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43288-AC10
Computational Study of Conduction and Breakdown Mechanisms in Metal Oxide Dielectric Insulators
As mentioned in the last annual report, in light of recent promising approaches developed in the PI's group, the scope of this project has been changed from studying conduction and breakdown mechanisms in metal oxide dielectric insulators to studying electrical properties (e.g., dielectric properties, band offsets, defect states).
This second year's report contains three sets of density functional theory (DFT) based results, and pertains to Si-HfO2 interfaces: (1) characterization of thermodynamic and kinetic driving forces for the segregation of point defects from bulk HfO2 to the Si-HfO2 interface; (2) application of the theory of the local dielectric permittivity to determining dielectric constant profiles across Si-HfO2 interfaces; and (3) determination of the band structure as a function of position across the Si-HfO2 interface. Below, each of these is elaborated.
Point defects close to the Si-HfO2 interface:
The first step in characterizing point defects in the neighborhood of interfaces is the development of realistic and computationally tractable atomic level models of the interface. This was described in the last annual report. The most stable monoclinic HfO2 based interface was used in the study of O vacancy and interstitial diffusion towards or across the interface. O vacancy and interstitial formation energies at various locations with respect to this interface, as well as the migration energies for the site-to-site diffusion of O vacancies and interstitials were determined. The vacancy formation energies were about 6.4-6.2 eV in the bulk part of HfO2, and the interstitial formation energy was about 0.95-0.66 eV, depending on the local coordination environment of the O sites. The formation energy values monotonically decreased as the interface is approached. At the interface, the formation energy for the vacancy and interstitial were, respectively, 5.3-5.1 eV and about -2.9 eV, indicating that the point defects strongly preferred to segregate to the interface. Likewise the barrier to the migration of O defects also decreased monotonically from the bulk (1.7-2.4 eV for the vacancy and 0.5 eV for the interstital) to the interface (0.45-0.25 eV for the vacancy and about 0.2 eV for the interstitial). Moreover, in the case of the O interstitial, there was a barrierless pathway for the interstitial to penetrate the first Si layer, resulting in the spontaneous formation of Si-O-Si bonds. These calculations clearly indicate that in the presence of O vacancies and interstitials, formation of nonequilibrium phases such as Hf silicide and SiOx are strongly preferred at the interface, in agreement with experimental observations.
Dielectric constant profiles across the Si-HfO2 interface:
As a first step in the determination of the extent to which surfaces and interfaces impact the dielectric properties of ultrathin HfO2 on Si, DFT total energy calculations and the theory of the local dielectric permittivity were used to determine static and optical dielectric constant profiles across the thickness of HfO2 slabs and Si-HfO2 interfaces. The theory of the local dielectric permittivity was developed and used earlier by the PI to determine the extent to which the permittivity is enhanced at surfaces and/or interfaces for a wide variety of systems including Si, SiO2, Si-SiO2, and Cu-phthalocynanine monomers and polymers. In the case of Si-HfO2 interfaces, deviations of the static and optical dielectric constants from the corresponding bulk values were encountered at free surfaces and at the interfaces. These deviations could be correlated to the coordinative unsaturations of the surface and interface atoms. This approach will be further applied to study the impact of interfacial point defects and phases on the dielectric response.
Position-dependent band structure across the Si-HfO2 interface:
In addition to the dynamics of point defects, and their role on dielectric response, trapping of charge carriers at interfaces is an important phenomenon that would impact dielectric degradation. In order to address this aspect, a layer-decomposed density of states (LaDOS) analysis was performed for the Si-HfO2 systems. The contribution to the total density of states by each layer of atoms was determined as a function of distance from the Si-HfO2 interface. This approach has yielded an efficient method for the identification of interface/surface states, band bending at interfaces/surfaces, and an understanding of the origin of these defect states and band bending. Moreover, the band offsets across a Si-HfO2 interface determined using this method (3.05 eV) is in excellent agreement with recent experimental determinations. The LaDOS approach is currently being used to study the role played by O point defects on the band offsets as a function of the distance from the interface.
Impact of ACS-PRF support:
Support of the PI's research by the ACS-PRF is gratefully acknowledged. Two graduate students were partially supported through this grant, and about 10 peer-reviewed journal papers and about 10 conference presentations emerged out this project. This grant was instrumental in providing a good start to the PI's scientific career, and has positioned him well for obtaining grants (as he has) from other funding agencies.
