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Lanthanides in Luminescent Thermometry Chapter 281 363 between points presenting a temperature difference higher than dT (or, equiv- alently, higher than the thermometer’s sensitivity, Eq. 4) (Kim et al., 2012): dx1⁄4 dT (20) ! where j r Tjmax is the maximum temperature gradient of the mapping. For a ! jrTjmax one-dimensional temperature profile the temperature gradient is ! j r Tjmax 1⁄4 jdT=dxjmax. The temporal resolution of the measurement (dt) is the minimum time interval between measurements presenting a temperature difference higher than dT: dt1⁄4 dT (21) jdT=dtjmax where jdT/dtjmax is the maximum temperature change per unit of time. Both temporal and spatial resolutions are important to evaluate the appli- cability of a thermometer for dynamic temperature measurements. The tech- nological areas with the highest spatiotemporal temperature discrimination demands are micro and optoelectronics, microelectromechanical (MEM) machines, memory chips, and Si-based biological sensors (Tao et al., 2012). The spatial resolution of luminescent thermometers (Eq. 20) can be improved either by decreasing the temperature uncertainty or by increasing the measured temperature gradient. The first approach requires the use of lower noise detectors (eg, cooled detectors or PMTs, see Section 3.2.1). The increasing of the temperature gradient can be achieved either by increasing the value of the temperature step or by mapping with low scanning steps. 3.3.1 Comparison of Spatial and Temporal Resolutions from Different Techniques The spatial and temporal resolutions (dx and dt) of luminescent thermometers were calculated in a handful of reports mapping the surface of thermographic films using optical fibers or scanning thermal microscopy (SThM) incorporat- ing a fluorescent probe in the scanning tip. These values are compared with those obtained using other (nonluminescent) noncontact techniques, such as thermoreflectance and Raman spectroscopy (Fig. 7). The use of SThMs adapted for fluorescence reading, by incorporating a fluorescent probe in the scanning tip, was initially reported by Aigouy et al. (Aigouy et al., 2005, 2009, 2011; Sa ̈ıdi et al., 2009, 2011) to work in the sub- wavelength spatial resolution regime. Regarding high-resolution thermal imaging of integrated circuits, Sa ̈ıdi et al. (2011) used a Yb3+/Er3+-doped PbF2 nanocrystal as temperature sensor. The technique presents temperature uncertainty $1.0 K, spatial resolution of 0.027 mm, despite the relatively long acquisition times (100 ms per pixel), that invalidates the transient mapping ofPDF Image | HANDBOOK ON THE PHYSICS AND CHEMISTRY OF RARE EARTHS
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