High Performance Multi Barrier Thermionic Devices

Thermoelectric transport perpendicular to layers in multiple barrier superlattice structures is investigated theoretically in two limiting cases of no lateral momentum scattering and strong scattering. In the latter regime when lateral momentum is not conserved, the number of electrons participating in thermionic emission will dramatically increase. The cooling power density is calculated using Fermi-Dirac statistics, density-of-states for a finite quantum well and the quantum mechanical transmission coefficient in the superlattice. Calculation results show that metallic based superlattices with tall barriers (>10 eV) can achieve a large power factor on the order of 0.06W/mK with a moderate electronic contribution to thermal conductivity of 1.8W/mK. If the lattice contribution to thermal conductivity is on the order of 1W/mK, ZT values higher than 5 can be achieved at room temperature. INTRODUCTION Thermoelectric figure-of-merit, ZT specifies how “good” the material is for thermoelectric cooling and power generation applications. Widely used thermoelectric material at room temperature is based on Bi2Te3. Heterostructure Integrated Thermionic (HIT) coolers have been recently made and characterized for applications in integrated cooling of optoelectronic and electronic devices . The idea of thermionic energy conversion was first seriously explored in the mid fifties during the development of vacuum diodes and triodes. Vacuum diode thermionic refrigerators were proposed by Mahan in 1994. 7 Efficiencies over 80% of the Carnot value were predicted, but the operating temperatures are still limited to greater than 500K. MULTI BARRIER THERMIONIC DEVICES Thermionic emission cooling in heterostructures was proposed by Shakouri et al. 3 to overcome the limitations of vacuum thermionics at lower temperatures. In these structures, a potential barrier is used for selective emission of hot electrons and evaporative cooling of the electron gas. The HIT cooler can be based on a single barrier or a multi barrier structure. In a single barrier structure in strong nonlinear transport regime, electron transport is dominated by the supply of electrons in the cathode layer and large cooling power densities can be achieved. 3 However, energy conversion efficiency in these structures is very low. On the other hand, in a multi barrier structure in linear transport regime, one can define an effective Seebeck coefficient and electrical conductivity. In linear transport regime calculations based on an effective conventional thermoelectrics or solid-state thermionics will converge and they represent two pointsof-views for the same electron transport phenomena in superlattices. One can describe the effect of potential barriers as a mean to increase the thermoelectric power factor (Seebeck coefficient square times electrical conductivity). Calculations presented in references [1,8] show that the conservation of lateral momentum for electron transport perpendicular to superlattice layers plays an important role in achieving high ZT values. In the following, we will study the thermionic energy conversion efficiency in superlattices in quasi linear transport regime. We will specifically examine the two cases of conserved and non-conserved lateral momentum. As a concrete example, thermoelectric properties of InGaAs/InAlAs superlattices is studied. Material properties of these superlattices are very well characterized for applications in intersubband quantum well infrared photodetectors and quantum cascade lasers. Structure and material parameters are tabulated in table 1: nw Lw (nm) Lb (nm) Eb (meV) meff (well/barr) β (W/mK) vs (cm/s) α (eV) 50 20 10 520 0.043/0.069 5 2x10 1.167 where nw is number of superlattice periods, Lw (Lb) is the well (barrier) thickness, Eb is barrier height, β is thermal conductivity of the whole structure, vs is electron saturation velocity and α is the non-parabolicity coefficient of the energy band. Mobility values in the well and barrier regions depend on doping concentrations and are determined using the following empirical quantities: