81.05.Dz II-VI semiconductors
Refine
Has Fulltext
- yes (2)
Is part of the Bibliography
- yes (2)
Document Type
- Doctoral Thesis (2)
Language
- English (2)
Keywords
- Epitaxie (1)
- Epitaxy (1)
- Gittergas (1)
- Halbleiter (1)
- Heterostruktur (1)
- HgTe (1)
- Kristallwachstum (1)
- Lattice Gas (1)
- Magnetischer Sensor (1)
- Micro-Hall Magnetometry (1)
Institute
Within the scope of this thesis two main topics have been investigated: the examination of micromagnetic sensors and transport of massive and massless Dirac fermions in HgTe quantum wells. For the investigation of localized, inhomogeneous magnetic fields, the fabrication and characterization of two different non-invasive and ultra sensitive sensors has been established at the chair ”Experimentelle Physik” of the University of Würzburg. The first sensor is based on the young technique named micro-Hall magnetometry. The necessary semiconductor devices (Hall cross structures) were fabricated by high-resolution electron beam lithography based on two different two dimensional electron gases (2DEGs), namely InAs/(Al,Ga)Sb- and HgTe/(Hg,Cd)Te- heterostructures. The characteristics have been examined in two different ways. Measurements in homogeneous magnetic fields served for characterization of the sensors, whereas the investigation of artificially produced sub-µm magnets substantiates the suitability of the devices for the study of novel nanoscale magnetic materials (e.g. nanowires). Systematic experiments with various magnets are in accordance with the theory of single-domain particles and anisotropic behavior due to shapes with high aspect ratio. The highest sensitivity for strongly localized fields was obtained at T = 4.2 K for a (200x200) nm^2 Hall cross - made from shallow, high mobility HgTe 2DEG. Although the field resolution was merely δB ≈ 100 µT, the nanoscale sensor size yields an outstanding flux resolution of δΦ = 2 10^(−3) Φ0, where Φ0 = h/2e is the flux quantum. Translating this result in terms of magnetic moment, the sensitivity allows for the detection of magnetization changes of a particle centered on top of the sensor as low as δM ≈ 10^2 µB, with the magnetic moment of a single electron µB, the Bohr magneton. The further examination of a permalloy nanomagnet with a cross-section of (100x20) nm^2 confirms the expected resolution ability, extracted from the noise of the sensor. The observed high signal-to-noise ratio validates the detection limit of this sensor in terms of geometry. This would be reached for a magnet (same material) with quadratic cross-section for an edge length of 3.3 nm. Moreover, the feasibility of this sensor for operation in a wide temperature range (T = mK... > 200 K) and high magnetic fields has been confirmed. The second micromagnetic sensor is the micro-SQUID (micro-Superconducting-QUantum-Interference-Device) based on niobium. The typical sensor area of the devices built in this work was (1.0x1.0) µm^2, with constrictions of about 20 nm. The characterization of this device demonstrates an amazing field sensitivity (regarding its size) of δB < 1 µT. Even though the sensor was 25 times larger than the best micro-Hall sensor, it provided an excellent flux resolution in the order of δΦ ≈ 5 10^(−4) Φ0 and a similar magnetic moment resolution of δM ≈ 10^2 µB. Furthermore, the introduction of an ellipsoidal permalloy magnet (axes: 200 nm and 400 nm, thickness 30 nm) substantiates the suitability for the detection of minuscule, localized magnetic fields. The second part of the thesis deals with the peculiar transport properties of HgTe quantum wells. These rely on the linear contribution to the band structure inherent to the heterostructure. Therefore the system can be described by an effective Dirac Hamiltonian, whose Dirac mass is tunable by the variation of the quantum well thickness. By fabrication and characterization of a systematical series of substrates, a system with vanishing Dirac mass (zero energy gap) has been confirmed. This heterostructure therefore resembles graphene (a monolayer of graphite), with the difference of exhibiting only one valley in the energy dispersion of the Brillouin zone. Thus parasitical intervalley scattering cannot occur. The existence of this system has been proven by the agreement of theoretical predictions, based on widely accepted band structure calculations with the experiment (Landau level dispersion, conductivity). Furthermore, another particularity of the band structure - the transition from linear to parabolic character - has been illustrated by the widths of the plateaus in the quantum Hall effect. Finally, the transport of ”massive” Dirac fermions (with finite Dirac mass) is investigated. In particular the describing Dirac Hamiltonian induces weak localization effects depending on the Dirac mass. This mechanism has not been observed to date, and survives in higher temperatures compared to typical localization mechanisms.
In this PhD thesis, we develop models for the numerical simulation of epitaxial crystal growth, as realized, e.g., in molecular beam epitaxy (MBE). The basic idea is to use a discrete lattice gas representation of the crystal structure, and to apply kinetic Monte Carlo (KMC) simulations for the description of the growth dynamics. The main advantage of the KMC approach is the possibility to account for atomistic details and at the same time cover MBE relevant time scales in the simulation. In chapter 1, we describe the principles of MBE, pointing out relevant physical processes and the influence of experimental control parameters. We discuss various methods used in the theoretical description of epitaxial growth. Subsequently, the underlying concepts of the KMC method and the lattice gas approach are presented. Important aspects concerning the design of a lattice gas model are considered, e.g. the solid-on-solid approximation or the choice of an appropriate lattice topology. A key element of any KMC simulation is the selection of allowed events and the evaluation of Arrhenius rates for thermally activated processes. We discuss simplifying schemes that are used to approximate the corresponding energy barriers if detailed knowledge about the barriers is not available. Finally, the efficient implementation of the MC kinetics using a rejection-free algorithm is described. In chapter 2, we present a solid-on-solid lattice gas model which aims at the description of II-VI(001) semiconductor surfaces like CdTe(001). The model accounts for the zincblende structure and the relevant surface reconstructions of Cd- and Te-terminated surfaces. Particles at the surface interact via anisotropic nearest and next nearest neighbor interactions, whereas interactions in the bulk are isotropic. The anisotropic surface interactions reflect known properties of CdTe(001) like the small energy difference between the c(2x2) and (2x1) vacancy structures of Cd-terminated surfaces. A key element of the model is the presence of additional Te atoms in a weakly bound Te* state, which is motivated by experimental observations of Te coverages exceeding one monolayer at low temperatures and high Te fluxes. The true mechanism of binding excess Te to the surface is still unclear. Here, we use a mean-field approach assuming a Te* reservoir with limited occupation. In chapter 3, we perform KMC simulations of atomic layer epitaxy (ALE) of CdTe(001). We study the self-regulation of the ALE growth rate and demonstrate how the interplay of the Te* reservoir occupation with the surface kinetics results in two different regimes: at high temperatures the growth rate is limited to one half layer of CdTe per ALE cycle, whereas at low enough temperatures each cycle adds a complete layer. The temperature where the transition between the two regimes occurs depends mainly on the particle fluxes. The temperature dependence of the growth rate and the flux dependence of the transition temperature are in good qualitative agreement with experimental results. Comparing the macroscopic activation energy for Te* desorption in our model with experimental values we find semiquantitative agreement. In chapter 4, we study the formation of nanostructures with alternating stripes during submonolayer heteroepitaxy of two different adsorbate species on a given substrate. We evaluate the influence of two mechanisms: kinetic segregation due to chemically induced diffusion barriers, and strain relaxation by alternating arrangement of the adsorbate species. KMC simulations of a simple cubic lattice gas with weak inter-species binding energy show that kinetic effects are sufficient to account for stripe formation during growth. The dependence of the stripe width on control parameters is investigated. We find an Arrhenius temperature dependence, in agreement with experimental investigations of phase separation in binary or ternary material systems. Canonical MC simulations show that the observed stripes are not stable under equilibrium conditions: the adsorbate species separate into very large domains. Off-lattice simulations which account for the lattice misfit of the involved particle species show that, under equilibrium conditions, the competition between binding and strain energy results in regular stripe patterns with a well-defined width depending on both misfit and binding energies. In KMC simulations, the stripe-formation and the experimentally reported ramification of adsorbate islands are reproduced. To clarify the origin of the island ramification, we investigate an enhanced lattice gas model whose parameters are fitted to match characteristic off-lattice diffusion barriers. The simulation results show that a satisfactory explanation of experimental observations within the lattice gas framework requires a detailed incorporation of long-range elastic interactions. In the appendix we discuss supplementary topics related to the lattice gas simulations in chapter 4.