# CNT-PUFs: Highly Robust and Heat-Tolerant Carbon-Nanotube-Based Physical Unclonable Functions +
## 7 Conclusions  
In this work, we presented a design for CNT-PUFs and revealed their properties for use under different temperatures. The reason for those excellent properties lies in the statistical distribution of the maximum current for the cells of the CNT-PUF, which form two clearly separated clusters. Furthermore, the size of these clusters, i.e., the number of cells with the respective maximum current, is directly adjustable by the fabrication process and the device layout. In conclusion, our raw CNT-PUF responses yielded nearly optimal results for all evaluated PUF metrics. This was demonstrated by a high level of uniqueness, as evidenced by an average inter-device Hamming distance of 0.48. A nearly uniform distribution of the PUF responses could be achieved by a ratio of 55.29% conducting and 44.71% non-conducting PUF cells. Furthermore, the PUF responses were found to be highly unpredictable through an evaluation utilising the well-known NIST SP 800-22 test suite. In repeated measurements at 23 \({}^{\circ}\)C and in the temperature range between 40 \({}^{\circ}\)C and 120 \({}^{\circ}\)C, the CNT-PUF responses were very robust, exhibiting an error rate of at most 2%. We attributed this excellent heat tolerance to the comparatively low extracted activation energies of less than 40 meV for the relevant binary states. Thus, our CNT-PUF architecture is able to generate robust security primitives in environments significantly exceeding the temperature limits of 70 \({}^{\circ}\)C for commercial semiconductor devices and 85 \({}^{\circ}\)C for industrial semiconductor devices. Furthermore, compared to other works in the relevant literature, we presented a CNT-based PUF design operating on passivated structures, further improving the robustness against environmental influences such as changes in the atmosphere around the device. The passivation, combined with the atomic sizes of CNTs and the low CNT density, makes them impervious to various attacks, like probing by optical microscopes. To safeguard against attacks based on the use of electron microscopes, additional metal layers could be added on top of the CNT-PUF. Finally, small remaining instabilities could easily be solved by a very lightweight post-processing scheme, in contrast to solutions in the existing literature that rely on computationally heavy error-correcting codes and fuzzy extractors. Despite the simplicity of the presented post-processing scheme, the algorithm allows stability errors to be fully corrected, resulting in a perfectly stable response with negligible overhead in terms of computing resources. The presented measurements were obtained using a highly sensitive parameter analyser. However, for practical use cases, integrated electronic components, such as amplifier circuits, analogue-digital conversion, and multiplexers are needed in order to allow efficient quantisation for large bit strings. For this reason, we reserve the demonstrated CNT-PUF architecture for heterogeneous system integration technologies such as chiplet or monolithic System-on-a-Chip (SoC) technologies connected to front-end electronics inherently offering these components. Furthermore, such a configuration also enables the nanomaterials to reveal the variety of their properties as they can take over multiple tasks for forthcoming cost-efficient hybrid electronic systems. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/nano13222930/s1](https://www.mdpi.com/article/10.3390/nano13222930/s1)]([https://www.mdpi.com/article/10.3390/nano13222930/s1](https://www.mdpi.com/article/10.3390/nano13222930/s1)), Figure S1: Absorbance of CNT dispersion and visualization of the sub-band transition energy branches for semiconducting (S22 + S33) and metallic (M11) CNTs limited to the diameter specifications provided by NanoIntegris Technologies Inc. [40].