Hopping transport on a fractal: ac conductivity of porous silicon

Universality of the Förster’s model for resonant exciton transfer in ensembles of nanocrystals

For nanocrystals in a strong quantum confinement regime, it has been confirmed analytically that resonant exciton transfer proceeds in full accordance with the Förster mechanism. This means that the virtual exciton transitions between the nanocrystals of close sizes are governed only by the dipole–dipole interaction of nanocrystals even in very dense ensembles, while the contributions of all other higher-order multipoles are negligibly small. Based on a simple isotropic model of the envelope function approximation and neglecting the electron–hole interaction inside each nanocrystal, we have computed the rate of the resonant exciton transfer between two nanocrystals. Using the obtained result, we have estimated, for some arbitrarily chosen nanocrystal, the total rate of the exciton non-radiative annihilation caused by the possibility of its resonant virtual transitions into all other nanocrystals of the ensemble. The total rate dependence on the nanocrystal size is determined only by the size distribution function of nanocrystals in the ensemble.

Exciton-Photon Interactions in Semiconductor Nanocrystals: Radiative Transitions, Non-Radiative Processes and Environment Effects

In this review, we discuss several fundamental processes taking place in semiconductor nanocrystals (quantum dots (QDs)) when their electron subsystem interacts with electromagnetic (EM) radiation. The physical phenomena of light emission and EM energy transfer from a QD exciton to other electronic systems such as neighbouring nanocrystals and polarisable 3D (semi-infinite dielectric or metal) and 2D (graphene) materials are considered. In particular, emission decay and FRET rates near a plane interface between two dielectrics or a dielectric and a metal are discussed and their dependence upon relevant parameters is demonstrated. The cases of direct (II–VI) and indirect (silicon) band gap semiconductors are compared. We cover the relevant non-radiative mechanisms such as the Auger process, electron capture on dangling bonds and interaction with phonons. Some further effects, such as multiple exciton generation, are also discussed. The emphasis is on explaining the underlying physics and illustrating it with calculated and experimental results in a comprehensive, tutorial manner.

Porous Si Partially Filled with Water Molecules-Crystal Structure, Energy Bands and Optical Properties from First Principles

The paper reports the results on first-principles investigation of energy band spectrum and optical properties of bulk and nanoporous silicon. We present the evolution of energy band-gap, refractive indices and extinction coefficients going from the bulk Si of cubic symmetry to porous Si with periodically ordered square-shaped pores of 7.34, 11.26 and 15.40 Å width. We consider two natural processes observed in practice, the hydroxylation of Si pores (introduction of OH groups into pores) and the penetration of water molecules into Si pores, as well as their impact on the electronic spectrum and optical properties of Si superstructures. The penetration of OH groups into the pores of the smallest 7.34 Å width causes a disintegration of hydroxyl groups and forms non-bonded protons which might be a reason for proton conductivity of porous Si. The porosity of silicon increases the extinction coefficient, k, in the visible range of the spectrum. The water structuring in pores of various diameters is analysed in detail. By using the bond valence sum approach we demonstrate that the types and geometry of most of hydrogen bonds created within the pores manifest a structural evolution from distorted hydrogen bonds inherent to small pores (∼7 Å) to typical hydrogen bonds observed by us in larger pores (∼15 Å) which are consistent with those observed in a wide database of inorganic crystals.

Metal-Insulator Transition in Nanoparticle Solids: Insights from Kinetic Monte Carlo Simulations

Progress has been rapid in increasing the efficiency of energy conversion in nanoparticles. However, extraction of the photo-generated charge carriers remains challenging. Encouragingly, the charge mobility has been improved recently by driving nanoparticle (NP) films across the metal-insulator transition (MIT). To simulate MIT in NP films, we developed a hierarchical Kinetic Monte Carlo transport model. Electrons transfer between neighboring NPs via activated hopping when the NP energies differ by more than an overlap energy, but transfer by a non-activated quantum delocalization, if the NP energies are closer than the overlap energy. As the overlap energy increases, emerging percolating clusters support a metallic transport across the entire film. We simulated the evolution of the temperature-dependent electron mobility. We analyzed our data in terms of two candidate models of the MIT: (a) as a Quantum Critical Transition, signaled by an effective gap going to zero; and (b) as a Quantum Percolation Transition, where a sample-spanning metallic percolation path is formed as the fraction of the hopping bonds in the transport paths is going to zero. We found that the Quantum Percolation Transition theory provides a better description of the MIT. We also observed an anomalously low gap region next to the MIT. We discuss the relevance of our results in the light of recent experimental measurements.

Carbon black networking in elastomers monitored by simultaneous rheological and dielectric investigations

The rheo-dielectric response of carbon black filled elastomer melts is investigated by dielectric relaxation spectroscopy in the frequency range from 0.1 Hz up to 10 MHz during oszillatory shearing in a plate-plate rheometer. Various concentrations and types of carbon blacks dispersed in a non-crosslinked EPDM melt are considered. It is demonstrated that during heat treatment at low strain amplitude a pronounced flocculation of filler particles takes place leading to a successive increase of the shear modulus and conductivity. Followed up by a strain sweep, the filler network breaks up and both quantities decrease simultaneously with increasing strain amplitude. Two relaxation times, obtained from a Cole-Cole fit of the dielectric spectra, are identified, which both decrease strongly with increasing flocculation time. This behaviour is analyzed in the frame of fractal network models, describing the effect of structural disorder of the conducting carbon black network on the diffusive charge transport. Significant deviations from the predictions of percolation theory are observed, which are traced back to a superimposed cluster-cluster aggregation process (CCA). During flocculation, a universal scaling behaviour holds between the conductivity and the corresponding high frequency relaxation time, which fits all the measured data. The scaling exponent agrees fairly well with the prediction obtained from CCA. It is demonstrated that the underlying basic mechanism is a change of the correlation length of the filler network, i.e. the size of the fractal heterogeneities. This decreases during flocculation due to the formation of additional conductive paths, making the system more homogeneous. An addition less pronounced effect is found from nanoscopic gaps between adjacent filler particles, which decrease during flocculation. The same universal scaling behaviour, as obtained for flocculation, is found for temperature-dependent dielectric measurements of the cured crosslinked systems, which are heated from room temperature up to 200 °C. Thereby, the conductivity decreases significantly and the relaxation time increases, indicating that the filler network breaks up randomly due to the thermal expansion of the rubber matrix.

Dielectric properties of porous silicon for use as a substrate for the on-chip integration of millimeter-wave devices in the frequency range 140 to 210 GHz

In this work, the dielectric properties of porous Si for its use as a local substrate material for the integration on the Si wafer of millimeter-wave devices were investigated in the frequency range 140 to 210 GHz. Broadband electrical characterization of coplanar waveguide transmission lines (CPW TLines), formed on the porous Si layer, was used in this respect. It was shown that the dielectric parameters of porous Si (dielectric permittivity and loss tangent) in the above frequency range have values similar to those obtained at lower frequencies (1 to 40 GHz). More specifically, for the samples used, the obtained values were approximately 3.12 ± 0.05 and 0.023 ± 0.005, respectively. Finally, a comparison was made between the performance of the CPW TLines on a 150-μm-thick porous Si layer and on three other radiofrequency (RF) substrates, namely, on trap-rich high-resistivity Si (trap-rich HR Si), on a standard complementary metal-oxide-semiconductor (CMOS) Si wafer (p-type, resistivity 1 to 10 Ω.cm) and on quartz.

PACS

84.40.-x; 77.22.Ch; 81.05.Rm.

High-yield preparation of blue-emitting colloidal Si nanocrystals by selective laser ablation of porous silicon in liquid

We demonstrate the higher-yield (one order of magnitude) preparation of blue-emitting colloidal Si nanocrystals with a diameter range of 1-3 nm by selective laser ablation of porous Si powder in an organic solution, compared with the ablation of bulk Si powder. This increase in yield is the result of the lower thermal conductivity and the larger surface area of porous Si. The prepared colloidal Si nanocrystal exhibits size-dependent, higher-lying bandgap energies and large radiative decay rates as a result of the quantum confinement effect. Reversible luminescence color change from blue to yellow and vice versa in the colloidal Si nanocrystal film is also observed, and this is attributed to the non-radiative inter-crystal energy transfer.

Thermal conductivity of highly porous Si in the temperature range 4.2 to 20 K

We report on experimental results of the thermal conductivity k of highly porous Si in the temperature range 4.2 to 20 K, obtained using the direct current (dc) method combined with thermal finite element simulations. The reported results are the first in the literature for this temperature range. It was found that porous Si thermal conductivity at these temperatures shows a plateau-like temperature dependence similar to that obtained in glasses, with a constant k value as low as 0.04 W/m.K. This behavior is attributed to the presence of a majority of non-propagating vibrational modes, resulting from the nanoscale fractal structure of the material. By examining the fractal geometry of porous Si and its fractal dimensionality, which was smaller than two for the specific porous Si material used, we propose that a band of fractons (the localized vibrational excitations of a fractal lattice) is responsible for the observed plateau. The above results complement previous results by the authors in the temperature range 20 to 350 K. In this temperature range, a monotonic increase of k with temperature is observed, fitted with simplified classical models. The extremely low thermal conductivity of porous Si, especially at cryogenic temperatures, makes this material an excellent substrate for Si-integrated microcooling devices (micro-coldplate).

PACS

61.43.-j; 63.22.-m; 65.8.-g.

Electric conductivity percolation in naturally dehydrating, lightly wetted, hydrophilic fumed silica powder

In studying the dehydration of surface-moistened fumed silica Aerosil powders, we found a conductivity percolation transition at low hydration levels. Both the percolation exponent and the threshold are typical for correlated site-bond transitions in complex two-dimensional (2D) systems. The exponent values, 0.94-1.10, are indicative of severe heterogeneity in the conducting medium. The surface moisture at the percolation threshold takes on a universal value of 0.65 mg([H2O])/m(2)([silica]), independent of the silica grain size, and equivalent to twice the first hydration monolayer. This level is just sufficient to sustain a quasi-2D, hydrogen-bonded water network spanning the silica surface.

Non-oxidized porous silicon-based power AC switch peripheries

We present in this paper a novel application of porous silicon (PS) for low-power alternating current (AC) switches such as triode alternating current devices (TRIACs) frequently used to control small appliances (fridge, vacuum cleaner, washing machine, coffee makers, etc.). More precisely, it seems possible to benefit from the PS electrical insulation properties to ensure the OFF state of the device. Based on the technological aspects of the most commonly used AC switch peripheries physically responsible of the TRIAC blocking performances (leakage current and breakdown voltage), we suggest to isolate upper and lower junctions through the addition of a PS layer anodically etched from existing AC switch diffusion profiles. Then, we comment the voltage capability of practical samples emanating from the proposed architecture. Thanks to the characterization results of simple Al-PS-Si(P) structures, the experimental observations are interpreted, thus opening new outlooks in the field of AC switch peripheries.

RF performances of inductors integrated on localized p+-type porous silicon regions

To study the influence of localized porous silicon regions on radiofrequency performances of passive devices, inductors were integrated on localized porous silicon regions, full porous silicon sheet, bulk silicon and glass substrates. In this work, a novel strong, resistant fluoropolymer mask is introduced to localize the porous silicon on the silicon wafer. Then, the quality factors and resonant frequencies obtained with the different substrates are presented. A first comparison is done between the performances of inductors integrated on same-thickness localized and full porous silicon sheet layers. The effect of the silicon regions in the decrease of performances of localized porous silicon is discussed. Then, the study shows that the localized porous silicon substrate significantly reduces losses in comparison with high-resistivity silicon or highly doped silicon bulks. These results are promising for the integration of both passive and active devices on the same silicon/porous silicon hybrid substrate.

Study of thioflavin-T immobilized in porous silicon and the effect of different organic vapors on the fluorescence lifetime

Steady-state and time-resolved emission techniques have been employed to study the fluorescence properties of thioflavin-T (ThT) adsorbed on oxidized porous silicon (PSi) surfaces, with an average pore size of ∼10 nm. We found that the average fluorescence decay time of ThT, when it is adsorbed on the PSi surface, is rather long, τ(av) = 1.3 ns. We attribute this relatively long emission lifetime to the effect of the immobilization of ThT on the PSi surface, which inhibit the rotation of the aniline with respect to the benzothiazole moieties of ThT. We also measured the fluorescence properties of ThT in PSi samples in equilibrium with vapors of several liquids, such as methanol, acetonitrile, and water. We found that the fluorescence intensity drops by a factor of 10, and the average decay time, measured by a time-correlated single-photon counting technique, decreases by a factor of 3. We explain these results in terms of liquid condensation of the vapors in the PSi pores, which leads to partial dissolution of the ThT molecules in the liquid pools.

Electrical transport in porous silicon from improved complex impedance analysis

An improved analysis of the electrical transport parameters in meso-porous silicon is presented. Our approach is based on a separate contribution of the crystallites and their interconnections to the total impedance of meso-porous silicon layers. Meso-porous silicon morphology exhibits a columnar structure without quantum confinement. The electrical conduction is thus, partially due to the bulk conductivity within continuous paths of crystallites. The samples were realized on 0.02ω-cm p-type Si substrates. Porous silicon layers of 100µm of thickness and 50% of porosity were inserted in Al/SiO2/porous-Si/Si structures. Their electronic transport parameters were determined using complex impedance measurements. A frequency range of 102 - 107 Hz was used allowing an accurate determination of the impedance components. Combined with thermal stimulation, theses measurements provide a powerful tool for the interpretation of basic properties such as the carriers density in the crystallites and the trapping mechanisms. Our results were interpreted in terms of free carriers conduction in partially compensated crystallites prevailing at low frequencies. At high frequencies (above 10 kHz), the electrical conductivity is mainly controlled by hopping transport on localized states in the chaotic porous structure. Finally, the free carriers mobility, evaluated from SCLC measurement is discussed.

Electron Time-of-Flight Measurements in Porous Silicon

Transient photocurrent measurements are reported in an electroluminescent porous silicon diode. Electron drift mobilities are obtained from the data as a function of temperature. Electron transport is dispersive, with a typical dispersion parameter α≈ 0.5. The range of mobilities is 10−5 − 10−4 cm2Vs between 225 K amd 400 K. This temperature-dependence is much less than expected for multiple-trapping models for dispersion, and suggests that a fractal structure causes the dispersion and the small mobilities.