Ba₄Al₂Ti₁₀O₂₇ based glass ceramic as dielectric in high frequency applications

Glass ceramics obtained via a true glassy phase have been known for more than 70 years.¹ In such a glass ceramic, a homogeneous glass is produced using standard glass melting technologies. The glass is pore free and, in most cases, also transparent. Since the glassy state is a metastable state, not in thermodynamic equilibrium, a glass is always (more or less) unstable toward crystallization. This instability is used to make glass ceramics. In the second and independent step, crystals are grown within this glass by applying a well-defined time-temperature profile. In most cases, nucleation agents play an important role to achieve homogeneous crystallization. In this way, one obtains homogeneous, pore free glass ceramics with a residual glass phase and crystallites. By tuning details of the time-temperature profile and of the nucleation agents, the crystal size, the crystal size distribution, and the volume filling of the crystalline phase can be controlled.

The main commercialization of such glass ceramics makes use of the low thermal expansion, which is found in Li-Al-Si oxide systems where high-quartz solid solution crystal phases show negative thermal expansion around room temperature, which is balanced out by the positive thermal expansion of the residual glassy phase to give a material with close to zero thermal expansion around room temperature. There are, however, many other properties which can be realized with crystallizing glasses. Ferroelectric glass ceramics² with BaTiO₃ as the main crystalline phase have been known for many decades but are still on their way to being commercialized. The main structural unit in BaTiO₃ is the TiO₆-octahedron. Its size enables the Ti⁴⁺ ion to occupy different positions, which is the main mechanism for the cubic to tetragonal phase transition in BaTiO₃ around 130 °C and, therefore, for the ferroelectricity. If linear dielectric properties are crucial, one can reduce the size of the TiO₆ octahedron and obtain materials which have a high polarizability but are not ferroelectric. The crystal phase BaTi₄O₉ is an example of such a crystalline material. Most of such crystalline phases are far away in composition from a glass forming region in the multidimensional phase diagram. A crystal phase, which has the advantage to be close in composition to a glass forming region, is Ba₄Al₂Ti₁₀O₂₇. At least a very similar phase with the same crystal structure is known to have excellent dielectric properties.³ Also, in the La-Ti-Si system, similar glass ceramics are possible.⁴ 

Using standard glass melting technologies for optical glasses, where platinum equipment for the final hot forming steps is applied, the green glass with a composition close to the targeted crystalline phase, Ba₄Al₂Ti₁₀O₂₇, is molten. In a continuous casting process, glass strips are formed with a cross section of around 120 × 20 mm² and are cut in lengths of around 280 mm. The blocks with an individual weight of 3–4 kg are put into a highly homogeneous oven for crystallization. Crystal growth starts around 750 °C, and careful cooling ensures the crack free, full crystallization of the blocks. In this way, highly homogeneously crystallized blocks are obtained, which are free of pores and have the material properties listed in Table I.

As a result, a highly homogeneous, barely translucent material is obtained. The relatively high thermal expansion is probably related to the fact that the crystalline phase is in composition not too far from ferroelectric phase transitions. The vicinity of the ferroelectric transition is responsible for the high electrical polarizability of the material, which is related to the displacement of the Ti⁴⁺ in the center of its 6 O²⁻ octahedron. A ferroelectric material is highly non-linear with respect to its dielectric properties. Despite this vicinity to the ferroelectric phase, the dielectric material properties are highly linear. The dielectric constant is ϵ′ = 33.2 and is only weakly dependent on temperature or frequency. The dielectric loss increases with frequency as shown in Fig. 1. The density, 4.67 t/m³, is much higher than the one of standard silica glasses. Also, the Young's modulus is with 162 GPa much larger than the one of the glasses (50–70 GPa) or LAS glass ceramics (70–110 GPa).

The material shows a large dielectric breakdown strength. Note that the breakdown strength is strongly dependent on experimental conditions, ramp-up times, sample geometry, and especially, sample thickness.⁵ For a measurement of the dielectric breakdown strength, a series of 24 samples was prepared with a diameter of 11 mm and a thickness of 0.2 mm. On each sample, a metallization with a diameter of 5 mm was applied in the center using silver sputtering with a Cr adhesion layer. The voltage was ramped 1 kV/s in steps of 0.5 kV with a holding time of 10 seconds. The resulting failure distribution follows a Weibull distribution with an average break down field strength of 93 kV/mm. A similar measurement using 30 samples with a diameter of 54 mm, a metallization diameter of 48 mm, and a sample thickness of 1.2 mm gets an average breakdown strength of 48 kV/mm, which again follows a clear Weibull distribution.

In Fig. 1, we show the dielectric loss tangent tan(δ) = ϵ″/ϵ′, which is the quotient of imaginary and real parts of the dielectric constant. The data are a combination of three different measurements. At low frequencies up to 20 MHz, standard dielectric spectroscopy is applied using a sample geometry of 40 mm round diameter and a sample thickness of 1 mm. For this measurement, silver contacts are sputtered on the sample with a Cr adhesion layer. In the lower GHz at 1, 1.8, 5, 10, and 15 GHz, measurements on split post dielectric resonators (SPDRs) are performed.⁶ For these measurements, different samples were prepared to fit in the resonators. The samples were made relatively thin to assure that the cavity perturbation theory still works.⁶ Due to the large dielectric constant of the material, the dielectric thickness, which is a factor of $ϵ′$ larger than the geometrical thickness, has to be taken into account. Care has been taken to obtain samples with uniform thickness and to accurately measure this thickness. For the measurements of the dielectric properties in the frequency range between 20 and 110 GHz, a series of 3 in. (75 mm) diameter wafer with a thickness of 0.1 mm was prepared. At this thickness, the wafer is already translucent. The wafer was placed in a Fabry Perot open resonator (FPOR), and the dielectric properties were derived using an automated evaluation of the eigenmodes.^7,8 At frequencies above 90 GHz, the sample leaves the regime, where even a 0.1 mm thin sample is electrically thin compared to the wavelength in the material, which strongly increases the measurement error. However, the overall data give a very consistent picture of the frequency dependent dielectric loss. The relatively strong increase in dielectric loss at higher GHz frequencies is probably caused by approaching a low-energy phonon mode, e.g., a libration mode from the lower frequency site.

For a frequency of 10 GHz, the temperature coefficient of the material was measured. Therefore, a SPDR with a resonance around 10 GHz was placed in a climate chamber, which was filled with dry air to avoid condensation of water. In the temperature range between –40 °C and +60 °C in temperature steps of 20 K, the dielectric constant of the material was measured. Since the empty resonator had to be measured prior to the loaded resonator, a setup with an automated sample changer was used. In this way, the dielectric constant and the dielectric loss were determined as functions of temperature. The derivative of the data around room temperature gives the temperature coefficient of the dielectric constant,

A glass ceramic can be fine tuned with respect to its properties. In Fig. 2, we show the temperature dependence of the temperature coefficient of the dielectric constant, $τϵ$⁠. From $τϵ$⁠, one can derive the temperature coefficient for a eigenresonance, τ_f. It is approximately given by⁹ 

where α is the thermal expansion of the material. The value τ_f is important for filter elements in telecommunication, which should filter the same frequency range independent of ambient temperature (see also Ref. 10).

The dielectric material properties are highly linear. In Refs. 11 and 12, a measurement using a combination of sophistically coupled resonators obtains a non-linearity in the dielectric response $χ3/χ1$⁠, which is of order 10^–17 m²/V²,

This high material linearity, which is a general property of glasses and, in this case, also of a glass ceramic, is important since it reduces side bands, which occur as intermodulation products. Cell phone base stations have a very large dynamic range. Sending signals have 15 orders of magnitude higher energy density compared to the sensitivity for receiving signals. If two sending signals of different frequencies ω₁ and ω₂ spaced by $Δω$ interact with a nonlinearity, intermodulation products are formed. This is called passive intermodulation (PIM). These intermodulation products occur as sidebands, which are spaced multiple times of $Δω$ besides the original frequencies. Such a sideband can block a receiving channel if the intermodulation product is of the order of the sensitivity for receiving signals. Therefore, already intermodulation signals of order 10^–15 become relevant in 5G applications and beyond.¹³ 

In the following, we give some examples for applying the Ba₄Al₂Ti₁₀O₂₇ glass ceramic in antenna and filter applications.

We start with a discussion of antenna structures. GNSS antenna with the helix structure¹⁴ has been successfully manufactured [see Fig. 3(a)]. In a series of 50 antennas, it was shown that the fluctuation in antenna performance was below the one of the comparable ceramic antenna products. Also, the gain of an antenna manufactured with the glass ceramic was comparable to the ceramic antennas even if the dielectric loss of the ceramic material was a factor of 10 lower than the one of the glass ceramics. In Ref. 14, the excellent performance of the glass ceramic was explained with the complete absence of pores in the glass ceramic opposite to the ceramic systems, which leads to an improved interface between dielectric and metallization.

Also, dielectric resonator antennas (DRAs) were manufactured in Refs. 15 and 16, which were done as well for GNSS applications [see Fig. 3(b)]. Here, a dual band antenna system was obtained by combining two types of antenna, and an antenna array was built from six antennas, which allowed the authors of Ref. 15 to separately treat different spatial segments. For example, it can block a sector from which a disturbing signal is detected. For the antenna array, the phase relation between the six different antennas in the same band was of crucial importance. The high material homogeneity ensured that all antennas in the array were identical in performance.

For 5G massive MIMO, an antenna [see Fig. 3(c)] using beam steering capability was built and exhibited at the Mobile World Congress 2017 by the company Kathrein.¹⁷ The antenna array is constructed for a frequency band at 4 GHz with a bandwidth of 200 MHz. The antennas are slit antennas, and the antenna near field is concentrated in a glass ceramic body of a dimension of 8 × 8 × 8 mm³. The concentration of the antenna near field reduces interferences between neighboring antennas and improves the beam steering capability. The high homogeneity of the glass ceramic material supports better polarization control.

GHz filter structures for the 1.8 GHz frequency band were produced. The design was provided by the company Luxshare¹⁸ for a linear filter with six individual resonators in a row [see Fig. 4(a)] and for a filter element with additional couplings between the individual resonator elements of the filter [see Fig. 4(b)]. The ceramic bodies were made from the Ba₄Al₂Ti₁₀O₂₇ glass ceramic Poweramic™_GHz_33 using CNC machining. The metallization was done using copper sputtering with a Ti adhesion promotor of approximately 10 nm. The filters are shown in Fig. 4. The electric response of the linear filter displayed in Fig. 4(a) is shown in Fig. 5 together with a field simulation using the COMSOL software. Filter characteristic and simulation show an overall good agreement. Even more important is that all five filters are close to identical with their frequency response, which demonstrates material homogeneity and tight manufacturing tolerances. The filters show an insertion loss of order –3 dB. This is more an upper boundary of the loss, since contacting was done with a simple hand-held structure.

In Fig. 6, the measured S-parameters for the U-shaped filter from Fig. 4(b) are shown. Also here, an overall good agreement is shown between the simulation using COMSOL and the measured S-parameters. Specifically, the stop-bands at 1.68 GHz and at 1.98 GHz caused by the coupling of resonators with more than two neighbors are clearly seen in simulation and measurement. For this geometry, the insertion loss is slightly larger around –5 dB.

A further application, besides antennas and filters, is planar transformers. They can be made out of a glass ceramic and are described in Refs. 19 and 20. In a design where a planar transformer is operated in resonance, this narrow resonance needs to be accurately hit. Therefore, material homogeneity plays an important role. Also, operating power electronics using evaporation cooling needs pore free dielectrics to avoid reboiling in pores, which leads to lift off metal layers.

In conclusion, the Ba₄Al₂Ti₁₀O₂₇ glass ceramic forms a material class, which is of interest for applications in 5G due to its highly homogeneous material properties and its low dielectric loss in combination with a high dielectric constant of ϵ′ = 33. The high material linearity makes applications in cell phone base stations attractive.

The authors thank Professor Rolf Jakoby and Holger Maune from the institute of microwave electronics and photonics at the Technische Universität Darmstadt for the support with the key measurement equipment. Also, the material characterization with the FPOR of Bartek Salski and T. Karpisz from the technical university of Warshaw for the data measured at higher GHz frequencies. Financial support from SCHOTT and support from the Graduate School of Excellence “Materials Science in Mainz” (DFG/GSC266) are gratefully acknowledged. The authors thank Bruce Lee from Luxshare for providing the filter designs and Stefano Caizzone from the DLR for sharing the results of the GNSS antenna characterization. They also thank Andreas Vollmer and Max Göttl, formerly from Kathrein and now from Ericsson, for the discussion on 5G massive MIMO antenna systems. They also thank Peter Pesch from the TZO for bringing in his metallization expertise and Christoph Bromberger for his support with regard to planar transformers.