Heavy-hole Mass Research Articles

Calculation of Curie Temperature and Carriers Effective Masses of (Ga, Mn)As Diluted Magnetic Semiconductor from the Eight-Band k.p Model

An important step toward the development of spintronic information processing, transfer, and storage devices is the discovery of a dilute magnetic semiconductor (DMS) that demonstrates carrier-mediated ferromagnetism and maintains its magnetic properties above room temperature. Despite considerable progress made in recent decades, the maximum Curie temperature (∼200 K) remains well below room temperature. Mndoped GaAs are among the various diluted magnetic semiconductor materials that have been studied and have emerged as one of the most promising contenders for technological usage. The key characteristic of GaMnAs is its ferromagnetic properties, which are critical for spintronic devices. The primary goal of this work is to compute two critical properties of GaMnAs: the effective masses and the Curie temperature. The 8-band k.p model put forth by Kane was utilized to compile the GaMnAs band parameters using a MATLAB program. Our calculations are based on Lowdin perturbation theory, where spin-orbit, sp-d exchange interaction, and biaxial strain are taken into account. We calculated the Curie temperature of the GaMnAs alloy, within the mean-field approach based on the Zener model. Our findings demonstrated a direct proportionality relationship between the Curie temperature and the hole concentration (p) in GaMnAs. Moreover, we looked into how the Mn content and strain affected the effective masses of electrons, heavy, and light holes that were calculated for various crystallographic directions in GaMnAs. The effective masses that were calculated were highly dependent on the Mn content, which ranged from 1% to 5%, and the strain, which varied from −2% (tensile strain) to 2% (compressive strain).

Symmetry breaking for semiconductor excitons induced by Coulomb coupling between heavy and light holes

Semiconductor excitons are commonly seen as hydrogen atom. This analogy requires a unique hole mass. In reality, this is not so due to the complexity of the semiconductor band structure. The precise consequences on the exciton physics of the Coulomb coupling between heavy and light holes remain a tricky open problem. Through an ``optimized perturbative'' approach that uses excitons with a flexible hole mass as a basis, we show that for zero exciton wave vector, the heavy-light hole mass difference does not split the $(2\times4)$ exciton degeneracy in zinc-blende-like semiconductors, the hole mass for binding energy being close to the average mass inverse. By contrast, for nonzero exciton wave vector, that physically breaks the crystal symmetry, the exciton degeneracy splits into two branches quantized along the exciton wave vector, with nontrivial center-of-mass dependence not only on the heavy and light hole masses, but also on the electron mass.

Gallium Antimonide Spherical Semiconductor Quantum Dots

The quantum effects at the nano-metric level have been observed in a variety of confined structures, particularly in semiconductor quantum dots. In this contribution, the electronic and optical properties of GaSb spherical semiconductor quantum dots are investigated. For the calculations, the pseudo potential approach was employed. The size dependence of the energy gaps at Г, X and L points, the effective masses of electrons and heavy-holes, the refractive index, and the dielectric function for a studied GaSb spherical quantum dot are analyzed and discussed. When the degree of quantum confinement effect was changed by decreasing the radius of the spherical quantum dots, a striking charge in comparison to the bulk values has been obtained. Our results indicate that as the quantum dot radius is raised, most of properties rapidly decrease. This demonstrates an improvement in the mobility of the material. However, the refractive index and the dielectric constant are increased with increasing the radius of the nano-crystal.

Anisotropic g -tensors in hole quantum dots: Role of transverse confinement direction

Qubits encoded in the spin state of heavy holes confined in Si- and Ge-based semiconductor quantum dots are currently leading the efforts toward spin-based quantum information processing. The virtual absence of spinful nuclei in purified samples yields long qubit coherence times and the intricate coupling between spin and momentum in the valence band can provide very fast spin-orbit-based qubit control, e.g., via electrically induced modulations of the heavy-hole $g$-tensor. A thorough understanding of all aspects of the interplay between spin-orbit coupling, the confining potentials, and applied magnetic fields is thus essential for the development of the optimal hole-spin-based qubit platform. Here we theoretically investigate the manifestation of the effective $g$-tensor and effective mass of heavy holes in two-dimensional hole gases as well as in lateral quantum dots. We include the effects of the anisotropy of the effective Luttinger Hamiltonian (particularly relevant for Si-based systems) and we focus on the detailed role of the orientation of the transverse confining potential. We derive general analytic expressions for the anisotropic $g$-tensor and we present a general and straightforward way to calculate corrections to this $g$-tensor for localized holes due to various types of spin-orbit interaction, exemplifying the approach by including a simple linear Rashba-like term. Our results thus contribute to the understanding needed to find optimal points in parameter space for hole-spin qubits, where confinement is effective and spin-orbit-mediated electric control over the spin states is efficient.

First principles calculation of electronic properties and effective mass of zinc-blende GaN

Based on the first principle pseudopotential plane wave method, the electronic structure of zinc-blende semiconductor GaN is calculated. Using the relativistic treatment of valence states, the spin orbit splitting energy of valence band top near the center of Brillouin region is calculated. Based on the effective mass approximation theory, the effective mass of electrons near the bottom of the conduction band and the effective mass of light and heavy holes near the Γ point along the directions of [100], [110] and [111] are calculated. These parameters are valuable and important parameters of optoelectronic materials.

Correlation between carrier mobility and effective mass in Sr2RuO4–xFx (x = 2) under uniaxial strain using the Yukawa screened PBE0 hybrid functional

We have investigated the electronic and thermoelectric features (carrier mobilities, scattering rates, etc.) of Sr2RuO4 and Sr2RuO4-xFx (x = 2) by combining computational approaches with experimental results reported in the pertinent literature. The electronic investigation has indicated a metallic character of Sr2RuO4 (Eg = 0 eV), but that the incorporation of fluorine opens the band gap. The findings suggest that Sr2RuO4-xFx (x = 2) is an indirect semiconductor (Eg = 1.55 eV), and that the electronic band gap can be tuned by applying an external compressive or tensile strain (CTS). The relative stability of the compound and the feasibility of its synthesis are firmly proved by positive phonon frequencies and negative cohesive energies. Moreover, electron and hole mobilities in strained and unconstrained Sr2RuO2F2 have been simulated through the Yukawa screened PBE0 hybrid functional (YS-PBE0). It is observed that carrier mobilities are very responsive to strain and can be enhanced or attenuated under pressure or uniaxial stretch. The effective masses of light and heavy holes are greater than those of the electrons, and exhibit opposite behavior to that of carrier mobilities. Under moderate strain and regardless of the process type, Sr2RuO2F2 maintains n-type conducting behavior.

Ultrafast hole spin qubit with gate-tunable spin-orbit switch functionality.

Quantum computers promise to execute complex tasks exponentially faster than any possible classical computer, and thus spur breakthroughs in quantum chemistry, material science and machine learning. However, quantum computers require fast and selective control of large numbers of individual qubits while maintaining coherence. Qubits based on hole spins in one-dimensional germanium/silicon nanostructures are predicted to experience an exceptionally strong yet electrically tunable spin-orbit interaction, which allows us to optimize qubit performance by switching between distinct modes of ultrafast manipulation, long coherence and individual addressability. Here we used millivolt gate voltage changes to tune the Rabi frequency of a hole spin qubit in a germanium/silicon nanowire from 31 to 219 MHz, its driven coherence time between 7 and 59 ns, and its Landé g-factor from 0.83 to 1.27. We thus demonstrated spin-orbit switch functionality, with on/off ratios of roughly seven, which could be further increased through improved gate design. Finally, we used this control to optimize our qubit further and approach the strong driving regime, with spin-flipping times as short as ~1 ns.

Hole and Electron Effective Masses in Single InP Nanowires with a Wurtzite-Zincblende Homojunction.

The formation of wurtzite (WZ) phase in III-V nanowires (NWs) such as GaAs and InP is a complication hindering the growth of pure-phase NWs, but it can also be exploited to form NW homostructures consisting of alternate zincblende (ZB) and WZ segments. This leads to different forms of nanostructures, such as crystal-phase superlattices and quantum dots. Here, we investigate the electronic properties of the simplest, yet challenging, of such homostructures: InP NWs with a single homojunction between pure ZB and WZ segments. Polarization-resolved microphotoluminescence (μ-PL) measurements on single NWs provide a tool to gain insights into the interplay between NW geometry and crystal phase. We also exploit this homostructure to simultaneously measure effective masses of charge carriers and excitons in ZB and WZ InP NWs, reliably. Magneto-μ-PL measurements carried out on individual NWs up to 29 T at 77 K allow us to determine the free exciton reduced masses of the ZB and WZ crystal phases, showing the heavier character of the WZ phase, and to deduce the effective mass of electrons in ZB InP NWs (me= 0.080 m0). Finally, we obtain the reduced mass of light-hole excitons in WZ InP by probing the second optically permitted transition Γ7C ↔ Γ7uV with magneto-μ-PL measurements carried out at room temperature. This information is used to extract the experimental light-hole effective mass in WZ InP, which is found to be mlh = 0.26 m0, a value much smaller than the one of the heavy hole mass. Besides being a valuable test for band structure calculations, the knowledge of carrier masses in WZ and ZB InP is important in view of the optimization of the efficiency of solar cells, which is one of the main applications of InP NWs.

P63/mmc-Ge and their Si–Ge alloys with a mouldable direct band gap

Physical properties, such as stability, electronic properties, hole effective mass, electron effective mass, mechanical properties, structural properties, and optical properties of P63/mmc-Ge6 and their Si6-xGex (x = 1, 2, 3, 4, 5) alloys are investigated using ab initio calculations based on density functional theory. The anisotropic mechanical properties of the Young’s modulus of Si6-xGex alloys are all slightly superior than those of diamond-Si, while the Young’s modulus of Si6-xGex alloys in the (001) plane are isotropic (Emax = Emin). With the increase in the number of germanium atoms, Si5Ge and Si4Ge2 exhibit direct band gaps of 0.63 eV and 0.18 eV, respectively. All other Si6-xGex (x = 3, 4, 5) alloys and P63/mmc-Ge6 exhibit metallicity properties. In addition, the effective masses of electrons and heavy holes of Si4Ge2 along the x and y directions become substantially smaller than those of Si6 and Si5Ge.

Electronic energy band parameters of CuInSe2 : Landau levels in magnetotransmission spectra

Magnetotransmission (MT) at magnetic fields up to 29 T was used to study the electronic structure of $\mathrm{CuInS}{\mathrm{e}}_{2}$ in thin polycrystalline films. The zero field absorption spectra exhibited resolved A, B, and C free excitons. Quantum oscillations, due to diamagnetic excitons comprising electrons and holes from Landau levels quantized in the conduction and valence band, respectively, appeared in the MT spectra at fields over 5 T. Spectral energies of Landau levels and binding energies of the corresponding diamagnetic excitons, theoretically calculated assuming a quasicubic approximation of the $\mathrm{CuInS}{\mathrm{e}}_{2}$ tetragonal lattice structure, helped to identify the character of the experimentally observed diamagnetic excitons. Spectral energies of diamagnetic excitons in the MT spectra with different circular polarizations were used to determine the electron and light hole effective masses, whereas heavy hole masses as well as the \ensuremath{\gamma} and ${\ensuremath{\gamma}}_{1}$ Luttinger parameters, ${E}_{p}$ Kane energy, and F parameter of the influence of remote bands, as well as their polaron values, were calculated using the Luttinger theory.

Fine Structure of Nearly Isotropic Bright Excitons in InP/ZnSe Colloidal Quantum Dots

The fine structure of exciton states in colloidal quantum dots (QDs) results from the compound effect of anisotropy and electron-hole exchange. By means of single-dot photoluminescence spectroscopy, we show that the emission of photoexcited InP/ZnSe QDs originates from radiative recombination of such fine structure exciton states. Depending on the excitation power, we identify a bright exciton doublet, a trion singlet, and a biexciton doublet line that all show pronounced polarization. Fluorescence line narrowing spectra of an ensemble of InP/ZnSe QDs in magnetic fields demonstrate that the bright exciton effectively consists of three states. The Zeeman splitting of these states is well described by an isotropic exciton model, where the fine structure is dominated by electron-hole exchange and shape anisotropy leads to only a minor splitting of the F = 1 triplet. We argue that excitons in InP-based QDs are nearly isotropic because the particular ratio of light and heavy hole masses in InP makes the exciton fine structure insensitive to shape anisotropy.

High performance short wave infrared photodetector using p-i-p quantum dots (InAs/GaAs) validated with theoretically simulated model

We demonstrate the highly promising p-i-p InAs/GaAs quantum dots based infrared photodetector (QDIP) which utilize intra-valence band hole transitions as against electron transitions operating at high temperatures. The photoluminescence spectroscopy at 9 K exhibited the ground state emission peak at 986 nm. The spectral response measured reveals the short wave infrared (SWIR) detection with a high-intensity peak at a wavelength of 2 μm. The measured dark current density at 77 K was 0.448 A/cm2 for an applied voltage of −1 V. The spectral response peak and blackbody signal measurements were recorded up to 245 and 270 K, respectively. Fabricated detector exhibited high confinement energy of 82.1 meV measured using temperature dependent current-voltage characteristics. We report high temperature infrared detection at 225 K in the short wave infrared regime with a peak responsivity of 3.813 A/W and a specific detectivity of 2.189 × 1010 cmHz1/2/W. In order to study the electronic properties of InAs/GaAs QD, a theoretical model is developed in which Vegard's law is applied to solve 3D-Schrodinger equation, which makes use of concentration-dependent equations for light hole and heavy hole masses instead of the effective mass approximation of holes. This study demonstrates the necessity of exploring hole-transitions rather than the conventional electron-transitions in QDIPs in order to achieve high temperature of operation and improved device efficiency.

Temperature dependent Hall effect in InAsSb with a 0.11 eV 77 K-bandgap

InAsSb is the only direct-bandgap III–V compound semiconductor alloy that absorbs and emits light over the entire long-wavelength infrared band (8–12 micron). We measured its free electron concentration and mobility as a function of temperature in materials with a 77 K-bandgap of 0.11 eV and compared the results with those of the II–VI compound, HgCdTe. The intrinsic electron concentration exhibits an expected freeze-out, which can be described with Fermi statistical electron and hole distributions, taking into account the non-parabolicity of the conduction band and the temperature dependence of the bandgap. Using known values for the electron mass, the heavy hole mass is estimated to be 0.4m0. The background concentration is n-type and is caused by a donor resonant with the conduction band of ∼8.7 meV above its bottom. The electron mobility exhibits a noticeably different behavior compared with HgCdTe. Between room temperature and ∼77 K, the InAsSb mobility is significantly higher, indicating a difference in phonon scattering, while at lower temperatures where alloy and impurity scattering dominate, the mobility of the unoptimized InAsSb is lower.

Biexciton Binding Energy in Spherical Quantum Dots with Γ8 Valence Band

The biexciton binding energy in spherical CdSe/ZnSe quantum dots is calculated variationally in the framework of kp-perturbation theory. Smooth and abrupt confining potentials with the same localization area of carriers are compared for two limiting cases of light hole to heavy hole mass ratio β = m lh /m hh : β = 1 and β = 0. Accounting for correlations between carriers results in their polarized configuration and significantly increases the biexciton binding energy in comparison with the first order perturbation theory. For β = 0 in smooth confining potentials there are three nearby biexciton states separated by small energy gap between 1S3/2 and 1P3/2 hole states.

Biexciton binding energy in spherical quantum dots with Gamma-=SUB=-8-=/SUB=- valence band

AbstractThe biexciton binding energy in spherical CdSe/ZnSe quantum dots is calculated variationally in the framework of kp-perturbation theory. Smooth and abrupt confining potentials with the same localization area of carriers are compared for two limiting cases of light hole to heavy hole mass ratio β = m_ lh /m_ hh : β = 1 and β = 0. Accounting for correlations between carriers results in their polarized configuration and significantly increases the biexciton binding energy in comparison with the first order perturbation theory. For β = 0 in smooth confining potentials there are three nearby biexciton states separated by small energy gap between 1 S _3/2 and 1 P _3/2 hole states.

Band calculation of lonsdaleite Ge

The band structure of Ge in the lonsdaleite phase is calculated using first principles. Lonsdaleite Ge has a direct band gap at the Γ point. For the conduction band, the Γ valley is anisotropic with the low transverse effective mass on the hexagonal plane and the large longitudinal effective mass along the c axis. For the valence band, both heavy-hole and light-hole effective masses are anisotropic at the Γ point. The in-plane electron effective mass also becomes anisotropic under uniaxial tensile strain. The strain response of the heavy-hole mass is opposite to the light hole.

Simulation of the Germanium-Tin Tunneling Field-Effect Transistors with a Ge Cap Layer: Improved Subthreshold Swing and Ion/Ioff Ratio

Tunneling field-effect transistors (TFETs) have been proposed as the possible candidates to replace the traditional MOSFETs for the ultrascaled low power applications [1]. The band-to-band tunneling (BTBT) of TFETs can achieve the sub-60 mV/dec subthreshold swing (SS). Recently, GeSn alloys are attracting interest for TFETs application due to the direct band gap and high carrier mobility [2]. The large interface trap density (Dit) at the GeSn/high-k interface degrades the GeSn device performance [3,4]. However, the effects of Dit have not been fully considered for the device structure design and optimization of GeSn TFETs at present. This work examines the Dit effects on GeSn TFETs performance by numerical simulation. The influences of a Ge cap layer on planar GeSn TFETs are investigated. Figure 1 illustrates the simulated GeSn pTFETs with and without the Ge cap layer. The Dit effects are included in the simulation, and the corresponding simulated structures are summarized in Table I. The dynamic nonlocal BTBT model in Synopsys Sentaurus device simulator is adopted to calculate both the direct and indirect tunneling currents of GeSn TFETs. We calculate the electron band structures of GeSn alloys by the nonlocal empirical pseudopotential method, and the carrier effective masses are extracted from the developed band diagrams. The Luttinger parameters [5] are extracted, and the hole density-of-states effective masses are calculated based on the spherically averaged light hole and heavy hole masses [6]. Some key parameters used in the simulation are listed in Table II. The effects of Dit on the Ge0.94Sn0.06 TFETs performance are evaluated (Fig. 2). The direct tunneling is the dominant component of the total tunneling current. The Dit has significant effects on both the direct and indirect tunneling. The Dit worsens the SS, and leads to the decreased driving current and the increased leakage level. To suppress the Dit effects, the Ge0.94Sn0.06 TFETs with 2-nm-thick and 5-nm-thick Ge cap layers are simulated (Fig. 3). For the 2 nm cap layer device, the better Dit would improve the SS and leakage current. In addition, the 2 nm Ge layer is effective to suppress the BTBT leakage current (inset of Fig. 3), which has a significant impact on decreasing the SS. Hence, the 2 nm Ge capped Ge0.94Sn0.06 TFETs achieve an enhanced driving current at the low supply voltages. The minimum point SS and Ion/Ioff ratio are extracted and compared in Fig. 4. The Voff is defined as the Vgs at the drain current of 50 pA/μm. The supply voltage Vdd is 0.4 V, and thus the Von and Ion are determined. The Ion/Ioff ratio is denoted as Ratio1. The minimum SS decreases from 56.3 mV/dec to 32.9 mV/dec when the 2 nm Ge layer is used, and the Ratio1 is also improved. For the 5 nm cap device, the leakage current is lower due to the best Dit and the further suppressed leakage, but the relative thick Ge layer will affect the tunneling current. Figure 5 presents the comparison of the on-state BTBT rate. The 2 nm Ge cap layer doesn’t have obvious effect on the BTBT rate compared with the no-capped device. However, for the 5 nm cap device, Ge BTBT contributes more to the total current, and the GeSn BTBT is weakened, leading to the degradation of SS and Ratio1. For larger Sn composition (8.5%), SS is degraded due to the Dit and leakage, but the enhanced BTBT may increase Ion (Fig. 4). Moreover, Voff is also extracted at the lowest leakage level, and the corresponding obtained Ion/Ioff ratio is denoted as Ratio2. The 2-nm-capped Ge0.94Sn0.06 device exhibits the best Ratio2 (Fig. 4), reflecting the benefit for low power applications. In summary, the SS and Ion/Ioff ratio of GeSn TFETs can be improved by inserting a Ge cap layer. The ultrathin cap layer will not affect the GeSn BTBT, and can suppress the leakage current. Although the large band gap material is commonly not preferred for BTBT, the Ge cap layer may be needed for GeSn TFETs from the practical point of view. The device performance can be further improved by structure optimization. Acknowledgments: This work was supported in part by the National Natural Science Foundation of China (No. 61306105). [1] C. Hu et al., IEDM, pp. 387, 2010. [2] Y. Yang et al., IEDM, pp. 379, 2012. [3] Y. Qiu et al., JAP 115, 234505, 2014. [4] S. Gupta et al., IEDM, pp. 375, 2012. [5] K. L. Low et al., JAP 112, 103715, 2012. [6] A. Baldereschi et al., PRB 8, 2697, 1973. Figure 1

Reduction of exciton mass by uniaxial stress in GaAs/AlGaAs quantum wells

It is experimentally shown that the pressure applied along the twofold symmetry axis of a heterostructure with a wide GaAs/AlGaAs quantum well leads to considerable modification of the polariton reflectance spectra. This effect is treated as the stress-induced decrease of the heavy-hole exciton mass. Theoretical modeling of the effect supports this assumption. The 5\%-decrease of the exciton mass is obtained at pressure P=0.23 GPa.

Particle-hole pair and beelectron states in ZnO/(Zn,Mg)O quantum wells and Dirac materials.

In this paper a theoretical studies of the space separation of electron and hole wave functions in the quantum well ZnO/Mg(0.27)Zn(0.73)O are presented. For this aim the self-consistent solution of the Schrödinger equations for electrons and holes and the Poisson equations at the presence of spatially varying quantum well potential due to the piezoelectric effect and local exchange-correlation potential is found. The one-dimensional Poisson equation contains the Hartree potential which includes the one-dimensional charge density for electrons and holes along the polarization field distribution. The three-dimensional Poisson equation contains besides the one-dimensional charge density for electrons and holes the exchange-correlation potential which is built on convolutions of a plane-wave part of wave functions in addition. The shifts of the Hartree valence band spectrums and the conduction band spectrum with respect to the flat band spectrums as well as the Hartree-Fock band spectrums with respect to the Hartree ones are found. An overlap integrals of the wave functions of holes and electron with taking into account besides the piezoelectric effects the exchange-correlation effects in addition is greater than an overlap integral of Hartree ones. The Hartree particles distribute greater on edges of quantum well than Hartree-Fock particles. It is found that an effective mass of heavy hole of Mg(0.27)Zn(0.73)O under biaxial strain is greater than an effective-mass of heavy hole of ZnO. It is calculated that an electron mass is less than a hole mass. It is found that the Bohr radius is grater than the localization range particle-hole pair, and the excitons may be spontaneously created.Schrödinger equation for pair of two massless Dirac particles when magnetic field is applied in Landau gauge is solved exactly. In this case the separation of center of mass and relative motion is obtained. Landau quantization $\epsilon=\pm\,B\sqrt{l}$ for pair of two Majorana fermions coupled via a Coulomb potential from massless chiral Dirac equation in cylindric coordinate is found. The root ambiguity in energy spectrum leads into Landau quantization for beelectron, when the states in which the one simultaneously exists are allowed. The tachyon solution with imaginary energy in Cooper problem ($\epsilon^{2}<0$) is found.

Carrier dynamics and related electronic band properties of InN films

In the present article, we focus our discussion on the carrier dynamics of the scattering and recombination processes of InN films and the related band-edge energy structure. Various reports on this matter are summarized and some issues are reexamined. The analysis result based on the apparent band–band transition matrix element is consistent with a reported effective heavy hole mass of 0.59 (±0.06) m0. An Ep value related to the transition matrix element of 10–14 eV is thought to be plausible. The ambiguity of the band-edge structure is evaluated by the uncertainty of electron density. The distortion of the conduction band bottom and the ambiguity of the estimation of the many-body effect are discussed. The enhancement of the anisotropic electron-scattering nature with the decrease in residual electron density reveals that the residual electron source has isotropic potentials: point defects or small complexes. Infrared reflectance spectrum analysis reveals the high electron mobility inside grains in spite of the scattering by edge-type dislocations which cause the anisotropic carrier scattering. The recombination processes at low temperatures are dominated by nonradiative processes related to edge-type dislocations, while the thermally activated nonradiative recombination process is independent of the dislocation density. The activation processes and energies of the recombination related to phonon localization are characterized. InN is a peculiar material that has high carrier mobility and a strong electron–phonon interaction, which possibly induces the high nonradiative carrier recombination rate. The control of phonon localization is thus required.