Session W47: Quantum Transport in Semiconductors: Theory and Experiment

Wigner approach to quantum transport in graded semiconductors

Graded electron bandstructures have long being used to beneficially influence the performance and functionality of electronic devices. In this work, we have developed a consistent fully quantum description of electron transport in terms of the Wigner distribution function, making use of the symmetric and hermitian effective-mass-like single band Hamiltonian that can be unambiguously constructed for graded systems. The generalized Wigner equation includes contributions that, in the quasiclassical limit, can be interpreted as directly corresponding to the drift and diffusion terms, but, unlike the homogeneous materials, the velocity operator is coordinate dependent and the electron is subject to the influence of the k-dependent quasielectric fields originating from both the inhomogeneous potential profile and composition-dependent modulation of the quasiparticle inertia. The approach is useful for the analysis of a broad class of transport phenomena in graded systems, where quantum effects are important, but a full quantum treatment would be prohibitively costly.   

Variational studies of quantum liquid crystal phases of 2DEG

The ground state of a nematic phase of the 2DEG at filling fraction$\nu =1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2$is studied. The pair distribution function and interaction energy are calculated for a wavefunction having the Jastrow form for the correlation part of$\prod\limits_{i [Preview Abstract]

Photoconductivity in AC-driven modulated two dimensional electron gas

We study the photoconductivity of two-dimensional electron system in a perpendicular homogeneous magnetic field, under the influence of periodic modulation potential and microwave irradiation. The model includes the microwave and Landau contributions in a non-perturbative exact way, the periodic potential is treated perturbatively. The Landau-Floquet states provide a convenient base with respect to which the lattice potential becomes time-dependent, inducing transitions between the Landau-Floquet levels. Based on this formalism, we provide a Kubo-like formula that takes into account the oscillatory Floquet structure of the problem. The total resistivity exhibits strong oscillations, leading to negative resistance states as the electron mobility and the intensity of the microwave power increases. It is proposed that, depending on the geometry, negative conductance sates or negative resistance states may be observed in lateral superlattices fabricated in $GaAs/AlGa As$ heterostructures.   

Charge transfer between a superconductor and a hopping insulator

We develop a theory of the low-temperature charge transfer between a superconductor and a hopping insulator. We show that the charge transfer is governed by the coherent two-electron -- Cooper pair conversion process, \textit{time reversal reflection}, where electrons tunnel into superconductor from the localized states in the hopping insulator located near the interface, and calculate the corresponding interface resistance. This process is an analog to conventional Andreev show that the time reversal interface resistance is accessible experimentally, and that in mesoscopic structures it can exceed the bulk hopping resistance.   

Simulating the interaction of a scanning probe with the quantum Hall liquid

Motivated by recent experiments [1], we have developed a simulation of the interaction of a metallic scanning probe with a 2D electron system (2DES) in the quantum Hall regime. The simulation is based on an electrostatic relaxation method, modified to include the non-linear screening of the 2D electron system at high magnetic fields. Using 2D simulations with cylindrical symmetry that allow us to account for the exact shape of the tip, we predict the diameter and width of ring shaped incompressible strips (ISs) induced by DC tip biases. Extending these results to 3 dimensions, we incorporate the effect of the disorder on the shape of the IS, and predict the formation of quantum dot islands observed in [1]. Comparison of the simulation results with experimental data provides a direct and quantitative view of the disorder of a very high mobility 2DES. [1] G. A. Steele, R. C. Ashoori, L. N. Pfeiffer, and K. W. West, Phys. Rev. Lett. 95, 136804 (2005)   

Quantum dynamics for a dissipative quantum harmonic oscillator as a model for a NEMS frequency control resonator

For the simplest model of dissipation, that is, a linear oscillator coupled to an infinite number of degrees of freedom to form a dissipative bath, it is found that the Heisenberg equation of motion for the oscillator displacement takes the form of a Langevin equation with a memory dependent dissipation [Ford, Lewis, O'Connell; Phys. Rev. A 37, 004419 (1988)]. When Fourier analyzed, this leads to a complex susceptibility which gives rise to a generalized frequency dependent ``quality factor'' which relates to the dissipative environment. We explore the limits of resonator integrity, especially with regard to insights afforded by the dependence of quality factor and other observables on the microscopic connection between resonator material parameters and circuit performance.   

Kohn localization in the quantum Hall regime

A two-dimensional electron fluid in the quantum Hall regime shows both quantized transverse conductivity and vanishing longitudinal conductivity: the latter property characterizes insulators. According to Kohn's theory of the insulating state, electron localization---defined in an appropriate sense---is the {\it cause} for the insulating behavior in any insulator. I show that a quantum Hall ``insulator'' is no exception; furthermore both quantization of the transverse conductivity and vanishing of the longitudinal one stem here from the same elegant formalism. Since 1999 onwards, the theory of the insulating state has been reformulated in term of a ``localization tensor'' which provides a measure of electron localization. This tensor is an intensive property, geometric in nature, having the dimensions of a squared length; it characterizes the ground wavefunction as a whole, {\it not} the individual states. It is finite in any insulator and divergent in any metal. A fluctuation-dissipation theorem relates this ground-state property to the system conductivity. So far, the theory has only addressed systems with time-reversal symmetry, in which case the localization tensor is real. I show that in absence of such symmetry the localization tensor is naturally endowed with an imaginary part, proportional to transverse dc conductivity, and quantized in two-dimensional systems. Therefore electron localization is the {\it common cause} for both vanishing of the dc conductivity and quantization of the transverse one in quantum Hall fluids.   

The mass of the electron in Shubnikov-de Haas effect:Spin-charge locking

At low temperatures, the integration over the Fermi distribution leads to x/$\sin$h x type expression which is called the Dingle's formula. The spin symmetry is found to modify this formula which determines the oscillation amplitude of resistivity as a function of magnetic field. The theory introduces the effective charge so that the cyclotron frequency gets fractionalized resulting into m/$\nu_{\pm}$. At a certain magnetic field 1.5m is found instead of m. The Shubnikov-de Haas effect uses quantization of Landau levels but not the flux quantization. Hence we find that there is a ``quantized S-dH effect'' which measures the m/h$^2$. We determine that when fractional values of the filling factor are taken into account, the mass of the electron, equal to the band mass is obtained. \newline 1. K. N. Shrivastava, Phys. Lett. A113, 435(1986). \newline 2. K. N. Shrivastava, Phys. Lett. A 326,469(2004). \newline 3. K. N. Shrivastava, Introduction to quantum Hall effect, Nova Sci. Pub. N.Y. (2002).   

Conductance reduction without shot noise in quantum wires

Shot noise can only be avoided in conductors without backscattering of conduction electrons. Such conductors without backscattering and a twofold spin-degeneracy have a minimal (nonzero) conductance of 2 $e^{2}/$h in the case of weak interactions. In recent experiments, however, also conductors with a reduced conductance of 1.4 $e^{2}/h$ have shown a clear tendency of noise suppression in zero magnetic field. It has been argued, that these experiments point to a lifted spin-degeneracy in these wires, spin-polarizing their conductance electrons. In this talk I will describe a model of an interacting quantum wire that is able to reproduce the transport behavior observed in these experiments qualitatively: that of the ``Coulomb Tonks gas'' of impenetrable electrons. It can be realized in ultra-thin wires, such as carbon nanotubes. We have studied transport through a finite-length Coulomb Tonks gas connected to bulk leads in various exactly solvable limits, both in and out of equilibrium. While we find a reduction of the conductance of such a wire to $e^{2}/h$ in all cases, the current in the wire does not exhibit any fluctuations at zero temperature. Most importantly, our model demonstrates that such noise suppression does not require a spin-polarization.   

Low-temperature transport in high quality strained Ge channels in SiGe

Presently, the mobility of holes in strained germanium achieved so far exceeds 100000 cm$^{2}$/Vs at a carrier density of $\sim $8*10$^{11}$cm$^{-2}$. For lower carrier density, the highest reported mobilities are roughly proportional to the carrier density. Accessing the upper left corner in the density-mobility diagram remains a challenge. Background charges, inhomogeneous strain distribution and growth defects are the main difficulties of growing strained Ge channels. We have fabricated high quality Ge channels and measured the transport parameters at temperatures down to 0.4 K. We discuss the influence of growth problems on the mobility as a whole and how these mechanisms may influence the magnetic field dependence of the sheet resistance. We explore the effects of different doping geometries, in particular backside doping and symmetrical doping on electrical transport, including the effects of dopant segregation. Our quantitative analysis shows that local charged impurities dominate the scattering rate. It also shows the effect of too low substrate temperature, leading to point defects whose existence can be detected by a pure transport measurement.   

Electronic transport properties of amorphous Sb$_2$Te$_3$ and Ge$_2$Sb$_2$Te$_5$ films

The electrical conductivity, Seebeck coefficient, and Hall coefficient of amorphous Sb$_2$Te$_3$ and Ge$_2$Sb$_2$Te$_5$ films have been measured as functions of temperature from room temperature down to as low as 200~K. The electrical conductivities manifest an Arrhenius behavior with a larger pre-exponential factor. In Sb$_2$Te$_3$ the energy characterizing the p-type Seebeck coefficient's temperature dependence, about 0.10~eV, is considerably smaller than the activation energy of the electrical conductivity, about 0.28~eV. In addition, the heat-of-transport constant of the Seebeck coefficient is much larger than that of conventional semiconductors. The Hall mobility is low (near 0.1~cm$^2$/V-sec at room temperature), anomalously signed (n-type), and increases with rising temperature with an activation energy of about 0.05~eV. These results are consistent with the charge carriers being hole-like small polarons that move by thermally assisted hopping. Ge$_2 $Sb$_2$Te$_5$ also has low mobility (0.7~cm$^2$/V-sec) and a high conductivity activation energy (0.41~eV), but Seebeck data is indicative of multi-band transport.   

Magnetic and transport properties of Fe$_{1-x}$Co$_{x}$Sb$_{2}$

Anisotropic magnetic and electronic transport measurements were carried out on large single crystals of Fe$_{1-x}$Co$_{x}$Sb$_{2}$, grown by self flux method, in the temperature range 1.8-350K for 0$\le $x$\le $1. The diamagnetic semiconducting state of FeSb$_{2}$ evolved into metallic by substitution of Fe with Co for x$<$0.5. With further doping there was a structural transformation from orthorhombic Pnnm structure of FeSb$_{2}$ to monoclinic P21/c structure of CoSb$_{2}$. Large magnetoresistance and anisotropy in electronic transport were observed.   

Transport Properties of Ag Nanoparticles in Carbon Matrix Prepared with a Cluster Gun

The use of ``cluster guns'' with in-situ processing capabilities has been found to be suitable for the fabrication of nanoparticles in a wide range of materials, avoiding external annealing and possible surface oxidation of the nanoparticles[1, 2]. In this study, we have used our cluster gun to fabricate Ag nanoparticles and embed them in a C matrix formed by conventional sputtering. With the increased amount of Ag, the transport properties of thin films show a gradual transition from a semiconductor-like behavior to a metallic one. At cryogenic temperatures, the magnetoresistance (MR) is generally negative at low fields and becomes positive at high fields. The field at which the MR changes sign increases with increased temperature. At higher temperatures (around 20 K), only negative MR is observed. For the samples with semiconductor-like behavior, the temperature dependence of resistance follows the relation $R=R_0 \exp \left[ {\left( {T_0 /T} \right)^{1/2}} \right]$ in the temperature range from 5 to 50 K. We are investigating the origin of this behavior and those results will be reported.   

Controlling the Inherent Magnetoresistance in thin InSb epilayers on GaAs (001)

There is great advantage to controlling the magnetoresistance (MR) in high mobility semiconductors for a number of applications which require thin active surface layers. Previously we have produced n type thin epilayers of InSb with the highest reported mobility\footnote{T. Zhang et al. Appl. Phys Lett. {\bf84}, 4463 (2004).} and we have used these epilayers to explore novel geometries that enhance the high field MR.\footnote{W.R. Branford et al., Appl. Phys Lett. {\bf86}, 202116 (2005).} Here we show that by virtue of the inherent inhomogeneity in the growth direction, thin InSb epilayers can be designed to have significant MR without external geometric manipulation. The observations can be explained using a transport model that describes the electrical properties of the layers including contributions from conduction and impurity bands.\footnote{J.J. Harris et al., Semicond. Sci. Tech. {\bf19}, 1406 (2004).} We will explore using the model, the possibility of maximizing or minimizing the inherent MR in these layers and we show experimentally how to create thin high mobility layers where the inherent MR is significantly reduced or enhanced without compromising the layer mobility.\footnote{T Zhang et al., Semicond. Sci. Tech., in press.}   

Magnetocapacitance of Semiconductors with Nonmagnetic and Magnetic Impurities

Positive magnetoresistance in semiconductors has been studied by previous investigators and found to have an exponential dependence on magnetic field in the regime of hopping conduction and a power law dependence at higher temperatures, due to band carriers. To our knowledge, little experimental study has been performed on the magnetocapacitance of semiconductors outside of the low temperature regime, where phenomena such as the quantum Hall effect have been studied. Here we report on the magnetocapacitance of lightly doped ($\rho $ ~$>$~1 $\Omega $-cm) n- and p-type silicon, using both Schottky and oxide barriers to form capacitor structures. The frequency-dependent negative magnetocapacitance can be as large as 30{\%} at 50K and decreases to a few percent at room temperature. We attribute this effect to a field-induced localization of shallow donor impurity wavefunctions in directions transverse to the applied magnetic field. The effect can only be observed if the measurement frequency ($\sim $1MHz) is comparable to or greater than the field-dependent transition rate between impurity sites. We will also contrast the differences in the magnetocapacitance effect for diluted magnetic semiconductors such as GaCrN and GaMnAs.