基于半导体异质结的光热制冷分析

We have examined the theory of optothermionic refrigeration combining the ideas of laser coolingand thermionic cooling Mal'shukov and Chao, Phys. Rev. Lett. 86, 5570 (2001)  and its estimatioron thermal energy extraction by using self-consistent calculations with the drift-diffusion model inthis paper, Both the Auger and the Shockley-Read-Hall dissipation processes are considered. ForGaAs/AlGaAs systems with arious impurity concentrations and different widths of quantum wellit is found that the optothermionic cooler can extract thermal energy at a rate as much as 10 W/cm'The information to perform optothermionic refrigeration in real devices have also been provided.

I.INTRODUCTION

In a thermoelectric device, there exist both electric cur-rent and heat flow. While a spatial temperature gradient gen-erates the useful electron current, the heat flow always tendsto reduce the required temperature difference. The thermo-electric current and the heat backflow are the two key issuesin the study of thermoelectric efficiency.Because the dynamics of charge carriers, i.e., electronsor holes, is sensitive to electric field and magnetic field, it iseasier to manipulate charge carriers than to manipulatephonons in a thermoelectric system. Consequently, the research and development of thermoelectricity have been fo-cused on the electron subsystem. The early calculations ofloffe, using a free electron gas model, suggested the dopedsemiconductors as the most favorable thermoelectric materials. However, the motion of electrons in a thermoelectricprocess is a diffusive transport due to various types of scat-tering. Hence, mechanisms and structures are needed in orderto further improve the thermoelectric efficiency.

To go beyond the diffusive transport of electrons, onehas to consider the ballistic motion, which was noticed byThomas Edison in 1883 in connection with the thermal emission of electrons. Since Mahan proposed the thermionic refrigeration in a system with a vacuum gap between parallelmetal electrodes, various types of thermionic cooling devices have been proposed.2-9One basic problem in thermionic systems is the charge accumulation. Although attempts have been made to overcome this problem,10-12 the expectedefficiency of the thermionic devices has never been achieved.

Improving the intrinsic thermionic efficiency will onlysolve one problem of thermionic refrigeration. For a typicalvalue of semiconductor thermal conductivity, when ther-mally excited carriers transfer heat from the cold region tothe hot region, the opposite heat flow due to the lattice heatconduction tends to reduce the temperature difference. Soanother approach is the fast extraction of heat from the system to be cooled. In conventional thermoelectric and/or ther-mionic coolers, if both electrons and holes participate in thetransport process, they are separated spatially. A few yearsago the optothermionic cooler was proposed,13which consisted of a narrow quantum well embedded in the middle ofa pn junction. Electrons in the n-doped region and holes inthe p-doped region are thermally excited into the quantumwell, where they can recombine to emit light. Thus, the pho-tons are mediums to extract the heat from the system. In thistheory, the ideas of thermionic cooling and traditional lasercooling are combined to extract the thermionic heat from thesystem. So this method is called as optothermionic refrigera-tion. As pointed out in Ref. 13 the idea of cooling a pnjunction with light emission was proposed about 40 yearsago but has never been realized.

The optothermionic refrigerating system proposed inRef. 13 has the typical heterostructure p-AlGaAs/AIGaAs/GaAs/AlGaAs/n-AlGaAs with 30% aluminum in the AlGaAs alloy. The impurity concentration is 1018 cm-3 for boththe p-AlGaAs and the n-AlGaAs. The band-edge profile of the system with no bias (V=0) applied is shown in Fig. 1.Region I is the p-AlGaAs and region V is the n-AlGaAs.Between the two regions Il and IV of undoped AlGaAs liesthe wide GaAs quantum well. When an electric current Jflows through the system under a finite applied bias V, ac-companying with the dissipation heat /V, an amount of radiation energy Qrad is emitted from the GaAs quantum well.If Orad is larger than /V, the central region of the heterostruc-ture is cooled down. Including the Auger recombination asthe only nonradiative process, the energy difference = Qrad-/V, which is called as the refrigeration heat in thispaper, was analyzed and estimated in Ref. 13. There it wasshown that optothermionic cooling can be realized withproper choice of heterostructures.

In the semiquantitative analysis of Ref. 13, electrons andholes are assumed to be distributed uniformly in the quantumwell. In such ideal systems, the optothermionic refrigerationcan be achieved in a finite range of bias voltage, and thecalculated cooling rate is at least several W/cm2. However.in a real system, both the carriers’ transport process and recombination process are affected seriously by various factors, resulting in the nonuniform distribution of carriers.Thus for practical applications, we have calculated the opto-thermionic refrigeration self-consistently in this work.