Upper Limitation to the Performance of Single-Barrier Thermionic Emission Cooling
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Upper Limitation to the Performance of Single-Barrier Thermionic Emission Cooling Marc D. Ulrich, Peter A. Barnes, and Cronin B. Vining1 Department of Physics, Auburn University, AL 36849 1 ZT Services, Auburn, AL 36830 ABSTRACT We have re-examined solid-state thermionic emission cooling from first principles and report two key results. First, electrical and heat currents over a semiconductor – semiconductor thermionic barrier are determined by the chemical potential measured from the conduction band edge, not the energy band offset between the two materials as is sometimes assumed. Second, we show the upper limit to the performance of thermionic emission cooling is equivalent to the performance of an optimized thermoelectric device made from the same material. An overview of this theory will be presented and instrumentation being developed to experimentally verify the theory will be discussed. INTRODUCTION Solid state thermionic emission cooling has received interest in the last decade as a possible alternative to standard thermoelectric cooling. It has been proposed that greater cooling power may be achieved with thermionic emission cooling [1,2]. Thermionic emission coolers comprised completely of semiconducting materials, such as in the diagram of figure 1, are also
Peltier cooling barrier C
Peltier heating
e-
e-
V emitter C F
emitter
n+ (InP)
barrier
collector
n (InGaAs)
n+ (InP)
Figure 1. Schematic and block diagram of a thermionic emission cooler. The arrows show the direction of electron flow causing Peltier cooling on the left and Peltier heating on the right.
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Mat. Res. Soc. Symp. Vol. 626 © 2000 Materials Research Society
desirable because they can be monolithically integrated with solid state devices that require temperature control. The basic principle of cooling in thermionic emission devices, modeled in figure 1, is the transport of heat utilizing the Peltier effect. The purpose of this paper is to present a first principles derivation of the electronic contributions to the cooling power for a semiconductor thermionic device and from this to determine the maximum cooling possible for both the ballistic and diffusive limits. FIRST PRINCIPLES DERIVATION The electrical current density, JE, and heat current density, JQ, over a semiconductorsemiconductor heterojunction barrier are derived from statistical mechanics [3]: JE = ∫
∞
∞
−∞ −∞
p xfree
JQ = ∫
∞
∞
∫ ∫ ∞
∫ ∫
− ∞ −∞
∞
p xfree
f ( p ) g ( p) q v x d 3 p ,
(1)
f ( p) g ( p )(ε ( p) − ε F ) v x d 3 p ,
(2)
where f(p) is the Fermi Dirac distribution function, g(p) is the density of states, q is the elementary charge, vx is the electron velocity in the x-direction, ε(p) is the electron kinetic energy measured from the conduction band edge, εF is the Fermi level measured from the condu
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