In this thesis, the existence and uniqueness of gradient trajectories near an A2singularity are analysed. The A2-singularity is called a birth-death critical point in the real case. The birth-death critical point appears in a one-parameter family of functions. Such a family of functions has precisely two Morse critical points of index difference one, on the birth side. The result of the real case states that these two critical points are joined by a unique gradient trajectory up to time-shift. Here the gradient flow is defined with respect to any family of Riemannian metrics. This can be viewed as a converse to Smale’s cancellation theorem. We also look at the complex analogue of the result in Picard–Lefschetz theory. This analogue considers a holomorphic one-parameter family with an A2-singularity. Such a family has two critical Morse critical points near the singularity for every small non-zero parameter. We prove that the two Lagrangian vanishing cycles associated to these critical points intersect transversally in exactly one point in all regular fibres along a straight line. The result is obtained by analysing the gradient trajectories of the real part of these functions. Both proofs start with a normal form in local coordinates for such families of functions. The gradient equations in these coordinates can be rescaled into a fast-slow system of non-linear differential equation. Existence will rely on an adiabatic limit analysis whereas uniqueness follows from a Conley index pair construction. The latter construction will also show that connecting gradient trajectories cannot leave the local charts. Even though the proof of these two results follow from similar lines of argument, the real case cannot be reduced to the complex case and vice versa.

Doctoral Thesis by

The excitation of surface-phonon-polariton (SPhP) modes in polar dielectric crystals and the associ- ated new developments in the field of SPhPs are reviewed. The emphasis of this work is on providing an understand- ing of the general phenomenon, including the origin of the Reststrahlen band, the role that optical phonons in polar dielectric lattices play in supporting sub-diffrac- tion-limited modes and how the relatively long opti- cal phonon lifetimes can lead to the low optical losses observed within these materials. Based on this overview, the achievements attained to date and the potential tech- nological advantages of these materials are discussed for localized modes in nanostructures, propagating modes on surfaces and in waveguides and novel metamaterial designs, with the goal of realizing low-loss nanophoton- ics and metamaterials in the mid-infrared to terahertz spectral ranges.

Low-loss, infrared and terahertz nanophotonics using surface phonon polaritons

Semiconductor structures and devices including strained material layers having impurity-free zones, and methods for fabricating same. Certain regions of the strained material layers are kept free of impurities that can interdiffuse from adjacent portions of the semiconductor. When impurities are present in certain regions of the strained material layers, there is degradation in device performance. By employing semiconductor structures and devices (e.g., field effect transistors or “FETs”) that have the features described, or are fabricated in accordance with the steps described, device operation is enhanced.

Semiconductor structures employing strained material layers with defined impurity gradients and methods for fabricating same

Methods for selectively depositing high quality epitaxial material include introducing pulses of a silicon-source containing vapor while maintaining a continuous etchant flow. Epitaxial material is deposited on areas of a substrate, such as source and drain recesses. Between pulses, the etchant flow continues such that lower quality epitaxial material may be removed, as well as any non-epitaxial material that may have been deposited. The pulse of silicon-source containing vapor may be repeated until a desired thickness of epitaxial material is selectively achieved in semiconductor windows, such as recessed source/drain regions.

Cyclical epitaxial deposition and etch

Epitaxial layers (125) are selectively formed in semiconductor windows (114) by a cyclical process of repeated blanket deposition and selective etching. The blanket deposition phases leave non-epitaxial material (120) over insulating regions (112), such as field oxide, and the selective etch phases preferentially remove non-epitaxial material (120) while deposited epitaxial material (125) builds up cycle-by-cycle. Quality of the epitaxial material (125) improves relative to selective processes where no deposition occurs on insulators (112). Use of a germanium catalyst during the etch phases of the process aids etch rates and facilitates economical maintenance of isothermal and/or isobaric conditions throughout the cycles. Throughput and quality are improved by use of trisilane, formation of amorphous material (120) over the insulating regions (112) and minimizing the thickness ratio of amorphous:epitaxial material in each deposition phase.

Selective epitaxial formation of semiconductor films

We have measured the dielectric function of bulk nitrogen-doped 4H and 6H SiC substrates from 700 to 4000 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ using Fourier-transform infrared spectroscopic ellipsometry. Photon absorption by transverse optical phonons produces a strong reststrahlen band between 797 and 1000 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ with the effects of phonon anisotropy being observed in the region of the longitudinal phonon energy (960 to 100 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$). The shape of this band is influenced by plasma oscillations of free electrons, which we describe with a classical Drude equation. For the 6H-SiC samples, we modify the Drude equation to account for the strong effective mass anisotropy. Detailed numerical regression analysis yields the free-electron concentrations, which range from $7\ifmmode\times\else\texttimes\fi{}{10}^{17}$ to ${10}^{19}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3},$ in good agreement with electrical and secondary ion mass spectrometry measurements. Finally, we observe the Berreman effect near the longitudinal optical phonon energy in $n\ensuremath{-}/n+$ homoepitaxial 4H SiC and hydrogen implanted samples, and we are able to determine the thickness of these surface layers.

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Carrier concentration and lattice absorption in bulk and epitaxial silicon carbide determined using infrared ellipsometry

HfO 2 films deposited via tetrakis diethylamido hafnium (TDEAH) precursor using MOCVD (metal organic chemical vapor deposition) are presented. TDEAH is a promising precursor candidate for the deposition of high permittivity gate dielectrics. We report the impact of process and annealing conditions on the physical and electrical properties of the film. Deposition and annealing temperatures influence the microstructure, density, and impurity levels of TDEAH HfO 2 films. Spectroscopic ellipsometry shows that film microstructure manifests itself in the optical properties of the film, particularly in the presence of a band edge related feature at 5.8 eV An impurity analysis using Auger electron spectroscopy, secondary ion mass spectroscopy, and Raman spectroscopy, indicates that carbon impurities from the precursor exist as clusters within the HfO 2 dielectric. The impact of deposition temperature and annealing temperature on the capacitance vs. voltage and current density vs. voltage characteristics of platinum gated capacitors is studied. Correlation of physical film properties with the capacitance and leakage behavior of the TDEAH HfO 2 films indicates that impurities, in the form of carbon clusters, and low HfO 2 film density are detrimental to the electrical performance of the gate dielectric.

HfO2 Gate Dielectrics Deposited via Tetrakis Diethylamido Hafnium

We present a study of the infrared absorption and Raman scattering intensity of the local carbon mode in Si1−yCy alloys grown by direct carbon implantation followed by different recrystallization procedures. For the case of laser-induced recrystallization, the integrated infrared absorbances are found to agree with an extrapolation of the calibration curve previously determined for very low substitutional carbon concentrations in Si. We argue that this finding provides strong evidence for the achievement of nearly perfect substitutionality in laser-recrystallized films, even though their carbon concentrations are three orders of magnitude beyond the solubility limit of carbon in Si. This conclusion is found to be consistent with measurements of the intensity of defect-induced Si Raman scattering relative to the Raman intensity of the local carbon mode. The Raman intensity of the local carbon mode at 605 cm−1 relative to the first-order Si Raman line at 521 cm−1 provides an ideal spectroscopic tool for the...

Substitutional carbon in Si1−yCy alloys as measured with infrared absorption and Raman spectroscopy

Boron concentration profiles in rapid thermally annealed Si and strained Si1−xGex in situ doped, epitaxial layers were measured using secondary‐ion‐mass spectroscopy. Comparison of the Si1−xGex samples to the Si samples after rapid thermal annealing revealed a retarded B diffusivity inside the strained Si1−xGex layers. A simple empirical expression for the B retardation, which depended linearly on the Ge concentration, was developed and incorporated into a diffusion model for dopants in heterostructures. This model accurately simulated the measured B concentration profiles over a wide range of Ge fractions (0%–10%), B peak concentrations (2×1018–3×1019cm−3), and rapid thermal annealing conditions (900–1025 °C for 20–30 s).

Measurement and modeling of boron diffusion in Si and strained Si1−xGex epitaxial layers during rapid thermal annealing

Si 12yC y alloys grown by solid-phase epitaxy of carbon-implanted Si were investigated with Raman spectroscopy. A comparison between the experimental Raman spectrum and the spectrum predicted from ab initio calculations shows that the carbon distribution in these samples is more randomized than in similar alloys grown by molecular-beam epitaxy. It is argued that epitaxial, layer-by-layer growth promotes the formation of ordered Si-C structures. @S0163-1829~97!06532-6#

Jim Christiansen

Papers

Carrier concentration and lattice absorption in bulk and epitaxial silicon carbide determined using infrared ellipsometry

HfO2 Gate Dielectrics Deposited via Tetrakis Diethylamido Hafnium

Substitutional carbon in Si1−yCy alloys as measured with infrared absorption and Raman spectroscopy

Measurement and modeling of boron diffusion in Si and strained Si1−xGex epitaxial layers during rapid thermal annealing

Microscopic carbon distribution in Si1-yCy alloys: A Raman scattering study