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Ultrathin Graphite Films
 Charge carrier dynamics in ultrathin graphite films

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Prof. Dr. Martin Wolf
Abt. Physikalische Chemie
Fritz-Haber Institut der MPG
Faradayweg 4-6
14195 Berlin, Germany
phone:+49 30 8413-5111
Fax: +49 30 8413-5106

hitherto (2010):
Department of Physics
Free University Berlin
Arnimallee 14
D - 14195 Berlin


The question of how charge carriers dissipate their excess energy and relax a current after a driving electric field has been switched off is of fundamental importance for technological applications such as nanoelectronics. We have addressed these issues in ultrathin graphite films, the basic constituent of carbon nanotubes, by time-resolved THz spectroscopy. Our results show that strongly coupled optical phonons in the graphite layer dominate the ultrafast energy and transport relaxation dynamics after optical excitation. These active modes heat up on a femtosecond time scale. They also significantly contribute to the current relaxation and therefore are expected to limit the performance of carbon nanotubes as key player in nanoelectronics at high frequencies, but also at elevated temperatures and high electric fields. In addition, however, the behavior of these optical phonons might also open new possibilities of tailored energy transfer in other areas like laser ablation and phonon-mediated surface femto­chemistry.

The ultrathin graphite samples of only few nm thickness are excited with a 780-nm pump pulse and the ensueing dynamics of conduction electrons near the Fermi level E F are then probed by our THz probe pulses. As illustrated in the experimental setup shown in the Introduction, the use of lock-in amplifiers enables us to simultaneously detect the THz electric fields E0(t) and Δ E (t,τ) transmitted through the un-pumped and pumped sample at t after photoexcitation, respectively. These measured E0(t) and Δ E (t,τ) are then Fourier-transformed with respect to the internal time t and subsequently Fresnel formulas are applied to obtain the complex dielectric function ε(ω), which contains the system reponse of graphite to the photoexcitation. Since amplitude and phase of the THz pulse are detected, full information of ε(ω) and its pump-induced changes Δε(ω,τ) is available without invoking Kramers-Kronig relations. This way, the data provide insights into the conduction electrons near the Fermi level EF and their transport properties after photoexcitation. Using appropriate models to describe the temporal evolution of De yield three important observables of the graphite sample; (i) the electronic temperature Te, (ii) the plasma frequency w pl and (iii) the Drude relaxation rate γ.

For understanding the basic physical processes initiated by the pump pulse, a simplified band structure of graphite is shown in Fig. 1. Photoexcitation of the graphite sample causes the generation of new electron-hole pairs, which will relax as time evolves. Initially possible direct optical transitions may then be blocked, while new indirect transition will be opened. Thus, the interplay of both kinds of these transitions crucially determines the pump-induced increased absorption versus bleaching (“negative” absorption) as found in the experiment.

Fig. 1: Simplified band structure of graphite. (left) Direct and indirect optical conserve the electronic wavevector k, respectively, or require additional wavevector sources like phonons or inpurities. (right) The pump pulse creates new electron-hole pairs, which during their relaxation may block direct transitions and enable additional indirect transitions.
                    E-Field THz              THz Spec Fig1                  

If one now considers the energy which is initially deposited by the optical excitation pulse (~5 µJ/cm2), an very intriguing consequence is found. With the electronic specific heat of graphite, the temperature of the electronic system Te should reach values as high as 1200 K immediately after the pump pulse terminates. However, as seen in Fig. 2, where we plot the electron temperature as a function of the pump-probe delay, the maximum Te obtained from our data amounts to only less than 400 K at t = 500 fs. This means that within this short time span more than 90 % of the initial excess energy must have left the electronic system and entered the phonon heat bath, since ultrafast heat transfer into the bulk does not occur in our thin sample.

Moreover, due to the small Fermi surface of graphite and the boundary condition that the wavevector has to be conserved, only a rather small subset of phonons can interact with the electronic system of the graphite sample. Their reduced heat capacity, in turn, causes that these phonons, which are strongly coupled optical phonons (SCOPs), heat up on this ultrafast time scale of only 500 fs. This finding is further supported by calculations in which one assumes cold SCOPs. Here, the electronic temperature decays much faster than experimentally observed (see dashed line in the left panel of Fig. 2). The extracted time constant of ~7 ps for the T e decay can therefore be interpreted as lifetime estimate of the hot phonon distribution.

Finally, the pump-induced increase in the Drude relaxation rate g is addressed. As Fig. 2, right panel, shows, we observe a dramatic g increase of more than 3 THz, which represent about 30 % of its initial value. This is especially peculiar, since the the electronic temperature has increased by only 80 K. Based on second-order pertubation calculations, we find that the SCOPs significantly contribute to the obseved Dg . This behavior is of crucial importance for electronic circuits applications, since the performance of graphite and carbon nanotubes in such devices at elevated temperatures and high frequencies might be considerably limited.

Fig. 2: (left) Temporal evolution of the electronic temperature T e as a function of the pump-probe delay t . The experimental data exhibit a decay time of 7 ps, which is much slower than what one would expect if the active phonons (SCOPs), which accomodate the electronic energy, remain cold (dashed line). (right) Pump-induced changes of the Drude relaxation rate γ plotted over the electronic temperature T e. Although the electronic system heat up only by ~80 K, Δγ increases significantly by ~30 % from 10 to 13 THz. The considerable contribution of the SCOPs to the γ increase is shown by the solid line
tempEvolution             PumpInducedChanges

(for further information see Phys. Rev. Lett. 95, 187403 (2005) )

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