Surface Damage Removal in Bespoke Micro-lens Moulds
Manufactured by Focused Ion-Beam
Mark T. Langridge1*, D.C. Cox1,2, R.P. Webb3, V. Stolojan2
1. Advanced Technology Institute, Faculty of Engineering and Physical Sciences,
University of Surrey, Guildford, GU2 7XH, UK
2. National Physics Laboratory, Hampton Road, Teddington, Middlesex, TW11 0LW
3. Surrey Ion Beam Centre, Nodus Laboratory, University of Surrey, Guildford,
Surrey, GU2 7XH, UK
*corresponding Author
Abstract
Aspheric lenses are the most common method for correcting for spherical aberrations
but, in microlens production, highly-controlled lens profiles are hard to achieve. We
demonstrate a technique for creating bespoke, highly-accurate profile silicon
microlens moulds, of almost any footprint, using focused ion-beam milling. Along
with this, we present a method of removing induced ion-beam damage in silicon, via a
hydrofluoric acid etch, helping to recover the surface’s optical and chemical
properties.
In this paper, we demonstrate that our milled and etched moulds have a roughness of
4.0-4.1nm, meaning they scatter less then 1% of light, down to wavelengths of 51nm,
showing that the moulds are suitable to make lenses that are able to handle light from
UV up to Infra-red.
Using empirical experiments and computer simulations, we show that increasing the
ion-dose when milling increases the amount of gallium a hydrofluoric acid etch can
remove, by increasing the degree of amorphisation within the surface. For doses
above 3000µC/cm² this restores previous surface properties, reducing adhesion to the
mould, allowing for a cleaner release and enabling higher quality lenses to be made.
Keywords
Aspheric microlenses, Micro-reflectors, Focused Ion Beam lithography, Chemical
Etching
Highlights
 We describe a method for ion-milling bespoke profile geometry.
 We discuss a technique for removing ion-beam damage using chemical
etching.
 Using Ion-range modelling we investigate how much damage and implantation
is removed by etching.
 We visibly show the massive extent of focused ion-beam tails, seen to be up to
50µm in radius.
 We manufacture parabolic micro-lenses using our technique.
1. Introduction
Due to the growing overlap between electronics and optics, microlenses are becoming
increasingly popular, finding use in enhancing the light-gathering ability of pixels in
digital cameras[1] and in improving optical-fibre coupling efficiency in the
communications industry[2]. In digital cameras, the ever decreasing size of camera
pixels necessitates a novel method of directing light into sensing regions[3]. With
pixels nearing the diffraction limit, approaching 1µm in size[4], the manufacture of
high quality lenses of this size could dramatically improve the detector’s quality and
sensitivity.
Current manufacturing techniques involve using conventional photolithography to
produce the large arrays of lenses needed, using the reflow technique[5]. A block of
photoresist is deposited and then subsequently melted, to form lens-like droplets. The
profile of these lenses is controlled by the wettability of the surface by the photoresist
material, allowing spherical or elliptical lenses to be formed. Whilst able to focus light,
these lenses suffer from spherical aberration, reducing their ability to accurately direct
light, and leading to pixel cross-talk and increased noise[6].
In the area of optical communications, fibre optic coupling is known to be an area
fraught with alignment issues. The use of microlenses to aid in alignment was first
demonstrated over 20 years ago, in 1991[2], showing an improvement in the
transmissivity between fibres. However, the refractive lenses made by modern
techniques also tend to suffer from spherical aberration, which is a major contributing
factor to coupling inefficiency[7]. This reduces the alignment gain achieved when
using microlenses.
Correcting spatial aberration through lens shape design can therefore lead to
significant advances in improving the quality and the sensitivity of digital image
detectors and in optical communications. The most common method of overcoming
spherical aberration on the macro-scale is to use a parabolic or hyperbolic lens profile,
two shapes that self-correct for such aberration[8]. When manufacturing micro-lenses
via conventional reflow, there is limited control over the lens profile, so making
parabolic lenses has proven difficult. Whilst attempts have been made using liquid
crystals[9], mask shading techniques in vacuum deposition[10], electrostatic pulling
and electrophoretic forces[11,12] among other methods, exotic profiles are still
difficult to attain.
Focused Ion-Beam Lithography (FIB) may hold the key, with its ability to precisely
sculpt surfaces at both the nano- and micro- scales. Milling of micro-lens moulds for
the creation of polymer lenses been demonstrated before [13], as has direct milling of
microlenses onto optical fibre ends[14]. In both cases, the process suffers from two
main problems: slow speed of milling and ion implantation damage. The speed of
milling is not such a huge problem when putting lenses on optical fibres, as milling
single lenses is a process of minutes to tens of minutes. For large arrays of lenses, the
time taken to mill will be long, but by replicating the mould itself using nano-imprint
replication, the mould only needs to be milled once to allow vast numbers of lenses to
be manufactured[15].
The second downside of FIB lithography is the damage and ion-implantation caused
to the substrate surface during conventional milling. In crystalline silicon (c-Si) the
ion beam amorphises the surface, creating an amorphous silicon (α-Si) layer[16]. The
ion used for milling, most commonly gallium (Ga), can be found implanted in very
high numbers at the surface. This reduces the transmisivity of the surface of the
substrate [17,18]. In directly-milled surfaces, this can lead to a higher degree of light
absorption in the material[19], whilst in nano-replication, the milled regions are
known to adhere more strongly to the soft polymers used, necessitating a thin metal
coating to allow for uniform removal. Whilst this overcomes adhesion issues, it
doesn’t allow for high temperature treatments, such as thermosetting polymers, as it
causes the Ga to diffuse to the Si-metal interface. It also is not a useful technique
when looking at direct milling of optical elements, as it only augments the problem of
reduced transmission through a Ga-implanted substrate. This means that removing the
Ga and reducing the size of the amorphous silicon (α-Si) region restoring crystallinity
are desirable for good quality, bespoke optics.
The most common method for removing this damage is a simple annealing process,
to force the gallium to diffuse out of the surface, whilst recrystallising the substrate
[20,21]. However, this has been shown somewhat unsurprisingly to lead to Ga
diffusing into the bulk[22], whilst the expelled Ga forms a hard GaO layer, causing
both optical and adhesion problems when replicating, and therefore requiring further
steps to remove[23].
In this paper, we start by demonstrating a novel method of manufacturing microlens
moulds using focused ion-beam (FIB) lithography. Due to the difficulty in removing
replicated lenses from the as-milled topography, we then investigate how chemical
etching can be used to remove implantation damage and restore the surface properties,
with minimal changes in shape and roughness. Previous papers have shown that Ga
implanted Si etches vigorously in Hydrofluoric acid (HF) [24] and is an etch stop to
potassium hydroxide (KOH)[25]. Whilst a use for this has been demonstrated in
nanofabrication, here, we show that this technique can be used as a simple method to
remove ion implantation damage.
We will discuss the effect HF etching has on the dish profile and roughness, and the
effect this has on the optical properties of the dish, which is a useful measure of the
quality of the lenses moulded from these dishes may have. By then moving on to look
at very low dose Siemens star patterns, we investigate the effect dose plays on etch
depth, to help us predict how the shape of milled dishes will change when HF- etched.
Comparing this information to computer simulations gives us an idea of the surface
amorphisation required to successfully etch, which helps us calculate the percentage
Ga left in the surface post-etch. Finally we confirm whether the implanted gallium is
removed during etching via cross-sectional scanning transmission electron
microscopy (STEM) with energy dispersive x-ray (EDX) mapping. We demonstrate
that wet chemical etching successfully removes implanted gallium, restoring the
surface properties closer to the original state. We show that that HF etching is more
effective at removing Ga at a high dose.
2. Method and Theory
2.1.
The ion-beam milling of a paraboloid
In focused ion-beam milling, the depth milled in any region is controlled by the dose
of ions to which an area is exposed. Due to a linear relationship between depth and
dose in silicon, any region exposed to a controlled dose will sputter to a known
depth[26]. This also gives the advantage that the depth for multiple patterns milled in
the same place will be a summation of the individual pattern depths. One of the
drawbacks to ion-milling is that, for very deep patterns (<1um), removing material
from the hole created in a single-exposure approach becomes challenging, as
redeposition rates increase, resulting in deviations from the linear dose-depth
relationship[27]. The technique we use involves an optimum combination between the
dose and number of passes to lead to ‘ideal’ milling, overcoming these drawbacks.
We make use of this by milling a series of concentric entities, milling from smallest to
largest, whilst linearly increasing the dose, such that the summation of the entity
depths follows a parabolic function.
This method allows for the milling of any footprint as a set of concentric shapes, such
as circles or n-sided polygons. In Figure 1 we show how increasing the depth starting
with the smallest entity in the pattern achieves an approximately parabolic profile. In
theory this leaves a step edge, creating areas where the surface is either above or
below the parabolic shape required. However, due to an edge effect whilst milling the
sharp peak of the corners will be eroded more quickly than the surrounded area. Some
of the sputtered material caused by milling will redeposit, filling in the corners which
dip below the parabolic function. We have found only a small number of circles are
necessary in the pattern to create a smooth profile, from 10-30 circles for 1-10um
dishes.
[Insert Figure 1 here]
As the dose is calculated by a combination of the ion-beam current (which is
intrinsically linked to the beam spot size) and the dwell of the spot, the choice of
beam current controls the speed of milling for a certain shape. Most of the dishes that
we have manufactured have been milled at 50-300pA, at an accelerating voltage of
30kV, optimizing the beam spot size for smoothness of the dish, whilst keeping
milling times to a minimum.
When designing a pattern before milling, we must consider the dimensions of a
parabolic dish. The focal length of a parabolic dish, FD, can be found from the
diameter of the dish, D, and its depth, c, linked by the equation 1:
FD 
D2
16c
(1)
From equation 1, the equation for the focal length of a plano-convex parabolic lens
moulded from such a dish can be derived. The focal length, FL, of a lens of refractive
index n, is given by equation 2 [28]:
FL 
D2
1
8c (n   1)
(2)
From this we know exactly how controlling the depth of the dish will control both the
dishes’ focal length, as well as the focal length of any lens moulded from it. Longer
focal length dishes and lenses are made from shallower dishes, requiring less material
to be removed and therefore shortening milling times for an increased focus.
The dose required for each entity in the pattern is calculated from the total dose, DT,
required to mill the full depth of the dish, using the following formula:
DT 
c
a
(3)
Here a represents an empirically found ratio of the depth to dose. It is found during a
calibration procedure by milling a pattern with a given value of a, and then cross
sectioning the pattern and measuring the depth visually with the SEM column,
pictured in Figure 1 b). a is usually found to be 1.80±0.18 nm/(µC/cm²).
The next step is to sub-divide the total dose into a parabolic series of n steps, where n
is the number of circles in the pattern. Due to the nature of a parabola, you can
calculate the smallest and largest doses required and linearly interpolate between them
to find all other doses.
The lowest dose, applied to the central entity is calculated using equation 4:
1
DL  2 DT
(4)
n
Whilst the highest dose, applied to the largest entity, comes from:
(2n  1)
DH 
DT
(5)
n2
Whilst this gives us the dosages for a parabolic profile, it is possible to mill spherical,
elliptical, hyperbolic or other profiles by using the relevant equation for the doses.
With the correctly calibrated doses applied, the pattern is then ready to run.
When milling samples, we first prepare the silicon by cleaning it in acetone,
methanol and IPA, finishing with an oxygen-plasma clean. The samples were then
milled in an FEI -Nova dual-beam, controlled by a Nabity Pattern Generation System
(NPGS) to handle the CAD drawn pattern. Figure 1 c) shows a series of milled dishes,
before etching. The dishes appear to be highly polished and free of debris upon
inspection. After milling, samples were measured by AFM before hydrofluoric (HF)
acid etching.
2.2.
Hydrofluoric Acid Etching
Before etching, the samples were washed in acetone, and de-ionised water, before
drying with nitrogen. This was done to remove silver electrodag used to attach the
sample to its SEM stub during milling. Samples were then placed in 48%
concentration hydrofluoric acid (HF) for 30 minutes, at room temperature. When
removed, they were washed in de-ionised water and dried with nitrogen.
Atomic force microscopy (AFM) profiles of the dishes before and after etching, seen
in Figure 2, were measured using a Veeco Dimension 3100 AFM system, with a tap300G tip.
2.3.
Low Dose
To look at the minimum amorphisation required to successfully etch, which ultimately
helps us understand how much Ga is left within the surface after etching, we
manufactured Siemens stars at a very low dose (Figure 3). By AFM measuring the
depth of HF etched stars milled at known doses, before and after etching, information
about the maximum depth the acid etches was found. Small doses were chosen, 1090µC/cm² with one additional pattern at 900μC/cm2, to limit the effect beam tails play
on the depth measurements. We call these doses small when compared to the doses
used in the milling of dishes, where a depth of 1µm requires 20000µC/cm² to mill.
To compare with these measurements, theoretical computer simulations were run
using SUSPRE (Surrey University Sputter Profile Resolution from Energy
deposition)[29], simulating the amorphisation and gallium ion concentration profiles
from the surface. The ion and target chosen were Ga and Si respectively, with an ion
energy of 30keV, and fluences reflecting the dosages used, 10-20,000μC/cm². The
system uses a bucket fill method for calculating number of ions implanted, throwing
away ions that pass the ion solubility limit, rather than relocating them. Whilst the ion
solubility of Ga in Si is low, less than 0.002 Ga ions/Si atom[30], we use 2 ions/atm
to compensate for the effect of ‘bucket filling’. This turns out to be more physical
than it first appears, as the system does not take into account interstitial Ga, only
substitutional Ga, meaning more ions can sit within the lattice than SUSPRE would
normally allow, which is similar to the effect of increasing the solubility limit.
When an ion is incident on the silicon surface, three events take place: 1) the ion
releases energy into the surface, causing the top most Si atoms to release from the
surface and sputter; 2) the ion usually then enters the surface, displacing Si atoms and
creating vacancies, whilst taking a random walk into the substrate and 3) when a large
number of ions are used, the amount of damage caused by the ions amorphises the
surface, leaving a thin layer of α-Si. A higher number of ions increases the degree of
amorphisation and leaves more ions sitting within this amorphous layer. SUSPRE
models this, showing the ion-implantation profile (approximately Gaussian) and the
degree of amorphisation with depth.
2.4.
Preparation of cross-sections
To examine the ion-beam damage, and to directly view the extent of the damage
before and after acid etching, cross sections of milled troughs were examined in a
scanning transmission electron microscope (STEM). Parabolic troughs were milled:
3µm diameter, 30µm in length and 300nm deep. A trough pattern was used to avoid
missing the centre when cross-sectioning a rotationally-symmetric structure
Thin cross sections were cut using an FEI nano-Nova dual-beam FIB microscope
system with a Zyvex manipulation system, via the conventional means[31]. This was
performed on an as-milled and an as-etched sample. High-angle Ga ion-polishing was
used to thin the sample to below 100nm to allow for high resolution imaging. By
using this method, the amount of Ga implanted into the cross section is limited, due to
the reduced chance of implantation at a grazing[32] . Whilst implantation does occur
during sample thinning, the amount of Ga implanted should be uniform across the
foil. Therefore, when looking at quantitative data (such as EDX) our arguments are
made with reference to this background of Ga that is present throughout the foil.
The STEM (Hitachi 2300A HD STEM with a Schottky Field Emission Gun, 200keV)
used to view the cross-sections had an attached EDX detector (EDAX Genesis),
which we used to map the chemical elements and their spatial distribution within the
sample.
2.5.
Replication of Lenses
In the final section of the paper, we look at how lenses replicated in
Polydimethylsiloxane (PDMS) adhere to the mould, and the visible effects etching has
on the mould. PDMS (Sylgard-184, Dow-Corning) was prepared using a 10:1 ratio of
base to hardener. It was then de-gassed for 1 hour, before being poured directly over
the silicon moulds. Once poured the PDMS was allowed to set at room temperature in
a vacuum chamber for 48 hours. When set, the PDMS was released from the moulds
by peeling. The lenses and moulds were then imaged in transmission under a 50x
optical microscope, whilst AFM profiles were taken of the moulds.
3. Results and Discussion
3.1.
AFM Profile
We begin by examining how closely a set of dishes follow a parabolic profile, before
and after etching. Figure 2 shows a parabola fitted to the profile of an as-milled and
as-etched dish (5um diameter, 10um focal length). We can see that the parabola fits
well at all points except for the bottom of the dish. The Chi² (chi-squared) value of the
as-milled and as-etched dish is 7.96 and 9.03 respectively, showing a measure of how
close the fit is to the measured data. As the Chi² of the as-milled dish is closer to 1,
the ideal fit, we know the fitting is not as ideal post etch, due to the increased
roughness at the dish bottom. Before etching, the increased deviation at the apex of the
parabola is due to redeposition of material (see section 2.1).
The etched sample appears to have been cleanly etched everywhere except for at the
bottom of the dish. This tends to occur in dishes with more redeposited material in the
dish centre than usual (eg. dishes where another dish is milled in close proximity). It
is caused by the extra, Ga rich, material shielding the dish bottom from incident ions,
lowering their implant depth. This means the α-Si region doesn’t get fully
amorphised, leading to non-uniform removal by the HF acid.
The roughness of the dish can be investigated by closely fitting the dish, using a high
order-polynomial (to account for skewness in the AFM measurement) and subtracting
the fitted shape, then calculating the RMS-roughness, δ, from leftover noise.
The mean RMS-roughness over several dishes, before etching in HF, shows to be
4.0nm, with the roughness changing very little after etching, reaching 4.1nm.
Using the RMS-roughness, the total integrated scattering (TIS) of the features can be
calculated using equation 6, which gives a percentage of the light scattered at a given
wavelength due to the roughness [28]:
 4 
TIS  
(6)

  
As we are interested in minimising scatter, we can re-arrange equation 6 to find the
smallest wavelength we use to illuminate our dishes, whilst keeping to below 1% light
scatter. This gives us a minimum wavelength of 51nm, well below that of visible
light. Lenses moulded from these dishes should, therefore, be of high enough quality
to work for the whole visible spectrum, starting from deep-UV up to infra-red,
depending on the optical properties of the lens material.
2
[Insert Figure 2 here]
3.2.
Dish shape change
In many of our deeper dishes, we see a larger variation from our intended profile than
in our shallower ones. It is well documented[33,34] how the ion-beam incidence angle
affects the sputter rate of material from a surface. When milling we begin with an ion
beam normal to the Si surface, however the topography quickly becomes curved.
When milling a curved surface there is a continuous change in incidence angle,
allowing certain angles that sputter more quickly to become more stable, changing the
surfaces final shape. We tend to see this as an increase in the width to depth ratio,
slightly flattening the profile of our dishes.
After etching, the shape of the dish can alter slightly again, due to the material
removed by the acid. Figure 2 shows an AFM profile of a 5um diameter dish, before,
a), and after b), etching. Whilst the dish remains parabolic after etching, the depth and
diameter of the dish are seen to change. The depth of the dish increases from 85.4nm
to 112.7nm after etching, comparing the dish edge to centre. As the dish edge profile
after etching changes from flat to skewed towards the dish, as indicated by the red
arrows, it suggests the dish edge has been etched along with the dish. The dish
diameter decreases from 5.7µm to 5.6µm, caused by the non-uniform removal of
material along the profile of the dish. Comparing the profiles of before (red dashed
line) and after (blue dotted line) in Figure 2 b) seems to show the flattening effect
caused by ion-beam incident angle is at least partially reversed by HF etching, with
the etched dish showing a smaller width to depth ratio.
The changes to the depth and diameter of the dish subtly change the focal length of
the dish. Other dishes, similarly measured, showed an increase of up to 30nm in depth
(for 1um deep samples) and 500nm increase in diameter (for 10um diameter samples).
For high precision work, this variation in depth caused by material removal will need
to be accounted for, so that the final profile conforms to the required dish. In section
3.4 we look at the depth of Si that 48%-concentrated HF removes in 30 minutes, as a
function of the milling dose.
The cause of the surface profile skew in Figure 2 is the ion beam-tails. Whilst the
ion-beam is modelled as a finite spot, its true shape is closer to a Gaussian
distribution[35]. The tails of the beam have enough sufficient ion to amorphise the
silicon, allowing it to etch, as shown later by STEM imaging in Figure 6. Due to this,
the near dish surface has been etched to a similar degree to the dish itself, causing the
measured dish depth to remain constant, whilst etching at the surface decreases with
increasing distance from the dish edge. As this keeps the depth of the dish close to the
original milled depth, this works in our favour, as changes to the dish depth change its
focal length. Our observations in section 3.5 put these beam tails going out to a radius
of as much as 50m from the dish centre, showing how large an area is affected even
when milling small structures.
3.3.
Ion beam damage and modelling (Siemens Stars)
Having seen the very low doses created by the ion beamtails are enough to allow the
Si to etch, we investigated how low an ion-dose can be etched, and how fully etched
the sample is with a varying dose. Doing so gives insight into how the depth etched is
linked to the dose. When using very small doses, the effect of the beam tails is
negligible, and so a true measurement of etch depth can be made by AFM. This
allows us to expose low dose samples, HF acid etch and then measure the depth
etched accurately.
To look at the effect of HF etching in this dose region, a series of Siemens stars
where milled, at doses between 10-90 μC/cm2. At the lowest doses, below 70µC/cm²,
the silicon surface sputters very little, causing a slight surface swelling due to
implantation and amorphisation (Figure 3 A), and only minor, inconsistent removal of
material at the highest dose used (Figure 3 C) .
[Insert Figure 3 here]
Before etching, the milled patterns are not visible using the AFM; after HF etching,
the depth of the stars increased, shown as the bottom images and profiles in figure 2,
with even the lowest dose increasing in depth to 12nm. This shows how little a dose is
required for the ion-beam to amorphise the surface sufficiently, to preferentially
increase the rate of etching. In Figure 4 a) we plot the experimentally measured depth
etched as a function of dose (black squares). The etch depth shows a logarithmic
relationship, with the curve rapidly increasing after 100µC/cm².
[Insert Figure 4 here]
From this data we needed to understand whether restoring the properties of the
surface is possible. To do this we need to investigate how much of the Ga is removed
along with the α-Si during etching. This was achieved by comparing the AFM
measured etch depth data to computational models of the ion stopping range in
silicon, giving information on the minimum amorphisation required to etch. This let
us model how much implanted Ga is left in the surface after etching, to understand
how well the surface may be restored.
The models, shown in
Figure 5, plot the concentration of implanted ions (black solid line) and the percentage
amorphisation (blue dashed line) as a function of depth, for four doses. The four
doses represent four points on the logarithmic scale between our lowest dose,
10µC/cm², and the dose required to mill to a depth of 1um in Si, 20000µC/cm². In all
four plots, the implanted ions form a Gaussian distribution, peaking at the same depth,
26nm under the surface. This is because the depth of implantation is controlled by the
accelerating voltage (ion-energy), which we keep constant, and not the beam current.
The blue-triangle line in Figure 4 a) shows the theoretically modelled percentage
amorphisation at the depth indicated by the black-squared line. Whilst the etch depth
increases, the percentage amorphisation of the silicon at the depth etched is roughly
constant, staying at 31%±5. This gives us a starting point for estimating the depth to
which other doses would etch, using further computer modelling.
The black-squared line in Figure 4 b) shows the modelled depth at which 31%
amorphisation is reached for a larger number of doses, showing similar results to our
AFM measured depths. If we look at
Figure 5, the vertical red lines mark the 31% amorphous depth. Any Ga above this
line is assumed to be removed during etching. As the dose increases, this red line
moves through the Gaussian implantation curve, showing a larger amount of the total
gallium implanted is removed by higher doses.
The blue-triangle line in Figure 4 b) plots the amount of Ga within the surface below
the 31% etch depth, as a function of dose. It shows how there is a careful balance
between introducing more ions, and increasing the surface amorphousness, allowing
the acid to etch deeper. Below a dose of 400µC/cm², the trend is an increase in the
amount of implanted Ga post-etch, with a dip at around 200-300µC/cm². This shows
that the amorphisation front is moving into the surface more slowly than the position
of the maximum of the implanted Ga. From dosages of 400-2000µC/cm², there is a
gentle decline in the quantity of implanted Ga, as the amorphisation front begins to
overtake the increase in implanted ions. The drop between doses of 2000-3000µC/cm²
shows the amorphisation front passing from the third to the fourth standard deviation
in the broadly Gaussian implantation profile. This leaves the smallest amount of total
Ga remaining within the surface, after etching. Above 3000µC/cm², increasing the
dose causes an exponential increase in the Ga remaining in the surface, meaning the
amorphisation front is no longer moving into the surface as quickly as additional Ga is
being introduced. This indicates that 3000µC/cm² is the ideal dosage to allow for Ga
removal, and although the increase from 3000µC/cm² is steep, even at a dose of
20000µC/cm², the Ga remaining is still below the lowest dose of 10µC/cm².
As we have used a standard etch time of 30 minutes, the depth etched across all our
samples is reasonable standard, getting down to 31%±5 amorphous material. By
increasing the etch time, it may be possible to etch further into the material, thereby
gaining a further advantage by removing more implanted Ga.
[Insert Figure 5 here]
So far we have shown that theory predicts HF acid etching will remove most of the
Ga implanted by FIB milling, with higher doses showing more efficient removal then
lower doses. The next step is to look at Ga removal experimentally. In the next
section we use scanning transmission electron microscopy (STEM) to image cross
sections of the damage caused when milling.
3.4.
STEM
To image the underlying damage caused by ion-milling, and confirm that HF acid
etching removes both the Ga and amorphous Si, restoring the original surface
properties, two cross-sectional electron-beam transparent foils were prepared using
the FIB. The first was cut from an as-milled trough, the second from an HF etched
trough; both imaged in a STEM. The brightfield image (transmission electron image
labelled (TE)) shown in Figure 6 shows four distinct layers, labelled 1-4, of an asmilled trough. The top two layers (1 and 2) are platinum, deposited to provide
contrast, and to protect the silicon during cross sectioning. Below this are two silicon
layers (3 and 4). Imaging layers 3 and 4 using high resolution TEM, shown in Figure
6 a), and taking Fourier transforms of each layer shows the loss of crystallinity in the
top silicon layer. The Fourier transform of layer 4, labelled c), shows the distinct
bright spots denoting crystallinity in the layer. Layer 3’s Fourier transform, labelled
b), has a smeared band of brightness surrounding the centre. Whilst this suggests a
lack of order in the material, indicating it’s amorphous, the band is not rotationally
symmetric in intensity, suggesting some vestiges of order.
Between the two silicon layers lies a thin black line, suggesting the change between
amorphous and crystalline silicon. The line is 4±2nm thick, and represents the drop
off from 100% to 0% amorphous. Relating this back to the SUSPRE models in
Figure 5 we see that, for a realistic milling dose, 20 000µC/cm², the change between
100 and 0% amorphous is dramatic, occurring over 4nm, which agrees well with the
measurements of this line.
The extent of the amorphous region shown in the TE and ZC images in Figure 6
varies between 46-52nm deep within the milled trough area (to the right of the red
arrow), and 61-70nm outside of the designated milling area (left of the red arrow).
From SUSPRE we expect the depth to be exactly 60nm, and no deeper, but neither
area agrees with this well.
Within the trough, this can be explained by the high percentage of Ga within the
surface after the first few passes of the ion beam. The implantation and amorphisation
depths decrease, which can account for this reduction in depth from theory. Our
method of using multiple passes helps to overcome this by helping a steady state to be
reached.
Outside of the trough, the deepest 70nm region is directly next to the trough, with the
depth reducing linearly to 61nm at a distance of 250nm away from the edge. We
know the surface is not directly milled, and is only damaged by the beam tails, as we
concluded in section 3.2. The much smaller dose of the beam tails drops off as you
move away from the dish, leading to a decrease in the amorphisation. This causes the
slanted profile of the Si/α-Si interface visible in Figure 6, which we also saw by AFM
in Figure 2. As much fewer ions are implanted in this region, with little redeposition,
this allows the Ga to reach the full implantation depth given by the model. The
additional depth, above that predicted by modelling, may have come from an edge
effect, with ions scattering from within the shallower trough and adding to the depth.
[Insert Figure 6 here]
Looking to the high-angle annular darkfield image (Z-contrast, labelled ZC) shown in
Figure 6, the brightness is proportional to the Z2 (atomic weight squared), density and
thickness (approximately constant) of the sample. We can see the ion-beam and ebeam deposited platinum (layers 1 and 2 respectively) as two brighter layers on top of
two much darker silicon layers. Within the amorphous layer (3) in the area where the
trough was milled, we can see a brighter line running near the top of the amorphous
region, below the platinum, which we have highlighted in red. As the line is high
contrast, suggesting a denser region or higher atomic weight, this could be indicating
the presence of Ga. The lack of such a line outside of the trough indicates a much
lower degree of Ga implantation.
To confirm the presence of Ga, an EDX map of the area around the trough edge was
taken for the as-milled and acid-etched troughs, as is shown in Figure 7 a) and b)
respectively. The images show the EDX Ga signal (blue dots) mapped onto the
transmission electron image (TE). Looking at the α-Si region within the trough for the
as-milled sample, a), we see an area of very high gallium concentration (highlighted
by the red ellipse) when compared with the α-Si outside of the trough, or the c-Si
region. This means that much of the Ga still sits within the α-Si layer in the trough,
changing the layer’s optical and chemical properties. Comparing this to an EDX map
of a chemically etched sample (denoted b), we see very little Ga within the left-over
silicon, and no distinct α-Si layer. This agrees nicely with our SUSPRE model that
suggested the bulk of the Ga is removed along with the damaged Si.
EDX linescans of both samples were taken, as shown in Figure 7 c). The red-triangle
and black-square lines show linescans through the as-milled sample, through the
trough-centre and trough-edge respectively, whilst the green-circle line is through the
centre of the as-etched trough.
For both as-milled sample profiles, the signal increases within the α-Si layer,
following a profile similar to the Gaussian profiles shown by SUSPRE. The Signal
then drops off within the c-Si layer. At the trough edge, the peak Ga profile is much
nearer to the surface, dropping off to the background before meeting the c-Si
interface. The difference in profile is caused by the change in angle of the surface
between the trough centre and edge. Compared to SUSPREs prediction (
Figure 5), both as-milled profiles peak nearer to the surface than expected, showing
some skew when compared with the modelled Gaussian distribution centred tens of
nanometres below the surface. Material removal by sputtering may account for this, as
the milled top surface moves into the implanted front; the peak implanted region
becomes spread, as new ions implant deeper into the surface, creating an overlapping
set of profiles.
In the as-etched sample the Ga signal drops off towards the Pt/c-Si interface, with a
reduced noise within the c-Si. Compared with the distinct peaks seen in the as-milled
samples, the Ga percentage appears to be just over the background found in the bulk
of the c-Si, showing most of the Ga has been removed along with the α-Si. This
means the surface properties of the material should be, if not entirely restored, much
closer to that of the original surface.
[Insert Figure 7 here]
3.5.
Silicon discolouration and Lens replication
Having demonstrated how HF acid can remove ion induced damage from silicon, we
now move on to look at the chemical and optical changes that etching has on the Si
mould, as well as lenses made from such a mould. Figure 8 a)-d) shows reflectance
optical images of a set of Si moulds, etched for increasing amounts of time. In all four
images, a bloom is visible around the dishes, caused by the beam-tail effects; note
how far out they extend. The first mould a) was left without etching, but a slight
lighter shading can be seen around the dishes. As the etch time increases, to 7 minutes
(b), 15 minutes (c) and 30 minutes (d), the size of the bloom around the dishes grows,
and is visible without optical magnification for all etched samples. In d) the etching
has created a colourful pattern, moving through hues of red and blue as you move
away from the dishes.
As the colour change radiates outward from the dishes, it follows that it is related to
the skew of the surface we saw in sections 3.2 and 3.4, caused by etching. From our
models in section 3.3 we have seen how a decreasing dose doesn’t change the depth to
which Ga is implanted, but does reduce the depth at which the minimum
amorphisation required to etch occurs, hence a smaller etch depth. It follows that for
smaller doses, the depth of the remaining implanted and amorphised region after
etching is larger. The colour we see in Figure 8 d) is likely caused by this partially
amorphous layer on the surface, where the change in colour relates to a change in
depth.
The graph in e) shows the profile of dishes from the un-etched sample (solid green
line), and the longest etched sample (dashed red line), after replicating lenses. Whilst
both dishes should have approximately identical profile, the green profile shows large
amounts of debris in the dish. This indicates a large amount of PDMS has remained
stuck to the dish. Whilst this did not happen to all lenses, it did occur multiple times,
across the small number replicated. In the 30 minute etch sample, no such problems
have been seen, with similar smoothness and profile before and after replication. This
shows that etching does reduce the adhesion between PDMS and the milled silicon
substrate, aiding the replication process.
Images f) and g) show transmission optical microscope images of the lenses formed
from the 30 minute etch mould. The lenses vary in depth and diameter, creating
varying focal lengths, with depths from 100-400nm, and diameters of 3, 5, 7 and
10µm. Image f) is of the lenses themselves, showing a set of well moulded lenses. In
g) we see the focussing power of the lenses. The microscope was focused at the focal
point of the top-right lens, which had the shortest focal length of the 10µm lenses. The
focal point of all of the lenses is quite tight, and very bright compared with the
background brightness at the edge of the image.
This means that using our milling and etching technique we can create high quality
micro-lenses, with good focussing ability. By HF etching the milled silicon, the
surface is prepared, reducing adhesion and allowing for replication of soft-polymer
lenses. These replication techniques will allow moulds to only be milled the once to
produce a large number of lenses, reducing the cost of manufacturing these high
quality, bespoke footprint, parabolic profile lenses.
[Insert Figure 8 here]
4. CONCLUSION
In this paper we have demonstrated a method for creating 3D -parabolic profile
geometries using a FIB microscope, along with a technique for removing the surface
damage introduced during milling. We have then shown how these parabolicallymilled structures can be used as moulds to form polymer lenses, which may be useful
in the digital camera and solar cell industries. As the technique also allows other
profiles, spherical, elliptical or hyperbolic, and a variety of highly tessellatable
footprints, it may allow for the creation of closely packed, precisely controlled profile
arrays of high quality micro-lenses.
We have shown that 30 minutes of concentrated HF etching removes most of the α-Si
and Ga at the surface of ion milled samples, restoring most of their optical and
chemical properties. This should increases the transmisivity of directly milled lenses,
and reduces adhesion to the mould by polymer lenses during replication, allowing for
a cleaner release.
Whilst we have seen that HF acid etching does change the size and shape of the dish,
by understanding the process and controlling factors during the milling it is possible
to control this change to reach the final geometry of our choosing. The roughness of
etched samples appears not to change, showing an average of 4nm RMS roughness
both before and after etching. Using this value for roughness, we calculated the
minimum wavelength usable on these dishes that would still have less then 1%
scattering of the light. The Dishes should scatter less then 1% for any wavelength
above 51nm, deep into the UV, suggesting any suitably high quality moulded replica
would have a similar degree of light scatter.
We estimated how much of the implanted Ga is removed with the α-Si when HF
etching, to determine how well the surface’s properties will be restored. Using AFM
on etched samples of known dose, and comparing the etch-depth to computer
simulations, we’ve shown that HF acid etches down through the amorphous silicon,
stopping where its only 31%±5 amorphous, for a 30 minute etch. As a portion of the
α-Si region is left, the Ga implanted in the region is also left. This means that
minimising the extent of the remaining α-Si region reduces the leftover implanted Ga,
improving optical and chemical properties. We have shown that increasing the iondose to 3000µC/cm² actually reduces the final amount of implanted Ga, as the
additional amount overcomes the extra it introduces. Beyond 3000µC/cm², the
amount remaining increases exponentially, but remains lower than when using doses
as low as 10μC/cm², until at least 20000μC/cm². This means that HF etching improves
the surface properties for milled features up to a micron in depth.
It was then shown, by imaging cross sections of milled profiles in a STEM, that a
very high concentration of Ga does indeed sit within the α-Si region. By removing the
α-Si with HF etching, the Ga is removed along with it, leaving the surface
comparatively free from Ga.
We saw the extent of the α-Si region was smaller then our SUSPRE models
predicted, 49nm when 60nm was predicted. This was accounted for by the reduction
in implantation depth caused by the addition of accrued implanted Ga within the
layer. The transition between the α-Si and c-Si layers was seen to be 4±2nm, agreeing
nicely with the predicted 4nm. When etched, only the c-Si layer could be found.
We further demonstrated using EDX maps and line-scans, the removal of the Ga
from the surface, showing defined gallium peaks before etching, whilst only a small
background amount after etching.
In the final section we used milled dishes as a mould to replicate PDMS polymer
lenses. We noted visual change to the silicon caused by etching, suggesting the
changes arise from the quantity of Ga and thickness of α-Si remaining. We next
looked at the material remaining in the dishes of the non-etched, and 30-minute
etched samples after replication. The non-etched sample showed large amounts of
PDMS stuck to the sides, whilst the etched sample was relatively clean, looking
similar to dishes that hadn’t been used in replication. Finally, we imaged the lenses
showing their tight focal spots, and the clean quality of the lenses.
In summary we have shown that we can produce high quality, bespoke-profile lens
moulds with FIB lithography, using chemical etching to restore the optical and
chemical properties of the moulds.
Acknowledgements
We would like to thank Emma Beer for her help in performing atomic force
microscopy. We would also like to thank the EPSRC for funding the project.
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Figure 1: Diagram of Parabolic milling and Calibration. a) shows a diagrammatic cross section of
how linearly increasing the depth milled, for a set of concentric circles can sum to a parabola.
Whilst this simple model predicts this method should create a step edge, over or under milling
areas, preferential edge erosion during milling removes edges, as indicated, whilst redeposited
material refill overfill areas to create a smooth parabola. b) shows a cross section taken through a
2µm trough, made during calibration of the depth to dose ratio ‘a’. The image c) is of a set of asmilled dishes, decreasing in depth from left to right, and decreasing in size from top to bottom.
Figure 2: AFM height map image and profile of parabolic dish. A) shows the profile of an asmilled dish whilst b) is as-etched in HF. The insets are topographical AFM images, with lines to
represent the locations from which the profiles were taken. The red dashed line in the profile
images show a parabola fitted to the as-milled dish, whilst the blue dotted line is a fitting of the
as-etched. A second order polynomial fitting fits well, showing how closely the dishes follow a
parabola. Under a visual inspection it appears that both before and after etching the roughness is
minimal, but has increased slightly due to etching.
Figure 3: Comparison of before and after HF etching Siemens stars of doses 10- and 900- µC/cm².
The inset in each profile shows the AFM heightmap the profile was taken from, with each profile
coming from a single arm of the star, in the position indicated by a green line. Both doses show
almost no depth to the pattern pre-etch, with the 10µC sample instead demonstrating surface
swelling. After etching, both samples have increased in depth to form trenches, with the 900µC
exhibiting a much greater etch depth. This increase in depth after an etch shows that the HF
preferentially removes the region amorphised by the ion beam.
Figure 4: a) shows the Dose vs AFM measured etch-depth for ion doses below 1000μC/cm² (black
line), along with the degree amorphisation at that depth from theory (blue line). It shows that a
30 minute etch stops etching at around 31% α-Si. b) plots the theoretical 31% α-Si depth for
doses up to 20000µC/cm² (black line), along with the implanted Ga left within the surface below
that depth, post-etching (blue line). The plot demonstrates that increasing the gallium dose
actually increases the amount of Ga the HF etch can remove, suggesting the surfaces properties
would be somewhat restored.
Figure 5: shows the SUSPRE plots of amorphisation and implantation after milling at the stated
doses. The red line indicates the etch stop depth at the dose. As the dose increases from 1090µC/cm² the etch stop passes through the peak gallium concentration, increasing the total
percentage of the gallium removed. As the dose reaches a usable milling dose the amorphisation
front lies well below the gallium peak, whilst the drop from 100%-0% amorphous occurs in only
1-2nm. This suggests at this dosage almost the entirety of the implanted gallium will be removed
during an HF acid etch.
Figure 6: shows the Transverse electron (Brightfield, labelled TE) and Z-contrast (Darkfield,
labelled ZC) images of the edge of a 3um silicon trough milled in silicon. The 4 layers labelled in
the image are as follows: 1) ion-beam deposited platinum, 2) electron-beam deposited platinum,
3) amorphised silicon, 4) crystalline silicon. The presence of a large amorphous region outside of
the intended milling area demonstrates the strong effect of ion-beam tails. Image a) shows a high
resolution TEM image of a area indicated in yellow on the TE image. The images width is 36nm.
Fourier transforms taken above (b) and below (c) the dark region show the region above is
amorphous, whilst below is crystalline silicon. The 4nm±2 dark line shows the change from
amorphous to crystalline silicon.
Figure 7: Shows the Ga L-edge EDX map overlaid on the TE image of a) an as-milled trough and
b) as-etched trough. The blue pixels show the concentration of gallium within the sample. Whilst
the background within the c-Si and pt is similar in both samples, a large quantity of Ga can be
seen within the α-Si region of A). The graph C) shows the line profiles through the edge and
centre of the as-milled dish (black and red respectively), and centre (green) of the as-etched dish.
It again shows the bulk of the Ga sits within the amorphous region, and is not present after
etching.
Figure 8: a)-d) shows images of a set of silicon moulds after replicating lenses. Whilst each was milled in
identical conditions, the etch time in HF increases from a) 0 minutes (no etch), b) 7m, c) 15m to d) 30m.
A coloured bloom surrounds the etches, showing where the acid has etched the beam tail irradiated
region. e) shows the AFM profile of moulds from the 0m etch (green line), and 30m etch (red line)
samples after replication, with inset images of the AFM topography of the two. The 0m etch sample
shows a large amount of PDMS still stuck to the dish surface, whilst the 30m etch shows a clean and
smooth surface. The final two images show the lenses replicated by the 30m etched sample, where f) is
at their focal point and g) is at their surface.