The measurement and modelling of ion scatter from nanometer scale collimating aperture for
use in a low energy deterministic ion implant
A.D.C Alves, J. Newnham, J.A van Donkelaar and D. N. Jamieson
School of Physics, University of Melbourne, Victoria 3010, Australia.
Email: aalves@unimelb.edu.au
Abstract
This paper studies ion transmission through a nanometre scale collimating aperture with respect to the
masking of ions in a deterministic dopant implant; a central technological achievement for future
classical and quantum semiconductor devices. An aperture with a width of 60 nm was fabricated by
focused ion beam (FIB) milling in a 3 µm thick Si cantilever. The energetic distribution of 500 keV
He ions passing through the aperture has been measured using a commercially available photodiode
detector operating at room temperature and the dependence of ion energy on tilt angle with respect to
the aperture has been observed. The energy of a transmitted ion is an easily measureable quantity
which has been compared against, and used to verify, simulation. GEANT 4 simulations were used to
model the ion-aperture scatter, providing ion direction vectors and energies. This simulation is a key
component when calculating the successful implant yield in deterministically doped devices. When
applied to 14 keV P+ ions the simulations show that 96% of the ions are transmitted without energy
loss and with no change in direction, indicating this method of implant is viable for top-down
deterministic doping.
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1. Introduction
Ion beam collimation with a nanometre scale scanned aperture has been proposed [Schenkel2002,
Persaud2005, Meijer2008] as a method for high spatial precision ion implants, the aim being to
provide deterministic incorporation of each dopant into a solid state device; an outcome unattainable
with conventional ion implantation or dopant diffusion. Controlling the location and the number of
individual dopants in a Si device is a difficult problem with considerable rewards.In classical
electronics a set of transistors with a predetermined number of accurately placed dopants will perform
with less variation compared to a set in which the dopants are placed stochastically [Shinada2005]. As
standard doping practices [Sze2001, Borland2006] are applied to nanometre scale devices the location
of each dopant atom can dramatically affect performance of a short-channel transistor [Rogge2010].
Beyond classical electronics deterministic doping opens a new paradigm in device physics. A potential
well formed around a single dopant is a possible building block for solid state devices with quantum
functionality. In a solid state quantum computer [Loss1998, Kane1999, Holl2006] a donor placed into
the Si matrix is controlled by metallic surface gates and functions as a quantum bit. Preceding the
creation of a solid-state quantum bit several experiments have studied the electronic transport through
a single donor in Si [Morello2009, Tan2010, Lansbergen2008, Sellier2006, Morello2010]. In these
prototype devices it is statistically probable to find a device with a single dopant in the right place to
perform the desired action; however, for transport between two or more dopants to be measureable a
higher degree of certainty is required than can be offered by random placement.
Recently the single ion detection aspect of deterministic implants has received much attention.
Detection of the ion implant has been achieved through ion impact signals from electron-hole pairs
[Jamieson2005, Bielejec2010], secondary electrons [Shinada2005], or modulation of the drain current
in a transistor [Weis2008, Bantra2007, Shinada2008, Johnson2010]. However, detection is only one
part of a deterministic strategy and ion placement must also be achieved. In the bottom-up process
scanning tunnelling microscopy (STM) hydrogen lithography on a Si surface can define a dopant
location with atomic precision [Fuhrer2009]. However, for rapid prototyping in the near term the topdown implant strategy is favoured.
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The proposed strategy is to use an unfocused keV ion beam collimated by a nanometre scale aperture
mask scanned in close proximity to the implant substrate. The resolution of this strategy is limited by
the mask resolution, the straggle of the ion implant, and the scatter of ions in the mask. Ion straggle in
the substrate has only recently been investigated with respect to its implication in the development of
the transport of quantum states in a solid state quantum computer using three-donor CTAP [van
Donkelaar2010]. Atomistic modelling in this area is continuing [Rahman2009]. However, no
consideration has been given to the scattering that may occur in the mask, possibly resulting in a
positive detection event but with the atom implanted outside the desired location. The schematic
shown in figure 1 demonstrates how an aperture scattered ion may corrupt the deterministic doping
process. A one-dimensional array of single 14 keV P+ implants is defined by a static mask on the
surface of the substrate. A piezo-electrically scanned [Taylor2007, Persaud2005, Meijer2008
Guo2007, Luthi1999] aperture selects which site is implanted. After detection of the implant the
scanned aperture is stepped to the next site and the process repeated. For each site of the array there is
a probability that an ion will scatter, thus reaching the substrate in the wrong location and
compromising the device. An alternative to the purely collimated approach is to focus and direct-write
the implant beam. In traditional focused beam applications, for example ion beam milling or ion beam
analysis, sub 100 nm resolution in the keV and MeV energy regimes has been achieved [Shinada2005,
van Kan2005]. De-magnifying an upstream micrometre scale collimated beam is the best way to
achieve a useful beam current in these applications. Aberrations, misaligned focusing elements or stray
fields can make this approach more technologically demanding than required for single ion implants
where only a few ions per second are needed. Further, ion-aperture scatter still exists and contributes
to ions in the penumbra of a focused beam and must also be considered when the aim is to
deterministically account for every single ion impact. Previous experiments have demonstrated
apertures fabricated with minimum widths in the order of 10 nm [Schenkel2003, Schenkel2003].
Aperture production has been achieved by focused ion beam (FIB) milling a Si cantilever or a SiN4
membrane combined with backfilling with metal from a FIB or electron beam cracked precursor gas.
For apertures prepared in this fashion the width is dependent on the thickness of material to be milled
(an aspect ratio in the order of 10:1 is expected). Thus, lower energy ions can be more finely
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collimated because the milling resolution that can be achieved is proportional to the thickness of
material required to stop the ion. This, of course, only considers the contribution to the resolution from
the non-interacting transmitted ions, and not the scattered component. To calculate the fundamental
resolution of the implant process one must accurately predict the scattering paths of ions from the
aperture using the relevant ion energy and species. Experimental work has been performed providing
empirical results for a specific scattering arrangement, for example 30keV He ion projection
lithography [Parekh2006]. However a fully configurable model allowing investigation of the large
parameter space of implant energies and species; aperture aspect ratios and materials; and the
influences of small tilt angles on the collimation would be extremely useful to the field of low energy
ion implantation. We have used the GEANT 4 [Geant4] particle physics simulation toolkit to simulate
the aperture scattered ions under varying implant geometries. Previously Gorelick et. al.
[Gorelick2009, Gorelick2009, Gorelick2009] used GEANT4 and Taylor et. [Taylor2006] used the
TRIM [Ziegler1998] ion transport code to predict the transmitted ion energy and spatial distribution
for collimated MeV ions. The objective of past investigations was to determine the potential of this
method for delivering few or single ions to sub-100 nm locations on substrates in the MeV regime for
ion beam lithography [Gorelick2008, Alves2007].
This work uses the easily measurable quantity, ion energy, to obtain experimental ion transmission
results at 500 keV which were compared to the simulation and used to verify its performance. The
simulation energy was then reduced to 14 keV, compatible with a deterministic implant (straggle of ~
20 nm). We have used simulated ion transmission data to show that the probability of a scattered,
therefore misplaced, ion is 4 % per ion implanted. In this work the contribution of beam divergence (<
0.01 degrees) to implant location is considered to be negligible This is because it is possible to place a
FIB milled cantilever or membrane in close proximity (~ 10 µm) to the substrate. The beam
divergence at this distance adds less than 2 nm to the collimated beam width. Therefore using a topdown, scanned and collimated ion beam approach to building devices containing more than one donor
is viable.
2. Experiment
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A FEI Nova Nanolab FIB (30 keV Ga) was used to mill a series of slots (10 × 0.1) µm2 in a 3 µm thick
Si cantilever (Fig. 2b). Backfilling with Pt was used to reduce the slot width (Fig. 2c). Four slots were
characterised using scanning electron microscope (SEM) and the minimum width was found to be of
60 nm (Fig. 2d and 2e). The SEM images provided the starting point aperture geometry for the
simulation. The ion transmission analysis was performed with the MP2 nuclear microprobe beamline
[Jamieson1998] on the 5 MeV NEC 5U Pelletron accelerator at the University of Melbourne with the
chamber pressure below 10-6 Torr. It is practical to experimentally measure the transmitted beam with
500 keV ions since it requires neither liquid N2 cooling or especially low noise electronics. (Set up
shown in Fig. 2a.) A scanning transmission ion microscopy (STIM) image of a 1000 mesh Cu grid
mounted above a Hamamastu s1223 test photodiode was acquired. The beam was found to be
approximately 1 µm in diameter with a current of several hundred ions per second. Next a STIM map
of the measurement photodiode with the milled cantilever mounted above it, at a distance of
approximately 100 µm, was acquired. The range of these ions in Si is approximately 2 µm plus 0.2 µm
longitudinal straggle; the 3 µm thick aperture material was therefore an adequate mask. Fig. 3a shows
the initial 250 × 250 µm2 scan revealing the whole cantilever and surrounding detector; no
precollimator was used. To collect only the spectrum of ions passing through the slot the scan was
reduced and centred onto the 40 µm wide cantilever (Fig. 3b and 3c). Ions in the beam penumbra
extended to wider than the 1 µm beam spot and beyond the outer edges of the cantilever, therefore, a
background of penumbra ion strikes can be seen inside the region blocked by the cantilever. Operating
with the stated beam current and chamber pressure it was found that the penumbra ions were at a level
where they could be easily subtracted from the spectral data of the slot. The whole assembly
(cantilever and diode) was mounted on a translation and rotation stage (rotation about the vertical
axis). The ion beam to aperture angle was incremented through -3.5 to +4.5 degrees in 0.5 degree steps
collecting a STIM map at each step. Small adjustments in horizontal translation were required so that
the slot stayed centred as the assembly was tilted. The low fluence of 104 ions per spectrum ensured
that damage to the ion detector was not problematic. With the change to the tilt the most intense part
of the beam moved due to parallax a distance of 1 µm; therefore accumulated damage wasn’t
concentrated in one location in the detector. A shift in pulse height due to detector damage of
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approximately 1 percent was expected—from 2 MeV He damage observed in Alves et. al.
[Alves2008]—and deemed acceptable for this experiment.
3. Results
Each spectrum contained contributions from penumbra ions, slot-end scattered ions, and slot scattered
ions (Fig. 3c). The spatially resolved data allowed the extraction of spectral data from regions of
interest in the STIM map. The normalised penumbra ion counts and ions scattered from the slot-ends
were subtracted from the spectral data of those ions transmitted and scattered from the slot. Seen in
Fig. 4c, the energy spectrum contains a full energy peak as well as lower-energy scattered ions. The
lower level discriminator was set above the noise level the of the data acquisition at 100 keV which
obscures only a small fraction of the scattered ions. The full energy-ratio is defined as the number of
ions with zero energy loss, N full energy, divided by the total number of transmitted ions, N total:
R full energy = N full energy / N total
This ratio has been plotted as a function of tilt angle in Fig. 4d showing that less than 30% of the ions
are transmitted without energy loss when the beam is at normal incidence. The dependence of ion
energy on tilt angle of the ion beam with respect to the aperture has been plotted also in an intensity
map in Fig. 4b.
The 500 keV He ions have been used because it is extremely challenging to acquire spectral data for
low energy dopant implants [Yang2003, Jamieson2005]. We have, however, qualitatively confirmed
that the aperture is acting as a reasonable mask for low energy implants. The collimation of a 14 keV
Ar ion beam through the 60 nm aperture was demonstrated by producing a series of lines in poly
methyl methacrylate (PMMA). The aperture was stepped 200 nm between each of the 10 exposures,
leading to the 10 trenches seen in Fig. 5a following the development of the PMMA. Additionally, a Si
substrate with native oxide was implanted with varying fluences of 14 keV P through the aperture. Fig.
5b shows that the highest fluence swells the Si to form a raised line. The lower fluences however, left
trenches in the surface. The mean width of the PMMA trenches was measured by AFM and is in good
agreement with the SEM aperture measurement of 60 nm.
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4. Simulation
For quantitative scattering results at low energy we turn to simulation. The code was set up with an
estimated geometry of the slot dimensions, but some details of the geometry of our aperture, unseen to
the SEM, have been iteratively altered to find a good match between experiment and simulation. The
simulated slot geometry is shown in Fig. 4a. A similar process [Vacik1998] reported ascertaining the
pore shape in nuclear tracks by comparing Monte Carlo simulation with the experimental iontransmission spectra. The ion count per simulation was set at 105 ions and the beam spot diameter set
as the mean slot width plus the mean lateral ion range plus straggle. For 500 keV He the beam size
was 800 nm. Beyond this width, ions are completely masked by the aperture and don’t contribute to
the simulated spectra. The beam divergence was set at 0 degrees. The simulation created the aperture
out of two materials Si and Pt. The standard nuclear recoil physics list was used as this includes
Mendenhall and Weller's model for screened nuclear stopping, an important correction at these
relatively low energies [Mendenhall 2005]. Spectral data was extracted from the list of ion energies
and positions exiting from the back plane of the simulation space. Gaussian smoothing was applied to
the spectral data to match the detector energy resolution of 4 keV. The 3 µm thick aperture geometry
in the simulation contains two main features: a tapered Si profile with an opening of 1 µm and an exit
of 200 nm and the Pt filled section that closes the slot down to a 60 nm width. It was found that the
filled section is what causes the high energy shelf feature seen in the experimental section. The
geometry pictured gives reasonable agreement between the measured and simulated energy
distributions when the beam is orientated at a range of angles, as shown in the comparison of tilt vs.
energy intensity maps in Fig 4b.
Once the simulation had been benchmarked against experimental results from 500 keV He ions the
simulation was used to model the ion-aperture interaction of 14 keV P ions, firstly with the same 60
nm aperture used in the 500 keV STIM experiment (labeled Aperture 1), and secondly with a 200 nm
thick SiN4 membrane (labeled Aperture 2), typical of the material that would be used for routinely
milling with a resolution less than 60 nm. In this case we have modeled a 50 nm wide aperture. With
the beam aligned with zero tilt the simulations found that in both cases 96 % of the transmitted ions
exited the aperture with no change in direction or ion energy. The simulations also show there is only
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a small variation (a few percent) in the full energy ratio due to tilt misalignment, demonstrating that
fine tilt alignment (< 1 degree) is not required, especially in the case of the thin membrane. The spatial
distribution of transmitted ions is shown in Fig. 6 with the substrate placed a distance of 10 µm from
the aperture centre. In the case of 14 keV ions the distribution of scattered ions is very broad and the
distribution of non-scattered ions is very sharp, and at this substrate distance the broadening of the
primary ion beam due to beam divergence would be negligible. This has excellent implications for
device yield in future experiments where more than one dopant must be accurately placed.
5. Conclusion
We have demonstrated that the ion scatter from a nanometre scale aperture can be quantified
experimentally with a 500 keV He beam. Experiment has been used to verify the results from a
GEANT4 simulation of the ion-aperture scatter. This modelling work draws attention to the fact that
with different experimental parameters there are different aperture scattering conditions. The 60 nm
wide aperture presented here showed very low scattering when modelled with 14 keV ions. To achieve
milling resolution less than 60 nm in a deterministic implant scenario we propose FIB milling on a
thinner membrane, for example a SiN4 membrane, less than 1 µm thick. Simulation shows that when
such a thin membrane is used there is no detrimental effect to the transmission of the ion beam. The
work shown in this paper demonstrates that we now have the necessary modelling tools to investigate
the ion-aperture scatter in a low energy deterministic implant scenario.
Acknowledgments
The authors acknowledge financial support from the Australian Research Council, the Australian
Government and the US Army Research Office under Contract No. W911NF-04-1-0290. The authors
are grateful to Roland Szymanski and Sergey Rubanov for technical support and to Brett Johnston and
for useful discussions.
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Figure 1. One failure mechanism in constructing a deterministically doped device is a scatter event
from the ion collimating aperture. In this figure the trajectories of 14 keV P+ ions have been plotted on
a 200 nm thick SiN4 mask. The aperture in the mask is 20 nm wide; a 10:1 aspect ratio. The static
mask for defining the implant sites also has a resolution of 20 nm. A deterministically doped device
may require a one-dimensional array of single dopants, therefore we must know the probability of a
scatter event to determine the device yield.
11
Figure 2. (a) The experimental setup for exposing an ion detector to aperture scattered ions. (b) Using
FIB milling and Pt deposition a series of slots have been fabricated in a 3 µm thick Si cantilever. (c) A
region of Pt deposition has been false coloured. (d and e) SEM was used to characterise the minimum
widths of the slot openings. Four slots were milled with minimum widths of 60-120 nm.
12
Figure 3. The 500 keV He ion microprobe (~ 1 µm beamsopt) scans over the cantilever mounted
above a Si detector to find the milled cantilever. The sizes of the images are (a) (250 × 250) µm2, (b)
(50 × 50) µm2, and (c) (20 × 20) µm2. There is a background of ion strikes due to ions in the beam
penumbra striking the detector when the primary beam is blocked by the cantilever. There is also a
contribution to each spectrum from ions passing through the slot, ions scattered from the slot, and ions
scattered from the slot-end. A normalised uniform portion of the penumbra ion counts has been
subtracted from the normalised spectrum in the region of the slot, excluding the slot-end, to give the
spectrum of only ions that pass through the slot, or scattered from the slot.
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Figure 4. The geometry of a Pt filled aperture in 3 µm thick Si (Aperture 1) has been programmed into
GEANT4 and a cross section is shown in (a). The transmission of 500 keV He ions was modelled so
that the simulation could be compared with experimental data. The experimental and simulated energy
spectra are shown: (b) as a function of the aperture angle with respect to the ion beam, and (c) at 0
degrees. The ratio of full energy ions, R full energy, in the transmission spectrum has been plotted as a
function of aperture angle in (d). When collimating 500 keV He ions the aperture transmits a large
percentage of scattered ions, less than 30 % are transmitted with full energy. When collimating 14 keV
P ions the aperture is much more effective and 96 % of the ions are transmitted with full energy. A
second aperture in 200 nm thick SiN4 has been modelled, shown in (e), and it is an effective mask for
14 keV P ions also transmitting 96% of the ions at full energy, also demonstrating a large angular
tolerance for good transmission.
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Figure 5. AFM Images of patterns fabricated with the scanned aperture. (a) A 14 keV Ar beam has
been collimated by aperture in the cantilever and is reproduced and repeated in the PMMA . (b)
Without PMMA some small swelling in the Si can also be observed.
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Figure 6. The GEANT4 code outputs the ion trajectories. The distribution of the position of ion strikes
(bin size = 25 nm) at a substrate distance of 10 µm has been plotted for (a) 500 keV He through
aperture 1, (b) 14 keV P through aperture 1, (c) 14 keV P through aperture 2. The broadening of the
primary ion beam due to a divergence of 0.01 degrees would only broaden these distributions by 2 nm,
a negligible effect.
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