Browsing by Subject "Capacitance"

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    Electronic Properties of Oxide and Semiconductor Heterostructures
    (2019-08) Sammon, Michael
    The modern world's dependency on electronics provides a constant need to discover new materials and devices. A promising technique to fabricate a new device is to create a heterostructure; a device consisting of two bulk crystals joined at an interface. These materials often support a low dimensional electron gas confined to the interface, which exhibits properties different than both the parent materials. These materials have led to the creation of MOSfets, the discovery of the quantum Hall effect, and in recent years the discovery of Majorana edge modes in nanowires. In this thesis, we study several different heterostructures. We begin with one of the most famous heterostructures, AlGaAs/GaAs. Modern AlGaAs/GaAs heterostructures support a high mobility two-dimensional electron gas (2DEG) in a quantum well. The 2DEG is provided by two remote donor $\delta$-layers placed on both sides of the well. Each $\delta$-layer is located in the midplane of a narrow GaAs well, flanked by narrow AlAs layers which capture excess electrons from donors. We show that each excess electron is localized in a compact dipole atom with the nearest donor. The excess electrons screen both the remote donors and background impurities, and are responsible for the observed high mobility. Still, we find that the mobility is substantially lower than theoretical estimates, which may be due to significant disorder in the donor layers, most likely roughness of the interfaces or spreading of the donors out of the midplane of the layer. Thus one should take care to make sure that the donor layers are as ideal as possible. We next move on to oxide heterostructures involving SrTiO$_3$ (STO). More specifically, we study the electron gas in accumulation layers of these heterostructures characterized by a density profile $n(x)$, where $x$ is the distance from the STO surface. SrTiO$_3$ at liquid helium temperatures has the highest dielectric constant which strongly enhances the role of nonlinear dielectric effects. It was recently shown that the nonlinear dielectric response results in an electron density profile $n(x)$ that slowly decays as $1/x^{12/7}$. We show that such a long tail of $n(x)$ causes the magnetization and the specific heat of the accumulation layer to diverge at large $x$. We explore the truncation of the tail by the finite sample width $W$, the transition from the nonlinear to linear dielectric response with dielectric constant $\kappa$, and the use of a back gate with a negative voltage $-\abs{V}$. We find that as a result both the magnetization and specific heat are anomalously large and obey nontrivial power law dependences on $W$, $\kappa$, or $\abs{V}$. In the linear dielectric regime under a strong magnetic field, the large dielectric constant of STO makes it easy to reach a quasi-one-dimensional state known as the extreme quantum limit (EQL) in which all electrons occupy the lowest Landau level. We present a theory of the EQL phase in STO accumulation layers. We find a phase diagram of the electron gas in the plane of the magnetic field strength and the electron surface concentration for different orientations of the magnetic field. In addition to the quasi-classical metallic phase (M), there is a metallic EQL phase, as well as an insulating Wigner crystal state (WC). Remarkably, the insulating Wigner crystal phase depends on the orientation of the magnetic field. We show that these effects can be measured through quantum capacitance measurements of the STO accumulation layer. The third material we study is semiconducting quantum wires. Though it is not a heterostructure, it supports a low dimensional electron gas which is often tuned with an external gate, making it similar to many of the devices we have studied. We have theoretically investigated the influence of interface roughness scattering on the low temperature mobility of electrons in quantum wires when electrons fill one or many subbands. We find the Drude conductance of the wire as a function of the linear concentration $\eta$ has a sharp peak. The height of this peak grows as a large power of the wire radius $R$, so that at large $R$ the conductance $G_{max}$ exceeds $e^2/h$ and a window of concentrations with delocalized states (which we call the metallic window) opens around the peak. Thus, we predict an insulator-metal-insulator transition with increasing concentration for large enough $R$. Furthermore, we show that the metallic domain can be sub-divided into three smaller domains: 1) single-subband ballistic conductor, 2) many-subband ballistic conductor 3) diffusive metal, and use our results to estimate the conductance in these domains. Finally we estimate the critical value of $R_c(\mathcal{L})$ at which the metallic window opens for a given length $\mathcal{L}$. We conclude the thesis with a discussion of a newer class of materials known as transition metal dichalcogenides (TMDs). We study a capacitor made of three monolayers TMD separated by hexagonal boron nitride (hBN). We assume that the structure is symmetric with respect to the central layer plane. The symmetry includes the contacts: if the central layer is contacted by the negative electrode, both external layers are contacted by the positive one. As a result a strong enough voltage $V$ induces electron-hole dipoles (indirect excitons) pointing towards one of the external layers. Antiparallel dipoles attract each other at large distances. Thus, the dipoles alternate in the central plane forming a 2D antiferroelectric with negative binding energy per dipole. The charging of a three-layer device is a first order transition, and we show that if $V_1$ is the critical voltage required to create a single electron-hole pair and charge this capacitor by $e$, the macroscopic charge $Q_c = eSn_c$ ($S$ is the device area) enters the three-layer capacitor at a smaller critical voltage $V_{c} < V_{1}$. In other words, the differential capacitance $C(V)$ is infinite at $V = V_{c}$. We also show that in a contact-less three-layer device, where the chemically different central layer has lower conduction and valence bands, optical excitation creates indirect excitons which attract each other, and therefore form antiferroelectric exciton droplets. Thus, the indirect exciton luminescence is red shifted compared to a two-layer device.
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    Large enhancement of capacitance driven by electrostatic image forces.
    (2011-04) Loth, Matthew Scott
    The purpose of this thesis is to examine the role of electrostatic images in determining the capacitance and the structure of the electrostatic double layer (EDL) formed at the interface of a metal electrode and an electrolyte. Current mean field theories, and the majority of simulations, do not account for ions to form image charges in the metal electrodes and claim that the capacitance of the double layer cannot be larger than that of the Helmholtz capacitor, whose width is equal to the radius of an ion. However, in some experiments, and simulations where the images are included, the apparent width of the capacitor is substantially smaller. Monte Carlo simulations are used to examine the interface between a metal electrode and a room temperature ionic liquid (RTIL) modeled by hard spheres (the “restricted primitive model”). Image charges for each ion are included in the simulated electrode. At moderately low temperatures the capacitance of the metal/RTIL interface is so large that the effective thickness of the electrostatic double-layer is up to 3 times smaller than the ion radius. To interpret these results, an approach is used that is based on the interaction between discrete ions and their image charges, which therefore goes beyond the mean-field approximation. When a voltage is applied across the interface, the strong image attraction causes counterions to condense onto the metal surface to form compact ion-image dipoles. These dipoles repel each other to form a correlated liquid. When the surface density of these dipoles is low, the insertion of an additional dipole does not require much energy. This leads to a large capacitance C that decreases monotonically with voltage V , producing a “bell-shaped” C(V ) curve. In the case of a semi-metal electrode, the finite screening radius of the electrode shifts the reflection plane for image charges to the interior of the electrode resulting in a “camel-shaped” C(V ) curve, which is parabolic near V = 0, reaches a maximum and then decreases. These predictions are in qualitative agreement with experiment. A similarly simple model is employed to simulate the EDL of superionic crystals. In this case only small cations are mobile and other ions form an oppositely charged background. Simulations show an effective thickness of the EDL that may be 3 times smaller than the ion radius. The weak repulsion of ion-image dipoles again plays a central role in determining the capacitance in this theory, which is in reasonable agreement with experiment. Finally, the problem of a strongly charged, insulating macroion in a dilute solution of multivalent counterions is considered. While an ideal conductor does not exist in the problem, and no images are explicitly included, simulations demonstrate that adsorbed counterions form a strongly correlated liquid of at the surface of the macroion and acts as an effective metal surface. In fact, the surface screens the electric field of distant ions with a negative screening radius. The simulation results serve to confirm existing non-mean-field theories.
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    Mechanics and charging of nanoparticle agglomerates.
    (2009-06) Shin, Weon Gyu
    This thesis consists of two parts. The first part concerns studies on mechanics of real agglomerate particles and the second part involves studies on unipolar diffusion charging of agglomerates. Understanding mechanics of real agglomerate particles consisting of multiple primary particles is important for aerosol sizing instrumentation using electrical mobility and nanoparticle manufacturing process where coagulation and sedimentation occur. A key quantity determining transport properties of agglomerates is the friction coefficient. However, quantitative studies for the friction coefficient of agglomerates are very limited. Transmission Electron Microscopy (TEM) image analysis results of silver agglomerates provides a basis for the comparison of experimental data with estimates based on free molecular models. A new quantitative method to determine the dynamic shape factor and the two exponents, η and Dfm, which characterize the power law dependence of friction coefficient on the number of primary spheres and the mass on the mobility diameter, was developed using Differential Mobility Analyzer (DMA)- Aerosol Particle Mass (APM) analyzer. Model predictions indicate that η is independent of agglomerate size while Dfm is sensitive to agglomerate size. Experimentally, it appears the opposite is true. Tandem DMA (TDMA) results also show that the massmobility diameter scaling exponent is not dependent on mobility size range. Estimates of non-ideal effects on the agglomerate dynamics were computed as perturbations to the Chan-Dahneke agglomerate model. After the corrections, an agreement between experimental data and model predictions becomes significantly improved. Unipolar diffusion charging becomes more attractive because it has higher charging efficiency than bipolar charging as well as important applications in aerosol sizing instrumentation using electrical mobility, powder coating, and the removal of toxic particles from air stream using Electrostatic Precipitator. It has been reported that the particle morphology affects both bipolar and unipolar charging processes. Nevertheless, knowledge about the charging of non-spherical particles such as asbestos fibers and fractal agglomerates is still lacking. From this study it was found that the effect of dielectric constant of materials on unipolar diffusion charging of nanoparticles is very small and the experimental results are in a good agreement with Fuchs (1963)’ theory. The effect of agglomerate morphology on unipolar charging characteristic was examined both experimentally and analytically in terms of the mean charge per particle. Both geometric surface area and electrical capacitance are known as two important parameters to determine the mean charge of non-spherical particles. A new model to predict the electrical capacitance of loose agglomerate particles as a function of mobility diameter was developed incorporating electrical mobility and electrostatics theories. This study shows that the electrical capacitance contributes to increase the mean charge per particle of agglomerates more than the geometric surface area, especially in the transition regime. The estimates of geometric surface area and electrical capacitance were used to predict the mean charge from Chang (1981)’s model and the predicted results are reasonably in good agreement with experimental data.