# Theoretical studies of silicon surfaces using finite clusters

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## Abstract

The objective of this thesis is to study the electronic structure, geometries and chemical binding characteristics of the surfaces of silicon and of the initial form of oxygenated Si. We examined the (111), (100), and (110) surfaces, relaxation on the (111) and (100) surfaces and reconstruction on the (100) surfaces. In addition we examined steps on the OM surfaces. In the oxygenated surface we considered the geometry, excited states and ion states of both 0 and 0_2 bonded to the perfect (111) surface. These studies indicated that surfaces and chemisorption lead to localized electronic states for which explicit inclusion of electronic correlation (many body) effects is essential. These effects are included through use of generalized valence bond (GVB) and configuration interaction (CI) techniques. These techniques require use of a finite collection of Si atoms to represent the surface. We find that very small clusters lead to reliable results if the model system is properly tied off with SiH bonds (to represent internal Si-Si bonds). In Chapter 1 we report an effective potential for replacing the ten core electrons in calculations involving the Si atom. The potential is obtained directly from ab initio calculations on the states of the Si atom and no empirical data or adjustable parameters are used. The ab initio effective potential is tested by carrying out Hartree-Fock generalized valence bond and configuration interaction calculations on various molecules. We considered Si, Si_2, SiH_3, Si_2H_6 and H_3S10_2 and calculated excitation energies, ionization potentials, and electron affinities both both using the effective potential and without it (ab initio). In essentially all cases the agreement is to better than 0.1 eV, providing strong evidence that the effective potential adequately represents the Si core. This potential is utilized in all of the calculations reported in subsequent chapters. In Chapter 2 we consider clean (111), (100) and (110) silicon surfaces. For the (111) surface the relaxation of silicon surface atoms is studied by means of an Si(SiH_3)_3 cluster. We find that the surface state is accurately described as a dangling bond orbital with 93% p character. We determined the .optimum relaxation of the surface layer to be 0.08Å toward the second layer. For the positive ion we find that the surface atom relaxes toward the second layer by an additional 0.30Å. Using an Si_3H_6 cluster we find that the interaction between adjacent dangling bond orbitals indicates that they are very weakly coupled (with a splitting of ~0.01 eV between the singlet and triplet spin couplings.) For the (100) surface we used an Si(SiH_3)_2 cluster. We find a relaxation distance of 0.10Å toward the vacuum. We also considered the 2x1 reconstruction of such surfaces using the results for Si_2H_4 and Si(SiH_3)_2 complexes. It is found that adjacent surface atoms form a bond (1.76 eV bond strength), leading to pairing up. of adjacent silicons with an optimum Si-Si bond length of 2.38Å). In Chapter 3 we consider the electronic structure of divalent steps on (111) silicon surfaces. We find three localized electronic states separated by less than 0.3 eV. These states have quite different electronic structure and are expected to be reactive toward a large range of chemical species. In Chapter 4 we study the chemisorption of oxygen upon Si (111) surfaces. For single oxygen atoms we find an optimum Si-0 bond length of 1.63Å. We also find ionization potentials in the range 11-16 eV. Then we consider a model in which an oxygen molecule chemisorbed onto the silicon surface has, an electronic structure corresponding to a peroxy radical. We find ionization potentials in the range 11-18 eV in agreement with experiment. We find an optimum 0-0 bond length of 1.37Å and a Si-0-0 bond angle of 126° for the chemisorbed peroxy radical.

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