Metallic State in Two-Dimensional Semiconductor Structures

In recent years, a new metallic state in ultra-thin (two-dimensional) electronic layers in semiconductor structures was discovered at very low temperatures. This is surprising, as the accepted theories predicted an insulating behavior in that regime. The importance of the topic lies in the ultimate understanding of quantum processes in electronic structures. Such processes are important for the interpretation of many effects in today`s nanostructures (mesoscopic systems) and in the future the may even play a dominant role in quantum computation. In the proposed project, semiconductor structures will be investigated by electrical measurements at temperatures down to 30 milli-Kelvin and in very high magnetic fields. This conditions are necessary, as then even weak quantum effects are clearly visible and they can be optimised and varied by external parameters. Different types of silicon-based semiconductor structures will be tailored in order to vary the symmetry of the electronic wave function in the active two-dimensional layer. With our investigations of the conductivity under extreme conditions, we will be able to test the current theories on the metallic state in two dimensions, which are electron scattering at charged trap states, electronic screening of scattering centers, and quantum corrections due to electron-electron interaction in the ballistic regime. We hope further to be able to clarify whether the quantum corrections are strong enough that they can form a fundamentally new electronic ground state or not. In order to perform the necessary investigations, a helium 3/4 dilution refrigerator together with a superconducting magnet is requested for the project. This device combinations allows to reach temperatures less than 0.03 degree above the absolute zero of temperature together with magnetic fields of 17 Tesla, about 10 times the field strength which can be reached in strong normal magnets. Inside the low temperature cryostat, the sample can be rotated so that the direction of the magnetic field can be varied relative to the surface of the two-dimensional electron layer. In this way, it can be chosen whether the orbital or the spin effects will dominate the electronic behavior during the measurement.

In the project "Metallic State in Two-Dimensional Semiconductor Structures" the unexpected properties of electrons in a thin layer at very low temperatures of about -270C, i.e. close to the absolute zero-point of temperature, were investigated. According to earlier theories all two-dimensional electron systems (those which are confined and quantized in an extremely thin layer) should become insulating in the limit towards zero temperature. On the first view it seems that such a deviation from theory at such low temperatures might not have any practical application. But as a basic topic, one wants to understand electron-electron interaction effects in the so called quantum limit. This might give new insight into the behaviour of interacting electrons and might have application in future electronic systems were quantum effects between interacting electrons will be important as it would e.g. be the case for quantum computation. The principles of quantum computation have been demonstrated experimentally and are quite well understood meanwhile. But it is absolutely not clear whether that principle can be used in the future for daily work or if only very sophisticated equipment can use such effects. In our work we have investigated the metallic state in common silicon-metal-oxide transistors as well as in more specific semiconductor structures. We found that the behaviour can fairly well be described with a recent theory of coherent electron-electron interaction in the ballistic regime. Coherent means here that the wave properties of overlapping electrons are important and determine the properties. In addition, we have investigated another model description, the so-called dipole-trap scattering, for the metal-to- insulator transition at low temperatures in thoroughly theoretical treatment as it is important to clarify whether the before mentioned ballistic interaction model is the only one which is able to explain the overall behaviour at slightly higher temperatures or if other effects might contribute or replace that model. We have performed both analytical as well as numerical calculations and could generalize the previously existing model to more realistic cases like energetically broadened or spatially limited trap states. With these enhancements the trap model is able to explain the resistivity changes at low temperatures and should be considered as an alternative explanation for the unexpected metallic state.