<p>Beta-gallium oxide (<i>β</i>-Ga₂O₃) is an emerging wide bandgap semiconductor for next generation power devices which offers the potential to replace GaN and SiC. It has an ultra-wide bandgap (UWBG) of 4.8 eV and a corresponding <i>E</i>_brof 8 MV/cm. <i>β</i>-Ga₂O₃also possesses a decent intrinsic electron mobility limit of 250 cm²/V<i>·</i>s, yielding high Baliga’s figure of merit of 3444. In addition, the large bandgap of <i>β</i>-Ga₂O₃gives stability in harsh environment operation at high temperatures. </p> <p>Although low-cost large-size <i>β</i>-Ga₂O₃native bulk substrates can be realized by melt growth methods, the unique property that (100) surface of <i>β</i>-Ga₂O₃has a large lattice constant of 12.23 Å allows it to be cleaved easily into thin and long nano-membranes. Therefore, <i>β</i>-Ga₂O₃FETs on foreign substrates by transferring can be fabricated and investigated before <i>β</i>-Ga₂O₃epitaxy technology becomes mature and economical viable. Moreover, integrating <i>β</i>-Ga₂O₃on high thermal conductivity materials has an advantage in terms of suppressing self-heating effects. </p><p>In this dissertation, structural and material innovations to overcome and improve critical challenges are summarized as follows: 1) Top-gate nano-membrane <i>β</i>-Ga₂O₃FETs on a high thermal conductivity diamond substrate with record high maximum drain current densities are demonstrated. The reduced self-heating effect due to high thermal conductivity of the substrate was verified by thermoreflectance measurement. 2) Local electro-thermal effect by electrical bias was applied to enhance the electrical performance of devices and improvements of electrical properties were shown after the annealing. 3) Thin thermal bridge materials such as HfO₂and ZrO₂were inserted between <i>β</i>-Ga₂O₃and a sapphire substrate to reduce self heating effects without using a diamond substrate. The improved thermal performance of the device was analyzed by phonon density of states plots of <i>β</i>-Ga₂O₃and the thin film materials. 4) Nano-membrane tri-gate <i>β</i>-Ga₂O₃FETs on SiO₂/Si substrate fabricated via exfoliation have been demonstrated for the first time. 5) Using the robustness of <i>β</i>-Ga₂O₃in harsh environments, <i>β</i>-Ga₂O₃ferroelectric FETs operating as synaptic devices up to 400 °C were demonstrated. The result offers the potential to use the novel device for ultra-wide bandgap logic applications, specifically neuromorphic computing exposed to harsh environments.<br></p>