Conservation of Lateral Momentum in Heterostructure Integrated Thermionic Coolers

Abstract

Thin film thermionic coolers use selective emission of hot electrons over a heterostructure barrier layer from emitter to collector resulting in evaporative cooling. In this paper a detailed theory of electron transport perpendicular to the multilayer superlattice structures is presented. Using Fermi-Dirac statistics, density-of-states for a finite quantum well and the quantum mechanical reflection coefficient, the currentvoltage characteristics and the cooling power density are calculated. The resulting equations are valid in a wide range of temperatures and electric fields. It is shown that conservation of lateral momentum plays an important role in the device characteristics. If the lateral momentum of the hot electrons is conserved in the thermionic emission process, only carriers with sufficiently large kinetic energy perpendicular to the barrier can pass over it and cool the emitter junction. However, if there is no conservation of lateral momentum, the number of electrons participating in thermionic emission will dramatically increase. The theoretical calculations are compared with the experimental dark current characteristics of quantum well infrared photodetectors and good agreement over a wide temperature range is obtained. Calculations for InGaAs/InGaAsP superlattice structures show that the effective thermoelectric power factor (electrical conductivity times the square of the effective Seebeck coefficient) can be improved comparing to that of bulk material. We will also discuss methods by which the conservation of lateral momentum in thermionic emission process can be altered such as by creating a controlled roughness at the interface of the superlattice barriers. The improvement in the effective power factor through thermionic emission can be combined with the other methods to reduce the phonon thermal conductivity in superlattices and thus obtain higher thermoelectric figure-of-merit ZT.

Electronic and thermoelectric transport in semiconductor and metallic superlattices

“…This structure is intentionally chosen to compare the model presented here with previous results on thermionic cooling performance. [30][31][32] It has been shown that the figure-of-merit for thermionic cooling is about half of that of thermoelectric cooling in InGaAs. In Fig.…”

Thermionic power generation at high temperatures using SiGe∕Si superlattices

“…Two cases of electron transports in the superlattice are considered: when transverse momentum during thermionic emission is conserved and when transverse momentum is not conserved. [10][11][12][13] The plot shows that, in both cases, superlattice transport does not improve much the ZT over the bulk values. 14 Basically, this is due to the small conduction band offset of the SiGe/ Si superlattice, which is about 12% ͑E b ϳ 23 meV for the proposed structure͒.…”

Thermoelectric, thermionic and thermophotovoltaic energy conversion

“…One can describe the effect of potential barriers as a mean to increase the thermoelectric power factor (the square of the Seebeck coefficient times the electrical conductivity). The fact that there is a trade-off between electrical conductivity and the Seebeck coefficient and that we can not keep increasing the number of free carriers and get higher and higher power factors is an intriguing effect which has not been discussed in detail from a fundamental point of view 18,19,20 . One way to look at this problem, is to consider the differential conductivity of electrons in typical semiconductors and metals.…”

“…volume V 1 in Fig. 2(b)) 16,17,19,31,32 . There are many hot electrons that have large transverse momentum.…”