TITLE:
Increases in Lorentz Factor with Dielectric Thickness
AUTHORS:
J. W. McPherson
KEYWORDS:
Dielectrics, Dielectric Breakdown, Local Electric Field, Lorentz Factor, Time-Dependent Dielectric Breakdown, TDDB, Bond Breakage, Thermochemical E-Model
JOURNAL NAME:
World Journal of Condensed Matter Physics,
Vol.6 No.2,
May
31,
2016
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 Eloc modeling presented in this work indicates that L = 1/3 is indeed valid for very thin solid dielectrics (tdiel ≤ 20 monolayers) but significant deviations from L = 1/3 start to occur for thicker dielectrics. For example, L ≈ 2/3 for dielectric thicknesses of tdiel = 50 monolayers and increases to L ≈ 1 for dielectric thicknesses tdiel > 200 monolayers. The increase in L with tdiel means that the local electric fields are significantly higher in thicker dielectrics and explains why the breakdown strength Ebd of solid polar dielectrics generally reduces with dielectric thickness tdiel. For example, Ebd for SiO2 reduces from approximately Ebd ≈ 25 MV/cm at tdiel = 2 nm to Ebd ≈ 10 MV/cm at tdiel = 50 nm. However, while Ebd for SiO2 reduces with tdiel, all SiO2 thicknesses are found to breakdown at approximately the same local electric field (Eloc)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.