Thermoelectric Properties of a Semiconductor Quantum Dot Chain Connected to Metallic Electrodes

TL;DR

This paper theoretically investigates the thermoelectric properties of semiconductor quantum dot chains connected to metallic electrodes, revealing conditions that optimize the figure of merit (ZT) for enhanced thermoelectric efficiency.

Contribution

It introduces a closed-form Landauer expression for transmission in quantum dot chains with arbitrary length, beyond mean-field approximation, and analyzes thermoelectric optimization conditions.

Findings

High ZT achievable with low energy level fluctuations.

Optimal ZT when QD levels are above Fermi level.

Conditions on tunneling rates and Coulomb interactions for maximum ZT.

Abstract

The thermoelectric properties of a semiconduct quantum dot chain (SQDC) connected to metallic electrodes are theoretically investigated in the Coulomb blockade regime. An extended Hubbard model is employed to simulate the SQDC system consisted of {\color{blue}N=2,3,4, and 5} quantum dots (QDs). The charge and heat currents are calculated in the framework of Keldysh Green's function technique. We obtained a closed-form Landauer expression for the transmission coefficient of the SQDC system with arbitrary number of QDs by using the method beyond mean-field theory. The electrical conductance ($G_e$), Seebeck coefficient (S), thermal conductance, and figure of merit (ZT) are numerically calculated and analyzed in the linear response regime. When thermal conductance is dominated by phonon carriers, the optimization of ZT is determined by the power factor ($pF=S^2G_e$). We find that the optimization of ZT value favors the following conditions:(1) QDs with low energy level fluctuations, (2) QD energy levels lie above the Fermi level of electrodes, (3) $\Gamma < t_c \ll U_0$, where $t_c$, $U_0$, and $\Gamma$ are electron interdot hopping strength, on-site electron Coulomb interaction, and tunneling rate, respectively, and (4) $\Gamma_L=\Gamma_R$ with $\Gamma_L+\Gamma_R$ kept constant, where $\Gamma_L (\Gamma_R)$ is the left (right) tunneling rate. It is predicted that high ZT values can be achieved by tailoring above conditions.