Energy Spectrum Of Holes Research Articles

Resonance states, heavy quasiparticles, and the thermoelectric figure of merit of IV–VI materials

A high thermoelectric figure of merit ZT, with a maximum value ZT = 1.5 at 670–800 K for the composition Ge0.9Pb0.05Bi0.05Te, has been obtained for GeTe solid solutions with Bi and Pb impurities. This is conducive to a decrease in the hole concentration, an increase in the Seebeck coefficient, and a decrease in the lattice thermal conductivity. The main attention in interpretation of the experimental data is given to specific features of the energy spectrum of holes in the initial GeTe compound. The model of resonance states, formed with involvement of Ge atoms and metal vacancies, has been further developed. The types of defects and their transformation depending on temperature and the concentration of superstoichiometric Te have been considered. The experimental results give reason to believe that the interaction of localized and free charge carriers at elevated temperatures leads to a pronounced hybridization of their states and the formation of heavy quasiparticles, a situation in many ways similar to that observed in materials with heavy fermions.

Spectroscopic Study on Ultrafast Carrier Dynamics and Terahertz Amplified Stimulated Emission in Optically Pumped Graphene

This paper reviews recent advances in spectroscopic study on ultrafast carrier dynamics and terahertz (THz) stimulated emission in optically pumped graphene. The gapless and linear energy spectra of electrons and holes in graphene can lead to nontrivial features such as negative dynamic conductivity in the THz spectral range, which may lead to the development of new types of THz lasers. First, the non-equilibrium carrier relaxation/recombination dynamics is formulated to show how photoexcited carriers equilibrate their energy and temperature via carrier-carrier and carrier-phonon scatterings and in what photon energies and in what time duration the dynamic conductivity can take negative values as functions of temperature, pumping photon energy/intensity, and carrier relaxation rates. Second, we conduct time-domain spectroscopic studies using an optical pump and a terahertz probe with an optical probe technique at room temperature and show that graphene sheets amplify an incoming terahertz field. Two different types of samples are prepared for the measurement; one is an exfoliated monolayer graphene on SiO2/Si substrate and the other is a heteroepitaxially grown non-Bernal stacked multilayer graphene on a 3C-SiC/Si epi-wafer.

Longitudinal piezoresistance and conductance of the p-type silicon nanostructures in ballistic transport regime: from bulk to nanowires

Longitudinal piezoresistance coefficient ? l and conductance in the p-type silicon nanostructures with different dimensionality of holes D such as quantum wires D=1, quantum films D=2 and bulk silicon D=3 are investigated in the ballistic transport regime. Energy spectrum of holes for the low dimensional structures was accepted in the quasi-classical approximation. Piezoresistance coefficient ? l and conductance of nanostructures oriented along the [100], [110] and [111] crystallographic directions are calculated as function of temperature, concentration of holes, confining dimensions and elastic stress. The origin of the giant pezoresistance effect in the p-type silicon nanostructures at room temperature is explained by the concentration of stress in regions of the nanostructure depleted by holes. Using the only one parameter (the stress concentration factor) both qualitative and quantitative agreement was obtained between computational results and known experimental data.

Effect of copper doping on kinetic coefficients and their anisotropy in PbSb2Te4

In anisotropic PbSb2Te4 and PbSb2Te4:Cu single crystals, nine main independent components of the Hall, electrical-conductivity, thermopower, and Nernst-Ettingshausen effects and their anisotropy in the range 77–450 K have been studied. PbSb2Te4 single crystals exhibit a high hole concentration (p ≈ 3 × 1020 cm−3). Copper exhibits a donor effect and significantly (approximately by a factor of 2) reduces the hole concentration in PbSb2Te4. The temperature dependences of the kinetic coefficients, except for the Hall effect, have a form typical of the one-band model. The significant anisotropy of the Hall coefficient R 123/R 321 ≈ 2 at low temperatures corresponds to the multi-ellipsoid model of the energy spectrum of holes in PbSb2Te4. An important feature of the data on transport phenomena is the high thermopower anisotropy (ΔS ≈ 60–75 μV/K) in the mixed conductivity region caused by the mixed scattering mechanism. Data on the anisotropy of the transverse Nernst-Ettingshausen effect confirm the mixed mechanism of hole scattering; in the cleavage plane, scattering at acoustic phonons dominates, while in the trigonal axis direction, impurity scattering appears significant. Doping with copper enhances the role of impurity scattering in the direction of the trigonal axis c 3; as a result, two components of the Nernst-Ettingshausen tensor Q 321 and Q 132 in the PbSb2Te4:Cu single crystal are positive at low temperatures, whereas, in the undoped crystal, only the Q 321 component is positive.

Approximate κ-state solutions to the Dirac-Yukawa problem based on the spin and pseudospin symmetry

Abstract Using an approximation scheme to deal with the centrifugal (pseudo-centrifugal) term, we solve the Dirac equation with the screened Coulomb (Yukawa) potential for any arbitrary spin-orbit quantum number κ. Based on the spin and pseudospin symmetry, analytic bound state energy spectrum formulas and their corresponding upper- and lower-spinor components of two Dirac particles are obtained using a shortcut of the Nikiforov-Uvarov method. We find a wide range of permissible values for the spin symmetry constant C s from the valence energy spectrum of particle and also for pseudospin symmetry constant C ps from the hole energy spectrum of antiparticle. Further, we show that the present potential interaction becomes less (more) attractive for a long (short) range screening parameter α. To remove the degeneracies in energy levels we consider the spin and pseudospin solution of Dirac equation for Yukawa potential plus a centrifugal-like term. A few special cases such as the exact spin (pseudospin) symmetry Dirac-Yukawa, the Yukawa plus centrifugal-like potentials, the limit when α becomes zero (Coulomb potential field) and the non-relativistic limit of our solution are studied. The nonrelativistic solutions are compared with those obtained by other methods.

Anderson localization and the pseudogap in the energy spectrum of holes in PbTe: Tl under resonant scattering

This paper reports on a comprehensive study of the effect of additional doping with the Na acceptor impurity on the low-temperature resistivity of PbTe samples doped with Tl (2 at %), an impurity producing a band of resonant states within the valence-band spectrum. By additional doping with Na, we have shifted the Fermi level within the band of the resonant states of Tl in PbTe and varied the hole filling (k h ) of the thallium impurity states. The larger part of the PbTe: (Tl,Na) samples transfers to the superconducting state with a critical temperature T c = 0.4–2.3 K. The T c (k h ) relation obtained argues for the fact that, in the region of resonant states in PbTe: Tl, Anderson localization of holes and a pseudogap in the density of delocalized states are observed.

Electron and hole energy levels in InAs/GaAs quantum dots: Size and magnetic field effects

We present a systematic study on the influence of strain, size, and magnetic field on the electronic properties of InAs/GaAs quantum dots. Using a 40-band k.p model, we have calculated the band diagram of strained InAs, and extract the band parameters which are useful for the electronic properties of InAs/GaAs quantum dots. Then, using an exact numerical diagonalization method on Fourier–Bessel function basis over a large cylinder domain, we calculated numerically the electron and hole eigenenergies and associated wave functions. We considered thereafter the effect of an external applied magnetic field, strain and quantum dot size variation on the charge carrier energy levels. It is clearly found that the strain strongly modifies the quantum dot potential profile, leading to a different electron and hole energy distribution. Our results revealed also that the electron and hole energy spectra change significantly when varying the quantum dot size as well as the magnetic field. Given this striking nanostructure size and magnetic field energy dependent property, these systems provide the opportunity to control and tune their optical and electronic properties through these parameters.

Doping of IV-VI semiconductors and the energy spectrum of holes with resonance states taken into account

Kinetic phenomena in the Pb0.5Sn0.5Te solid solution have been studied in wide ranges of concentrations and temperatures in the case of two types of acceptor doping: with overstoichiometric tellurium and with a combination of equal amounts of Na and Te atoms; in the latter case, two additives amounting to 1.0 and 1.5 at % of each element have been used. Hole densities attained in this case significantly exceeded the largest values corresponding to the Pb0.5Sn0.5 Te:Te samples. For both types of acceptors, the hole concentration in the solid solution is found to be a factor of 2 higher than in PbTe with the same level of doping. The specific features of behavior of the Hall coefficient, thermopower, and electrical conductivity are interpreted in the context of a model of a single-valence-band spe ctrum with a wide band of resonant levels. The mechanism of formation of resonant levels in PbTe and Pb0.5Sn0.5 Te solid solutions is discussed.

Ferromagnetism of low-dimensional Mn-doped III-V semiconductor structures in the vicinity of the insulator-metal transition

The structural and transport properties of GaAs/Mn/GaAs/InxGa1−xAs/GaAs quantum wells (x≈0.2) with Mn δ-layer (4–10 at. %), separated from the well by a GaAs spacer, have been studied. The hole mobility in the investigated structures has exceeded the values known for magnetic III-V heterostructures by two orders of magnitude. For structures with the conductivity of the metal type, we have succeeded to observe at low temperatures Shubnikov–de Haas oscillations just confirming the two dimensionality (2D) of the hole energy spectrum. Exactly those 2D holes promote the ferromagnetic ordering of the Mn layer. That has been proven by (i) observing maxima (at 25–40 K) in temperature dependencies of the resistance, which positions agree with calculated values of Curie temperatures (for structures with the indirect interaction of Mn atoms via 2D holes), and (ii) revealing the negative spin-dependent magnetoresistance (NMR) as well as the anomalous Hall effect (AHE), which values are also in good agreement with calculations relating to ferromagnetic 2D III-V systems. As for the structures with the insulator type of the conductivity, their NMR and AHE features evidence the phase separation—the sample fragmentation with the formation of mesoscopic ferromagnetic areas separated by paramagnetic strata of the high tunnel conductivity.

Ferromagnetism of low-dimensional structures based on III-Mn-V semiconductors in the vicinity of the insulator-to-metal transition

The structural and transport properties of the GaAs/Mn/GaAs/InxGa1 − xAs/GaAs quantum wells (QWs) with the Mn layer distant from the QW and the Mn content ranging from 4 to 10% that correspond to the reentrant metal-to-insulator transition observed in the bulk GaMnAs are studied. The X-ray diffractometry and reflectometry are used to reconstruct the distribution profile of the Mn layers and to demonstrate the absence of the Mn atoms in the QW volume. The mobility of holes in the objects under study is greater than the known mobilities for the GaMnAs magnetic heterostructures by more than two orders of magnitude, which makes it possible to observe the Shubnikov-de Haas oscillations, proving the 2D character of the hole energy spectrum. A significant role of the 2D holes in the ferromagnetic ordering of the Mn layer is demonstrated under such conditions. The supporting evidence results from the observation of a maximum on the curves of the resistance versus temperature (at 25–40 K), whose position is in agreement with the calculated Curie temperature for the structures with indirect exchange interaction via the 2D-hole channel and the observation of the negative spin-dependent magnetoresistance (NM) and the anomalous Hall effect (AHE) that correlates with the theoretically calculated results for the ferromagnetic 2D III-Mn-V systems. The features of the NM and AHE revealed in the structures with the dielectric conduction indicate the effects of phase separation lying in the fragmentation of the sample into mesoscopic ferromagnetic domains separated by tunnel transparent paramagnetic layers. Such NM and AHE features are also observed in the weakly dielectric InMnAs films, which points to an important role of such effects in the III-Mn-V systems in the vicinity of the insulator-to-metal transition.

Ferromagnetic transition in GaAs/Mn/GaAs/In x Ga1 − x As/GaAs structures with a two-dimensional hole gas

The transport properties of GaAs/Mn/GaAs/In x Ga1 − x As/GaAs structures with a layer that is separated from the quantum well and contains Mn impurities in the concentration range 4–10 at % corresponding to the reentrant metal-insulator transition observed in the bulk GaMnAs material [17] have been investigated. The hole mobility in the objects under investigation is more than two orders of magnitude higher than the known values for the GaMnAs semiconductor and GaMnAs-based magnetic heterostructures. This makes it possible to observe Shubnikov-de Haas oscillations, which confirm a two-dimensional character of the hole energy spectrum. The calculated Curie temperature for heterostructures with indirect exchange interaction through a two-dimensional hole channel is in good agreement with the position of the maximum (at 25–40 K) in the temperature dependences of the electrical resistance of the channel. This suggests that two-dimensional holes play an important role in ferromagnetic ordering of the Mn layer under these conditions. The observations of a negative spin-dependent magnetoresistance and an anomalous Hall effect, whose magnitude correlates well with the results of theoretical calculations for two-dimensional ferromagnetic systems based on III-Mn-V, also indicate a significant role of the two-dimensional channel in ferromagnetic ordering.

Quantum size effects and transport phenomena in thin Bi layers

For thin Bi films with thicknesses d=10–60nm the dependences of the Hall coefficient, Seebeck coefficient, electrical conductivity, and Hall carrier mobility on d have been obtained at room temperature. Distinct oscillations of the transport properties with period Δd=(5±1)nm have been observed in the thickness range d=25–60nm and attributed to quantization of the energy spectrum of holes. It has been suggested that a deep minimum observed in the thickness dependences of the kinetic coefficients at d∼25nm is connected with the manifestation of the electronic spectrum quantization and/or manifestation of a semimetal–semiconductor transition. The experimental data are in good agreement with the results of theoretical calculations.

Nonadiabatic theory of excitons in wurtzite AlGaN/GaN quantum‐well heterostructures

AbstractWe have theoretically studied exciton states and photoluminescence spectra of the strained wurtzite AlxGa1–xN/GaN quantum‐well heterostructures. The electron energy spectrum is found through numerical solving of the one‐band Schrödinger equation, while the hole and exciton energy spectra are determined from the Schrödinger equation with the non‐symmetrical 6‐band Hamiltonian, including deformational and spin‐orbit interaction. The oscillator forces are calculated and the exciton states are determined, which are active in the process of the optical absorption. Three quantitative conclusions are made in a good agreement with experiments for different values of x as concerns: (i) the red shift of the zero‐phonon photoluminescence (PL) peaks with increase of the quantum‐well width, (ii) the relative intensities of the zero‐phonon and one‐phonon PL peaks, found within the non‐adiabatic approach, and (iii) the values of the PL decay time as a function of the quantum‐well width. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Electron Lande g-factor in GaAs/Al xGa 1−xAs quantum wires

Energy spectrum of charge carriers is researched with and without magnetic field in Kane-type semiconductor quantum nanostructures in case of finite potential barrier V. The model that is considered in the present study is composed of two concentric quantum wires. The inner part and outer part are made up of GaAs and Al x Ga 1− x As, respectively. In the first part, it is shown that energy spectrum of carriers depends on quantum wire radius for finite potential barrier without magnetic field by using Kane model. In the second part, energy spectra of charge carriers are calculated as the function of magnetic field by using Kane model in Al x Ga 1− x As/GaAs quantum wire and compared with results of parabolic approach. It is also shown that g-factors of electrons rely on radius. It is seen that g-factor of electrons is increasing while radius is decreasing. The applied model is also useful for obtaining the energy spectra of light holes and spin–orbit splitting holes.

Measurement of cyclotron masses of spin-orbit-split quasi-two-dimensional holes in GaAs(100) narrow quantum wells

The magnetic field dependence of the cyclotron mass of heavy holes in asymmetric GaAs(100) quantum wells is measured by optical detection of resonant microwave absorption for various concentrations of quasi-two-dimensional holes. The effect of spin-orbit splitting on the cyclotron masses of heavy holes is discovered and investigated. The energy spectrum of holes is calculated on the basis of experimental data. The energy range in which spin-plasmon oscillations are observed in hole systems with various concentrations is predicted.

Excitons in wurtziteAlGaN∕GaNquantum-well heterostructures

We have theoretically studied exciton states and photoluminescence spectra of strained wurtzite AlGaN/GaN quantum-well heterostructures. The electron and hole energy spectra are obtained by numerically solving the Schr\"odinger equation, both for a single-band Hamiltonian and for a non-symmetrical 6-band Hamiltonian. The deformation potential and spin-orbit interaction are taken into account. For increasing built-in field, generated by the piezoelectric polarization and by the spontaneous polarization, the energy of size quantization rises and the number of size quantized electron and hole levels in a quantum well decreases. The exciton energy spectrum is obtained using electron and hole wave functions and two-dimensional Coulomb wave functions as a basis. We have calculated the exciton oscillator strengths and identified the exciton states active in optical absorption. For different values of the Al content x, a quantitative interpretation, in a good agreement with experiment, is provided for (i) the red shift of the zero-phonon photoluminescence peaks for increasing the quantum-well width, (ii) the relative intensities of the zero-phonon and one-phonon photoluminescence peaks, found within the non-adiabatic approach, and (iii) the values of the photoluminescence decay time as a function of the quantum-well width.

Anomalous splitting of the hole states in silicon quantum dots with shallow acceptors

Hole wavefunctions and energy spectra have been calculated in a silicon quantum dot witha shallow acceptor. Within the framework of the envelope function approach we have foundanomalously strong splitting of the energy levels caused by the Coulomb and the spin–orbitinteractions as compared to bulk silicon. If the quantum dot has been doped with boron,the short range part of the Coulomb field turns out to be weak, and the long rangehydrogenic part plays a crucial role in the energy splitting. In the case where the dot isdoped with any other element of the third group, the role of the short range Coulombinteraction becomes determinative. The latter provides stronger energy splitting comparedto that in the model of hydrogen-like impurity. In both cases the energy of the splittingsubstantially exceeds the typical bulk values for these acceptors due to the quantumconfinement effect. We have also analysed the charge distribution in the dot andthe hole spectrum, depending on the acceptor position inside the nanocrystal.

Electron, hole, and exciton spectra in a quantum wire crossing the quantum well

The electron, hole, and exciton energy spectra are calculated within the effective mass and rectangular potential approximations for a combined semiconductor nanoheterosystem consisting of a cylindrical semiconductor quantum wire crossing the plane quantum well. It is shown that the electron (hole) in such a system is characterized by five quantum numbers related to five degrees of freedom for a quasiparticle. The dependences of the quasiparticle energy on the quantum wire radius and the quantum well width are researched.

Charge-carrier states and light absorption in ordered quantum dot superlattices

We have theoretically investigated the electron and hole energy spectra and light absorption in the three-dimensionally ordered quantum dots superlattices (QDS) made of the direct band-gap semiconductors. The calculations were performed for QDS of the rhombic symmetry with a substantial electron (hole) wave-function overlap using a one-band Hamiltonian for the electrons and six-band Hamiltonian for the holes. The obtained results were compared with the predictions of the simplified models for the uncoupled heavy, light, and split-off holes. It has been shown that the energy spectra of the electrons and holes in the ordered QDS are distinctively different from those in the single quantum dots (QD) or conventional quantum-well superlattices. The charge-carrier dispersion and localization are very sensitive to the quasicrystallographic directions defined by the dots, which play a role of the atoms in such QD supracrystal. We found that in the ordered QDS the oscillator strength for the interband optical transitions can be high for a relatively wide range of the photon energies. The obtained results are important for the proposed applications of QDS in solar cells, photodetectors, and thermoelectrics.

Plasma waves in two-dimensional electron-hole system in gated graphene heterostructures

Plasma waves in the two-dimensional electron-hole system in a graphene-based heterostructure controlled by a highly conducting gate are studied theoretically. The energy spectra of two-dimensional electrons and holes are assumed to be conical (neutrinolike), i.e., corresponding to their zero effective masses. Using the developed model, we calculate the spectrum of plasma waves (spatio-temporal variations of the electron and hole densities and the self-consistent electric potential). We find that the sufficiently long plasma waves exhibit a linear (soundlike) dispersion, with the wave velocity determined by the gate layer thickness, the gate voltage, and the temperature. The plasma wave velocity in graphene heterostructures can significantly exceed the plasma wave velocity in the commonly employed semiconductor gated heterostructures. The gated graphene heterostructures can be used in different voltage tunable terahertz devices which utilize the plasma waves.