Picosecond nonlinear optoelectronics in graphene

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The terahertz spectroscopy group of Petr Kužel in collaboration with the Charles University described nonlinear behavior of charge carriers during early times after pulsed optical excitation in epitaxially grown graphene layers. The time evolution of the system is determined by nonlinear electronic response of graphene, which opens the possibility of the increase of the speed of optoelectronic elements. The results the study were published in journal Advanced Functional Materials.

Graphene is a single sheet of carbon atoms forming a two-dimensional infinite honeycomb lattice. For example, a macroscopic ordered stack of such layers forms the graphite; however, the behavior of the graphene single atomic layer is dramatically different from that of graphite.

The electronic properties of graphene are determined by the behavior of charge carriers (electrons and holes); their energy band structure is quite different from typical structures of classical semiconductors or metals and resembles much more the energy scheme of photons.

Depending on the position of the so-called Fermi level* (which may be shifted, e.g., due to the nature of the surrounding material and dynamically controlled by illumination or by electric current) graphene can be an excellent conductor or a good insulator. Applications of graphene in electronics and optoelectronics rely on various approaches to the Fermi level tuning by electronic, chemical or optical stimuli.

Scheme of terahertz optoelectronic probing of graphene films

Fig. 1. Upper part: scheme of terahertz optoelectronic probing of graphene films on silicon carbide substrate. Optical pulse (red) excites charge carriers and a delayed ultrashort terahertz pulse (blue, 1 THz = 1012 Hz) probes the state of these carriers. By inspecting changes in the terahertz pulse shape, we determine the conductivity spectra Δσ of graphene, which reflect the distribution of charges within the energy band structure.  Bottom left: typical measured conductivity spectrum containing the plasmon resonance. Bottom right: ultrafast evolution of the temperature of carriers (Tc) and of the Fermi level (μ) deduced from the experiments.

Free-standing graphene layer is very fragile and is not very useful for practical applications. Therefore, in this study, the group of Petr Kužel focused on graphene layers epitaxially grown on silicon carbide (SiC) substrates. Properties of films prepared under certain conditions approach those of an ideal free-standing graphene layer. By varying the technological conditions, the properties of graphene can be tuned. However, the substrate surface is not perfectly flat even if the greatest care is devoted to its preparation. Instead, it always consists of a set of nanoscopic terraces.

The researchers studied graphene layers using ultrashort laser pulses and terahertz optoelectronic probing (see Fig. 1): an optical pulse excited charge carriers and a delayed ultrashort terahertz pulse tested the state of these carriers. Measured changes in the terahertz pulse shape provided the conductivity spectra, which reflect the distribution of charges within the energy band structure.

The obtained spectra exhibited the so-called localized plasmon resonance, which expresses the collective motion of charge carriers, and which is related to the existence of terraces on the substrate surface. In the investigated graphene samples the build-up and decay of these plasmons on picosecond time scale (1 ps = 10–12 s) was observed.

In brief, the observed behavior can be described as follows. Before the arrival of the optical laser pulse a significant concentration of equilibrium charge carriers exists in the sample, the graphene film is conducting. Immediately after the optical excitation, the newly generated carriers gain a very high temperature, they exchange energy with equilibrium carriers through elastic scattering, undergo a fast recombination process, and efficiently transfer their energy to the graphene crystal lattice.

During the first picosecond the optically generated carriers practically vanish, and only significantly heated equilibrium carriers remain; the Fermi level exhibits a pronounced decrease with respect to the equilibrium state. The subsequent nonlinear dynamics of plasmons are entirely controlled by the Fermi level of excited carriers through their temperature Tc (see Figure 1). The nonlinear behavior of graphene in this state is a consequence of the unique band structure of graphene which enables very high rate of elastic collisions of carriers. The decay of the nonlinear regime depends on the degree of disorder in the graphene layer. The technological control of the disorder in graphene layers thus allows one to tune the THz response of the material which is important for its optoelectronic applications.

*Fermi level determines the probability of occupancy of states at different energies. For electrons the filling of energy levels occurs in agreement with the Pauli exclusion principle, i.e., that two or more electrons cannot occupy the same state. At absolute zero temperature the states are filled from bottom and the Fermi level corresponds to the energy of the highest occupied state. At higher temperatures some electrons can be thermally excited to higher-energy states and the Fermi level corresponds to the state with the occupancy probability of ½. Doping of samples leads to stationary shifts of the Fermi level. Optical excitation by ultrashort pulse can induce significant shifts of the Fermi level on ultrafast time scale.


Contact: Petr Kužel,  kuzelp [at] fzu [dot] cz

Citace: V. C. Paingad, J. Kunc, M. Rejhon, I. Rychetský, I. Mohelský, M. Orlita, and P. Kužel, Ultrafast plasmon thermalization in epitaxial graphene probed by time-resolved THz spectroscopy, Adv. Funct. Mater. 31, 2105763 (2021), doi.org/10.1002/adfm.202105763.

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