Intrinsic Breakdown Strength: Theoretical Derivation and First-Principles Calculations

Intrinsic breakdown strength (F_{bd}), as the theoretical upper limit of electric field strength that a material can sustain, plays important roles in determining dielectric and safety performance. The well accepted concept is that a larger band gap (E_{g}) often leads to a larger intrinsic breakdown strength. In this work, we analytically derive a simplified model of F_{bd}, showing a linear relationship between F_{bd} and the maximum electron density of states (DOS_{max}) within the energy range spanning from the conduction band minimum (CBM) to CBM+E_{g}. Using the Wannier interpolation technique to reduce the cost of calculating the F_{bd} for various three- and two-dimensional materials, we find that the calculated F_{bd} did not show any simple relationship with band gap, but it behaves linearly with the DOS_{max}, consistent with our theoretical derivation. Our work shows that the DOS_{max} is more fundamental than the band gap value in determining the F_{bd}, thus providing useful physical insights into the intrinsic dielectric breakdown strength and opening directions for improving high-power devices. The dimensional effects on F_{bd} has also been revealed that monolayers tend to have larger F_{bd} due to reduced screening effects.