Electroabsorption in Semiconductors: The Excitonic Absorption Edge

Dow, John D.; Redfield, David

doi:10.1103/physrevb.1.3358

Cited by 421 publications

(169 citation statements)

References 40 publications

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“…The origin of the modulation is not completely understood [21][22][23]. Dow and Redfield [24,25] modified the classical FK effect for electron-hole interactions, although these results do not account for 1D quantum confinement in a nanotube. It is well known that the semiconducting SWNT have large exciton binding energies.…”

Section: Prl 102 047402 (2009) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

Unusually Large Franz-Keldysh Oscillations at Ultraviolet Wavelengths in Single-Walled Carbon Nanotubes

et al. 2009

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We report large electroabsorption susceptibilities in the ultraviolet region for single-walled carbon nanotubes (SWNT) supported on quartz that are approximately 10 3 larger than the highest values reported to date for any system. The oscillatory behavior is described using a convolution of Airy functions in photon energy ascribing the effect to Franz-Keldysh oscillations. The metallic and semiconducting SWNT composition is varied, and it is shown that the confinement energy correlates with the average band gap for semiconducting SWNT in the film. The large susceptibilities arise from a subpercolated network of metallic SWNT that enhances the local electric field. DOI: 10.1103/PhysRevLett.102.047402 PACS numbers: 78.67.Ch, 78.20.Jq, 78.40.Ri, 78.66.Tr Semiconducting single-walled carbon nanotubes (SWNT) have attracted significant attention recently due to many unique properties and the potential for new nanophotonic applications [1]. They possess sharp singularities in their density of states as a consequence of onedimensional (1D) quantum confinement leading to strong and discrete absorption maxima throughout the ultraviolet (UV), visible, and near-infrared (IR) regions of the electromagnetic spectrum [2,3]. This confinement also leads to theoretical predictions of large exciton binding energies, later confirmed using two photon photoluminescence spectroscopy [4,5]. Franz-Keldysh (FK) oscillations, in particular, are calculated [6] to be quite strong for semiconducting SWNT near the first and second band edge, a property of importance for electro-optical applications. In pioneering work several decades ago, Franz and Keldysh predicted that photo-excited electrons could tunnel into an otherwise classically forbidden energy gap under the influence of an electric field, modifying the linear optical properties of bulk semiconductors near the absorption band edge [7,8]. Modulation spectroscopy uses this effect experimentally to understand highly localized electric fields that develop at semiconductor interfaces [9,10]. Nanowires and nanotubes can amplify such fields manyfold by virtue of their geometry. Hence, there is interest in using phenomena such as the FK effect to understand how electric fields can be manipulated on the nanometer scale, although to date, no experimental observation of the effect has been reported for any of the carbon family of nanomaterials.In this Letter, we report the first observation of FK oscillations for semiconducting SWNT films supported on fused quartz substrates, although the effect is strongest for excitonic states much higher than those near the band edge. Electroabsorption susceptibilities in the UV region are more than 10 3 larger than the highest values reported for typical semiconductor systems, such as III-V semiconductors [9] and semiconductor-doped glasses [11]. We make use of recent progress [12] in the enrichment of metallic and semiconducting SWNT to show that the confinement energy correlates with the average band gap for semiconducting SWNT in the film. The unusua...

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Section: Prl 102 047402 (2009) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

Unusually Large Franz-Keldysh Oscillations at Ultraviolet Wavelengths in Single-Walled Carbon Nanotubes

et al. 2009

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“…As stated before, no analytical solution exists for the Schrödinger equation of a Wannier exciton in an electric field, and excitonic electroabsorption theories rely on two different approaches: they either resort to approximations (for example to model the external potential) to go back to an analytically solvable problem [37,38] or focus on the development of numerical resolution routines. [26,36,[39][40][41][42] …”

Section: Eas Of Molecules or Confined Excitonic Statesmentioning

confidence: 99%

Unveiling the Nature of Charge Carrier Interactions by Electroabsorption Spectroscopy: An Illustration with Lead-Halide Perovskites

Bouduban

Burgos‐Caminal

Teuscher

et al. 2017

Chimia

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Unravelling the nature of the interactions between photogenerated charge carriers in solar energy conversion devices is key to enhance performance. In this perspective, we discuss electroabsorption spectroscopy (EAS), as the spectral bandshape of the electroabsorption (EA) signal directly depends on the strength of the charge carrier interactions. For instance, the electroabsorption response in molecular or confined excitonic systems can be modelled perturbatively yielding the Stark effect. In contrast, most solids exhibit weaker interactions, and a perturbative approach cannot be taken in general. For solids with negligible charge carrier interactions, one resorts to the Franz-Keldysh theory of a continuum in a field, that, in the low-field limit, simplifies to the low-field FKA effect. Alternatively, when the continuum approximation breaks down, the problem of a Wannier exciton in a field has to be solved, and numerical methods emerged as the best solution. We illustrate our discussion with two examples involving lead-halide perovskites, a new, high-stake solar cell material. In the first example, we discuss the lineshape of the electroabsorption response for thin-films of lead-iodide perovskite, that sustains the photogeneration of free carriers. In the second example, we address a confined excitonic case with lead-bromide perovskite nanoparticles, and demonstrate the presence of so-called charge-transfer excitons.

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“…The optical width E decreases more rapidly than would be expected by the expression (9). Obviously, the cause of this effect is absorption of light on free carriers.…”

Section: Optical Bandwidth Of the Forbidden Band In Non-crystalline Smentioning

confidence: 69%

“…(c) The theory of the exciton line broadening by an electric field. Dow and Redfield [9] investigated the problem of absorption in a direct transition of exciton in a homogenous electric field. They pointed out that the tail shape is exponential.…”

Section: Introductionmentioning

confidence: 99%

An explanation of optical phenomena in non-crystalline semiconductors

Banik

2005

Open Physics

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Barrier model of a non-crystalline semiconductor is described in this article. The most important optical phenomena, which are typical for this group of materials, are explained on the base of this model. The model assumes that in non-crystalline semiconductors the potential barriers exist, which separate certain microscopic areas from each other, assuming barriers possess a parabolic profile. This conception explains the rise of exponential tails of optical absorption at the end of optical edge as well as electroabsorption, photoelectric conductivity, photoluminescence, and others. Using this model, many electric transport properties of non-crystalline semiconductors can be explained successfully.

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Electroabsorption in Semiconductors: The Excitonic Absorption Edge

Cited by 421 publications

References 40 publications

Unusually Large Franz-Keldysh Oscillations at Ultraviolet Wavelengths in Single-Walled Carbon Nanotubes

Unusually Large Franz-Keldysh Oscillations at Ultraviolet Wavelengths in Single-Walled Carbon Nanotubes

Unveiling the Nature of Charge Carrier Interactions by Electroabsorption Spectroscopy: An Illustration with Lead-Halide Perovskites

An explanation of optical phenomena in non-crystalline semiconductors

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