Patent Application
20240092809
The disclosed technology is generally directed to covalent organic framework materials. More particularly the technology is directed to highly thermally conductive, ultra-low k two-dimensional covalent organic framework dielectric layers.
To take advantage of sub-10 nanometer integrated circuit components, interlayer low-dielectric constant (low-k) materials with high thermal conductivities must be developed. As dielectric layers have thinned, electronic crosstalk and capacitive signal delay significantly diminish device performance. The Semiconductor Industry Association has identified the development of mechanically robust, thermally stable, few-nanometer, low-k (k<2.4) and ultra-low-k (k<1.9) materials as needed to address this challenge. Ultimately, the realization of such materials will reduce parasitic capacitance, enabling faster gate operations and minimizing dynamic power dissipation. To realize this goal, it is necessary that low-k dielectric materials and thin film (<200 nm) fabrication techniques be advanced. Towards this end, two major classes of low-k dielectric materials have been developed: 1) organic materials that are inherently low-k because of the limited polarizability of covalent bonds and 2) porous oxides that are low-k as a result of their large free volumes. However, all known low-k materials have large thermal resistances that arise from their disordered morphologies and high porosities, which limit high power density chip performance due to inadequate heat management.
Disclosed herein are low dielectric constant (low-k) two-dimensional covalent organic framework materials that have a dielectric constant k less than 2.4 and, in some embodiments, less than 1.9. Suitably the 2-D COFs comprise regularly porous, covalently linked, layer structures that may be prepare from a variety of starting materials.
An advantage of the presently disclosed COFs is that they possess a high thermal conductivity. Suitably, thermal conductivity κ may be greater than 0.8 W m−1 K−1 in a cross-plane direction. In some embodiments, the thermal conductivity anisotropy ratio is greater than 3 between an in-plane thermal conductivity and a cross-plane thermal conductivity.
The COFs having the properties described herein are high-quality COF thin films. In some embodiments, the COFs have a cross-plan thickness of less than 75 nm. An advantage of the presently disclosed technology is that the thickness of the film may be controlled by sequentially applying fresh starting material. The COFs described herein are substantially uniform and free of contamination. In some embodiments, the COFs have a root-mean-square roughness less than 5 nm.
The Examples demonstrate the preparation of these COFs via boronate ester linking chemistries, but other chemistries may also be used to prepare these materials. The COFs may be prepared from poly-ol or catechols and a difunctional aryl boronic acid, such as PBBA, PyBA, BBBA, DPB-BA, or IBBA, but other building units and linking groups may also be used to prepare low-k materials.
Another aspect of the invention provides for heterostructures comprising any of the two-dimensional COFs described herein and further comprising a templating substrate. The templating substrate may provide significant van der Waals or other suitable interaction that allows for nucleation of the COF on the substrate. To encourage nucleation of thin layer films, the templating structure may comprise a thin film such as monolayer graphene or monolayer MoS2. Such thin films may be prepared by a number of different methods such as growth, chemical vapor deposition, or graphitization on a support. Suitably the templating substrate may also comprise a support. Many different supports may be employed that are amenable to the described polymerization strategy and that could survive conditions sufficient for preparing the COFs described herein, such as temperature, time, and solvent requirements. An exemplary support may comprise Si, such as SiC.
Another aspect of the invention provides for dielectric bilayers comprising any of the two-dimensional COFs described herein and further comprising a blocking layer configured to minimize leakage current. The blocking layer may be comprised of an inorganic dielectric layer, such as a metal oxide. Exemplary inorganic dielectric layers may be comprised of Al2O3, HfO2, ZrO2, ZnO, TiO2, SiO2, or Ta2O5, and the like. The blocking layer may be a thin film. Suitably, the blocking layer is less than 10 nm, and as little as about 0.3 nm, when prepared via atomic layer deposition.
Another aspect of the invention provides for capacitors that may be prepared from any of the two-dimensional COFs described herein positioned between two conductive plates.
Another aspect of the invention provides for preparing any of the two-dimensional COFs described herein. The method may comprise contacting a solution with a templating substrate in a reaction vessel under conditions sufficient for preparing a covalent organic framework, whereby a heterotructure comprising a first layer of two-dimensional covalent organic framework deposited on the templating substrate and a liquid phase is formed within the reaction vessel, and removing an insoluble covalent organic framework dispersed within the liquid phase, wherein the solution comprises a plurality of building units, a plurality of linking units, and a solvent. The solvent should be selected to ensure that the monomers are solubilized by the mixture and the solvent mixture stabilizes the COF as a colloidal suspension. In some embodiments, the solvent comprises a Lewis basic solvent, such as a nitrile. In some embodiments, the Lewis basic solvent comprises at least 25% vol.
In some embodiments, the method may further comprise contacting the heterostructure with the solution in the reaction vessel having the insoluble covalent organic framework removed therefrom under conditions sufficient for preparing the covalent organic framework, whereby an additional layer of two-dimensional covalent organic framework is deposited on the heterostructure. Such a step may be repeated one or more times to provide for the desired thickness. In some embodiments, the removing step comprises decanting a portion of the liquid phase from the reaction vessel and diluting, with additional solvent, the liquid phase remaining within the reaction vessel. In some embodiments, at least 80% of the liquid phase is decanted but more or less of the liquid phase may be decanted.
Non-limiting embodiments of the present invention will be described by way of example with reference to the accompanying figures, which are schematic and are not intended to be drawn to scale. In the figures, each identical or nearly identical component illustrated is typically represented by a single numeral. For purposes of clarity, not every component is labeled in every figure, nor is every component of each embodiment of the invention shown where illustration is not necessary to allow those of ordinary skill in the art to understand the invention.
Here we report the fabrication of high-quality COF thin films, which enable time- and frequency-domain thermoreflectance and impedance spectroscopy measurements. These measurements reveal that 2D COFs have high thermal conductivities for porous solids with ultra-low dielectric permittivities. These results show that oriented, layered 2D polymers are promising next-generation dielectric layers and that these molecularly precise materials offer unique and tunable property combinations.
As the features of microprocessors continue to be miniaturized, low dielectric constant (low-k) materials are necessary to limit electronic crosstalk, charge buildup, and signal propagation delay. However, all known low-k dielectrics exhibit low thermal conductivities, which complicate heat dissipation in high power-density chips. 2D covalent organic frameworks (2D COFs) combine immense permanent porosities, which may lead to low dielectric permittivities, and periodic layered structures, which may grant relatively high thermal conductivities. However, conventional synthetic routes produce 2D COFs that are unsuitable for the evaluation of these properties and integration into devices.
Two-dimensional covalent organic frameworks (2D COFs) are a class of modular, molecularly precise, highly porous, layered polymer sheets. These attributes impart a unique combination of physical properties compared to conventional polymers, such as high thermomechanical stabilities and low densities. Challenges associated with characterizing conventionally isolated polycrystalline COF powders have restricted the exploration of many 2D COF properties. To address this challenge, COFs have been fabricated as thin films via direct growth, exfoliation, or interfacial polymerization. However, none of these methods have proven general for wafer-scale synthesis of oriented and crystalline COF films without powder contamination. Synthetic limitations have hindered the evaluation of COFs' fundamental properties related to their use as low-k dielectric layers.
As used herein, a “covalent organic framework” or “COF” is a two- or three-dimensional organic solid with extended, periodic, and porous structures in which a plurality of linking groups (LGs) and functional building units (FBUs) are linked by covalent bonds. Suitably, COFs may be made entirely from light elements (e.g., H, B, C, N, and O). Two-dimensional COFs can self-assemble into larger structures. In some embodiments, layered 2D COF sheets adopt nearly eclipsed stacked structures, providing continuous nanometer-scale channels normal to the stacking direction, as well as significant π-orbital overlap between monomers in adjacent layers. These features can provide an accessible high surface area interface.
Dielectric constant, or relative permittivity, means the factor by which the electric field between charges is decreased in a material relative to vacuum. In some embodiments, the materials described herein may be a low-k dielectric material. A low-k dielectric material has a smaller dielectric constant relative to silicon dioxide. In some embodiments, the COFs described herein are low-k materials that have a dielectric constant less than 2.4 2.3, 2.2, 2.1, or 2.0. In particular embodiments, the COFs described herein as low-k materials may be ultra-low-k materials that have a dielectric constant less than 1.9.
COFs are crystalline. For example, the COFs can form crystallites (i.e., discrete structures) where the longest dimension of the crystallites can be from 50 nm to 10 microns, including all values to the nanometer and ranges of nanometers therebetween. In various embodiments, COFs can comprise at least 2 unit cells.
COFs, as well as other materials described herein, may be present as a thin film. A film may have a thickness of 0.3 nm to 10 microns, including all values and ranges therebetween. In some embodiments, the COF thin film has a thickness of 10 nm to 1 micron, 10 nm 800 nm, 10 nm to 600 nm, 10 nm to 400 nm, 10 nm to 200 nm, 10 nm to 100 nm, 10 nm to 75 nm, 10 nm to 50 nm, 10 nm to 25 nm, including all values and ranges therebetween.
COF are porous materials. In some embodiments, COFs are microporous, i.e., have pores with a longest dimension of less than 2 nm, or mesoporous, i.e., have pores with a longest dimension of 2 nm to 50 nm. The porous structure may form a repeating pattern rather than a random distribution of pores. In an embodiment, the framework has pores, where the pores run parallel to the stacked aromatic moieties.
COFs can have high surface areas. COFs can have surface areas ranging from 500 m2/g to 3000 m2/g, including all values to the m2/g and ranges of surface area therebetween. The surface area of the COFs can be determined by methods known in the art, for example, by BET analysis of gas (e.g., nitrogen) adsorption isotherms.
A “building unit” or “BU” comprises a molecular subunit having two or more functional termini that can be covalently bonded to an equal number of different linker groups (LGs). The covalent linkages between the BUs and LGs provide robust materials with precise and predictable control over composition, topology, and porosity. The relative geometries of the functional termini in the starting materials determine the COF topology.
A “linking group” or “LG” comprises a molecular subunit having two or more functional termini that can be covalently bonded to an equal number of BUs. In some embodiments, at least three BUs are each connected to a LG by covalent bond(s) or at least three LGs are each connected to a BU by covalent bond(s). For example, a BU and a LG may be connected by at least one covalent bond. In other examples, the BUs and LGs are connected by one covalent bond, two covalent bonds, or three covalent bonds. The BUs and LGs can be connected by, for example, carbon-boron bonds, carbon-nitrogen bonds (e.g., an imine bond or a hydrazone bond), carbon-oxygen bonds, carbon-carbon bonds, or boron-oxygen bonds (e.g., boronate ester bonds). Suitable chemistries for preparing COF materials include boronate-ester, imine, ketoenamine, Knoevenagle, and other suitable chemistries.
BUs and LGs may be selected to prepare a COF having a desired geometry, crystalline structure, chemical functionality, and/or porosity. Exemplary BUs and LGs may be selected to allow for the formation of COFs having 2-D arrangements. BUs and LGs suitable for formation of 2D COFs include, without limitation, BUs and LGs having linear, trigonal planar, square planar, or hexagonal planar geometries. BUs and LGs suitable for formation of 3D COFs include, without limitation, BUs or LGs having tetrahedral or octahedral geometries. Suitably, the COFs may comprise BUs or LGs having trigonal planar geometries such as 1,3,5-trisphenyl benzene groups.
In some embodiments, the BU and/or LG is comprised of an aryl moiety but BUs or LGs without an aryl moiety may also be used. The term “aryl” is art-recognized and refers to a carbocyclic aromatic group. Representative aryl groups include phenyl, naphthyl, anthracenyl, and the like. The term “aryl” includes polycyclic ring systems having two or more carbocyclic rings in which two or more carbons are common to two adjoining rings (the rings are “fused rings”) wherein at least one of the rings is aromatic and, e.g., the other ring(s) may be a cycloalkyl, cycloalkenyl, cycloalkynyl, and/or aryls. The term “aryl” includes polycyclic ring systems having two or more carbocyclic rings in which one carbon is common to a directly-adjoining ring (e.g., a biphenyl) or an indirectly adjoining ring, where the indirectly a joining rings are linked by a linker comprising one or more atoms (e.g., diphenylbutadiyne), wherein at least one of the rings is aromatic and, e.g., the other ring(s) may be a cycloalkyl, cycloalkenyl, cycloalkynyl, and/or aryls. Unless specified otherwise, the aromatic ring may be substituted at one or more ring positions with, for example, halogen, azide, alkyl, aralkyl, alkenyl, alkynyl, cycloalkyl, hydroxyl, alkoxyl, amino, nitro, sulfhydryl, imino, amido, carboxylic acid, —C(O)alkyl, —CO2alkyl, carbonyl, carboxyl, alkylthio, sulfonyl, sulfonamido, sulfonamide, ketone, aldehyde, ester, heterocyclyl, aryl or heteroaryl moieties, or the like. In certain embodiments, the aromatic ring is substituted at one or more ring positions with an amine-terminated substituent or azide-terminated substituents, which may be useful in preparing the amine substituted COF. In certain other embodiments, the aromatic ring is not substituted, i.e., it is unsubstituted. In certain embodiments, the aryl group is a 6-10 membered ring structure. In some embodiments, the LG is comprised of a poly-ol or catechol. Exemplary poly-ols or catechols include HHTP, porphyrins, phthalocyanines, macrocyclic catechols, and the like.
In some embodiments, the BU comprises two or more boric acid moieties. When the BU comprises boric acid moieties and the LG comprises hydroxyl groups, boron-oxygen bonds may be formed. Exemplary BUs include, without limitation, PBBA, PyBA, BBBA, DPB-BA, or IBBA.
The Examples demonstrate the synthesis of high-quality wafer-scale 2D COF films through a templated colloidal approach. The templated colloidal approach described herein prevents powder contamination. Although it was known that supported graphene substrates template the formation of oriented 2D COF thin films, films obtained by this method are often unsuitable for device measurements because of contamination by insoluble COF powders that form during the synthesis. Here, colloidal approaches are used to grow COF thin films of few-nm roughness with controllable thicknesses on device-relevant substrates without contamination by insoluble precipitates. The robustness of this technique is demonstrated with five different 2D COFs, including a previously unreported structure, which are synthesized on different templating substrates. Furthermore, these 2D COF films are amenable to sequential polymerization cycles, enabling nanometer precise thickness control not possible in traditional precipitant-contaminated solvothermal syntheses.
The solution-stable colloidal suspension comprises a dispersion of COF crystals in a continuous phase. The use of solution-stable colloidal suspensions prevents the precipitation of insoluble COF products dispersed within the liquid phase. The insoluble COF crystals may have a diameter from about 10-2000 nm, including any value or range therebetween. For example, the COF crystals may have a diameter of 20-200 nm or 30-100 nm. Methods of preparing colloidal COFs are disclosed in Smith, B. J. et al. Colloidal covalent organic frameworks. ACS Cent. Sci. 3, 58-65 (2017); Evans, A. M.; et al., Seeded Growth of Single-Crystal Two-Dimensional Covalent Organic Frameworks. Science 2018, 361, 52-57; Rodríguez-San-Miguel, D. & Zamora, F. Processing of covalent organic frameworks: an ingredient for a material to succeed. Chem. Soc. Rev. 48, 4375-4386 (2019); and Li, H. et al. Nucleation-Elongation Dynamics of Two-Dimensional Covalent Organic Frameworks. J. Am. Chem. Soc. 142, 1367-1374 (2020). The use of Lewis basic solvents, such as nitrile cosolvents, prevents the precipitation of insoluble products and provides insoluble COFs crystals as a solution-stable colloidal suspension.
The unprecedented quality of these films enables the measurement of thermomechanical and optoelectronic properties of COF films. Optical absorption and emission spectroscopies showed that boronate ester-linked COF films are electronically insulating. These results are consistent with density functional theory (DFT) calculations that predict pristine COF-5 films have an indirect electronic bandgap of 3.6 eV and a direct bandgap of 3.9 eV. Impedance spectroscopy performed on COF-5 thin films reveals that they are electronically insulating, ultra-low-k (k<1.7) dielectric layers, which are consistent with DFT-calculated low electronic dielectric tensors (εxx,yy,zz<2) for all COFs investigated.
Due to their regularly porous, covalently linked, layered structure, 2D COFs circumvent the low thermal conductivities that afflict leading low-k dielectrics. Using time- and frequency-domain thermoreflectance (TDTR and FDTR, respectively) and molecular dynamics (MD) simulations, it is found that 2D COFs have a unique combination of low densities (ρ<1 g cm−3) and relatively high thermal conductivities (κ>0.8 W m−1 K−1 in the cross-plane direction with a predicted anisotropy ratio of >3 in the in-plane direction). These findings show that 2D COFs may be prepared as ultra-low-k dielectrics with desirable heat management characteristics. More broadly, accessing high-quality 2D COF thin films provides a means to rationally design solid-state organic materials to unlock technologically useful combinations of properties.
As demonstrated in the Examples, 2D COF films were polymerized directly by a templated colloidal approach. First, a templated substrate, such as SiO2-supported graphene or an Al2O3-supported monolayer MoS2, was contacted with a solution comprising a plurality of BUs and LUs, such as submerged into a solution of 2,3,6,7,10,11-hexahydroxytriphenylene (HHTP) and a difunctional aryl boronic acid (
The polymerization mixtures were contacted with the templating substrate under conditions sufficient for preparing a COF. For example, the polymerization mixtures may be sealed and heated to 80° C. for 24 h. In some embodiments, the templating substrate is contacted with the solution at a temperature from 50° C. to 500° C., 50° C. to 400° C., 50° C. to 300° C., 50° C. to 200° C., 50° C. to 100° C., or any temperature therebetween. In some embodiments, the templating substrate is contacted with the solution at a temperature from 30 min to 1 month, 30 min to 1 week, 30 min to 72 h, 30 min to 48 h, or 30 min to 24 hr, or any time therebetween.
The COF deposited on the templated substrate may be removed from the reaction mixture, rinsed with clean solvent, and dried. The methods described herein result in an optically homogenous film across the entirety of the substrate.
To probe whether these films were being polymerized from solution or whether colloidal species were templating on the surface, a graphene-supported substrate was immersed in a prepolymerized colloidal 2D COF suspension and subjected to the polymerization conditions. No films form in the presence of prepolymerized reaction mixtures. Taken together, these observations suggest that homogenous nucleation occurs in solution and templated-heterogeneous nucleation occurs on the substrate simultaneously, which then polymerize independently.
As demonstrated by the Examples, all COF films are found to be crystalline, oriented, and smooth. Atomic force microscopy (AFM) reveals that the materials are obtained as thin films (<75 nm) with <5 nm root-mean-square roughness in all cases (
The high quality of these films allows for their repeated polymerization by the introduction of unreacted monomers (
Boronate ester-linked 2D COF films studied here are sufficiently electrically insulating to serve as dielectric layers. DFT calculations using the PBE0 functional predict that COF-5 has an indirect bandgap of 3.6 eV and a direct gap of 3.9 eV (
The pristine nature of the films prepared by colloidal syntheses permits the observation of their anisotropic optical emission. The polarization-dependent emission of a COF-5 film has a strong cross-plane emission feature at 530 nm, which has been assigned to the formation of triphenylene exciplexes (
Impedance measurements conducted on parallel plate capacitors confirm that COF-5 is a low-k dielectric. First, we synthesized COF-5 thin films directly onto epitaxially grown graphene (EG) on doped SiC wafers. Next, a 6-nm-thick Al2O3 layer was deposited by atomic layer deposition to prevent shorting through the COF-5 pores before depositing top Au electrodes onto the Al2O3, which produced a series of devices over an area of 40 mm2 (
COF-5 capacitors show leakage current of less than 0.1 nA for applied bias range of −4 V to +4V (area 104 μm2,
COF thin films are found to be substantially more thermally conductive than previously studied low-k dielectrics. To measure the thermal properties of COF thin films with time-domain thermoreflectance, we first deposited Al transducer layers onto several sub-100 nm thick COF films (
Compared to other organic or porous materials, 2D COFs have unusually high thermal conductivities. This finding is consistent with the structural regularity, large porosities, strong interlayer interactions, and low heat capacities unique to 2D COFs. From picosecond acoustics, we determine sound speeds for COF-5 (
Molecular dynamics (MD) simulations give additional insight into COF-5's high anisotropic thermal conductivities. The MD-predicted cross-plane thermal conductivities are slightly lower than the measured values, which could be a consequence of the insufficiencies of the interatomic potential used to model our 2D COFs. However, these differences are equivalent in all crystallographic directions and so, through the same analysis, we extract an anisotropy ratio of 3.4 between in-plane and cross-plane COF-5 thermal conductivities (
2D COFs overcome the traditional tradeoff between dielectric permittivity and thermal conductivity found in all known low-k dielectric materials (
In conclusion, we find that 2D COFs unique combination of structural, thermal, and electronic properties make them promising as low-k dielectric layers. Through a templated colloidal synthetic approach, we access smooth COF thin-film dielectrics of tailorable thickness on technologically relevant substrates. Through our experimental and computational investigations, we find that boronate ester-linked 2D COFs are electronically insulating, consistent with their lack of long-range conjugation, and are low-k dielectrics, consistent with their permanent porosities. We also find that 2D COFs exhibit unusually high thermal conductivities for low density, low-k dielectrics, a combination of properties that was recently identified by the International Roadmap for Semiconductors as a necessary materials development for next-generation integrated circuits. Taken together, these results demonstrate that exotic combinations of properties can be unlocked by using synthetic chemistry to generate precise materials.
Unless otherwise specified or indicated by context, the terms “a”, “an”, and “the” mean “one or more.” For example, “a molecule” should be interpreted to mean “one or more molecules.”
As used herein, “about”, “approximately,” “substantially,” and “significantly” will be understood by persons of ordinary skill in the art and will vary to some extent on the context in which they are used. If there are uses of the term which are not clear to persons of ordinary skill in the art given the context in which it is used, “about” and “approximately” will mean plus or minus ≤10% of the particular term and “substantially” and “significantly” will mean plus or minus >10% of the particular term.
As used herein, the terms “include” and “including” have the same meaning as the terms “comprise” and “comprising.” The terms “comprise” and “comprising” should be interpreted as being “open” transitional terms that permit the inclusion of additional components further to those components recited in the claims. The terms “consist” and “consisting of” should be interpreted as being “closed” transitional terms that do not permit the inclusion additional components other than the components recited in the claims. The term “consisting essentially of” should be interpreted to be partially closed and allowing the inclusion only of additional components that do not fundamentally alter the nature of the claimed subject matter.
All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The use of any and all examples, or exemplary language (e.g., “such as”) provided herein, is intended merely to better illuminate the invention and does not pose a limitation on the scope of the invention unless otherwise claimed. No language in the specification should be construed as indicating any non-claimed element as essential to the practice of the invention.
All references, including publications, patent applications, and patents, cited herein are hereby incorporated by reference to the same extent as if each reference were individually and specifically indicated to be incorporated by reference and were set forth in its entirety herein.
Preferred aspects of this invention are described herein, including the best mode known to the inventors for carrying out the invention. Variations of those preferred aspects may become apparent to those of ordinary skill in the art upon reading the foregoing description. The inventors expect a person having ordinary skill in the art to employ such variations as appropriate, and the inventors intend for the invention to be practiced otherwise than as specifically described herein. Accordingly, this invention includes all modifications and equivalents of the subject matter recited in the claims appended hereto as permitted by applicable law. Moreover, any combination of the above-described elements in all possible variations thereof is encompassed by the invention unless otherwise indicated herein or otherwise clearly contradicted by context.
GIWAXS measurements were performed at either:
Advanced Photon Source at Argonne National Laboratory using the 8-ID-E Beamline under vacuum. All measurements were conducted with an incidence angle of 0.14° using 10.92 keV (λ=1.135 Å) X-rays. The scattered photons were recorded on a Pilatus 1 M detector located 228 mm from the sample. Exposure times were varied such that the pixel with maximum counts was at 80% of saturation. In some cases, significant silicon substrate scatter was observed. The raw images were merged, pixel coordinates were transformed to q-space, and line cuts were generated using GIXSGUI for Matlab.1
or
Advanced Light Source-Lawrence Berkeley National Laboratory using Beamline Station 7.3.3 under a He atmosphere. A photon energy of 10 keV (λ=1.24 Å). Data was collected by a Pilatus 2M detector with a pixel size of 0.172×0.172 mm and 1475×1679 pixels used to capture the 2D scattering patterns at a distance of 300 mm from the sample. A silver behenate standard was used as a calibrant. The grazing angle, α, was varied from 0.08° to 0.25°. Data were analyzed using the Nika macro for Igor Pro.2
All data is shown as a function of the scattering vector:
The electronic band structures of COF-5 were calculated with the CRYSTAL17 package8,9 at the DFT PBEO level10,11 using the POB-TZVF basis set with D3 van der Waals (vdW) corrections12. 2×2×14 and 2×2×18Γ-centered Monkhorst-Pack k-meshes were adopted in the geometry optimizations and self-consistent calculations (SCF), respectively.
The macroscopic static dielectric tensors taking account of the electronic contributions13 were calculated at the DFT PBE level using the Vienna Ab initio Simulation Package (VASP)14 and D3 vdW corrections. Γ-centered Monkhorst-Pack k-meshes were adopted in both geometry optimizations and SCF calculations (see Table 1). The convergence criterion for the total energy was set at 10−8 eV; the one for the forces was set at 0.01 eV Å−1. We considered a Gaussian smearing of 0.01 eV. The lattice parameters after geometry optimization of each COF are shown in Table 2. The off-diagonal components in the calculated macroscopic static dielectric tensors are vanishingly small. The ionic contributions to the macroscopic static dielectric tensors of COF-5 were calculated via density functional perturbation theory (DFPT)15 using VASP (Table 3).
Emission and excitation spectra were recorded on a Horiba Jobin Yvon Fluorolog-3 fluorescence spectrophotometer equipped with a 450 W Xe lamp, emission and excitation polarizer, double excitation and double emission monochromators, a digital photon-counting photomultiplier and a secondary InGaAs detector for the NIR range. Correction for variations in lamp intensity over time and wavelength was achieved using a solid-state silicon photodiode as the reference. The spectra were further corrected for variations in photomultiplier response over wavelength and for the path difference between the sample and the reference by multiplication with emission correction curves generated on the instrument. To collect emission spectra of the 2D COF films, films were mounted in a proprietary film holder. When emission polarization was noted as “normalized”, we divided the intensity of all emission intensities by the maximum emission intensity.
Impedance measurements were carried out by a Solartron 1260 impedance analyzer using an AC amplitude of 100 mV in a frequency range of 100 Hz to 10 kHz. This frequency range was chosen because the signal was too noisy below 100 Hz and series resistance from the SiC wafer interfered with measurements above 10 kHz. Au pads were contacted by tungsten cat whisker soft-probes (Signatone, SE-SM) to avoid puncturing the COF dielectric. Capacitance-frequency (C-f) measurements were performed at zero dc bias, and capacitance-voltage (C-V) measurements were conducted at 1 kHz. Capacitance values were verified independently using the C-V module of a 4200 Semiconductor Characterization System (SC S), Keithley Instruments. Leakage measurements were also carried by the 4200 SCS system using a remote current preamplifier. Impedance data was analyzed by model fitting using ZPlot/ZView software from Scribner Associates, Inc.
In our time-domain thermoreflectance (TDTR) setup, sub-picosecond laser pulses emanate from a Ti:Saphhire oscillator at 80 MHz repetition rate. The pulses are separated into a pump path that heats up the sample and a time-delayed probe path that is reflected from the Al transducer. The reflected probe beam provides a measure of the change in the thermoreflectance due to the decay of the thermal energy deposited by the pump beam. A modulation of 8.8 MHz is applied by an electro-optic modulator on the pump beam and the ratio of the in-phase to out-of-phase signal of the reflected probe beam recorded at that frequency by a lock-in amplifier (−Vin/Vout) for up to 5.5 ns after the initial heating event. The pump and probe beams are focused on to the Al transducer at 1/e2 radii values of 10 and 5 μm, respectively. To simultaneously measure the thermal conductivity and heat capacity of our COFs, we fit a three-layer thermal model to our experimental data. We also perform FDTR measurements on our COF-5 sample. Similar to TDTR, FDTR is also a laser-based metrology implemented to measure thermal properties of a sample. The Au-coated sample is periodically heated via a sinusoidally modulated (100 kHz-5 MHz) pump laser at 488 nm wavelength. The sample's temperature will fluctuate with the same frequency as the pump laser, but with a time delay. This phase delay is characteristic of the thermal properties of the sample. The temperature is measured using a concentric probe laser (532 nm), which is sensitive to the thermoreflectance of Au. The frequency-dependent time delay measured as a phase delay of the reflected probe laser with respect to the pump laser modulation frequency is measured with a photodiode connected to a lock-in amplifier.
Our molecular dynamics (MD) simulations are performed with the LAMMPS code22 and the interatomic interactions are described by the adaptive intermolecular reactive empirical bond order (AIREBO) potentia1. 23 We apply periodic boundary conditions in all directions. The computational domains are equilibrated under the Nose-Hoover thermostat and barostat,24 (which is the NPT83 integration with the number of particles, pressure and temperature of the system held constant) for a total of 1 ns at 0 bar pressure. Following the NPT integration, an NVT integration (with constant volume and number of particles) is prescribed to fully equilibrate the structures at the desired temperature for another 1 ns. Note, we prescribe a time step of 0.5 fs for all our simulations. For the simulations, we vary the total cross-plane thickness, d, and length of the computational domain, L, to check for size effects in our thermal conductivity predictions as detailed below.
After equilibration, the thermal conductivities of our COFs at different temperatures predicted via the Green-Kubo (GK) approach under the EMD framework. In this formalism, the thermal conductivities of our COFs along the x-,y-(in-plane) and z-(cross-plane) directions are calculated as,
Here t is time, T and V are the temperature and volume of the systems, respectively, and <Ss,t,z(t) Sx,y,z(0)>is the component of the heat current autocorrelation function (HCACF) in the prescribed directions.
To ensure that the HCACF decays to zero, we set the total correlation time period for the integration of the HCACF to 50 ps as shown in the inset of
The GK approach has been extensively used to predict the lattice thermal conductivity of different crystalline and amorphous material systems. However, there has been considerable ambiguity in efficiently calculating the thermal conductivity via Eq. 2 due to uncertainties associated with finite simulation times and domain sizes. To ensure that the EMD-predicted thermal conductivities are not influenced by size effects, the dimensions of the simulation box are chosen to produce converged values of thermal conductivities. To this end, the thermal conductivities of structures with cross-sections of 15×13 nm2 and 30×26 nm2 are comparable within uncertainties. Similarly, the thermal conductivities of structures with computational domain sizes of 15.1×13.1×3.4 nm3, and 15.1×13.1×10.2 nm3 are also similar within uncertainties.
Since there has been contention on the use of the heat current calculations in LAMMPS to predict the thermal conductivity of structures with many-body interatomic potentials, we run nonequilibrium MD (NEMD) simulations to gain more confidence in our in-plane thermal conductivity predictions for our COF-5 structure. For the NEMD simulations, a steady-state temperature gradient is established by adding a fixed amount of energy per time step to a heat bath at one end of the computational domain, while removing an equal amount of heat from a cold bath at the other end of the domain; energy is added and removed at specified rate of 0.4 eV ps−1 under the microcanonical ensemble where the number of atoms (N), volume (V), and energy (E) of the system are held constant. A fixed wall at either side of the domain is enforced for our NEMD simulations. The temperature profile along the in-plane direction is obtained by averaging the temperature of the atoms along equally spaced bins in the applied heat flux direction for a total of 10 ns and the thermal conductivity is predicted via Fourier's law; the initial 3 ns of data are ignored to create time-averaged steady-state temperature profiles. We calculate thermal conductivities for different domain lengths to accurately predict the bulk in-plane thermal conductivity of our COF-5 structure. For this, we plot the inverse of thermal conductivity, κ−1, as a function of the inverse of the computational domain length, d−1, which shows a linear trend as shown in
To get an estimate for the heat capacity of these COFs, we calculate the vibrational density of states (DOS) from our MD simulations. The velocities of the atoms in the COF-5 structure are output every 10 time steps for a total of 1 ns. A velocity autocorrelation function algorithm is used to obtain the local phonon DOS in the cross-plane and in-plane directions as shown in
where m is the atomic mass, kB is the Boltzmann constant, T is the local temperature, and ρ is the atomic density. We use the DOS to calculate the room temperature heat capacity as,
where ωc is the cutoff frequency, and f is the Bose-Einstein distribution. We estimate a value of Cv˜0.54 J cm−3 K−1 for our COF-5 at room temperature, which agrees well with our experimentally determined value (Cv˜0.52±0.08 J cm−3 K−1).
To generalize our results and to investigate the effect of varying porosities on the thermal conductivity of 2D COFs, we perform additional GK simulations on structures with varying densities in the range of 0.5 g cm−3 to 1 g cm−3. The structures compared are based on TP-COF, COF-5, and COF-1 (with pore sizes of ˜3.6 nm, 2.7 nm and 1.3 nm, respectively). To investigate the effect of varying porosities while maintaining similar internal microstructure, we modify the COF-1 structure by adding a phenyl ring to the linkers (COF-1-2R, where ‘R’ stands for ‘rings’). We compare the thermal conductivity of these four different 2D COFs with varying porosities and internal architectures in the zig-zag, arm-chair and cross-plane directions as a function of their densities. The thermal conductivity in the zig-zag and arm-chair directions are similar within uncertainties for a particular COF. More interestingly, the thermal conductivity of 2D COFs is significantly dictated by their corresponding density, both in the in-plane and cross-plane directions. These additional simulations provide design criteria for the synthesis of 2D COFs with potentially modular thermal conductivities based on controlling their porosity.
XRR measurements were carried out using a Rigaku ATXG diffractometer equipped with an 18 kW Cu rotating anode (λ=1.5418 Å) operating at a voltage of 50 kV and a current of 240 mA, with a collimated beam of 0.1 mm×2 mm (0.2 mm2). All measurements are plotted in terms of the scattering vector Q, normalized to the measured incident beam intensity, and corrected for geometrical footprint and background signal. The XRR analysis was performed using Motofit software. 3 Three different systems were studied: COF-5/EG/SiC, COF-5/EG/SiO2/Si and Al2O3/COF-5/EG/SiO2/Si. The fittings show a well-resolved electron density profile which confirms no intermixing or degradation of the COF-5 film. All the electron densities correspond to the expected bulk-like values. The electron density for the COF-5 film was a free parameter determined from the fit. The fitting parameters are included in Tables 4-6. The fit determined electron density profiles are shown as insets in each of the XRR figures.
Atomic force microscopy (AFM) was conducted using the facilities at the Northwestern Atomic and Nanoscale Characterization Experiment Center (NUANCE) on a SPID Bruker FastScan AFM using a gold tip under the non-contact mode in air. To prepare films for imaging, they were scored with a pair of Teflon-coated forceps so as to not damage the underlying Si. These films were then imaged across the score to evaluate their thickness and roughness.
2D COF films were cleaved and mounted with carbon tape or double-sided copper taper on vertical SEM mounts. Each sample was coated with 7 nm of Os (SPI Osmium Coater, with OsO4 as a volatile source) to create a conformal conductive coating prior to imaging. Images were collected with a Hitachi SU 8030 scanning electron microscope with an acceleration voltage of 5 kV at a magnification of 80,000.
Epitaxial graphene was grown on 4H-SiC(0001) wafers (Cree, Inc.) by ultra-high vacuum (UHV) annealing. The SiC wafers were diced into 5×9 mm rectangles (American Precision Dicing, Inc.) and the resulting substrates were first degreased via sonication in acetone and isopropanol before being introduced into the UHV chamber with base pressure ˜5·10−11 Torr. Substrates were degassed for 12 hours at 500° C. prior to graphitization at 1200° C. for 20 minutes while maintaining chamber pressure below 5·10′ Torr. During annealing, substrate temperature was monitored using an infrared pyrometer (ε=0.85).
1H NMR spectra were acquired on a 400 MHz Agilent DD MR-400 system or Bruker Avance III 500 MHz spectrometer and recorded at 25° C. All chemical shifts were calibrated using residual solvent as internal reference (CDCl3: 7.26 ppm for 1H NMR. DMSO: 2.5 ppm for 1H NMR).
First, atomic layer deposition (ALD) was used to grow Al2O3 on COF-coated EG-SiC substrates using a Savannah S100 ALD reactor (Cambridge Nanotech, Cambridge MA). The substrates were loaded into the chamber pre-heated to 100° C. The base pressure of the chamber was maintained at 0.8 Torr with a constant N2 flow rate of 20 sccm. The growth was done at 100° C. by exposing samples to sequential doses of the metal oxide precursor (trimethyl aluminum (TMA), Aldrich, 99%) and deionized water interspersed with dry N2 purge steps between each precursor dose. For Al2O3 growth, a single ALD cycle consisted of a TMA pulse for 0.015 s and a 30 s purge, followed by a H2O pulse for 0.015 s and a second 30 s purge. During growth, TMA precursor bottles were kept at room temperature. An approximately 6-nm-thick Al2O3 was grown on COF layer by using 75 pulses of TMA using 0.8 Å/cycle growth rate, as verified independently for atomic force microscopy and ellipsometry. The thickness of Al2O3/COF-5 dielectric bilayer was extracted from topography images (
Parallel plate capacitors were completed by growing 100-nm-thick Au films on Al2O3/COF-5 dielectric bilayer using a thermal evaporator (Nano38, Kurt J. Lesker Company). The evaporation was done through a shadow mask with rectangular holes of 100 μm×100 μm using a growth rate of 1 Å/sec.
All monomers, solvents, and catalysts were either purchased from commercial sources or prepared following literature reported protocols. All materials were used as received without further purification, including 2,3,6,7,10,11-Hexahydroxytriphenylene Hydrate (HHTP) (TCI America), 1,4-phenylenebisboronic acid (PBBA) (Sigma Aldrich), and 4,4′-biphenylbisboronic acid (BBBA) (Sigma Aldrich). Anhydrous THF was obtained from a solvent purification system (JC Myer System).
Synthesis of 2,7-pyrenebisboronic acid. PyBA was prepared by an adaptation of a previously reported synthesis.4 A THF:H20 mixture (300 mL, 4:1 vol) of pyrene-2,7-diboronicester (5g, 11 mmol, 1.0 equiv.) and NaIO4 (3.5 g, 27.5 mmol, 2.5 equiv.) was prepared in a 500 mL RBF and stirred at room temperature for 16 hrs under N2. During the course of this reaction, a white precipitate was formed. The reaction mixture was then diluted with H2O (300 mL) and filtered. During filtration, the product was washed with an additional 300 mL of H2O, taking care to not allow the product to dry completely on the filter paper. The product was then flushed with hexanes and dried, which produced a white powder (2.6 g, 81%). 1H NMR analysis of this product was consistent with a previous report.4 1H NMR (400 MHz, DMSO-d6, 298 K): δ ppm 8.68 (4H, s, 1,3,6,7-H-pyrene), 8.44 (4H, s, 4,5,9,10-H-pyrene), 8.16 (4H, s, BO-H)
Synthesis of 4,4′-diphenylbutadiynebis(pinacolborane). The synthesis of this product was adapted from a previous report.5 A 100 mL round bottom flask was charged with CuI (0.752 g, 3.94 mmol, 0.05 equiv.), NiCl2⋅ 6H2O (0.936 g, 3.94 mmol, 0.05 equiv.), and tetramethylethylenediamine (TMEDA) (1.836 g, 15.784 mmol, 0.25 equiv.). Acetone (50 mL) was added, and as the solids dissolved the mixture became dark green. 4-ethynylbenzeneboronic acid pinacole ester (18 g, 78.8 mmol, 1.0 equiv.) was added to this mixture, which was then stirred for 16 hours. The solvent was removed by rotary evaporation to yield a green residue that was washed with H2O (300 mL). The resultant solid was isolated via filtration through a Bilchener funnel. This solid was subsequently recrystallized from CH3CN as a white solid, collected via filtration through a Büchener funnel, and dried under vacuum (5.25 g, 12 mmol, 30%). 1H NMR analysis of this product was consistent with a previous report.5 1H-NMR (CDCl3, 400 MHz, 298 K) δ 7.65 (d, J=9.0 Hz, 4H); 7.52 (d, J=9.0 Hz, 4H); 1.34 (s, 24H).
Synthesis of 4,4′-diphenylbutadiynebis(boronic acid). The synthesis of this compound was adapted from a previous report. 5 In a 20 mL scintillation vial, 4,4′ -diphenylbutadiyne pinacole borane (1.00 g, 2.20 mmol, 1.00 equiv.) and sodium periodate (1.0 g, 5.00 mmol, 2.27 equiv.) were dissolved in THF:H2O (4:1 v/v, 30 mL). This mixture was stirred at room temperature with nitrogen actively bubbling through it for 30 minutes, after which 1M HCl (5 mL) was added via syringe. The reaction vessel was subsequently sealed and allowed to stir for an additional 24 hours. At this point, the reaction mixture was poured into 100 mL of H2O, filtered through a Buchener funnel, and washed with an additional 100 mL of H2O. This product was then flushed with 100 mL of diethyl ether. This powder was dried under vacuum for 10 minutes to afford a fine white powder (444 mg, 1.5 mmol, 69%). 1H NMR analysis of this product was consistent with a previous report.5 1H-NMR (DMSO-d6, 400 MHz, 298 K) δ 8.26 (s, 4H); 7.82 (d, J=7.5 Hz, 4H); 7.57 (d, J=7.5 Hz, 4H).
Synthesis of N,N′-dibutyl-6,6′-bisbromoisoindigo. To a flame-dried 300 mL RBF, dibromoisoinidio (750 mg, 1.785 mmol, 1.0 equiv.), K2CO3 (1.65 g, 11.90 mmol, 6.67 equiv.), and DMF (32 mL) were added. Then, butylbromide (0.56 mL, 5.24 mmol, 2.93 equiv.) was added via syringe and heated to 110° C. After 14 hours, the reaction mixture was cooled to room temperature and quenched with saturated NH4Cl. The product was then extracted with EtOAc (2×100 mL). These fractions were then combined, washed with water (5×100 mL) and brine (2×100 mL). The organic fraction was then collected, dried with anhydrous MgSO4, filtered, and concentrated in vacuo to give N,N′-dihexyl-6,6′-bisbromoisoindigo as a deep red product (590 mg, 1.1 mmol, 62%). 1H NMR analysis of this product was consistent with a previous report.6 1H NMR (400 MHz, cdcl3) δ 9.07 (d, J=8.6 Hz, 1H), 7.17 (dd, J=8.6, 1.9 Hz, 1H), 6.93 (d, J=1.9 Hz, 1H), 3.74 (t, J=7.4 Hz, 2H), 1.66 (d, J=7.4 Hz, 2H), 1.41 (d, J=7.8 Hz, 2H), 0.97 (t, J=7.4 Hz, 3H).
Synthesis of N,N′-dibutyl-6,6′-isoindigobis(pinacolborane). The following were added to a 50 mL Schlenk flask: N,N′-dihexyl-6,6′-bisbromoisoindigo (500 mg, 0.94 mmol, 1.0 equiv.), (BPin)2 (596 mg, 2.35 mmol, 2.5 equiv), KOAc (332 mg, 3.38 mmol, 3.6 equiv.), Pd(dppf)Cl2.CH2Cl2 (80 mg, 0.09 mmol, 0.10 equiv.), and 1,4-dioxane (8 mL). This flask was then closed with a septum and degassed under constant N2 flow for 15 min. The reaction mixture was then heated at 80° C. for 40 hrs. Then, the reaction was cooled to room temperature and diluted with CH2Cl2. This mixture was then passed through a silica gel plug on a fritted funnel and washed with CH2Cl2. The filtrate was then concentrated in vacuo to yield a sticky red residue, which was mixed with MeOH (15 mL) and placed in a freezer. After 2 hrs, the precipitate was collected and dried to give N,N′-dihexyl-6,6′-isoindigobis(pinacolborane) as a deep red product (510 mg, 0.82 mmol, 87%). 1H NMR analysis of this product was consistent with a previous report.6 1H NMR (499 MHz, cdcl3) δ 9.15 (d, J=7.9 Hz, 1H), 7.49 (dd, J=7.9, 1.1 Hz, 1H), 7.15 (s, 1H), 3.81 (t, J=7.4 Hz, 2H), 1.73-1.68 (m, 2H), 1.46-1.41 (m, 2H), 1.37 (s, 12H), 0.97 (t, J=7.4 Hz, 3H).
Synthesis of N,N′-dibutyl-6,6′-isoindigobis(boronic acid). To a 20 mL scintillation vial N,N′-dihexyl-6,6′-isoindigobis(pinacolborane) (100 mg, 0.16 mmol, 1.0 equiv.), NaIO4 (85 mg, 0.4 mmol, 2.5 equiv.), a THF:H2O 4:1 vol. (15 mL) were added. The vial was then placed under N2. After 3 days, the reaction was diluted with H2O (15 mL) and filtered while continuously adding water (50 mL), taking care to not let the product dry to completion on the filter paper. Finally, the product was washed with hexanes and dried under vacuum. This yielded N,N′-dihexyl-6,6′-isoindigobis(boronic acid) as a bright red solid (52 mg, 0.112 mmol, 70% yield). Reliable NMR analysis was not possible due to insolubility of the product.
2D COF-5 Films. First, a graphene-coated Si/SiO2 (1 cm×1 cm, UniversityWafer, Inc.) was placed into a scintillation vial. Then, solutions of HHTP (2 mM) and PBBA (3 mM) were prepared separately in a solvent blend of 80/16/4 vol CH3CN:1,4-dioxane:1,3,5-trimethylbenzene. These solutions were then filtered to remove any insoluble particulates. These solutions were then added in a 1:1 vol ratio to the substate-containing scintillation vial, producing a 20 mL solution of 1 mM HHTP and 1.5 mM PBBA. This scintillation vial was then sealed and heated to 80° C. for 24 hrs. After 24 hrs, a milky suspension had formed in the scintillation vial. Approximately 90% of the solution was then decanted and diluted with fresh 80/16/4 vol CH3CN:1,4-dioxane:1,3,5-trimethylbenzene. This procedure was repeated 3 times to sufficiently dilute any colloidal species present in solution. The wafer was then removed from solvent with forceps and allowed to dry in air.
2D COF-10 Films. First, a graphene-coated Si/SiO2 (1 cm×1 cm, University Wafer, Inc.) was placed into a scintillation vial. Then, solutions of HHTP (2 mM) and BBBA (3 mM) were prepared separately in a solvent blend of 80/16/4 vol CH3CN:1,4-dioxane:1,3,5-trimethylbenzene. These solutions were then filtered to remove any insoluble particulates. These solutions were then added in a 1:1 vol ratio to the substate-containing scintillation vial, producing a 20 mL solution of 1 mM HHTP and 1.5 mM BBBA. This scintillation vial was then sealed and heated to 80° C. for 24 hrs. After 24 hrs, a milky suspension had formed in the scintillation vial. Approximately 90% of the solution was then decanted and diluted with fresh 80/16/4 vol CH3CN:1,4-dioxane:1,3,5-trimethylbenzene. This procedure was repeated 3 times to sufficiently dilute any colloidal species present in solution. The wafer was then removed from solvent with forceps and allowed to dry in air.
2D TP-COF Films. First, a graphene-coated Si/SiO2 (1 cm×1 cm, University Wafer, Inc.) was placed into a scintillation vial. Then, solutions of HHTP (2 mM) and PyBA (3 mM) were prepared separately in a solvent blend of 80/16/4 vol CH3CN:1,4-dioxane:1,3,5-trimethylbenzene. These solutions were then filtered to remove any insoluble particulates. These solutions were then added in a 1:1 vol ratio to the substate-containing scintillation vial, producing a 20 mL solution of 1 mM HHTP and 1.5 mM PyBA. This scintillation vial was then sealed and heated to 80° C. for 24 hrs. After 24 hrs, a milky suspension had formed in the scintillation vial. Approximately 90% of the solution was then decanted and diluted with fresh 80/16/4 vol CH3CN:1,4-dioxane:1,3,5-trimethylbenzene. This procedure was repeated 3 times to sufficiently dilute any colloidal species present in solution. The wafer was then removed from solvent with forceps and allowed to dry in air.
2D DPB-COF Films. First, a graphene-coated Si/SiO2 (1 cm×1 cm, UniversityWafer, Inc.) was placed into a scintillation vial. Then, solutions of HHTP (2 mM) and DPB-BA (3 mM) were prepared separately in a solvent blend of 80/16/4 vol CH3 CN:1,4-dioxane:1,3,5-trimethylbenzene. These solutions were then filtered to remove any insoluble particulates. These solutions were then added in a 1:1 vol ratio to the substate-containing scintillation vial, producing a 20 mL solution of 1 mM HHTP and 1.5 mM DPB-BA. This scintillation vial was then sealed and heated to 80° C. for 24 hrs. After 24 hrs, a milky suspension had formed in the scintillation vial. Approximately 90% of the solution was then decanted and diluted with fresh 80/16/4 vol CH3CN:1,4-dioxane:1,3,5-trimethylbenzene. This procedure was repeated 3 times to sufficiently dilute any colloidal species present in solution. The wafer was then removed from solvent with forceps and allowed to dry in air.
2D COF-117 Films. First, a graphene-coated Si/SiO2 (1 cm×1 cm, UniversityWafer, Inc.) was placed into a scintillation vial. Then, solutions of HHTP (2 mM) and IBBA (3 mM) were prepared separately in a solvent blend of 80/16/4 vol CH3CN:1,4-dioxane:1,3,5-trimethylbenzene. These solutions were then filtered to remove any insoluble particulates. These solutions were then added in a 1:1 vol ratio to the substate-containing scintillation vial, producing a 20 mL solution of 1 mM HHTP and 1.5 mM IBBA. This scintillation vial was then sealed and heated to 80° C. for 24 hrs. After 24 hrs, a milky suspension had formed in the scintillation vial. Approximately 90% of the solution was then decanted and diluted with fresh 80/16/4 vol CH3CN:1,4-dioxane:1,3,5-trimethylbenzene. This procedure was repeated 3 times to sufficiently dilute any colloidal species present in solution. The wafer was then removed from solvent with forceps and allowed to dry in air.
First, a graphene-coated Si/SiO2 (1 cm×1 cm, UniversityWafer, Inc.) was placed into a scintillation vial. Then, solutions of HHTP (10 mM) and PBBA (15 mM) were prepared separately in a solvent blend of 80/16/4 vol CH3CN:1,4-dioxane:1,3,5-trimethylbenzene. These solutions were then filtered to remove any insoluble particulates.
These solutions were then mixed in a 1:1 vol ratio, which was then diluted with additional 80/16/4 vol CH3CN:1,4-dioxane:1,3,5-trimethylbenzene to yield solutions with HHTP concentrations of 5 mM (PBBA=7.5 mM), 2 mM (PBBA=3 mM), 1 mM (PBBA=1.5 mM), and 0.5 mM (PBBA=0.75 mM). These solutions were then added to the scintillation vial that contained the graphene-supported substrate. This scintillation vial was then sealed and heated to 80° C. for 24 hrs. After 24 hrs, a milky suspension had formed in the scintillation vial. Approximately 90% of the solution was then decanted and diluted with fresh 80/16/4 vol CH3CN:1,4-dioxane:1,3,5-trimethylbenzene. This procedure was repeated 3 times to sufficiently dilute any colloidal species present in solution. The wafer was then removed from solvent with forceps and allowed to dry in air.
First, a graphene-coated Si/SiO2 (1 cm×1 cm, UniversityWafer, Inc.) was placed into a scintillation vial. Then, solutions of HHTP (2 mM) and corresponding boronic acid (3 mM) were prepared separately in a solvent blend of 80/16/4 vol CH3CN:1,4-dioxane:1,3,5-trimethylbenzene. These solutions were then filtered to remove any insoluble particulates. These solutions were then mixed in a 1:1 vol ratio. This solution was then added to the scintillation vial that contained the graphene-supported substrate. This scintillation vial was then sealed and heated to 80° C. for 24 hrs. After 24 hrs, a milky suspension had formed in the scintillation vial. Approximately 90% of the solution was then decanted and diluted with fresh 80/16/4 vol CH3CN:1,4-dioxane:1,3,5-trimethylbenzene. This procedure was repeated 3 times to sufficiently dilute any colloidal species present in solution.
Then, to instigate another round of growth, additional monomer species (prepared as described above) were added to the scintillation vial containing the wafer. This scintillation vial was then sealed and heated to 80° C. for 24 hrs. After 24 hrs, a milky suspension had formed in the scintillation vial. Approximately 90% of the solution was then decanted and diluted with fresh 80/16/4 vol CH3CN:1,4-dioxane:1,3,5-trimethylbenzene. This procedure was repeated 3 times to sufficiently dilute any colloidal species present in solution. This procedure was repeated for as many times as described. Finally, the wafer was removed from solvent with forceps and allowed to dry in air.
To prepare our samples for time-domain thermoreflectance (TDTR), we first deposit an 80 nm thick Al transducing layer via electron beam evaporation at 6·10−6 Torr. In our TDTR setup, sub-picosecond laser pulses emanate from a Ti:Saphhire oscillator at 80 MHz repetition rate. The pulses are separated into a pump path that heats up the sample and a time-delayed probe path that is reflected from the Al transducer. The reflected probe beam provides a measure of the change in the thermoreflectance due to the decay of the thermal energy deposited by the pump beam. A modulation of 8.8 MHz is applied by an electro-optic modulator on the pump beam and the ratio of the in-phase to out-of-phase signal of the reflected probe beam recorded at that frequency by a lock-in amplifier (−Vin/Vout) for up to 5.5 ns after the initial heating event. The pump and probe beams are focused on to the Al transducer at e−2 radii values of 10 and 5 μm for our pump and probe spots, respectively.
To simultaneously measure the thermal conductivity and heat capacity of our COFs, we fit a three-layer thermal model to our experimental data. However, we first consider the appropriate range of pump-probe delay times, in which the thermal model is extremely sensitive to changes in the thermophysical quantities. This is quantified by the sensitivity of the ratio (Vin/VNout) to the various thermal properties defined by,
where α is the thermophysical parameter of interest.16
Characteristic TDTR data and the best-fit of the thermal model for TP-COF at 8.8 MHz modulation frequency is shown in
where Rm and Rd are the ratios from the model and data, respectively, and n is the total number of time delays considered.
From time-domain thermoreflectance measurements, we determine that the thermal resistivity of the Al/COF-5 boundary is minimal (
We plot sensitivity contour plots (
In the scenario where interfacial resistances dominate heat transfer, decreasing the film thickness will have a negligible effect on total thermal transport. However, if heat transfer is dominated by the intrinsic resistance of the film, a change in the thickness results in a noteable change in the total conductance across the sample. To differentiate between these different possibilities, we synthesized an additional COF-5 film with a different thickness of that measured previously. TDTR measurements (
To cross-validate and gain confidence in our TDTR results, we perform Frequency domain thermoreflectance (FDTR) measurements on our COF-5 sample. Similar to TDTR, FDTR is also a laser-based metrology implemented to measure thermal properties of a sample.19,20 A thin (73.1 nm measured by KLA Tencor P-15 Profilometer) coating of Au is sputter deposited (PerkinElmer6J) on top of the sample. The Au-coated sample is periodically heated via a sinusoidally modulated (100 kHz-5 MHz) pump laser at 488 nm wavelength. The sample's temperature will fluctuate with the same frequency as the pump laser, but with a time delay. The phase delay is characteristic of the thermal properties of the sample. The temperature is measured using a concentric probe laser (532 nm), which is sensitive to the thermoreflectance of Au. The frequency-dependent time delay measured as a phase delay of the reflected probe laser with respect to the pump laser modulation frequency is measured with a photodiode connected to a lock-in amplifier. The phase delay, as shown in
COF thermal conductivity is the targeted property, but its value depends on the heat capacity of the COF, which is also unknown. We evaluated the quality of the fit between the model and data based on the mean squared error (MSE). The MSE was calculated assuming a range of thermal conductivity and heat capacity combinations and averaged for four independent data sets. In
1 Jiang, Z. GIXSGUI: a MATLAB toolbox for grazing-incidence X-ray scattering data visualization and reduction, and indexing of buried three-dimensional periodic nanostructured films. J. Appl. Crystallogr. 48, 917-926 (2015).
2 Ilaysky, J. Nika: software for two-dimensional data reduction. J. Appl. Crystallogr. 45, 324-328 (2012).
3 Nelson, A. Co-refinement of multiple-contrast neutron/X-ray reflectivity data using MOTOFIT. J Appl. Crystallogr. 39, 273-276 (2006).
4 Wan, S., Guo, J., Kim, J., Thee, H. & Jiang, D. A belt-shaped, blue luminescent, and semiconducting covalent organic framework. Angew. Chem. Int. Ed. 47, 8826-8830 (2008).
5 Spitler, E. L. et al. A 2D covalent organic framework with 4.7-nm pores and insight into its interlayer stacking. J. Am. Chem. Soc. 133, 19416-19421 (2011).
6 Dharmapurikar, S. S., Arulkashmir, A., Das, C., Muddellu, P. & Krishnamoorthy, K. Enhanced hole carrier transport due to increased intermolecular contacts in small molecule based field effect transistors. ACS Appl. Mater. Inter. 5, 7086-7093 (2013).
7 Colson, J. W. et al. Oriented 2D covalent organic framework thin films on single-layer graphene. Science 332, 228-231 (2011).
8 Dovesi, R. et al. Quantum-mechanical condensed matter simulations with CRYSTAL. WIREs Computational Molecular Science 8, e1360, doi:10.1002/wcms.1360 (2018).
9 R. Dovesi, V. R. S., C. Roetti, R. Orlando, C. M. Zicovich-Wilson, F. Pascale, B. Civalleri, K. Doll, N. M. Harrison, I. J. Bush, P. D'Arco, M. Llunell, M. Causà, Y. Noël, L. Maschio, A. Erba, M. Rerat, S. Casassa. CRYSTAL17 User's Manual (University of Torino, Torino, 2017).
10 Adamo, C. & Barone, V. Toward reliable density functional methods without adjustable parameters: The PBE0 model. The Journal of Chemical Physics 110, 6158-6170, doi:10.1063/1.478522 (1999).
11 Peintinger, M. F., Oliveira, D. V. & Bredow, T. Consistent Gaussian basis sets of triple-zeta valence with polarization quality for solid-state calculations. Journal of Computational Chemistry 34, 451-459, doi :10.1002/j cc.23153 (2013).
12 Grimme, S., Ehrlich, S. & Goerigk, L. Effect of the damping function in dispersion corrected density functional theory. Journal of Computational Chemistry 32, 1456-1465, doi:10.1002/jcc.21759 (2011).
13 Gajdos̆, M., Hummer, K., Kresse, G., Furthmüller, J. & Bechstedt, F. Linear optical properties in the projector-augmented wave methodology. Physical Review B 73, 045112, doi :10.1103/PhysRevB .73.045112 (2006).
14 Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized Gradient Approximation Made Simple. Physical Review Letters 77, 3865-3868, doi:10.1103/PhysRevLett.77.3865 (1996).
15 Gonze, X. Adiabatic density-functional perturbation theory. Physical Review A 52, 1096-1114, doi:10.1103/PhysRevA.52.1096 (1995).
16 Costescu, R. M., Wall, M. A. & Cahill, D. G. Thermal conductance of epitaxial interfaces. Phys. Rev. B 67, 054302 (2003).
17 Giri, A., Niemeld, J.-P., Szwejkowski, C. J., Karppinen, M. & Hopkins, P. E. Reduction in thermal conductivity and tunable heat capacity of inorganic/organic hybrid superlattices. Phys. Rev. B. 93, 024201 (2016).
18 Wang, X., Liman, C. D., Treat, N. D., Chabinyc, M. L. & Cahill, D. G. J. P. R. B. Ultralow thermal conductivity of fullerene derivatives. Phys. Rev. B 88, 075310 (2013).
19 Schmidt, A. J., Cheaito, R. & Chiesa, M. A frequency-domain thermoreflectance method for the characterization of thermal properties. Rev. Sci. Instrum. 80, 094901 (2009).
20 Malen, J. A. et al. Optical measurement of thermal conductivity using fiber aligned frequency domain thermoreflectance. J. Heat Trans. 133 (2011).
21 Koh, Y. K., Bae, M.-H., Cahill, D. G. & Pop, E. Heat conduction across monolayer and few-layer graphenes. Nano Lett. 10, 4363-4368 (2010).
22 Plimpton, S. J. Comp. Phys. 117, 1-19 (1995).
23 Stuart, S. J., Tutein, A. B. & Harrison, J. A. A reactive potential for hydrocarbons with intermolecular interactions. J. Chem. Phys. 112, 6472-6486 (2000).
24 Hoover, W. G. & Posch, H. A. Direct measurement of Lyapunov exponents. Phys. Let. A 113, 82-84 (1985).
25 Giri, A. & Hopkins, P. E. Resonant phonon modes in fullerene functionalized graphene lead to large tunability of thermal conductivity without impacting the mechanical properties. J. Appl. Phys. 125, 205102 (2019).
26 Salaway, R. N. & Zhigilei, L. V. Molecular dynamics simulations of thermal conductivity of carbon nanotubes: Resolving the effects of computational parameters. Int. J. Heat Mass Trans! 70, 954-964 (2014).
27 Lukes, J. R. & Zhong, H. Thermal conductivity of individual single-wall carbon nanotubes. J. Heat Trans. (2007).
28 Allen, M. P. & Tildesley, D. J. Computer simulation of liquids. (Oxford university press, 2017).
29 Schelling, P. K., Phillpot, S. R. & Keblinski, P. Comparison of atomic-level simulation methods for computing thermal conductivity. Phys. Rev. B 65, 144306 (2002).
30 McGaughey, A. & Kaviany, M. Thermal conductivity decomposition and analysis using molecular dynamics simulations. Part I. Lennard-Jones argon. Int. J. Heat Mass Transf. 47, 1783-1798 (2004).
31 McGaughey, A., Kaviany, M. J. I. J. o. H. & Transfer, M. Thermal conductivity decomposition and analysis using molecular dynamics simulations: Part II. Complex silica structures. Int. J. Heat Mass Transf. 47, 1799-1816 (2004).
32 Henry, A. S. & Chen, G. Spectral phonon transport properties of silicon based on molecular dynamics simulations and lattice dynamics. J. Comput. Theor. Nanos. 5, 141-152 (2008).
33 Wang, Z., Safarkhani, S., Lin, G. & Ruan, X. Uncertainty quantification of thermal conductivities from equilibrium molecular dynamics simulations. Int. J. Heat Mass Transf. 112, 267-278 (2017).
34 Lv, W. & Henry, A. Direct calculation of modal contributions to thermal conductivity via Green-Kubo modal analysis. New. J. Phys. 18, 013028 (2016).
35 Chalopin, Y., Esfarjani, K., Henry, A., Volz, S. & Chen, G. Thermal interface conductance in Si/Ge superlattices by equilibrium molecular dynamics. Phys. Rev. B 85, 195302 (2012).
36 Che, J. Ç. a. T., Deng W and Goddard. Thermal conductivity of diamond and related materials from molecular dynamics simulations. J. Chem. Phys. 113, 6888 (2000).
37 Chen, J., Zhang, G. & Li, B. How to improve the accuracy of equilibrium molecular dynamics for computation of thermal conductivity? Phys. Let. A 374, 2392-2396 (2010).
38 Volz, S. G. & Chen, G. Molecular-dynamics simulation of thermal conductivity of silicon crystals. Phys. Rev. B 61, 2651 (2000).
39 Dong, H., Fan, Z., Shi, L., Harju, A. & Ala-Nissila, T. Equivalence of the equilibrium and the nonequilibrium molecular dynamics methods for thermal conductivity calculations: From bulk to nanowire silicon. Phys. Rev. B 97, 094305 (2018).
40 Sun, L. & Murthy, J. Y. Domain size effects in molecular dynamics simulation of phonon transport in silicon. Appl. Phys. Let. 89, 171919 (2006).
41 Fan, Z. et al. Force and heat current formulas for many-body potentials in molecular dynamics simulations with applications to thermal conductivity calculations. Phys. rev. B 92, 094301 (2015).
42 Boone, P., Babaei, H., Wilmer, C. E. J. J. o. c. t. & computation. Heat flux for many-body interactions: Corrections to LAMMP S. J. Chem. Theory Comp. 15, 5579-5587 (2019).
43 Sellan, D. P., Landry, E. S., Turney, J., McGaughey, A. J. & Amon, C. H. Size effects in molecular dynamics thermal conductivity predictions. Phys. Rev. B 81, 214305 (2010).
44 Braun, J. L., Szwejkowski, C. J., Giri, A. & Hopkins, P. E. On the steady-state temperature rise during laser heating of multilayer thin films in optical pump—probe techniques. J. Heat Transfer 140 (2018).
This application claims benefit of priority to U.S. Patent Application Ser. No. 63/140,141, filed Jan. 21, 2021, the contents of which is incorporated by reference in its entirety.
This invention was made with government support under grant numbers W911NF-15-1-0447 awarded by Army Research Office (ARO) and N00014-20-1-2686 awarded by Office of Naval Research (ONR). The government has certain rights in the invention.
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/US22/13260 | 1/21/2022 | WO |
| Number | Date | Country | |
|---|---|---|---|
| 63140141 | Jan 2021 | US |
