Carbon Systems

The electronic states of a “quantum dot-graphene monolayer-SiO₂ + n ⁺-Si substrate” system in an external magnetic field are studied. An analytical expression for charge transfer in this system is obtained. The electronic states of a “quantum dot-graphene bilayer-SiO₂ + n ⁺-Si substrate” system are considered. The systems under study are interesting from the viewpoint of controlling the optical properties of a quantum dot by means of an applied electric field.     

Quantum-confined Stark shift in electroreflectance of a cylindrical GaN quantum dot

The electroreflectance (ER) spectra in the presence of the modulated electric field have been employed to study the fine structure of a cylindrical GaN quantum dot (QD), including the light hole and heavy hole interband transitions, and the ER spectra exhibit Franz-Keldysh oscillation characteristics with abscissa of energy (E−E_g). The quantum-confined Stark shift (QCSS) happened when the electric field intensity increased and the light and heavy holes dependent characteristics have been shown. The three-dimensional Schrödinger equation of QD has been calculated within the framework of effective-mass approximation, and the ER indices have been obtained from modulation absorption coefficients using the Seraphin coefficients and the Kramer-Kroning relation.     

Landé g-factor and cyclotron effective mass in a cylindrical GaAs-(Ga,Al)As quantum pillbox under the influence of an axis-parallel applied magnetic field

We have performed a theoretical study of electronic states and the parallel Landé g-factor in a quantum dot (QD), assumed to be in the form of a pillbox, in the presence of an uniform magnetic field applied parallel to the pillbox axis. The quantum pillbox is assumed to consist of a finite length cylinder of GaAs material surrounded by Ga_1-xAl_xAs which describe the realistic finite potential confinement. The calculations have been performed by using the Kummer confluent hypergeometric functions. This study is performed for different radii and lengths of the cylindrical GaAs pillbox and the limit cases have been studied to prove the validity of the model. Our results are in good agreement with the previous theoretical results [F.E. López, B.A. Rodríguez, E. Reyes-Gómez, L.E. Oliveira, in press] in the limit geometry of a quantum well wire (QWW).     

Dynamic characteristics of double-barrier nanostructures with asymmetric barriers of finite height and widths in a strong ac electric field

The theory of the interaction of a monoenergetic flow of injected electrons with a strong high-frequency ac electric field in resonant-tunneling diode (RTD) structures with asymmetric barriers of finite height and width is generalized. In the quasi-classical approximation, electron wavefunctions and tunneling functions in the quantum well and barriers are found. Analytical expressions for polarization currents in RTDs are derived in both the general case and in a number of limiting cases. It is shown that the polarization currents and radiation power in RTDs with asymmetric barriers strongly depend on the ratio of the probabilities of electron tunneling through the emitter and collector barriers. In the quantum mode, when δ = ? ? ? _r = ?ω ? Γ (? is the energy of electrons injected in the RTD, ? is Planck’s constant, ω is the ac field frequency, ? _r and Γ are the energy and width of the resonance level, respectively), the active polarization current in a field of E ≈ 2.8?ω/ea (e is the electron charge and a is the quantum-well width) reaches a maximum equal in magnitude to 84% of the direct resonant current, if the probability of electron tunneling through the emitter barrier is much higher than that through the collector barrier. The radiation-generation power at frequencies of ω = 10¹²–10¹³ s^?1 can reach 10⁵–10⁶ W/cm² in this case.     

Wannier-Stark states in a superlattice of InAs/GaAs quantum dots

Electron and hole emission from states of a ten-layer system of tunneling-coupled vertically correlated InAs/GaAs quantum dots (QDs) is studied experimentally by capacitance—voltage measurements and deep-level transient spectroscopy. The thickness of GaAs interlayers separating sheets of InAs QDs was ≈3 nm, as determined from transmission electron microscope images. It is found that the periodic multimo-dal DLTS spectrum of this structure exhibits a pronounced linear shift as the reverse-bias voltage U _r applied to the structure is varied. The observed behavior is a manifestation of the Wannier—Stark effect in the InAs/GaAs superlattice, where the presence of an external electric field leads to the suppression of coupling between the wave functions of electron states forming the miniband and to the appearance of a series of discrete levels called Wannier—Stark ladder states.     

Energy spectrum of a nonideal quantum well in an electric field

The effect of an electric field on the energy spectrum of a quantum well with macroscopic fluctuations is studied. The Stark shift of the quasibound states in a quantum well and three field-dependent broadening mechanisms (field-induced homogeneous broadening and broadening due to well width and depth fluctuations) are calculated in a wide range of electric fields. As an example, the effect of an electric field on the energy spectrum of electrons in a 12-nm-wide GaAs/Al_0.3Ga_0.7As quantum well with 5% width and depth fluctuations is determined. Fiz. Tekh. Poluprovodn. 32, 1108–1113 (September 1998)     

In‐plane coupling effect on absorption coefficients of InAs/GaAs quantum dots arrays for intermediate band solar cell

Coupled semiconductor quantum dot (QD) arrays emerged recently as promising structures for the next generation of high efficiency intermediate band solar cell (IBSC), because of their ability to facilitate the formation of minibands. The quantum coupling effect that exists between states in QDs in an array influences the electronic and optical properties of such structures. So far, great experimental and theoretical efforts have been devoted to study the vertically coupled QD arrays. We present here a method based on multi‐band k ⋅ p Hamiltonian combined with periodic boundary conditions, applied to predict the electronic and optical properties of InAs/GaAs QDs‐based lateral QD arrays. Formation of the intermediate band (IB) in all cases was achieved via delocalisation of the electron ground state (e0). We show that the IB in a laterally coupled QD‐IBSC is more robust against external electric field from the solar cell's pn junction than that in a vertically coupled arrangement. Because of symmetry of the QD array lattice and QD states itself, which are C_2v for the zinc blend QDs, the electronic and absorption structures were obtained via sampling throughout the reciprocal space in the first Brillouin zone of QD arrays. Copyright © 2014 John Wiley & Sons, Ltd.     

Ferroelectric and leakage current characteristics of (Pb0.72La0.28)Ti0.93O3 thin films prepared by a sol-gel process

(Pb_1 − xLa_x)Ti_1 − x/4O₃(x = 28 mol%, denoted as PLT) thin films were grown on Pt/Ti/SiO₂/Si substrates by using a sol-gel process. The Pt/PLT/Pt film capacitor showed well-saturated hysteresis loops at an applied electric field of 500 kV/cm with spontaneous polarization (P_s), remanent polarization (P_r) and coercive electric field (E_c) values of 9.23 μC/cm², 0.53 μC/cm² and 19.7 kV/cm, respectively. At 100 kHz, the dielectric constant and dissipation factor of the film were 748 and 0.026, respectively. The leakage current density is lower than 1.0 × 10⁻⁷ A/cm²over the electric field range of 0 to 200 kV/cm. And the Pt/PLT interface exist a Schottky emission characteristics.     

Parameter-dependent third-order nonlinear susceptibility of parabolic InGaN/GaN quantum dots

The electron states confined in wurtzite In_xGa_1−xN/GaN-strained quantum dots (QDs) have been investigated in the effective-mass approximation by solving the Schrödinger equation, in which parabolic confined potential and strong built-in electric field effect due to the piezoelectricity and spontaneous polarization have been taken into account. The third-order nonlinear susceptibility of the QDs in various directions (both parallel to z direction and vertical to z direction) have been calculated, and the magnitude reaches 10⁻¹⁴ m²/V². It has been shown from the results that the order of the built-in electric field in the strained QD is of MV/cm. Furthermore, the results of how the third-order nonlinear susceptibility depend on the radius R of QDs, the height L of QDs, the In content x of QDs and the relaxation rate Γ₁₀ have been given.     

A detailed analysis of the metal-semiconductor contact

A general quantum and electronic theory able to explain the electric and photoelectric experimental properties of the metal-semiconductor contacts is proposed. The theory consists firstly in calculating the electric space charge due to the quantum mechanical tunneling of the electrons from the metal into the semiconductor, and vice-versa, and to the metal and semiconductor bands bending. Then the electric charge so obtained is utilised to solve in an appropriate and complete way the Poisson equation so as to determine the electric field and potential as functions of the abscissa x. The electric field F(x) is employed to obtain a new expression for the junction capacitance C, holding in the general case of a non-uniform charge, whereas the electric potential ν_i(x) is used to calculate general expressions for the thermionic and photoelectric currents i and i_ph, respectively, taking into account in this both the tunneling probability through the energy barrier and the many-valley structure of the semiconductor energy bands. Finally, from ν_i(x), C, i and i_ph four new expressions of the energy barrier height of the contact are deduced. The theoretical results relative to the barrier height so determined (which hold for both n-and p-type semiconductors) are compared with published experimental values obtained, by means of capacitance and photocurrent measurements: (a) on contacts between n-type CdS and Au, Cu, Ag and Pt; (b) on contacts between n-type GaAs and Au, Ag, Cu, Sn, Al and Pt and; (c) on contacts between p-type GaAs and Au and Al. The agreement between the theoretical and experimental values is very good.     

Investigation of electron properties of semiconductor surface by modulation spectroscopy of electroreflection

The relation of the Franz-Keldysh oscillations to electronic parameters of semiconductor materials is analyzed using the high-field measurement mode. The potential of using modulation spectroscopy of electroreflection for investigating electronic properties of a semiconductor surface is shown by the example of electroreflection spectra of n-GaAs (100) homoepitaxial films with the electron concentration of 10¹⁷–10¹⁸ cm^?3. The spectra are measured by the Schottky-barrier method at a room temperature using unpolarized light in the spectral range of 1.3–1.65 eV in the vicinity of the transition E ₀ (Γ_8V -Γ_6C ). From the quantitative analysis of electroreflection spectra, electronic parameters of films are obtained: the electron-transition energy E ₀, the electro-optical energy ??, the surface electric field F _s, the energy-relaxation time τ of charge carriers, the oscillation length λ_KF of the wave function of a quantum-mechanical particle with a reduced effective mass μ for a given surface electric field F _s, and the electron mobility μ_e.     

Light-emitting tunneling nanostructures based on quantum dots in a Si and GaAs matrix

InGaAs/GaAs and Ge/Si light-emitting heterostructures with active regions consisting of a system of different-size nanoobjects, i.e., quantum dot layers, quantum wells, and a tunneling barrier are studied. The exchange of carriers preceding their radiative recombination is considered in the context of the tunneling interaction of nanoobjects. For the quantum well-InGaAs quantum dot layer system, an exciton tunneling mechanism is established. In such structures with a barrier thinner than 6 nm, anomalously fast carrier (exciton) transfer from the quantum well is observed. The role of the above-barrier resonance of states, which provides “instantaneous” injection into quantum dots, is considered. In Ge/Si structures, Ge quantum dots with heights comparable to the Ge/Si interface broadening are fabricated. The strong luminescence at a wavelength of 1.55 μm in such structures is explained not only by the high island-array density. The model is based on (i) an increase in the exciton oscillator strength due to the tunnel penetration of electrons into the quantum dot core at low temperatures (T < 60 K) and (ii) a redistribution of electronic states in the Δ₂-Δ₄ subbands as the temperature is increased to room temperature. Light-emitting diodes are fabricated based on both types of studied structures. Configuration versions of the active region are tested. It is shown that selective pumping of the injector and the tunnel transfer of “cold” carriers (excitons) are more efficient than their direct trapping by the nanoemitter.     

Diagnostics of the hot-hole distribution function in quantum wells in a strong electric field

Modulation of the fundamental absorption edge by a high lateral electric field in a p-type In_0.21Ga_0.79As/GaAs heterostructure with quantum wells was studied at 4.2 K and electric fields as high as 1.9 kV/cm. The field-induced change in the symmetric part of the hole distribution function was measured.     

Atom-like behaviors and orbital-related Tomonaga-Luttinger liquids in carbon nano-peapod quantum dots

We report ballistic charge transport phenomena observed in carbon nano-peapod quantum dots. We find atom-like behaviors (shell filling) sensitive to applied back-gate voltages (V_bg) by single electron spectroscopy. Doubly degenerate electronic levels are found only around ground states at very low V_bg. Those correlations with the presence of nearly free electron states unique to the peapods are discussed. Moreover, we find power laws in conductance versus energy relationships with anomalously high values of power, which are strongly associated with shell filling to the doubly degenerate levels. It is investigated that the powers originate from Tomonaga-Luttinger liquid via the occupied doubly degenerate levels. These results imply that a ballistic charge transport is still preserved at low-V_bg regions in carbon nano-peapod quantum dots in spite of the presence of the encapsulated C₆₀ molecules.     

Tight-binding study of the optical properties of GaN/AlN polar and nonpolar quantum wells

The electronic structure of wurtzite semiconductor superlattices (SLs) and quantum wells (QWs) is calculated by using the empirical tight-binding method. The basis used consists of four orbitals per atom (sp³ model), and the calculations include the spin-orbit coupling as well as the strain and electric polarization effects. We focus our study on GaN/AlN QWs wells grown both in polar (C) and nonpolar (A) directions. The band structure, wave functions and optical absorption spectrum are obtained and compared for both cases.     

Current-voltage characteristics of silicon metallic-silicide interfaces

The general quantum and electronic theory of the metal-semiconductor contacts, proposed in previous works, is applied to silicon-metallic silicide interfaces in order to calculate their current-voltage characteristics. The analysis takes into account the actual potential profile due both to the semiconductor depletion layer and to the electric dipole created, around the metal-semiconductor interface (MSI), by the quantum mechanical tunneling of the metal free electrons into the semiconductor and by the metal conduction band bending. The current across the MSI, ascribed to the thermionic assisted tunneling, is calculated by taking into account the anisotropy of the effective masses, the many valley-structure of the semiconductor energy bands and the quantum mechanical reflection and tunneling through the energy barrier by means of the generalized transmission probability of Kemble. The results shown by the analysis, which excludes explicity the image-force lowering of the energy barrier height, are the reduction of the height and width of the barrier itself and (hence) the increase of its “transparency” to the thermionic current produced by the increase of the reverse bias voltage and/or of the semiconductor impurity concentration. The effects of such properties of the energy barrier on the current-voltage characteristics of the MSI are the absence of a true reverse saturation current, an ideality factor n greater than 1 and a value of the energy barrier height, deduced from the forward current-voltage characteristics, lower than that true and than that obtained from the measured of the junction capacitance vs the bias voltage. The analysis, applied to interfaces between n-type silicon and the metallic silicides RhSi, ZrSi₂, PtSi and Pd₂Si, yields numerical values which agree well with the experimental ones obtained by several authors on the same contacts which, when it is necessary to eliminate field-enhancement at the electrode periphery and leakage currents, incorporate a guard ring. Effectively such a guard ring and the absence of intervening layers of oxide and of other contaminants in the silicon-metal silicide contacts allow one to acquire experimental data more easy to interpret quantitatively than those relative to other contact types.     

Effects of quantum confinement and compositional grading on the band structure of heterojunctions

The band structure of a heterojunction may have discrete electronic states arising from quantum confinement; in addition the band edge is perturbed by grading in the composition. A new method is introduced to analyse these effects by an effective field “F_eff” in the transition region, including the position-dependence of space charge and of composition. The F_eff is position-dependent and is zero-valued at the positions which correspond to extrema of the band edges. For most practical cases it is shown that F_eff can be approximated as a linear function of position near the zero-valued positions, thus yielding harmonic oscillator states. The effective force constant can be expressed in terms of position-dependent material parameters. The effects of position-dependent effective masses are also considered. The analysis is applied to the p-n GaAsAl_0.4Ga_0.6As heterojunction; changes of the order of $\text{1}\text{10}$ eV in the effective band gap are predicted.     

Subband structure and effective mass of relaxed and strained Ge (1 1 0) PMOSFETs

Effective mass and mobility of strained Ge (1 1 0) inversion layer in PMOSFET are studied theoretically in this paper. The strain condition considered in the calculations is the intrinsic strain resulting from growing the Ge layer on the (1 1 0) Si substrate. The quantum confinement effect resulting from the vertical effective electric field is incorporated into the k · p calculation. Various effective masses, such as quantization effective mass, m_z, density of states effective mass, m_DOS, and conductivity mass, m_C, as well as the hole mobility of strained Ge (1 1 0) inversion layer for PMOS under substrate strain and various effective electric field strengths are all investigated.     

Electronic structure and optical transitions in Sn and SnGe quantum dots in a Si matrix

Self-assembled quantum dots in the Si-Ge-Sn system have attracted research attention as possible direct band gap materials, compatible with Si-based technology, with potential applications in optoelectronics. In this work, the electronic structure near the Γ-point and the interband optical matrix elements of strained Sn and SnGe quantum dots in a Si matrix are calculated using the eight-band k.p method, and the competing L-valley conduction band states were found by the effective mass method. The strain distribution in the dots was found within the continuum mechanical model. The bulk band-structure parameters, required for the k.p or effective mass calculation for Sn were extracted by fitting to the energy band structure calculated by the non-local empirical pseudopotential method (EPM). The calculations show that the self-assembled Sn/Si dots, with sizes between 4 and 12 nm, have indirect interband transition energies (from the size-quantized valence band states at Γ to the conduction band states at L) between 0.8 and 0.4 eV, and direct interband transitions between 2.5 and 2.0 eV, which agrees very well with experimental results. Similar good agreement with experiment was also found for the recently grown SnGe dots on Si substrate, covered by SiO₂. However, neither of these is predicted to be direct band gap materials, in contrast to some earlier expectations.     

Stark effect in vertically coupled quantum dots in InAs-GaAs heterostructures

The results of studies of hole energy states in vertically coupled quantum dots in InAs-GaAs p-n heterostructures by deep-level transient spectroscopy are reported. Spectra were recorded at different reverse-bias voltages. Levels related to bonding and antibonding s and p states of vertically coupled quantum dots were revealed. The energies of these states significantly depend on an external electric field applied to a heterostructure. This dependence was attributed to the quantum-dimensional Stark effect for the hole states of vertically coupled quantum dots. In addition to this, it was found that the energy of thermal activation of carriers from vertically coupled quantum dots depends on the conditions of isochronous annealing that was carried out both with the reverse bias switched-on and switched-off and both in the presence and absence of illumination. These changes, as in the case of isolated quantum dots, are typical of a bistable electrostatic dipole formed by carriers, localized in a coupled quantum dot, and ionized lattice point defects. The built-in electric field of this dipole reduces the energy barrier for the carriers in the coupled quantum dot. The investigated structures with vertically coupled quantum dots were grown using molecular-beam epitaxy taking account of self-assembling effects.