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

Implanted B and P dopants in Si exhibit transient enhanced diffusion (TED) during annealing which arises from the excess interstitials generated by the implant. In order to study the mechanisms of TED, transmission electron microscopy measurements of implantation damage were combined with B diffusion experiments using doping marker structures grown by molecular-beam epitaxy (MBE). Damage from nonamorphizing Si implants at doses ranging from 5×1012 to 1×1014/cm2 evolves into a distribution of {311} interstitial agglomerates during the initial annealing stages at 670–815 °C. The excess interstitial concentration contained in these defects roughly equals the implanted ion dose, an observation that is corroborated by atomistic Monte Carlo simulations of implantation and annealing processes. The injection of interstitials from the damage region involves the dissolution of {311} defects during Ostwald ripening with an activation energy of 3.8±0.2 eV. The excess interstitials drive substitutional B into electric...

/pdf/physical-mechanisms-of-transient-enhanced-dopant-diffusion-zkysm82pgr.pdf

Physical mechanisms of transient enhanced dopant diffusion in ion-implanted silicon

A number of vacancy and interstitial defect migration mechanisms are characterized for crystalline silicon using supercells containing 64 and 216 atoms and a tight-binding approach. We investigate various defect configurations corresponding to minima and the pathways that connect them. A modified eigenvector-following approach is used to locate true transition states. We exploit the fact that only one Hessian eigenvector is needed to define the uphill search direction and use conjugate gradient minimization in the tangent space to produce a hybrid algorithm. Two implementations of this approach are considered, the first where second derivatives are available but full diagonalization of the Hessian would be the most time-consuming step, and the second where only first derivatives of the energy are known.

http://www-wales.ch.cam.ac.uk/pdf/PRB.59.3969.1999.pdf

Defect migration in crystalline silicon

Primary radiation damage: A review of current understanding and models

Ion-beam-induced amorphization in Si has attracted significant interest since the beginning of the use of ion implantation for the fabrication of Si devices. A number of theoretical calculations and experiments were designed to provide a better understanding of the mechanisms behind the crystal-to-amorphous transition in Si. Nowadays, a renewed interest in the modeling of amorphization mechanisms at atomic level has arisen due to the use of preamorphizing implants and high dopant implantation doses for the fabrication of nanometric-scale Si devices. In this paper we will describe the most significant experimental observations related to the ion-beam-induced amorphization in Si and the models that have been developed to describe the process. Amorphous Si formation by ion implantation is the result of a critical balance between the damage generation and its annihilation. Implantation cascades generate different damage configurations going from isolated point defects and point defect clusters in essentially ...

https://www.ele.uva.es/~mmm/papers/2004_Pelaz_JAP_96.pdf

Ion-beam-induced amorphization and recrystallization in silicon

Tight-binding molecular dynamics simulations are performed to study self-diffusion, interstitial-vacancy recombination, and formation volumes of point defects in crystalline silicon. The results show that (i) self-diffusion is dominated by vacancies (V) at low temperature and by interstitials (I) at high temperature; (ii) interstitial-vacancy recombination at room temperature leads to formation of a metastable I-V complex, which has an annihilation energy barrier of 1.1 eV; (iii) interstitial and vacancy relaxation volumes in silicon are approximately equal in magnitude and opposite in sign.

Intrinsic point defects in crystalline silicon: Tight-binding molecular dynamics studiesof self-diffusion, interstitial-vacancy recombination, and formation volumes

The ab initio pseudopotential method was used to study the boron diffusion and pairing process in crystalline silicon. The results show that substitutional B attracts interstitial Si with a binding energy of 1.1 \ifmmode\pm\else\textpm\fi{} 0.1 eV. We show that B diffusion is significantly enhanced in the presence of the Si interstitial due to the substantial lowering of the migrational barrier through most likely a kick-out mechanism. The resulting mobile boron can also be trapped by another substitutional boron with a binding energy of 1.8 \ifmmode\pm\else\textpm\fi{} 0.1 eV, forming an immobile and electrically inactive two-boron pair along a 〈001〉 direction. It is also found that the pairing of these two boron atoms involves the trapping of a Si interstitial. Alternatively, two B pairs that do not trap the Si interstitial were found to be energetically unfavorable. All of these findings are consistent with experimental results. \textcopyright{} 1996 The American Physical Society.

Ab initio pseudopotential calculations of B diffusion and pairing in Si

Ab initio pseudopotential calculations of dopant diffusion in Si

Atomic scale models of ion implantation and dopant diffusion in silicon

Ab initio pseudopotential calculations were performed to obtain the formation energies of point defects in crystalline Si. A supercell of 64 Si atoms was used for the calculations. For the self-interstitial defect, a weak bond is formed between two defect Si atoms. However, no evidence of extra bond formation is found in the vacancy study. The formation energies of both defects are comparable, i.e. 3.7 eV for the vacancy and 3.25 eV for the self-interstitials, respectively. Our self-interstitial formation energy agrees well with other theoretical results, while the vacancy formation energy is much smaller. We also present the results of boron substitutional impurities in Si where the charge density plot indicates an ionic character of the BSi bonding.

Jing Zhu

Papers

Intrinsic point defects in crystalline silicon: Tight-binding molecular dynamics studiesof self-diffusion, interstitial-vacancy recombination, and formation volumes

Ab initio pseudopotential calculations of B diffusion and pairing in Si

Ab initio pseudopotential calculations of dopant diffusion in Si

Atomic scale models of ion implantation and dopant diffusion in silicon

Ab initio pseudopotential calculations of point defects and boron impurity in silicon