Diamonds are forever… oscillating coherently
Diamond is the quintessential covalently bonded crystal: it has the highest hardness and thermal conductivity of known materials. These unique properties are determined by or deeply related to the phonon spectrum of diamond. (Phonons are collective vibrations of crystal lattice ions.) Doping of diamond by group III (e.g., boron) or V atoms (e.g., phosphorus) turns it into a p- or n-type semiconductor, enabling applications such as UV-light emitting diodes1 and diamond-based UV lasers. Heavily doped diamonds undergo a superconducting phase transition above the liquid helium temperature,2 in which electron-phonon interaction is thought to play a critical role.
Raman spectroscopy is a widely used method for evaluating the crystallinity of diamond-related materials. Moreover, through interference between the vibrational and electronic scattering amplitudes, it can determine electron-phonon interactions.3 Time-resolved measurements of coherent—i.e., in phase—optical phonons give complementary and more detailed information on the femtosecond dynamics of phonons and their coupling with electrons.4,5 Because of the challenging requirement for ultra-broad laser bandwidth, however, the coherent excitation of C–C bond vibrations has been demonstrated only in molecular systems6 and, very recently, in carbon nanotubes7 and graphite.5 (Like these materials, diamond consists entirely of carbon atoms.)
To excite coherent phonons requires intense laser pulses with duration shorter than the half-period of the phonon oscillation. A self-made Ti (titanium):sapphire oscillator provides sub-10fs, near-UV optical pulses with 200mW output power and a 65MHz repetition rate. To detect the weak signal modulation from the coherent optical phonons in the diamond, we applied a simple pump-probe electro-optic reflectivity technique without spectral resolution or phase modulation. Fast scan of the delay between pump and probe pulses at 20Hz typically enables the averaging of 20,000 transient reflectivity traces. To achieve high precision, the time delay is carefully calibrated by incorporating it into the scanning arm of a Mach-Zehnder interferometer.
Figure 1 shows the change in transient reflectivity of a synthetic single-crystal diamond sample. Following the impulsive optical excitation at t=0, which macroscopically excites in-phase lattice vibration (coherent phonon), the reflectivity starts to oscillate with a period of 25fs.8 The frequency of ∼40THz, or ∼1330cm-1, agrees well with the Raman active optical phonon of diamond: i.e., lattice phonons induced by Raman-scattering-type light-material interactions. In the short time window of the figure, the oscillation is hardly damped. The oscillations persist for more than 300 cycles before dephasing on an 8ps timescale. Correspondingly, the linewidth of the peak in the Fourier transform spectrum in the figure inset is very narrow (∼0.05THz). Since the lifetime and frequency of the coherent optical phonon depend on the concentration of the impurity, time-resolved measurement can serve to evaluate the crystallinity of diamond—as Raman scattering does—but with even higher accuracy.
The coherent phonon signal essentially vanishes after rotating the sample by 45° within the plane of the surface. The orientation dependence with respect to the light polarization is consistent with the off-diagonal Γ25′ symmetry Raman tensor that is primarily responsible for coherent phonon generation in group IV crystals such as silicon4 and germanium.9 Doping by parts per million amounts of nitrogen impurities affects coherent phonon features—e.g., amplitude, lifetime, frequency—as well as the color of single-crystal diamond.
With increasing pump power, the amplitude of coherent lattice vibration increases linearly, as measured by changing reflectivity. Since the excitation photon energy of 3.14eV that we obtained is too low for single-photon indirect (5.48eV) or direct (7.3eV) bandgap excitation, the linear power dependence indicates the off-resonant Raman nature of coherent phonon generation. The extraordinarily long lifetime is independent of pump power or phonon amplitude and, for that reason, is not affected by photoexcited carriers. Thus, diamond provides a textbook example of an electromagnetic field driving coherent lattice oscillations through stimulated Raman scattering, without generating photoexcited carriers.
In summary, we applied a simple pump-probe technique to investigate the ultra-fast dynamics of coherent, 40THz optical phonons of diamond. The coherent phonon response shows strong sensitivity to doping and provides a powerful method for evaluating ultra-fast electron-phonon coupling dynamics in semiconducting and superconducting diamonds.
The authors thank Takeshi Mitani for Raman measurement. This work was supported by KAKENHI-17540305 and -18340093, and NSF CHE-0209706.