Analysis of the dependence of critical electric field on semiconductor bandgap
Oleksiy Slobodyan, Jack Flicker, Jeramy Ray Dickerson, Jonah Shoemaker, Andrew Binder, Trevor Smith, Stephen M. Goodnick, Robert Kaplar, M.A. Hollis
Abstract
Abstract Understanding of semiconductor breakdown under high electric fields is an important aspect of materials’ properties, particularly for the design of power devices. For decades, a power-law has been used to describe the dependence of material-specific critical electrical field ( $${\mathcal{E}}_{\text{crit}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>E</mml:mi> <mml:mtext>crit</mml:mtext> </mml:msub> </mml:math> ) at which the material breaks down and bandgap ( E g ) . The relationship is often used to gauge tradeoffs of emerging materials whose properties haven’t yet been determined. Unfortunately, the reported dependencies of $${\mathcal{E}}_{\text{crit}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>E</mml:mi> <mml:mtext>crit</mml:mtext> </mml:msub> </mml:math> on E g cover a surprisingly wide range in the literature. Moreover, $${\mathcal{E}}_{\text{crit}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>E</mml:mi> <mml:mtext>crit</mml:mtext> </mml:msub> </mml:math> is a function of material doping. Further, discrepancies arise in $${\mathcal{E}}_{\text{crit}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>E</mml:mi> <mml:mtext>crit</mml:mtext> </mml:msub> </mml:math> values owing to differences between punch-through and non-punch-through device structures. We report a new normalization procedure that enables comparison of critical electric field values across materials, doping, and different device types. An extensive examination of numerous references reveals that the dependence $${\mathcal{E}}_{\text{crit}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>E</mml:mi> <mml:mtext>crit</mml:mtext> </mml:msub> </mml:math> ∝ E g 1.83 best fits the most reliable and newest data for both direct and indirect semiconductors. Graphical abstract