MIPT has enhanced the conductivity of single-walled carbon nanotubes.

The results of the experiment and the theoretical model are published in the journal Carbon. Carbon exists in several forms (allotropic modifications) and can assemble into various structures. It forms coal, soot, diamonds, graphite (which is used in pencil leads), graphene, fullerenes, and more. In organic chemistry, everything is based on carbon compounds, which create the frameworks of molecules. Almost all carbon materials conduct electricity well, leading to enhanced absorption of electromagnetic waves in the terahertz frequency range, which is considered the foundation for the sixth generation of wireless communication (6G).

One method of controlling the electrical conductivity of materials is through doping. Unlike the doping of bulk semiconductors, most known methods for doping carbon nanotubes are unstable in air. An effective way to address this issue is by encapsulating different materials, which involves embedding them inside the nanotubes. By altering the material, the characteristics of the nanotubes can be tuned for various applications. However, not all materials are suitable for doping, as it is crucial to achieve a high degree of filling of the nanotube channels. In their study, the researchers utilized phosphorus and demonstrated that phosphorus molecules effectively fill the nanotubes, forming double chains within them.

“To study the dynamics of charge carriers on ultra-short time scales, a non-contact method of measuring conductivity based on terahertz spectroscopy was used. Additional optical pumping in this experiment allows for the detection of the dynamics of photo-generated charge carriers on a picosecond time scale.

Thus, we experimentally investigated the effect of phosphorus encapsulation on conductivity and photoconductivity, including enhanced generation of charge carriers after photo-excitation in carbon nanotube films. The results obtained were also supported by theoretical calculations that accounted for the dependence of carrier scattering rates on energy within the framework of the semi-classical Boltzmann model,” explains Maria Burdanova, a senior researcher at the Laboratory of Nanooptics and Plasmonics at MIPT.

In the experiment, the sample was irradiated with a laser pulse with photon energy exceeding the bandgap width. This excited free charge carriers (electrons and holes) in the material. These charge carriers are termed 'hot' because their kinetic energy significantly exceeds the characteristic thermal energy. It is important to note that the carriers remain in this state for some time (relaxation time), after which energy is converted into heat. The probing of the sample was conducted using a second beam.

This beam arrives at the sample after the excitation pulse (optical pumping) with a controllable delay. This beam allows tracking the dynamics of cooling hot electrons and holes in the material excited by the optical pulse. The choice of terahertz radiation (0.3–3 THz) as the probing method was determined by the fact that the response in this frequency range is most sensitive to the characteristics of free charge carriers. Additionally, the terahertz spectroscopy method is non-ionizing, meaning it does not damage the sample.

The theoretical description of the measurement results was obtained by the researchers within the framework of semi-classical transport theory based on the Boltzmann equation. The classical kinetic Boltzmann equation describes the statistical distribution of particles in a gas or liquid. The equation describes the motion of charges in liquids and gases, and from it, dynamic characteristics such as electrical conductivity, viscosity, and thermal conductivity can be determined. Here, free carriers are treated as an ideal gas, making the Boltzmann equation applicable.

“The semi-classical theory, strictly speaking, differs from the simple Boltzmann model for an ideal gas in that it takes into account the Pauli exclusion principle for electrons and holes, the complex dependence of charge carrier energy on their momentum, and considers that the scattering rate of electrons, calculated from quantum mechanical considerations, depends on their energy,” explains Andrey Vishnevyy, head of the Laboratory of Nanooptics and Plasmonics at MIPT.

The scientists showed that filled nanotubes have more charge carriers compared to empty ones. Physicists calculated that if the Fermi level for empty nanotubes is 0.01 eV, then for filled ones, it is already 0.07 eV. The Fermi level characterizes the energy of the system below which all energy states are filled with electrons. Energy levels above the Fermi level are empty. The higher the Fermi level, the more free electrons are present in the nanotube.

“We found that the Fermi level, just like temperature, determines the distribution of electrons across quantum states in nanotubes, which influences photoconductivity. In doped nanotubes, not only are there initially more electrons, but also a significantly greater number of electron-hole pairs are generated under the influence of the optical pulse. This is important for various applications, including the creation of efficient photodetectors,” commented Maxim Paukov, a graduate student at the LFI MIPT.

The temperature and Fermi level, determined by comparing theoretical calculations and experimental data, allow for the calculation of the carrier multiplication factor. This value indicates how many electron-hole pairs are generated per absorbed photon. The researchers demonstrated that in the case of filled carbon nanotubes, the multiplication factor is higher than that for empty ones.

“We found that the high efficiency of carrier multiplication in semiconductor empty nanotubes can be further increased to 1.5 through doping by encapsulating phosphorus within the nanotubes themselves,” explains Maria Burdanova.

The researchers believe that doping through encapsulation is not only stable but can also be enhanced by more effective filling of the nanotubes. The search for such fillers will enable an increase in the carrier multiplication factor. Overall, determining the carrier multiplication factor is important for various applications. For example, carrier multiplication allows for the rapid detection of photons with high sensitivity, making it valuable for use in photodetectors. Furthermore, carrier multiplication has the potential to enhance the efficiency of energy conversion in solar cells.

The research involved scientists from MIPT, Beijing Key Laboratory of Metamaterials and Devices, Beijing Advanced Innovation Center for Imaging Technology, Faculty of Physics, A.V. Nikolaev Institute of Inorganic Chemistry, Siberian Branch of the Russian Academy of Sciences, XPANCEO New Technologies Research Center, Yerevan State University, A.M. Prokhorov General Physics Institute of the Russian Academy of Sciences, and the Institute of Solid State Physics of the Russian Academy of Sciences.