ABSTRACT
In practice, there are challenges that can forbid laser cooling of solids by the above simple picture. One important issue is the existence of nonradiative recombination pathways that turn all of the absorbed energy into heat. For semiconductors, the nonradiative recombinations can be divided into two main categories: (1) the Shockley-Reed-Hall (SRH) recombination and (2) the Auger recombination process. The SRH process is mainly due to the interaction of the carriers with crystal nonidealities such as surface states and defects. On the other hand, the Auger recombination arises from the Coulomb interaction and scattering of three carriers; the interaction between two carriers gives energy to the third carrier and scatters it to a state with a higher energy. The third carrier eventually relaxes to a lower energy, losing its excess energy to the phonon bath. To realize laser cooling, both of the aforementioned processes should be suppressed. While the SRH process can be suppressed by increasing the material quality, surface passivation and preventing the carriers from reaching the defective area, the Auger recombination can be suppressed by appropriate band structure engineering [27] and operating at lower laser powers to avoid overly high photogenerated carrier densities. It should be noted that the ratio of the radiative to the nonradiative recombination rates increases as the operating temperature decreases. But unfortunately, at the same time, the thermal energy gained by the carriers (approximately equal to kT) decreases. Another important challenge is to extract the PL out of the material. For the case of rare earth-doped glass, the refractive index of the host crystal is close to air (for glass it is approximately 1.5). However, the difference between the index of the semiconductors (around 3) and air is high. As a result, the issue of PL trapping arises in semiconductors. The PL trapping results in photon recycling and eventually wastes some portion of the luminescent energy to nonradiative and heat-producing mechanisms. For this reason, effective luminescence extraction methods need to be developed for materials with a higher index of refraction. To have a better understanding of the above explanations, we note that the cooling efficiency (ηc) can be calculated as [41]:h h hc abs ex pl
= - E
E 1 (13.1)
where Epl is the average energy of the PL, Ei is the average energy of the incident photons, and ηex and ηabs are the external quantum efficiency and the absorption efficiency, respectively. The external quantum efficiency (ηex) can be calculated as [42]: h h
= + +
Bn
An Bn Cn
2 3 (13.2)where ηe is the extraction efficiency [28], n is the photogenerated carrier density, and A, B, and C are the SRH, radiative, and Auger
recombination coefficients, respectively. This parameter is a measure of the fraction of luminescence power extracted out of the material before getting reabsorbed. The absorption efficiency is equal to: h a
a aabs b =
+ (13.3)where α is the absorption in the active region and αb is the background
absorption due to free carriers, impurities, and the defects of the material. It is straightforward to conclude from Eqs. 13.2 and 13.3 that in order to maximize the net cooling efficiency, both the external quantum efficiency and the absorption efficiency should be maximized. The external quantum efficiency is dependent on the material quality, the extraction efficiency, and the carrier density. The extraction efficiency can be increased to almost 100% using novel techniques that suppress both the total internal reflection and the Fresnel reflection inside a high-index material. However, the material quality sets a limit on maximum attainable external quantum efficiency and absorption efficiency. The materials of choice for semiconductor laser cooling up to now are GaAs [42] and CdS [51]. Considering the bandgaps of these materials, the maximum net cooling efficiency is approximately 2% for gallium arsenide and 1% for cadmium sulfide at room temperature. These values are quite low, rendering the laser cooling of bulk GaAs impossible, and for CdS, only a particular nanoribbon structure has been cooled using a laser. This is due to the insufficient external and absorption efficiencies of these materials. These challenges suggest that mechanisms other than anti-Stokes should be developed and employed in order to have practical laser cryocoolers in the future. While different methods of laser cooling for gaseous systems (such as Doppler cooling, Sisyphus, resolved-sideband cooling, and sympathetic cooling) have
been implemented, the laser cooling of solids has remained a vast area to explore new ideas. In the following sections, we start by describing different types of Coulomb interactions in semiconductor quantum wells (QWs), which have the potential for optical refrigeration. The approach that we are going to explain is based on the Coulomb interaction between the photogenerated electron and holes in piezoelectric QW structures. For this reason, the next section is devoted to the topic of piezoelectricity in semiconductors and its previous application. We also discuss the effects of Coulomb interactions in semiconductors in Section 13.4. This provides the essential basis for understanding laser cooling of piezoelectric semiconductors, which is explained in Section 13.2. We finish the chapter with our concluding remarks about limitations and the possible improvement of the described systems in Section 13.8.
