FIG. 1.6 (a) Ionized doping concentration in different semiconductors with respect to the background doping considering compensation effect of acceptor-like impurities ( Zhang and Speck, 2020 ). (b) Modified BFOM contour plot estimated from the on-resistance and breakdown field accounting ionized dopants. β-Ga₂O₃ shows the highest BFOM when material purity and dopant ionization efficiency are considered to estimate BFOM. Reproduced with permission from Zhang et al., Semicond. Sci. Technol. 35 (12), 125018. (2020). Copyright 2020 AIP Publishing LLC. More about this image found in (a) Ionized doping concentration in different semiconductors with respect t...

FIG. 7.2 Velocity and the impact ionization rates from Monte Carlo. (a) The velocity-field curves in β-Ga₂O₃ for three different directions at room temperature. Reproduced with permission from Ghosh and Singisetti, J. Appl. Phys. 122 , 035702 (2017a). Copyright 2017a AIP Publishing LLC. (b) Electronic bands in β-Ga₂O₃ computed under DFT. The conduction bands are scissor shifted to match the experimental bandgap. Reproduced with permission from Ghosh and Singisetti, J. Appl. Phys. 124 , 085707 (2018). Copyright 2020 AIP Publishing LLC. (c) The ionization rates along the two high-symmetry directions in the Brillouin zone. Reproduced with permission from Ghosh and Singisetti, J. Appl. Phys. 124 , 085707 (2018). Copyright 2020 AIP Publishing LLC. (d) The ionization rates with respect to energy for all the k points in the Brillouin zone. Reproduced with permission from Ghosh and Singisetti, J. Appl. Phys. 124 , 085707 (2018). Copyright 2020 AIP Publishing LLC. More about this image found in Velocity and the impact ionization rates from Monte Carlo. (a) The velocity...

FIG. 1.4 (a) Relationship of bandgap and critical breakdown electric field for direct and indirect semiconductors ( Kaplar et al., 2016 ). (b) Theoretical limits of on-resistance and breakdown field of the semiconductors showing their predicted contours of BFOM ( Tsao et al., 2017 ). Note that the theoretical BFOM contours assume that the dopant is completely ionized, which is often not the case in real WBG and UWBG semiconductors. Hence, a modified BFOM is used to evaluate the true material case accounting incomplete dopant ionization and background compensation effects that is shown later in Fig. 1.6 . More about this image found in (a) Relationship of bandgap and critical breakdown electric field for direc...

FIG. 6.6 The deep donor level E_d2 at ∼E_C–0.12 eV (a) increases with Si doping in β-Ga₂O₃ ( Ghadi et al., 2020a ) and (b) associated effect of E_d2 level with an estimated increase of on-resistance due to incomplete ionization during forward bias operation of β-Ga₂O₃ Schottky diodes ( Neal et al., 2017 ). More about this image found in The deep donor level E_d2 at ∼

FIG. 9.1 Simplified sketch of ionization process. A pulse E(t) is impinging on an isolated atom, and an electronic wavepacket is released. A detector placed at a far distance and at a solid angle Ω_r = (θ, ϕ) counts the electrons per unit time; this counting is related closely to the electronic radial current j_r(Ω_r; t). The laser pulse and the electronic current are varying in both space and time (not to scale in the figure). More about this image found in Simplified sketch of ionization process. A pulse E(

FIG. 9.2 Left: schematic of energy domain of an ionized wavepacket from a weak-field pulse; γ_L ≃ 1/τ_L. Right: H 2 + ionization with pulse polarized linearly along its internuclei quantization axis. More about this image found in Left: schematic of energy domain of an ionized wavepacket from a weak-field...

FIG. 9.3 Ionization wavepacket released following interaction of hydrogen molecular ion H 2 + with a pulse (40 eV, 10¹³ W/cm², 24 cycles, Hann). The horizontal axis represents the position along the symmetry axis of the system (z axis) after a 24-cycle laser pulse and post-propagation of 3.5 times the length of the pulse. For the calculation, the full TDSE was propagated. The position of the first peak confirms the approximate relation z = k_Lt_d. More about this image found in Ionization wavepacket released following interaction of hydrogen molecular ...

FIG. 6.17 The calculated transition levels of several candidate donor dopants in β-(Al_xGa_1–x)₂O₃ alloys shown as a function of Al content, as adapted with permission from (a) Varley et al., Appl. Phys. Lett. 116 , 172104 (2020). Copyright 2020 AIP Publishing LLC and (b) Mu et al., Phys. Rev. B 105 (2022). Copyright 2020 AIP Publishing LLC. The lines denote the ε(±) transition for C, Si, and Sn, and the ε(±) transition for Ge, Zr, Hf, and Ta dopants on the most favorable cation sites. The CBM energy (shaded green and yellow) is plotted with respect to the VBM energy of Ga₂O₃ for all compositions using the calculated energies from Peelaers et al. (2018) . The Al content at which a given dopant's defect level falls within the bandgap and thus the dopant is no longer expected to efficiently ionize at room temperature is included in parentheses. More about this image found in The calculated transition levels of several candidate donor dopants in β-(A...