Size-quantization Subbands Research Articles

Giant quantum oscillations of acoustoelectric current in narrow graphene nanoribbons

A theory is presented for the acoustoelectric (AE) effect in narrow graphene nanoribbons (GNRs) deposited on a piezoelectric substrate when a surface acoustic wave (SAW) is launched onto the surface of the piezoelectric. It is assumed that the electron density in such GNRs can be controlled by applying an external gate voltage, and the acoustic wavelength is much smaller than the mean free path of electrons, so that the quantum mode of interaction of those electrons with the SAW in realized. Using the kinetic theory approach, we calculate the AE current flowing through the GNR sample and arising as a result of momentum transfer from coherent SAW phonons to conduction electrons. It is shown that size quantization of the electron energy spectrum in narrow GNRs leads to giant periodic oscillations of the AE current with a change in the gate voltage. AE current surges occur whenever the Fermi level, rising with increasing gate voltage, crosses in turn the bottom of each of the successive size-quantized electron energy subbands. The oscillations predicted are giant in the sense that the maximum values of the current exceed its minimum values by at least an order of magnitude, and they can be observed in narrow GNRs ∼10 nm wide even at room temperature.

High-temperature magneto-inter-chirality oscillations in 2D systems with strong spin–orbit coupling

Conventional Shubnikov–de Haas oscillations of conductivity in 3D are washed out as the temperature exceeds the spacing between the Landau levels. This is due to smearing of the Fermi distribution. In 2D, in the presence of two or more size-quantization subbands, there is an additional type of magneto-oscillations, usually referred to as magneto-inter-subband oscillations, which do not decay exponentially with temperature. The period of these oscillations is determined by the condition that the energy separation between the subbands contains an integer number of Landau levels. Under this condition, which does not contain the Fermi distribution, the inter-subband scattering rate is maximal. Here we show that, with only one subband, high-temperature oscillations are still possible. They develop when the electron spectrum is split due to the spin–orbit coupling. For these additional oscillations, the coupling enters both the period and the decay rate.

Confined Stark effect and statistical distribution of charge carriers in β-HgS cylindrical quantized layer

The spectrum of single-particle states of charge carriers in the β-HgS quantized layer of the β-CdS/β-HgS/β-CdS cylindrical nanoheterostructure is considered in the approximation of the isotropic effective mass. Consideration is carried out for the most interesting case, when only the first size quantization subband is filled. The cases of strong quantization of the carriers’ motion in both the transverse-radial and longitudinal directions are considered separately. The splitting of the valence band into subbands of heavy and light holes is also taken into account. The dependence of the position of the chemical potential of electrons and holes on the quantization energy of charge carriers is obtained. Explicit expressions are obtained for the dependence of the density, internal energy, and heat capacity of charge carriers in the β-HgSlayer on the geometric sizes of the system and its temperature, and the corresponding graphic illustrations are presented. The influence of a longitudinal external uniform electric field on the statistical distribution of carriers in the β-HgS layer is also considered. An explicit dependence of the chemical potential and other statistical characteristics of the sample on the magnitude of the perturbing field has been obtained.

Multiphoton absorption and Rabi oscillations in armchair graphene nanoribbons

We present an analytical approach to the problem of the multiphoton absorption and Rabi oscillations in an armchair graphene nanoribbon (AGNR) in the presence of a time-oscillating strong electric field induced by a light wave directed parallel to the ribbon axis. The two-dimensional Dirac equation for the massless electron subject to the ribbon confinement is employed. In the resonant approximation the electron-hole pair production rate, associated with the electron transitions between the valence and conduction size-quantized subbands, the corresponding multiphoton absorption coefficient and the frequency of the Rabi oscillations are obtained in an explicit form. We trace the dependencies of the above quantities on the ribbon width and electric field strength for both the multiphoton assisted and tunneling regimes relevant to the time-oscillating and practically constant electric field, respectively. A significant enhancement effect of the oscillating character of the electric field on the intersubband transitions is encountered. Our analytical results are in qualitative agreement with those obtained for the graphene layer by numerical methods. Estimates of the expected experimental values for the typically employed AGNR and laser parameters show that both the Rabi oscillations and multiphoton absorption are accessible in the laboratory. The data relevant to the intersubband tunneling makes the AGNR a 1D condensed matter analog in which the quantum electrodynamic vacuum decay can be detected by applying an external laboratory electric field.

Multiphoton intersubband transitions in an armchair graphene nanoribbon

We present an analytical approach to the problem of the interband transitions in an armchair graphene nanoribbon (AGNR), exposed to the time-periodic electric field of strong light wave, polarized parallel to the ribbon axis. The two-dimensional Dirac equation for the massless electron subject to the ribbon confinement is employed. In the resonant approximation the probability of the transitions between the valence and conduction size-quantized subbands are calculated in an explicit form. We trace the dependencies of the Rabi frequency for these transitions on the ribbon width and electric field strength for both the multiphoton-assisted and tunneling regimes relevant to the fast oscillating and practically constant electric field, respectively. Estimates of the expected experimental values for the typically employed AGNR and laser technique facilities show that the Rabi oscillations can be observed under laboratory conditions. The data, corresponding to the intersubband tunneling, makes the AGNR a 1D condensed matter analog, in which the quantum electrodynamic vacuum decay can be detected by the employment of the attainable electric fields.

Scattering of Charge Carriers by Impurity Ions in InAs/AlSb Heterostructure

The mechanism of charge carrier scattering on ionized impurity atoms in an InAs/AlSb heterostructure with two filled size quantization subbands is studied. The purpose of the article is to develop a theory that fully describes quantum-mechanical processes in the structure under study. The calculation performed within the framework of the proposed transport time algorithm showed that the developed theory describes with high accuracy the mechanism of scattering of two-dimensional carriers by donor impurity ions in an active InAs layer. It was established that the lifetime limiting the mobility of two-dimensional carriers upon scattering by impurity ions is of the order of 10–12 s.

Solution of Self-Consistent Kohn–Sham and Poisson Equations for Quasi Two-Dimensional Electron Gas in the Accumulation Layer of Semiconductor with Nonparabolic Conduction Band

We generalize the method proposed previously for a self-consistent solution of the system of the Kohn–Sham and Poisson equations to the case of high density of electrons localized near the surface of a semiconductor due to size quantization of the electron spectrum in a potential well in the band banding region. We obtain a completely self-consistent iterative solution for a quasi two-dimensional electron gas in the accumulation layer at the surface of a semiconductor with a degenerate electron gas in the bulk. Both parabolic and non-parabolic energy spectra of conduction electrons are considered. For a parabolic conduction band, we obtain the spatial distributions of the electron density and electrostatic potential, as well as the energies of size-quantized levels and their dependence on the depth of the near-surface potential well. A significant decrease in the density of three-dimensional electrons was revealed in the region where the quasi two-dimensional electron gas occupied the accumulation layer. We calculated the dependencies of the excess electron surface density and the capacitance of the structure on the surface potential. The results are presented in dimensionless form that can be used to semi-quantitatively evaluate the parameters of accumulation layers by the known level of doping and the value of band bending. In the case of the nonparabolic conduction band, due to the finite bandgap width, the spectrum of quasi two-dimensional electron gas is obtained in the two-band Franz–Kane approximation by solving the eigenvalue problem for the new single-band equation of the effective-mass method. The density of states and the effective mass of electrons in the 2D subbands is found to increase linearly with energy. We have derived the expression that analytically approximates the calculated energy spectrum. The position of levels, the dispersion of energy spectrum, and the dependence of effective mass on energy, which were found for the size-quantized sub-bands, are in agreement with the published results for characteristics of quasi two-dimensional electrons at n-InAs surface that were directly measured by angle resolved photoelectron spectroscopy and magnetotunneling spectroscopy. Conditions are considered when the nonparabolicity of the conduction band enables quasi two-dimensional electrons to absorb the normally incident radiation due to intersubband transitions.

Effect of barrier width between GaAs/InGaAs/GaAs double coupled quantum wells on bipolar transport and terahertz radiation by hot carriers in lateral electric field

The dependences of the current and integral intraband terahertz electroluminescence intensity on the electric field in the n-InGaAs/GaAs heterostructures with asymmetric double tunnel-coupled quantum wells under the conditions of bipolar lateral transport are established to differ qualitatively for different interwell barrier widths. In the case of the thick (∼50 Å) barriers at electric fields less than those corresponding to the Gunn instability, high-frequency current oscillations are observed, and the emission intensity monotonously increases with increasing electric field strength over the entire studied range up to 3 kV/cm. At small barrier widths (∼30 Å), the current oscillations are practically absent, and the emission intensity substantially increases with the field strength between 1.5 and 2 kV/cm. The emission intensity increase is explained by the addition of direct electron and hole transitions between the size-quantization subbands to the indirect intrasubband transitions. The observed differences may be explained by the different relationships between the interband radiative recombination time of the minority charge carriers (holes) in the narrow wells and the hole tunneling time into the wide wells, dependent on the interwell barrier width.

Acceptor-related terahertz and infrared photoconductivity in p-type GaAs/AlGaAs quantum wells

Photoconductivity in GaAs/AlGaAs quantum well nanostructures doped with acceptors was studied at low lattice temperatures in the infrared and terahertz spectral ranges. The photocurrent spectra revealed features that can be attributed to the hole transitions from the ground acceptor state to the excited acceptor states and size-quantized subbands.

Nonparabolicity of size-quantized subbands of bilayer semiconductor quantum wells with heterojunction.

This paper presents a theory of size quantization and intersubband optical transitions in bilayer semiconductor quantum wells with asymmetric profile. We show that, in contrast to single-layer quantum wells, the size-quantized subbands of bilayer quantum wells are nonparabolic and characterized by effective masses that depend on the electron wave number and the subband number. It is found that the effective masses are related to the localization of the electron wave function in the layers of the quantum well and can be controlled by varying the chemical composition or geometric parameters of the structure. We also derive an analytical expression for the probability of optical transitions between the subbands of the bilayer quantum well. Our results are useful for the development of laser systems and photodetectors based on colloidal nanoplates and epitaxial layers of semiconductor materials with heterojunctions.

Photon avalanche effect in quantum wells: controlling light with light

A new mechanism of controlling the absorption of high-intensity signal light with frequency $\omega $ω and intensity ${j_\omega }$jω by complementary control light with frequency $\Omega \gt {2}\omega $Ω>2ω and 2 or 3 orders of magnitude lower intensity ${j_\Omega }$jΩ is proposed. The mechanism is based on the photon avalanche effect in quantum wells. The electron concentrations in size-quantization subbands and conduction band continuum and the absorbed power of signal light are obtained as functions of the intensities ${j_\omega }$jω and ${j_\Omega }$jΩ and the time of exposure to laser radiation $t$t. It is established that the resulting dependences exhibit well-pronounced threshold behavior. For example, at ${j_\Omega }\;\sim\;{0.2 - 1}\;{\text{kW/cm}^2}$jΩ∼0.2−1kW/cm2 and $t\;\sim\;{0.1 - 5}\;\text{ns}$t∼0.1−5ns, it is possible to control the absorption of signal light, so that the absorption of this light is practically lacking at intensities ${j_\omega }$jω below the threshold intensity (${40 - 200}\;{\text{kW/cm}^2}$40−200kW/cm2) and becomes very strong at intensities above the threshold intensity. The case when control light $\Omega $Ω is the third harmonic of high-intensity signal light is also considered.

Exciton absorption spectra in narrow armchair graphene nanoribbons in an electric field

We present an analytical investigation of the exciton optical absorption in a narrow armchair graphene nanoribbon (AGNR) in the presence of a longitudinal external electric field directed parallel to the ribbon axis. The two-body 2D Dirac equation for the massless electron and hole subject to the ribbon confinement, Coulomb interaction and electric field is employed. The ribbon confinement is assumed to be much stronger than the internal exciton electric field which in turn considerably exceeds the external electric field. This justifies an adiabatic approximation implying a slow longitudinal and fast transverse electron-hole relative motion governed by the exciton attraction and accompanied by the external electric field and ribbon confinement effects, respectively. In the single subband approximation of the isolated size-quantized subbands induced by the ribbon confinement the exciton electroabsorption coefficient is determined in an explicit form. The pronounced dependencies of the exciton peak positions, widths and intensities on the ribbon width and electric field strength are traced. The electron-hole exciton attraction modifies remarkably the Franz-Keldysh electroabsorption in the frequency region both below and above the edges determined by the size-quantized energy levels. In the double-subband approximation of the interacting ground and first excited subbands the combined effect of the exciton electro- and autoionization caused by the electric field and intersubband coupling, respectively, are explored. Estimates of the expected experimental values for the typically employed AGNR show that for a weak electric field the exciton quasi-discrete states remain sufficiently stable to be observed in optical experiments, while relatively strong fields free the captured carriers to further restore their contribution to the transport.

Nonlinear Photoexcitation of Heterostructures with Deep Quantum Wells: I. Probabilities of Elementary Processes

The probabilities of different types of optical processes involved in the formation of a photon avalanche in type-I heterostructures with deep quantum wells are calculated. The processes include two-electron transitions with participation of a photon, phototransitions between electronic states of size-quantized subbands and continuum of band states, and two-photon interband transitions in quantum wells. The obtained probabilities will be used in the forthcoming parts of the study for analysis of photon-avalanche kinetics.

Determination of Electron Temperature in DA-pHEMT Heterostructures by Shubnikov – de Haas Oscillation Method

The electron temperature of a two-dimensional electron gas heated by an electric field in DA-pHEMT heterostructures was determined by the Shubnikov – de Haas (SdH) oscillation method separately for each size-quantization subband. An analysis of the Fourier spectra of SdH oscillations showed that throughout the entire range of electron temperatures obtained, harmonics associated with different size-quantization subbands and transitions between the Landau levels of these subbands dominate in the spectra. To separate the SdH oscillations into individual harmonics, we used the approximation of the magnetic-field dependences of the oscillations by theoretical expressions using the ratio between the peak heights in the Fourier spectra. It is shown that this method allows one to determine the values of the electron temperature in case when the electron concentrations in the first and second subbands are close in magnitude. The obtained values of the electron temperature correspond to the literature data.

To the Theory of the Polarized Radiation Absorption in a Semiconductor (001) Quantum Well

The paper considers absorption of linearly polarized radiation in a semiconductor size-quantized well related to optical transitions both between the branches of light and heavy holes and between the size-quantized subbands. Main features of the light absorption in an infinitely deep symmetric well are elucidated. These features are characterized by intraband absorption of light and associated with the direct optical transitions of holes between the subbands of the semiconductor valence band formed due to the size quantization.

Подвижность двумерного электронного газа в DA-pHEMT гетроструктурах с различной шириной профиля delta-n-слоев

AbstractThe effect of the silicon-atom distribution profile in donor δ-layers of AlGaAs/InGaAs/AlGaAs heterostructures with donor–acceptor doping on the mobility of the two-dimensional electron gas is studied. The parameters of the δ-layer profiles are determined using the normal approximation of the spatial distributions of silicon atoms, measured by secondary-ion mass spectroscopy. It is shown that the standard deviation σ of the δ-layer profile can be reduced from 3.4 to 2.5 nm by the proper selection of growth conditions. Measurements of the magnetic-field dependences of the Hall effect and conductivity show that such a decrease in σ allowed an increase in the mobility of the two-dimensional electron gas in heterostructures by 4000 cm^2/(V s) at 77 K and 600 cm^2/(V s) at 300 K. The mobility calculation taking into account filling of the first two size-quantization subbands shows that an increase in the mobility is well explained by a reduction in the Coulomb scattering at ionized donors due to an increase in the effective thickness of the spacer layer with decreasing σ of the δ-layer profile.

Mobility of the Two-Dimensional Electron Gas in DA-pHEMT Heterostructures with Various δ–n-Layer Profile Widths

The effect of the silicon-atom distribution profile in donor δ-layers of AlGaAs/InGaAs/AlGaAs heterostructures with donor–acceptor doping on the mobility of the two-dimensional electron gas is studied. The parameters of the δ-layer profiles are determined using the normal approximation of the spatial distributions of silicon atoms, measured by secondary-ion mass spectroscopy. It is shown that the standard deviation σ of the δ-layer profile can be reduced from 3.4 to 2.5 nm by the proper selection of growth conditions. Measurements of the magnetic-field dependences of the Hall effect and conductivity show that such a decrease in σ allowed an increase in the mobility of the two-dimensional electron gas in heterostructures by 4000 cm2/(V s) at 77 K and 600 cm2/(V s) at 300 K. The mobility calculation taking into account filling of the first two size-quantization subbands shows that an increase in the mobility is well explained by a reduction in the Coulomb scattering at ionized donors due to an increase in the effective thickness of the spacer layer with decreasing σ of the δ-layer profile.

Ferromagnetism in the vicinity of Lifshitz topological transitions

We show that the critical temperature of a ferromagnetic phase transition in a quasi-two-dimensional hole gas confined in a diluted magnetic semiconductor quantum well strongly depends on the hole chemical potential and hole density. The significant variations of the the Curie temperature occur close to the Lifshitz topological transition points where the hole Fermi surface acquires additional components of topological connectivity due to the filling of excited size-quantization subbands. The model calculations demonstrate that the Curie temperature can be doubled by a small variation of the gate voltage for the CdMnTe/CdMgTe quantum well based device.

Effect of electric field on the ratio between the rashba and dresselhaus parameters in III–V heterostructures

The size-quantized energy subbands and envelope wave functions for [001] quantum wells based on zinc-blende III–V semiconductors are numerically calculated using the eight-band Kane model and finite-difference discretization scheme in coordinate space. The effect of the quantum-well band parameters and external electric field oriented along the structure growth direction on the ratio between the Rashba and Dresselhaus spin–orbit coupling parameters is studied. It is demonstrated that at certain electric-field values the spin–orbit coupling parameters in GaAs/InGaAs structures can be equal, which ensures the condition for forming stable spin helices. In addition, it is established that the spin–orbit coupling linear in wave vector in symmetric GaAs/InGaAs wells can disappear under certain well widths and barrier chemical compositions.

Electric-field-induced Nonlinear Optical Rectification, Second- and Third-harmonic Generation in Asymmetrical Quantum Well

The effects of a static electric field on the nonlinear optical rectification, second- and third-harmonic generation in a quantum well described by Morse potential are theoretically investigated. Analytical expressions for the optical coefficients due to intersubband optical transitions with an applied electric field are extracted from the compact-density matrix approach and iterative scheme. Numerical results presented for a typical GaAs quantum well reveal the feasibility of control of optical transitions between the size-quantized subbands. In addition, we have to emphasize the fact that the optical response of the system is remarkably sensitive to the electric field and structural range parameter.