In-plane Thermal and Electronic Transport in Quantum Dot Superlattice
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In-plane Thermal and Electronic Transport in Quantum Dot Superlattice
A. Khitun* , J.L. Liu *, K.L.Wang* and G.Chen +
* Device Research Laboratory, Electrical Engineering Department +
Nanoscale Heat Transfer and Thermoelectricity Laboratory, Department of Mechanical and Aerospace Engineering
University of California - Los Angeles, Los Angeles, California 90095 E-mail: [email protected]
phone: (310) 206-7987
fax: (310) 206-4685
Abstract
We present a theoretical model in order to describe both thermal and electronic in-plane transports in quantum dot superlattice. The model takes into account the modifications of electron and phonon transport due to the space confinement caused by the mismatch in electronic and thermal properties between dot and host materials. The developed model provides the analysis of the in-plane superlattice electronic and thermal properties versus quantum dot size and their arrangement. Numerical calculations were carried out for a structure that consists of multiple layers of Si with regimented germanium quantum dots. The simulation results of the lattice thermal conductivity are in a good agreement with experimental data.
I.
INTRODUCTON
Recent achievements in epitaxial grown techniques made possible the synthesis of quantum dot superlattices with regimented dot position in-plane direction [1]. It opens new opportunities for separate electronic and thermal properties control by arranging size and displacement of quantum dots. The separate control of the thermal and electronic properties in QDS is very important for it possible application in thermoelectric cooling. Thus, decrease of the lattice thermal conductivity with increase of the electronic transport AA4.9.1
may lead to the substation thermoelectric figure of merit enhancement, ZT=S2σΤ/(κ+κe) where T is the temperature, S is the Seebeck coefficient, σ is the electric conductivity, κ is the phonon thermal conductivity, and κe is the electronic thermal conductivity. The experimentally observed enhancement of the thermoelectric figure of merit in QDS was already reported [2].
II . MODEL The general expressions for the electric transport coefficients σ, S and κe are [3]:
σ = L( 0 ) 1 S = − ( L( 0) ) −1 L(1) eT
1 κ e = 2 ( L( 2 ) − L(1) ( L( 0) ) −1 L(1) ) e T Lx
(α )
= e2 ∫
dke ∂f 2 α − τ (ke )v (ke )( E (ke ) − ς ) 4π 3 ∂E
(1)
where e is the electron charge, f is the Fermi distribution function, k e is the electron wave vector, E is the electron energy, τ is the electron relaxation time, v( k e ) is the electron group velocity v (k e ) = for multi-band materials,
1 ∂E ( k e ) and ς is the chemical potential. In general, h ∂k e
L(α ) has to be replaced by the sum of L for all filled bands. In
order to find the transport coefficients one have to solve the Schrodinger equation taking into account particular conduction band offset between host and dot materials and size and mutual displacement of the quantum dots. In general, the solution can be found only numerically [4]. For some special ca
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