We compute the distribution of electronic levels of native defects in amorphous silica from total energy differences of charge-state density functional theory calculations over an ensemble of atomic structures. The predicted distributions reproduce results from trap spectroscopy by charge injection experiments, validating the calculations. Furthermore, our study characterizes the experimentally inaccessible contributions of individual defect types to the overall distribution. Computed electron and hole trapping levels provide insight into the positive charge buildup in bulk silica observed in negative-bias-temperature-instability, an important degradation mechanism of metal-oxide-semiconductor devices.
ABSTRACT:We present a first principles study of the effect of atomic variability on the structure, mechanical and electronic properties of amorphous silicon nitride. Using a combination of molecular dynamics and density functional theory calculations we predict an ensemble of statistically independent, well-relaxed and stress-free amorphous silicon nitride structures. We analyze the short, intermediate, and long-range order of the structures generated using radial distribution functions, ring statistics, bond angle distributions, and translational invariance parameters. Though energetically very similar, these structures span a wide range of densities (2.75-3.25 g/cm 3 ) and bulk moduli (115GPa to 220 GPa) in good agreement with the fabrication-dependent experimental range. Chemical bonds and atomic defects are identified via a combination of bond distance cutoff and maximally localized Wannier function analysis. A significant number of the amorphous structures generated (~30%) are defect-free providing an ideal reference to characterize the formation energy of the various point defects and their defect energy levels. An analysis of the Kohn-Sham density of states and energetics of the structures reveals that defects in amorphous dielectrics have a distribution of associated properties (e.g. formation energies and electronic energy levels) due to variations in local atomic structure; this should be taken into consideration in physics-based continuum models of these materials.
We present a dielectric charging model that combines ab initio calculations of trap levels with a continuum-level transport model and apply it to interpret charging currents in amorphous silicon nitride. Density functional theory calculations on an ensemble of structures predict a distribution of electron trap levels up to 1.8 eV below the conduction band edge and provide insight into the physical trapping mechanisms. Incorporating this information in the continuum model, as opposed to the standard approach of a single adjustable trap level, not only leads to a more accurate description of experimental current transients in metal-insulator-metal capacitors, but also to a more precise and physical determination of associated material properties such as metal-dielectric barrier height.
a b s t r a c tWe quantify uncertainties in density functional theory predictions of several fundamental materials properties of amorphous dielectrics focusing on those that arise from the intrinsic atomic variability of the glass structures and those stemming from approximations in the theory. The intrinsic, or aleatoric, uncertainties are quantified by performing calculations over ensembles of structures obtained by annealing independent liquid samples. We estimate model form, or epistemic, uncertainties by comparing results from two exchange and correlation functionals that exhibit different bonding characteristics: the local density approximation (that typically overbinds), and the generalized gradient approximation (that often underbinds). In the case of density, bulk modulus, and point defect formation energies predictions obtained from systems containing between 72 and 192 atoms, typical of current state-of-the-art calculations, show that the intrinsic variability in the atomic structure leads to uncertainties a factor of two to four times greater than those originating from model form. While model form discrepancies remain important, our results emphasize the importance of using ensembles of structures to make predictions of amorphous materials. The use of such probabilistic atomic-level data as input in multiscale materials or device models is critical for predictions with quantified uncertainties but also to uncover how atomic variability affects device performance.
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