Anisotropic charge carrier transport in black phosphorus limited by ionized impurity scattering at finite temperature is explored theoretically. The anisotropic electronic structure enters the calculation for the polarizability (screening), the momentum relaxation time, and the mobility. For finite temperature, scattering is not limited to the Fermi surface and the polarizability is temperature dependent. The impact of screening is investigated in detail with its dependence on carrier density and temperature. Competing with the thermal excitation effects, the temperature dependence of the polarizability is found to dominate for T<100K. As a result, the charge carrier mobility slowly decreases with increasing temperature. The weak temperature dependence of the mobility and its anisotropy ratio of 1.9-3.2 agree with published experimental data.
We study the effect of impurity scattering effect in black phosphorurene (BP) in this work. For single impurity, we calculate impurity induced local density of states (LDOS) in momentum space numerically based on tight-binding Hamiltonian. In real space, we calculate LDOS and Friedel oscillation analytically. LDOS shows strong anisotropy in BP. Many impurities in BP are investigated using $T$-matrix approximation when the density is low. Midgap states appear in band gap with peaks in DOS. The peaks of midgap states are dependent on impurity potential. For finite positive potential, the impurit…
We have performed the numerical modeling of Ge(111)-(2x1) surface electronic properties in vicinity of P donor impurity atom located near the surface. We have found a notable increase of surface $LDOS$ around surface dopant near the bottom of empty surface states band $π^*$, which we called split state due to its limited spatial extent and energetic position inside the band gap. We show, that despite of well established bulk donor impurity energy level position at the very bottom of conduction band, surface donor impurity on Ge(111)-(2x1) surface might produce energy level below Fermi energy, …
An approach to calculation of the ionized impurity and surface roughness scattering rates of electrons in very thin semiconductor quantum wires taking into account the energy level broadening is worked out. It is assumed that all the electrons in the structure are in the electric quantum limit. The screening is taken into account while considering the ionized impurity scattering. Comparison of the surface roughness scat-tering rates calculated using the exponential and Gaussian autocorrelation functions is done.
The ground-state energy and fine-structure splitting of ionized shallow donor impurity-exciton complex in quantum dots are investigated. It is found that fine-structure splitting could be largely reduced by the off-center ionized impurities since the anisotropic shape of exciton envelope function is significantly changed. Anomalous Stark shifts of the ground-state energy and efficient tuning of the fine-structure splitting by the external electric field due to the local electric field produced by the ionized impurities are discussed. The scheme may be useful for the design of the quantum dots-…
Boltzmann diffusive transport including relaxation time and mobility in graphene limited by ionized impurity scattering is investigated. The relaxation time is evaluated with two different methods, first one directly use Boltzmann transport equation via scattering matrix, second one is based on scattering cross-section. Two methods yield the same relaxation time results for graphene. Assume linear Thomas-Fermi screening and a reasonable electron carrier density, relaxation time and mobility can be calculated and plotted, which demonstrates graphene is a very promising high mobility material fo…
Black phosphorus has attracted great research interest due to its numerous applications in electronic devices, optoelectronic devices, energy storages and so on. Compared with the majority of two-dimensional materials, black phosphorus possesses a unique property, i.e. the strong in-plane anisotropy. All the properties reported so far, including its effective mass, electron mobility, light absorption, thermal conductivity and so on, have shown great anisotropy in the basal plane. This property renders black phosphorus unique applications not achievable with other two-dimensional materials. In …
We show that by computing the electron-impurity scattering rate at the first order via Fermi's golden rule, and assuming that the localized impurity potential is of Yukawa form, one obtains a wave vector transfer distribution which is inconsistent with the finite temperature linearized Thomas-Fermi approximation for {\it n}-type semiconductors. Our previous findings show that this is not the case for the carrier nondegenerate dynamics, because the average wave vector transferred being in general negligible in this regime. Moreover, we examine the behavior of the electron-impurity differential …
The ground state energy of exciton bound by distant ionized donor impurity in quasi-two-dimensional GaAs/AlGaAs semiconductor quantum well (QW) is studied theoretically within the Hartree approach in the effective mass approximation. The influence of the distance between QW plane and ionized donor, as well as of the magnetic field aligned across the QW plane and varying dielectric constant of the barrier material on the stability of exciton bound by ionized donor impurity is analyzed and discussed.
Atomically thin black phosphorus (BP) field-effect transistors show strong-weak localization transition which is tunable through gate voltages. Hopping transports through charge impurity induced localized states are measured at low-carrier density regime. Variable-range hopping model is applied to simulate the charge carrier scattering behavior. In the high-carrier concentration regime, a negative magnetoresistance signals the weak localization effect. The extracted phase coherence length is power-law temperature dependent ($\sim T^{-0.48\pm0.03}$) and demonstrates electron-electron interactio…
We study the competition of hole capture between an In(Ga)As quantum dot and a directly adjacent ionized impurity in view of spin-photon interfaces. The Kerr rotation noise spectroscopy at 4.2 K shows that the hole-capture probability of the In(Ga)As quantum dot is about one order of magnitude higher compared to the hole-capture probability of the ionized impurity and suggests that a simultaneous occupation of quantum dot and impurity by a hole is efficiently suppressed due to Coulomb interaction. A theoretical model of interconnected spin and charge noise allows the quantitative specification…
The ground state energy of exciton bound by distant ionized donor impurity in two-dimensional semiconductor quantum well (QW) is studied theoretically within the Hartree approach in the effective mass approximation. The influence of the distance between QW plane and ionized donor, as well as of the electron-hole mass ratio, the magnetic field aligned across the QW plane and dielectric constant of the barrier material on the stability of exciton bound by ionized donor impurity is analyzed and discussed.
Bistable valency in individual atoms presents a new approach toward single-atom memory, as well as a building block to create tunable and stochastic multi-well energy landscapes. Yet, this concept of orbital memory has thus far only been observed for cobalt atoms on the surface of black phosphorus, which are switched using tip-induced ionization. Here, we show that individual iron atoms on the surface of black phosphorus exhibit orbital memory using a combination of scanning tunneling microscopy and spectroscopy with ab initio calculations based on density functional theory. Unlike cobalt, the…
We investigate transport properties of gate-all-around Si nanowires using non-equilibrium Green's function technique. By taking into account of the ionized impurity scattering we calculate Green's functions self-consistently and examine the effects of ionized impurity scattering on electron densities and currents. For nano-scale Si wires, it is found that, due to the impurity scattering, the local density of state profiles loose it's interference oscillations as well as is broaden and shifted. In addition, the impurity scattering gives rise to a different transconductance as functions of tempe…
We report on the vertical electron mobility versus temperature by applying the interface roughness scattering and ionized impurity scattering in InAs/GaSb superlattices. Using the Finite difference K.P method, we calculated the band structure of InAs/Gasb superlattices and then studied the transport properties of these systems. Several structural parameters such as layer thicknesses, interface roughness height, correlation length and ion density have been investigated and characterized that how the vertical mobility change with varying these parameters. Theoretical modeling results show that t…
The in-plane electron mobility has been calculated in InAs/GaSb type-II superlattices at low temperatures. The interface roughness scattering and ionized impurity scattering are investigated as the dominant scattering mechanisms in limiting the electron transport at low temperatures. For this purpose, the band structures and wave functions of electrons in such superlattices are calculated by solving the K.P Hamiltonian using the numerical Finite Difference method. The scattering rates have obtained for different temperatures and structural parameters. We show that the scattering rates are high…
Development of new, high quality functional materials has been at the forefront of condensed matter research. The recent advent of two-dimensional black phosphorus has greatly enriched the material base of two-dimensional electron systems. Significant progress has been made to achieve high mobility black phosphorus two-dimensional electron gas (2DEG) since the development of the first black phosphorus field-effect transistors (FETs)$^{1-4}$. Here, we reach a milestone in developing high quality black phosphorus 2DEG - the observation of integer quantum Hall (QH) effect. We achieve high quality…
Nominally-pure black phosphorus (BP) is commonly found to be a p-type semiconductor, suggesting the ubiquitious presence of impurity species or intrinsic, charged defects. Moreover, scanning tunnelling microscopy (STM) images of black phosphorus reveal the presence of long-ranged double-lobed defect features superimposed onto the surface atomic lattice. We show that both the p-type doping of BP and the defect features observed in STM images can be attributed to substitutional tin impurities. We show that black phosphorus samples produced through two common synthesis pathways contain tin impuri…
The advent of black phosphorus field-effect transistors (FETs) has brought new possibilities in the study of two-dimensional (2D) electron systems. In a black phosphorus FET, the gate induces highly anisotropic 2D electron and hole gases. Although the 2D hole gas in black phosphorus has reached high carrier mobilities that led to the observation of the integer quantum Hall effect, the improvement in the sample quality of the 2D electron gas (2DEG) has however been only moderate; quantum Hall effect remained elusive. Here, we obtain high quality black phosphorus 2DEG by defining the 2DEG region…
The absorption of electromagnetic radiation of an anisotropic quantum dot is theoretically investigated taking into account the processes associated with simultaneous scattering from ionized impurities. It is shown that the scattering of electrons by impurities leads to the resonance absorption even if we have only one impurity in the quantum dot. Explicit formula is derived for the absorption coefficient. The positions of the resonances peaks are found. The effects of external magnetic field on the resonance absorption are studied.
Black phosphorus (BP) is receiving significant attention because of its direct 0.4-1.5 eV layer-dependent band gap and high mobility. Because BP devices rely on exfoliation from bulk crystals, there is a need to understand native impurities and defects in the source material. In particular, samples are typically p-doped, but the source of the doping is not well understood. Here, we use scanning tunneling microscopy and spectroscopy to compare atomic defects of BP samples from two commercial sources. Even though the sources produced crystals with an order of magnitude difference in impurity ato…
Atomic layers of Black Phosphorus (BP) present unique opto-electronic properties dominated by a direct tunable bandgap in a wide spectral range from visible to mid-infrared. In this work, we investigate the infrared photoluminescence of BP single crystals at very low temperature. Near-bandedge recombinations are observed at 2 K, including dominant excitonic transitions at 0.276 eV and a weaker one at 0.278 eV. The free-exciton binding energy is calculated with an anisotropic Wannier-Mott model and found equal to 9.1 meV. On the contrary, the PL intensity quenching of the 0.276 eV peak at high …
Atomically thin black phosphorus (BP) is a promising two-dimensional material for fabricating electronic and optoelectronic nano-devices with high mobility and tunable bandgap structures. However, the charge-carrier mobility in few-layer phosphorene (monolayer BP) is mainly limited by the presence of impurity and disorders. In this study, we demonstrate that vertical BP heterostructure devices offer great advantages in probing the electron states of monolayer and few-layer phosphorene at temperatures down to 2 K through capacitance spectroscopy. Electronic states in the conduction and valence …
We report on the longitudinal and Hall resistivities of a HgTe quantum well with inverted energy spectrum (dQW = 20.3 nm) measured in the quantum Hall (QH) regime at magnetic fields up to 9 T and temperatures 2-50 K. The temperature dependence of the QH plateau-plateau transition (PPT) widths and of variable range hopping (VRH) conduction on the Hall plateaus are analyzed. The data are presented in a genuine scale form both for PPT regions and for VRH regime. Estimations for the degree of the carrier localization length divergence reveal a decisive role of the long-range random potential (the …
Tuning band gaps in two-dimensional (2D) materials is of great interest in the fundamental and practical aspects of contemporary material sciences. Recently, black phosphorus (BP) consisting of stacked layers of phosphorene was experimentally observed to show a widely tunable band gap by means of the deposition of potassium (K) atoms on the surface, thereby allowing great flexibility in design and optimization of electronic and optoelectronic devices. Here, based on the density-functional theory calculations, we demonstrates that the donated electrons from K dopants are mostly localized at the…
Semiconductor superlattices have been extensively investigated for thermoelectric applications, to explore the effects of compositions, interface structures, and lattice strain environments on the reduction of thermal conductivity, and improvement of efficiency. Most studies assumed that their electronic properties remain unaffected compared to their bulk counterparts. However, recent studies demonstrated that electronic properties of silicon (Si)/germanium (Ge) superlattices show significant variations depending on compositions and growth substrates. These studies used a constant relaxation t…
The electron transport properties of atomically thin semiconductors such as MoS2 have attracted significant recent scrutiny and controversy. In this work, the scattering mechanisms responsible for limiting the mobility of single layer semiconductors are evaluated. The roles of individual scattering rates are tracked as the 2D electron gas density is varied over orders of magnitude at various temperatures. From a comparative study of the individual scattering mechanisms, we conclude that all current reported values of mobilities in atomically thin transition-metal dichalcogenide semiconductors …
We present a gating scheme to separate even strong parallel conductance from the magneto-transport signatures and properties of a two-dimensional electron system. By varying the electron density in the parallel conducting layer, we can study the impact of mobile charge carriers in the vicinity of the dopant layer on the properties of the two-dimensional electron system. It is found that the parallel conducting layer is indeed capable to screen the remote ionized impurity potential fluctuations responsible for the fragility of fractional quantum Hall states.
In the present work we calculate the non-linear additives to the Brooks-Herring electrostatic screened potential. We also calculate the corresponding additives to the ionized impurity scattering mobility in n-GaAs over a wide range of doping levels and temperatures. It is demonstrated that the additives to the mobility changes its value up to 50%. The most dramatically mobility is changed near the Mott transition, when the doping level is about $10^{14}$ - $2\times10^{16}$ cm$^{-3}$ and temperature is below 50 K. Also, the results allow us to conclude that the non-linear additives break the cr…
Detailed experimental and theoretical studies of the temperature dependence of the effect of different scattering mechanisms on electrical transport properties of graphene devices are presented. We find that for high mobility devices the transport properties are mainly governed by completely screened short range impurity scattering. On the other hand, for the low mobility devices transport properties are determined by both types of scattering potentials - long range due to ionized impurities and short range due to completely screened charged impurities. The results could be explained in the fr…
The temperature dependent Hall mobility data from La-doped SrTiO3 thin films has been analyzed and modeled considering various electron scattering mechanisms. We find that a ~6 meV transverse optical phonon (TO) deformation potential scattering mechanism is necessary to explain the dependence of transport on temperature between 10-200 K. Also, we find that the low temperature electron mobility in intrinsic (nominally undoped) SrTiO3 is limited by acoustic phonon scattering. Adding the above two scattering mechanisms to longitudinal optical phonon (LO) and ionized impurity scattering mechanisms…
We report the observation of a fully developed fractional quantum Hall state at $ν=5/2$ in GaAs/Al$_{x}$Ga$_{1-x}$As quantum wells with mobility well below $10^{7}$\thinspace cm$^{2}$/Vs. This is achieved either by strong illumination or reducing the barrier Al composition without illumination. We explain both results in terms of screening of the ionized remote impurity (RI) potential by nearby neutral shallow donors. Despite the dramatic improvement in the transport features, the energy gap $Δ_{5/2}$ is limited to a rather small value ($\sim100$ mK), which indicates that once the RI potential…
Evidence is given for the effectiveness of InAs surface passivation by the growth of an epitaxial InAlAs shell. The electron mobility is measured as a function of temperature for both core-shell and unpassivated nanowires, with the core-shell nanowires showing a monotonic increase in mobility as temperature is lowered, in contrast to a turnover in mobility seen for the unpassivated nanowires. We argue that this signifies a reduction in low temperature ionized impurity scattering for the passivated nanowires, implying a reduction in surface states.
We report on a systematic study of the density dependence of mobility in a low-density Carbon-doped (100) GaAs two-dimensional hole system (2DHS). At T= 50 mK, a mobility of 2.6 x 10^6 cm^2/Vs at a density p=6.2 x 10^10 cm^- was measured. This is the highest mobility reported for a 2DHS to date. Using a back-gated sample geometry, the density dependence of mobility was studied from 2.8 x 10^10 cm^-2 to 1 x 10^11 cm^-2. The mobility vs. density cannot be fit to a power law dependence of the form mu ~ p^alpha using a single exponent alpha. Our data indicate a continuous evolution of the power la…
A novel breakdown (BD) mechanism of shallow impurity under the electric field at low temperatures is suggested for n-GaAs samples with the donor concentrations $N_D=10^{14} ÷10^{16}cm^{-3}$ and the compensation degree $K=\frac{N_A}{N_D}=0.3 ÷0.8$ with acceptors of concentration N_A in the external magnetic fields up to H=6.5~T. Diagnosis of the BD mechanism was performed by SI Zeeman and cyclotron resonance photoelectric spectroscopy methods in the wide interval of the electric field including the BD region too. The obtained results reveal that the BD electric field $\mathcal{E}_{BD}$ does not…
Near-surface InAs two-dimensional electron gas (2DEG) systems have great potential for realizing networks of multiple Majorana zero modes towards a scalable topological quantum computer. Improving mobility in the near-surface 2DEGs is beneficial for stable topological superconducting states as well as for correlation of multiple Majorana zero modes in a complex network. Here, we investigate near-surface InAs 2DEGs (13 nm away from the surface) grown on GaSb(001) substrates, whose lattice constant is closely matched to InAs, by molecular beam epitaxy. The effect of 10-nm-thick top barrier to th…
We report temperature-dependent photoluminescence (PL) studies and PL relaxation dynamics for uncoated and silver-coated CdS quantum dots (QDs). Room-temperature photoluminescence studies indicate that the presence of silver coating on CdS QD samples enhances the blue luminescence corresponding to the band-to-band transitions by a factor of ten compared to the uncoated samples. Furthermore, the decay time measurements using Time Correlated Single Photon Counting technique demonstrate Förster resonance energy transfer (FRET) between silver-shell and CdS-core in silver-coated CdS QD samples. A d…
We study molecular beam epitaxially grown, undoped Al$_{x}$Ga$_{1-x}$Sb/InAs/AlSb quantum wells with different buffer and barrier designs and varying quantum well width. The highest mobilities were achieved with Al$_{0.33}$Ga$_{0.67}$Sb buffers and lower barriers and a quantum well width of 24 nm. These quasi-single-interface InAs/AlSb quantum well devices reached a gate-tuned mobility of 2.4$~\times~10^{6}~$cm$^2$/Vs at a density of 1$\times 10^{12}$ cm$^{-2}$ and 1.3 K. In Hall bar devices boundary scattering is found to strongly influence the mobility determination in this mobility regime. …
