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Calculations of band-to-band impact ionisation rates performed in the semi-classical Fermi’s Golden Rule approximation are presented here for the semiconductors GaAs, In(_0.53)Ga(_0.47)As and Si(_0.5)Ge(_0.5) at 300K. The crystal band structure is calculated using the empirical pseudopotential method. To increase the speed with which band structure data at arbitrary k-vectors can be obtained, an interpolation scheme has been developed. Energies are quadratically interpolated on adapted meshes designed to ensure accuracy is uniform throughout the Brillouin zone, and pseudowavefunctions are quadratically interpolated on a regular mesh. Matrix elements are calculated from the pseudowavefunctions, and include the terms commonly neglected in calculations for narrow band gap materials and an isotropic approximation to the full wavevector and frequency dependent dielectric function. The numerical integration of the rate over all distinct energy and wavevector conserving transitions is performed using two different algorithms. Results from each are compared and found to be in good agreement, indicating that the algorithms are reliable. The rates for electrons and holes in each material are calculated as functions of the k-vector of the impacting carriers, and found to be highly anisotropic. Average rates for impacting carriers at a given energy are calculated and fitted to Keldysh-type expressions with higher than quadratic dependence of the rate on energy above threshold being obtained in all cases. The average rates calculated here are compared to results obtained by other workers, with reasonable agreement being obtained for GaAs, and poorer agreement obtained for InGaAs and SiGe. Possible reasons for the disagreement are investigated. The impact ionisation thresholds are examined and k-space and energy distributions of generated carriers are determined. The role of threshold anisotropy, variation in the matrix elements and the shape of the bands in determining characteristics of the rate, particularly the softness of the rate's threshold behaviour are investigated.

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Currently, there are two main methodologies for the calculation of the electronic structure and properties of crystalline solids. Known as the Hartree-Fock Method (HF) and the Density Functional Theory (DFT) methods, they are based on two different theories for the numerical solution of the many electron Schrödinger equation. Unfortunately, in highly correlated electron systems like transition metal complexes, both the HF and DFT methods have severe shortcomings. In some cases they fail to provide the correct description of the electronic structure. <p>In general, the HF method overestimates the energy band gap due to the neglect of electron correlation effects and the incorrect description of electron interactions in the unoccupied orbitals. In contrast, even though electron correlation effects are implicitly included in the density functional, DFT often underestimates the band gap due to the improper treatment of the electron self-interaction. <p> To amend these problems, two approaches have been proposed. The deficiency in the HF scheme can be corrected using a hybrid method which adds exchange correlation energy borrowed from DFT to help reduce the band gap energy and bring the predictions in better agreement with experiment. To improve DFT, the LDA+U approach, which uses a model Hubbard-like Hamiltonian including an on-site repulsion parameter U, can be employed. This method is a convenient semi-quantitative way to efficiently calculate the band gap of insulators and semiconductors.<p> In this thesis, the electronic structure of YTiO₃ under pressure is investigated using the aforementioned approaches. The performance and reliability of these methods will be examined, compared and discussed.

Currently, there are two main methodologies for the calculation of the electronic structure and properties of crystalline solids. Known as the Hartree-Fock Method (HF) and the Density Functional Theory (DFT) methods, they are based on two different theories for the numerical solution of the many electron Schrödinger equation. Unfortunately, in highly correlated electron systems like transition metal complexes, both the HF and DFT methods have severe shortcomings. In some cases they fail to provide the correct description of the electronic structure. <p>In general, the HF method overestimates the energy band gap due to the neglect of electron correlation effects and the incorrect description of electron interactions in the unoccupied orbitals. In contrast, even though electron correlation effects are implicitly included in the density functional, DFT often underestimates the band gap due to the improper treatment of the electron self-interaction. <p> To amend these problems, two approaches have been proposed. The deficiency in the HF scheme can be corrected using a hybrid method which adds exchange correlation energy borrowed from DFT to help reduce the band gap energy and bring the predictions in better agreement with experiment. To improve DFT, the LDA+U approach, which uses a model Hubbard-like Hamiltonian including an on-site repulsion parameter U, can be employed. This method is a convenient semi-quantitative way to efficiently calculate the band gap of insulators and semiconductors.<p> In this thesis, the electronic structure of YTiO₃ under pressure is investigated using the aforementioned approaches. The performance and reliability of these methods will be examined, compared and discussed.

The field of molecular electronics has been under investigation by materials scientists for the last two decades, activity that has increased in recent years as their potential to be components in modern quantum computing devices began to be discussed in a more sophisticated manner. In this field, the challenge is to obtain stable highly conducting materials and to manipulate their properties with external stimuli. As one of the most stable organic radicals, the singly reduced form of TCNQ (7,7,8,8-tetracyanoquinodimethane) has played a central role in the design of many unprecedented conducting materials including the first purely organic conductor (TTF)(TCNQ) (TTF = tetrathiafulvalene) which is nearly metallic and the electrically bistable switching material Cu(TCNQ). The research in this dissertation focused on the application of TCNQ and its derivatives in order to tune the structure and conductivity of these materials, with the overarching goal being to understand the mechanism of conductivity. This dissertation reports the details of the first main-group TCNQ binary compound, Tl(TCNQ). Two distinct polymorphs have been discovered and a remarkable water-induced phase transition from one to the other was observed. With different modes of TCNQ stacking (alternating or homogenous distances), the two polymorphs exhibit very different conductivities, namely 2.4×10^-4 S/cm and 5.4×10^-1 S/cm. With this inspiration, a series of semiconductors, Tl(TCNQX2) (X =Cl, Br, I) was prepared and structurally characterized. The steric effect of the halogen substituents leads to a variety of structures and a band structure simulation has suggested a clear structure-property relationship that involves perturbation of the Tl 6s orbital into the conduction band. Inspired by the switching material Ag(TCNQ), semiconducting frameworks Ag(TCNQCl2) and Ag(TCNQBr2) were prepared by electrocrystallization methods. Importantly, the former material exhibits a high room temperature conductivity of 0.25 S/cm and an unusual room temperature negative differential resistance (NDR) which is the source of intrinsic switching behaviors. The effect of solvent on the structure of these binary phases was also investigated. The series M(TCNQX2)(MeCN)n (M = Cu, Ag; X = Br, I; n =1, 2) was discovered and the interconversion of these solvated phases was studied. The effect of coordinated solvent molecules decreases the density of conducting stacks, consequently leading to a decrease of conductivity.

GaAs(1-x)Bi(x) (x = 0 to 17%) optical properties were investigated by spectroscopic ellipsometry (in energy ranges of 0.37–9.0 eV). Optical features in the dielectric function, known as the critical points, were distinguished and modeled using standard analytic line shapes. The energy dependence of the critical points energies was thoroughly investigated as a function of Bi content and thin film strain. Critical points analysis in the Brillion zone showed that the top of the valence band is most strongly dependent on Bi content compared to other parts of the band structure. In addition, an interesting new critical point was observed that is attributed to alternative allowed optical transitions made possible by changes to the top of the valence band caused by resonant interactions with Bi orbitals. Several of the critical points were extrapolated to 100% Bi and showed reasonable agreement with the calculated band structure of GaBi. GaAs(1-x)Bi(x) (x= 03, 0.7 and 1.1%) based p+/n and n+/p heterostructure photovoltaic performance was characterized through IV and CV measurement. By introduction of Bi into GaAs, a non-zero EQE below the GaAs band edge energy was observed while the highest efficiency was obtained by ~ 0.7% Bi incorporation. EQE spectrum was modeled to find the minority carrier diffusion lengths of ~ Ln = 1600 and Lp = 140 nm for p-doped and n-doped GaAs92Bi08 in the doping profile of 10^15 - 10^16 cm^-3. Analysis of the CV measurement confirmed the background n-doping effect of Bi atom and the essential role of the cap layer to reduce multi-level recombination mechanisms at the cell edge to improve ideality factor. Low temperature grown GaAs was optimized to be used as photoconductive antenna in THz time-domain spectroscopy setup. The As content was investigated to optimize photo-carrier generation using 1550 nm laser excitation while maintaining high mobility and resistivity required for optical switching. A barrier layer of AlAs was added below the LT-GaAs to limit carrier diffusion into the GaAs substrate. Moreover, LT-GaAs layer thickness and post-growth annealing condition was optimized. The optimized structure (2-µm LT-GaAs on 60-nm AlAs, under As2:Ga BEP of ~7, annealed at 550°C for 1 minute) outperformed a commercial InGaAs antenna by a factor of 15 with 4.5 THz bandwidth and 75 dB signal-to-noise ratio at 1550 nm wavelength. / Graduate

One of the challenges in graphene fabrication is the production of large scale, high quality sheets. To study a possible approach to achieve quasi-freestanding graphene on a substrate by the intercalation of alkali metal atoms, Cs intercalation between graphene and Ni(111) is investigated. It is known that direct contact between graphene and Ni(111) perturbs the Dirac states. Cs intercalation restores the linear dispersion characteristic of Dirac fermions, which agrees with experiments, but the Dirac cone is shifted to lower energy, i.e., the graphene sheet is n-doped. Cs decouples the graphene sheet, while the spin polarization of Ni(111) does not extend through the intercalated atoms to the graphene sheet, for which we find virtually spin-degeneracy. In order to employ graphene in electronic applications, one requires a finite band gap. We engineer a band gap in metallic bilayer graphene by substitutional B and/or N doping. Specifically, the introduction of B-N pairs into bilayer graphene can be used to create a band gap that is stable against thermal fluctuations at room temperature. Introduction of B-N pairs into B and/or N doped bilayer graphene likewise hardly modifies the band dispersions, however, the size of the band gap is effectively tuned. We also study the influence of terrace edges on the electronic properties of graphene, considering bare edges and H, F, Cl, NH2 terminations. Periodic structural reconstruction is observed for the Cl and NH2 edge terminations due to interaction between the terminating atoms/groups. We observe that Cl edge termination p-dopes the terraces, while NH2 edge termination results in n-doping.

<p> The Augmented Plane Wave method has been used to calculate the one-electron energy band structure of MnF2 . The bands were computed at the r point and along the ^ line for cases representing the "paramagnetic" and anti-ferromagnetic states of MnF2.</p> / Thesis / Master of Science (MSc)