Franz Keldysh Research Articles

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.

Characterization of surface electric field in β-FeSi2 by Franz–Keldysh oscillations

The surface electric field (F) of β-FeSi2 has been investigated by Franz–Keldysh oscillations (FKOs) observed in photoreflectance spectra. The FKO signals were observed in an undoped β-FeSi2 epitaxial layer (3 nm) grown on p+-type β-FeSi2 layers (UP+ structure) by molecular beam epitaxy. The surface electric field obtained from the FKO at 11 K was F = 220 kV/cm. The surface electric field was almost independent of the excitation light power and temperature, showing that the surface electric field was not affected by the surface photovoltage effect. In the dependence of F on the thickness of the undoped layer (d), F was nearly constant at d = 2–56 nm. The result showed that the surface electric field of β-FeSi2 was applied to a thin region (&amp;lt;2 nm) at the surface.

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

Onset of Quantum-Confined Stark Effects in Multijunction Photovoltaic Laser Power Converters Designed with Thin Subcells

Photovoltaic multijunction power-converting III–V semiconductor devices generate electrical power from the optical energy of laser beams. They exhibit conversion efficiencies reaching values greater than 60% and 50% for the GaAs and the InP material systems, respectively. The applications of optical wireless power transmission and power-over-fiber greatly benefit from employing such laser power converters constructed with multiple subcells; each is designed with either thin GaAs or InGaAs absorber regions. This study elucidates how the application of electric fields on thin heterostructures can create specific current–voltage characteristics due to modifications of the absorption characteristics from Franz–Keldysh perturbations and the onset of quantum-confined Stark effects. Negative differential photocurrent behavior can be observed as the reverse bias voltage is increased, until the corresponding current-clamping subcell reaches its reverse breakdown condition. The reverse voltage breakdown characteristics of the subcells were also measured to depend on the thickness of the subcell and on the optical intensity. The onset of the reverse breakdown was found to be at ~2.0–2.5 V under illumination and the thinner subcells exhibited higher levels of reverse bias currents. These effects can produce distinctive current–voltage behavior under spectrally detuned operations affecting the thinner subcells’ biases, but have no significant impact on the performance and maximum power point of multijunction power converters.

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.

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.

Influence of interface states on built-in electric field and diamagnetic-Landau energy shifts in asymmetric modulation-doped InGaAs/GaAs QWs

The impact of interface defect states on the recombination and transport properties of charges in asymmetric modulation-doped InGaAs/GaAs quantum wells (QWs) is investigated. Three sets of high-mobility InGaAs QW structures are systematically designed and grown by the metal-organic vapor phase epitaxy technique to probe the effect of carrier localization on the electro-optical processes. In these structures, a built-in electric field drifts electrons and holes towards the opposite hetero-junctions of the QW, where their capture/recapture processes are assessed by temperature-dependent photoreflectance, photoluminescence, and photoconductivity measurements. The strength of the electric field in the structures is estimated from the Franz Keldysh oscillations observed in the photoreflectance spectra. The effects of the charge carrier localization at the interfaces lead to a reduction of the net electric field at a low temperature. Given this, the magnetic field is used to re-distribute the charge carriers and help in suppressing the effect of interface defect states, which results in a simultaneous increase in luminescence and photoconductivity signals. The in-plane confinement of charge carriers in QW by the applied magnetic field is therefore used to compensate the localization effects caused due to the built-in electric field. Subsequently, it is proposed that under the presence of large interface defect states, a magnetic field-driven diamagnetic-Landau shift can be used to estimate the fundamental parameters of charge carriers from the magneto-photoconductivity spectra instead of magneto-photoluminescence spectra. The present investigation would be beneficial for the development of high mobility optoelectronic and spin photonic devices in the field of nano-technology.

Damping of the Franz–Keldysh oscillations in the presence of disorder

Franz–Keldysh oscillations of the optical absorption in the presence of short-range disorder are studied theoretically. The magnitude of the effect depends on the relation between the mean-free path in a zero field and the distance between the turning points in electric field. As is adopted in the literature, turning points are the points where the net energy is equal to potential energy. Damping of the Franz–Keldysh oscillations by the disorder develops at high absorption frequency. Effect of damping is amplified by the fact that, that electron and hole are most sensitive to the disorder near the turning points. This is because, near the turning points, velocities of electron and hole turn to zero.

Sub-bandgap refractive indexes and optical properties of Si-doped β-Ga2O3 semiconductor thin films

In this article, we present a theoretical study on the sub-bandgap refractive indexes and optical properties of Si-doped β-Ga2O3 thin films based on newly developed models. The measured sub-bandgap refractive indexes of β-Ga2O3 thin film are explained well with the new model, leading to the determination of an explicit analytical dispersion of refractive indexes for photon energy below an effective optical bandgap energy of 4.952 eV for the β-Ga2O3 thin film. Then, the oscillatory structures in long wavelength regions in experimental transmission spectra of Si-doped β-Ga2O3 thin films with different Si doping concentrations are quantitively interpreted utilizing the determined sub-bandgap refractive index dispersion. Meanwhile, effective optical bandgap values of Si-doped β-Ga2O3 thin films are further determined and are found to decrease with increasing the Si doping concentration as expectedly. In addition, the sub-bandgap absorption coefficients of Si-doped β-Ga2O3 thin film are calculated under the frame of the Franz–Keldysh mechanism due to the electric field effect of ionized Si impurities. The theoretical absorption coefficients agree with the available experimental data. These key parameters obtained in the present study may enrich the present understanding of the sub-bandgap refractive indexes and optical properties of impurity-doped β-Ga2O3 thin films.

2D materials-enabled optical modulators: From visible to terahertz spectral range

Two-dimensional (2D) materials with layered structures have a variety of exceptional electronic and optical attributes for potentially developing basic functions of light wave technology from light-emitting to -modulating and -sensing. Here, we present state-of-the-art 2D materials-enabled optical intensity modulators according to their operation spectral ranges, which are mainly determined by the optical bandgaps of the 2D materials. Leveraging rich electronic structures from different 2D materials and the governed unique light–matter interactions, the working mechanisms and device architectures for the enabled modulators at specific wavelength ranges are discussed. For instance, the tunable excitonic effect in monolayer transition metal dichalcogenides allows the modulation of visible light. Electro-absorptive and electro-refractive graphene modulators could be operated in the telecom-band relying on their linear dispersion of the massless Dirac fermions. The bendable electronic band edge of the narrow bandgap in few-layer black phosphorus promises the modulation of mid-infrared light via the quantum-confined Franz–Keldysh or Burstein–Moss shift effect. Electrically and magnetically tunable optical conductivity in graphene also supports the realizations of terahertz modulators. While these modulators were demonstrated as proof of concept devices, part of them have great potential for future realistic applications, as discussed with their wavelength coverage, modulation depth, insertion loss, dynamic response speed, etc. Specifically, benefiting from the well-developed technologies of photonic chips and optical fibers in telecom and datacom, the 2D materials-based modulators integrated on these photonic structures are expected to find applications in fiber and chip optical communications. The free-space mid-infrared and terahertz modulators based on 2D materials can expect application in chemical bond spectroscopy, free-space communications, and environment/health sensing.

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.

Simple and direct estimation method for split-off hole effective mass from Franz–Keldysh oscillations appearing in photoreflectance spectra: a feasibility study using GaAs epitaxial layer structures at room temperature

We investigated the feasibility of directly estimating split-off hole effective mass m so from Franz–Keldysh oscillations using non-destructive and non-invasive photoreflectance spectroscopy. We used an undoped/n-type GaAs epitaxial structure and two GaAs p–i–n diode structures. We observed the phenomenon that Franz–Keldysh oscillations, which originate both the E 0 fundamental transition and from the E 0 + Δso transition energy, appear in the photoreflectance spectra at room temperature. Initially, from the electro-optic constant ℏΘ HH of the Franz–Keldysh oscillations originating from the E 0 fundamental transition, we deduced the built-in electric field F in each sample with the use of the relation ℏΘ HH = (e 2ℏ2 F 2/2μ HH)1/3, where the quantity μ HH is the reduced effective mass of the electron and heavy hole. In the next step, we calculated the reduced effective mass μ so of the electron and split-off hole using the relation ℏΘ so = (e 2ℏ2 F 2/2μ so)1/3, where the quantity ℏΘ so is the electro-optic constant of the Franz–Kelysh oscilations from the E 0 + Δso transition. Finally, we estimated the split-off hole effective mass m so from the reduced effective mass μ so. The estimated split-off hole effective mass agrees with the reported value obtained experimentally. Thus, we conclude that the split-off hole effective mass is estimatable from analyzing the Franz–Keldysh oscillations in the photoreflectance spectra. We also compare the present hole effective masses to those theoretically known and discuss the appropriateness of the electronic-band calculations.

Electro-optical properties of excitons in Cu2O quantum wells. II. Continuum states

We present theoretically calculated optical functions for Cu$_2$O quantum well (QW) with Rydberg excitons in an external, homogeneous electric field parallel to the QW planes for the energy region above the gap, suitable to observe the Franz-Keldysh (FK) oscillations. We quantitatively describe the amplitudes and periodicity of FK modulations and the influence of both Rydberg excitons and confinement effect on this phenomenon.

Impact of Built‐In Electric Field on the Emission Characteristics of InAs/GaAs Quantum Dot Laser Structure

The impact of the built‐in electric field on the emission characteristics of an InAs/GaAs quantum dot (QD) laser structure is investigated by performing systematic spectroscopic measurements. Photoluminescence (PL) features related to the ground state (GS) and excited state (ES) transitions of a QD ensemble are clearly observed in the temperature range of 8–300 K. The cross‐sectional transmission electron microscopy image and a systematic analysis of temperature‐dependent PL data confirm the excellent crystalline and optical quality of the QD laser structure. It is found that the values of the activation energy associated with GS and ES transitions of the QD sample reasonably match with the energy splitting of PL features. This successfully explains the trends observed in temperature‐dependent PL spectra, where thermal transfer of carriers to the wetting/barrier layer via QD excited states is proposed to be a major decay channel. An interesting observation is made where the integrated intensity of PL features increases up to 75 K and falls thereafter during the heating cycle. Such a peak‐like behavior of the integrated intensity is explained by invoking the temperature dependence of the built‐in electric field, which is estimated from the analysis of Franz–Keldysh oscillations observed in photoreflectance spectra and is important in the design of QD lasers.

Impact ionization coefficients and critical electric field in GaN

Avalanche multiplication characteristics in a reverse-biased homoepitaxial GaN p–n junction diode are experimentally investigated at 223–373 K by novel photomultiplication measurements utilizing above- and below-bandgap illumination. The device has a non-punch-through one-side abrupt p–-n+ junction structure, in which the depletion layer mainly extends to the p-type region. For above-bandgap illumination, the light is absorbed at the surface p+-layer, and the generated electrons diffuse and reach the depletion layer, resulting in an electron-injected photocurrent. On the other hand, for below-bandgap illumination, the light penetrates a GaN layer and is absorbed owing to the Franz–Keldysh effect in the high electric field region (near the p–n junction interface), resulting in a hole-induced photocurrent. The theoretical (non-multiplicated) photocurrents are calculated elaborately, and the electron- and hole-initiated multiplication factors are extracted as ratios of the experimental data to the calculated values. Through the mathematical analyses of the multiplication factors, the temperature dependences of the impact ionization coefficients of electrons and holes in GaN are extracted and formulated by the Okuto–Crowell model. The ideal breakdown voltage and the critical electric field for GaN p–n junctions of varying doping concentration are simulated using the obtained impact ionization coefficients, and their temperature dependence and conduction-type dependence were discussed. The simulated breakdown characteristics show good agreement with data reported previously, suggesting the high accuracy of the impact ionization coefficients obtained in this study.

Electroabsorption in gated GaAs nanophotonic waveguides

We report on the analysis of electroabsorption in thin GaAs/Al0.3Ga0.7As nanophotonic waveguides with an embedded p–i–n junction. By measuring the transmission through waveguides of different lengths, we derive the propagation loss as a function of electric field, wavelength, and temperature. The results are in good agreement with the Franz–Keldysh model of electroabsorption extending over 200 meV below the GaAs bandgap, i.e., in the wavelength range of 910–970 nm. We find a pronounced residual absorption in forward bias, which we attribute to Fermi-level pinning at the waveguide surface, producing over 20 dB/mm loss at room temperature. These results are essential for understanding the origin of loss in nanophotonic devices operating in the emission range of self-assembled InAs semiconductor quantum dots toward the realization of scalable quantum photonic integrated circuits.

Electro-optical imaging of electric fields in silicon sensors

A conceptual set-up for measuring the electric field in silicon detectors by electro-optical imaging is proposed. It is based on the Franz–Keldysh effect which describes the electric field dependence of the absorption of light with an energy close to the band gap in semiconductors. Using published data for silicon, a measurement accuracy of 1 to 4kV/cm is estimated. The set-up is intended for determining the electric field in radiation-damaged silicon detectors as a function of irradiation fluence and particle type, temperature and bias voltage. The overall concept and the individual components of the set-up are presented.

Investigation of the Carrier Movement through the Tunneling Junction in the InGaP/GaAs Dual Junction Solar Cell Using the Electrically and Optically Biased Photoreflectance Spectroscopy

For examining the carrier movements through tunnel junction, electrically and optically-biased photoreflectance spectroscopy (EBPR and OBPR) were used to investigate the internal electric field in the InGaP/GaAs dual junction solar cell at room temperature. At InGaP and GaAs, the strength of p-n junction electric fields (Fpn) was perturbed by the external DC bias voltage and CW light intensity for EBPR and OBPR experiments, respectively. Moreover, the Fpn was evaluated using the Fast Fourier Transform (FFT) of the Franz—Keldysh oscillation from PR spectra. In the EBPR, the electric field decreased by increasing the DC bias voltage, which also decreased the potential barrier. In OBPR, when incident CW light is absorbed by the top cell, the decrement of the Fpn in the GaAs cell indicates that the photogenerated carriers are accumulated near the p-n junction. Photogenerated carriers in InGaP can pass through the tunnel junction, and the PR results show the contribution of the modification of the electric field by the photogenerated carriers in each cell. We suggest that PR spectroscopy with optical-bias and electrical-bias could be analyzed using the information of the photogenerated carrier passed through the tunnel junction.