Introduction
Carbon nanotubes (CNTs) are potential candidates for flexible thermoelectric (TE) materials because of their flexibility and good thermoelectric property. The as-grown CNT sample is a mixture of metallic and semiconducting CNTs in a ratio of 1:2. This ratio can be controlled when a film is formed with the CNTs and significantly influence the TE performance of the film. According to the recent experimental work by Ichinose et al, the single-walled CNTs (SWCNTs) with semiconductor purity over 99 % exhibit a Seebeck coefficient of 200~300 µV/K when optimal carrier doping is achieved using a FET setup [1]. The Seebeck coefficient in this experiment was very high, but the electrical conductivity was less than 1 S/m. On the other hand, in the TE experiment on aligned SWCNTs with metal purity over 96 %, the electrical conductivity was above 100 S/m, which is about 10 times larger than that of non-aligned film, whereas their Seebeck coefficient was only about 30 µV/K.
These experimental results indicate that the TE performance of CNT films highly depends on both semiconductor purity and CNT alignment. In addition, the CNT films seem to have a trade-off relationship between the electrical conductivity and the Seebeck coefficient, resulting in the difficulty of enhancing TE power.
Modeling and Optimization Method
To address the tradeoff relationship mentioned above, we explored the optimal semiconductor purity and structure using a Thermoelectric Random Stick Network (TE-RSN) method [2] and Nondominated Sorting Genetic Algorithm Ⅱ (NSGA-Ⅱ) [3]. Our recently developed TE-RSN is a simulation method that combines a random stick network model and electrical and thermal circuit network equations [2]. The NSGA-Ⅱ is among the multiobjective genetic algorithm methods.
In the present simulation, the CNT film size has been fixed to 5 µm in length and 5 µm in width. The number of CNTs was 1250, the length was 500 nm and the diameter was 1.4 nm. Also, the semiconductor purity of the film, as well as the position and alignment angle of each CNT, were chosen randomly. We put in place 200 initial structures under these conditions and evaluated TE performance using the TE-RSN method. We then repeated the loops of the genetic algorithm (non-dominated sorting, crowded distance sorting, crossover and mutation) until the TE performance converged.
Results
As a result of optimization up to 2,000 generations, an averaged electrical conductivity increased from 100 S/m to 300 S/m and an averaged Seebeck coefficient increased from 60 µV/K to 120 µV/K compared to the initial generation. Thus, we succeeded in resolving the trade-off relationship between the electrical conductivity and the Seebeck coefficient. Furthermore, we identified the following 3 characteristic features by analyzing samples from the 2,000 generation.
・The semiconductor purity of CNT films existing in the 2,000 generation is about 90 %.
・The CNT alignment angle θ (|θ| ≦ 90°) in the CNT film is aligned in the direction of the electric field with a standard deviation σ = 50°.
・Some high-density regions appear in the CNT film parallel to the electric field and temperature gradient.
References
[1] Y. Ichinose et al., Nano Lett. 19, 7370 (2019).
[2] J. Kobayashi and T. Yamamoto, Jpn. J. Appl. Phys. 61, 095001 (2022).
[3] K. Deb et al., IEEE Trans. Evol. Comput. 6, 182 (2002).
