Ultrafast photoconductivity and charge carrier transport in semiconductor nanostructures

Transport of charges is a fundamental process in many high-tech applications including photovoltaic or optoelectronic devices, but also in more ordinary components such as unsophisticated wires and other circuitry. The development of nanotechnologies resulted in the fabrication of highly complex materials consisting of a large variety of nano-sized elements, which inevitably involve a multitude of charge transport processes occurring on various time- and length-scales.

Terahertz spectroscopy has been used for almost two decades for investigations of nanomaterials, including nanocrystals, nanoparticles or various nanowires and nanotubes. Its importance stems from the non-contact character of measurements; in addition, owing to its high frequency and broadband character, it is able to characterize charge transport properties within individual nanoobjects and also among them. Probing of ultrafast charge dynamics after photoexcitation is possible owing to the sub-picosecond time resolution. Despite this potential, the interpretation of the measured terahertz conductivity spectra is still intensively debated in many materials and systems.

Response of charge carriers in bulk semiconductors is in a vast majority of cases described by a Drude model. The conductivity spectra then exhibit two prominent properties: the real part decreases with frequency and the imaginary part is positive. However, the conductivity observed in small semiconductor nanoparticles often behaves quite differently: it is characterized by a real part increasing with frequency and a negative imaginary part.

For nanoparticles with size smaller or comparable to the carrier mean free path, it is necessary to consider the interaction of carriers with nanoparticle boundaries. In the case of weak confinement, it is possible to employ models developed within the laws of classical physics. Monte-Carlo simulations of the carrier motion in weakly confining environment developed within our group are accepted as a reliable linear classical model. Here, the charge carriers trajectories are calculated and the charges are allowed to scatter in the volume of the nanocrystal (isotropic scattering) and at the nanocrystal boundary (possibly anisotropic scattering consisting of the forward scattering accompanied by a transfer of the charge into a neighboring nanocrystal and the backward scattering preserving the charge in the original nanocrystal). [1]

Description

Schemes of confinement regimes for model silicon nanocrystals in the form of cubes with a side length d and with a probing frequency f; momentum scattering time τ = 150 fs, temperature T = 300 K. In the cyan region the charge carriers show a delocalized (Drude-like) response; the green region is roughly delimited by the lines indicating the carrier transport distance in the ballistic (Lbal) and diffusion (Ldiff) regimes within a single period of the probing radiation and it features a conductivity peak interpreted within the framework of the classical physics. The yellow region is below the lowest quantum transition energy denoted E1; here the conductivity signal is small, the spectra are featureless and typical for the localized response (Drude-Smith-like behavior). The three dash-dot horizontal lines delimit a zone marking a transition from the classical to the quantum regime. Finally, in the red regime, several quantum transitions appear in the spectra; naturally, this triangle broadens toward the optical region where these phenomena are usually observed.

For small nanostructures or at low temperatures, the confinement of carriers is stronger, and the quantum-mechanical calculations of the THz conductivity should be employed. The usual approach based on the Kubo formula introduces a phenomenological charge scattering rate (or relaxation time) accounting for all the scattering processes. This approximation is highly pertinent in the optical range. However, the approach fails at low frequencies in nanocrystals in the regime where the scattering rate is comparable to the probing frequency; e.g., it always yields nonzero conductivity at zero frequency (dc regime) even if the nanocrystals are mutually perfectly isolated.

We have shown [2] that the broken translation symmetry of the nanostructures induces a broadband drift-diffusion current, which is not taken into account in the analysis based on Kubo formula in the relaxation time approximation. The proper introduction of this current removes all the contradictions, fulfills the classical limit in the case of large nanocrystals and it is at the origin of significant reshaping of the conductivity spectra up to terahertz or multi-terahertz spectral ranges.

Most of our experimental works are based on the above described fully microscopic approach. The investigated systems include silicon nanocrystals,[3] CdS nanocrystals, [4] various nanostructures of TiO₂,[5], InP nanowires,[6] or Sb-doped SnO₂ nanoparticles.[7] For example, we carried out a comparative study using the dc and THz measurements complemented also the conductive AFM characterization of antimony-doped SnO₂ nanoparticles. This combination of methods has proven to be a powerful tool for the investigation of intra- an inter-nanoparticle transport and, namely, for guiding the optimization of the sample conductive properties by various technological steps.

[1] H. Němec, P. Kužel, and V. Sundström, Phys. Rev. B 2009, 79, 115309.
[2] T. Ostatnický, V. Pushkarev, H. Němec, and P. Kužel, Phys. Rev. B 2018, 97, 085426.
[3] V. Zajac, H. Němec, C. Kadlec, K. Kůsová, I. Pelant, and P. Kužel, New J. Phys. 2014, 16, 093013; H. Němec, V. Zajac, P. Kužel, P. Malý, S. Gutsch, D. Hiller, and M. Zacharias, Phys. Rev. B 2015, 91, 195443.
[4] Z. Mics, H. Němec, I. Rychetský, P. Kužel, P. Formánek, P. Malý, and P. Němec, Phys. Rev. B 2011, 83, 155326.
[5] H. Němec, V. Zajac, I. Rychetský, D. Fattakhova-Rohlfing, B. Mandlmeier, T. Bein, Z. Mics, and P. Kužel, IEEE Trans. Terahertz Sci. Technol. 2013, 3, 302; H. Němec, Z. Mics, M. Kempa, P. Kužel, O. Hayden, Y. Liu, T. Bein, and D. Fattakhova-Rohlfing, J. Phys. Chem. C 2011, 115, 6968; J. Kuchařík, H. Sopha, M. Krbal, I. Rychetský, P. Kužel, J. M. Macak, and H. Němec, J. Phys. D: Appl. Phys. 2018, 51, 014004; H. Němec, J. Rochford, O. Taratula, E. Galoppini, P. Kužel, T. Polívka, A. Yartsev, and V. Sundström, Phys. Rev. Lett. 2010, 104, 197401.
[6] C. S. Ponseca, Jr., H. Němec, J. Wallentin, N. Anttu, J. P. Beech, A. Iqbal, M. Borgström, M.-E. Pistol, L. Samuelson, and A. Yartsev, Phys. Rev. B 2014, 90, 085405.
[7] K. Peters, P. Zeller, G. Štefanić, V. Skoromets, H. Němec, P. Kužel, and D. Fattakhova-Rohlfing, Chem. Mater. 2015, 27, 1090.
V. Skoromets, H. Němec, J. Kopeček, P. Kužel, K. Peters, D. Fattakhova-Rohlfing, A. Vetushka, M. Müller, K. Ganzerová, and A. Fejfar, J. Phys. Chem. C 2015, 119, 19485.