6 eV was determined. The experimental data were complemented by DFT calculations of the periodic MOF framework and on cluster models. Apart from a peak which originates from the local d-d excitations and cannot be excited by light, the experimentally determined excitation energy spectrum could be reproduced by the computations. The optical excitation with the lowest energy is assigned to transitions from the linker molecule to empty Cu-3d orbitals. It shows that the excitation spectra are the result of the entire framework and cannot be explained by excitations within the isolated organic, BTC, or inorganic, (Cu++)2, MOF components. Furthermore, the importance of the unpaired 3d electrons was verified by the model calculations where Cu was replaced by Zn, resulting in a significantly larger band gap. Because of the large unit cell, the calculated band structure of HKUST-1 MOFs shows flat bands. This study demonstrates that spectroscopic ellipsometry applied to thin, homogeneous MOF films complemented by DFT calculation is a powerful tool for determining the electronic structure of MOFs.
Parts of the theoretical work were performed on the computational resources bwUniGrid and HC3 funded by the Ministry of Science, Research and Arts and the Universities of the State of Baden-Württemberg, Germany, within the framework program bwHPC. Tobias Neumann acknowledges the funding by the Landesgraduiertenförderung of the state Baden-Württemberg and Dr. Velimir Meded for fruitful discussion. Qiang Li was financially supported by the Helmholtz school “Energy related catalysis.” Karin Fink thanks Professor Dr. W. Klopper and Dr. A. Bihlmeyer for helpful discussions.