Ab-Initio Theory of Defect Structure in a-Si iH
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AB-INITIO THEORY OF DEFECT STRUCTURE IN a-Si iH
YANEER BAR-YAM AND J.D. JOANNOPOULOS Massachusetts Institute of Technology, Department of Physics, 77 Massachusetts Avenue, Cambridge, MA 02139, U.S.A.
ABSTRACT
It has recently become feasible that theory Will be able to predict the structure of solids "ab-initio", using only the atomic number of the based on recent advances in This is constituent atoms as input. A simple physical density-functional theory and pseudopotential theory. introduction of the concepts underlying these theories is presented. Special emphasis is given to examining the structure and effective correlation energies of defects in amorphous Si.
INTRODUCTION One of the oldest fundamental problems in condensed matter physics has been the prediction of the crystal structure of solids from first principles. Given only the atomic number of the constituent atoms as input, what are the possible geometric structures of a solid? In the past, nearly all theories attempting to derive structural A specific information about a solid have been spectroscopic in nature. configuration of atoms would be postulated and a Hamiltonian formulated. various elementary excitations would be calculated and compared with If the comparison was not experimental measurements of excited states. satisfactory, the original guess of atomic positions would be readjusted until some kind of agreement between theory and experiment emerged. Although this approach can be useful in certain cases, it is not very satisfactory in general. In order to predict the structure of a solid directly, one must first be able to calculate the total energy of the solid and minimize it with Four obstacles nuclear and electronic coordinates. respect to its These have to do with dealing immediately arise when one tries to do this. with the positions of 1023 nuclei, the strong interactions among 1023 electrons, the strong interactions between the electrons and the nuclei, and finally, solving the entire problem quantum mechanically. In recent years sufficient advances in condensed matter theory and computer technology have been achieved that many of these obstacles can now Specifically, the Born-Oppenheimer approximation allows the be overcome. If we assume that in atoms of the solid to be "frozen" in some pattern. general this pattern can be modeled in terms of super-cells, then the Bloch's theorem immediately reduces the problem of pattern is periodic. solving for 1023 atoms to that of solving the problem within some unit cell The electron-electron of the solid containing only several atoms. interactions can be handled within the framework of Density Functional 1 5 . In principle, this theory allows one to map, exactly, the Theory problem of an interacting electron gas onto that of a system of The strong non-interacting particles in some external effective potential. electron-ion interaction can be handled effectively within the framework of
Mat- Res. Soc. Symp. Proc. Vol. 70. ' 1986 Materials Research Society
98
Pseudopotential Theory 6 - 1 4 . H
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