## Abstract

In this work a new theoretical formalism is introduced in order to simulate the phononinduced relaxation of a non-equilibrium distribution to equilibrium at a semiconductor surface numerically. The non-equilibrium distribution is effected by an optical excitation. The approach in this thesis is to link two conventional, but approved methods to a new, more global description: while semiconductor surfaces can be investigated accurately by density-functional theory, the dynamical processes in semiconductor heterostructures are successfully described by density matrix theory. In this work, the parameters for density-matrix theory are determined from the results of density-functional calculations. This work is organized in two parts. In Part I, the general fundamentals of the theory are elaborated, covering the fundamentals of canonical quantizations as well as the theory of density-functional and density-matrix theory in 2{sup nd} order Born approximation. While the formalism of density functional theory for structure investigation has been established for a long time and many different codes exist, the requirements for density matrix formalism concerning the geometry and the number of implemented bands exceed the usual possibilities of the existing code in this field. A special attention is therefore attributed to the development of extensions to existing formulations of this theory, where
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## Citation Formats

Buecking, N.
Optical excitation and electron relaxation dynamics at semiconductor surfaces: a combined approach of density functional and density matrix theory applied to the silicon (001) surface.
Germany: N. p.,
2007.
Web.

Buecking, N.
Optical excitation and electron relaxation dynamics at semiconductor surfaces: a combined approach of density functional and density matrix theory applied to the silicon (001) surface.
Germany.

Buecking, N.
2007.
"Optical excitation and electron relaxation dynamics at semiconductor surfaces: a combined approach of density functional and density matrix theory applied to the silicon (001) surface."
Germany.

@misc{etde_21065990,

title = {Optical excitation and electron relaxation dynamics at semiconductor surfaces: a combined approach of density functional and density matrix theory applied to the silicon (001) surface}

author = {Buecking, N}

abstractNote = {In this work a new theoretical formalism is introduced in order to simulate the phononinduced relaxation of a non-equilibrium distribution to equilibrium at a semiconductor surface numerically. The non-equilibrium distribution is effected by an optical excitation. The approach in this thesis is to link two conventional, but approved methods to a new, more global description: while semiconductor surfaces can be investigated accurately by density-functional theory, the dynamical processes in semiconductor heterostructures are successfully described by density matrix theory. In this work, the parameters for density-matrix theory are determined from the results of density-functional calculations. This work is organized in two parts. In Part I, the general fundamentals of the theory are elaborated, covering the fundamentals of canonical quantizations as well as the theory of density-functional and density-matrix theory in 2{sup nd} order Born approximation. While the formalism of density functional theory for structure investigation has been established for a long time and many different codes exist, the requirements for density matrix formalism concerning the geometry and the number of implemented bands exceed the usual possibilities of the existing code in this field. A special attention is therefore attributed to the development of extensions to existing formulations of this theory, where geometrical and fundamental symmetries of the structure and the equations are used. In Part II, the newly developed formalism is applied to a silicon (001)surface in a 2 x 1 reconstruction. As first step, density-functional calculations using the LDA functional are completed, from which the Kohn-Sham-wave functions and eigenvalues are used to calculate interaction matrix elements for the electron-phonon-coupling an the optical excitation. These matrix elements are determined for the optical transitions from valence to conduction bands and for electron-phonon processes inside the conduction bands, where the coupling to phonons is realized by a deformation potential approach. A special interest is attributed to the interplay of bulk and surface bands originating from the surface reconstruction, which partly reach into the band gap. From these matrix elements, the dynamical evolution of the initial electron distribution is calculated using the derived equations. The thesis is completed by a comparison to experimental data. Here, a good agreement is found, both for the temporal evolution of the electron population, and for the relaxation timescales that can be extracted from the simulated data. (orig.)}

place = {Germany}

year = {2007}

month = {Nov}

}

title = {Optical excitation and electron relaxation dynamics at semiconductor surfaces: a combined approach of density functional and density matrix theory applied to the silicon (001) surface}

author = {Buecking, N}

abstractNote = {In this work a new theoretical formalism is introduced in order to simulate the phononinduced relaxation of a non-equilibrium distribution to equilibrium at a semiconductor surface numerically. The non-equilibrium distribution is effected by an optical excitation. The approach in this thesis is to link two conventional, but approved methods to a new, more global description: while semiconductor surfaces can be investigated accurately by density-functional theory, the dynamical processes in semiconductor heterostructures are successfully described by density matrix theory. In this work, the parameters for density-matrix theory are determined from the results of density-functional calculations. This work is organized in two parts. In Part I, the general fundamentals of the theory are elaborated, covering the fundamentals of canonical quantizations as well as the theory of density-functional and density-matrix theory in 2{sup nd} order Born approximation. While the formalism of density functional theory for structure investigation has been established for a long time and many different codes exist, the requirements for density matrix formalism concerning the geometry and the number of implemented bands exceed the usual possibilities of the existing code in this field. A special attention is therefore attributed to the development of extensions to existing formulations of this theory, where geometrical and fundamental symmetries of the structure and the equations are used. In Part II, the newly developed formalism is applied to a silicon (001)surface in a 2 x 1 reconstruction. As first step, density-functional calculations using the LDA functional are completed, from which the Kohn-Sham-wave functions and eigenvalues are used to calculate interaction matrix elements for the electron-phonon-coupling an the optical excitation. These matrix elements are determined for the optical transitions from valence to conduction bands and for electron-phonon processes inside the conduction bands, where the coupling to phonons is realized by a deformation potential approach. A special interest is attributed to the interplay of bulk and surface bands originating from the surface reconstruction, which partly reach into the band gap. From these matrix elements, the dynamical evolution of the initial electron distribution is calculated using the derived equations. The thesis is completed by a comparison to experimental data. Here, a good agreement is found, both for the temporal evolution of the electron population, and for the relaxation timescales that can be extracted from the simulated data. (orig.)}

place = {Germany}

year = {2007}

month = {Nov}

}