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(a) Schematic diagram of the ErAs/GaAs superlattice sample structure, functionalized probe tip, and electronic circuitry and signals required to perform scanned probe 3ω measurement of thermal conductivity. (b) Scanning electron micrograph of atomic force microscope probe tip functionalized with Pd thin-film resistor that serves as a local heater and thermometer. (c) Schematic diagram of probe tip and ambient water meniscus geometry used to model thermal transport between tip and sample.
(a) V 3ω signal amplitude measured as function of frequency for SiO2, ErAs/GaAs superlattice structure, GaAs, Si, and 1000 nm SOI. (b) Measured (symbols) and numerically modeled (lines) V3 ω signal amplitude and phase for Si sample, confirming excellent agreement between modeled and measured frequency dependence of V3 ω . (c) V 3ω signal amplitude predicted by numerical modeling (solid line) and measured at 50 Hz for SiO2, ErAs/GaAs superlattice structure, GaAs, Si, and 1000 nm SOI. For all materials except the ErAs/GaAs superlattice, the thermal conductivity is assumed to be known, enabling calibration of the numerical model. The thermal conductivity of the ErAs/GaAs superlattice structure is then determined from its measured V 3ω signal amplitude and the numerical model.
(a) Schematic diagram and scanning electron micrograph of focused-ion-beam milled wedge sample structure showing the milling geometry and cross-sectional ramp to expose the ErAs/GaAs superlattice and underlying GaAs; the approximate location of images in (b) is indicated by the white dotted line. (b) Atomic force topograph and 3ω signal image, obtained simultaneously, of wedge structure across surface region with ErAs/GaAs superlattice thickness varying from 200 nm to 0 nm. White dotted lines indicate regions from which plots in (c) were extracted. (c) Plots of surface height and 3ω signal amplitude showing that 3ω signal is constant (blue dotted line, corresponding to constant sample thermal conductivity) for ErAs/GaAs superlattice thicknesses of ∼150–200 nm, then decreased gradually for reduced superlattice thicknesses, due to the increased contribution from the GaAs substrate, eventually reaching a value corresponding to the thermal conductivity of the GaAs buffer layer and substrate (red dotted line). Each data point represents an average and, for V 3ω amplitude, standard deviation indicated by error bars, along a 1500 nm line parallel to the white dotted lines shown in (b).
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