Scandium diboride: a semi-metallic, lattice, thermally matched substrate for vertical AlGaN power electronics
We report the properties of hexagonal (space group P6/mmm) scandium diboride ($\mathrm{ScB}_2$) single crystals grown by a laser diode floating zone method at growth rates of ~1mm/hr under B-rich conditions with (002) rocking curve widths $Δω$=38'' approaching the quality of commercial SiC/GaN substrates. Lattice expansion measurements reveal matching to $\mathrm{Al_{0.55}Ga_{0.45}N}$ with a coefficient of thermal expansion ~5ppm/K at typical AlGaN growth temperatures, enabling thick AlGaN layers for ultra-wide bandgap (UWBG) power electronics >1kV. We measure semi-metallic room temperature resistivity ~15$μΩ$ cm, climbing to ~93$μΩ$ cm at 773K with a $T^2$ dependence effectively eliminating substrate parasitic resistance, the limiting factor in exploiting the full potential of UWBG. The Debye temperature $θ_{D,ScB_2}$ from heat capacity and lattice expansion is ~850K well matched to $θ_{D,ScB_2}$, but lower than the 1100K measured for Sc-rich growth conditions. We discuss Debye matching as a key substrate codesign criterion providing significant overlap in phonon modes for heat removal and thermal matching during AlGaN growth. The competitive thermal conductivity at room temperature 53W/mK is half that from full first principles calculations, a discrepancy we attribute to the presence of Sc-vacancies generated by B-rich growth. while the resistivity is ~2x the theoretical value, indicating that both electrons and phonons play equal role in thermal transport. The smooth ~2.5nm rms roughness surface enables advanced heat removal modalities through engineered phonon bridges and phonon polaritons in $\mathrm{ScB}_2$/AlGaN interfacial heterostructures, potentially allowing ~10-100x increase in power handling over state-of-the-art GaN/SiC.