GOX 2023 Session TM-TuM: Characterization/Modeling III

β-gallium oxide (β-Ga₂O₃) is of intense current interest because of its ultra-wide bandgap, high critical field, and availability of melt-grown substrates. Point defects and complexes determine the properties of bulk crystals as well as epitaxial layers, thus, predictive models of defect concentrations under various impurity and processing scenarios are of very high value. First-principle calculations of defect energetics have provided critical insights into the defect system in β-Ga₂O_3, but translating computed enthalpies into defect concentrations corresponding to real-world crystal growth requires additional steps. Material processing in terms of growth or annealing typically controls the sample’s thermochemical trajectory in terms of temperatures and partial pressures, while computational papers frequently present results holding chemical potentials constant.

Here we report quantitative modelling of equilibrium defect concentrations in Ga₂O₃, considering especially the temperature dependence of the bandgap and temperature-dependent chemical potentials from the Ga-O binary system’s known thermochemistry. Additionally, we compute results for realistic sample types such as Fe- or Sn-doped wafers accounting for the fixed concentrations of these impurities as opposed to their fixed chemical potentials. Results are presented for various background n-type doping and for equilibrium and quenching, corresponding respectively to 0 or infinite cooling rates. We find significant departures from prior simpler predictions, especially in the case of the bandgap temperature dependence which tends to suppress V_Ga. We compare our predicted results to experimental cases such as annealing in O₂ or Ga₂O vapors.

Finally, to give semi-quantitative insight into defect concentrations expected in finite-sized samples subjected to finite cooling rates without full-fledged defect reaction-diffusion simulations, we introduce the concept of generalized quenching as a 3^rd type of computation. At the heart of generalized quenching is the insight that, because of their different diffusion constants, different types of defects located at different distances from free surfaces will be “frozen-in” at different temperatures. By combining the correct series of equilibrium and quenching calculations, it is possible to predict defect concentrations present in real-world samples e.g. as a function of radius within a boule or for thin films of different thicknesses. We compare these results to the known phenomena from bulk crystal growth, indicating differences in carrier density between the center and periphery of CZ-grown boules.

Gallium Oxide (Ga₂O₃) has emerged as a highly promising material for power devices due to its wider bandgap and high critical electric field. In this paper, we investigate the drift layer design for Ga₂O₃ power devices through theoretical analysis and trade-offs. The drift layer, similar to other wide-bandgap materials, plays a crucial role in the performance of Ga₂O₃ power semiconductor devices. The two primary drift layer configurations, non-punch through (NPT) and punch-through (PT), are analyzed with a focus on key design parameters such as drift layer thickness (W_D) and doping concentration (N_D), and their impact on specific on-resistance (R_on,sp) for both NPT and PT structures. Furthermore, we extend the specific on-resistance to breakdown voltage (BV) trade-off analysis by considering the additional resistance components for both lateral and vertical MOSFETs, providing a practical guide for device researchers to pursue the appropriate architectures based on the voltage rating.

The ionization rate of the electrons in Ga₂O₃ shown in Fig. 1, is utilized for the evaluations. The electric field at the onset of BV (referred to as the critical electric field, E_c) is extracted iteratively by solving the ionization integral with the ionization rates for both non-punch through (NPT) and punch-through (PT) structures. The critical electric field exhibits a strong dependence on the doping concentration for both non-punch through (NPT) and punch-through (PT) structures (with varying widths) as illustrated in Fig. 2. The impact of doping concentration and width on the BV for both NPT and PT structures (with varying widths) is depicted in Fig. 3. The ionization ratio as a function of doping concentration is extracted from the ionization energies of donors is shown in Fig. 4. With reduced doping concentration and width, the optimal R_on,sp of the punch-through (PT) structure is about 8% lower than that of the non-punch through (NPT) structure at a particular BV, as depicted in Fig. 5. To further explore the trade-off analysis, a Ga₂O₃ MOSFET with both lateral and vertical architectures was considered. Using reasonable assumptions and practical specifications, the channel, drift, and substrate resistances were evaluated. Fig. 6 depicts the individual and total resistance components associated with lateral devices (channel and drift resistances represented by red curves) and vertical devices (channel, drift, and substrate resistances represented by blue curves). It is evident from Fig. 6 that, at breakdown voltages lower than ~2kV, the lateral device offers the lowest possible R_on,sp but beyond ~2kV, the vertical device dominates by offering a lower R_on,sp.