On why dielectric breakdown strength reduces with dielectric thickness

An intrinsic/fundamental-physics reason is presented for why the dielectric breakdown strength E_bd reduces with dielectric thickness t_diel. Through extensive use of layered dipole summations, it is shown that the Lorentz factor L tends to increase with thickness. The increase in L with dielectric thickness produces a higher local electric field (E_loc) in thicker dielectrics. Higher E_loc produces more polar-bond distortion (stretching, compressing, bending, etc.) and this leads to a reduction in bond strength. A reduction in bond strength causes E_bd and TDDB reductions regardless of the actual bond breakage mechanism (standard Boltzmann processes, current driven processes, or hydrogen release processes). While thicker SiO₂ layers have lower E_bd, all SiO₂ thicknesses tend to breakdown at roughly the same local electric field (E_loc)_bd ≈ 40MV/cm.