Increases in Lorentz Factor with Dielectric Thickness

Abstract

For many years, a Lorentz factor of L = 1/3 has been used to describe the local electric field in thin amorphous dielectrics. However, the exact meaning of thin has been unclear. The local electric field E loc modeling presented in this work indicates that L = 1/3 is indeed valid for very thin solid dielectrics (t diel ≤ 20 monolayers) but significant deviations from L = 1/3 start to occur for thicker dielectrics. For example, L ≈ 2/3 for dielectric thicknesses of t diel = 50 monolayers and increases to L ≈ 1 for dielectric thicknesses t diel > 200 monolayers. The increase in L with t diel means that the local electric fields are significantly higher in thicker dielectrics and explains why the breakdown strength E bd of solid polar dielectrics generally reduces with dielectric thickness t diel . For example, E bd for SiO 2 reduces from approximately E bd ≈ 25 MV/cm at t diel = 2 nm to E bd ≈ 10 MV/cm at t diel = 50 nm. However, while E bd for SiO 2 reduces with t diel , all SiO 2 thicknesses are found to breakdown at approximately the same local electric field (E loc ) bd ≈ 40 MV/cm. This corresponds to a coordination bond strength of 2.7 eV for the silicon-ion to transition from four-fold to three-fold coordination in the tetrahedral structure.