5.3.1 Thermovoltage
Table 5.1 summarizes the measured thermovoltages VTh, which differ in sign and size.
The sign is defined by the heating position, already shown in measurements of the GCQS (Fig. 5.2). To understand this behavior, one has to consider the contacts as a thermo-couple, for example Au-Ag and Ag-Au like illustrated in Fig. 5.1d). By focusing the heating spot on the other side of the contact, ∆T changes its sign. Thereby the sign of
∆V switches since ∆V =−∆S·∆T.
Further, there is a variation of the size of thermovoltage values which cannot be described only by the heating position since in most cases the position of heating was chosen to maximize the signal. A difference of one order of magnitude between Cu-Au-Cu and Ag-Ni-Ag NThC was observed. To describe this effect, it is necessary to study the Seebeck coefficients of the thermocouples. Tab. 5.2 lists the relevant Seebeck coefficients, taken from Ref. [88].
For example, a Cu-Au-Cu NThC has a ∆SCu-Au-Cu =SCu−SAu= 0.7µV K−1, where the given ranges of the Seebeck coefficients were averaged. The other combinations of ∆S are listed in Tab. 5.1. It is obvious that the thermovoltages in Tab. 5.1 differ since the values here also vary about one order of magnitude from each other. Tab. 5.3 lists the calculated temperature differences across the thermocouples with ∆TCalc = −V∆STh. Fur-ther the materials of the lead as well as the absorbed intensityPAbs, which was calculated by reflection coefficients (for λ= 514 nm :rAu= 0.58, rNi = 0.59, rPt = 0.62 [89]) and the laser intensity PLaser. The ∆TCalc amount to 0.8 K to 2.9 K for similar absorbed intensity.
Compared to the GCQS measurements (see Fig. 5.2b)), the ∆TCalcare smaller by factor of 3 and 10, although the absorbed intensity was higher. Reasons for this discrepancy can be residue of the electrolyte, though it was removed, or the different substrate. Metallic
Measurement NThC Substrate PLaser VTh ∆SCalc Cu-Au-Cu 1 (Fig. 5.7b)) Kapton 45 mW −1.94µV −0.7µV K−1
Table 5.1: Thermovoltages of NThC and GCQS experiments. The sign ofVThis defined by the position of illumination and the sign of∆SCalc.
Metal Seebeck coefficient Ag 6.7µV K−1 to 7.9µV K−1 Au 5.6µV K−1 to 8.0µV K−1 Cu 7.2µV K−1 to 7.7µV K−1 Ni −19.4µV K−1 to −12.0µV K−1
Pt 0µV K−1
Table 5.2: Seebeck coefficients for different metals. Taken from Ref. [88].
substrates like bronze and spring steel were used in the GCQS experiments. But these materials have a higher thermal conductivity, which should result in a smaller tempera-ture difference and thus smaller thermovoltages. By expecting a linear dependence of the calculated temperature difference ∆TCalc on the absorbed intensity PAbs (see Fig. 5.11), the deviation of the GCQS results is significant small among each other compared to NThC results.
In conclusion, the measured thermovoltage values on NThC can be explained in sign and size among each other. The small variations can be described with the position depen-dent values discovered in the GCQS measurements (see Fig. 5.2b)). The deviation of the NThC results compared to the GCQS results is possibly caused by an unknown influence of the electrolyte residue.
Measurement NThC ∆TCalc Lead PAbs Cu-Au-Cu 1 (Fig. 5.7b)) 2.8 K Au 18.9 mW Cu-Au-Cu 2 (Fig. 5.8b)) 2.9 K Au 18.9 mW Cu-Au-Cu 3 (Fig. 5.8b)) −1.2 K Au 18.9 mW Ag-Ni-Ag (Fig. 5.10b)) 0.8 K Ni 18.4 mW Measurement GCQS
Au-Ag-Au (Fig. 5.2d)) 10.3 K Au 2.5 mW Pt-Ag-Pt (Fig. 5.2d)) 31.6 K Pt 13.5 mW
Table 5.3: ∆TCalc andPAbs of NThC and GCQS experiments.
Measurement NThC ∆R Lead PAbs α (between 0◦C to 100◦C)
Table 5.4: Results of resistance changes due to illumination. The temperature coefficientαfor different metals were taken from Ref. [88].
5.3.2 Temperature-dependent resistance change
The second quantity to discuss is the resistance change (slope) of ∆V = ∆R·I +VTh as a function of the current, see Fig. 5.7b), Fig. 5.8b) and Fig. 5.10b). It describes the resistance change of the leads due to heating. In Tab. 5.4 the resistance changes ∆R are listed which all deviate from zero. Measurements on the Cu-Au-Cu NThC show similar values in the range from 0.64 Ω to 0.77 Ω, whereas the slope of the Ag-Ni-Ag measure-ments is about 4 times higher (2.6 Ω).
In macroscopic systems, the thermoelectric current is added to the bias current. The thermovoltage is a only dependent on the temperature difference and independent of the applied current. Thus, the slope is expected to be zero, but all experiments reveal a non-zero slope. In order to exclude a thermoelectric effect, the following measurement was performed:
The position of illumination was chosen in a way that the contributions of the thermocou-ple cancel each other at zero current bias. This results in a flat curve with no significant signal, here the red curve is shown in Fig. 5.11a). When applying currents of −10µA and 10µA clear signals occur (black and green curve in Fig. 5.11a)). This proves the assumption that a non-thermoelectric effect causes the slope. If a thermoelectric effect causes the slope, no signal should occur, since the contributions of the two thermocouples would, independent of the applied current, annihilate each other.
Another observation is that in all experiments a positive slope is observed, shown in Tab.
5.4. All these indicators fit to the assumption that the slope is a resistance change of the leads caused by temperature, as is consistent with the known temperature dependence of gold.
For example, the resistance of a 40 nm thick gold film (length 1 mm and width 40µm) changes by 0.66 Ω due to an increased temperature of about 13 K.
Even the consideration of the temperature coefficientαin combination with the absorbed
0 10 20 30 40 50 0
5 10 15 20 25
Voltagechange[µV]
Laser intensity [mW]
0 25 50 75 100 125 150 175 2000 1
Laserpulse
5 µV
Voltage[arb.offset]
Time [ms]
Bias current 10µA0µA -10µA
a)
b)
Voltage [arb. offset]
Figure 5.11: a) Signal occurred by illumination of the center of the contact, with different currents of 10µA (green curve), 0µA (red curve) and −10µA (black curve). b) Intensity dependent voltage changes on a Ag-Ni-Ag NThC. The linear fit (red line) with ∆V = 0.45 mV W−1−0.48µV. The error bars denote the standard deviation of the laser off-time multiplied by a factor of√
2.
Metal α (between 0◦C to 100◦C) Au 3.98×10−3K−1 Ni 6.82×10−3K−1 Pt 3.92×10−3K−1
Table 5.5: Temperature coefficientαfor different metals. Taken from Ref. [88].
intensity PAbs the sizes of the resistance changes of the NThC samples by a factor of 2 among each other. Compared to the GCSQ samples, the resistance changes are too small, maybe also caused by the electrolyte residue. Furthermore, a possible reason could be a deviation of the optimized position of the laser spot on the lead.
Finally, the linear correlation between the laser intensity and the voltage changes ∆V is shown in Fig. 5.11b). The fit leads to an equation ∆V = 0.45 mV W−1−0.48µV, whereby the linearity indicates a thermal effect, not an optical one.