Surface Damage Removal in Bespoke Micro-lens Moulds Manufactured by Focused Ion-Beam

Surface Damage Removal in Bespoke Micro-lens Moulds Manufactured by Focused Ion-Beam

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

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

• 
  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

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

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 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, F_D, can be found from the diameter of the dish, D, and its depth, c, linked by the equation 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, F_L, of a lens of refractive index n, is given by equation 2 [28]:

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, D_T, required to mill the full depth of the dish, using the following formula:

(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 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:

Whilst the highest dose, applied to the largest entity, comes from:

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 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

Atomic force microscopy (AFM) profiles of the dishes before and after etching, seen in Figure , were measured using a Veeco Dimension 3100 AFM system, with a tap-300G tip.

2.3.Low Dose

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

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

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 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]:

(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.

[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 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 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 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 . 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 A), and only minor, inconsistent removal of material at the highest dose used (Figure 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 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

, 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 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 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

, 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 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 shows four distinct layers, labelled 1-4, of an as-milled 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 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

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 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 , which we also saw by AFM in Figure . 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 , 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 e-beam 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 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 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 (

), 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 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 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 parabolically-milled 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 ion-dose 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 : 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 as-milled dishes, decreasing in depth from left to right, and decreasing in size from top to bottom.


Figure : AFM height map image and profile of parabolic dish. A) shows the profile of an as-milled 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 : 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 : 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 : 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 10-90µC/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 : 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 : 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 : 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.

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