Cold sintering of microwave dielectric ceramics and devices

Microwave (MW) dielectric ceramics are used in numerous electronic components for modern wireless communication systems, including antennas, resonators, capacitors and filters. However, to date, MW ceramics are manufactured by an energy-intensive, conventional high-temperature (> 1000 °C) sintering technology and thus cannot be co-sintered with low melting point and base electrodes (Ag, Al, etc., < 1000 °C), nor directly integrated with polymers (< 200 °C). Cold sintering is able to densify ceramics at < 200 °C via a combination of external pressure and a transient liquid phase, reducing the energy consumed and facilitating greater integration with dissimilar materials. This review outlines the basics of MW ceramics alongside the mechanism of cold sintering. Recent developments in cold sintering of MW ceramics, composites and devices are described, emphasizing new materials and progress towards component/device fabrication. Future prospects and critical issues for advancing cold-sintered MW materials and devices, such as unclear mechanism, low Q × f values and poor mechanical properties, are discussed.


Introduction
In this review, we present a brief introduction to microwave (MW) ceramics alongside an overview of the mechanisms and state-of-the-art in cold sintering. Subsequently, the review focuses on recent developments in cold sintering MW materials and devices, emphasizing new materials and progress towards component/device fabrication. Finally, the future prospects and critical issues for cold-sintered MW materials and devices are discussed.

Microwave ceramics
MW dielectrics play important roles in the Internet of Things (IoT), fifth-generation (5G) mobile communication technology and global navigation satellite systems (GNSS), as filters, resonators, antennas and substrates [1,2]. The three selective parameters for MW dielectric materials are relative permittivity (ε r ), quality factor (Q, often multiplied by the resonant frequency, f 0 , to give a material constant Q × f) and the temperature coefficient of resonant frequency (TCF or τ f ).
In conventional electrical circuits, ε r defines the energy storage capacity of a material when a potential is applied. In the context of MW ceramics however, it is a measure of the interaction of the electromagnetic (EM) wave with the phonon modes of the crystal structure. Generally speaking, the higher the ionic polarizability of the ions within a crystal structure, the larger the value of ε r at MW frequencies. When MWs travel in a dielectric medium, the wavelength is inversely proportional to the √ ε r , according to the equation [2]:

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where λ d and λ 0 is the wavelength in the dielectric and vacuum, respectively, c is the speed of light and ν is frequency. At f 0 , ν = f 0 and λ d is approximately the diameter of the resonating body (D), depending on the resonant mode, such that [1,2] Circuit miniaturization for low-frequency applications (2)(3)(4)(5)(6), therefore, requires larger ε r , whereas higher working frequencies (e.g. mm-wave communication) need smaller values. For 4G and the current generation of 5G (2-6 GHz) telecommunications, ceramics with medium ε r (20 < ε r < 50) are typically used for resonators and filters in mobile phone networks (e.g. base stations) [1,2]. As the 5G network expands however, mm-wave technology will dominate and lower values of ε r are required with ultralow loss (Q × f > 100,000 GHz). Q is the reciprocal of the dielectric loss (tanδ) and indicates the quantitative dissipation of the electrical energy within a dielectric. In a MW ceramic, it is a function of the width of the resonant peak, measured at 3 dB below peak height (∆f 0 ) and is given by f 0 /∆f 0 . tanδ is the summation of intrinsic and extrinsic losses; intrinsic losses relate to the crystal structure and are described by the interaction of the phonons with the EM field and define the lower limit of tanδ and the upper limit of Q in a defect-free single crystal, whereas extrinsic losses are associated with imperfections in the crystal lattice such as impurities, defects, grain boundaries, pores, microcracks, order-disorder, random crystallite orientation, dislocations, vacancies and dopant atoms [1,2]. Extrinsic losses can be eliminated or minimized by optimizing material processing. Generally speaking, Q linearly decreases with increasing frequency [1].
The TCF or τ f indicates the thermal stability of a resonating body and describes the drift of f 0 as a function of temperature. It is given by [1] where τ ε and α L are the temperature coefficient of ε r and the linear expansion coefficient, respectively.
For base stations, unmetallized ceramics are used within cavities as filters and resonators and are required to have τ f = ± 1 ppm/ °C, ultra-high Q × f (> 40, 000 GHz) and 5<τ r < 50 depending on the operating frequency. For antennas and radio frequency (RF) substrates which typically have surface metallizations, τ f (± 10 ppm/ °C) is relaxed with lower values of Q × f acceptable. τ r depends on the application but rarely exceeds 100.

Cold sintering
MW ceramics are discussed in detail in section "Microwave Dielectric Materials and Devices by Cold Sintering" but here we present a brief overview of a broader range of functional ceramics that have been shown to cold sinter, alongside a detailed description of the process and its mechanism.

The cold sintering process
Sintering is a process which promotes the coalescence of materials (e.g. powders) into a solid with much higher densities than the initial state. The thermodynamic driving force is lowering of the total surface free energy, i.e. [87] where γ A is total surface free energy, γ is surface energy and A is the total specific surface area. During sintering, coarsening of grains contributes to Δγ, whereas the formation of solid-solid interfaces contributes to ΔA. However, ΔG of a sintering process is only a few tens of cal/mol, whereas the formation energies of inorganic solid crystals are typically several thousand cal/mol. A significant energy input is, therefore, required to trigger the sintering process which is usually provided by heating to ~ 1/2 to 3/4 of a material's melting temperature in °C.
Different sintering methods possess different mass transport mechanisms/routes which ultimately lead to different energy (temperature) requirements. Sintering temperature may be reduced by the application of external pressure (e.g. hot pressing) or the addition of a component that forms a liquid at the sintering temperature. Effectively, these two factors act in combination in cold sintering, leading to a dramatic lowering of the sintering temperature for specific materials [42].
Randall et al. [47] utilized ZnO to study the mechanism(s) of cold sintering, revealing that the gradient of the densification rate varied from 1 to 1/3. They also noticed that the rate of both stages remains almost unchanged with applied pressure, suggesting similar mechanisms are valid over a range of densification conditions. The two different densification rates are attributed to two stages of densification. The first is dominated by particle compaction and rearrangement, whereas the second, with a lower densification rate, relates to a "dissolution-precipitation" mechanism.

Stage 1: particle compaction
At the beginning of stage 1, particles are separated with a solution/void. Densification at this stage is mainly from the compaction (i.e. external pressure pushes particles closer to each other) and rearrangement of particles, as shown in Fig. 2. The solution will also redistribute at this stage due to the combination of external and capillary pressure [88]. Generally speaking, this stage is similar to dry uniaxial pressing but with three extra factors: transient solution, elevated temperature and higher pressure, which help the process individually and collectively.
The transient solution contributes to the particle rearrangement by (i) acting as a lubricant between particles and assists the rearrangement and sliding process, (ii) exerting capillary pressure to pull the particles closer, and (iii) smoothing the particle surface/shape by dissolving sharp edges and contacts to reduce surface energy, further facilitating particle rearrangement and sliding. The high pressure is the main driving force to the compaction/rearrangement of particles, but in cold sintering, the solubility of particles also increases according to [89] where N is the mole fraction of the component in the solution, P is the pressure, T is temperature, V aq is the partial molar volume of component in the solution, V cr is the partial molar volume of component in the dissolving solid, and R is the universal gas constant. The pressure is concentrated at acicular points of contact and sharp edges (GPa can be realized), which promotes preferential dissolution [90], smoothing particles and helping rearrangement. The elevated temperature is not as critical as the transient solution and high pressure at this stage but increases the solubility and accelerates the dissolution. At the end of stage 1, a relatively rigid skeleton is formed with further particle rearrangement giving only a minor contribution to densification.

Stage 2: dissolution-precipitation and grain coarsening
Stage 2 relies on filling of gaps/voids between grains. In solid-state sintering, mass transport is achieved via two main mechanisms, evaporation-condensation and diffusion through different routes (e.g. surface, grain boundary). In most cases, the contribution from the former is negligible due to low vapour pressure in air, and mass transport is dominated by solid-state diffusion. However, in cold sintering, the temperature is remarkably lower than that of conventional solid state and solid-state diffusion is unlikely. The solid-gas interface is replaced with a solid-liquid interface and dissolution-precipitation is possible, since the energy required for liquid-phase transport is significantly lower than for solidstate diffusion. Dissolution-precipitation is only viable for compositionally sensitive ceramics, if the material can congruently dissolve. For those systems with limited solubility or exhibit incongruent dissolution, densification may still be achieved but this limits properties.

Congruent dissolution
Temperature and pressure both influence the solubility of a material. Within a cold sintering system, the distribution of temperature is generally homogeneous but the pressure is concentrated at the contact points. As a result, the solubility is higher which creates a concentration gradient. Solute is then redistributed by diffusion to other locations with lower concentration (i.e. lower pressure), Fig. 2. The concentration gradient induces the Marangoni effect [91] which causes mass transfer along an interface between two fluids due to a gradient of surface tension, caused by local variations in chemical concentration. As the concentration rises, the solution becomes super-saturated to the point where precipitation begins. With the help of external and capillary pressure to keep the particles in close proximity, dissolution-precipitation initially leads to necking, similar to that observed in solid-state sintering, Fig. 2. As the aqueous solution evaporates, coarsening of particles occurs through precipitation on their surface or alternatively new particles nucleate [65], Fig. 2. An amorphous rather than crystalline phase can form if the solute is strongly bonded with solution [3,56,68]. The crystalline phase may, however, be recovered through post-annealing [57,58]. We note that the gel/glass phase may be beneficial for the cold sintering process by facilitating plastic flow, thereby filling voids.

Incongruent dissolution and limited dissolution
Incongruent dissolution means the composition of the solute in solution does not match that of the solid. An inert surface (passive) layer forms from oxide component(s) which is(are) least soluble. In the case of BaTiO 3 , Ba 2+ ions possess a much higher solubility than Ti 4+ [54] and a Ba-depleted layer (i.e. amorphous TiO 2 ) forms on the surface of particles. To overcome this issue, a pre-saturated Ba(OH) 2 water solution with TiO 2 nanoparticle suspension is introduced [57,58]. Hydrothermal synthesis takes place at the particle interfaces, densifying the ceramic body, through the formation of a nanocrystalline or amorphous BaTiO 3 phase with uniformly distributed Ba and Ti ions. The ρ r of the composite is ~ 93% which can be improved to 96% by post-annealing at 900 °C to recrystallize the glass phases [57,58]. For low solubility compounds such as Pb(Zr,Ti)O 3 , there is less chance of the formation of a depletion layer and aqueous Pb(NO 3 ) 2 has been used as the transient solution to achieve 89% theoretical density [59].

General discussion of the cold sinter process
Comparing congruent with incongruent dissolution, it is evident that higher density (ρ) is much easier to achieve in the former rather than the latter. In some cases, even the external pressure or elevated temperature is not absolutely necessary if the material is highly soluble [42,92,93] such as lithium molybdate (Li 2 MoO 4 , LMO) and NaCl [42,88].
Other than the nature of the solvent (e.g. polarity), the solubility may be modified by several factors, including pressure, temperature and particle size (i.e. specific surface area) [94]. The effect of pressure has already been discussed above but temperature follows Le Chatelier's principle [95] which states that solubility increases with increasing temperature for an endothermic reaction (e.g. NaCl in water), whereas it decreases with the increasing temperature in an exothermic reaction (e.g. CaCO 3 in water). Smaller particles possess higher solubility due to their higher surface free energy according to where *K A is the solubility constant for the solute particles with the molar surface area A, *K A→0 is the solubility constant for substance with molar surface area tending to zero, γ is the surface tension of the solute particle in the solvent, A m is the molar surface area of the solute, R is the universal gas constant, and T is the absolute temperature. However, this effect only becomes significant when the particle size is at the nanoscale.

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Finally, we note the solubility can increase through chemical reaction. When water is used as solvent, the solubility of ZnO is only 0.0004% at room temperature [96]. Yet when hydrochloric acid is used as solvent, the following reaction takes place: It is therefore reasonable to predict that the outcome of ZnO cold sintered with water or acid as solution will be different. Funahashi et al. [65] reported that the ρ r of ZnO after cold sintering is only 65% when pure water or 0.1 mol L −1 acetic acid solution was used, whereas a high ρ r of > 90% can be achieved with 1 mol L −1 acetic acid solution.
Ostwald ripening has also been observed in some cold sintering experiments [97]. However, as Ostwald ripening is strictly a surface effect, it does not involve particle movement, and contributes to particle/grain enlargement but not increasing density.

Monophase materials
As early as 2014, Kähäri et al. [93] reported the cold sintering of LMO at room temperature with the assistance of deionized water under a pressure of 130 MPa, as shown in the backscattered electron (BSE) images, Fig. 3. ρ r of 87-93% was achieved with ε r of 4.6-5.2 and Q × f of 10,200-18,500 after post-annealing. In 2015, the same authors reported that ρ and MW properties of LMO could be improved by an increase of powder particle size, applied pressure and post-processing time [98] but there was no significant effect on ρ r as a function of the amount of deionized water beyond initial wetting.
The following year, Guo et al. [3] proposed that the 'cold sintering offered a new era for ceramic packaging and microwave device development' . To illustrate this point, (Li,Bi) 0.5 MoO 4 (LBMO) was cold sintered at 120 °C, Fig. S1, with ρ r of 88.5%, ε r of 33.7, Q × f of 2300 and τ f of +184 ppm/ °C. The grain size of cold-sintered LBMO was limited to the initial particle size of ceramic powders, since most systems were coarse-grained and do not achieve > 92% density and grain growth is suppressed.
Hong et al. [92,99] systematically studied the effect of applied pressure and water on cold sintering of NaCl ceramics at room temperature. As applied uniaxial pressure increased, ρ r of dry NaCl water increased from 80% (50 MPa) to 99.3% (300 MPa), which is due to the plastic deformation [92]. They found that the addition of 4% water promoted the dissolution-precipitation process, giving a homogenous microstructure, leading to ρ r ~ 99.3% and optimal MW properties, ε r ~ 5.55, Q × f ~ 49,600 GHz and τ f ~ − 173 ppm/ °C at 300 MPa, as plotted in Fig. S2. The same authors [99] also found that ρ r and ε r decreased from 99.3 to 93.4% and 5.88 to 5.44, respectively, with excess water from 0 to 10%, which was attributed to the volume increase caused by the water evaporation. The highest Q × f (49,600 GHz) was obtained with 4% water, due to the homogenous microstructure.
The fabrication of ceramic-ceramic layered composites is difficult by conventional sintering technology, due to interfacial reaction, delamination and wrapping, caused by inequivalent densification rates and differential thermal expansion on cooling. These issues are completely resolved by cold sintering either due to the ultralow sintering temperatures or the absence of lateral shrinkage. Wang et al. demonstrated using NBMO-xLMO (Fig. 9A), a three-layered macroscopic ceramic-ceramic graded dielectric composite for the fabrication of MW dielectric GRaded INdexed (GRIN) lenses, Fig. 9B [100]. The graded composite had a high density with no delamination or wrapping.
To our knowledge, all MW ceramics and composites fabricated to date by cold sintering are summarized in Table 1 which illustrates the range of ε r , τ f and Q × f values which can be achieved and indicates their great promise for fabrication of RF devices.

RF devices
To demonstrate the potential of cold sintering for RF applications, different devices have been designed and fabricated. In 2016, Baker et al. printed LMO monolithic capacitors on PET/ Ni foil substrates with Ag internal electrodes [53], as shown in  Compound  Fig. 10, thereby demonstrating a facile and flexible method for the production of single and multilayer capacitors using cold sintering, Fig. S4 [3]. Simultaneously, the first microstrip patch antenna was designed and fabricated using a cold-sintered LMO disk as a substrate, Fig. 11 [112]. Lateral dimensions were controlled by the mould, simplifying the design/modelling of the antenna performance. However, due to high relative humidity (80%) and water absorption, a lower f 0 and a reduced antenna efficiency were observed compared to the simulated results, which was subsequently resolved using a silicone conformal coating.
Following on from Kohari et al. Wang et al. [51] utilized a temperature stable cold-sintered composition, CTO-KMO, to design and fabricated a microstrip patch antenna (40.0 mm × 40.0 mm × 1.4 mm), with copper tape (27.5 mm × 23.0 mm × 0.05 mm) as the radiation element and ground plane, as shown in the inset of Fig. 13a. The microstrip patch antenna operated at a centre operating frequency of ~ 2.5 GHz (Fig. 13a) and the realized gain was 2.73 dBi at 2.5 GHz, leading to a radiation efficiency of 62% [51].
A 5G prototype microstrip patch antenna was further fabricated by Li et al. [109] using cold-sintered CaSnSiO 5 -KMO composite ceramics, as shown in the inset of Fig. S6a, which exhibited a centre operating frequency of 5.2 GHz with good impedance match and a 144 MHz bandwidth (− 10 dB) (Fig.   S6a). A high total efficiency of 88.4% was obtained in this antenna at the frequency of 5.2 GHz with an antenna gain of 5.7 dBi (Fig. S6c), again suggesting CaSnSiO 5 -KMO compositions are suitable for antenna applications.
Most importantly from a manufacturing perspective, Wang et al. [52] have demonstrated that cold-sintered, temperature stable 0.9BMO-0.1KMO (30 × 30 × 7 mm, ε r ~ 31) could be directly pressed onto PCBs (T M < 200 °C) with a satellite navigation antenna subsequently fabricated using the standard Cu metallization as the ground plane, as shown in Fig. 14A [52]. No chemical reaction/delamination was observed at the interface between ceramic and Cu layers, as shown in the SEM images and EDS elemental line-scans in Fig. 14B. An S11 of − 10 dB and a bandwidth of 59 MHz was measured in the antenna with an axial ratio < 3 dB (Fig. 14C), which covered the desired frequency bands 1561 MHz for BeiDou and 1575 MHz for GPS/Galileo with high efficiencies of 87-88%, as shown in Fig. 14D. This latter contribution demonstrates the potential of cold sintering for the fabrication of low-cost integrated ceramic-polymer substrate technology, opening up new design space for a plethora of directly integrated devices ranging from antennas to dielectric resonator arrays. In addition to the reduction in manufacturing costs, the much lower temperature with cold sintering enables precise control of lateral dimensions of the ceramic body, which is a great asset in manufacturing since f 0 is determined based on the mould dimensions (no lateral shrinkage) and the powder charge without the need for post-fabrication tuning, a weakness in conventional processing.

Summary and perspectives
In this contribution, the underpinning principles of MW ceramic technology and cold sintering have been reviewed. MW ceramics and RF devices (substrates, resonators, filters, etc.) are widely used in wireless and satellite communication technology, recently accelerated by the deployment of 5G and ultimately mm-wave networks. They are manufactured typically www.mrs.org/jmr at high temperatures and are expensive due to the large amount of energy required for densification in addition to the high raw materials costs. Cold sintering, particularly for congruent dissolving ceramics and composites, offers, through its unique "dissolution-precipitation" process, a feasible and sustainable technology to realize ultralow-temperature and low-carbon manufacturing of MW devices. Temperature stable cold-sintered compositions are now available with 2.9 < ε r < 48 and Q × f suitable for a wide range of applications. Furthermore, the unique compatibility that cold sintering offers with polymers and metals creates a hitherto, unexplored design space for component fabrication and manufacturing, such as directly integrated ceramics on metallized PCBs and new functionality through graded structures. However, several critical issues need to be addressed in future: (1) Although the cold sintering process has been investigated and discussed by Randall et al. [47], its mechanism(s) still require(s) further clarification. At the moment, the prevailing view is that there are strong similarities with liquid-phase sintering but we acknowledge that the exact processes that occur inside the die at temperature and pressure still remain to be elucidated.  [47] attribute this phenomenon to the complex microstructure of grain boundary (amorphous phase, interfacial films, etc.) and limited grain growth (small grain size). It is critical, therefore, to modify the process of cold sintering to eliminate interfacial amorphous phase and promote grain growth so that Q × f may be optimized. There are nascent related technologies based on hybrid techniques such cold/flash sintering or MW-assisted cold sintering that could, if successfully developed, not only expand the range of cold-sintered ceramics but also improve the interparticle interface and thus Q × f. (4) Sensitivity to atmospheric moisture due to the partially soluble nature of cold-sintered ceramics may also pose issues for long-term usage. In addition, mechanical properties (and thus handling characteristics) have been reported to be significantly worse than their con- ventionally sintered counterparts. Humidity sensitivity may well be resolved through a low-cost polymer encapsulation process [112] but how to mitigate against low mechanical strength remains unclear and could limit cold sintering to integrated structures on PCBs which would supply superior handling characteristics. (5) Many RF devices (antennas, resonators, filters, etc.) have relatively simple geometries (rectangular blocks or cylinders). Further work required to understand and control the cold-sintered process in more complex pressed or moulded shapes. In principle however, if a shape can be uniaxially pressed prior to conventional sintering, then it is feasible that it can fabricated by cold sintering.

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