Franz-Keldysh Effect Research Articles

Collector breakdown in the heterojunction bipolar transistor laser

Data are presented on a quantum-well (QW)-based InGaP∕GaAs∕InGaAs (QW) heterojunction bipolar transistor laser modified with external (increased) mirror reflection yielding lower threshold current (IB=23→19mA) and higher collector breakdown voltage (⩾2.5V). Increased breakdown at lower currents is observed on the collector I-V characteristics, at constant base current IB, as a slope change, a corner, and a narrow-line to broadband spectral shift from stimulated (high coherent optical field) to spontaneous (lower incoherent field) operation, a consequence of quenching or reducing photon-assisted tunneling (Franz-Keldysh effect) under the constraint IE+IB+IC=0 as α→1(α≡ΔIC∕ΔIE).

Phonon-assisted two-photon absorption in the presence of a dc-field: the nonlinear Franz–Keldysh effect in indirect gap semiconductors

The two-photon absorption coefficient of an indirect gap semiconductor (phonon-assisted two-photon absorption) in the presence of a strong dc-electric field applied perpendicular to the direction of propagation of the optical field is calculated using the formalism developed elsewhere (Aspnes 1996 Phys. Rev. B. 147 554). We show that depending on the type of transition (i.e., allowed–allowed, allowed–forbidden or forbidden–forbidden), the absorption coefficient followed different dispersion relations. In the limit of a weak electric field, we recovered results previously calculated using perturbation theory. In the strong dc-field regime, we found that below the rescaled energy gap given by Eg/N, where N is the number of photons, the tunnelling effect is present, but to our surprise, above the rescaled gap, the Franz–Keldysh oscillations are present only for the allowed–allowed transition. This absence of the oscillations in the allowed–forbidden and forbidden–forbidden transitions is possible due to the weak coupling of the tails of the electron and hole wavefunctions.

Electroreflectance Spectra of InGaN/AlGaN/GaN p-n-Heterostructures

ABSTRACTElectroreflectance (ER) spectra of InGaN/AlGaN/GaN p-n- heterostructures with multiple quantum wells (MQW) are studied. Structures with MQW InGaN/GaN were grown for blue LEDs by MOCVD technology and “flip-chip” mounted. The ER spectral maxima correspond to the high energy side of electroluminescence spectral line. The ER spectra caused by Franz-Keldysh effect are approximated by Aspnes theory. The ER spectra in a range 400 ÷ 800 nm have interference bands caused by the change of refraction index in the structure.

Femtosecond pump-probe spectroscopy of propagating coherent acoustic phonons inInxGa1−xN∕GaNheterostructures

We show that large amplitude, coherent acoustic phonon wavepackets can be generated and detected in In$_x$Ga$_{1-x}$N/GaN epilayers and heterostructures in femtosecond pump-probe differential reflectivity experiments. The amplitude of the coherent phonon increases with increasing Indium fraction $x$ and unlike other coherent phonon oscillations, both \textit{amplitude} and \textit{period} are strong functions of the laser probe energy. The amplitude of the oscillation is substantially and almost instantaneously reduced when the wavepacket reaches a GaN-sapphire interface below the surface indicating that the phonon wavepackets are useful for imaging below the surface. A theoretical model is proposed which fits the experiments well and helps to deduce the strength of the phonon wavepackets. Our model shows that localized coherent phonon wavepackets are generated by the femtosecond pump laser in the epilayer near the surface. The wavepackets then propagate through a GaN layer changing the local index of refraction, primarily through the Franz-Keldysh effect, and as a result, modulate the reflectivity of the probe beam. Our model correctly predicts the experimental dependence on probe-wavelength as well as epilayer thickness.

Optical piezoelectric transducer for nano-ultrasonics

Piezoelectric semiconductor strained layers can be treated as piezoelectric transducers to generate nanometer-wavelength and THz-frequency acoustic waves. The mechanism of nano-acoustic wave (NAW) generation in strained piezoelectric layers, induced by femtosecond optical pulses, can be modeled by a macroscopic elastic continuum theory. The optical absorption change of the strained layers modulated by NAW through quantum-confined Franz-Keldysh (QCFK) effects allows optical detection of the propagating NAW. Based on these piezoelectric-based optical principles, we have designed an optical piezoelectric transducer (OPT) to generate NAW. The optically generated NAW is then applied to one-dimensional (1-D) ultrasonic scan for thickness measurement, which is the first step toward multidimensional nano-ultrasonic imaging. By launching a NAW pulse and resolving the returned acoustic echo signal with femtosecond optical pulses, the thickness of the studied layer can be measured with <1 nm resolution. This nano-structured OPT technique will provide the key toward the realization of nano-ultrasonics, which is analogous to the typical ultrasonic techniques but in a nanometer scale.

Effect of well width on the electro-optical properties of a quantum well

The direct way to investigate the effect of an electric field F on the optical properties of a quantum well (QW) is to change the well width (Miller et al 1986 Phys. Rev. B 33 6976). Photoreflectance studies of a 100 Å and a 250 Å Ge/GeSi modulation doped QWs possessing 104 V cm−1 perpendicular fields are presented. This technique modulates the QW electro-absorption, which we compute using wavefunctions obtained from a 8 × 8 k ⋅ p calculation. They are shown to have a pronounced tunnelling into the bandgap in the 250 Å QW, in contrast to the 100 Å QW. Kramers–Kronig analysis is used to determine the corresponding changes in the QW refractive index, and overall reflection from the entire sample (including barriers) is obtained within a 2 × 2 matrix formalism. In a QW of width Lz, the Franz–Keldysh effect is expected to be important in an energy interval extending from near the bandgap Eo to Eo + eFLz. Its role in altering QW optical properties as a function of Lz is tested by comparing calculated and experimental spectra in this interval.

Design and simulation of silicon microring optical routing switches

Using two-dimensional (2-D) scattering matrix theory, the switching behavior of inplane waveguided 2 /spl times/ 2 resonant optical switches in silicon-on-insulator was analyzed at the 1.33, 1.55, and 10.6 /spl mu/m wavelengths. The switch consisted of two straight bus waveguides coupled independently and laterally to a pair of microring resonators. Switching actuated by a /spl Delta/n + i/spl Delta//spl kappa/~ complex index perturbation of the rings was investigated. The switching effects discussed include the free-carrier-plasma dispersion, Franz-Keldysh, quantum-confined Stark, Kerr, and thermooptic effects. Each effect has its /spl Delta//spl kappa/~//spl Delta/n signature. For waveguides /spl les/0.3/spl lambda/ wide, an optimum switch design was determined in the weak coupling regime. Complete switching was found for /spl Delta/n/spl sim/2/spl times/10/sup -3/, together with significant modulation for /spl Delta/n in the 10/sup -4/ range.

Studies of the Electron Spectrum in Structures with InGaN Quantum Dots Using Photocurrent Spectroscopy

Structures with InGaN/GaN quantum dots have been studied using photocurrent spectroscopy. The dynamic range of measurements is found to amount to four orders of magnitude under preservation of the signal-to-noise ratio at a level higher than ten. Within the experimental accuracy, the shape of the spectrum is independent of an applied reverse external bias, whereas the spectrum itself shifts to shorter wavelengths, which is attributed to the Franz-Keldysh effect. Variation of the temperature brings about a change in the spectrum shape. This effect is found to be different for structures grown under different conditions. This behavior can be attributed to homogeneous broadening of the electronic states, the statistics of charge carriers at the levels of quantum dots, and the effect of temperature on the position of these levels.

Laser-Induced Above-Band-Gap Transparency in GaAs

We report the observation of large (approximately 40%) laser-induced above-band-gap transparency in GaAs at room temperature. The induced transparency is present only during the pulse width of the driving midinfrared laser pulses and its spectral shape is consistent with a laser-induced blueshift of the band edge. Our simulations based on the dynamic Franz-Keldysh effect reproduce the salient features of the experimental results, demonstrating, in particular, that the amount of the band edge shift is approximately given by the ponderomotive potential.

Comparative electroabsorption studies of organic and inorganic solids

Spectral changes induced by moderate electric fields provide detailed insight into the electronic states of organic and inorganic solids. Although the basic effects, Stark effect and Franz–Keldysh effect, are the same in both types of material, the electroabsorption spectra vary strongly in size and spectral lineshape due to competing interactions. The large variance of the effects is demonstrated by representative examples of high mobility semiconductors, quantum wells, π -conjugated polymers, and charge transfer transitions in single crystals, disordered films and a double-quantum well. It is shown that only high-quality samples reveal the quantum mechanics of field-induced effects which are very sensitive to disorder.

Differential reflectivity and photoemission study of ZnTe and CdTe (1 1 0) surface

The surface differential reflectivity (SDR) and photoemission methods were used to study surface electronic structure of CdTe and ZnTe (110) surface. The changes of reflectivity coefficient were caused by the changes of electric field (band bending) induced at the surface region by high power laser illumination of the sample. The SDR spectra were obtained as a function of laser power illumination. The shift of the surface potential was estimated on photoemission spectra as a shift of the Cd 4d level position caused by the laser illumination of the sample. The exponential time decay of the amplitude of SDR spectra were measured after turning of the laser illumination. The decay time constant was estimated at 22min for clean surface of CdTe and 60min for real surface of ZnTe. The attempts were done to discuss obtained results in the frame of the Franz–Keldysh effect description.

Franz-Keldysh effect in semiconductor T-wire in applied magnetic field

We have calculated the optical absorption spectra of magnetoexcitons in T-wire semiconductor. It is calculated using the semiconductor Bloch equations in time and real-space domains. The peak and the linewitdth of the fundamental exciton transition are investigated as a function of the applied magnetic and static electric field. The latter is applied along the wire axis and induces a broadening in the absorption spectra line, energy shift, and the characterisitic Franz-Keldysh oscillations. The exciton binding energy enhances increasing the magnetic field strength.

Dynamics of Berry-phase polarization in time-dependent electric fields

We consider the flow of polarization current J(t)=dP/dt produced by a homogeneous electric field E(t) or by rapidly varying some other parameter in the Hamiltonian of a solid. For an initially insulating system and a collisionless time evolution, the dynamic polarization P(t) is given by a nonadiabatic version of the King-Smith--Vanderbilt geometric-phase formula. This leads to a computationally convenient form for the Schroedinger equation where the electric field is described by a linear scalar potential handled on a discrete mesh in reciprocal space. Stationary solutions in sufficiently weak static fields are local minima of the energy functional of Nunes and Gonze. Such solutions only exist below a critical field that depends inversely on the density of k points. For higher fields they become long-lived resonances, which can be accessed dynamically by gradually increasing E. As an illustration the dielectric function in the presence of a dc bias field is computed for a tight-binding model from the polarization response to a step-function discontinuity in E(t), displaying the Franz-Keldysh effect.

A nonlocal theory of the Franz–Keldysh effect in semiconductor quantum wires

We have formulated an analytic expression for the one-dimensional (1D) Franz–Keldysh effect (FKE) in terms of the nonlocal description of the optical response, a more rigorous approach than the long-wavelength approximation (LWA). Present results are compared with a 1D Franz–Keldysh (FK) theory recently developed in the scheme of LWA. Focusing on the FK oscillation extrema positions, we discuss effect of the nonlocality on the 1D FK.

Photocurrent spectroscopy as a tool for determining piezoelectric fields inInxGa1−xN/GaNmultiple quantum well light emitting diodes

We discuss photocurrent spectroscopy as a powerful tool for the determination of piezoelectric fields in ${\mathrm{In}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}/\mathrm{G}\mathrm{a}\mathrm{N}$ multiple-quantum well light emitting diodes. The observed photocurrent spectra can be interpretted in terms of the Franz-Keldysh effect, and allow for the simultaneous determination of band gap and piezoelectric field in the quantum wells. As an illustration of the method we use results obtained on a structure with an 8% indium content in the quantum well. We find a band gap of 3.10 eV at 300 K and a piezoelectric field of $1.1\ifmmode\pm\else\textpm\fi{}0.2\mathrm{M}\mathrm{V}/\mathrm{c}\mathrm{m}.$ The observed photocurrent spectra can be accurately accounted for by invoking the presence of indium fluctuations, which cause the formation of an exponential band tail in the band gap. This band tail is seen to increase with increasing electric field. With these band tail extensions, a good agreement is obtained between the experimental data and simulations based on the Franz-Keldysh effect.

Analytic Franz–Keldysh effect in one-dimensional polar semiconductors

The optical properties of a one-dimensional polar semiconductor in a strongelectric field are considered. This class of materials includes non-centrosymmetricIII–V inorganic quantum wires but also polar conjugated polymers such aspolymethineimine. The polar Franz–Keldysh effect is derived via an analyticexpression for the complex dielectric constant including line broadening and linearfield terms. Results for the high-field non-perturbative regime as well as thelow-field expansion are presented.

Phase and intensity dependence of the dynamical Franz-Keldysh effect

We present theoretical results on the nonlinear optics of semiconductor quantum wells in intense THz electric fields (the dynamic Franz-Keldysh effect or DFKE). The absorption spectra show a rich variety of behavior, including THz replicas of the $2p$ exciton and THz sidebands of the $1s$ exciton. We calculate the dependence of these features on the phase and intensity of the THz field using the extended semiconductor Bloch equations, and discuss the relevance of our results to future experiments. The $1s$-sideband absorption feature shows a strong dependence on the phase of the THz field, and phase averages to zero. We also discuss the relative advantages and disadvantages of reflectivity and absorption spectroscopies for probing the DFKE.

High-electric-field photocurrent in thin-film ZnS formed by pulsed-laser deposition

Photocurrent spectra of thin-film ZnS on glass fabricated by pulsed-laser deposition have been studied employing electric fields up to 20 kV/cm. The spectra show a shift towards lower energy at and beyond 10 kV/cm. By modeling the film absorption with the density of states and the Urbach rule, it is shown that, without the involvement of the Franz–Keldysh effect and excitonic transitions, the slope of the Urbach tail depends on the electric field, owing to impurity ionization.

The Franz–Keldysh effect in shocked GaN:Mg

The band gap of uniaxially strained semi-insulating GaN:Mg has been examined using time-resolved optical transmission measurements in shock-wave experiments. For longitudinal stresses between 2.9 and 4.6 GPa, the absorption edge broadened significantly. Such a broadening is consistent with the presence of large piezoelectric fields (Franz–Keldysh effect) generated due to shock compression. For stresses greater than 4.6 GPa, however, the absorption edge remained relatively sharp. The sharp absorption onset suggests the presence of free charge carriers that screen the piezoelectric field, thereby suppressing the Franz–Keldysh effect. These observations indicate that electrical breakdown occurs at a field of 1 MV/cm. One possible mechanism that could result in free carriers is the dissociation of Mg–H complexes under the very high piezoelectric fields.

Strain-induced band gap shrinkage in Ge grown on Si substrate

Band gap shrinkage induced by tensile strain is shown for Ge directly grown on Si substrate. In Ge-on-Si pin diodes, photons having energy lower than the direct band gap of bulk Ge were efficiently detected. According to photoreflectance measurement, this property is due to band gap shrinkage. The origin of the shrinkage is not the Franz–Keldysh effect but rather tensile strain. It is discussed that the generation of such a tensile strain can be ascribed to the difference of thermal expansion between Ge and Si. Advantages of this tensile Ge for application to photodiode are also discussed.