The Surface Green's Function in Semiconductors by the Tight-Binding Linear Muffin-Tin Orbital Method
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THE SURFACE GREEN'S FUNCTION IN SEMICONDUCTORS BY THE TIGHT-BINDING LINEAR MUFFIN-TIN ORBITAL METHOD
M. 9OB* AND J. KUDRNOVSKý**
*Czechoslovak Academy of Sciences, Institute of Physical Metallurgy, hi~kova 22, 616 62 Brno, Czechoslovakia, and University of Pennsylvania, Department of Materials Science and Engineering, 3231 Walnut Street, Philadelphia, PA 19104-6272, U.S.A. **Czechoslovak Academy of Sciences, Institute of Physics, Na Slovance 2, 180 40 Prague, Czechoslovakia
ABSTRACT
A computationally efficient method for the determination of the Green's function (GF) of an ideal semi-infinite semiconductor crystal within the first-principles TB-LMTO approach is developed. Our sample is described by a semi-infinite stack of principal layers with only nearestneighbor interaction between them. The projection of the GF of the ideal semi-infinite crystal onto the top principal layer is the surface GF (SGF), which is evaluated from the condition of removal invariance: by adding (removing) a principal layer of bulk atoms to (from) the semi-infinite crystal we recover the same semi-infinite crystal. This approach avoids the knowledge of the bulk GF and the surface-normal k-integration common in other treatments. Our method is illustrated on the evaluation of k,-resolved densities of states, both on the surface and deep in the sample, for the (1 10) and (001) faces of typical elemental and AIIIBv semiconductors.
INTRODUCTION
The electronic structure of semiconductor surfaces and interfaces has become a subject of large theoretical and experimental activity in the past decade. The reason is both the practical relevance of the topic and its fundamental physical importance. From the theoretical point of view, the presence of the solid surface introduces two new complications compared with the bulk solids: (i) the lack of periodicity normal to the surface and (ii) possible rearrangement of atoms in the outermost layers giving rise to relaxations and reconstructions of surfaces. Many different theoretical methods [11 are currently used to study the electronic properties of surfaces, both in metals and semiconductors. These methods may be divided into two groups: (i) standard band structure techniques applied to slabs or supercells and (ii) Green's function (GF) formalism employed for a true semi-infinite solid. The methods of the first group are mostly first-principles ones that also allow to avoid any shape approximations concerning the atomic potentials. On the other hand, they introduce artificial boundary conditions to the problem. The latter limitation is removed by the methods of the second group, which are mostly empirical, based on the tight-binding (TB) models. These methods have a great appeal due to their simplicity and applicability to various surface-related problems. Mat. Res. Soc. Symp. Proc. Vol. 209. Q1991 Materials Research Society
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The first-principles layer-KKR method .J21 and the scattering theoretical method (STM) [3] belong also to this group. The layer-KKR method is mostly suitable for metalli
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