利用Landauer-Buttiker formalism探討理想化元件的傳輸與熱電性質

Abstract

Thermoelectric effect was discovered in 1821, but the related field didn’t develop be- cause of the small value of figure of merit ”Z”. Fortunately, in 1954 someone found that the figure of merit of semiconductor was larger than before[1]. So most of people start to pay attention to this field. The research of thermoelectric material began to flourish. In order to find the higher figure of merit we need to find the material which have poor thermal conductance and good conductance. Disappointingly, according to Wiedemann- Franz law[2], the electron thermal conductance is proportional to the conductance. We know that electrons and phonons are contribute to the thermal conductance, so the way of increasing the figure of merit is to reduce the phonon thermal conductance. In 1993 L. D. Hicks and M. S. Dresselhaus found that the figure of merit of nano-scale meterial was higher than macroscopic material[3]. N. Mingo also discovered that the figure of merit of one-dimension nano-scale devices was increased because of reducing the phonon thermal conductance[4].Now people want to find suitable nano-scale mate- rial to provide good figure of merit. Because of micro-scale view, the transport property of electron is different. So we need a new method to calculate the thermoelectric coefficients. The non-equilibrium Green’s function method(NEGF) provide a way to study nano-scale device. Ideally, if we know the Hamiltonian of material we can calculate the thermoelectric coefficients so we can solve the problem of any shape of device. This report will be repeated the result of an article in 2009[5] and a book named Quan- tum transport:Atom to Transistor[6].We will calculate thermoelectric coefficients from semi-classical model[5], and compare the number of modes of 1-dimensional-chain tight binding model using NEGF method with semi-classical model.