Franz-Keldysh Effect Research Articles

Pseudospins revealed through the giant dynamical Franz-Keldysh effect in massless Dirac materials

The dynamical Franz-Keldysh effect, indicative of the transient light-matter interaction regime between quantum and classical realms, is widely recognized as an essential signature in wide bandgap condensed matter systems such as dielectrics. In this theoretical study, we applied time-resolved transient absorption spectroscopy to investigate ultrafast optical responses in graphene, a zero-bandgap system. We observed in the gate-tuned graphene that the massless Dirac materials notably enhance intraband light-driven transitions, significantly leading to the giant dynamical Franz-Keldysh effect compared to the massive Dirac materials, a wide bandgap system. In addition, employing the angle-resolved spectroscopy, it is found that the unique polarimetry orientation, i.e., perpendicular polarizations for the pump and the probe, further pronounces the optical spectra to exhibit the complete fishbone structure, reflecting quantum pseudospin natures of Dirac cones. Our findings expand the establishment of emergent transient spectroscopy frameworks into not only zero-bandgap systems but also pseudospin-mediated quantum phenomena, moving beyond dielectrics.

Behavior of defects in GaN avalanche photodiodes grown on GaN substrates

GaN avalanche photodiodes grown on GaN substrates were successfully fabricated. These devices displayed a low dark current, measuring <80 pA at a reverse bias of 82.0 V. Notably, the response spectrum of the devices showed new out-of-band response peaks with increasing reverse bias. Moreover, at high reverse bias, the devices emitted visible light. These phenomena were attributed to inherent defects within the materials. The defect level fitted from the tunneling currents closely matched the experimental value, indicating that the defect-assisted tunneling effect, with a defect level at 0.127 eV relative to the conduction band, contributed to the out-of-band response peak in the response spectrum. The Franz–Keldysh effect led to a redshift in the response spectrum. Additionally, the Mg-related deep energy level situated approximately 0.498 eV above the valence band, facilitated radiative recombination at high reverse bias. Meanwhile, the device’s luminescent image displayed a consistently square shape, suggesting uniform avalanche breakdown throughout the device.

Influence of Franz Keldysh effect on the modulation depth and distortion characteristics of transistor laser

Influence of Franz Keldysh effect on the modulation depth and distortion characteristics of transistor laser

The Franz–Keldysh effect in the optical absorption spectrum of a TlGaSe2 layered semiconductor caused by charged native defects

The Franz–Keldysh effect in the optical absorption edge of a bulk TlGaSe2 layered semiconductor poled under an external electric field was investigated in the present work. The Franz–Keldysh shift below the optical bandgap absorption region, as well as the quasi-periodic oscillations above the fundamental bandgap of TlGaSe2, were observed. The measured changes in optical light absorption of the TlGaSe2 sample were revealed after poling processing. The poling technique is used to produce the built-in internal electric field within the TlGaSe2 semiconductor. The frozen-in internal electric field in TlGaSe2 was experimentally monitored through changes in the lineshape of the absorption spectra at the fundamental band edge. The observed results are accurately fitted with the theoretical lineshape function of the Franz–Keldysh absorption tail below the bandgap of TlGaSe2 and quasi-periodic oscillations above the bandgap. A good agreement between the theoretical and experimental results was observed. The present study demonstrated that the Franz–Keldysh effect can be used to identify and characterize the localized internal electric fields originating from electrically active native imperfections in the TlGaSe2 crystals.

Room-Temperature Self-Powered Infrared Spectrometer Based on a Single Black Phosphorus Heterojunction Diode.

Infrared spectrometers with the ability to resolve the spectral intensity and wavelength simultaneously are widely used in industry and the laboratory. However, their huge volume, high price, and cryogenic operating temperature limit their applications in the rapidly developing field of portable devices. Here, we demonstrate a room-temperature self-powered infrared spectrometer based on a single black phosphorus (BP) heterojunction diode. The nonlinearly gate-tunable photocurrent spectrum involving quantum-confined Franz-Keldysh and Burstein-Moss effects in a single BP/MoS2 diode instead of using space-consuming detector arrays provides a new dimension for resolving the intensity and wavelength information of spectra simultaneously. The active area for spectral sensing is only 1500 μm2, and the photodetection range is from 1.7 to 3.6 μm. Room-temperature operation, micrometer-scale size, and silicon-compatible technology make the BP/MoS2 heterojunction a promising configuration for portable spectrometer applications.

Dynamical Franz-Keldysh Effect in Diamond in the Deep Ultraviolet Probed by Transient Absorption and Dispersion Spectroscopy Using a Miniature Beamline.

Here, we introduce a miniature beamline for transient absorption and dispersion spectroscopy, using a tailored deep ultraviolet field immediately after the noncollinear generation without subsequent optical elements. We explore the near-band-gap region in diamond in the presence of a few-femtosecond pump pulse where the delayed dynamical Franz-Keldysh effect and the almost instantaneous optical Kerr effect coexist.

The Franz-Keldysh effect in silicon–ultrathin (3.7 nm) oxide–polysilicon structures

The manifestation of the Franz–Keldysh effect was discovered when illuminated by indirect daylight Al–n+-Si:P–SiO2–(100) n-Si structures with ultrathin (3.7 nm) oxide. It has been shown that the use of backlight even at low field voltages (up to 3 V) leads to an increase in the tunneling current through the oxide compared to the current in darkness by three orders of magnitude. A model of the influence of radiation on the process of electron tunneling through an ultrathin insulating layer has been constructed. At first as a result of the Franz–Keldysh effect, a radiation quantum is captured by an electron and this charge carrier tunnels through the barrier at a higher level compared to darkness. After a charge carrier enters a semiconductor, its energy is sufficient for several events of electron–hole pair production during impact ionization of silicon.

Floquet-Bloch resonances in near-petahertz electroabsorption spectroscopy of SiO2

Complex nonadiabatic dynamics are observed when the quiver energy of an electron-hole pair in a strong laser field becomes comparable to the photon energy. Here, the authors extend quasistatic electromodulation spectroscopy based on the Franz-Keldysh effect to this regime and show that in this limit it is governed by resonant transitions between Floquet-Bloch states. This regime opens opportunities to probe the effective mass as well as the ponderomotive and binding energies of the electron-hole pair on the attosecond timescale.

High-performance Ge/Si electro-absorption optical modulator up to 85°C and its highly efficient photodetector operation.

We studied a high-speed Ge/Si electro-absorption optical modulator (EAM) evanescently coupled with a Si waveguide of a lateral p-n junction for a high-bandwidth optical interconnect over a wide range of temperatures from 25 °C to 85 °C. We demonstrated 56 Gbps high-speed operation at temperatures up to 85 °C. From the photoluminescence spectra, we confirmed that the bandgap energy dependence on temperature is relatively small, which is consistent with the shift in the operation wavelengths with increasing temperature for a Ge/Si EAM. We also demonstrated that the same device operates as a high-speed and high-efficiency Ge photodetector with the Franz-Keldysh (F-K) and avalanche-multiplication effects. These results demonstrate that the Ge/Si stacked structure is promising for both high-performance optical modulators and photodetectors integrated on Si platforms.

First principle calculation of the photocurrent in a short carbon nanotube: the effect of an external bias

We studied the transport properties of a short carbon nanotube between two different metal electrodes. Specifically, the photocurrents under a series of bias voltages are investigated. The calculations are completed within the non-equilibrium Green’s function method, where the photon–electron interaction is taken as a perturbation. The rule-of-thumb that a forward bias decreases while a reverse bias increases the photocurrent under the same illumination is verified. The first principle results demonstrate the characteristic of the Franz–Keldysh effect, where the photocurrent response edge shows a clear red-shift trend in electric fields along both axial directions. An obvious Stark splitting is observed when some reverse bias is applied to the system due to the huge field strength. In this short-channel situation, intrinsic nanotube states are strongly hybridized with metal electrode states, which results in dark current leakage and specific features such as a long tail and fluctuations in the photocurrent response.

Effects of an external electric field on the electronic properties and optical excitations of germanane and silicane monolayers

Using density functional theory in conjunction with many-body perturbation theory, we theoretically investigated the electronic structures of monolayers germanane and silicane in an applied out-of-plane uniform electric field. Our results show that although the band structures of both monolayers are affected by the electric field, the band gap width cannot be reduced to zero even for high field-strengths. Moreover, excitons are shown to be robust under electric fields, so that Stark shifts for the fundamental exciton peak is only of the order of a few meV for fields of 1 V Å−1. The electric field has also no significant effect on electron probability distribution, as the exciton dissociation into free electron–hole pairs is not observed even at high electric field strengths. Franz-Keldysh effect is also studied in monolayers germanane and silicane. We found that, due to the shielding effect, the external field is prevented to induce absorption in the spectral region below the gap and only above-gap oscillatory spectral features are allowed. One can benefit from such a characteristic where the absorption near the band edge is not altered by the presence of an electric field, especially since these materials have excitonic peaks in the visible range.

Measuring Band Modulation of MoS2 with Ferroelectric Gates.

Electronic properties of two-dimensional (2D) materials can be significantly tuned by an external electric field. Ferroelectric gates can provide a strong polarization electric field. Here, we report the measurements of the band structure of few-layer MoS2 modulated by a ferroelectric P(VDF-TrFE) gate with contact-mode scanning tunneling spectroscopy. When P(VDF-TrFE) is fully polarized, an electric field up to ∼0.62 V/nm through the MoS2 layers is inferred from the measured band edges, which affects the band structure significantly. First, strong band bending in the vertical direction signifies the Franz-Keldysh effect and a large extension of the optical absorption edge. Photons with energy of half the band gap are still absorbed with 20% of the absorption probability of photons at the band gap. Second, the electric field greatly enlarges the energy separations between the quantum-well subbands. Our study intuitively demonstrates the great potential of ferroelectric gates in band structure manipulation of 2D materials.

Пленение излучения и субзонный пик в спектрах квантового выхода фотоэмиссии из p-GaAs(Cs,O)

In the spectra of the photoemission quantum yield of p-GaAs(Cs,O) measured in the reflection geometry, a peak was found at a photon energy lower than the band gap of GaAs. It is shown that the appearance of the peak is due to the trapping of weakly absorbed radiation, which scatters diffusely on the rough back face of the epitaxial structure. Possible microscopic mechanisms of the appearance of the peak are discussed: the Franz-Keldysh effect in the surface electric field and adsorption-modified optical transitions in cesium adatoms.

Light trapping and subbandgap maximum in photoemission quantum yield spectra of p-GaAs(Cs,O)

In the spectra of the photoemission quantum yield of p-GaAs(Cs,O) measured in the reflection geometry, a peak was found at a photon energy lower than the band gap of GaAs. It is shown that the appearance of the peak is due to the trapping of weakly absorbed radiation, which scatters diffusely on the rough back face of the epitaxial structure. Possible microscopic mechanisms of the appearance of the peak are discussed: the Franz-Keldysh effect in the surface electric field and adsorption-modified optical transitions in cesium adatoms. Keywords: photoemission, GaAs, negative electron affinity, quantum yield spectra.

Determination of band tail widths in MOCVD grown InGaN single layer within GaN based p-i-n LED structure through photo-induced measurements

Within a p-i-n LED structure, energy band gaps of MOCVD grown %10 In content InGaN and GaN layers were obtained through traditional UV–Visible transmission-absorption measurements and utilizing surface photovoltage (SPV) and spectral photoconductivity (SPC) measurements. Moreover, all applied techniques determined that the total band offset between InGaN and GaN layers were around 0.3–0.4 eV. Furthermore, the temperature dependence of band gaps of each InGaN and GaN layer was analyzed through a modified Varshni relation where both Varshni coefficients and band tail energy width were explored. Band tails in a modified Varshni relation, SPV and SPC measurements were in agreement with each other and originated Franz-Keldysh Effect attributed to the presence of photon assisted tunneling.

A Novel Hemispherical Retro-Modulator for Free-Space Optical Communication Links

We introduce a hemispherical retro-modulator in this work for use in passive free-space optical (FSO) communication links. It incorporates a high-refractive-index glass (S-LAH79) hemisphere for retroflection and a semi-insulating-InP (SI-InP) layer for modulation via electroabsorption. The electroabsorption is interpreted through a unified model of the Franz-Keldysh effect, on field-induced changes to absorption, and Einstein model, detailing band-edge characteristics of absorption. The model is fit to experimental data with good agreement and is used to optimize the SI-InP layer. The hemispherical retro-modulator is realized with a 600- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula> -thick SI-InP layer to give strong retroflection and modulation, at a depth of roughly 34%. Such operation can enable improved performance in passive FSO communication links.

Franz-Keldysh and Stark Effects in Two-Dimensional Metal Halide Perovskites

The established theory of a two-dimensional (2D) Wannier exciton in a uniform electric field is used to analyze the electroabsorption response of an archetypal 2D metal halide perovskite (MHP), phenethylammonium lead iodide. The high level of agreement between the electroabsorption simulation and measurement allows for a deepened understanding of the redshift of exciton energy, according to the quadratic Stark effect, and the continuum wave function leaking, according to the Franz-Keldysh effect. We find the field dependency of each of these effects to be rich with information, yielding measurements of the exciton Bohr radius, transition dipole moment, polarizability, and reduced effective mass of the exciton. Most importantly, the band-gap energy and exciton binding energy are unambiguously determined with 1σ variance of 4 meV. The high precision of these new measurement methods opens the opportunity for determining the influence of chemical and environmental factors on the optoelectronic properties of MHPs, which would enable the fabrication of highly efficient and reproducible light-harvesting and light-emitting optoelectronic devices.8 MoreReceived 21 September 2021Revised 22 December 2021Accepted 2 February 2022DOI:https://doi.org/10.1103/PRXEnergy.1.013001Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasStark effectPhysical SystemsPerovskitesQuantum wellsTechniquesOptical absorption spectroscopyCondensed Matter, Materials & Applied Physics

Band-edge absorption characteristics of semi-insulating indium phosphide under unified Franz-Keldysh and Einstein models

The foundational Franz-Keldysh effect and Einstein model are applied in this work to characterize semiconductor band-edge absorption---and its departures from ideality. We unify the Franz-Keldysh and Einstein models to fully characterize the field-induced tunneling of photoexcited electrons from degenerate valence bands into the conduction band, with encroachment into the band gap arising as an Urbach tail. Our unified model is implemented for semi-insulating indium phosphide (SI-InP) with strong agreement seen between the theoretical and experimental results for varied photon energies and electric fields.

A discussion on various experimental methods of impact ionization coefficient measurement in GaN

Impact ionization coefficients play a critical role in semiconductors. In addition to silicon, silicon carbide and gallium nitride are important semiconductors that are being seen more as mainstream semiconductor technologies. As a reflection of the maturity of these semiconductors, predictive modeling has become essential to device and circuit designers, and impact ionization coefficients play a key role here. Recently, several studies have measured impact ionization coefficients. We dedicated the first part of our study to comparing three experimental methods to estimate impact ionization coefficients in GaN, which are all based on photomultiplication but feature characteristic differences. The first method inserts an InGaN hole-injection layer, the accuracy of which is challenged by the dominance of ionization in InGaN, leading to possible overestimation of the coefficients. The second method utilizes the Franz–Keldysh effect for hole injection but not for electrons, where the mixed injection of induced carriers would require a margin of error. The third method uses complementary p–n and n–p structures that have been at the basis of this estimation in Si and SiC and leans on the assumption of a constant electric field, and any deviation would require a margin of error. In the second part of our study, we evaluated the models using recent experimental data from diodes demonstrating avalanche breakdown.

Linear bounded potential model for semiconductor band bending

We propose a simple but unexplored model for the semiconductor band bending with the aim to obtain a relatively simple expression to calculate the energy spectrum for the confined levels and the analytical expressions for wave-functions. This model consists of a linear potential but it is bounded or trimmed in energy unlike the well known wedge potential (WP) model. We present exact solutions for this potential in the frame of the effective mass approximation and they are valid for electron or hole confinement potential. This model provides a more adequate physical scenario than the WP since it takes into account the charge balance involved in the band bending potential. These results allow to treat confined potential problems as in the case of a two-dimensional electron gas in a simplified way. We discuss the application of this approximation to the recombination time of electrons an holes and for the Franz–Keldysh effect.