Network-Structured BST/MBO Composites Made from Core-Shell-Structured Granulates

A finite element method (FEM)-based simulation approach to predict the tunability in composite materials was developed and tested with analytical data. These tests showed good prediction capabilities of the simulation for the test data. The simulation model was then used to predict the tunability of a network-structured composite, where the dielectric phase formed clusters in a paraelectric network. This was achieved by simulating a reciprocal core-shell unit cell of said network. The simulation showed a high tunability for this network model, exceeding the tunability of the analytically evaluated layered, columnar, and particulate model. The simulation results were experimentally verified with a Ba0.6Sr0.4TiO3/Mg3B2O6 (BST/MBO) composite, where core-shell granulates were made with a two-step granulation process. These structured samples showed higher tunability and dielectric loss than the unstructured samples made for comparison. Overall, the structured samples showed higher tunability to loss ratios, indicating their potential for use in tunable radio frequency applications, since they may combine high performance with little energy loss

Electromagnetic modeling of tunability of Barium Strontium Titanate and Magnesium Borate composites

A complete tunability electromagnetic simulation model for the Ba$_{0.6}$Sr$_{0.4}$TiO$_3$ (BST), with ≈ 2000, and Mg$_2$B$_2$O$_6$ (MBO), with ≈ 7, composites is proposed here. The model is based on electrostatics, to simulate the effects of bias fields distribution in the composite varactor at the unbiased state to create the biased state for all volumetric mixture compositions. A bulk-ceramic varactor approach is chosen for the fabricated varactors. Varactors are fabricated with different volume compositions of BST and MBO, ranging from 10 to 100 vol-% of BST. Simulated results of the varactor model are then verified with the measured results of the varactor. The simulated and measured tunability shows considerable discrepancy at room temperature, which leads to Curie temperature _ investigation of the fabricated varactors. It has been observed that a shift in _ is directly proportional to the discrepancies in the simulated and measured tunability. After incorporating the _ shifts in the model, the results show close proximity between measured and _ -shifted simulated tunabilities with differences being reduced from around 32% to 2% for 80 vol-% BST varactor

Network-Structured BST/MBO Composites Made from Core-Shell-Structured Granulates

A finite element method (FEM)-based simulation approach to predict the tunability in composite materials was developed and tested with analytical data. These tests showed good prediction capabilities of the simulation for the test data. The simulation model was then used to predict the tunability of a network-structured composite, where the dielectric phase formed clusters in a paraelectric network. This was achieved by simulating a reciprocal core-shell unit cell of said network. The simulation showed a high tunability for this network model, exceeding the tunability of the analytically evaluated layered, columnar, and particulate model. The simulation results were experimentally verified with a Ba₀.₆Sr₀.₄TiO₃/Mg₃B₂O₆ (BST/MBO) composite, where core-shell granulates were made with a two-step granulation process. These structured samples showed higher tunability and dielectric loss than the unstructured samples made for comparison. Overall, the structured samples showed higher tunability to loss ratios, indicating their potential for use in tunable radio frequency applications, since they may combine high performance with little energy loss

Ridge Gap Waveguide Based Liquid Crystal Phase Shifter

In this paper, the gap waveguide technology is examined for packaging liquid crystal (LC) in tunable microwave devices. For this purpose, a line based passive phase shifter is designed and implemented in a ridge gap waveguide (RGW) topology and filled with LC serving as functional material. The inherent direct current (DC) decoupling property of gap waveguides is used to utilize the waveguide surroundings as biasing electrodes for tuning the LC. The bed of nails structure of the RGW exhibits an E-field suppression of 76 dB in simulation, forming a completely shielded device. The phase shifter shows a maximum figure of merit (FoM) of 70 °/dB from 20 GHz to 30 GHz with a differential phase shift of 387° at 25 GHz. The insertion loss ranges from 3.5 dB to 5.5 dB depending on the applied biasing voltage of 0 V to 60 V. © 2013 IEEE

Electromagnetic Modelling of Barium Strontium Titanate and Magnesium Borate Bulk Composite Varactors - Tunability and Acoustic Resonances Suppression

Barium strontium titanate (BST) composite ceramic varactors find their application in high-power impedance matching circuits in low-frequency ISM bands, particularly around 13.56 MHz. In this work, the modeling and in-house development of such varactors are presented, with emphasis on capacitance tunability and acoustic resonance behavior. These matching circuits are critical for plasma processes in the semiconductor industry, as they increase integrability and reduce the size of integrated circuits (ICs). Currently, mechanically-tuned varactors dominate implementation in these matching circuits because they are extremely low-loss and exhibit high linearity. However, they suffer from a limited tuning time of more than 1 ms, which opens up the possibility of implementing fast-tunable and comparatively compact tunable ferroelectrics such as pure BST-based varactors. In comparison, these varactors usually have higher losses. Consequently, to match the low-loss standards of mechanically tuned varactors, this work aims for BST-based composite varactors, where a low-loss and linear elastic dielectric such as magnesium borate (MBO) is added to the BST to reduce the material loss. BST losses are composed of two major components: dielectric loss and acoustic resonance loss. While dielectric loss has been extensively studied in the past, acoustic resonances due to electrostrictively induced piezoelectricity are less studied so far. Hence, they are one of the main focuses of modeling in this work. Another aspect of BST composites, tunability, has also been extensively researched, as previous models were either not sufficiently accurate or the tunability deviated significantly from experiments. Therefore, modeling of tunability becomes another focus area. A first distinct model is proposed that accurately and precisely predicts the tunable behavior of the BST composite varactor for arbitrary volume compositions of BST and MBO. Subsequently, the models are validated with the extracted measurements from the in-house electrical and Curie temperature TC characterization setup. The tunability calculated from the electromagnetic simulations show massive differences compared to the measured tunability. As a result, an in-house solution is formulated for incorporating Curie temperature shifts into the model due to the material changes during mixing, which helps to mitigate the massive deviations in tunability. For the 80 vol-% BST varactor, the tunability deviation between simulations and measurements decreases from 32% to about 2%, indicating the importance of integrating Curie temperature shifts. Moreover, in modeling acoustic resonances, a multiphysics approach consisting of RF and structural mechanics domains is implemented to mimic the effects of induced piezoelectricity under the influence of bias electric fields, which is responsible for such resonances. The model confirms the presence of acoustic resonances at the same frequencies as in the measurements. A quasi-complete suppression of acoustic resonances is achieved in the BST composite varactor. A decrease of the equivalent series resistance from about 60 Ω to 10 Ω in the simulations and an increase of the Q-factor Qε from about 5 to 300 at 10 MHz under electric fields of 1.1 kV/mm, showing the crucial advantage of adding MBO to the BST material

Network-Structured BST/MBO Composites Made from Core-Shell-Structured Granulates

A finite element method (FEM)-based simulation approach to predict the tunability in composite materials was developed and tested with analytical data. These tests showed good prediction capabilities of the simulation for the test data. The simulation model was then used to predict the tunability of a network-structured composite, where the dielectric phase formed clusters in a paraelectric network. This was achieved by simulating a reciprocal core-shell unit cell of said network. The simulation showed a high tunability for this network model, exceeding the tunability of the analytically evaluated layered, columnar, and particulate model. The simulation results were experimentally verified with a Ba0.6Sr0.4TiO3/Mg3B2O6 (BST/MBO) composite, where core-shell granulates were made with a two-step granulation process. These structured samples showed higher tunability and dielectric loss than the unstructured samples made for comparison. Overall, the structured samples showed higher tunability to loss ratios, indicating their potential for use in tunable radio frequency applications, since they may combine high performance with little energy loss

Suppression of Acoustic Resonances in All-Oxide Varactors

Barium strontium titanate (BST) thin-film varactors promise very good performance in RF frontends in terms of low loss and high tunability. However, their application is commonly limited to lower GHz frequencies. For higher frequencies, acoustic resonances drastically reduce the device quality in metal-insulator-metal (MIM) structures under bias voltage. In this work, this limitation is overcome by replacing the metal electrodes with conducting oxides that structurally match to BST and, therefore, avoid acoustic impedance mismatch. A detailed analytic model is derived, incorporating electric and acoustic behavior. Four samples with an oxide bottom electrode and varying BST thickness are characterized and fitted by the derived model with very high accuracy. Each shows a significantly reduced degradation due to acoustic loss. A model-wise comparison of stacks with metal and oxide electrodes demonstrates the strong benefit of all-oxide varactors, the possibility of complete suppression of acoustic resonances

All-Oxide Varactor Electromechanical Properties Extracted by Highly Accurate Modeling Over a Broad Frequency and Electric Bias Range

Since the dielectric permittivity of ferroelectric materials depends on the electric field, they allow designing switchable and continuously tunable devices for adaptive microwave front ends. Part of the ongoing research is the field of all-oxide devices, where epitaxial oxide conductors are used instead of polycrystalline metal electrodes, leading to epitaxial ferroelectric layers and resulting in high device performance. In particular, they allow engineering the acoustic properties separated from the electric ones due to the structural similarity between the dielectric and conducting oxide films. Two major results are reported in this work. First, a highly accurate model for the microwave impedance of ferroelectric varactors is derived that tracks the superposition of induced piezoelectricity and field extrusion into the substrate caused by thin electrodes. In difference to previous works, this model covers both a wide frequency and biasing range up to 12 GHz and 100 V/ μ \textm . Second, the high model accuracy enables the determination of all relevant electric and mechanic properties based on a mere microwave characterization. This approach will be especially valuable when independent measurements of mechanical properties of the thin-film materials are impeded by a high integration of the devices. Though derived for all-oxide varactors, the presented model can as well be adapted for thin-film bulk acoustic wave resonators (FBARs) and varactors with conventional metal electrodes when eventual dead layers at the interface are modeled correctly

Suppression of Acoustic Resonances in BST-Based Bulk-Ceramic Varactors by Addition of Magnesium Borate

This work presents a method for reducing acoustic resonances in ferroelectric barium strontium titanate (BST)-based bulk ceramic varactors, which are capable of operation in high-power matching circuits. Two versions of parallel-plate varactors are manufactured here: one with pure BST and one with 10 vol-% magnesium borate, Mg₃B₂O₆ (MBO). Each varactor includes a 0.85-mm-thick ferroelectric layer. Acoustic resonances that are present in the pure BST varactor are strongly suppressed in the BST-MBO varactor and, hence, the Q-factor is increased over a wide frequency range by the addition of small amounts of a low-dielectric-constant (LDK) MBO. Although the tunability is reduced due to the presence of non-tunable MBO, the increased Q-factor extends the varactor’s availability for low-loss and high-power applications

Ridge Gap Waveguide Based Liquid Crystal Phase Shifter

In this paper, the gap waveguide technology is examined for packaging liquid crystal (LC) in tunable microwave devices. For this purpose, a line based passive phase shifter is designed and implemented in a ridge gap waveguide (RGW) topology and filled with LC serving as functional material. The inherent direct current (DC) decoupling property of gap waveguides is used to utilize the waveguide surroundings as biasing electrodes for tuning the LC. The bed of nails structure of the RGW exhibits an E-field suppression of 76 dB in simulation, forming a completely shielded device. The phase shifter shows a maximum figure of merit (FoM) of 70 °/dB from 20 GHz to 30 GHz with a differential phase shift of 387° at 25 GHz. The insertion loss ranges from 3.5 dB to 5.5 dB depending on the applied biasing voltage of 0 V to 60 V