Using scanning tunneling spectroscopy in an ultrahigh vacuum at low temperature (T=0.3 K) and high magnetic fields (B

We numerically investigate the interplay of disorder and electron-electron interactions in the integer quantum Hall effect. In particular, we focus on the behaviour of the electronic compressibility as a function of magnetic field and electron density. We find manifestations of non-linear screening and charging effects around integer filling factors, consistent with recent imaging experiments. Our calculations exhibit g-factor enhancement as well as strong overscreening in the centre of the Landau bands. Even though the critical behaviour appears mostly unaffected by interactions, important implications for the phase diagram arise. Our results are in very good agreement with the experimental findings and strongly support the relevance of electron-electron interactions for understanding integer quantum Hall physics.

Scanning tunneling spectroscopy is used to study the real-space local density of states of a two-dimensional electron system in a magnetic field, in particular within higher Landau levels. By Fourier transforming the local density of states, we find a set of n radial minima at fixed momenta for the nth Landau levels. The momenta of the minima depend only on the inverse magnetic length. By comparison with analytical theory and numerical simulations, we attribute the minima to the nodes of the quantum cyclotron orbits, which decouple in a Fourier representation from the random guiding center motion due to disorder. Adequate Fourier filtering reveals the nodal structure in real space in some areas of the sample with relatively smooth potential disorder.

As feature sizes shrink, random fluctuations gain importance in semiconductor manufacturing and integrated circuit design. Therefore, statistical device variability has to be considered in circuit design and analysis to properly estimate their impact and avoid expensive over-design. Statistical MOSFET compact modeling is required to accurately capture marginal distributions of varying device parameters and to preserve their statistical correlations. Due to limited simulator capabilities, variables are often assumed to be normally distributed. Although correlations may be captured using Principal Component Analysis, such an assumption may be inaccurate. As an alternative, Nonlinear Power Models have been proposed. Since we see some limitations in this approach, we analyze whether the multivariate Generalized Lambda Distribution is an alternative for statistical device modeling. Applying both approaches to extracted statistical device parameters, we conclude that both methods do not differ significantly in accuracy, but the multivariate Generalized Lambda Distribution is more general and less computationally expensive

IntroductionThe integer quantum Hall effect (IQHE) -observed in two-dimensional electron systems (2DES) subject to a strong perpendicular magnetic field [1] -has been well studied using single-particle arguments [2][3][4][5][6][7][8][9][10][11]. However, experiments on mesoscopic MOSFET devices have questioned the validity of such a simple single-particle picture. Measurements of the Hall conductance as a function of magnetic field B and gate voltage [12] exhibited regular patterns along integer filling factors. It was argued that these patterns should be attributed to Coulomb blockade effects. Similar patterns have been found recently also in measurements of the electronic compressibility κ as a function of B and electron density e n in the IQHE [13] as well as the fractional quantum Hall effect (FQHE) [14]. From these measurements it turns out that deep in the localised regime between two Landau levels, stripes of constant width with particularly small κ can be identified. These stripes consist of a collection of small-κ lines, identifiable with localised states, and their number is independent of B. This is inconsistent with a single-particle picture where one expects a fan-diagram of lines emanating from (0, 0) in the