# Thermal Relaxation Spectra for Evaluating Luminescence Quantum Efficiency of CASN:Eu2+
###### Abstract
One of the reasons is that thermal detection is less sensitive than luminescence detection, so that a laser is often used as an excitation light source, making it difficult to measure photothermal spectra over a wide wavelength region. Another reason is that highly luminescent material, which is expected to show a photothermal spectrum clearly different from the absorption spectrum, has a low heat-generation efficiency to make it difficult to obtain the photothermal spectrum. The difference between the photothermal spectrum and absorption spectrum is expected to be relevant to the relaxation mechanism. Important examples may be in biological systems. For example, this kind of process may be taking place in higher plants: Excessive light energy causes damage to the photosynthetic system, so that excess energy is dissipated by heat dissipation process for the photosynthetic mechanism to be protected. Such a dissipation process is important in nature where the environment changes, known as non-photochemical quenching [8]. Since this heat dissipation process is known to work even with the excitation intensity as weak as 5 mW/cm\({}^{2}\) @ 680 nm, it is necessary to measure the photothermal spectrum in the weak excitation limit for acquisition of the thermal relaxation spectrum reflecting the quantum efficiency of photosynthesis. In the past, however, the photothermal spectrum of a leaf has not been measured with sufficiently weak excitation, and an apparent difference between the photothermal and the absorption spectra has never been observed [5]. In photothermal deflection spectroscopy (PDS), representative of photothermal conversion spectroscopy because it is said that PDS is by one order of magnitude more sensitive than photoacoustic spectroscopy (PAS) [9], a laser is generally used as an excitation light source, and a sample is immersed in a medium having a large temperature coefficient of the refractive index (\(dn\)/\(dT\)) as the surrounding deflection medium, such as carbon tetrachloride. When a bright white light source such as a Xe lamp is used, the wavelength is often selected by a narrow band filter instead of a diffraction grating spectrometer having a low throughput. The typical spectral excitation light intensity in that case is 1 nW/\(\mu\)m\({}^{2}\) = 0.1 W/cm\({}^{2}\). Since photothermal deflection spectroscopy detects heat generation accompanying non-radiative relaxation after light absorption of a specimen, many researches have been carried out since the analysis of its physical properties can be carried out non-destructively irrespective of the morphology of the specimen. Previously we developed the Sagnac-interferometer photothermal deflection spectroscopy (SIPDS) to improve the signal to noise ratio (S/N) by one order of magnitude (detectable temperature change \(6\times 10^{-5}\) K) [10; 11] compared with the original report on PDS [12]. As a result, measurement of broadband photothermal spectra is realized in the air by excitation with a weak narrow-spectrum light from a white-light lamp through a monochromator. The photothermal spectrum is equivalent to the absorption spectrum if 100% of the excitation energy is nonradiatively relaxed, but if it is converted to photoluminescence and/or chemical reaction energies, it becomes different from the absorption spectrum. The difference enables us to evaluate the quantum efficiency of luminescence or chemical energy conversion. In this paper, we have implemented balanced detection into SIPDS and achieved fourfold improvement in S/N compared with SIPDS without balanced detection. We have applied this system to the measurement of photothermal excitation spectrum (PTES) of Eu\({}^{2+}\)-doped CaAlSiN\({}_{3}\) phosphors [13; 14] and estimated the luminescence quantum efficiency solely from comparison with the photoluminescence excitation spectrum (PLES), in good agreement with that measured independently by the absolute quantum efficiency measurement system using integrating sphere [15].