Generalized Boltzmann relations in semiconductors including band tails

Boltzmann relations are widely used in semiconductor physics to express the charge-carrier densities as a function of the Fermi level and temperature. However, these simple exponential relations only apply to sharp band edges of the conduction and valence bands. In this article, we present a generalization of the Boltzmann relations accounting for exponential band tails. To this end, the required Fermi-Dirac integral is first recast as a Gauss hypergeometric function, followed by a suitable transformation of that special function, and a zeroth-order series expansion using the hypergeometric series. This results in simple relations for the electron and hole densities that each involve two exponentials. One exponential depends on the temperature and the other one on the band-tail parameter. The proposed relations tend to the Boltzmann relations if the band-tail parameters tend to zero. This work comes timely for the modeling of classical semiconductor devices at cryogenic temperatures for large-scale quantum computing

Konzessionsmodelle für Fernstraßen in Deutschland: eine ökonomische Analyse der Risikoallokation beim F- und A-Modell

This paper analyzes the risk allocation in concession models for German highways, according to the "F-Model" and the "A-Model". We first assess the deficits of traditional construction and management of highways in Germany and present the two concession models. Next, theoretical backgrounds and rules of thumb for risk allocation in concessions for road infrastructure are presented and applied to the F- and A-Model. Both models show significant weaknesses with regard to risk allocation. We propose to award F-Model concessions following the PVR-principle (present value of revenue). The main criticism of the A-Model is that the concessionaire carries the entire traffic risk; also, the A-Model does not seem to be compatible with future privatization plans for German highways. In diesem Beitrag wird die Risikoallokation bei Betreibermodellen für Bundesfernstraßen nach dem F- und A-Modell untersucht. Zunächst werden kurz die Defizite des traditionellen Modells der Herstellung und Bereitstellung von Fernstraßen in Deutschland dargestellt und die Struktur der beiden Konzessionsmodelle bewertet. Dann werden Handlungsempfehlungen zur Risikoallokation bei Konzessionsmodellen für Straßeninfrastruktur abgeleitet und die Risikoallokation beim F- und beim A-Modell analysiert. Bei beiden Modellen weist die Risikoallokation große Schwachstellen auf. Es wird empfohlen, Konzessionen nach dem FModell zukünftig in Anlehnung an das Barwertmodell zu vergeben. Wesentlicher Kritikpunkt an der Risikoallokation beim A-Modell ist die Übertragung des Verkehrsmengenrisikos auch nach der Bauphase an den Konzessionär; es ist unklar, ob das A-Modell kompatibel mit zukünftigen Privatisierungs- bzw. Organisationskonzepten für die Bundesautobahnen ist.Concession models, Germany, highways, infrastructure, regulation, risk allocation

Reform der Erdgaswirtschaft in der EU und in Deutschland: wie viel Regulierung braucht der Wettbewerb?

This article analyses the reform process in the European and the German natural gas sector. Competition in the industry and intra-European trade have been underdeveloped thus far. We argue that the European gas pipelines are a monopolistic bottleneck that require some form of access regulation, e.g. in the form of an Entry-Exit System. We discuss how regulation should be implemented at the European level and, subsequently, in Germany. We conclude that the European Gas Directive 2003/55/EC and the proposal for a new Energy Law in Germany offer a good point of departure for further reforms towards an integrated European market for natural gas.

Inflection Phenomenon in Cryogenic MOSFET Behavior

This brief reports the analytical modeling and measurements of the inflection in the MOSFET transfer characteristics at cryogenic temperatures. Inflection is the inward bending of the drain current versus gate voltage, which reduces the current in weak and moderate inversion at a given gate voltage compared to the drift-diffusion current. This phenomenon is explained by introducing a Gaussian distribution of localized states centered around the band edge. The localized states are attributed to disorder and interface traps. The proposed model allows to extract the density of localized states at the interface from the dc current measurements

Cryogenic MOS Transistor Model

This paper presents a physics-based analytical model for the MOS transistor operating continuously from room temperature down to liquid-helium temperature (4.2 K) from depletion to strong inversion and in the linear and saturation regimes. The model is developed relying on the 1D Poisson equation and the drift-diffusion transport mechanism. The validity of the Maxwell-Boltzmann approximation is demonstrated in the limit to zero Kelvin as a result of dopant freeze-out in cryogenic equilibrium. Explicit MOS transistor expressions are then derived including incomplete dopant-ionization, bandgap widening, mobility reduction, and interface charge traps. The temperature dependency of the interface-trapping process explains the discrepancy between the measured value of the subthreshold swing and the thermal limit at deep-cryogenic temperatures. The accuracy of the developed model is validated by experimental results on a commercially available 28-nm bulk CMOS process. The proposed model provides the core expressions for the development of physically-accurate compact models dedicated to low-temperature CMOS circuit simulation.Comment: Submitted to IEEE Transactions on Electron Device

Evaluation of Operation IceBridge quick-look snow depth estimates on sea ice

We evaluate Operation IceBridge (OIB) ‘quick-look’ (QL) snow depth on sea ice retrievals using in situ measurements taken over immobile first-year ice (FYI) and multi-year ice (MYI) during March of 2014. Good agreement was found over undeformed FYI (-4.5 cm mean bias) with reduced agreement over deformed FYI (-6.6 cm mean bias). Over MYI, the mean bias was -5.7 cm but 54% of retrievals were discarded by the OIB retrieval process as compared to only 10% over FYI. Footprint scale analysis revealed a root mean square error (RMSE) of 6.2 cm over undeformed FYI with RMSE of 10.5 cm and 17.5 cm in the more complex deformed FYI and MYI environments. Correlation analysis was used to demonstrate contrasting retrieval uncertainty associated with spatial aggregation and ice surface roughness

[P4H]+[Al(OTeF5)4]−: protonation of white phosphorus with the Brønsted superacid H[Al(OTeF5)4](solv)

A sustainable transformation of white phosphorus (P4) into chemicals of higher value is one of the key aspects in modern phosphorus research. Even though the chemistry of P4 has been investigated for many decades, its chemical reactivity towards the simplest electrophile, the proton, is still virtually unknown. Based on quantum-chemical predictions, we report for the first time the successful protonation of P4 by the Brønsted acid H[Al(OTeF5)4](solv). Our spectroscopic results are in agreement with acid-mediated activation of P4 under protonation of an edge of the P4-tetrahedron and formation of a three-center two-electron P–H–P bond. These investigations are of fundamental interest as they permit the activation of P4 with the simplest electrophile as a new prototype reaction for this molecule