Efficient luminescence extraction strategies and anti-reflective coatings to enhance optical refrigeration of semiconductors

Abstract

Laser refrigeration of solids has emerged as a viable solution for vibration-free and compact cooling that does not require any moving parts or cryogenic liquid. So far, rare-earth doped glasses are the only bulk materials that have provided efficient laser cooling based on the anti-Stokes process. These materials have low indices of refraction and are suitable for efficient luminescence extraction. However, up until this date, laser cooling of bulk semiconductors has not been achieved. One major challenge that needs to be addressed is the photoluminescence trapping and the consequent photon recycling. In this paper, we explain various methods to enhance light extraction for the purpose of laser cooling. We specifically provide guidelines for design and fabrication of graded index and subwavelength structures to maximize the extraction efficiency. Furthermore we present novel techniques for increasing the external quantum efficiency and enhancing the overall laser cooling efficiency. * . These include Coulomb assisted laser cooling in piezoelectric materials[8], luminescence-up conversion (known as anti-Stokes optical refrigeration[9]) , frequency down-conversion[10] and superradiance[11] to name a few. However, anti-Stokes has been the dominant mechanism used for laser cooling of condensed matter [9,[12][13][14][15][16][17][18] .Although anti-Stokes optical refrigeration is the subject of this study, efficient luminescence extraction is required to increase the cooling efficiency of all of the aforementioned laser cooling methods. The anti-Stokes mechanism is schematically shown in Fig. 1. The laser source, which is tuned slightly below the bandgap, produces electrons at the bottom of conduction band and holes at the top of the valence band. These carriers interact with the phonons and scatter to the empty energy states. After reaching equilibrium, i.e. once they thermalize with the phonons, the average electron energy increases by kT where k is the Boltzmann Constant and T is the temperature. Therefore, at equilibrium the average energy of the emitted photons by radiative recombination is higher than the absorbed laser photons. In this process, if all of the photogenerated carriers undergo radiative recombination and all the luminescence energy transfers out of the material, there will always be a net energy extraction (i.e. net cooling). The energy extraction results in the temperature drop and continues up to point where kT becomes so small that laser cooling power gets balanced by the heating produced due to parasitic absorption of the laser. The first observation of such a phenomenon was not realized experimentally until 1995, in trivalent ytterbium ion doped heavy-metal-fluoride glass [19]. In rare earth ions, the electronic 4f levels are shielded from the surrounding by the filled 5s and 5p shells, leading to suppression of multi-phonon relaxation[20] and a high radiative recombination rate favorable for optical refrigeration. In addition, the refractive index of the host material is close to the refracti...