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Electron localization in CdS nanocrystals

Semiconductor nanocrystals exhibit a plethora of new electronic and optical phenomena owing to their increased surface to volume ratio and carrier confinement. However, the absence of a long-range crystal order fundamentally complicates the charge transport in nanocrystalline films. The underlying physics is very complex as it involves a chain of processes occurring on several different space and time scales.

We have investigated nanocrystalline films of cadmium sulfide (CdS) prepared by chemical bath deposition. In particular, we wish to contribute to the discussion of the long-lasting controversy that nanocrystalline films show the quantum confinement of charges, which is clearly apparent in the optical absorption and emission spectra, and, simultaneously, a long-range bulk-like transport in the electrical measurements. Results obtained by time-resolved terahertz (THz) spectroscopy lead to the following major conclusions:

Two length scales (nanocrystals and their clusters) control electron localization on the nanoscale
Electrons with high excess energy have higher mobility than electrons with low excess energy
The reduced mobility of electrons with low excess energy seems to originate from Coulombic interaction of electron with a localized hole

The spectra of transient conductivity in the THz spectral range are directly related to the nanostructure of the films (Fig. 1a). Firstly, electron localization in nanocrystals leads to a capacitive response characterized by an increasing real part of conductivity and negative imaginary part [1]. By a more detailed inspection we realize that the measured real part is concave above at least 0.4 THz (Fig. 1b) – this is a signature that there is a second length scale of electron localization, which we attribute to nanocrystal clusters seen in Fig. 1a [3]. A more detailed analysis based on Monte-Carlo calculations of conductivity spectra then allows quantitative determination of parameters of electron transport (Fig. 1c). Namely, we found that the probability of electron transport between NCs is rather high (~34%) which shows that the NCs within the cluster are closely packed together. Conversely, the probability of electron transport between NC clusters is much lower (~3%) which indicates that there is much lower contact area between NC clusters as these form a network filled by air pores.

Fig. 1. (a) Transmission-electron-microscope (TEM) image of the cross-section of a CdS film prepared by chemical bath deposition. (b) Example of normalized transient conductivity spectrum (excitation wavelength: 400 nm, pump-probe delay: 10 ps, excitation density: 0.58 photons/NC). Symbols: measured data, lines: calculations by Monte Carlo method [3]. (c) Scheme of the electron transport in the CdS nanocrystalline film (parameters shown are for electrons with low excess energy).

We measured a set of time-dependent conductivities for various excitation fluences. This allowed us to assess the mechanisms of the initial phases of electron transport on the nanoscale. Excitation by highly energetic photons (wavelength λ_exc = 400 nm) generates electrons with high initial excess energy. If the excitation density is very low (Fig. 2a), electrons lose their excess energy rapidly (τ_HL = 0.54 ps) and at the same time, their mobility decreases from μ_H = 96 cm²V⁻¹s⁻¹ down to μ_L = 34 cm²V⁻¹s⁻¹. This manifests itself as the rapid initial drop in the conductivity (Fig. 2e). However, for high excitation densities all electron states with low mobility μ_L are filled (Fig. 2b) which means that most electrons remain in the state with the high mobility μ_H – in turn, there is no ultrafast drop in the conductivity (Fig. 2e). The slower conductivity decay is attributed to either electron trapping (processes τ_LT and τ_HT) and electron recombination (processes B_L and B_H). This picture of electron energy and mobility relaxation is supported by the measurement using less energetic photons (wavelength λ_exc = 510 nm) which generate electrons with lower excess energy (Fig. 2c) – indeed, the amplitude of the initial rapid drop is reduced considerably.

Fig. 2. (a), (b), (c) Schemes illustrating the occupancy of the conduction-band states after photoexcitation (0 ps) and after the subsequent energy relaxation process (>1 ps) for various experimental conditions. (d) Scheme of the kinetic model of electron energy and mobility relaxation, trapping and recombination. (e) Time-dependent THz conductivities (curves are horizontally shifted for clarity; the signal rise for each curve corresponds to the pump-probe overlap). Symbols: measured data, lines: results of fits with kinetic model.

The last question concerns the origin of the potential barriers E_B which hinder the motion of electrons with low excess energy and which are not felt by electrons with the high excess energy. We believe that this barrier has a Coulombic origin, i.e., that a hole localized in one NC prevents the electron to escape to another NC. Indeed, the energy required to move an electron from the nanoparticle surface to infinity (when the hole is in the center of the NC) is

(1)

for NC radius r = 5 nm and CdS permittivity ε = 9. The estimated value is thus in a perfect agreement with the experimental result E_B = 33 meV. Furthermore, this expression predicts that the barrier energy should decrease with increasing NC radius, which is also confirmed by experiment. Finally, let’s note that a Coulombic interaction with a positive charge responsible for reduction of electron mobility was observed in dye-sensitized ZnO nanoparticles [2].

Related publications

[1]	Z. Mics, H. Němec, I. Rychetský, P. Kužel, P. Formánek, P. Malý, and P. Němec, Charge transport and localization in nanocrystalline CdS films: a time-resolved terahertz spectroscopy study, Phys. Rev. B 83, 15 5326 (2011).
[2]	H. Němec, J. Rochford, O. Taratula, E. Galoppini, P. Kužel, T. Polívka, A. Yartsev, and V. Sundström, Influence of the electron-cation interaction on electron mobility in dye-sensitized ZnO and TiO₂ nanocrystals: a study using ultrafast terahertz spectroscopy, Phys. Rev. Lett. 104, 19 7401 (2010).
[3]	H. Němec, P. Kužel, and V. Sundström, Far-infrared response of free charge carriers localized in semiconductor nanoparticles, Phys. Rev. B 79, 11 5309 (2009).