Comparison between experiment and two simulation strategies for the extraction of focused ion beams

Abstract

Computer simulation codes for the extraction of ion beams have been used for over three decades. Here we describe medium current extraction ͑ϳ1 mA͒ from a high density plasma source (Ͼ10 12 cm Ϫ3) with a three electrode extraction system and compare the extracted current and the angular divergence with the results of two computer simulation programs. The first is called PBgun and is a commercially available ray tracing code; the second, called simulation d'extraction de faisceaux d'ions ͑SEFI͒ uses a particle-in-cell code to simulate the plasma and ion beam. It is the purpose of this article to ascertain whether these codes can adequately model the plasma/beam interface and hence successfully predict the extracted current and beam form across a broad range of extraction parameters. We found that SEFI could accurately predict the function of extracted current versus extraction voltage and that PBgun gave accurate simulations when the current or current density could be specified near the meniscus. Also for a thin plasma aperture and a fixed current at the meniscus, PBgun gave roughly 60% of the functional dependence of the extracted current on the extraction voltage and the other 40% on variations in the plasma pre-sheath. Both codes had some error from beam crossing near the axis which changed the amount of meniscus curvature predicted.

Generalization of the Langmuir–Blodgett laws for a nonzero potential gradient

“…The flow is not limited in the sense that the charge density in the extraction gap impedes the flow of particles from the plasma ͑as this is fixed by the plasma's natural ambipolar flux͒, but the potential and charge distributions in the extraction gap do approach those that would be obtained if the emission surface had a fixed geometry and an undepleteable source of particles. However, a change in any of these three quantities causes a change in the shape of the plasma meniscus 25 which, in order to maintain the strict symmetry constraints of the theory, would require a recalculation of the extractor geometry ͑or interelectrode spacing for a diode͒. In this sense Eqs.…”

“…Furthermore, in space-charge limited systems it is commonly thought that a virtual anode/cathode is formed in response to an increase in extraction voltage, however, in the case of ion extraction from a plasma there is no physical reason for one to appear at the meniscus and it has never been observed in particle-in-cell or ray-tracing simulations undertaken by Sutherland et al. 25 Instead, the meniscus adjusts its position and shape so as to enable the electric field in the extractor to equal that in the sheath. It is this variation in the shape of the meniscus that results in the various beam shapes that are observed.…”

“…Second, unlike the emission surface of a field emitter which does not change geometry as a function of extraction voltage, the shape of the plasma meniscus is sensitive to the plasma density, extraction potential, and the electric field structure in the extractor. 25 This implies that for given plasma conditions the strict geometry assumptions of the standard diode models can only be guaranteed by specific electrode structures. An analytical approach for the design of such electrodes was developed by Radley 13 and relied on the series formulation of the Langmuir-Blodgett laws but assumed a zero electric field at the emission surface.…”

A Study on Beam Extraction Characteristics of RF and DC Filament Ion Source for High Current Ion Implanters

“…In Fig. 3(b), the ion beam extracted from the RF ion source proceeds as parallel, and a slightly concave meniscus shape is achieved [6]. Because electric potential difference of RF aperture wall is much thinner than the filament-type ion source, a higher quality beam, which proceeds in the direction normal to the equipotential plane, can be achieved.…”

High voltage breakdown in an inductively coupled ion source

“…Bright and narrow ion beams can be extracted and accelerated from the plasma by a set of biased grids, commonly referred to as the ion optics. In some cases the extraction method involves applying an anodic bias voltage to the entire discharge so that the plasma floats up to a potential of typically 10-30 kV positive, in order to accelerate ions to a kinetic energy of 10-30 keV as they reach a grounded surface [4,5,8]. An rf antenna powered by rf in the megahertz range needs a matching network to allow efficient transfer of power from the 50 generator to the plasma; in a simple and quite common case this involves a pi-matching system where one side of the antenna is grounded via the generator.…”