Phononic thermal conductivity in silicene: the role of vacancy defects and boundary scattering

We calculate the thermal conductivity of free-standing silicene using the phonon Boltzmann transport equation within the relaxation time approximation. In this calculation, we investigate the effects of sample size and different scattering mechanisms such as phonon-phonon, phonon-boundary, phonon-isotope and phonon-vacancy defect. Moreover, the role of different phonon modes is examined. We show that, in contrast to graphene, the dominant contribution to the thermal conductivity of silicene originates from the in-plane acoustic branches, which is about 70\% at room temperature and this contribution becomes larger by considering vacancy defects. Our results indicate that while the thermal conductivity of silicene is significantly suppressed by the vacancy defects, the effect of isotopes on the phononic transport is small. Our calculations demonstrate that by removing only one of every 400 silicon atoms, a substantial reduction of about 58\% in thermal conductivity is achieved. Furthermore, we find that the phonon-boundary scattering is important in defectless and small-size silicene samples, specially at low temperatures.Comment: 9 pages, 11 figure

Partial discharge behavior under operational and anomalous conditions in HVDC systems

Power cables undergo various types of overstressing conditions during their operation that influence the integrity of their insulation systems. This causes accelerated ageing and might lead to their premature failure in severe cases. This paper presents an investigation of the impacts of various dynamic electric fields produced by ripples, polarity reversal and transient switching impulses on partial discharge (PD) activity within solid dielectrics with the aim of considering such phenomena in high voltage direct current (HVDC) cable systems. Appropriate terminal voltages of a generic HVDC converter were reproduced - with different harmonic contaminations - and applied to the test samples. The effects of systematic operational polarity reversal and superimposed switching impulses with the possibility of transient polarity reversal were also studied in this investigation. The experimental results show that the PD is greatly affected by the dynamic changes of electric field represented by polarity reversal, ripples and switching. The findings of this study will assist in understanding the behaviour of PDs under HVDC conditions and would be of interest to asset managers considering the effects of such conditions on the insulation diagnostics

Generalized shuffles related to Nijenhuis and TD-algebras

Shuffle and quasi-shuffle products are well-known in the mathematics literature. They are intimately related to Loday's dendriform algebras, and were extensively used to give explicit constructions of free commutative Rota-Baxter algebras. In the literature there exist at least two other Rota-Baxter type algebras, namely, the Nijenhuis algebra and the so-called TD-algebra. The explicit construction of the free unital commutative Nijenhuis algebra uses a modified quasi-shuffle product, called the right-shift shuffle. We show that another modification of the quasi-shuffle product, the so-called left-shift shuffle, can be used to give an explicit construction of the free unital commutative TD-algebra. We explore some basic properties of TD-operators and show that the free unital commutative Nijenhuis algebra is a TD-algebra. We relate our construction to Loday's unital commutative dendriform trialgebras, including the involutive case. The concept of Rota-Baxter, Nijenhuis and TD-bialgebras is introduced at the end and we show that any commutative bialgebra provides such objects.Comment: 20 pages, typos corrected, accepted for publication in Communications in Algebr

Hot electron currents in MOSFETs.

Silicon has become the material of choice for fabrication of high circuit density, low defect density and high speed integration devices. CMOS technology has been favoured as an attractive candidate to take advantage of the performance enhancements available through miniturisation. However, hot carrier effects in general, and hot electron currents in particular, are posing as the main obstacle to a new era of sub-micron architecture in semiconductor device technology. Electron transport in modern sub-micron device is often governed by mechanisms that were not relevant to long-channel devices. Many of the classical device models are based upon such convenient assumptions as "thermal equilibrium" and "uniform local electric field". With the downscaling of devices, hot electron currents are becoming increasingly inherent. These currents arise from the fact that electrical fields in small geometry devices can reach very high values and can vary rapidly in space. The large electric field can Impart significant kinetic energies to the carriers. In thermal equilibrium, all elementary excitations in a semiconductor (eg. Electrons, holes, phonons) can be characterised by a temperature that is the same as the lattice temperature. Under the influence of large electric fields, however, the distribution function of these elementally excitations deviate from those in thermal equilibrium. The term "Hot Carriers" is often used to describe these non-equilibrium situations. In this thesis hot electron currents, in particular their physical origins and dependence upon various operational and geometrical parameters, have been discussed and then quantified in a number of models based on the "Lucky Drift" theory of transport. Temperature is then used as a tool to differentiate between the underlying physical processes, and to determine if reliability problems related to hot electron effects would improve under cryogenic operation. It has been the prime objective of this work from the outset to concentrate on the study of N-channel devices. This is primarily due to the fact that N-channel MOSFET's are more prone to hot electron effects, and therefore, studies in the nature of this enhanced susceptibility could prove to be more fruitful

Mixable Shuffles, Quasi-shuffles and Hopf Algebras

The quasi-shuffle product and mixable shuffle product are both generalizations of the shuffle product and have both been studied quite extensively recently. We relate these two generalizations and realize quasi-shuffle product algebras as subalgebras of mixable shuffle product algebras. As an application, we obtain Hopf algebra structures in free Rota-Baxter algebras.Comment: 14 pages, no figure, references update