# Thermal Relaxation Spectra for Evaluating Luminescence Quantum Efficiency of CASN:Eu2+
###### Abstract  
Highly sensitive broadband photothermal spectroscopy with a white-light lamp as the excitation source was developed by combining a Sagnac interferometer and balanced detection with a photothermal deflection method. A probe beam was split by a birefringent crystal CaCO\({}_{3}\) into signal and reference beams with a balanced intensity. This balanced detection enabled the measurement of photoexcited thermal relaxation spectra of materials in the air over the whole visible range in the weak excitation limit 50 uW/cm\({}^{2}\). The photothermal excitation spectrum of Eu\({}^{2+}\)-doped CaAlSiN\({}_{3}\) phosphorus (CASN:Eu\({}^{2+}\)) with a high luminescent quantum efficiency was measured to be distinctly different from the photoluminescence excitation spectrum which reflects the absorption spectrum, revealing the thermal relaxation mechanism of the phosphor. Assuming a typical non-radiative relaxation from the higher excited states to the lowest excited state and successively to the ground state, it is demonstrated that the photoluminescence efficiency of the phosphors is readily evaluated simply by comparing the photothermal and photoluminescence excitation spectra. photothermal deflection spectroscopy; Sagnac interferometer; CASN:Eu\({}^{2+}\); luminescence quantum efficiency; photothermal excitation spectrum; photoluminescence excitation spectrum; thermal relaxation spectrum; balanced detection; birefringent crystal CaCO\({}_{3}\); thermal diffusion length +
Footnote †: journal: Applied Physics Letters  
_Applied Physics Letters_
emission energy, generated electric power, or metabolite yield (output power). As demonstrated in this paper, by contrast, if the photothermal spectrum can be measured over a wide spectral range showing the difference in shape from the absorption spectrum, the light energy conversion efficiency can be evaluated based on physically reasonable assumptions about thermal relaxation. For most substances (especially condensed matter) excluding atoms in a vacuum, most of the excitation energy relaxation rate is dominated by a non-radiative thermal relaxation rate, where the energy is finally released as heat to the surroundings of the sample. As a method for measuring this heat generation, photothermal spectroscopy including photoacoustic spectroscopy has been carried out for a long time. Since the photothermal spectrum is a measure of the heat generation rather than the luminescence amount as a function of the excitation light wavelength, it will be referred to as the photothermal excitation spectrum (PTES) in the rest of this paper as a counterpart of the photoluminescence excitation spectrum (PLES). The advantage of PTES over PLES is that it can be applied to all samples because any material has a non-radiative relaxation process, which is the main relaxation process for most substances except highly fluorescent material. Relaxation between the higher excited states is dominated by a non-radiative thermal relaxation, while relaxation from the lowest excited state to the ground state is characterized by the increased apparent photoluminescence rate including both radiative and non-radiative rates \(k\)(apparent) = \(k\)(radiative) + \(k\)(non-radiative). Thus, information of relaxation paths is obtained by comparing PTES with the absorption spectrum or PLES. To emphasize this feature, PTES is also called the thermal relaxation spectrum in this paper. However, in the long history of photothermal spectroscopy including photoacoustic spectroscopy, this capability of PTES has not been fully explored. Although there are many pioneering studies that have evaluated various quantum yields (luminescence, metabolite, or triplet-state formation via intersystem crossing) with these spectroscopic methods [2; 3; 4; 5; 6; 7] there are only a few examples [4] of PTES with a clear difference from PLES.