# Seebeck coefficient, Peltier coefficient, and figure of merit ZT

*label*Science

*timer*Asked: Jan 6th, 2019

*account_balance_wallet*$15

**Question Description**

Stating all the relevant equations, briefly explain how:

1. to investigate electron-phonon scattering via nonequilibrium Green’s function approach and the effect on *Seebeck*

2. to calculate the Seebeck coefficient, *S*, of a tunnel transistors, the figure of merit using Landauer approach

3. to determine the transmission coefficient of electrons tunneling between closely aligned graphene lattices using Bardeen transfer Hamiltonian approach

Give the references.

## Tutor Answer

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Running head: Seebeck coefficient, Peltier coefficient, and figure of

merit ZT

Seebeck coefficient, Peltier coefficient, and figure of merit ZT

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Running head: Seebeck coefficient, Peltier coefficient, and figure of

merit ZT

Seebeck coefficient, Peltier coefficient, and figure of merit ZT

Introduction

Thermoelectric material work under the concept of figure of merit (zT ) , which is expressed as;

S 2

zT =

T

k

Where k is the thermal conductivity, δ is the electrical conductivity, S is the coefficient of

seebeck, while T is the mean temperature between the cold and the hot contacts [1]. To facilitate

enhancement of the figure of merit, to approaches are typically followed. First, the thermal

conductivity k is lowered. The second approach involves improving the power component

( S 2 ) . Electronic Engineering is aimed at manipulating the power factor of a thermal electric

generator and to enhance power generation. Reinforcement of generated power is done through

energy filtering at a specific operating efficiency. This is a property of unmerged scattering and

is not available in ballistic appliances. By allowing for a relaxation time ( E ) = kE r , that is

dependent on energy, we derive the value rmin . This is the least value that will lead to enhanced

generation of thermoelectric power.

How to investigate electron-phonon scattering via non-equilibrium Green’s function

approach and the effect on Seebeck

There has been progressive research to improve understanding and performance of carbonnanotube (CNT) transmits, since their first demonstration in 1998. Both optoelectric and

electronic devices have been realized based on CNTs, as well as optimization of the fabrication

process. At low temperatures, CNTs ballistic transport has been demonstrated experimentally [2]

The formalism of non-equilibrium Green’s Function (NEGF) has been used to explain transport

in dissipative quantum for nanoscale devices [3]. Different structures that use channel

conducting have prompted use of variations of nontrivial form in the application of NEGF

Approaches. Phonon scattering finds a wide range of application in organic nanostr...

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