Crystal Structure and Microwave Dielectric Property of xMgO-SiO₂ (x = 1~2) System for 5G Applications

Abstract

Mg₂SiO₄ and MgSiO₃ ceramics with superior microwave dielectric properties are considered to be promising candidates for 5G applications. However, a slight deviation from the stoichiometric Mg/Si ratio will significantly influence their microwave dielectric properties, which will hinder their practical applications. In this work, the xMgO-SiO₂ (x = 1~2) ceramics were synthesized by a solid-state reaction method. The influence of the Mg/Si ratio x on the crystalline phase, microstructure, and microwave dielectric properties was investigated through X-ray diffraction (XRD), a scanning electron microscope (SEM), and the resonant cavity method. The XRD patterns revealed the coexistence of Mg₂SiO₄ and MgSiO₃ within the x range of 1~2, which was further demonstrated by the energy-dispersive X-ray spectra. The SEM images show a typical polycrystalline morphology of ceramics with an inhomogeneous grain size distribution. It is found that the microwave dielectric properties fluctuate at both sides of the x range while those remain relatively stable with minor changes at the intermediate components, indicating an obvious low composition dependence helpful for practical applications. Further, a demonstrator of a microstrip patch antenna for 5G applications using the 1.5MgO-SiO₂ ceramic was designed and fabricated, and a return loss of −16.2 dB was demonstrated, which demonstrated the potential applications.

1. Introduction

In recent years, 5G communication applications have demonstrated tremendous potential owing to their low latency and high-speed capabilities [1,2]. With the continuous advancement of higher frequencies, faster speeds, and reduced power consumption, these applications have a brilliant future in various fields such as the Internet of Things (IoT), intelligent transport systems (ITS), and cloud computing. As a critical dielectric component in 5G communication, microwave dielectric ceramics (MWDCs) play a vital role in the form of dielectric antennas, filters, resonators, substrates, and more [3,4,5]. To meet the increasing performance demands, MWDCs must possess a relatively low dielectric constant and low dielectric loss. Additionally, for practical applications and large-scale production, it is essential to consider factors such as the cost effectiveness, ease of manufacturing, and consistent reliability of MWDCs.

Considering the aforementioned factors, there has been extensive research on low-cost MWDCs with low dielectric constants, particularly those below 10, due to their significant relevance. For instance, cordierite ceramics with a dielectric constant around 6 have gained much attention. However, their composition is complex. It is challenging to control the phase transition between cordierite and indialite. Therefore, the presence of the secondary phase always affects the dielectric loss, and the Q × f value usually remains relatively low, at less than approximately 40,000 GHz [6,7]. Another example is alumina (Al₂O₃) ceramics with a dielectric constant of 10, exhibiting exceptionally low dielectric loss and a Q × f value that can exceed 300,000 GHz [8,9]. However, a prolonged high-temperature sintering is necessary to obtain dense ceramics [10,11]. Similarly, MgO microwave dielectric ceramics also require a high sintering temperature with a prolonged sintering time above 1500 °C, though they have an ultrahigh Q × f value exceeding 200,000 GHz with a dielectric constant of approximately 9~10 [12,13]. On the other hand, SiO₂ has a low dielectric constant, which can be as low as less than 4. It exhibits exceptionally ultralow dielectric loss with very high Q × f values of above 1,000,000 GHz in single-crystal form [14]. However, the preparation of ceramics is difficult and the Q × f value is quite low due to high sensitivity with sintering temperature and various accompanying defects, such as inhomogeneous microstructures originating from complex polymorphs and phase transformations [15]. Fang et al. have prepared cristobalite ceramics with a Q × f value of 80,000 GHz and a dielectric constant of 3.8 [16].

In the MgO-SiO₂ binary system, Mg₂SiO₄ (Mg/Si = 2) has emerged as a promising microwave dielectric ceramic with a high Q × f value of up to 200,000 GHz and a low dielectric constant of about 7 [17,18,19]. However, there are fluctuations in the component near Mg/Si = 2 during the actual synthesis and preparation process, resulting in a small amount of the MgSiO₃ (Mg/Si = 1) phase that deteriorates the Q × f value [20,21]. MgSiO₃ ceramics synthesized by Song et al. also have good microwave dielectric properties of ε_r = 6.7 and Q × f = 121,200 GHz [22]. Nevertheless, Mg₂SiO₄ usually appears at the stochiometric ratio (Mg/Si = 1), which can also cause fluctuations in microwave dielectric properties [19]. On the other hand, Yeon et al. achieved a coexistence of Mg₂SiO₄ and MgO in a multi-phase ceramic by varying the Mg/Si ratio (2~5) [23]. Inspired by the above consideration, in order to find the composition interval with stable properties, there is potential to achieve MgSiO₃-Mg₂SiO₄ coexisting ceramics in the MgO-SiO₂ system by adjusting the Mg/Si ratio in the range of 1~2, which would reduce the sensitivity to composition during the ceramic preparation process to facilitate practical applications.

In this paper, xMgO-SiO₂ (x = 1~2) ceramics were synthesized and prepared using a solid-state reaction method. The influence of the ratio x on the crystalline phase, microstructure and microwave dielectric property was investigated. Based on this, a demonstrator of microstrip patch antenna for 5G application using MgO-SiO₂ system ceramics was designed, fabricated, and evaluated.

2. Materials and Methods

The xMgO-SiO₂ (x = 1, 1.05, 1.2, 1.36, 1.5, 1.66, 1.8, 1.98, and 2) ceramics were synthesized and prepared by a solid-state reaction method. High-purity oxides (>99.9%, all from aladdin) of MgO and SiO₂ were dried before use and weighed according to the different molar ratios of the compositions. The mixed raw material powder was ball-milled for 24 h in ethanol and then dried at 60 °C for 24 h. The dried powders were ground and calcined at 1150 °C for 3 h. After that, the calcined powders were ball-milled again. Subsequently, the dried powders were mixed with 8 wt% binder (polyvinyl alcohol, PVA) and pressed into green pellets at a pressure of 98 MPa. The pellets were firstly heated at 650 °C in atmosphere for 2 h to burn out the PVA, then sintered at 1375 °C~1425 °C for 3 h. The heating and cooling rates were set as 5 °C/min and 2 °C/min, respectively.

The densities of the sintered xMgO-SiO₂ ceramics were measured by the Archimedes method. The phase structures of the ceramics were analyzed with an X-ray diffractometer (XRD, Bruker D2 Phaser, Bruker, Karlsruhe, Germany) using CuK_α radiation in the 2θ range of 10–80° at a step of 0.02°. The microstructure and grain size characterization were carried out by scanning electron microscopy (SEM, Sigma Zeiss 300, Carl Zeiss, Jena, Germany). The dielectric constant (ε_r) and Q × f of the sintered ceramics were measured through a network analyzer (Keysight N5234B, Keysight Technologies, Santa Rosa, CA, USA) using a resonant cavity method, while the values of the temperature coefficient of resonant frequency (τ_f) were determined by the following formula:

$${\tau }_f=\frac{f_2-f_1}{f_1\times (T_2-T_1)}\times {10}^6(\mathrm{ppm}/°\mathrm{C})$$

(1)

where f₁ and f₂ are the resonant frequencies measured at 20 °C and 80 °C, respectively.

The design and simulation of the microstrip patch antenna prototype using xMgO-SiO₂ ceramics were conducted by the Computer Simulation Technology (CST) software. The as-sintered dried xMgO-SiO₂ ceramic powder was added with 10 wt% PVA and then pressed into a 4 mm thick sample in a 30 mm × 30 mm custom-made mold. The green body was sintered at 1400 °C for 5 h to obtain the ceramic substrate. With the help of the CST simulation, double-sided conductive copper foil was attached to the ceramic substrate. A Sub-Miniature version A (SMA) connector was also soldered onto the patch to connect the ground plane and surface electrode.

3. Results

Figure 1a,b exhibit the room-temperature X-ray diffraction patterns within the 2θ range of 10°~80° and the enlargement of 26°~34° for xMgO-SiO₂ ceramics with various Mg/Si ratios. The pattern of x = 1 is composed of the peaks of major MgSiO₃ (Protoenstatile, PEN, PDF#11-0273), minor MgSiO₃ (Clinoenstatite, CEN, PDF#76-0526), and residual SiO₂ (see Figure 1b). The existence of CEN could be related to the phase transition from PEN to CEN during the cooling process of ceramic sintering [24]. Actually, there is a very weak peak of Mg₂SiO₄ (Forsterite, PDF#85-1346) at about 32.3°. As x slightly increases to 1.05, the weak characteristic peaks of Mg₂SiO₄ appear near both 22.9° and 32.3°. Further, when x increases to 1.2, the peak of CEN almost disappears within the accuracy, which could be attributed to the decrease in PEN. Subsequently, the intensity of Mg₂SiO₄ peaks gradually increases while the intensity of PEN peaks decreases. This indicates that the content of Mg₂SiO₄ gradually increases with the increasing Mg/Si ratio, while the content of PEN decreases. Although the peak intensity of PEN has been weakening, the characteristic peaks of PEN are still observed when x = 2. A similar scenario also occurred in previous reports [20,21]. Meanwhile, the trace SiO₂ always exists within the x range of 1~2. According to the study of Kazakos et al., the above phenomena demonstrate the incompleteness of the chemical reaction in the preparation process of xMgO-SiO₂ ceramics [25]. Overall, the phase development of xMgO-SiO₂ system ceramics essentially leads to the composite of MgSiO₃ and Mg₂SiO₄. This may be related to two aspects. On the one hand, the diffusion rate of MgO and SiO₂ is relatively slow during the reaction process, which results in the reaction process being affected by the degree of diffusion. On the other hand, the thermodynamic and kinetic factors of the reaction of MgSiO₃ and Mg₂SiO₄ could be affected by local compositional fluctuations [25,26].

In order to gain a more intuitive understanding of the influence of Mg/Si on the phase composition of the system, Figure 2a,b depict the schematic diagram of the ideal case of a xMgO-SiO₂ ceramic phase diagram and the semi-quantitative calculation results of the phase content. Generally speaking, when Mg/Si is less than 1, the phase composition is mainly composed of MgSiO₃ and SiO₂. When Mg/Si is larger than 2, Mg₂SiO₄ will be the major composition accompanied by excessive MgO [23]. As for Mg/Si within the range of 1~2, the phase compositions can be considered to be the coexistence of MgSiO₃ and Mg₂SiO₄. To further analyze the phase composition, the semi-quantitative calculation results of the phase content are obtained from the X-ray diffraction patterns by the RIR (Ratio of Intensity Reference) of PDF data. It can be discovered that the contents of MgSiO₃ and Mg₂SiO₄ exhibit a decreasing and increasing trend with an almost linear relationship as increasing x, though a trace of residual SiO₂ also exists.

Figure 3 shows the curve of the relative density of the ceramics versus the sintering temperature. The sintering temperatures of microwave ceramics in MgO-SiO₂ systems are generally between 1300 °C and 1500 °C. Herein, 1375 °C, 1400 °C, and 1425 °C were selected as sintering temperatures. It can be observed that the maximum relative densities for all samples were obtained at almost 1400 °C. Based on this, the subsequent experimental measurements were carried out on the samples sintered at 1400 °C.

Figure 4a–i show the SEM images of xMgO-SiO₂ (x = 1~2) as-sintered ceramics at 1400 °C. Though more or less pores can be observed for all the components, the SEM images show the typical polycrystalline morphology of ceramics with well grain crystalline. However, the grain size and shape vary. In order to analyze the variation in grain size with Mg/Si, the grain size of each component in the SEM images was calculated statistically. The statistical results of grain size are presented as insets in each figure, while the variation in average grain size with Mg/Si changing is shown in Figure 5a. It is observed that there is a significant variation in grain size at both ends of the range of x = 1~2. The average grain size increases from 0.77 mm at x = 1 to 1.04 mm at x = 1.2, while that decreases from 1.56 mm at x = 1.8 to 1.07 mm at x = 2. However, the average grain size and distribution at the intermediate components (x = 1.36, 1.5, and 1.66) keep quite close to each other, which could be ascribed to the coexistence of two phases of MgSiO₃ and Mg₂SiO₄ with comparable contents. In addition, the large average grain size at x = 1.8 should be related to the involvement of the liquid phase with the residual traces, which can be observed with some bending morphological features at the grain boundary in Figure 4g. This leads to irregular grain growth in local areas, which is detrimental to the densification of ceramics [27,28].

For further analyzing the coexistence of MgSiO₃ and Mg₂SiO₄ in xMgO-SiO₂ ceramics, EDS were collected from the selected areas of some representative components (see Figure 5b–g). At x = 1.36, the two circled areas of A and B were selected to analyze the element composition. It is observed that there are five peaks referring to C, O, Mg, Si, and Pt, respectively, in the EDS patterns for area A. The C signal comes from the background of the sample, while the Pt signal comes from the surface coating of the sample. The contents of elements O, Mg, and Si are shown in the figure. The Mg/Si ratio is calculated to be approximately 0.95, indicating that it should be MgSiO₃. For area B, the Mg/Si ratio is obtained as being about 1.19, indicating that it should contain both MgSiO₃ and Mg₂SiO₄. At x = 1.66, the analysis results of areas C and D from the EDS signals show that the Mg/Si ratios are 1.6 and 1.49, respectively, which are close to the nominal x value of 1.66. It also indicates the presence of both MgSiO₃ and Mg₂SiO₄ phases. For both areas E and F at x = 2, the Mg/Si ratios increase to 1.79 and 1.49, respectively, indicating that Mg₂SiO₄ should be the main phase with a small amount of MgSiO₃ as the minor phase. The above results are consistent with the previous XRD results.

The dielectric constant and relative density with various Mg/Si ratios of the xMgO-SiO₂ ceramics are plotted in Figure 6a, where ε_L and ε_exp are the theoretical dielectric constant and the experimental data. In general, the dielectric constant of ceramics is determined by numerous factors such as ion polarizability, phase composition, porosity, etc. Herein, according to the results of XRD and EDS analyses, xMgO-SiO₂ (x = 1~2) ceramics can be considered as composites with the coexistence of Mg₂SiO₄ and MgSiO₃. In this case, the theoretical dielectric constant ε_L of the composite can be calculated by the Lichteneker mixing rule [29], given as

$$\ln {\epsilon }_L={\displaystyle \sum _{i=1}^n}{V}_i{\epsilon }_i$$

(2)

where n is the number of phases and V_i and ε_i are divided into the volume fraction and dielectric constant of the i-th phase. As can be seen from Figure 6a, the calculated ε_L value increases monotonically, which can be attributed to the larger dielectric constant of Mg₂SiO₄ (ε_r~7) than MgSiO₃ (ε_r~6.7). On the other hand, the values of ε_exp also increase monotonically as the Mg/Si ratio increases. However, the trend of ε_L has a deviation from the ε_exp value, which may imply that the influence of phase composition on the dielectric constant is not dominant in xMgO-SiO₂ ceramics. In addition, the variation in relative density with various Mg/Si ratios is also plotted in Figure 6a. With an increasing Mg/Si ratio, the relative density basically shows a monotonic increasing trend with an exception at x = 1.8, where a significant decrease occurs relating to the involvement of the liquid phase. Interestingly, the trend of relative density is somewhat similar to the experimental data ε_exp, suggesting the decisive role of porosity in controlling the dielectric constant for xMgO-SiO₂ ceramics.

Figure 6b records the Q × f and τ_f of the xMgO-SiO₂ (x = 1~2) ceramics to evaluate the influence of Mg/Si ratios on microwave performance. The Q × f value reaches about 53,300 GHz at x = 1 and drops significantly to 34,500 GHz at x = 1.05. At the other end of the x range, the Q × f value increases from 40,600 GHz at x = 1.8 to a maximum of 102,900 GHz at x = 1.98 and then descends to 81,500 GHz at x = 2. Overall, the Q × f value fluctuates significantly at both ends of the x range. However, the Q × f values at the intermediate components of the x range (x = 1.36, 1.5, and 1.66) change little and remain basically between 50,000 and 60,000 GHz. Further, considering the deviation, it is calculated that the rate of change of Q × f is found to be less than ±10% when x is in the range of 1.36~1.66. Generally speaking, there are intrinsic and extrinsic factors that affect the Q × f value. The former are mainly related to the phonon system within the crystal, while the latter are related to many factors such as secondary phases, grain boundaries, dislocations, oxygen vacancies, inclusions, pores, etc. [30]. Here, the fluctuation at both ends may be mainly related to the inhomogeneous distribution of two phases of MgSiO₃ and Mg₂SiO₄ and the fluctuation of the microstructure, while the relative stability of the Q × f values at the intermediate components should be related to the relatively homogeneous composition and microstructure of the two phases. The decrease in sensitivity of the Q × f value to components is beneficial for industrial production.

In addition, τ_f is also an important parameter for evaluating microwave performance. Similarly, τ_f remains relatively stable with less variation at intermediate components, while it fluctuates at both ends. In general, the τ_f value of a two-phase composite can be written as the following equation [31]:

$${\tau }_{fmix}=V_1{\tau }_{f1}+V_2{\tau }_{f2}$$

(3)

where τ_fmix is the temperature coefficient of the resonant frequency of the two-phase composite and V₁, V₂ and τ_f1, τ_f2 are the volume fraction of each phase (here mainly MgSiO₃ and Mg₂SiO₄) and the corresponding τ_f value, respectively. On the other hand, the τ_f value is also influenced by other factors such as crystal structure, microstructure, and porosity [32]. The final τ_f value is determined by a combination of multiple factors.

Considering the relatively stable performance at the intermediate components with low sensitivity, in order to evaluate the feasibility of practical applications, a microstrip patch antenna based on the 1.5MgO-SiO₂ ceramic was simulated and fabricated. The initial dimensions of the patch were calculated based on Equations (4)–(7) and then adjusted according to the simulation results [33].

$$W_p=\frac{c}{2f_r}\sqrt{\frac{2}{{\epsilon }_r+1}}$$

(4)

$$L_p=\frac{c}{2f_r{\epsilon }_{eff}}-2\Delta L$$

(5)

$${\epsilon }_{eff}=\frac{{\epsilon }_r+1}{2}+\frac{{\epsilon }_r-1}{2\sqrt{1+12h/W_p}}$$

(6)

$$\Delta L=0.412h\frac{({\epsilon }_{eff}+0.3)(W_p/h+0.264)}{({\epsilon }_{eff}-0.258)(W_p/h+0.8)}$$

(7)

where c denotes the velocity of light in a vacuum, f_r is the resonant frequency (7.08 GHz in this study), ε_eff and ΔL represent the effective dielectric constant and correction length, W_p and L_p are the width and length of the patch, and h is the thickness of the 1.5MgO-SiO₂ ceramic substrate. Figure 7a displays the schematic image and the photograph of the antenna substrate and patch. The dimension of the fabricated 1.5MgO-SiO₂ substrate is 28 mm × 28 mm × 1.3 mm. An ultrathin copper foil (thickness: ~0.06 mm) was adopted as the conducting electrode on both sides of the substrate. In addition, a 50 Ω SMA (Sub-Miniature version A) connector was assembled at the bottom of the antenna as the feeding. Figure 7b plots the measured and simulated S₁₁ curves of the microstrip patch antenna, which represents the return loss characteristics and describes the ratio of incident power to reflected power (i.e., radiation efficiency) [34]. Herein, the profile of the measured S₁₁ curve has a deviation from the simulated one. The resonant frequency of the measured results is 7.20 GHz with a bandwidth of 120 MHz, which is slightly larger than the simulated one (7.08 GHz and 102 MHz). The above phenomena can be ascribed to the size deviation during antenna handmaking and the ambient humidity of the test environment [35]. However, it is worth mentioning that the optimum value of S₁₁ measured was −16.2 dB, which is obviously lower than −10 dB, indicating that more than 90% of the power is radiated through the antenna and demonstrating the commercial potential of the 1.5MgO-SiO₂ microstrip patch antenna for 5G applications.

4. Conclusions

In this paper, xMgO-SiO₂ (x = 1, 1.05, 1.2, 1.36, 1.5, 1.66, 1.8, 1.98, and 2) ceramics were synthesized and prepared by a solid-state reaction method. The XRD results show that the phase composition is mainly MgSiO₃ and Mg₂SiO₄ with a trace residual SiO₂. As x increases from 1 to 2, the content of MgSiO₃ continues to decrease, while the amount of Mg₂SiO₄ continues to increase. The SEM images show that the grain size of ceramics is inhomogeneous with a significant variation in average grain size at both ends of the x range. The results of the EDS confirm that MgSiO₃ and Mg₂SiO₄ coexist. The dielectric constant of xMgO-SiO₂ ceramics is greatly influenced by the relative density. Both Q × f and τ_f values show a significant change at both ends of the x range, while they remain relatively stable with slight changes at the intermediate component. This may be related to the microstructure and two-phase constitution and distribution of ceramics. Finally, a microstrip patch antenna based on the 1.5MgO-SiO₂ ceramic was designed and fabricated, demonstrating excellent performance to indicate its commercial potential in 5G applications.