## Introduction to our fields of research

### Fields of research

- density functional theory,
*ab initio*molecular dynamcis,- surfaces,
- impurities in semiconductors,
- semiconductor quantum structures.

### What is theoretical solid state physics?

Solids emerge from a large number of atoms, which combine to a connected formation. Solid state physics investigates the microscopic structure of such materials to obtain a preferably quantitative characterisation and explanation of their properties (e.g. mechanical, electrical, optical and magnetic properties). Due to the large number of atoms involved solids form an extremely complex system. Therefore many various techniques and concepts from theoretical physics are used for their theoretical description (for example quantum mechanics, many-particle physics, statistical physics and computer modelling).

### Simple equations for complex systems

"Often, people in some unjustified fear of physics say you can't write an equation of life. Well, perhaps we can. As a matter fo fact, we very possibly already have the equation to a sufficient approximation when we write the equation of quantum mechanics.

We have just seen that the comlexities of things can so easily and dramatically escape the simplicity of the equations which describe them. Unaware of the scope of simple equations, man has often concluded that nothing short of God, not mere equations, is required to explain the complexities of the world."

(Richard P. Feynman, Lectures on physics)

The discovery of quantum mechanics was one of the most important events in the physics of the 20th century, one, which made it possible to explain the attributes of atoms. Therefore all chemical, physical and biological phenomenons result from the basic equations of quantum mechanics, as the atoms are the components of the matter surrounding us. However it's a very long way until we reach that point. Nature gave us only a few exact solvable examples for the Schroedinger equation, for the other objects the solutions are as complicated as possible. Although the solvable examples show, that the Schroedinger equation is always correct, that alone is not enough to let us advance further. Nature keeps physics always exiting and unpredictable.

At the chair of solid state theory we deal with the calculation of the attributes of realistic solids (metals, semiconductors, thin layers, surfaces, eg.) starting from the basic equations of quantum mechanics. That would be impossible without modern computers. Thus the development and application of computer programms distinguish themselves as most important tools of theoretical physics. Why show some insulators metallic behaviour on their surface? How often jumps a diffusing atom in a crystal, and which way will it take? What happens in a crystal lattice, when the matter gets strong exited by laser radiation? How do electrons behave in tiny semiconductor quantum structures, which can be considered as artificial atoms? These are the questions, that characterise the research at our chair. The following two examples may explain this further.

### Chemical bonds and diffusion in crystals

The most beautiful expression of high crystal symmetry is a brilliant's fire. However this hides another fascinating phenomenon - perpetually single atoms move apparently unnoticed through the solid. This is called diffusion. It takes enough energy to break the chemical bonds, which hold an atom in place, for it to move.

When microscopically enlightening these mechanisms, one almost exclusively depends on theoretical methods. In the scope of density functional theory the atom's movement in the solid can be reproduced with ab-initio-molecular-dynamic methods.

Vacancies diffuse for instance by leaping of adjacent atoms from their lattice site into the vacancy. Still the mechanism isn't immediately clear in detail. This arises for example at the Gallium-(Ga)-diffusion in Galliumarsenide (GaAs). In GaAs a Ga-atom has four As-atoms as nearest neighbours and twelve Ga-atoms as the next but one neighbours. Accordingly either an As-atom (next neighbour) or a Ga-atom (next neighbour but one) can leap into a Ga-vacancy. Calculations show, that the diffusion results from next-neighbour-but-one-leaps (Fig. 1). The diffusion constant calculated for this mechanism can quantitatively explain the experimentally observed diffusion in GaAs.

Fig. 1: Simulated path of the Gallium-atom (Ga) and its
Arsenic-neighbor (As) during the leap. The Ga-atom leaves its
lattice site and jumps in direction of the arrow into the vacancy.
Another vacancy (V_Ga) is left at the lattice site of the Ga-atom.
Here a snapshot on the verge of the leap's finish is shown.

### Semiconductor microstructures as quantum mechanical model systems

During the last two decades physicists managed to apply microscopic structures consisting of semiconductor materials on the surface of other semiconductor crystals. These tiny systems can't be described by classical Newton mechanics; instead quantum mechanics is required. As meantime it is possible to produce nearly arbitrary structures on demand, these systems are applied particulary as quantum mechanical model systems (for instance "artificial atoms"). So separate phenomenons of quantum mechanics can be specifically researched ("Do-it-yourself quantum mechanics").

At the chair we deal with the theoretical descriptions of these system's electronic properties, with the interpretation of experiments and with the prediction of new phenomenons. That concerns both simple analytic calculations and complex computer-assisted calculations.