Intersubband Excitations Research Articles

Far-infrared absorption in parallel quantum wires with weak tunneling.

We study collective and single-particle intersubband excitations in a system of quantum wires coupled via weak tunneling. For an isolated wire with parabolic confinement, the Kohn's theorem guarantees that the absorption spectrum represents a single sharp peak centered at the frequency given by the bare confining potential. We show that the effect of weak tunneling between two parabolic quantum wires is twofold: (i) additional peaks corresponding to single-particle excitations appear in the absorption spectrum, and (ii) the main absorption peak acquires a depolarization shift. We also show that the interplay between tunneling and weak perpendicular magnetic field drastically enhances the dispersion of single-particle excitations. The latter leads to a strong damping of the intersubband plasmon for magnetic fields exceeding a critical value.

Photovoltaic effect in coupled quantum wells under intersubband excitation

The photovoltaic effect in tunnel-coupled double quantum wells (DQWs) due to resonant infrared (IR) excitation of the electrons from the lower ground state to the excited state is considered. Intra- and interwell relaxation of electrons are studied self-consistently, taking into account modification of the electron states in DQWs due to the upper ground state occupation under IR pumping. The photoinduced potential is calculated for different energies of IR excitation, and the correlation between this potential and modification of the ground states in DQWs is discussed.

Collective excitations in coupled quantum wells

The dielectric response of a modulated three-dimensional electron system composed of a periodic array of quantum wells with weak coupling and strong coupling are studied, and the dispersions of the collective excitations and the single particle excitations as functions of wave vectors are given. It is found that for the nearly isolated multiple-quantum-well case with several subbands occupation, there is a three-dimensional-like plasmon when q z =0 ( q z is the wave-vector component in the superlattice axis). There also exist inter-subband collective excitations in addition to one intra-subband mode when q z ≠0. The intra-subband mode has a linear dispersion relation with q | (the wave-vector component perpendicular to the superlattice axis) when q | is small. The inter-subband modes cover wider ranges in q | with increasing values of q z . The energies of inter-subband collective excitations are close by the corresponding inter-subband single-particle excitation spectra. The collective excitation dispersions show obvious anisotropy in the 2D quantum limit. The calculated results agree with the experiment. The coupling between quantum wells affects markedly both the collective excitations and the single particle excitations spectra. The system shows gradually a near-three-dimensional electron gas character with increasing coupling.

Combined 1D–2D intersubband excitations nd 1D single-particle spectrum in narrow quantum wires

Electronic excitations in AlGaAs-GaAs quantum wires have been investigated by means of resonant inelastic light scattering. Besides a rich spectrum of 1D electronic excitations at low frequencies we fin d at higher frequencies transitions in the regime of the original 2D intersubband excitations. Interestingly, we observe not only the original 2D intersubband excitations but additional modes ω k in polarized scattering geometry. The experimental observation is that the frequencies of these modes obey the relationship, ω 2 k = ω 2 2D + ω 2 1D, where ω 2D is the vertical intersubband plasmon frequency and ω 1D the lateral confined plasmon frequency. This relationship suggests that the additional modes are combined 2D-1D intersubband excitations of collective charge-density type.

Intersubband photocurrent from double barrier resonant tunneling structures

Simple models of semiconductor-based double barrier resonant tunneling structures predict a large accumulation of charge carriers in the structure. These carriers can be excited optically from one subband to another generating photocurrent. In this work we have investigated the photo-induced current due to intersubband excitation in double barrier structures. We have found that the origin of the photocurrent is accumulation of quantized carriers in the emitter-barrier junction of the structure, rather than accumulation of carriers in the double barrier quantum well. This photon assisted tunneling process in double barrier structures may be used for infrared detection.

Coupling of lateral and vertical electron motion in GaAs-AlxGa1-xAs quantum wires and dots.

Electronic excitations in ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As-GaAs quantum wires and quantum dots have been investigated by means of resonant inelastic light scattering. At low frequencies, we find quasi-one-dimensional and quasi-zero-dimensional confined plasmons. Interestingly, we observe, at higher frequencies, not only the original two-dimensional (2D) intersubband excitations, but additional modes ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$ in polarized scattering geometry. The experimental finding is that the frequencies of these modes obey the relation ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}^{2}$\ensuremath{\approxeq}${\mathrm{\ensuremath{\omega}}}_{2\mathrm{D}}^{2}$+${\mathrm{\ensuremath{\omega}}}_{\mathrm{}1\mathrm{D}/0\mathrm{D}}^{2}$, where ${\mathrm{\ensuremath{\omega}}}_{2\mathrm{D}}$ is the frequency of the vertical intersubband charge-density excitation. ${\mathrm{\ensuremath{\omega}}}_{1\mathrm{D}}$ is a lateral quasi-one-dimensional confined plasmon frequency in wires and ${\mathrm{\ensuremath{\omega}}}_{0\mathrm{D}}$ is the frequency of a quasi-zero-dimensional confined plasmon in dots. This relation shows that the additional modes are collective charge-density excitations, which occur due to a coupling of lateral and vertical electron motion. \textcopyright{} 1996 The American Physical Society.

Collective excitations in the coupled quantum wires

The dielectric response of an electron system composed of an array of parallel quantum wires with weak coupling and strong coupling are studied, and the dispersions of the collective excitations and the single particle excitations (SPE) as functions of wave-vectors are given. It is found that for the nearly isolated quantum wires with several subbands occupation, there are a series of intra-subband collective excitations between corresponding intra-subband SPE spectra. There also exist inter-subband collective excitations when q x ≠0 ( q x is the wave-vector component in the modulation direction), whose energies are close by the corresponding inter-subband SPE spectra. The energy of the intra-subband mode decreases and that of inter-subband mode increases with q x increasing. The collective excitation dispersions show obvious anisotropy in the 1D quantum limit. The calculated results agree with the experiment well. The coupling between quantum wires affects markedly both the collective and single-particle excitations spectra. The system changes to a near-two-dimensional electron system gradually with increasing coupling.

Temperature Dependence of Raman Spectra in Si-doped GaAs/AlAs Multiple Quantum Wells

We investigated the temperature dependence of Raman spectra due to two coupled longitudinal-optical phonon-collective intersubband excitations in Si-doped GaAs/AlAs multiple quantum wells. The frequency of the respective coupled modes shifts with a change in the electron density in intersubbands related to the modes. The Raman intensity due to the higher-frequency coupled mode becomes weaker with increasing temperature. Under a certain condition, electron density in the ground subband changes with the temperature because of the temperature dependence of the Fermi energy. Furthermore we observed a reproducible drastic position shift of the Raman peak originating from the higher-frequency coupled mode with temperature.

Dielectric response of an inhomogeneous quasi-two-dimensional electron gas.

The solution of the integral equation required to invert the dielectric function of a confined quasi-two-dimensional electron gas is studied by means of a formal analysis which yields a convergent algorithm. The dielectric function can then be inverted in real space for an arbitrary number of populated subbands and taking into account the effect of intersubband excitations involving empty subbands to any desired degree of accuracy. Plasma modes and screened potential can then be easily studied by using a basis which bears out explicitly the consequences of symmetry in symmetric systems. A model calculation of dynamical screening at frequencies of the order of those of confined polar optical modes in usual GaAs wells indicates that the empty states may play a quite significant role and the screened potential, explicitly obtained in real space, may exhibit a great variety of behaviors: the sign of the potential may change and its magnitude may be either reduced (ordinary screening) or enhanced (antiscreening).

Correlation between intersubband Raman scattering and electric-field domains in quantum-well structures

We report on Raman scattering by intersubband excitations in GaAsAlAs superlattices which exhibit electric-field domains resulting from sequential resonant tunneling. At a given bias, the Raman spectra reveal two peaks in voltage ranges where two domains coexist. An unexpected result of our studies is the observation of significant differences in the dependence of charge- and spin-density scattering on the electric field.

Effect of Intense Intersubband Optical Excitation on the Electron Distribution in GaAs/AlAs Quantum Wells

Hot electrons were generated in n-doped GaAs/AlAs multiple quantum wells by optical intersubband excitation and their energy distributions were studied at 10 K. By measuring photoluminescence (PL) spectra, the hot-electron temperature T el was quantitatively evaluated, taking into account such effects as the degenerate distribution of electrons, impurity-induced level broadening, and the distribution of holes. It was found that, when the intensity P of the excitation was 30 kW cm-2, i.e. a few percent of the onset intensity for absorption saturation, T el increased from 10 K to 120 K while the lattice temperature remained unchanged. When P was between 10 W cm-2 and 30 kW cm-2, the rise of T el was well explained by the balance between the photon energy absorption and the energy loss due to the LO phonon emission inside the ground subband.

Response functions for quasi- n-dimensional ( n = 2, 1, 0) electron systems

We present an exact analytical method to calculate the inverse dielectric functions for quasi-two-dimensional electron systems (quantum wells), quasi-one-dimensional electron systems (quantum wires) and quasi-zero-dimensional electron systems (quantum dots). This is done for multiple subband occupancy within the random-phase approximation. The resulting expessions for the inverse dielectric functions pave the way to a simpler means of investigating the collective (both intraand intersubband) excitations and constitute a legitimate basis for studying, for example, the energy loss by a fast charged particle to the respective systems.

Experimental Observation of Intersubband Excitations in Si-Doped GaAs/AlAs Multiple Quantum Wells

Experiments are carried out to observe optical phonon modes coupled with intersubband transition in doped GaAs/AlAs multiple quantum wells (MQW) by attenuated total reflection (ATR) and Raman scattering methods. A step due to intersubband transition is found at an energy corresponding to the calculated subband level in ATR spectra. Two peaks related to charge-density intersubband excitation are observed in the Raman spectrum. From these spectra, we evaluated the parameters of intersubband transitions and the sheet carrier density in the well region.

Intersubband excitations of quasi-one-dimensional electron systems in a magnetic field

Intersubband excitation spectra of quasi-one-dimensional electron systems in quantum wires are calculated by the perturbation expansion with respect to the Coulmb interaction between electrons in the presence of perpendicular magnetic fields. We find the peak structure at the upper edge of spectra of the single-particle excitation, in addition to the main peak corresponding to the magnetoplasmon. With increasing the magnitude of magnetic fields, this additional peak separates from the spectra of the single-particle excitation and the intensity of this peak is gradually decreased. We consider that the additional peak is connected with the attractive interaction between electrons which appears only in the presence of magnetic fields.

Inelastic electron scattering and magnetic collective response of mesoscopic carbon structures.

We obtain analytically the self-consistent quasiparticle energy (QPE) spectra associated with certain fullerenes, e.g., ${\mathrm{C}}_{50}$, ${\mathrm{C}}_{60}$, ${\mathrm{C}}_{70}$, and the graphitic nanotubules. A random-phase approximation-level formalism for calculating the collective electronic excitations is then developed using the above QPE spectra as input. Multipole excitations are obtained for ${\mathrm{C}}_{60}$ and related quasispherical fullerenes. In the presence of a strong external magnetic field applied along the axis of the nanotubule, an extra peak in the de Haas--van Alphen oscillations predicted previously manifests itself as a discontinuity in the highest magnetoplasmon dispersion curve for the nanotubules in the infrared regime. The magnetic field breaks the degeneracy of the subbands such that each intersubband excitation branch is split into four distinct branches. An approximate plasmon dispersion relation in the high frequency regime is also derived. Furthermore, the inelastic electron scattering cross section characterized by the density-density correlation function is calculated. Our results are in good agreement with experiments on photoionization, gas phase electron-energy loss spectroscopy (EELS), transmission EELS, and high-resolution electron-energy loss spectroscopy.

Single-particle excitations in quasi-zero- and quasi-one-dimensional electron systems.

Resonant inelastic light scattering is used to probe electronic excitations in shallow etched GaAs/AlGaAs quantum dots and wires. In both types of structures, intersubband excitations are observed in depolarized scattering geometries. They show significant blueshift with decreasing confinement length. In dot structures these transitions appear as dispersionless, whereas in wires they show strong broadening and an intensity dip at the energetic center of the excitation with increasing wave vector parallel to the wires, as expected for single-particle excitations. Their line shape correlates with the linear wave vector dispersion of additionally observed intrasubband excitations.

Inelastic light scattering by the two-dimensional electron gas: Fractional quantum Hall regime and beyond

Abstract Mechanisms of resonant inelastic light scattering by the electron gas are evaluated here for their impact in the current research of semiconductor nano-structures. Recent experiments in the fractonal quantum Hall regime highlight the power of the resonant inelastic light-scattering method in studies of electron-electron interactions in semiconductors of reduced dimensions. These applications follow from its capabilities to measure spin-density and charge-density collective modes as well as excitations that are not predicted by conventional response functions of the electron gas. We consider measurements of intersubband excitations of two-dimensional systems in GaAs quantum wells and observations of gap excitations in the fractional quantum Hall effect.

Growth of electric-field domains in quantum-well structures: Correlation with intersubband Raman scattering.

We report on Raman scattering by intersubband excitations in GaAs-AlAs superlattices which exhibit electric-field domains resulting from sequential resonant tunneling. In regions where two domains coexist, the scattering intensity varies linearly with the applied voltage. This behavior, consistent with the standard domain picture, can be explained by a model relying on the electric-field dependence of the cross section and the domain size.

Inelastic light scattering by spin-density, charge-density, and single-particle excitations in GaAs quantum wires.

We report the observations of inelastic light scattering by the elementary excitations of the one-dimensional electron gas. The quantum wires are fabricated from a modulation-doped single GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As quantum well electron-beam lithography and shallow electron-cyclotron-resonance reactive-ion etching. In spectra of intersubband excitations we observe a clear separation of spin-density and charge-density collective modes. The splitting associated with the lateral potential of the wires is also seen in transitions to states of the first excited level of the parent quantum well. Determinations of electron-electron interactions in intersubband excitations of the one-dimensional electron gas show large corrections due to the exchange terms (or vertex corrections) that represent the excitonic binding of the particle-hole pairs.

Cyclotron and intersubband resonance studies in [001] and piezoelectric [111] InAs/(Ga,In)Sb superlattices

Cyclotron resonance and inter-subband excitation experiments have been performed on superlattices of the semimetallic, strained type II system InAs/(Ga,In)Sb. We observe simultaneously one cyclotron resonance from the 2D electrons located in the InAs and two resonances from the 2D holes in the (Ga,In)Sb layers. The two hole resonances originate from the M J = ¦ 3 2 > states. We have found a strong crystallographic anisotropy in the hole masses between structures grown along [001] and [111]A orientations attributed to the strain decoupling of the heavy and light hole levels in the GrmGa 1- x In x Sb valence band. In addition, we demonstrate for the first time that intersubband resonances can be directly seen for the electrons at large tilt angles.