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Theory Of Dielectrics Frohlich Pdf Converter

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Theory of Homogeneous Dielectrics. The dielectric permittivity (ε) and conductivity (σ) of a material are, respectively the charge and the current densities induced in the response to an applied electric field of unit amplitude. Get Textbooks on Google Play. Rent and save from the world's largest eBookstore. Read, highlight, and take notes, across web, tablet, and phone.

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Abstract

The integration of porous metal-organic frameworks onto the surface of materials, for use as functional devices, is currently emerging as a promising approach for gas sensing and flexible displays. However, research focused on potential applications in electronic devices is in its infancy. Here we present a facile strategy by which interpenetrated, crystalline metal-organic framework films are deposited onto conductive metal-plate anodes via in situ temperature-controlled electrochemical assembly. The nanostructure of the surface as well as the thickness and uniformity of the film are well controlled. More importantly, the resulting films exhibit enhanced dielectric properties compared to traditional inorganic or organic gate dielectrics. This study demonstrates the successful implementation of the rational design of metal-organic framework thin films on conductive supports with high-performance dielectric properties.

Introduction

Considerable efforts have been devoted to preparing high-dielectric-constant (high-κ) materials with low leakage and a high breakdown strength as functional devices, such as thin-film transistors and high-electron-mobility transistors¹. Conventional silicon-based electronics have been dominating as gate dielectric materials^2,3; however, their relatively low dielectric constant and large static power dissipation limit their practical application. Therefore, exploitation of new high-κ materials that allow for a proportional increase in the gate thickness remains a challenge for the design of gate dielectric materials^4,5. Inorganic hafnium dioxide (HfO₂) and zirconium dioxide (ZrO₂) have been widely studied as dielectric materials with high κ values. However, these materials are too brittle to be compatible with substrates, and the deposition techniques typically require high temperatures and expensive vacuum equipment⁶. Organic polymers have been deposited onto flexible plastic substrates to address this issue; however, the obtained organic polymer thin films typically suffer from low dielectric constants because of weak intermolecular forces in the gate devices. Moreover, organic polymer thin films typically have limited thermal management due to their modest thermal stability^7,8,9.

Recently, organic and inorganic hybrid materials have emerged as a new type of electronic material that combines the distinctive properties of the high-κ of metal oxides and the flexibility of organic molecules¹⁰. However, one of the major challenges in the fabrication of these films is the low compatibility of the organic and inorganic components, which typically leads to the generation of defects in the resulting films and a significant decrease in device performance¹¹.

As a hybrid material, metal-organic frameworks (MOFs) have garnered significant interest because their crystalline porous structures can be easily designed and functionalized through judicious choices or modifications of the metal nodes and organic linkers^{12,13,14,15,16,17}. This approach provides an avenue for the rational design of a gate device on the nanoscale through electrochemical deposition of MOFs onto substrates. The coordination interactions of the metal centre and organic linkers endow the hybrid components with good compatibility and prevent the formation of defects on the self-assembled multilayers. In fact, good compatibility between the integrated MOF films and the surface of the substrate is imperative for their practical application in electronic devices^{18,19,20,21,22}. To the best of our knowledge, although the ferroelectric properties of MOFs have been studied, investigations concerning control of the mechanical properties of porous MOFs, especially their dielectric constants, have been limited^23,24. The dielectric constants of MOFs without guest molecules are typically small and independent of temperature because the framework does not have positional freedom in the crystalline state; however, polar guest molecules in such porous materials are typically highly free to move. Therefore, MOF materials with large dielectric constants could be achieved by entrapping or coordinating guest molecules with high polarizability^25,26. However, preventing the loss of guest molecules is another issue that must be addressed. An interpenetrated MOF structure would enhance the binding of guest molecules with the framework^27,28,29. Therefore, an ingenious combination of porous backbones and polar guest molecules could synergistically affect the polarizability of MOFs, resulting in materials that exhibit unique dielectric behaviours that they do not exhibit as a single component or amorphous polymer^18,30. To the best of our knowledge, although MOFs, especially conductive MOFs, have attracted considerable attention because of their promising applications in electronic devices, the rational design of MOF structures on conductive supports to improve the electronic performance has not been previously reported.

Herein, a zinc MOF material based on a flexible ligand (i.e., 1, 3, 5-tris[4-(carboxyphenyl)oxamethyl]-2, 4, 6-trimethylbenzene (H₃TBTC)), {[H₂N(CH₃)₂][Zn(TBTC)]}·2DMF·EtOH (1), is designed and synthesized via a solvothermal reaction. 1 is a 2-fold interpenetrating anionic network with H₂N(CH₃)²⁺ counterions located inside the pore. The existence of the interpenetrating structure and the asymmetric cations that can induce dipole moments encourage us to investigate the dielectric properties of thin films of 1 (ref. 31). Inspired by Müller and co-workers’ studies of the fabrication of bulk MOFs by electrochemical anodic oxidation of metal electrode³², Dinc and co-workers’ results on the electrochemical reductive synthesis of MOF thin films³³, De Vos as well as Ameloot and co-workers’ studies of the fabrication of MOF thin films by electrochemical anodic oxidation of metal plates³⁴, we deposit interpenetrated compound 1 onto a zinc plate using a temperature-controlled electrochemical anodic oxidation method. The proposed temperature-controlled electrochemical anodic oxidation method combines the merits of the electrochemical anodic oxidation method and the electrochemical reductive protonation of organic ligand method. Therefore, compound 1 is integrated onto a zinc plate via the fast production of Zn²⁺ from metal plates with simultaneous protonation of the ligand under mild conditions. After the deposition of 1 on the zinc plate using a facile electrochemical assembly approach, the morphology and thickness of the MOF thin film can be tuned by the temperature, reaction time and voltage. More importantly, the obtained thin film exhibits a dielectric constant that is more than three times higher than that of the bulk MOF material. In this study, we successfully demonstrate that the interpenetration of the structure effectively improved the dielectric properties of the MOF thin film. This phenomenon is further confirmed by experimental and theoretical studies of the dielectric properties of another pair of MOFs with a non-interpenetrated structure (MOF-123) and interpenetrated structure (MOF-246). In this study, we systematically investigate the relationship between the structure and the dielectric properties; the results may provide a new perspective for the design of electronic devices.

Results

Crystal structure of {Zn(TBTC) [H₂N(CH₃)₂]}·2DMF·EtOH (1)

Compound 1 crystallized in the Pbcn space group. The asymmetric unit of 1 contains a Zn²⁺ cation, a dimethylammonium (H₂N(CH₃)₂⁺), a fully deprotonated TBTC³⁻ ligand, two uncoordinated N,N-dimethylformamide (DMF) molecules and one ethanol molecule (Supplementary Fig. 2, Supplementary Fig. 3, Supplementary Data 1). As shown in Supplementary Fig. 1, each Zn²⁺ is coordinated to three carboxyl O atoms from three different TBTC³⁻ and one N atom from a H₂N(CH₃)₂⁺; therefore, TBTC³⁻ is considered to be a tri-bridging ligand that links the metal centres to the 3D network structure featuring 1D (13 × 17 Å) channels along the b-axis (Fig. 1a). The two aforementioned identical networks appeared in the same crystal lattice of compound 1, which resulted in an overall 2-fold interpenetrated framework (Fig. 1b). The solvent-accessible volume of 1 was 4370.8 Å³ per unit cell, which is 44.4% of the total crystal volume calculated using the PLATON software³⁵. The UV–vis diffuse reflection spectrum confirmed that the bulky MOF material exhibited an experimental energy gap of 4.24 eV (Fig. 1c). Materials with such a relatively large, broad energy gap (energy gaps of typical inorganic microelectronic materials: Si 1.1 eV, Pr₂O₃ 3.9 eV, HfO₂ 5.6 eV) are believed to be good candidates for use as microelectronic materials³⁶.

Characterization of MOF thin films

The MOF film was prepared using an electrochemical assembly method (Fig. 2a). Briefly, after electrolysis started, Zn²⁺ ions were produced via anodic oxidation on the surface of the Zn plate (anode). In addition, the TBTC³⁻ anions moved to the anode driven by the electric field. Then, the self-assembly of Zn²⁺ and TBTC³⁻ occurred, which resulted in deposition of a {[H₂N(CH₃)₂] [Zn(TBTC)]}·2DMF·EtOH thin film onto the anodic Zn plate (Supplementary Fig. 4).

PXRD was carried out to evaluate the phase and crystallinity of the as-prepared MOF thin films (Supplementary Fig. 5). The peaks in the resulting diffractogram of the film match those for bulk MOF powder.

Attenuated total reflection infrared (ATR-IR) spectra were recorded to confirm the composition of the MOF thin films. The ATR-IR spectra of the as-prepared MOF thin films are consistent with that of the bulk material (Supplementary Fig. 6). The characteristic absorbance at 1,606 cm⁻¹ was assigned to the stretching vibration of C=C, and the characteristic absorbance at 1,422 cm⁻¹ was attributed to the deformation vibration of CH₃ in the ligands. The peaks located at 783 and 706 cm⁻¹ were attributed to out-of-plane deviational vibrations of Ar-H, and the peaks at 1,237, 1,169, 1,059 and 868 cm⁻¹ were attributed to the vibrations of Ar-C=O (deviational vibration), Ar-O-C (stretching vibration), N-H (bending vibration) and CH₂ (rocking vibration), respectively³⁷.

The atomic force microscopy (AFM) observations and morphological studies conducted using scanning electron microscopy (SEM) indicated that the block-shaped Zn-MOF microcrystals grew densely on the anodic Zn plate, forming a compact and uniform MOF film (Fig. 2b). The configuration of the prepared film was film-metal-film, which can be considered an insulator-metal-insulator device. When Ag was sputtered onto both sides of the MOF film, the geometry of the constructed device was metal-insulator-metal-insulator-metal. As shown in Supplementary Fig. 7, the Zn-MOF microcrystals could also be integrated onto indium tin oxide (ITO) glass and a silicon surface using electrochemical technology³⁸, which would extend the applications of rationally designed compound 1 in electronic devices^39,40.

We next investigated the characteristics and properties of the Zn-MOF film on Zn plates as an example. The UV–vis diffuse reflection spectrum confirmed that the as-prepared MOF film possessed the same band-gap value (4.23 eV) as that of the bulk MOF material (Fig. 1d).

Morphology and thickness study

The surface morphology and film thickness of the as-prepared MOF thin films were investigated through regulation of the reaction time and voltage. As shown in Fig. 3, a series of MOF thin films, which exhibited good coalescence of microcrystals with fairly small intergranular voids, as confirmed by SEM, were obtained via adjusting the voltage. The particle size on the film surface decreased as the voltage increased, which may decrease the leakage current caused by large grains^41,42. The roughness of the MOF films decreased from 205.71 to 150.09 nm when the reaction voltage was increased from 1 to 3 V (Fig. 3, Supplementary Fig. 8), which indicates that the morphology of the as-prepared MOF film is controllable via changing the reaction voltage. Moreover, the thickness of the as-prepared MOF film was tuned by changing the reaction time (Fig. 4, Supplementary Fig. 9). When the reaction time was decreased from 420 to 60 s, the thickness of the MOF film decreased from 22.0 to 5.26 μm (Supplementary Fig. 9). This result suggests that the thickness of the MOF film is controllable via changing the reaction time.

The charge carrier transport in gate dielectrics is strongly related to the morphology of the film. Therefore, precise control of the morphology of the film is paramount for thin-film synthesis with regards to charge carrier transport properties^41,42. In addition, control of the thickness of the film is also important to decrease the leakage current. Here, we prepared films with smooth surface morphologies and preferably small intergranular voids by controlling the voltage and reaction time.

Dielectric properties of the MOF thin film

The optimized conditions consist of a voltage of 3 V and a reaction time of 60 s. The plots of the dielectric constant (κ) as a function of the frequency indicate that MOF thin film possesses a dielectric constant (κ) of 19.5 at a frequency of 1 MHz, which is much larger than those of most previously reported MOFs (except for ferroelectric MOFs)^43,44,45. By contrast, the bulky sample of 1 only exhibits a small κ of 5.9 (Fig. 5a). The dielectric constant is a complex function that depends on the density of the material and the total polarizability of the molecules. The total polarizability is influenced by several factors, such as (a) space-charge polarization, (b) dipolar orientation and (c) displacement of electrons of atomic, ionic⁴⁶. In the case of powder MOFs, a sluggish increase was observed as temperature was increased from room temperature to 55 °C (Supplementary Fig. 10). This phenomenon may result from the space-charge distribution that arose from the polarizability of the guest molecules in the pores of the MOF materials (Fig. 4c). However, the dielectric constant of 1 decreased with increasing temperature and remained constant at 5.8 during the cooling cycles (Supplementary Fig. 10). This decrease in the dielectric constant of 1 was most likely due to the ring distribution of the space charge weakening the total polarization of the bulky MOF (Fig. 4c)⁴⁶. However, the measured dielectric constant of bulk 1 is still substantially larger than most of the previously reported dielectric constants for MOFs (typically less than 4.0)^47,48,49. This result may be due to the interpenetrated structure of 1, which would enhance the polarization of 1 and increase its dielectric constant^35,47,48,49.

Theoretical calculations

Comprehensive experimental studies and theoretical calculations were also carried out to confirm the aforementioned conclusion concerning the increase in the dielectric constant of interpenetrated 1. A pair of interpenetrated and non-interpenetrated MOF structures (i.e., MOF-123 (non-interpenetrated) and MOF-246 (interpenetration)) was measured to determine whether the interpenetration of the structure enhances the dielectric properties of the MOF^50,51. As shown in Fig. 6, concatenated MOF-246 exhibited an experimental dielectric constant of 14.7 at 323.15 K, which is approximately 2 times larger than that of interpenetrated MOF-123 (6.3 at 323.15 K). Theoretical calculations of the dielectric constants of MOF-123 and MOF-246 were also carried out. As calculated using CASTEP MODE in Materials Studio 7.0, MOF-246 exhibited a theoretical dielectric constant of 15.5 at 0 K, which is 12 times larger than that of MOF-123 (1.3 at frequencies below 4.0 × 10³² Hz and at 0 K) (Fig. 6e). The results confirmed that the interpenetration of the framework can enhance the dielectric properties of MOFs, especially at low frequencies. In addition, the dielectric constants of a series of other interpenetrated MOFs were also calculated using Materials Studio for comparison to the dielectric constants of their non-interpenetrated structures. As theoretically calculated, interpenetrated MOF-5 has a dielectric constant of 423.7, which is approximately 326 times larger than that of non-interpenetrated MOF-5 (1.3) (Supplementary Fig. 11).

In the case of the fabrication of compound 1 on a conductive solid surface, the space-charge relaxation phenomenon occurred at low frequencies, as evident from the slight increase in the dissipation factor at frequencies above 10⁵ Hz (Supplementary Fig. 12). Moreover, when the temperature was increased, the dielectric constant of the MOF thin film remained ca. 19.0 at 120 °C, which is 20% larger than the dielectric constant at 55 °C (ca. 16.0). These results may be due to the increase in temperature activating the relaxation phenomenon in the MOF thin film with polar guest molecules, which will further enhance the total polarizability of the thin film and increase the dielectric constant^18,19. As shown in Fig. 5d, during the heating and cooling cycles at 100 kHz, the dielectric constant of the MOF film remained at ca. 15.1 upon heating to 80 °C and then increased to 17.4 in the temperature range from 80 to 123 °C. During the cooling process from 123 to 55 °C, the dielectric constant gradually increased to ca. 18.7 (Fig. 5d) and finally stabilized at ca. 19.9. This increase in the dielectric constant may result from either the dipole moments or orientational polarization according to the Debye model^46,52. However, the phenomenon observed in the thin film differs from the dielectric behaviour of bulk 1, whose dielectric constant decreased with increasing temperature (Supplementary Fig. 10). This behaviour of the prepared MOF thin film is interesting for applications involving high-κ materials because the dielectric constants of the bulk MOFs and those of previously reported MOFs typically decrease during heating and cooling cycles^47,48,49. The difference in the case of our MOF films most likely stems from the homogeneous distribution of the space charge inside the MOF particles on the two sides of the conductive substrate surface, which improves the capacitance of the entire MOF thin film and further increases its dielectric constant (Fig. 5c, equation 1). These results further indicate that the fabrication of interpenetrated MOFs on conductive substrates as thin films can enhance the dielectric constant of the MOFs, which is critical for their application as charge carriers in gate dielectrics⁵³.

Study of mechanical properties and leak current tests

Mechanical properties are important for the practical application of MOFs as semiconductors. The elastic modulus and hardness are two important parameters for the evaluation of the mechanical behaviour of films. Nanoindentation measurements were performed using a spherical diamond tip (radius=20 μm) in continuous measurement (CSM) mode (Supplementary Fig. 13) with a Poisson’s ratio of 0.3 according to a previously reported protocol⁵⁴. Representative P-h curves for the prepared thin films are shown in Fig. 7a. The load displacement of the MOF thin film is smooth, indicating that the plastic deformation that occurs underneath the spherical diamond tip during indentation is relatively homogeneous in nature. The average values of the elastic modulus (E) and hardness (H) of the MOF thin film, which were extracted from the P-h curves, are calculated for depths of 1–2 μm to avoid interference from the spherical diamond tip and substrate^54,55,56,57. The average elastic modulus and hardness of this film were determined to be 32.00 (±1.71) GPa and 0.33 (±0.02) GPa, respectively, which satisfies the basic requirements for electrical devices^54,55,56,57. The elastic moduli and hardness of the thin films fabricated under different conditions were also determined to be similar to these values (Supplementary Table 1). The similarity of the experimental values indicates good grain coalescence of the intergranular voids, which should improve the films’ mechanical properties. The results also suggest that the as-prepared thin films can be assembled as an electronic device that can withstand large mechanical stress. As a practical gate dielectric layer, the MOF-1 thin film exhibited a leakage current and breakdown voltage of 10⁻⁷ A·cm⁻¹ (at 1 kV·cm⁻¹) and 10 kV·cm⁻¹, respectively (Fig. 7b). These results indicate that the as-prepared MOF films exhibit good insulating properties and a high breakdown strength.

Discussion

A MOF thin film based on a 2-fold interpenetrated MOF that was constructed using a flexible ligand and metal ions was deposited onto conductive metal plates via a facile approach involving the electrochemical assembly method. The morphology and thickness of the as-prepared MOF films were controlled via tuning the reaction time and voltage. Importantly, the dielectric properties of the interpenetrated MOF thin films were systematically studied for the first time. Significantly, the interpenetrated MOF thin film exhibits a dielectric constant larger than both those of their bulk forms and those of most of the previously reported MOF materials. Furthermore, the dielectric constant of the as-prepared films was tuned through adjustment of the synthesis conditions. We propose that this remarkable increase in the dielectric constant may originate from the packing of the microcrystal polarization of the well-trapped solvent molecules and the interpenetrated framework on the conductive supports. The MOF thin films offer high mechanical flexibility and can sustain a large mechanical stress, which makes this material very promising for application in microelectronic devices.

Our research demonstrated the importance of the interpenetrating structure of the MOF thin films to achieve good dielectric and mechanical properties. This study provides a platform for the utilization of interpenetrated MOF materials in microelectronics, such as gate dielectrics and semiconductor devices.

Methods

Chemicals

1, 3, 5-Tris(bromomethyl)-2, 4, 6-trimethylbenzene was purchased from TCI. Ethyl-p-hydroxybenzoate and Zn(NO₃)₂·6H₂O were purchased from Sinopharm Chemical Reagent Beijin Co., Ltd. They were all used without further purification. All reagents and solvents were commercially available and used as received. Ultrapure water (18.24 MΩ cm⁻¹) is used directly from a Milli-Q water system. Zinc plates and ITO glasses were commercially available and used as received. AZO/silicon plates was obtained by magnetron sputtering AZO layer onto silicon surface.

Voltage supply

Voltage supply was performed by Epsilon electrochemical workstation and Agilent E3 612A DC power supply.

Powder X-ray diffraction measurements

PXRD test of MOF thin film was carried out on MiniFlex600 by scraping thin film from the surface of zinc plate. The simulated powder patterns were calculated using Mercury 2.0. The purity and homogeneity of the thin film were determined by comparison of the simulated and experimental X-ray powder diffraction patterns.

Infrared spectroscopy

Attenuated total reflection infrared (ATR-IR) spectra of the samples were measured using Vertex 70 Fourier transform infrared (FTIR) spectrometer with an ATR sampling accessory. The ATR cell was made of a horizontal diamond crystal with an incidence angle of 45°.

Scanning electron microscopy

The scanning electron microscopy (SEM) measurement was carried out on a Phenom G2 instrument. The scanning probe microscopy (SPM) measurement was carried out on a NanoscopeШa instrument.

Energy band tests

Band gaps of samples were determined by using a Lambda 950 spectrometer working in Diffused Reflectance mode. The Kubelka-Munk equation was used to calculate absorption at the various wavelengths. Using the absorption versus energy plot, the first derivative of the absorption spectrum equation was calculated, and the inversion points could be identified.

Dielectric permittivity measurements

The dielectric permittivity of the MOF thin film was carried out by TH2828 Precision LCR Meter. The electrodes were made by sputtering silver onto both sides of MOF film and attaching copper leads with silver paste. Calibration of standard capacitor reveals that the overall errors are less than±3% for the experimental results. The real part of the dielectric constant (κ) was calculated using the following formula (equation):

in which C is capacitance, t is the thickness of the dielectric film, A_m is the Silver dot area, and ɛ₀ is the permittivity of vacuum.

Theoretical calculations

Theoretical study of dielectric properties of prototypical MOFs were performed with CASTEP (Cambridge Sequential Total Energy Package)^58,59,60 code based on the plane-wave ultrasoft pseudopotential method of Materials Studio 7.0 (ref. 61). The exchange and correlation functional was treated by generalized gradient approximation(GGA)—Perdew-Burke-Ernzerhof. The cutoff energy of 351.0 eV and k-points of 1 × 1 × 1 for all hypothetical structures were applied to calculate the total energy.

Nanoindentation and leakage current measurements

Nanoindentation measurement was carried out on a MTS XP instrument. The leakage current and breakdown voltage were measured by KEITHLETY-2400 instrument.

Thermogravimetric analyses

Thermogravimetric analyses (TGA) were performed under a nitrogen atmosphere with a heating rate of 10 °C/min using NETZSCH STA 449F3 thermogravimetric analyzer. H NMR spectra were recorded at ambient temperature on a BRUKER AVANCE III spectrometer; the chemical shifts were referenced to TMS in the solvent signal in d₆-DMSO.

Synthesis of {Zn(TBTC)[H₂N(CH₃)₂]}·2DMF·EtOH (1)

The 1, 3, 5-tris[4-(carboxyphenyl)oxamethyl]-2, 4, 6-trimethylbenzene (H₃TBTC) ligand was synthesized as following^18,62: Under a nitrogen atmosphere, a dimethylformamide (DMF) (80 ml) solution of 1, 3, 5-Tris(bromomethyl)-2, 4, 6-trimethylbenzene (2.55 g, 6.4 mmol), ethyl-p-hydroxybenzoate (4.00 g, 24.1 mmol), and anhydrous potassium carbonate (K₂CO₃) (10.95 g, 79.2 mmol) was heated under vigorous stirring at 90 °C for 96 h. The obtained mixture was cooled to room temperature, and the solvent was removed under reduce pressure. Ultrapure water (H₂O) (100 ml) was added to mixture, and extraction with dichloromethane (CH₂Cl₂) three times. Then, the intermediate ester was obtained after removing the CH₂Cl₂. Subsequently, under a nitrogen atmosphere, the intermediate ester (3.00 g, 6.6 mmol) was dissolved in a refluxing mixture of 80 ml of ethanol (EtOH) and 60 ml tetrahydrofuran (THF). To this solution was added 50 ml of 20% KOH solution. After 2 h, the mixture was cooled to room temperature and concentrated to dryness. The obtained residue was dissolved in 30% aqueous EtOH (40 ml) and acidified with glacial acetic acid to give the partially protonated product which precipitated from solution. This precipitated was collected and dissolved in THF (30 ml) and trimethylsilyl chloride (1.73 g) was added to the solution. The mixture was stirred at room temperature for half an hour and precipitated into water (300 ml). The precipitate of fully protonated product was collected by suction filtration and dried to get H₃TBTC ligand. Zn(NO₃)₂·6H₂O (2.00 mmol, 0.590 g) and H₃TBTC (1.00 mmol, 0.570 g) were dissolved in a mixture consisting of 10 ml of 4:1:1 (volume ratio) DMF/Ethanol/H₂O with stirring and heating for 20 min. The solution was then transferred to a Teflon-lined stainless steel vessel (23 ml). After heating under an autogenous pressure at 120 °C for 72 h, the Teflon-lined stainless-steel vessel was slowly cooled to room temperature at a constant rate of 0.04 °C·min⁻¹. Colourless crystals of 1 were obtained and dried in air at ambient temperature.

Single-crystal X-ray crystallography

Crystal data for {[H₂N(CH₃)₂][Zn(TBTC)]}·2DMF·EtOH (1) (Supplementary Table 2, Supplementary Table 3), orthorhombic, P_bcn, Mr=676.99 Å, a=29.2649(4) Å, b=7.89750(10) Å, c=42.5654(7) Å, α=90.00°, β=90.00°, γ=90.00°, V=9837.7(2) Å³, D_calcd=0.914 g·cm⁻³. μ=1.006 mm⁻¹, F(000)=2,816, GOF=1.084. A total of 36,658 reflections were collected, 8,596 of which were unique (R_int=0.0697). R1/ωR₂= 0.0809/0.2105 for 415 parameters and 8,596 reflections (I>2σ(I)). Measurement of crystal was conducted on SuperNova diffractometer which equipped with a copper microfous X-ray source (λ=1.5406 Å) at 100(3) K. The structure was solved by direct methods and refined on F² by full-matrix least-squares using the SHELXL-97 program package⁶³. The positions of H atoms were generated geometrically. Non-hydrogen atoms were refined with anisotropic displacement parameters. Given that refinement of the metal-organic coordination framework is essentially uninfluenced by the presence of the disordered solvent and lattice solvent molecules were badly disordered, the SQUEFZE routine in the PLATON software was applied to subtract the diffraction contribution from the solvent molecules³⁵. The number of free DMF molecules per unit cell was estimated from the TGA or ¹H NMR.

Electrochemical assembly of MOF thin films

H₃TBTC (1.00 mmol, 0.570 g) and ammonium fluoride (NH₄F, 2.7 mmol, 0.100 g) were dissolved in a mixture solution of 100 ml of 4:1:1 (volume ratio) DMF/EtOH/H₂O with stirring for 10 min under heating. The solution was then bubbled with N₂ (approximately three bubbles per second) for 1 h to remove the oxygen from the solution. Two Zn-plate electrodes were then immersed into the solution. The MOF film was grown on the Zn plate serving as the anode by applying a voltage while maintaining continuous N₂ bubbling through the solution. The as-prepared MOF film was washed thoroughly with DMF to remove excess ligand and NH₄F, respectively. MOF films with different morphologies were prepared using different voltages and reaction times. With respect to the deposition of compound 1 on ITO glass and AZO/silicon surface (AZO, aluminium-doped zinc oxide, the width and length were approximately 10 × 30 mm), Zn (NO₃)₂·6H₂O (2.00 mmol, 0.590 g) and H₃TBTC (1.00 mmol, 0.570 g) were dissolved in 4:1:1 (volume ratio) DMF/EtOH/H₂O, respectively. The Zn²⁺ solution was then slowly poured into the TBTC³⁻ solution under heating, and colloidal compound 1 nanocrystals were formed in solution. The colloidal nanocrystals were dispersed into a methylbenzene solution or methanol solution. The films were electrochemically obtained by inserting two ITO glass electrodes or AZO/silicon plates into the colloidal nanocrystal solutions under an applied voltage.

Data availability

Crystallographic data (excluding structure factors) for the structure reported in this paper have been deposited at the Cambridge Crystallographic Data Center, under the deposition number 1043020. Copies of the data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif. The data that support the finding of this study are available from the corresponding author upon request.

Additional information

How to cite this article: Li, W.-J. et al. Integration of metal-organic frameworks into an electrochemical dielectric thin film for electronic applications. Nat. Commun. 7:11830 doi: 10.1038/ncomms11830 (2016).

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Acknowledgements

This work was supported by the 973 Program (2014CB845605 and 2012CB821705), NSFC (21521061, 21331006, and 51572260) 'Strategic Priority Research Program' of the Chinese Academy of Sciences (XDB20030000). We thank Dr Qi Wei for assistance with the UV–vis diffused-reflectance spectroscopy measurements and Dr Qi-Chang Hu for assistance with the I-V measurements. We also thank Dr Yingpin Chen for helpful discussions on PXRD and Dr Lei Zhao for discussions related to the mechanical properties of hardness and elastic moduli.

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State Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Mater, Chinese Academy of Science, Fuzhou 350002, P.R. China
- Wei-Jin Li
- , Juan Liu
- , Zhi-Hua Sun
- , Tian-Fu Liu
- , Jian Lü
- , Shui-Ying Gao
- , Chao He
- , Rong Cao
- & Jun-Hua Luo
Collaborative Innovation Center of Chemistry for Energy Materials (2011-iChEM), Xiamen 361005, P.R. China
- Wei-Jin Li
University of Chinese Academy of Sciences, Beijing 100049, P.R. China
- Wei-Jin Li
- , Juan Liu
- & Chao He

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Contributions

W.J.L. conceived and designed the experiments, carried out most of the experiments and wrote the manuscript. R.C. directed and supervised the overall project and co-wrote the manuscript. T.F.L., J.L. and S.Y.G. analysed the data and co-wrote the manuscript. J.L and T.F.L contributed to the synthesis and solution of the structure. Z.H.S. and J.H.L contributed to the experiments related to dielectric constants. C.H. contributed to the discussion of the band gap and theoretical calculations. All of the authors contributed to the analysis and interpretation of the data.

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The authors declare no competing financial interests.

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Correspondence to Rong Cao.

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Published online 2013 Oct 21. doi: 10.1038/srep02999

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Abstract

Using first principles calculations based on density functional theory and a coupled finite-fields/finite-differences approach, we study the dielectric properties, phonon dispersions and Raman spectra of ZnO, a material whose internal polarization fields require special treatment to correctly reproduce the ground state electronic structure and the coupling with external fields. Our results are in excellent agreement with existing experimental measurements and provide an essential reference for the characterization of crystallinity, composition, piezo- and thermo-electricity of the plethora of ZnO-derived nanostructured materials used in optoelectronics and sensor devices.

ZnO is a wide-band gap, transparent, polar semiconductor with unparalleled optolectronic, piezoelectric, thermal and transport properties, which make it the material of choice for a wide range of applications such as blue/UV optoelectronics, energy conversion, transparent electronics, spintronic, plasmonic and sensor devices¹. Understanding the infra-red (IR) properties of the bulk crystal is crucial for the intrinsic characterization of the material and is a prerequisite for the viable application of all ZnO-derived systems (e.g. nanostructures, interfaces, alloys) that are now the leading edge of research in many optoelectronic fields. In fact, at IR wavelengths, the vibrational polar modes affect also the dielectric response of the material (i.e. the optical properties), and thus its final performance. This justifies the uninterrupted sequence of experimental reports on vibrational properties of wurtzite ZnO crystal, which started in the sixties and continues nowadays²^,3^,^,5^,6^,7^,8.

Raman spectroscopy is one of the most common investigation techniques exploited for this purpose because it provides information on the structural and chemical properties such as orientation, crystallinity and existence of defects and impurities. However, despite the profuse research efforts pursued in the last decades, there are still open questions on the unambiguous identification of high-frequency phonon modes or unusual line-width variations and the interpretation of angular-dependent Raman spectra of ZnO: The uniaxial crystal structure along with the pronounced mass difference and the strong bond polarity imparts a large LO-TO splitting that mixes phonon bands and makes the interaction with external radiation largely anisotropic. Clearly, a unified theoretical approach able to treat at the same level of accuracy both the phonon dispersion and the Raman spectra is highly desirable. Although semiempirical approaches could provide a simple and computationally inexpensive way to treat this problem^,10, the parameterization of the force fields strongly reduces the transferability of the interatomic potentials, which must be carefully tested for each specific system and morphology especially in the presence of doping, defects and impurities. On the other hand, while a few attempts to reproduce ZnO phonon bands through ab initio techniques exist⁷, no simulations of Raman spectra have appeared so far. The challenge resides in the proper treatment of the response of a highly polar material like ZnO to external electric fields.

In principle, Density Functional Perturbation Theory (DFPT)¹¹^,12 is an elegant and accurate approach for simulation of both phonon and Raman spectra. In practice, the required computational effort, and the difficulty in improving the description of the electronic structure beyond the common functional approximations (LDA, PBE, etc.) prevent the application of this techniques for a large class of realistic structures and materials. ZnO is a prototypical example: a standard Density Functional Theory (DFT) description of the band structure of bulk ZnO severely underestimates repetition the band gap ( vs ). This is not simply due to the lack of many-body corrections typical of DFT, but rather to an unphysical enhancement of the covalent character of the Zn-O bonds. In turn, the wrong description of the electronic structure affects the electrostatic properties of the system and thus the phonon distribution and the coupling with the external fields. This problem may be easily overcome by including Hubbard-like corrections or using hybrid functionals. However, these features are not readily accessible in DFPT approaches for their large computational cost¹⁸.

In this paper we have solved the problem of simulating with comparable accuracy both the electronic and vibrational spectrum of ZnO using a unified finite-fields/finite-differences approach that is independent of the choice of the functional. This allows us to simulate the phonons, the high and low-frequency dielectric constant and the nonresonant Raman spectra of any material through a finite set of electronic structure and force calculations using the finite displacement method¹⁹.

Results

Unified finite-fields/finite-differences theory

The interatomic Force Constants (IFCs) K and the electronic susceptibility χ are obtained as finite differences of forces and polarizations with respect to atomic displacements or external electric fields.

IFCs are the second derivatives at equilibrium of the total energy versus the displacements of the ions u(R), or alternatively, the derivative of the atomic forces F versus the ionic displacements:

where R and R′ are Bravais lattice vectors, I, J are the I-th and J-th atom of the unit cell, and α and β represent the Cartesian components. Phonon frequencies (ω_ph) and normal modes () are routinely obtained from the resolution of the eigenvalue equation: , where the dynamical matrix D_Iα_,Jβ(q) is the Fourier transform of the IFC. The acoustic sum rule (ASR) in real space is defined as in Ref. ¹², while long-wavelength dipole-dipole effects are included by means of specific non-analytical correction to the IFCs, as proposed by Yi Wang et al.²¹.

The proper treatment of the long wavelength macroscopic polarization field requires also the evaluation of the dielectric tensor and of the Born effective charges. For this purpose we consider the electronic susceptibility:

where is the total energy in the presence of electric field and P^el is the electronic polarization along the direction of . Here, and P^el are evaluated following the method proposed by Umari and Pasquarello, where the introduction of a non local energy functional allows electronic structure calculations for periodic systems under finite homogeneous electric fields. E⁰ is the ground state total energy in the absence of external electric fields; P^ion is the usual ionic polarization, and P^el is given as a Berry phase of the manifold of the occupied bands.

The high-frequency dielectric tensor is then computed as , and the Born effective charge tensor is defined as the induced polarization along the direction i by a unitary displacement of the I-th atom in the j direction, or alternatively in terms of atomic forces in the presence of the electric field :

Finally, the contribution of the polar optical modes to the static dielectric constant is computed using the Lyddane-Sachs-Teller relation¹²^,13: where ω(LO) (ω(TO)) are the LO (TO) phonon frequencies and s denotes the electric field polarizations parallel ( ) and perpendicular (⊥) to the polar axis. This alternative method is implemented and fully integrated in the Quantum ESPRESSO suite of codes (www.quantum-espresso.org; the finite-fields/finite-differences approach is implemented in the package FD in PHonon.).

The calculation of the Raman spectra proceeds along similar lines. The non-resonant Raman intensity for a Stokes process is described by the Placzek's expression²⁴:

where e_i (e_s) are the polarization of the incident (scattered) radiation, ω_m is the frequency of the generated optical phonon, n_m is the Bose-Einstein distribution, and is the Raman tensor, defined as:

Within the finite-field approach, the third rank tensor is evaluated in terms of finite differences of atomic forces in the presence of two electric fields:

In practice, the tensor is obtained from a set 19 calculations, which combine the finite electric fields along the cartesian coordinates. is then symmetrized to recover the full C_6v symmetry of the wurtzite structure.

Dielectric and vibrational properties

The calculated high and low frequency dielectric constants, summarized in Table I, are in agreement with experimental spectroscopic ellipsometry data³, as well as Hartree-Fock calculations²⁶. Born effective charges (Table I) are also in agreement with values extracted from transverse IR reflectance spectra²⁷, and may be easily associated to piezolectric properties of ZnO and its modifications under pressure²⁸.

Table 1

High-frequency () and static () dielectric constant and effective Born charges (Z*) of wurtzite ZnO, for electric field polarization parallel and perpendicular to the c-axis. Corresponding experimental values are reported in parenthesis

Z*
3.14 (3.78)^a	7.76 (8.91)^a	2.12
3.08 (3.70)^a	6.98 (7.77)^a	2.06 (2.02)^b

^bfrom Ref. ²⁷.

PBE and PBE + U phonon dispersions are reported in Fig. 1 and phonon frequencies at the Brillouin Zone center (Γ) are summarized in Table II, where we also display the LDA values for comparison. Experimental Inelastic Neutron Scattering (red diamond and blue circles) and Raman (green squares) data are extracted from Ref. ⁷ and superimposed in Fig. 1 to the first principles data. While LDA and PBE results clearly underestimate the experimental frequencies, mostly in the optical branches, with PBE + U the agreement is very good. Here only the highest-frequency LO bands are slightly overestimated. Notably, these phonon branches suffer of anharmonic renormalization effects, which are not included in the present approach. Furthermore, the error bar on the experimental Raman results is higher for these bands, due to the low cross-section of the corresponding phonon-photon scattering processes (see below).

Calculated (black lines) phonon dispersions for wurtzite ZnO calculated with (a) PBE and (b) PBE + U. Solid/open diamonds (red) and open circles (blue) represent experimental INS data, green squares represent Raman frequencies.

Experimental data reproduced from Ref. ⁷.

Table 2

Phonon frequencies (in cm⁻¹) of ZnO at Brillouin Zone center (Γ), calculated with LDA, PBE, PBE + U and compared to experimental Raman data from Ref. ⁷

Mode (Γ)	LDA	PBE	PBE + U	Exp (Raman)
TA/TA	0	0	0	0
87	89	106	100
258	243	283	-
A₁(TO)	398	343	384	380
E₁(TO)	420	363	408	410
446	392	436	438
539	505	578	-
A₁(LO)	547	498	607	(584)
E₁(LO)	560	508	615	(595)

Following the irreducible representation of the wurtzite symmetry group C_6v, the phonon modes of ZnO can be classified as Γ = 2A₁ + 2B₁ + 2E₁ + 2E₂. One low energy A₁ and one double E₁ modes correspond to the transverse and longitudinal acoustic branches, the others are optical modes. B₁ modes are IR and Raman inactive. The two E₂ modes are non polar IR inactive but Raman active. In A₁ and E₁ polar modes, atoms move parallel and perpendicular to the c-axis respectively and are the ones responsible for the LO-TO splitting. The labeling in Fig. 1 and Table II is based on the direct analysis of the phonon eigenmodes and their underlying symmetry. Note that PBE calculations give an incorrect ordering of the B₁ and A₁(LO) modes that is instead correct in PBE + U (see Table II).

Raman spectroscopy

We calculated the Raman spectra for different propagation (k) and polarization (e_i_,s) directions of the incoming and scattering light, as shown in Fig. 2. We simulated the Raman spectra for different rotation angles (θ) of the polarization vectors in the planes parallel (a-plane) and perpendicular (c-plane) to the c-axis. Following the standard experimental setups, for c-plane spectra we considered only parallel polarization of the incoming and scattered light . We used the Porto notation: symbols inside the parentheses indicate the direction of e_i and e_s, while symbols outside the parentheses indicate the directions of propagation of light (k). In the a-plane case, two different orientations of e_i_,s can be experimentally detected: and .

Calculated Raman spectra for different rotation angles on the a-plane in the parallel (a) and perpendicular polarization vector configurations. The inset of panel (b) shows the modification of the spectrum upon relaxation of the ideal scattering geometry. (c) Scheme of the wurtzite lattice and high symmetry planes perpendicular (c-plane) and parallel (a-plane) to the polar (0001) c-axis. k_i indicates the propagation direction of light, e_i_,s are the incident and scattered polarization vectors; θ is the rotation angle in the plane perpendicular to the k_i direction.

Results for room temperature boson distribution are summarized in Fig. 2. Panel (a) shows the a-plane spectra for parallel polarization vector configurations, which reproduces the angular modification of experimental spectra³^,8 and the reciprocal intensity ratio of the main peaks. The spectra are, in fact, dominated by Stokes processes due to the A₁(TO) and phonon modes at 384 and 436 cm⁻¹, respectively, only 2 cm⁻¹ from the experimental values. The intensity of the A₁(TO) peak is independent from the orientation of incident polarization, while the peak reaches a maximum at 90° and minima at 0° and 180°. For 20°, 40°, 120°, and 140° a small contribution from E₁(TO) also appears at 410 cm⁻¹. The phonon mode at 106 cm⁻¹ is not visible in this energy scale, the LO modes are not allowed by symmetry for this incident light direction.

Similar arguments apply for the a-plane spectra for e_i ⊥ e_s polarizations, as displayed in panel (b). Here the main contributions stem from the E₁(TO) and modes, whose reciprocal intensity depends on the θ angle. The two peaks are in counter phase: the former has maxima at 0°, 90° and 180°, where the latter reaches the minimum, and vice versa. Besides these two peaks, experimental results for crossed polarization vectors exhibit small, angular-dependent features associated to A₁(TO) and E₁(LO) that should be symmetry forbidden in this geometry. This is indeed a consequence of the deviation from the ideal geometry set-up and/or a deviation from perfect hexagonal crystallinity of the sample. Following Ref. ⁸ we considered non-orthogonal polarization vectors,

through the inclusion of an arbitrary constant p. The angular distribution and intensity of the peaks depend on the choice of the p factor, i.e. on the characteristic crystallinity of the sample. Results for p = 0.5 are reported in the inset of panel (b) where the A₁(TO) peak and a small contribution from E₁(LO) appear.

From the spectra of Fig. 2 we can also extract the relative intensity ratio between the main Stokes peaks, which are univocally related to the non-zero matrix elements of the Raman tensor for the C_6v point group (see for instance Ref. ²⁹). Calculated ratios between A₁ (E₁) and , taken as reference, are 0.54 and 0.23, respectively; the corresponding experimental values are 0.6 and 0.4⁸. The agreement is quite satisfactory for A₁, while it is slightly worse for E₁. However, in the latter case the experimental value is extracted from e_i ⊥ e_s polarizations spectra, which may suffer of non-ideal hexagonal symmetry, as discussed above (Fig. 2b).

Discussion

Our results demonstrate that the coupled finite-fields/finite-differences DFT approach is essential to accurately evaluate the dielectric properties, phonon dispersions and Raman spectra of ZnO. By reducing high order derivatives of the total energy (i.e. of the charge density) to lower order differences of polarizations and forces obtained from a limited set of self-consistent DFT simulations, it favors the inclusion of advanced corrections to the ground-state electronic structure that are essential for the proper description of the system. In particular, the ground state electronic structure and the coupling with external fields in ZnO require the use of ad hoc corrections to the position of the d-bands of Zn that can be achieved with a DFT + U treatment, as summarized in Fig. 3. In the case of standard LDA and PBE calculations we observe a severe underestimation of the bandgap (E_gap) and a wrong energy position of the d-bands of the Zn atoms, that in turn give an inadequate description of the phonon dispersions (see Fig. 1(b) and discussion therein). The choice of functional influences directly the electrostatics and thus also the characteristics of the vibrational response of the system. In fact, the IFCs are the sum of two contributions:

where are the second derivatives of Ewald sums corresponding to the ion-ion repulsion potential, while the electronic contributions are the second derivatives of the electron-electron and electron-ion terms in the ground state energy. It is the last term that reflects directly in the vibrational spectrum the wrong position of the d-states and the dramatic underestimation of the gap. On the other hand, LDA, with its overestimation of the bonding (shorter lattice parameter and stiffer IFCs) accidentally gives results that are marginally closer to the experimental data thanks to a fortuitous cancellation of errors. The inclusion of the Hubbard U, by correcting the d-Zn p-O hybridization, properly describes not only the electronic bands but also the vibrational and dielectric properties in agreement with the experimental results. Notably, the values of the dielectric constants obtained with LDA (, ) and PBE (, ) are much higher than in experiments, a clear indication of a lesser polarity of the system in these approximations.

Density of states of hexagonal ZnO crystal with LDA, PBE and PBE + U (from top to bottom).

Energies are referred to the respective top of valence bands. The vertical lines indicate the experimental energy gap (E_gap) and 3d-band width (E_d) from Ref. .

Finally, the finite-fields/finite-differences framework allows straightforward developments of the theory to include 3rd order terms in the IFCs (i.e. anharmonic contribution to phonons) or susceptibility χ⁽²⁾ for the simulation of non-linear optical properties such as hyper-Raman or electro-optic effects. One example of the latter is the Raman signal along the parallel c-plane , shown in Fig. 4, where the A₁(LO) and modes dominate the spectrum for all angles (0–180°) (black solid line). However, although allowed by symmetry, A₁(LO) is invisible or hardly visible in most experimental data collections²^,3^,6^,8. This effect is due to a competitive interaction with the Fröhlich term², which couples with the macroscopic field generated by the A₁(LO) mode and cancels most of the deformation potential contributions. This effect may be evaluated including a non-linear correction to the tensor for the longitudinal q_l mode³⁰

where the third order tensor may be straightforwardly calculated extending the finite field approach to the case of three electric fields, or alternatively:

Indeed, the inclusion of the Fröhlich term suppresses the A₁(LO) (red dashed line) in agreement with experiments.

Calculated Raman spectra of c-plane sample in the parallel polarization vector configuration with (red) and without (black) Fröhlich correction to longitudinal optical phonons.

In conclusion, we have demonstrated that our unified finite-fields/finite-differences technique provides a general framework for the calculation of the vibrational, dielectric and Raman properties of materials, without any limitation in the choice of the DFT framework. We have applied this method to the study of ZnO, a material that for its complex electronic structure requires a special treatment in order to obtain a faithful representation of its properties. Our results are in excellent agreement with available experimental data.

Methods

Rutgers University

Computational details

We calculated vibrational and Raman spectra of wurtzite ZnO bulk using PBE-GGA ultrasoft pseudopotentials for all the atomic species, a 28 (280) Ry energy cut off in the plane wave expansion of wavefunctions (charge) and a (12 × 12 × 8) regular k-point mesh. LDA calculations have been done with norm-conserving Troullier-Martins pseudopotentials, with a kinetic energy cutoff of 100 Ry. 3d electrons of Zn have been explicitly included in the valence for both cases. For PBE + U, a Hubbard-like potential with U = 12.0 eV and U = 6.5 eV is applied on the 3d orbitals of zinc and on the 2p orbitals of oxygen, respectively. Note that the Hubbard U values included in the calculations do not have to be considered as physical on-site electron-electron screened potentials, in the sense of the many-body Hubbard Hamiltonian, but as empirical parameters introduced to correct the gap. This is an efficient and computationally inexpensive way to correct for the severe underestimation of the bandgap and the wrong energy position of the d-bands of the Zn atoms^,34. This procedure has also been applied to other similar systems³⁵^,36^,37^,38. P^el and α^m are obtained applying a.u along the cartesian axes. All calculations have been run with lattice parameters optimized for each functional.

For the calculation of phonon modes we considered a (8 × 8 × 2) hexagonal supercell (512 atoms) and we calculated forces (i.e. IFC) displacing only 2 atoms in primitive ZnO cell along the two inequivalent directions. This corresponds to a set of 4 DFT calculations. The Raman tensor has been calculated on the primitive wurtzite cell.

Author Contributions

A.C. and M.B.N. designed the research, performed the calculations, analyzed the data and co-wrote the paper. M.B.N. wrote the finite-difference codes for phonon calculations. A.C. wrote the code for the finite-field calculation of the Raman tensor.

Acknowledgments