Atomic Beam Laser-cooled Ion Source : towards sub-nm ion beam milling

This work discusses the predicted performance of the Atomic Beam Laser-cooled Ion Source (ABLIS) and the progress in its experimental realization. The ABLIS is a new source for focused ions beams (FIBs), which are tools that are used on a large scale in the semiconductor industry, to image and modify structures on the smallest possible length scale. On the contrary to other FIB sources such as the Liquid Metal Ion Source (LMIS), the ABLIS is based on the fact that the ions are created from atoms with a very small spread in velocity instead of a very small spread in position. The biggest application of an ABLIS-based FIB will be so called milling in which material is physically etched at the nanometer length scale.In the ABLIS setup a beam of atomic rubidium is created from a Knudsen cell. This beam is laser-cooled and -compressed after which it is photo-ionized by means of a very intense laser. The ions will be accelerated immediately to their demanded energy (mostly 30 keV) and finally focused to an as small as possible spot by a set of electrostatic lenses. Since the ionization will take place over a certain region, the energy spread of the ion beam, and therefore also the amount of chromatic aberration of the lens system, will be proportional to the electric field.The bottleneck of the setup will be disorder induced heating, which was investigated in this work. It is the effect that ions, which were created at random initial positions, will heat up due to relaxation of the potential energy associated with these random initial positions. Investigations in this work show that this effect can be counteracted by increasing the electric field at the position they are ionized. A relation was found between the electric field needed to suppress disorder induced heating and the beam current. This relation was used to calculate the amount of chromatic aberration of the lens system as a function of the current. Using this information, an analytical calculation was performed of the possible spot size of the ABLIS setup, including all individual contributions to the spot size, i.e., the brightness, spherical aberration and chromatic aberration. The result showed that a spot size of 0.2 nm is possible at a current of 1 pA, compared to the 5 nm spot size which is possible with the LMIS. The calculation was verified with particle tracking simulations, which were in good agreement.In order to perform laser cooling and compression, a laser is needed which is stable and can be precisely detuned from the cooling transition in rubidium. Furthermore a repump beam is needed which is tuned to a different transition in rubidium. The laser system which matches these requirements was finalized in the work discussed here. A double pass acousto-optic modulator (AOM) configuration was built to detune the laser frequency. Furthermore, an electro-optic modulator (EOM) was added to the setup, to create the repump beam.An experimental setup was built in which the efficiency of laser cooling can be tested with laser induced fluorescence. Simulations of this setup were performed, which showed the setup should be capable of measuring the effect of laser cooling on the atom beam. Furthermore, a simulation of the atoms in the collimating tube of the Knudsen cell is set up. Its results are in good agreement with earlier performed measurements and a theoretical model. This work discusses the predicted performance of the Atomic Beam Laser-cooled Ion Source (ABLIS) and the progress in its experimental realization. The ABLIS is a new source for focused ions beams (FIBs), which are tools that are used on a large scale in the semiconductor industry, to image and modify structures on the smallest possible length scale. On the contrary to other FIB sources such as the Liquid Metal Ion Source (LMIS), the ABLIS is based on the fact that the ions are created from atoms with a very small spread in velocity instead of a very small spread in position. The biggest application of an ABLIS-based FIB will be so called milling in which material is physically etched at the nanometer length scale.In the ABLIS setup a beam of atomic rubidium is created from a Knudsen cell. This beam is laser-cooled and -compressed after which it is photo-ionized by means of a very intense laser. The ions will be accelerated immediately to their demanded energy (mostly 30 keV) and finally focused to an as small as possible spot by a set of electrostatic lenses. Since the ionization will take place over a certain region, the energy spread of the ion beam, and therefore also the amount of chromatic aberration of the lens system, will be proportional to the electric field.The bottleneck of the setup will be disorder induced heating, which was investigated in this work. It is the effect that ions, which were created at random initial positions, will heat up due to relaxation of the potential energy associated with these random initial positions. Investigations in this work show that this effect can be counteracted by increasing the electric field at the position they are ionized. A relation was found between the electric field needed to suppress disorder induced heating and the beam current. This relation was used to calculate the amount of chromatic aberration of the lens system as a function of the current. Using this information, an analytical calculation was performed of the possible spot size of the ABLIS setup, including all individual contributions to the spot size, i.e., the brightness, spherical aberration and chromatic aberration. The result showed that a spot size of 0.2 nm is possible at a current of 1 pA, compared to the 5 nm spot size which is possible with the LMIS. The calculation was verified with particle tracking simulations, which were in good agreement.In order to perform laser cooling and compression, a laser is needed which is stable and can be precisely detuned from the cooling transition in rubidium. Furthermore a repump beam is needed which is tuned to a different transition in rubidium. The laser system which matches these requirements was finalized in the work discussed here. A double pass acousto-optic modulator (AOM) configuration was built to detune the laser frequency. Furthermore, an electro-optic modulator (EOM) was added to the setup, to create the repump beam.An experimental setup was built in which the efficiency of laser cooling can be tested with laser induced fluorescence. Simulations of this setup were performed, which showed the setup should be capable of measuring the effect of laser cooling on the atom beam. Furthermore, a simulation of the atoms in the collimating tube of the Knudsen cell is set up. Its results are in good agreement with earlier performed measurements and a theoretical model

Cavity-enhanced photoionization of an ultracold rubidium beam for application in focused ion beams

A two-step photoionization strategy of an ultracold rubidium beam for application in a focused ion beam instrument is analyzed and implemented. In this strategy the atomic beam is partly selected with an aperture after which the transmitted atoms are ionized in the overlap of a tightly cylindrically focused excitation laser beam and an ionization laser beam whose power is enhanced in a build-up cavity. The advantage of this strategy, as compared to without the use of a build-up cavity, is that higher ionization degrees can be reached at higher currents. Optical Bloch equations including the photoionization process are used to calculate what ionization degree and ionization position distribution can be reached. Furthermore, the ionization strategy is tested on an ultracold beam of $^{85}$Rb atoms. The beam current is measured as a function of the excitation and ionization laser beam intensity and the selection aperture size. Although details are different, the global trends of the measurements agree well with the calculation. With a selection aperture diameter of 52 $\mu$m, a current of $\left(170\pm4\right)$ pA is measured, which according to calculations is 63% of the current equivalent of the transmitted atomic flux. Taking into account the ionization degree the ion beam peak reduced brightness is estimated at $1\times10^7$ A/(m$^2\,$sr$\,$eV).Comment: 13 pages, 9 figure

Direct magneto-optical compression of an effusive atomic beam for high-resolution focused ion beam application

An atomic rubidium beam formed in a 70 mm long two-dimensional magneto-optical trap (2D MOT), directly loaded from a collimated Knudsen source, is analyzed using laser-induced fluorescence. The longitudinal velocity distribution, the transverse temperature and the flux of the atomic beam are reported. The equivalent transverse reduced brightness of an ion beam with similar properties as the atomic beam is calculated because the beam is developed to be photoionized and applied in a focused ion beam. In a single two-dimensional magneto-optical trapping step an equivalent transverse reduced brightness of $(1.0\substack{+0.8-0.4})$ $\times 10^6$ A/(m$^2$ sr eV) was achieved with a beam flux equivalent to $(0.6\substack{+0.3-0.2})$ nA. The temperature of the beam is further reduced with an optical molasses after the 2D MOT. This increased the equivalent brightness to $(6\substack{+5-2})$$\times 10^6$ A/(m$^2$ sr eV). For currents below 10 pA, for which disorder-induced heating can be suppressed, this number is also a good estimate of the ion beam brightness that can be expected. Such an ion beam brightness would be a six times improvement over the liquid metal ion source and could improve the resolution in focused ion beam nanofabrication.Comment: 10 pages, 8 figures, 1 tabl

Application of laser-cooling to achieve an ultra-cold ion beam for FIB

A new type of ultra-cold ion source is under development which employs transverse laser cooling and compression of a thermal atomic rubidium beam followed by photo-ionization. The resulting ultra-cold plasma is focused to a nanometer-sized spot using an existing Focused Ion Beam column and this spot can be used for the fabrication of nano-structures. Simulations of a 10 cm long laser-cooling stage and of disorder-induced heating of the resulting ion beam, predict an achievable brightness for87Rb+ of order 107 A/m2 sr eV at an longitudinal energy spread of less than 1 eV and a current of tens of pA, which is substantially better than conventional ion sources. Experimental realization of the compact ion source has recently started with the development of an efficient high-flux atom source and a 2D laser cooler. Progress on these items will be reported

Proof for an upper bound in fixed-node Monte Carlo for lattice fermions

We justify a recently proposed prescription for performing Green Function Monte Carlo calculations on systems of lattice fermions, by which one is able to avoid the sign problem. We generalize the prescription such that it can also be used for problems with hopping terms of different signs. We prove that the effective Hamiltonian, used in this method, leads to an upper bound for the ground-state energy of the real Hamiltonian, and we illustrate the effectiveness of the method on small systems.Comment: 14 pages in revtex v3.0, no figure

Issues and Observations on Applications of the Constrained-Path Monte Carlo Method to Many-Fermion Systems

We report several important observations that underscore the distinctions between the constrained-path Monte Carlo method and the continuum and lattice versions of the fixed-node method. The main distinctions stem from the differences in the state space in which the random walk occurs and in the manner in which the random walkers are constrained. One consequence is that in the constrained-path method the so-called mixed estimator for the energy is not an upper bound to the exact energy, as previously claimed. Several ways of producing an energy upper bound are given, and relevant methodological aspects are illustrated with simple examples.Comment: 28 pages, REVTEX, 5 ps figure

Stripes and spin-incommensurabilities are favored by lattice anisotropies

Structural distortions in cuprate materials give a natural origin for anisotropies in electron properties. We study a modified one-band t-J model in which we allow for different hoppings and antiferromagnetic couplings in the two spatial directions ($t_x \ne t_y$ and $J_x \ne J_y$). Incommensurate peaks in the spin structure factor show up only in the presence of a lattice anisotropy, whereas charge correlations, indicating enhanced fluctuations at incommensurate wave vectors, are almost unaffected with respect to the isotropic case.Comment: accepted for publication on Physical Review Letters, one color figur

Performance predictions of a focused ion beam from a laser cooled and compressed atomic beam

Focused ion beams are indispensable tools in the semiconductor industry because of their ability to image and modify structures at the nanometer length scale. Here we report on performance predictions of a new type of focused ion beam based on photo-ionization of a laser cooled and compressed atomic beam. Particle tracing simulations are performed to investigate the effects of disorder-induced heating after ionization in a large electric field. They lead to a constraint on this electric field strength which is used as input for an analytical model which predicts the minimum attainable spot size as a function of amongst others the flux density of the atomic beam, the temperature of this beam and the total current. At low currents (I<10 pA) the spot size will be limited by a combination of spherical aberration and brightness, while at higher currents this is a combination of chromatic aberration and brightness. It is expected that a nanometer size spot is possible at a current of 1 pA. The analytical model was verified with particle tracing simulations of a complete focused ion beam setup. A genetic algorithm was used to find the optimum acceleration electric field as a function of the current. At low currents the result agrees well with the analytical model while at higher currents the spot sizes found are even lower due to effects that are not taken into account in the analytical model