Electron Thermal Transport Properties of a Quantum Dot
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0913-D04-08
Electron Thermal Transport Properties of a Quantum Dot Xanthippi Zianni Dept. of Applied Sciences, Technological Educational Institution of Chalkida, Psachna, Chalkida, 34400, Greece
ABSTRACT The electron thermal conductance of a dot has been calculated within a linear response theory in the regime of weak coupling with two electrode leads. Coulomb oscillations are found. We discuss the effect of the interplay between the charging energy, the thermal energy and the confinement in the behavior of the electron thermal conductance.
INTRODUCTION For the past two decades structures based on semiconductor quantum dots have attracted a lot of research interest. Recently, there is an increased interest in studying the thermal properties in quantum dots structures [1-16]. In the recent years, there have been proposed thermoelectric applications of quantum dot superlattices made of different material systems as well as periodic arrays of dots[4,8-15]. Nanocrystalline silicon has recently proposed for designing efficient ultrasound emitter due to the measured low thermal conductivity relative to the bulk [5]. For a quantum dot the conductance for purely sequential tunneling has been investigated theoretically by Beenakker[17]. The developed theory has been extended to the thermopower by Beenakker and Staring [18] and it has been investigated experimentally by Staring et al [19]. The cotunneling regime [20] and the crossover have been studied by Turek and Matveev [21]. In the case of a quantum dot strongly coupled to one lead, the thermopower has been investigated by Matveev and Andreev [22]. Here, the electron thermal conductance of a quantum dot in the regime of weak coupling with two electrode leads is calculated within a linear response theory. THEORY We consider a double barrier tunnel junction. It consists of a quantum dot that is weakly coupled to two electron reservoirs via tunnel barriers. Each reservoir is assumed to be in thermal equilibrium and there are a voltage difference V and a temperature difference ∆Τ between the two reservoirs. A continuum of electron states is assumed in the reservoirs that are occupied according to the Fermi-Dirac distribution: ⎡ ⎛ E − EF f ( E − E F ) = ⎢1 + exp⎜⎜ ⎝ k BT ⎣
⎞⎤ ⎟⎟⎥ ⎠⎦
−1
,
(1)
where the Fermi energy, EF, in the reservoirs is measured relative to the local conduction band bottom. The quantum dot is characterized by discrete energy levels Ep (p=1,2,..) that are measured from the bottom of the potential well. Each level can be occupied by either one or zero electrons. It is assumed that the energy spectrum does not change by the number of electrons in the dot. The energy levels are assumed to be weakly coupled to the states in the electrodes so that the charge of the quantum dot is well defined. We adopt the common assumption in the Coulomb blockade problems for the electrostatic energy U(N) of the dot with charge Q=-Ne: U ( N ) = ( Ne) 2 / 2C − Nφ ext ,
(2)
where C is the effective capacitance between the dot and the reservoirs and φext is the external
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