Investigation of Nanoscale Potential Fluctuations and Defects in 2D semiconducting structures by Scanning Tunneling Microscopy

During the last 40 years the number of transistors in integrated circuits has doubled roughly every two years, as predicted as early as 1965 by the cofounder of the Intel corporation Gordon Moore [1]. Since the overall dimensions of the integrated circuits remained almost constant, the size of individual transistors decreased by many orders of magnitude. For example, since early 2007 transistors with a gate length of 45 nm have been produced commercially by the Intel corporation (so-called 45 nm technology) [2]. A dual core processor fabricated by this technology contains more than 400 million transistors. Or to illustrate it more clearly for a better understanding of the feature density, one could fit more than 30 million transistors with a 45 nm gate length onto the head of a pin of 1.5 mm diameter. This is about twice the density of the previous 65 nm technology. The miniaturization is proceeding rapidly, and Intel is presently developing commercial microprocessors with a transistor gate length of 32 nm, which are expected to be ready in 2009[3]. A current transistor with 45 nm gate length can be switched on and off about 300 billion times per second, which means that a beam of light travels only about 1 mm during one switching cycle. Since no information can be transmitted faster than light, the signal transmission lengths in current processors are becoming most critical. This is one of the major reasons why the feature size in semiconductor devices will ultimately be pushed to its limits. The International Technology Roadmap for Semiconductors (ITRS) states that the commercially available gate length of a transistor will reach less than 10 nm in 2015 and less than 3 nm in 2022 [4]. This push for smaller and smaller semiconductor structures is increasing the importance of controlling the location of every individual atom in semiconductor devices [5]. Dopant atoms, which are deliberately inserted impurities, are the most critical, because they provide free charge carriers into the bands of the host crystal and thereby allow almost all of the properties of semiconducting materials to betuned. With the presently achievable maximum dopant concentrations of a few 10$^{20} cm^{-3}$ the discrete nature of dopants will become critical with future device dimensions. Misplacing even a single dopant atom can then significantly affect or ruin the performance of nanometer-sized devices. Unfortunately, in commercial manufacturing processes, the distribution of dopant atoms is not yet controllable with the desired atomic precision, e.g. an ordered array of dopants. Instead, nanoscale fluctuations in the distribution of dopant atoms occur [6, 7]. These inhomogeneities in the dopant distribution cause nanoscale fluctuations in the potential [8], which can lead to a lowering of the threshold voltages relative to those of continuously doped field-effect transistor devices by the formationof percolated paths within the device [9]. Therefore, the importance of statistical fluctuations in the dopant distribution becomes a pressing topic. These repercussions illustrate that the exact influence of the dopant on the local band structure and an in-depth understanding of the interrelation between the exact dopant positions and the local potential on a nanometer scale is vital forengineering the performance of future nanometer-sized devices. Despite this, no solid experimentally proven facts exist about the effect of nanoscale dopant inhomogeneities. Nanoscale potential fluctuations have only been investigated without quantitative correlation with the dopant (or adatom impurity) distribution (see e.g. Refs. [8] and [10]). It is still unclear how the nanoscale potential and dopant fluctuations should be dealt with, and what conceptional physical models can be used for accurate simulations. In order to address these issues, as a first step an artificially engineered twodimensional (2D) $\sqrt{3} x \sqrt{3}$ Ga on Si(111) structure is utilized, where the dopant [...