Sintering, Microstructure, and Dielectric Properties of Copper Borates for High Frequency LTCC Applications

New ceramic materials based on two copper borates, CuB2O4 and Cu3B2O6, were prepared via solid state synthesis and sintering, and characterized as promising candidates for low dielectric permittivity substrates for very high frequency circuits. The sintering behavior, composition, microstructure, and dielectric properties of the ceramics were investigated using a heating microscope, X-ray diffractometry, scanning electron microscopy, energy dispersive spectroscopy, and terahertz time domain spectroscopy. The studies revealed a low dielectric permittivity of 5.1–6.7 and low dielectric loss in the frequency range 0.14–0.7 THz. The copper borate-based materials, owing to a low sintering temperature of 900–960 °C, are suitable for LTCC (low temperature cofired ceramics) applications.


Introduction
Modern high frequency communication systems create demand for new substrate materials with specific dielectric characteristics comprising a low dielectric permittivity, a low dielectric loss, and a low temperature coefficient of dielectric permittivity. Such dielectric properties of a substrate for microwave and mm-wave circuits improve the signal speed and quality, selectivity, and temperature stability of the operating frequency [1][2][3][4][5].
The copper metaborate CuB 2 O 4 crystallizes in a tetragonal structure with I-42d space group [25][26][27]. Its structure is composed of a BO 4 tetrahedra sharing four common oxygen ions. Cu 2+ ions are situated between them in two different crystallographic positions corresponding to a planar square or an elongated octahedral coordination [25][26][27].
Cu 3 B 2 O 6 has a more complex structure and a lower symmetry [28] as compared with CuB 2 O 4 . The best known is Cu 3 B 2 O 6 with a triclinic structure, although the crystallization of this compound in the monoclinic and orthorhombic structures was also reported. In Cu 3 B 2 O 6 , Cu 2+ ions occupy 16 nonequivalent crystallographic positions, which can be divided into the following three types-predominant square planar positions (CuO 4 ) with the coordination number four, distorted square pyramids (CuO 5 ) with the coordination number five, and distorted octahedral positions (CuO 6 ) with the coordination number six. For this compound, the calculated average effective coordination number is close to four for the triclinic structure. In Cu 3 B 2 O 6 , boron also shows different coordination  [28].
This work reports on sintering behavior, microstructure, and dielectric properties in the THz range of new ceramics based on two pure copper borates, CuB 2 O 4 and Cu 3 B 2 O 6 , and CuB 2 O 4 -Cu 3 B 2 O 6 mixtures. These ceramics offer a low dielectric permittivity and a low dielectric loss at very high frequencies, and a relatively low sintering temperature adequate for LTCC (low temperature cofired ceramics) technology.

Materials and Methods
Two copper borates, CuB 2 O 4 and Cu 3 B 2 O 6 , were synthesized using the conventional solid state reaction method. The high purity starting materials, H 3 BO 3 and CuO (Sigma Aldrich, St. Louis, MO, USA), were mixed in stoichiometric proportions, ball milled (Pulverisette 5, Fritsch, Germany) for 8 h in isopropyl alcohol, and dried. Then, the powders were pressed into pellets and calcined in a two-step process-at 200-400 • C for 2 h to decompose boric acid, and at 700 • C for 5 h to carry out solid state syntheses.
The resulting materials were ball milled for 8 h to obtain fine CuB 2 O 4 and Cu 3 B 2 O 6 powders. In addition, three CuB 2 O 4 -Cu 3 B 2 O 6 mixtures containing 35, 50, and 70 wt.% Cu 3 B 2 O 6 were prepared by ball milling for 8 h. For the last two compositions, 5 wt.% CuBi 2 O 4 was added as a sintering aid. Finally, the powders were granulated with polyvinyl alcohol, pressed into pellets, and sintered in the temperature range 900-960 • C.
The phase compositions of the materials were investigated using the X-ray diffraction method (Empyrean, PANalytical, Almelo, The Netherlands) using Cu K α1 radiation within a 2θ range of 10 to 90 • . Optimal sintering conditions and melting points of the samples were established based on observations in a heating microscope (Leitz, Germany) in the temperature range 20-1040 • C. Scanning electron microscopy and X-ray energy dispersive spectroscopy (FEI Nova Nano SEM 200 with EDAX Genesis EDS system, Hillsboro, OR, USA) were used to characterize the microstructure and elemental composition of the ceramics.
Dielectric properties at room temperature in the frequency range 0.12-2.5 THz were studied using time domain spectroscopy (TDS) (TPS Spectra 3000, Teraview, Cambridge, UK) according to the procedure reported previously [12]. The measurements were performed in purged air to avoid interference related to the presence of water vapor.

Phase Composition
As illustrated in Figure 1a,b, the XRD phase analysis confirmed the presence of the planned copper borates CuB 2 O 4 and Cu 3 B 2 O 6 as crystalline phases. CuB 2 O 4 shows the tetragonal structure with the space group I-42, while Cu 3 B 2 O 6 was detected as triclinic Cu 15 B 10 O 30 with the space group P-1. For the compositions prepared as CuB 2 O 4 -Cu 3 B 2 O 6 mixtures with a 5% CuBi 2 O 4 addition, the XRD analysis revealed two main crystalline copper borate phases, but additional crystalline phases were not detected (Figure 1d). This implies that the sintering aid, CuBi 2 O 4 , formed an amorphous phase or entered the crystal lattice of the main crystalline components.         These studies helped to establish the optimal firing profiles for each composition based on information about the temperature range in which the shrinkage occurs and about the softening and melting points. For pure copper borates (Figure 2a,b), the samples start to shrink at 891 and 893 • C, and the relevant optimal sintering temperatures are 940 and 930 • C for CuB 2 O 4 and Cu 3 B 2 O 6 , respectively. The melting points are 1000 • C for CuB 2 O 4 and 1040 • C for Cu 3 B 2 O 6 . The Cu 3 B 2 O 6 ceramic shows a higher melting point than CuB 2 O 4 , but it has a similar temperature of the shrinkage onset and exhibits an advantageous feature of a broader sintering range. Consequently, its optimal sintering temperature is close or even lower as compared with CuB 2 O 4 . For mixed copper borates, the optimal sintering temperatures were established as 960, 920, and 900 • C for 65% CuB 2 O 4 -35% Cu 3

Microstructural Studies
The SEM studies of all the sintered samples based on pure and mixed copper borates showed a very compact microstructure with a small contribution of porosity. It follows from the comparison of the images in Figure 3a,b that the microstructure for pure copper borates is similar, fine-grained, and uniform, with grain sizes in the 0.5-3 µm range.
These studies helped to establish the optimal firing profiles for each composition based on information about the temperature range in which the shrinkage occurs and about the softening and melting points. For pure copper borates (Figures 2a,b), the samples start to shrink at 891 and 893 °C, and the relevant optimal sintering temperatures are 940 and 930 °C for CuB2O4 and Cu3B2O6, respectively. The melting points are 1000 °C for CuB2O4 and 1040 °C for Cu3B2O6. The Cu3B2O6 ceramic shows a higher melting point than CuB2O4, but it has a similar temperature of the shrinkage onset and exhibits an advantageous feature of a broader sintering range. Consequently, its optimal sintering temperature is close or even lower as compared with CuB2O4. For mixed copper borates, the optimal sintering temperatures were established as 960, 920, and 900 °C for 65% CuB2O4-35% Cu3B2O6, 50% CuB2O4-50% Cu3B2O6 with 5% CuBi2O4, and 30% CuB2O4-70% Cu3B2O6 with 5% CuBi2O4, respectively.

Microstructural Studies
The SEM studies of all the sintered samples based on pure and mixed copper borates showed a very compact microstructure with a small contribution of porosity. It follows from the comparison of the images in Figures 3a,b that the microstructure for pure copper borates is similar, fine-grained, and uniform, with grain sizes in the 0.5-3 μm range.  For the mixed borates compositions, the dense microstructure was preserved, although there was a more significant variation in grain sizes as compared with the single-phase copper borate ceramics. For the ceramics with 5% CuBi 2 O 4 added (Figure 3c,d), small grains 1-3 µm in diameter prevail, although a fraction of much bigger grains appears with sizes ranging from 4 to 12 µm. Thus, it seems that the sintering aid causes a grain growth effect, even though the sintering temperature is slightly lower as compared with  Table 1 presents the results of the EDS analysis at the points marked in Figure 3d for 30% CuB 2 O 4 -70% Cu 3 B 2 O 6 ceramic doped with 5% CuBi 2 O 4 . Point one represents a big grain attributed to CuB 2 O 4 (Cu/B ratio close to 0.5), while points two, four, and five were assigned to smaller grains of Cu 3 B 2 O 6 (Cu/B ratio close to 1.5). Grain boundaries were enriched with Bi originating from the dopant CuBi 2 O 4 (point three). The EDS results are distorted due to the imprecise detection of boron using this method.

Dielectric Properties
A theoretical prediction of dielectric permittivity based on the knowledge about the composition and crystal structure of the compound should be considered to design a substrate material with dielectric properties tailored for high frequency applications. For a simple assessment of the real part of relative dielectric permittivity ε r , one can use the Clausius-Mossotti equation, which relates this quantity with the polarizability α: where V m is the molar volume. For a compound, molecular polarizability can be calculated using the additive rule, as a sum of the polarizabilities of particular ions that built the molecule. Thus, the molecular polarizabilities of the investigated copper borates can be expressed as follows: The polarizabilities of the constituent ions are 2.11, 0.05, and 2.01 Å 3 for Cu 2+ , B 3+ , and O 2− , respectively [40]. However, the predictions based on the Clausius-Mossotti relationship are consistent with the experimentally measured values mainly for a high symmetry cubic crystallographic system. For the materials characterized by structural peculiarities related to the presence of "rattling" or "compressed" cations, ionic or electronic conductivity, dipolar impurities, or piezoelectric behavior, distinct deviations from the additivity rule were observed [40].
Low polarizability is responsible for confining ionic polarization in a material. A lower average bond length diminishes the rattling effect of cations in a polyhedral structural unit. A lower cell volume restricts the interaction of polarizable dipoles [41][42][43]. Qin et al. [41] proposed a universal model based on machine learning for predicting microwave dielectric permittivity. These authors stated that there are three most important features related to the crystal structure of a compound determining its dielectric permittivity. According to this model, the dielectric permittivity decreases with a decrease in the polarizability per unit cell volume ppv and with a decrease in the average bond length blm. The average cell volume per atom va is also an important parameter that should be maintained in an optimal range. Qin et al. [41] stated that the ranges of the decisive parameters that favor creating materials with a low dielectric permittivity are ppm < 0. 15 leads to the conclusion that these parameters are close to the ranges indicated in [41] for low permittivity candidate materials. Figure 4a,b compare the frequency dependences of the dielectric permittivities and the dissipation factors of copper borate ceramics at 20 • C in the 0.12-2.5 THz range.
Qin et al. [41] proposed a universal model based on machine learning for predicting microwave dielectric permittivity. These authors stated that there are three most important features related to the crystal structure of a compound determining its dielectric permittivity. According to this model, the dielectric permittivity decreases with a decrease in the polarizability per unit cell volume ppv and with a decrease in the average bond length blm. The average cell volume per atom va is also an important parameter that should be maintained in an optimal range. Qin et al. [41] stated that the ranges of the decisive parameters that favor creating materials with a low dielectric permittivity are ppm < 0. 15 [26]. For Cu3B2O6, the average Cu-O bond length is 2.1 Å [28]. The analysis of ppm, va, and blm values for CuB2O4 and Cu3B2O6 leads to the conclusion that these parameters are close to the ranges indicated in [41] for low permittivity candidate materials. Figure 4a and Figure 4b compare the frequency dependences of the dielectric permittivities and the dissipation factors of copper borate ceramics at 20 °C in the 0.12-2.5 THz range.  In the 0.14-0.7 THz range, the dielectric permittivities are low, at a level of 5. ceramic without the sintering aid. For all the materials under investigation, the dielectric permittivity changes very slightly with a frequency up to 0.7 THz and then reaches a maximum at about 1 THz for Cu 3 B 2 O 6 and at about 0.9 THz for the rest of the copper borate-based ceramics. Figure 5a,b show the comparison of the dielectric permittivities and dissipation factors of the CuB 2 O 4 ceramics sintered at three different temperatures-930, 940, and 950 • C. The dielectric permittivity increases, while the dissipation factor decreases with an increasing sintering temperature. This is typical behavior that can be attributed to a lower porosity of the samples sintered at higher temperatures. In the 0.14-0.7 THz range, the dielectric permittivities are low, at a level of 5.3-5 CuB2O4, 6.4-6.7 for Cu3B2O6, 5.1-5.2 for 65% CuB2O4-35% Cu3B2O6, 5.8-6.0 for 50% Cu 50% Cu3B2O6 with 5% CuBi2O4, and 5.8-6.1 for 30% CuB2O4-70% Cu3B2O6 with 5% Cu The lowest dielectric permittivities were shown by pure CuB2O4 ceramic and 65% Cu 35% Cu3B2O6 ceramic without the sintering aid. For all the materials under investig the dielectric permittivity changes very slightly with a frequency up to 0.7 THz and reaches a maximum at about 1 THz for Cu3B2O6 and at about 0.9 THz for the rest copper borate-based ceramics. Figure 5a and Figure 5b show the comparison of the dielectric permittivities an sipation factors of the CuB2O4 ceramics sintered at three different temperatures-930 and 950 °C. The dielectric permittivity increases, while the dissipation factor decr with an increasing sintering temperature. This is typical behavior that can be attribu a lower porosity of the samples sintered at higher temperatures. The dissipation factors are relatively low (0.004-0.01) in the 0.14-0.7 THz range, with a flat minimum at 0.4-0.6 THz. A few peaks on the dissipation factor versus frequency plots were observed above 0.9 THz at the positions corresponding to those of the dielectric permittivity maxima.
At very high THz frequencies, some types of dielectric polarization, such as space charge and dipolar polarizations, cannot follow the changes of the external electrical field. In this case, the dielectric behavior is determined by ionic, atomic, and electronic polarization. The dielectric properties can be described by the damped harmonic oscillators model [44]. This model explains the observed frequency independent constant value of the real part of dielectric permittivity ε', an increase in its imaginary part ε" and, consequently, the dissipation factor (ε"/ ε') in the region of THz frequencies.
Peaks on the dielectric permittivity/dissipation factor versus frequency plots that occur above 0.7 THz are supposed to be attributed to phonon modes related to vibrations in Cu-O complexes [26,28]. Due to the large number of atoms that form the unit cells of both copper borates (42 atoms for CuB 2 O 4 , 110 atoms for Cu 3 B 2 O 6 [26,28]), phonon modes for these compounds are numerous, which was confirmed using infrared and Raman spectroscopic studies [26][27][28][29].
In Figure 6a,b, the dielectric permittivities and dissipation factors for a few frequencies in the 0.2-0.7 Hz range (the region of a weak frequency dependence) are plotted as a function of temperature in the range 30-150 • C for the CuB 2 O 4 ceramic. The temperature dependence of dielectric permittivity is very weak up to 90 • C, while the dissipation factor is almost temperature independent in the whole analyzed range. The frequencies corresponding to the peaks of dielectric permittivity and dissipation factor do not change with temperature, which implies that the phenomena responsible for these peaks are not thermally activated processes. It was found that the temperature coefficient of dielectric permittivity of CuB 2 O 4 ceramic in the temperature range 30-90 • C is negative and changes from −19 to −55 ppm/ • C in the 0.2-0.7 THz range.
Materials 2021, 14, x FOR PEER REVIEW 8 of 11 plots were observed above 0.9 THz at the positions corresponding to those of the dielectric permittivity maxima.
At very high THz frequencies, some types of dielectric polarization, such as space charge and dipolar polarizations, cannot follow the changes of the external electrical field. In this case, the dielectric behavior is determined by ionic, atomic, and electronic polarization. The dielectric properties can be described by the damped harmonic oscillators model [44]. This model explains the observed frequency independent constant value of the real part of dielectric permittivity ε', an increase in its imaginary part ε" and, consequently, the dissipation factor (ε"/ε') in the region of THz frequencies.
Peaks on the dielectric permittivity/dissipation factor versus frequency plots that occur above 0.7 THz are supposed to be attributed to phonon modes related to vibrations in Cu-O complexes [26,28]. Due to the large number of atoms that form the unit cells of both copper borates (42 atoms for CuB2O4, 110 atoms for Cu3B2O6 [26,28]), phonon modes for these compounds are numerous, which was confirmed using infrared and Raman spectroscopic studies [26][27][28][29].
In Figure 6a and Figure 6b, the dielectric permittivities and dissipation factors for a few frequencies in the 0.2-0.7 Hz range (the region of a weak frequency dependence) are plotted as a function of temperature in the range 30-150 °C for the CuB2O4 ceramic. The temperature dependence of dielectric permittivity is very weak up to 90 °C, while the dissipation factor is almost temperature independent in the whole analyzed range. The frequencies corresponding to the peaks of dielectric permittivity and dissipation factor do not change with temperature, which implies that the phenomena responsible for these peaks are not thermally activated processes. It was found that the temperature coefficient of dielectric permittivity of CuB2O4 ceramic in the temperature range 30-90 °C is negative and changes from −19 to −55 ppm/°C in the 0.2-0.7 THz range. The dielectric permittivities determined experimentally in this work are distinctly lower than those calculated using the Clausius-Mossotti equation. This discrepancy cannot be assigned only to porosity, considering the high relative density of the sintered samples at a level of 95-98%. It is supposed to be related to the complex noncentrosymmetric crystallographic structures of the copper borates under investigation. For such systems, deviations from the Clausius-Mossotti relationship have often been observed [40]. The dielectric permittivities determined experimentally in this work are distinctly lower than those calculated using the Clausius-Mossotti equation. This discrepancy cannot be assigned only to porosity, considering the high relative density of the sintered samples at a level of 95-98%. It is supposed to be related to the complex noncentrosymmetric crystallographic structures of the copper borates under investigation. For such systems, deviations from the Clausius-Mossotti relationship have often been observed [40].
For commercially available LTCC materials, the values of dielectric permittivity in the range 4-7 and tanδ below 0.012 at 1 THz are considered low values, suitable for millimeter wave systems. The dielectric properties of CuB 2 O 4 and CuB 2 O 4 -Cu 3 B 2 O 6 ceramics in the 0.14-0.7 THz range are comparable with those reported for the commercial LTCC material Ferro A6M at 1 THz (ε r ' = 6.06, tanδ = 0.012) [45]. We plan to use the developed powders based on copper borates for tape casting and the fabrication of multilayer LTCC substrates appropriate for very high frequency applications in future work.

Conclusions
New ceramics based on two copper borates, CuB 2 O 4 and Cu 3 B 2 O 6 , were successfully prepared via solid state synthesis and sintering processes. These ceramics exhibit the following advantageous features: a low sintering temperature suitable for LTCC technology, a very dense microstructure, a low and temperature stable dielectric permittivity (5.1-6.7), and a low dielectric loss (0.004-0.01) in the 0.14-0.7 THz range. The developed ceramics are promising substrate materials for submillimeter wave applications and have been investigated for the first time in such a frequency range.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author. The data are not publicly available as the data also form part of an ongoing study.