Preliminary First Principles Study Of Hf and Zr Aluminates as Replacement High-k Dielectrics
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Preliminary First Principles Study Of Hf and Zr Aluminates as Replacement High-k Dielectrics Michael Haverty1,2, Atsushi Kawamoto3, Gyuchang Jun1,2, Kyeongjae Cho2, and Robert Dutton3 1 Materials Science and Engineering, Stanford University, Stanford, CA 94305, U.S.A. 2 Multiscale Simulation Laboratory, Stanford University, Stanford, CA 94305, U.S.A. 3 Center For Integrated Systems, Stanford University, Stanford, CA 94305, U.S.A. ABSTRACT Bulk Density Functional Theory calculations were performed on Hf and Zr substitutions IRU$OLQ -alumina. The lowest energy configuration found was an octahedrally coordinated Zr site. Zr dissolution was favorable with an enthalpy of -2eV/unit cell for forming Al1.875Zr0.125O3 IURPSXUH=UDQG -alumina. Hf and Zr substitution for Al atoms introduced empty d-states below the conduction band edge reducing the EgRISXUH -alumina (7.5eV) to 6.4-5.9eV. The edge of the valence band however remained fixed by the O p-state character. The substitution of Hf and Zr into the alumina structure may lead to a higher dielectric constant, but will also reduce Eg and result in a trade off in tunneling currents in devices.
INTRODUCTION The semiconductor industry is experimenting with materials with higher dielectric constants • WRUHSODFHVLOLFD 6L22 DVDJDWHGLHOHFWULFLQWUDQVLVWRUVLQWKHQH[W decade. Silicates (Si1-xZrxO2), HfO2, ZrO2, alumina (Al2O3 DQGDOXPLQDWHV $O2-xZrxO3) are all possible candidates1,2,3. We show the utility of Density Functional Theory (DFT) in examining alumina and aluminates, as high-k gate dielectric replacement materials. DFT relies on periodic structure and is primarily used for crystalline structures. Although most alumina gate dielectrics are amorphous materials, Kawamoto4 and Jun5 have shown that similar studies of crystalline SiO2 and silicates provide meaningful and relevant results using structures with metal bonding and coordination similar to the amorphous high-k materials’ structures.
COMPUTATIONAL THEORY Density Functional Theory (DFT) was developed in the 1950’s to efficiently perform quantum mechanical total energy calculations solving the many-electron Shrödinger wave equation. Many detailed papers present the theory and background on the approximations and conventions used.6,7 DFT accurately predicts the energy of interactions between electrons by a term called the exchange correlation. A number of different schemes, such as the Local Density Approximation (LDA) and GW approximation estimate this exchange correlation. However, the increase in computational cost is proportional to the increase in accuracy. We utilize the LDA method that typically gives total energy values with 1-3% error in lattice constant and 3-10% error in bulk modulus.
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DFT calculations are performed at 0°K to minimize the potential energy of the ionic configurations. We have used the Vienna Ab-initio Simulation Package (VASP)8 that utilizes DFT theory and ultrasoft psuedo-potentials. The program input is the atom positions and constituents that
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