title: Electromagnetic Modelling of Barium Strontium Titanate and Magnesium Borate Bulk Composite Varactors - Tunability and Acoustic Resonances Suppression
Creators: name: Agrawal, Prannoy
Publisher: name: UNSPECIFIED
Year: 2024

description: 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.