Uncertainty analysis to minimise risk in designing micro-electronics manufacturing processes

A design methodology based on numerical modelling, integrated with optimisation techniques and statistical methods, to aid the process control of micro and nano-electronics based manufacturing processes is presented in this paper. The design methodology is demonstrated for a micro-machining process called Focused Ion Beam (FIB). This process has been modelled to help understand how a pre-defined geometry of micro- and nano- structures can be achieved using this technology. The process performance is characterised on the basis of developed Reduced Order Models (ROM) and are generated using results from a mathematical model of the Focused Ion Beam and Design of Experiment (DoE) methods. Two ion beam sources, Argon and Gallium ions, have been used to compare and quantify the process variable uncertainties that can be observed during the milling process. The evaluations of the process performance takes into account the uncertainties and variations of the process variables and are used to identify their impact on the reliability and quality of the fabricated structure. An optimisation based design task is to identify the optimal process conditions, by varying the process variables, so that certain quality objectives and requirements are achieved and imposed constraints are satisfied. The software tools used and developed to demonstrate the design methodology are also presented.

Optimisation methodology for risk mitigation in advanced micro-system electronics manufacturing

This paper presents a design methodology based on numerical modelling, integrated with optimisation techniques and statistical methods, to aid the development of new advanced technologies in the area of micro and nano systems. The design methodology is demonstrated for a micro-machining process called Focused Ion Beam (FIB). This process has been modelled to provide knowledge of how a pre-defined geometry can be achieved through this direct milling. The geometry characterisation is obtained using a Reduced Order Models (ROM), generated from the results of a mathematical model of the Focused Ion Beam, and Design of Experiment (DoE) methods. In this work, the focus is on the design flow methodology which includes an approach on how to include process parameter uncertainties into the process optimisation modelling framework. A discussion on the impact of the process parameters, and their variations, on the quality and performance of the fabricated structure is also presented. The design task is to identify the optimal process conditions, by altering the process parameters, so that certain reliability and confidence of the application is achieved and the imposed constraints are satisfied. The software tools used and developed to demonstrate the design methodology are also presented.

Radiative lifetimes of metastable states of negative ions

We present a technique for measuring the radiative lifetimes of metastable states of negative ions that involves the use of a heavy-ion storage ring. The method has been applied to investigate the radiative decay of the np3 2P1/2 levels of Te–(n=5) and Se–(n=4) and the 3p3 2D state of Si– for which the J=3/2 and 5/2 levels were unresolved. All of these states are metastable and decay primarily by emission of E2 and M1 radiation. Multi Configuration Dirac-Hartree-Fock calculations of rates for the transitions in Te– and Se– yielded lifetimes of 0.45 s and 4.7 s, respectively. The measured values agree well with these predicted values. In the case of the 2D state of Si–, however, our measurement was only able to set a lower limit on the lifetime. The upper limit of the lifetime that can be measured with our apparatus is set by how long the ions can be stored in the ring, a limit determined by the rate of collisional detachment. Our lower limit of 1 min for the lifetime of the 2D state is consistent with both the calculated lifetimes of 162 s for the 2D3/2 level and 27.3 h for the 2D5/2 level reported by O'Malley and Beck and 14.5 h and 12.5 h, respectively, from our Breit-Pauli calculations.

Scaling of domain periodicity with thickness measured in BaTiO3 single crystal lamellae and comparison with other ferroics

The focused ion beam microscope has been used to cut parallel-sided {100}-oriented thin lamellae of single crystal barium titanate with controlled thicknesses, ranging from 530 nm to 70 nm. Scanning transmission electron microscopy has been used to examine domain configurations. In all cases, stripe domains were observed with {011}-type domain walls in perovskite unit-cell axes, suggesting 90 degrees domains with polarization in the plane of the lamellae. The domain widths were found to vary as the square root of the lamellar thickness, consistent with Kittel's law, and its later development by Mitsui and Furuichi and by Roytburd. An investigation into the manner in which domain period adapts to thickness gradient was undertaken on both wedge-shaped lamellae and lamellae with discrete terraces. It was found that when the thickness gradient was perpendicular to the domain walls, a continuous change in domain periodicity occurred, but if the thickness gradient was parallel to the domain walls, periodicity changes were accommodated through discrete domain bifurcation. Data were then compared with other work in literature, on both ferroelectric and ferromagnetic systems, from which conclusions on the widespread applicability of Kittel's law in ferroics were made.

Three-dimensional macroporous silicon photonic crystal with large photonic band gap

Three-dimensional photonic crystals based on macroporous silicon are fabricated by photoelectrochemical etching and subsequent focused-ion-beam drilling. Reflection measurements show a high reflection in the range of the stopgap and indicate the spectral position of the complete photonic band gap. The onset of diffraction which might influence the measurement is discussed.

Ferroelectricity and isotope effects in hydrogen-bonded KDP crystals

Based on an accurate first principles description of the energetics in H-bonded potassium-dihydrogen-phosphate crystals, we conduct a first study of nuclear quantum effects and of the changes brought about by deuteration. Tunneling is allowed only for clusters involving correlated protons and heavy ion displacements, the main effect of deuteration being a depletion of the proton probability density at the O-H-O bridge center, which in turn weakens its proton-mediated covalent bonding. The ensuing lattice expansion couples self-consistently with the proton off-centering, thus explaining both the giant isotope effect and its close connection with geometrical effects.

Impulsive electric fields driven by high-intensity interactions

The interaction of high-intensity laser pulses with matter releases instantaneously ultra-large currents of highly energetic electrons, leading to the generation of highly-transient, large-amplitude electric and magnetic fields. We report results of recent experiments in which such charge dynamics have been studied by using proton probing techniques able to provide maps of the electrostatic fields with high spatial and temporal resolution. The dynamics of ponderomotive channeling in underdense plasmas have been studied in this way, as also the processes of Debye sheath formation and MeV ion front expansion at the rear of laser-irradiated thin metallic foils. Laser-driven impulsive fields at the surface of solid targets can be applied for energy-selective ion beam focusing.

Excited ions in intense femtosecond laser pulses: Laser-induced recombination

Electron-ion recombination in a laser-induced electron recollision is of fundamental importance as the underlying mechanism responsible for the generation of high harmonic radiation, and hence for the production of attosecond pulse trains in the extreme ultraviolet and soft X-ray spectral regions. By using an ion beam target, remotely prepared to be partially in long-lived excited states, the recombination process has for the first time been directly observed and studied.

Electron and laser interactions with positive ions

Recent progress in laboratory-based electron-ion scattering is reviewed, and the sensitivity of observed interference structure as a probe of collision dynamics is discussed. The extension of our use of positive ions as scattering targets to photon-ion interactions is demonstrated with the first ion-beam measurements for the fragmentation of a molecular ion, H-2(+), using intense femtosecond laser pulses.

Nanoscale ferroelectrics machined from single crystals

This paper summarises some of the most recent work that has been done on nanoscale ferroelectrics as a result of a joint collaborative research effort involving groups in Queen's University Belfast, the University of Cambridge and the University of St. Andrews. Attempts have been made to observe fundamental effects of reduced size, and increasing morphological complexity, on ferroelectric behaviour by studying the functional response and domain characteristics in nanoscale single crystal material, whose size and morphology have been defined by Focused Ion Beam (FIB) patterning. This approach to nanoshape fabrication has allowed the following broad statements to be made: (i) in single crystal BaTiO3 sheets, permittivity and phase transition behaviour is not altered from that of bulk material down to a thickness of similar to 75 nm; (ii) in single crystal BaTiO3 sheets and nanowires changes in observed domain morphologies are consistent with large scale continuum modeling.

Size Effects on Thin Film Ferroelectrics: Experiments on Isolated Single Crystal Sheets

Thin lamellae were cut from bulk single crystal BaTiO3 using a Focused Ion Beam Microscope. They were then removed and transferred onto single crystal MgO substrates, so that their functional properties could be measured independent of the original host bulk ferroelectric. The temperature dependence of the capacitance of these isolated single crystal films was found to be strongly bulk-like, demonstrating a sharp Curie anomaly, as well as Curie-Weiss behaviour. In addition, the sudden change in the remanent polarisation as a function of temperature at TC was characteristic of a first order phase change. The work represents a dramatic improvement on that previously published by M. M. Saad, P. Baxter, R. M. Bowman, J. M. Gregg, F. D. Morrison & J. F. Scott, J. Phys: Cond. Matt., 16 L451-L456 (2004), as critical shortcomings in the original specimen geometry, involving potential signal contributions from bulk BaTiO3, have now been obviated. That the functional properties of single crystal thin film lamellae are comparable to bulk, and not like those of conventionally deposited heteroegenous thin film systems, has therefore been confirmed.

The Dissociative Recombination of Protonated Acrylonitrile, CH2CHCNH+, with Implications for Nitrile Chemistry in Dark Molecular Clouds and the Upper Atmosphere of Titan

Measurements on the dissociative recombination (DR) of protonated acrylonitrile, CH2CHCNH+, have been performed at the heavy ion storage ring CRYRING located in the Manne Siegbahn Laboratory in Stockholm, Sweden. It has been found that at~2meV relative kinetic energy about 50% of the DR events involve only ruptures of X–H bonds (where X=C or N)while the rest leads to the production of a pair of fragments each containing two heavy atoms (alongside H and/or H2). The absolute DR cross section has been investigated for relative kinetic energies ranging from ~1 meV to 1 eV. The thermal rate coefficient has been determined to follow the expression k(T) = 1.78 × 10-6 (T/300)-0.80 cm3 s-1 for electron temperatures ranging from ~10 to 1000 K. Gas-phase models of the nitrile chemistry in the dark molecular cloud TMC-1 have been run and results are compared with observations. Also, implications of the present results for the nitrile chemistry of Titan’s upper atmosphere are discussed.

Imaging domains in BaTiO3 single crystal nanostructures: comparing information from transmission electron microscopy and piezo-force microscopy

This article compares and contrasts information
obtained, using transmission electron microscopy (TEM)
and piezo-force microscopy (PFM), on domain configurations
adopted in single crystal lamellae of BaTiO3, that had
been cut directly from bulk using a focused ion beam
microscope with top and bottom surfaces parallel to
{100}pseudocubic. Both forms of imaging reveal domain
walls parallel to {110}pseudocubic, consistent with sets of 90
domains with dipoles oriented parallel to the two
\001[pseudocubic directions in the plane of the lamellae.
However, the domain width was observed to be dramatically
larger using PFM than it was using TEM. This suggests
significant differences in the surface energy densities
that drive the domain formation in the first place, that could
relate to differences in the boundary conditions in the two
modes of imaging (TEM samples are imaged under high
vacuum, whereas PFM imaging was performed in air).
Attempts were made to map local dipole orientations
directly, using a form of ‘vector’ PFM. However, information
inferred was largely inconsistent with the known
crystallography of the samples, raising concern about the
levels of care needed for accurate interpretation of PFM
images.

Domains in Ferroelectric Nanodots

Almost free-standing single crystal mesoscale and nanoscale dots of ferroelectric BaTiO3 have been made by direct focused ion beam patterning of bulk single crystal material. The domain structures which appear in these single crystal dots, after cooling through the Curie temperature, were observed to form into quadrants, with each quadrant consisting of fine 90° stripe domains. The reason that these rather complex domain configurations form is uncertain, but we consider and discuss three possibilities for their genesis: first, that the quadrant features initially form to facilitate field-closure, but then develop 90° shape compensating stripe domains in order to accommodate disclination stresses; second, that they are the result of the impingement of domain packets which nucleate at the sidewalls of the dots forming “Forsbergh” patterns (essentially the result of phase transition kinetics); and third, that 90° domains form to conserve the shape of the nanodot as it is cooled through the Curie temperature but arrange into quadrant packets in order to minimize the energy associated with uncompensated surface charges (thus representing an equilibrium state). While the third model is the preferred one, we note that the second and third models are not mutually exclusive.

Polarization studies of radiative electron capture into highly-charged uranium ions

Recent advances in the development of 2D microstrip detectors open up new possibilities for hard x-ray spectroscopy, in particular for polarization studies. These detectors make ideal Compton polarimeters, which enable us to study precisely the polarization of hard x-rays. Here, we present recent results from measurements of Radiative Electron Capture into the K-shell of highly-charged uranium ions. The experiments were performed with a novel 2D Si(Li) Compton polarimeter at the Experimental Storage Ring at GSI. Stored and cooled beams of U91+ and U92+ ions, with kinetic energies of 43 MeV/u and 96 MeV/u respectively, were crossed with a hydrogen gasjet. The preliminary data analysis shows x-rays from the K-REC process, emitted perpendicularly to the ion beam, to be strongly linearly polarized.