Single Impurity Level Research Articles

Quasiparticle Mass Enhancement as a Measure of Entanglement in the Kondo Problem.

We analyze the quantum entanglement between opposite spin projection electrons in the ground state of the Anderson impurity model. In this model, a single level impurity with intralevel repulsion U is tunnel coupled to a free electron gas. The Anderson model presents a strongly correlated many body ground state with mass enhanced quasiparticle excitations. We find, using both analytical and numerical tools, that the quantum entanglement between opposite spin projection electrons is a monotonic universal function of the quasiparticle mass enhancement Z in the Kondo regime. This indicates that the interaction induced mass enhancement, which is generally used to quantify correlations in quantum many body systems, could be used as a measure of entanglement in the Kondo problem.

Quantized Electronic Doping towards Atomically Controlled "Charge-Engineered" Semiconductor Nanocrystals.

"Charge engineering" of semiconductor nanocrystals (NCs) through so-called electronic impurity doping is a long-standingchallenge in colloidal chemistry and holds promise for ground-breaking advancements in many optoelectronic, photonic, and spin-based nanotechnologies. To date, our knowledge is limited to a few paradigmatic studies on a small number of model compounds and doping conditions, with important electronic dopants still unexplored in nanoscale systems. Equally importantly, fine-tuning of charge engineered NCs is hampered by the statistical limitations of traditional approaches. The resulting intrinsic doping inhomogeneity restricts fundamental studies to statistically averaged behaviors and complicates the realization of advanced device concepts based on their advantageous functionalities. Here we aim to address these issues by realizing the first example of II-VI NCs electronically doped with an exact number of heterovalent gold atoms, a known p-type acceptor impurity in bulk chalcogenides. Single-dopant accuracy across entire NC ensembles is obtained through a novel non-injection synthesis employing ligand-exchanged gold clusters as "quantized" dopant sources to seed the nucleation of CdSe NCs in organic media. Structural, spectroscopic, and magneto-optical investigations trace a comprehensive picture of the physical processes resulting from the exact doping level of the NCs. Gold atoms, doped here for the first time into II-VI NCs, are found to incorporate as nonmagnetic Au+ species activating intense size-tunable intragap photoluminescence and artificially offsetting the hole occupancy of valence band states. Fundamentally, the transient conversion of Au+ to paramagnetic Au2+ (5d9 configuration) under optical excitation results in strong photoinduced magnetism and diluted magnetic semiconductor behavior revealing the contribution of individual paramagnetic impurities to the macroscopic magnetism of the NCs. Altogether, our results demonstrate a new chemical approach toward NCs with physical functionalities tailored to the single impurity level and offer a versatile platform for future investigations and device exploitation of individual and collective impurity processes in quantum confined structures.

Tunneling current noise spectra of biased impurity with a phonon mode

We report the results of theoretical investigations of the tunneling current noise spectra through a single-level impurity both in the presence and in the absence of electron–phonon interaction based on the nonequilibrium Green’s functions formalism. We show that due to the quantum nature of tunneling, the Fano factor is dramatically different from the Poisson limit both in the presence and in the absence of inelastic processes. The results are demonstrated to be sensitive to the tunneling contact parameters.

Biased impurity tunneling current emission spectrum in the presence of quasi-particle interaction

Abstract We performed theoretical investigations of the tunneling current noise spectra through single-level impurity in the presence of quasi-particle (electron-phonon) interaction by means of the non-equilibrium Green function formalism. We demonstrated a fundamental link between quantum noise in tunneling contact and light emission processes. We calculated tunneling current noise spectra through a single level impurity atom both in the presence and in the absence of quasi-particle interaction for a finite bias voltage and identified it as a source of experimentally observed light emission from bias STM contacts. The results turn out to be sensitive to the tunneling contact parameters. Our findings provide important insight into the nature of non-equilibrium electronic transport in tunneling junctions with quasi-particle interaction.

Surface hopping with a manifold of electronic states. II. Application to the many-body Anderson-Holstein model.

We investigate a simple surface hopping (SH) approach for modeling a single impurity level coupled to a single phonon and an electronic (metal) bath (i.e., the Anderson-Holstein model). The phonon degree of freedom is treated classically with motion along--and hops between--diabatic potential energy surfaces. The hopping rate is determined by the dynamics of the electronic bath (which are treated implicitly). For the case of one electronic bath, in the limit of small coupling to the bath, SH recovers phonon relaxation to thermal equilibrium and yields the correct impurity electron population (as compared with numerical renormalization group). For the case of out of equilibrium dynamics, SH current-voltage (I-V) curve is compared with the quantum master equation (QME) over a range of parameters, spanning the quantum region to the classical region. In the limit of large temperature, SH and QME agree. Furthermore, we can show that, in the limit of low temperature, the QME agrees with real-time path integral calculations. As such, the simple procedure described here should be useful in many other contexts.

THE ABSORPTION AND CONDUCTIVITY FOR MICROSTRUCTURED SILICON IN THE IMPURITY-DEFECT MODEL

In this paper, a model for the optical absorption and carrier concentration in microstructured silicon is presented based on Gaussian energy distribution of defect and impurity, as well as the Boltzmann distribution of carriers. The parameters of the impurity and defect model contributing to the absorption and carrier concentration are investigated. The simulation results show that the absorption in the single level impurity-defect model ranges from 64% to 68%; larger than that in the single level impurity model (55%–65%); as well as that in the defect model (50%–66%). It also indicates that the absorption increases with bigger correlation energy (U) and the best bandwidth (d) is 0.92 eV. However, the carrier concentration gets stronger with bigger bandwidth, smaller correlation energy and higher temperature. Thus, these calculations would play an important role in the applications of microstructured silicon.

Direct Determination of the Chemical Bonding of Individual Impurities in Graphene

Using a combination of Z-contrast imaging and atomically resolved electron energy-loss spectroscopy on a scanning transmission electron microscope, we show that the chemical bonding of individual impurity atoms can be deduced experimentally. We find that when a Si atom is bonded with four atoms at a double-vacancy site in graphene, Si 3d orbitals contribute significantly to the bonding, resulting in a planar sp(2) d-like hybridization, whereas threefold coordinated Si in graphene adopts the preferred sp(3) hybridization. The conclusions are confirmed by first-principles calculations and demonstrate that chemical bonding of two-dimensional materials can now be explored at the single impurity level.

Impurity-modulated electron properties in a double-quantum-dot Aharonov–Bohm ring

The impurity-modulated electron transport properties in a double quantum dot (QD) Aharonov–Bohm ring are theoretically studied, by considering impurities locally and nonlocally coupled to the QDs in the ring arms, respectively. It is found that the impurities influence the electron transport in a nontrivial way: in the case of zero magnetic flux, a single-level impurity leads to the appearance of Fano line shapes in the conductance spectra, and the positions of Fano antiresonances are determined by both the impurity-QD couplings and the QD levels separated from the Fermi level; whereas when a magnetic flux is introduced with the phase factor ϕ=π the Breit–Wigner line shapes appear in the conductance curves. Compared with the local-impurity case, nonlocal impurities alter the conductance period versus the magnetic flux. In addition, when many-body effect is considered within the second-order approximation, we find the important role of the Coulomb interaction in modifying the electron transport.

Quantum Wire Hybridized With a Single-Level Impurity

We have studied low-temperature properties of interacting electrons in a one-dimensional quantum wire (Luttinger liquid) side-hybridized with a single-level impurity. The hybridization induces a backscattering of electrons in the wire which strongly affects its low-energy properties. Using a one-loop renormalization group approach valid for a weak electron-electron interaction, we have calculated a transmission coefficient through the wire, T(epsilon), and a local density of states, nu(epsilon) at low energies epsilon. In particular, we have found that the antiresonance in T(epsilon) has a generalized Breit-Wigner shape with the effective width Gamma(epsilon) which diverges at the Fermi level.

Advanced solar cell concepts

Material limitations of wafer-based silicon (Si) cell technology and efficiency limitations of thin film solar cell technologies need to be overcome in order to have affordable PV technology. New concepts that strive for better utilization of the sun's spectrum, hence better cell efficiency, are under development. These include multi-junction solar cells, intermediate band solar cells, cells utilizing impurity levels, quantum well and quantum dot solar cells, hot carrier cells and solar cell concepts incorporating spectrum conversion. In multi-junction solar cells, better spectrum utilization is obtained by stacking several solar cells. A record efficiency of over 39% has been achieved under 236 times the sun's light concentration. Analysis of impurity of photovoltaic and intermediate band solar cells has shown that theoretical cell efficiency is about 63.2% for single impurity level and single intermediate band. Energy-shifting of UV photons has been demonstrated by fabricating Si nanocrystals in SiO x and SiN x matrices. Proof of concept has been shown for quantum confinement in Si quantum dots and enhanced photon absorption using metal nanoparticles on the solar cell surface. Similarly, most of the advanced concepts are in the initial stage of experimentation. Significant breakthroughs are required before these concepts can contribute to mainstream PV production.

Anomalous nonlinearity of IR photoconductivity of diamond polycrystalline films

Nonlinearity of the lux-ampere characteristics of undoped polycrystalline diamond films is revealed. The spectral dependences of this nonlinearity and photoconductivity are analyzed in the framework of the available models with a single impurity level or a single type of traps. It is shown that, for undoped polycrystalline diamond films in the range of impurity photoconductivity, the lux-ampere characteristics exhibit an anomalous nonlinearity when their slopes change from 1/2 to approximately unity with a decrease in the wavelength and an increase in the excitation level and the carrier lifetime. The results obtained are explained within the model of the coexistence of two different channels of conduction in diamond films. Two ranges of carrier photogeneration are established. For photon energies below 1.4 eV, the carrier generation with quadratic recombination is observed in a single channel. At higher photon energies, the carrier generation occurs in two channels simultaneously (in addition, the carriers are excited with linear recombination in the second channel). It is demonstrated that the equilibrium concentration of carriers in the second channel with linear recombination substantially exceeds the equilibrium concentration of carriers in the first channel with quadratic recombination, which hampers the detection of the first channel without photoexcitation.

The influence of a photoinduced volume charge on the weak-radiation-induced interband photoproduction of carriers in semiconductors with impurity recombination centers

Analytical expressions for the average concentrations of photogenerated electrons and holes are obtained outside the framework of the quasineutrality approximation in the case of a strong surface recombination in the presence of a single-level impurity recombination centers. It is shown that the quasineutrality approximation becomes incorrect with decreasing sample size in the direction of irradiation.

Relaxation of post-illumination electric fields in strongly biased high-resistance structures with a single deep impurity level

This paper examines how an electric field relaxes when a discontinuous large carrier-depleting voltage applied to high-resistance symmetric metal-semiconductor-metal (MSM) and metal-insulator-semiconductor-insulator-metal (MISIM) structures having a single impurity level, and how its energy level ɛt=Ec−Et and the tunneling transparency Tn,p of the metal-semiconductor or metal-insulator boundary affect the relaxation. It is shown that the relaxation of the field and the form of its steady-state distribution depend on the ratio of the time constant tp in the majority-carrier (hole) region to the ionization time τt−1=αn(n*+n1)+αp(p*+p1) of a deep trap in the bulk. This ratio determines the relative contributions of free ρp,n and bound charge dnsities ρt (where αn,p is the coefficient for capture by an impurity, and p*, n*, p1, n1 are equilibrium concentrations and Shockley-Read constants in the bulk). For τt≈(τt)max≫tp,ρt≫ it is found that ρp,n and ρt≫ρp,n, which corresponds to a trap energy close to \(\varepsilon _t = {{E_g } \mathord{\left/ {\vphantom {{E_g } 2}} \right. \kern-\nulldelimiterspace} 2} + kT\ln \sqrt {{{N_c \alpha _n } \mathord{\left/ {\vphantom {{N_c \alpha _n } {(N_\upsilon \alpha _p )}}} \right. \kern-\nulldelimiterspace} {(N_\upsilon \alpha _p )}}} \), independent of the value of Tn,p, decaying oscillations arise in the concentration distribution, bulk charge, and field appear in the bulk. The amplitude of these oscillations reaches a maximum at time t≈0.4τt. Decreasing the ratio αp/αn causes τt to deviate from (τt)max. When this happens, the field no longer oscillates; instead, it increases with positive curvature in the cathode portion of the bulk. The quantity Tn,p determines the behavior of the field in the neighborhood of the anode. The value of (dE/dx)0 is positive for MSM structures (Tn,p≈1), and negative for MISIM structures (Tn,p≈0). For transparencies close to a critical value Tn,p0, the field in the structure remains almost uniform over an impurity ionization time.

Image of local density of states fluctuations in disordered metals in the differential conductance of tunneling via a resonant impurity level

Differential conductance of the resonant-tunneling structure with a single impurity level studied in the current plateau regime undergoes fluctuations around a zero average manifesting the energy dependence of the local density of states in a disordered electrode. Although the rms value of dI/dV depends on disorder and barrier transparencies, it is almost independent of temperature and, as a function of bias voltage, has a correlation function scaled by the intrinsic width of the resonance, which can be regarded as a tool to measure this quantity beyond the main differential-conductance peak. The analysis is extended to the regime of classically high magnetic fields where both the amplitude and correlation magnetic field are expected to increase.

Injected carrier lifetimes and double-injection currents in semiconductors with a single impurity level

Theoretical analyses of the lifetimes of injected electrons and holes, and the double-injection currents in long p-i-n diodes with a single impurity level, are treated by evaluating the space-charge density formed by the injection of the minority carrier lifetimes and the current-voltage characteristics are obtained in a low- and a high-injection regime, and approximately in an intermediate-injection regime, when the physical parameters of the i region and the dependence of the equilibrium majority-carrier density upon temperature have been measured beforehand.

Double injection into structures with a low-conductivity region. I. General considerations

In the case of p+−π−n+ structure, the general regularities of distribution of non-equilibrium charge carriers in the low-conductivity layer are considered under condition of double injection. The boundary conditions are proposed for the quasi-neutral region. They emphasize the features of low-conductivity layer and are unified for long as well as for short structures. The number and mutual disposition of drift and diffusion regions are determined and their influence on the I–U characteristic is evaluated. The general expressions for the calculation of voltage drop due to current are obtained. The Dember e.m.f. as well as the voltage drop in the junctions p+−π, π−n+ are taken into consideration. The presented method is suitable also for the case, when lifetime of non-equilibrium charge carriers and ambipolar diffusion coefficient vary with the increase of the injection level. In the next part of this work the presented method is utilized for the calculation and classification of I–U characteristics of semiconductors with the single impurity level under conditions of double injection. [Russian Text Ignored].

Variation of impurity−to−band activation energies with impurity density

A theory of the variation of conduction electron density with the temperature for various impurity concentrations is presented. In addition to previously noted effects of condcution band edge lowering and screening of the impurity potential by the conduction electrons, the influence of a finite energy transfer integral and spatial fluctuation in the potential are included. The results show that for ND≳1017 cm−3 in silicon one must not view the activation as occurring between a single impurity level and a well−defined conduction band edge, but must include the broadening of the impurity level and tailing of the conduction−band density of states. Calculations for the shallow donors P, Sb, and As in Si are found to be in satisfactory agreement with experiment.

Conductivity and Hall Effect of ZnO at Low Temperatures

The Hall effect and conductivity of zinc oxide have been measured in dense polycrystalline samples and two single crystals.It has been found that the usual simple Wilson semiconductor model is inadequate for the proper interpretation of results. Several modifications and additions have been suggested for the usual single-level impurity semiconductor. Allowance has been made for the polycrystalline nature of the sintered specimens in deducing the bulk properties.Three models are successful in giving the correct interpretation for the experimental results of the Hall curves. These are: (1) orbital degeneracy of electrons attached to an interstitial zinc atom; (2) additional energy levels at traps at the impurity level, where the number of traps is much greater than the number of donors; (3) traps far below the donor level that greatly outnumber the donors [this is mathematically the same as (2) but necessitates other lattice imperfections for physical realization].Physical realization of these energy level schemes is considered in the light of the other physical properties of ZnO, such as luminescence and photoconductivity. These physical models are examined with the aid of present-day knowledge of the alkali halides and other ionic crystals. It is found that pairs of positive (zinc) plus negative (oxygen) ion vacancies with excess oxygen ion vacancies are capable of reproducing the diversified electrical and optical properties of zinc oxide semiconductor. The previous scheme of frozen-in interstitial zinc atoms is shown to be incompatible with our experimental results. Experiments are proposed for further verification of the proposed model.