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R( x,y)= R0 ( x,y)+ ΔR(x,y)(3)where R 0 (x,y) is the reflectivity of the sample when notelectrically supplied (optical image) and ΔR(x,y) is thereflectivity variation induced by the temperature variationΔT(x,y). In the following sections, we will not mention theposition (x,y) dependency anymore. ΔR is given by:Δ R = ΔR0 + ΔRf cos( 2π ft + ϕ f ) + ΔR2f cos(2π2 ft + ϕ2f ) (4)where ΔR 0 , ΔR f and ΔR 2f are the reflectivity variationsrespectively induced by the power dissipated at DC, f and 2ffrequencies and ϕ f and ϕ 2f are respectively the f and 2finduced thermal phase-shifts. We distinguish three terms inthe reflectivity variation ΔR: a DC one, a f frequency oneand a 2f frequency one. As we use a lock-in amplifier, wedetect the photodiode signal at only one frequency. Lookingat expression(2), we see that the power is mainly dissipatedat frequency f. Using the lock-in amplifier locked on the ffrequency, we detect the f frequency relative reflectivityvariation amplitude and phase signals, ΔR f and ϕ f .But, to have an image of the temperature variation ΔT f atfrequency f, we actually need the reflectivity R and ΔR f . So,we also measure the signal at the photodiode output beforethe lock-in amplifier input to deduce the mean reflectivity Rimage and hence the f frequency ΔR f /R amplitude. Finally,every thermal amplitude image presented corresponds to:ΔRf 1 ∂R= ΔTf = κ × ΔTfR R ∂Tand we will simply note it ΔR/R image. In the same way, theϕ f image will be simply noted ϕ image.Finally, the reflectivity variation implies an intensityvariation of the light reflected to the detector, here aphotodiode. Thus, measuring the relative variation ofphotocurrent ΔI/I of the detector, we deduce the relativevariation of reflectivity ΔR/R and then the temperaturevariation ΔT if κ is known, which demands a calibration[21]as κ depends on the illumination wavelength[4], the natureof the materials, the passivation layer thickness[22]…(5)24-26 September 2008, Rome, ItalyA. Scanning thermoreflectance on Sample AA 100×100 µm 2 ΔR/R image obtained for sample A ispresented in figure 4. The resistors are supplied by a f=70kHz sine voltage varying from 0 to 7V (V 0 =3.5 V), whichcorresponds to a 13 mW power dissipated in each of the 9resistors. The optical parameters (image resolution, imagesize) are identical to the previous section apart for the pixelclock frequency chosen equal to 2 kHz. The time spent toobtain this image is then about 30 seconds. To improve thesignal to noise ratio, we have accumulated 10 images.In figure 4, we clearly see a temperature increase locatedon the resistors with a maximum corresponding to areflectivity relative variation equal to 1.1×10 -3 , which iscomparable to the smallest value measurable with a CCDimaging thermoreflectance set-up within a few minutesimages accumulation. Thus, we have evaluated the noisestandard deviation over about one hundred pixels and wehave measured 2×10 -5 . For an accumulation of 10 images,therefore a 5 minutes accumulation, we can hence apparentlyreach reflectivity relative variations as low as a few 10 -5 .B. Scanning thermoreflectance on Sample BThen, we have also studied the sample B constituted ofnine thin (0.35µm) dissipative resistors, the distance betweentwo resistors being equal to 0.8 µm. Each resistor value is2934 Ω. The pixel clock frequency is still 2 kHz, the imagesize is unchanged but the image resolution is this time500×500 pixels. Every image presented from now is theresult of an accumulation of 10 images. Consequently, theacquisition time is about 20 minutes.In figure 5, ΔR/R amplitude (fig.5(a)) and φ phase(fig.5(b)) images obtained for sample B are presented. In thiscase, the resistors are supplied by a f=50 kHz cosine voltagevarying from 0 to 4.5V (V 0 =2.25 V), which corresponds to a3.45 mW power dissipated in each of the 9 resistors. Weclearly see a temperature increase located on the resistors.Over about one hundred pixels on the resistors, we measure1.4×10 -3 for the mean reflectivity relative variation. The 5(b)phase image shows an uniform value on the heating resistorsand a linear discrepancy when moving away, which has leadto the diffusion length identification[20].Fig. 4. ΔR/R thermoreflectance amplitude image of sample A for a 7Vpositive cosine supplying voltage, f=70 kHz.(a)Fig. 5. Thermoreflectance (a) ΔR/R amplitude image and (b) φ phase imageof sample B for a 4.5V positive cosine supplying voltage, f=50 kHz.(b)©EDA Publishing/THERMINIC 2008 185ISBN: 978-2-35500-008-9