Computational Modeling of Transverse Peltier Coolers

Transverse thermoelectric effect can be produced artificially by stacking at an angle layers of a thermoelectric material with another material that may or may not be a thermoelectric material. In this exploratory computational study, a new metamaterial, comprised of tilted alternating layers of an n-type thermoelectric alloy and a metal, is investigated to gain an understanding of how much cooling can be produced by transverse thermoelectric effect and the conditions under which maximum cooling is attainable. The governing conservation equations of energy and electric current, with the inclusion of thermoelectric effects, are solved on an unstructured mesh using the finite-volume method to simulate a transverse Peltier cooler under various operating conditions. First, the code is validated against experimental data for a n-Bi2Te3-Pb metamaterial, and subsequently explored. It is found that intermediate applied currents produce maximum temperature depression (ΔT). Optimum values of the geometric design parameters such as tilt angle and device aspect ratio are also established through parametric studies. Finally, it is shown that the ΔT can be amplified by constricting the phonon (heat) transport cross-section while keeping the electron (current) transport cross-section unchanged — a strategy that cannot be employed in conventional thermoelectric devices where electrons and phonons follow the same path. This makes transverse Peltier coolers particularly attractive for generating large ΔT without multi-stage cascading.

MONTE CARLO CALCULATION OF SLOW ELECTRON BEAM TRANSPORT IN SOLIDS: REFLECTION COEFFICIENT THEORY IMPLICATIONS

The reflection coefficient theory developed by Vicanek and Urbassek showed that the backscattering coefficient of light ions impinging on semi-infinite solid targets is strongly related to the range and the first transport cross-section as well. In this work and in the electron case, we show that not only the backscattering coefficient is, but also most of electron transport quantities (such as the mean penetration depth, the diffusion polar angles, the final backscattering energy, etc.), are strongly correlated to both these quantities (i.e. the range and the first transport cross-section). In addition, most of the electron transport quantities are weakly correlated to the distribution of the scattering angle and the total elastic cross-section as well. To make our study as straightforward and clear as possible, we have projected different input data of elastic cross-sections and ranges in our Monte Carlo code to study the mean penetration depth and the backscattering coefficient of slow electrons impinging on semi-infinite aluminum and gold in the energy range up to 10 keV. The possibility of extending the present study to other materials and other transport quantities using the same models is a valid process.

MONTE CARLO SIMULATION OF THE TRANSPORT OF ELECTRONS IN SEMI-INFINITE SOLIDS: THE EFFECT OF THE FIRST TRANSPORT CROSS-SECTION

The purpose of this work is to show the hidden effect of the first transport cross-section in the study of the beam electrons transport impinging in solid targets by using the Monte Carlo method. For this, our study is based on our model of differential elastic cross-section given [A. Bentabet, Z. Chaoui, A. Aydin and A. Azbouche, Vacuum85 (2010) 156] by leaving only one free parameter adjusted, on one hand, to the elastic total cross-section and to transport cross-section, on the other hand. We think that this work is useful for those who develop semi-empirical or analytical models of elastic cross-sections. The present work deals with the total elastic cross-section, the first transport cross-section, the diffusion polar angle and the backscattering coefficient, from low energy electrons, normally incident, impinging on Al , Si , Ag and Au solid targets, where the results are compared to those of the literature and discussed.