The source meter was connected to both metallic pads to apply an ac electrical current (I 0), as shown on the right side of Figure 3a. I 0 with an angular modulation frequency of 1ω was applied to generate Joule heat and temperature fluctuations at a frequency of 2ω. The resistance of the narrow metal strip is proportional to the temperature that leads to a voltage fluctuation V = IR of 3ω across the specimen. A lock-in amplifier (A − B mode) connected to the two electrodes in the middle receives the 3ω voltage fluctuation along the narrow metal strip;
that gives the information about the thermal conductivity of the films. A few early studies by our group showed that the thermal conductivities of 1D silicon carbide nanowires (SiC NWs)  and Bi NWs  were measured successfully with our experimental setup and equipment. For the measurement of the thermal conductivity VX-809 in vitro selleck products of nonporous and nanoporous
Bi thin films, the third-harmonic voltage (V 3ω ) must be plotted against the natural logarithm of the applied frequencies ln ω resulting in a linear relationship. The thermal conductivity is then determined from the slope in the linear region. Figure 3b shows the linear regions of the plot of V 3ω versus ln ω at various applied ac currents ranging from 5 to 10 μA. The characteristic parameters of the linear region calculated from the graphs, as well as other required information, are summarized in Table 1. The difference between two V 3ω values (i.e., V 3ω1 and V 3ω2) is equated to the temperature drop across the Bi film and is used to calculate the cross-plane thermal
conductivity, which is defined by the following Equation: (1) Figure 3 Thermal conductivities of both nonporous and nanoporous Bi thin films. (a) Experimental setup and circuit (left side) and corresponding circuit (right side), equipped with thermal management and electrical measurement systems for thermal conductivity measurements via the 3ω method at room Sulfite dehydrogenase temperature. (b) Linear regions of the third-harmonic voltage versus the applied frequency at various applied ac currents ranging from 5 to 10 μA. (c) Thermal conductivities of nonporous Bi thin films in terms of applied ac currents. Table 1 Summary of the characteristic measuring parameters I 0 (μA) V 0 (mV) κ (W/m·K) I 0 (μA) V 0 (mV) κ (W/m·K) 5.0 564.38 1.76 × 104 2.90 7.0 601.34 1.45 × 104 2.90 5.5 560.23 1.82 × 104 2.94 8.0 627.17 1.24 × 104 2.80 6.0 565.74 1.77 × 104 2.94 9.0 618.19 1.27 × 104 2.76 6.5 607.28 1.41 × 104 2.89 10.0 630.10 1.17 × 104 2.67 The parameters used for the calculation of the thermal conductivity of nonporous Bi thin films as a function of the applied electrical ac current. R 0 , dR/dT, and l were determined to be 39.38 Ω, 53.64 mΩ/K, and 3 mm, respectively.