Microscopic origin of the Drude-Smith model

Cocker, Tyler L.; Baillie, Devin; Buruma, M.; Titova, Lyubov V.; Sydora, R. D.; Marsiglio, F.; Hegmann, Frank A.

doi:10.1103/physrevb.96.205439

Cited by 160 publications

(186 citation statements)

References 96 publications

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“…The semiclassical formula still agrees quite well with the Monte-Carlo result (position of the resonance and its amplitude). Note that this condition is not obvious from the classical derivation of the modified Drude-Smith model [85] while it clearly appears if derived from the full quantum model. The modified Drude-Smith model starts to disagree significantly with the principal shape of the mobility spectrum; this is because its validity is limited by the condition τ th ≫ τ′ (the charge carrier should be scattered several times during its round-trip in the NC) and this is no more fulfilled in 32 nm-sized crystal: τ th ≈ 0.3τ′ for d = 32 nm and τ th ≈ 10τ′ for d = 1024 nm.…”

Section: Discussionmentioning

confidence: 99%

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Terahertz Spectroscopy of Nanomaterials: a Close Look at Charge‐Carrier Transport

Kužel

Němec

2019

Advanced Optical Materials

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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 nanosized elements, which inevitably involve a multitude of charge transport processes occurring on various time-and length-scales. Figure 1 summarizes the most common nanoelements with high application potential.For example, the electrodes employed in Grätzel solar cells [1] are composed of percolated networks of a huge number of metal oxide nanoparticles (top-left panel in Figure 1). Colloidal nanocrystals form the basis for thin film electronics and flexible electronic devices. [2] The synthetic approaches control their composition, size and electronic structure (energy levels, density of states within the bands and in the bandgap) and the charge-carrier transport. [2,3] Nanowires and nanotubes made of conventional semiconductors are quasi 1D systems combining Terahertz spectroscopy has been used for almost two decades for investigations of nanomaterials, including nanocrystals, nanoparticles, nanowires, nanotubes or 2D crystals. Its great importance stems from the fact that it is a noncontact method and, owing to its high frequency and broadband character, it is capable of characterizing charge transport properties within individual nano-objects but also among them. In addition, probing of photoinitiated ultrafast charge dynamics is possible thanks to the sub-picosecond time resolution. Despite this unprecedented potential, the interpretation of the measured terahertz conductivity spectra in many materials is still intensively debated. Herein is presented a review of the experiments performed on nanostructures of conventional semiconductors and on carbon nanomaterials (graphene and carbon nanotubes) during the past decade. The state of the art of the theoretical formalism is provided and discussed, including the intrinsic response, as well as the role of inherent heterogeneity and of the experimental conditions.

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Section: Discussionmentioning

confidence: 99%

“…[85] that the low-frequency decrease of the confined carriers mobility-and thus the Drude-Smith-like term in parentheses at the right-hand-side of (12)-finds its origin in the diffusion-restoring current in systems without the translational invariance. Indeed, it has been argued in ref.…”

Section: Simple Closed-form Models Of Carrier Mobilitymentioning

confidence: 99%

Terahertz Spectroscopy of Nanomaterials: a Close Look at Charge‐Carrier Transport

Kužel

Němec

2019

Advanced Optical Materials

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“…Finally, a much slower component that we attribute to free carrier recom bination decays over >250 ps. In general, the complex conductivity (σ ) of both of these samples can be described by Equation (2), (also known as the Drude-Smith model), where N is the charge carrier density, m* is the effective carrier mass, τ DS is the effective scattering time, and the cparameter character izes the degree of carrier localization due to the presence of boundaries [50,[52][53][54][55][56][57][58][59][60] σ ω τ ωτ ωτ However, while ≈250 ps is the lower limit of the photoexcited carrier lifetime, the radiative lifetime of ≈1.3 ns determined by TRPL is the upper limit.…”

Section: Characterization Of Structural and Optoelectronic Propertiesmentioning

confidence: 99%

Balancing Light Absorption and Charge Transport in Vertical SnS₂ Nanoflake Photoanodes with Stepped Layers and Large Intrinsic Mobility

Giri

Masroor

Yan

et al. 2019

Advanced Energy Materials

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Significant optical absorption in the blue–green spectral range, high intralayer carrier mobility, and band alignment suitable for water splitting suggest tin disulfide (SnS2) as a candidate material for photo‐electrochemical applications. In this work, vertically aligned SnS2 nanoflakes are synthesized directly on transparent conductive substrates using a scalable close space sublimation (CSS) method. Detailed characterization by time‐resolved terahertz and time‐resolved photoluminescence spectroscopies reveals a high intrinsic carrier mobility of 330 cm2 V−1 s−1 and photoexcited carrier lifetimes of 1.3 ns in these nanoflakes, resulting in a long vertical diffusion length of ≈1 µm. The highest photo‐electrochemical performance is achieved by growing SnS2 nanoflakes with heights that are between this diffusion length and the optical absorption depth of ≈2 µm, which balances the competing requirements of charge transport and light absorption. Moreover, the unique stepped morphology of these CSS‐grown nanoflakes improves photocurrent by exposing multiple edge sites in every nanoflake. The optimized vertical SnS2 nanoflake photoanodes produce record photocurrents of 4.5 mA cm−2 for oxidation of a sulfite hole scavenger and 2.6 mA cm−2 for water oxidation without any hole scavenger, both at 1.23 VRHE in neutral electrolyte under simulated AM1.5G sunlight, and stable photocurrents for iodide oxidation in acidic electrolyte.

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“…However, the exact physical meaning of the parameter C 1 is ambiguous, because it introduces an additional average estimate on carrier scattering probability, which has already been described by the scattering time t in the original Drude term. 62 Both the LMD model and the DS model base the optical conductivity on a conductive free charge carrier term (the Drude term, dashed lines in Fig. 1) that is suppressed by modification terms based on negative-amplitude oscillators.…”

Section: Previous Modifications Of the Drude Model Applied To Ecpsmentioning

confidence: 99%

On the anomalous optical conductivity dispersion of electrically conducting polymers: ultra-wide spectral range ellipsometry combined with a Drude–Lorentz model

et al. 2019

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Electrically conducting polymers (ECPs) are becoming increasingly important in areas such as optoelectronics, biomedical devices, and energy systems. Still, their detailed charge transport properties produce an anomalous optical conductivity dispersion that is not yet fully understood in terms of physical model equations for the broad range optical response. Several modifications to the classical Drude model have been proposed to account for a strong non-Drude behavior from terahertz (THz) to infrared (IR) ranges, typically by implementing negative amplitude oscillator functions to the model dielectric function that effectively reduce the conductivity in those ranges. Here we present an alternative description that modifies the Drude model via addition of positive-amplitude Lorentz oscillator functions. We evaluate this so-called Drude-Lorentz (DL) model based on the first ultra-wide spectral range ellipsometry study of ECPs, spanning over four orders of magnitude: from 0.41 meV in the THz range to 5.90 eV in the ultraviolet range, using thin films of poly(3,4-ethylenedioxythiophene):tosylate (PEDOT:Tos) as a model system. The model could accurately fit the experimental data in the whole ultrawide spectral range and provide the complex anisotropic optical conductivity of the material. Examining the resonance frequencies and widths of the Lorentz oscillators reveals that both spectrally narrow vibrational resonances and broader resonances due to localization processes contribute significantly to the deviation from the Drude optical conductivity dispersion. As verified by independent electrical measurements, the DL model accurately determines the electrical properties of the thin film, including DC conductivity, charge density, and (anisotropic) mobility. The ellipsometric method combined with the DL model may thereby become an effective and reliable tool in determining both optical and electrical properties of ECPs, indicating its future potential as a contact-free alternative to traditional electrical characterization.Fig. 4 (a) In-plane real optical conductivity dispersion of PEDOT:Tos represented by multiple Lorentz oscillators (the Drude contributions are removed) derived from the DL model. (b) The contributions of the real optical conductivity from THz (blue curve), broad oscillators (brown curve), interband transitions (green curve), and molecular vibrations (grey curves) are indicated. (c and d) Display the amplitude and broadening parameters for each Lorentz oscillator as well as their resonance energy (frequency).Their out-of-plane counterparts are shown in Fig. S10 (ESI †). The parameters for these Lorentz oscillators are listed in Table S2 (ESI †).

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Microscopic origin of the Drude-Smith model

Cited by 160 publications

References 96 publications

Terahertz Spectroscopy of Nanomaterials: a Close Look at Charge‐Carrier Transport

Terahertz Spectroscopy of Nanomaterials: a Close Look at Charge‐Carrier Transport

Balancing Light Absorption and Charge Transport in Vertical SnS₂ Nanoflake Photoanodes with Stepped Layers and Large Intrinsic Mobility

On the anomalous optical conductivity dispersion of electrically conducting polymers: ultra-wide spectral range ellipsometry combined with a Drude–Lorentz model

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Microscopic origin of the Drude-Smith model

Cited by 160 publications

References 96 publications

Terahertz Spectroscopy of Nanomaterials: a Close Look at Charge‐Carrier Transport

Terahertz Spectroscopy of Nanomaterials: a Close Look at Charge‐Carrier Transport

Balancing Light Absorption and Charge Transport in Vertical SnS2 Nanoflake Photoanodes with Stepped Layers and Large Intrinsic Mobility

On the anomalous optical conductivity dispersion of electrically conducting polymers: ultra-wide spectral range ellipsometry combined with a Drude–Lorentz model

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Balancing Light Absorption and Charge Transport in Vertical SnS₂ Nanoflake Photoanodes with Stepped Layers and Large Intrinsic Mobility