Increases in Lorentz Factor with Dielectric Thickness  

作　　者：J. W. McPherson J. W. McPherson(McPherson Reliability Consulting LLC, Plano, Texas, USA)

机构地区：[1]McPherson Reliability Consulting LLC, Plano, Texas, USA

出　　处：《World Journal of Condensed Matter Physics》2016年第2期152-168,共17页凝固态物理国际期刊（英文）

摘　　要：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 SiO₂ 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 SiO₂ reduces with t_diel, all SiO₂ 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.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 SiO₂ 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 SiO₂ reduces with t_diel, all SiO₂ 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.

关 键 词：Dielectrics Dielectric Breakdown Local Electric Field Lorentz Factor Time-Dependent Dielectric Breakdown TDDB Bond Breakage Thermochemical E-Model 

分 类 号：Q17[生物学—水生生物学]