# CNT-PUFs: Highly Robust and Heat-Tolerant Carbon-Nanotube-Based Physical Unclonable Functions +
## 5 Evaluation of the Fabricated CNT-PUFs
### Heat-Tolerant CNT-PUFs  
Due to their preferred use as lightweight safety components in embedded systems, PUFs are often exposed to various demanding environmental conditions. Most commonly, these are conditions characterised by temperature fluctuations, typically in industrial or Internet-of-Things (IoT) applications. Regardless of how challenging these conditions may be, the PUFs should produce a stable response under all circumstances. To this end, in this work, we investigated the tolerance of CNT-PUFs to high heat, up to \(120\,\mathrm{\SIUnitSymbolCelsius}\), well above the usual operating temperature limits of \(70\,\mathrm{\SIUnitSymbolCelsius}\) for commercial semiconductor devices and \(85\,\mathrm{\SIUnitSymbolCelsius}\) for industrial semiconductor devices and close to the operating temperature limit of \(125\,\mathrm{\SIUnitSymbolCelsius}\) for military semiconductor devices [43]. Our CNT-PUF can be deployed in all of these domains, significantly exceeding the temperature robustness of consumer and industrial applications.  
In particular, we investigated the robustness of our CNT-PUFs at the temperatures \(T\coloneqq\{23,40,60,80,100,120\}\,\mathrm{\SIUnitSymbolCelsius}\). Here, we always compared the PUF responses at a temperature of \(t\in T\), with the reference measurement obtained at a temperature of \(23\,\mathrm{\SIUnitSymbolCelsius}\). Figure 11a shows the fraction of unstable cells of a single 144-bit CNT-PUF instance captured at all temperatures \(t\in T\) as a function of the threshold \(l_{th}\). As we can see, the temperature curves show no significant difference.  
In addition, the wide window of usable thresholds obtained from Figure 10 can be confirmed for all temperature settings. This means that, even when comparing, within this window, responses at \(23\,\mathrm{\SIUnitSymbolCelsius}\) to those at temperatures up to \(120\,\mathrm{\SIUnitSymbolCelsius}\), at most 2% of cells were unstable, as shown in Figure 11a. We further investigated the temperature dependence of individual PUF cells. The maximal current \(I_{D,\mathrm{max,p}}\), as well as the minimal current \(I_{D,\mathrm{min}}\) for conductive cells exhibited an increase with increasing temperature, which is typical for semiconductors. This can be seen in the transfer curves of a representative CNT-FET in Figure 11b measured at different temperatures, as well as in the Arrhenius plot in Figure 11c. There, the resistance at the maximal p-current (\(R_{\mathrm{on,p}}\)) and at the minimal current (\(R_{\mathrm{off}}\)) of the CNT-FET is logarithmically plotted against the inverse temperature. This allowed the extraction of the activation energy \(E_{A}\) as a met  
Figure 10: Amount of stable measurements calculated for different thresholds over the range of \(0.1\,\mathrm{pA}\) to \(1\,\mathrm{\SIUnitSymbolMicro\SIUnitSymbolMicro\SIUnitSymbolMicro  
dependency of the currents [44]. Thereby, a lower activation energy implies a higher heat tolerance. It turned out that, in the on-state of the cell, \(E_{\rm A}\) was 37 meV (at \(R_{\rm on,p}\)) and 96 meV in the off-state (at \(R_{\rm off}\)). In comparison to other low-dimensional nanomaterials such as platinum diselenide (50 meV-200 meV) [45; 46], molybdenum disulfide (\(\approx\)570 meV) [47], and hexagonal boron nitride (\(\approx\)450 meV) [47], the \(E_{\rm A}\) for our CNT-PUFs was rather small. Next, the activation energy was extracted from 81 non-conductive cells. These currents originated from leakage between the gate and source/drain electrodes, as well as from measurement noise. There, a low average \(E_{\rm A}\) of 12 meV was obtained. This implies an even lower temperature dependence compared to conductive cells. Consequently, our CNT-PUF cells featured an excellent heat tolerance characterised by activation energies lower than approximately 40 meV for both binary states, conductive (\(R_{\rm on,p}\)\(\rightarrow\) logical 1) and non-conductive (\(R_{\rm non-conductive}\)\(\rightarrow\) logical 0).