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 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 threefold coordination in the 3 O Si O − ≡ tetrahedral structure.

Van der Waals Epitaxially Grown Molecular Crystal Dielectric Sb2O3 for 2D Electronics

“…As shown in Figure a, the breakdown field sharply increased as the thickness of Sb 2 O 3 decreased, leading to a high breakdown field of 18.6 MV/cm for 1.3 nm-thick Sb 2 O 3 (bilayer). The inverse relationship between thickness and breakdown field in Sb 2 O 3 (as shown in the inset of Figure a) is due to enhanced local electric fields by the additional contribution of polarization and increased defect density for thicker dielectrics, which aligns with observations found in conventional dielectrics like SiO 2 and the 2D dielectric of hBN. − The insets of Figures a and S5 summarize the breakdown fields obtained in other studies, where various dielectrics are directly grown on 2D materials. ,− It shows that the Sb 2 O 3 nanosheet grown on graphene shows higher breakdown fields than the other dielectrics and Sb 2 O 3 grown by different methods in a broad thickness range. The band gap of Sb 2 O 3 measured by electron energy loss spectroscopy (EELS) in Figure b is 4.4 eV, close to the values in previous studies. , To measure the dielectric constant of Sb 2 O 3 , we used a dual-gate transistor with a top dielectric of hBN ( k = 3.76) as depicted in Figure c. , The epitaxially grown Sb 2 O 3 and graphene heterostructure were used as the bottom dielectric and the bottom gate, respectively.…”

Dielectric Breakdown in Single-Crystal Hexagonal Boron Nitride

“…The general trends show that ξ BD reduces with an increase in the h-BN thickness. In conventional amorphous gate dielectrics, such as SiO 2 , a reduction of ξ BD for thicker dielectric occurs because the local electric fields (the applied field plus the contribution from the material polarization) are higher at a given applied voltage. , Increasing the local field is also the most reasonable explanation for the decrease of ξ BD with the increasing thickness for h-BN as well, although given the scarcity of data at present, alternative possibilities cannot be entirely discarded, e.g., thicker films may have a greater density of defects.…”

“…Dielectric breakdown field strength (ξ BD ) and statistical analysis of breakdown in h-BN: (a) ξ BD was measured as a function of h-BN thickness with statistical error bars. Previously reported ξ BD values for both h-BN , and SiO 2 are plotted for comparison. (b) Plot of breakdown voltage ( V BD,h‑BN ) distributions at different h-BN thicknesses on a Weibull scale, with the Weibull slope β indicated.…”

Modified Dynamic Physical Model of Valence Change Mechanism Memristors

“…Also, it is a stochastic process where the filament configuration is not controllable, thus causing a severe device-to-device variation issue. Therefore, EF-free memristors, enabled by decreasing the switching oxide layer thickness in VCM memristors to a several nanometer range, make a more desirable candidate. − In such thin oxides, the breakdown voltage remains constant regardless of the thickness due to the dominant effect of the surface dipole layer, making the EF and set voltages identical. − Nonetheless, such thin oxides (≲5 nm) are generally too electrically leaky to ensure a stable RS behavior. Therefore, it is crucial to suppress the leakage current by selecting appropriate electrodes and optimizing the oxygen content. , In this regard, an electrode material with a high work function and oxygen supply capability is preferred, such as RuO 2 , adopted in this work.…”