A maskless method of electron beam lithography is described which uses the reflection of an electron beam from an electrostatic mirror to produce caustics in the demagnified image projected onto a resist–coated wafer. By varying the electron optics, e.g. via objective lens defocus, both the morphology and dimensions of the caustic features may be controlled, producing a range of bright and tightly focused projected features. The method is illustrated for line and fold caustics and is complementary to other methods of reflective electron beam lithography.

Electron optical systems have emerged as attractive candidates for high resolution lithography.1,2 Direct–write e–beam lithography (EBL) utilising scanning electron microscopy (SEM), for example, is of significant value in laboratory based nanofabrication.2–6 However, the serial nature of this inherently scanning technique renders it too slow for high–throughput industrial applications involving large scale circuits.1,3,7 Projection methods utilising a parallel electron beam and mask can, in principle, overcome such patterning speed limitations.2,7–13 However, significant demands are placed on the design of the electron mask due to the requirement of sufficiently high aspect ratio between thick/thin regions which absorb/transmit electrons.3 This has limited the approach to stencil masks and low energy electrons, compromising the attainable resolution.2 

The mask limitation is therefore a serious issue in the application of projection electron lithography methods. This has led to innovative approaches such as SCALPEL which utilises the angular scattering properties of electrons, rather than absorption in the mask, to create intensity variations across a resist.2,8,9,11 In addition there has been a development of maskless approaches, including the use of multiple beams,14,15 low energy electron microscopy,10 and reflective electron beam lithography (REBL) wherein the electron beam is reflected by an array of electrostatic mirrors.12,13 In this letter we describe a complementary approach to REBL and electron projection lithography which is based on the formation of intense electron caustics which can be subsequently projected onto a resist by suitable electron optics. The caustics are formed within the cathode lens of a mirror electron microscope (MEM) in which electrons turn around in the vicinity of a negatively biased specimen surface.16–18 Rather than using an array of individually controlled electrostatic mirrors as in REBL, a single mirror surface is lithographically patterned to create perturbations in the uniform electric field above the specimen which can be used to form caustics. This perturbed electric potential mirror therefore entirely replaces the conventional mask and specific caustics can be tuned by the patterning and subsequently projected onto a resist coated wafer. The method has the advantage that for a given lithographically patterned mirror surface, the caustic pattern projected onto the resist can be varied by simply adjusting the electron optics, e.g. the objective lens defocus.

Caustics are regions of very high intensity created naturally by focusing optics. For example, the sharp bright lines on the floor of a swimming pool are formed by sunlight shining through the perturbed water surface. As caustics are regions of very high intensity, reflected electron caustics projected onto a resist–coated wafer would apply a high electron dose to the resist producing a strong response. A variety of caustic classes can be formed in MEM.19 Here we consider line and fold caustics which produce bright focused points and lines respectively when projected onto a resist. These caustic features form the basic building blocks or elements of a projected lithographic pattern, and can include more complex caustic classes such as an elliptic umbilic, which could form a three way junction element. Importantly, caustics are typically sharper and finer than the mirror surface variations producing them. In the analogy of swimming pool caustics, a gently perturbed water surface produces much finer caustics on the swimming pool floor. The combination of bright and finely focused features therefore makes caustic mirrors of significant value to EBL.

The proposed experimental arrangement for mirror electron caustic lithography (ECL) is shown in Fig. 1. An electron beam is directed into the immersion objective lens providing parallel illumination of the cathode, which is negatively charged so that the electron beam turns around above the surface. Variations in the cathode surface topography and/or potential result in a varying electric field close to the surface, which deflect the electron beam in the vicinity of the turn–around region. These deflections and distortions create caustics in the returning electron beam, which in Fig. 1 is demagnified and directed onto a resist such that the cathode is acting as a caustic mirror (CAM). As a proof of concept, we now consider two examples of CAMs which produce point, circular, and line elements of a projected lithographic pattern.

FIG. 1.

(a) Proposed experimental arrangement for mirror electron caustic lithography (ECL). The electron beam (blue line) provides parallel illumination of the cathode specimen. The electron beam is slowed by the electric field in the region above the cathode, and the cathode is negatively charged so that the electron beam turns around just before the surface. The electron beam interacts with and is deflected by the electric field above the cathode surface, is reaccelerated away, and carries these distortions back through the system to the resist. (b) Electron ray trajectories (blue lines) projected onto the resist–coated wafer (dashed box in (a)). Where initially adjacent electron rays cross (marked by arrow) a caustic C is formed, creating a focused region of very high intensity and high dose to the resist.

FIG. 1.

(a) Proposed experimental arrangement for mirror electron caustic lithography (ECL). The electron beam (blue line) provides parallel illumination of the cathode specimen. The electron beam is slowed by the electric field in the region above the cathode, and the cathode is negatively charged so that the electron beam turns around just before the surface. The electron beam interacts with and is deflected by the electric field above the cathode surface, is reaccelerated away, and carries these distortions back through the system to the resist. (b) Electron ray trajectories (blue lines) projected onto the resist–coated wafer (dashed box in (a)). Where initially adjacent electron rays cross (marked by arrow) a caustic C is formed, creating a focused region of very high intensity and high dose to the resist.

Close modal

As a first example of a CAM, we consider circular microholes in a GaAs surface which produce line and fold caustics as shown in Fig. 2(a)–2(c). As discussed by Kan and Phaneuf,20 microholes act to focus the reflected electron beam forming very bright central spots, which are seen experimentally in Fig. 2(a). These are line caustics,19 and are evident as bright spots when projected onto the resist. Decreasing the objective lens current introduces darker circular regions around the diminished central spots. Fold caustics form at the edges of these darker regions, which are evident as bright circular outer rings in Fig. 2(b). As objective lens current is further decreased, the central spot or line caustic fades, leaving larger darker central regions with fold caustics or bright circular boundaries in Fig. 2(c). These begin to overlap with the images of adjacent microholes, eventually becoming a grid of vertical and horizontal bright lines.

The range of caustic shapes of varying sizes and intensities produced in ECL may be understood using the recently developed caustic imaging theory.21–23 This approach interprets caustic features as the natural result of electron redistribution created by the perturbed electric field above the cathode surface. In Fig. 3 we show the simulated positions of initially equidistant electrons that are projected onto the resist with objective lens defocus Δf. This simulated electron ray family shows the formation of a central line caustic in the vicinity of Δf = −5 μm and the surrounding fold caustic for Δf > 25 μm, where initially adjacent electron ray paths overlap. By comparing the spacing of originally adjacent rays to the original spacing at a specific defocus (solid horizontal lines in Fig. 3), we may simulate the projected caustic features21–23 as shown in Fig. 2(d)–2(f). The simulated caustics are in good agreement with experimental caustics, and further highlights that by varying the objective lens current (i.e. defocus) we can control both the dimensions and the type of caustic features that are produced. The caustic imaging theory can be used to simulate and predict the caustics that will be produced in MEM, and so develop a suitable CAM to produce the desired lithographic pattern.

FIG. 3.

Simulated electron ray path positions projected onto the resist, having reflected from a caustic mirror of a surface hole in GaAs, for defocus Δf which is controlled by the objective lens current. A line caustic is formed at the region marked ‘a,’ a fold caustic at the region marked ‘b,’ these caustics are regions of strongly enhanced electron intensity. The mirror or cathode surface is held at a potential of V = −20000.4, the electron energy is U = 20 keV, and the cathode–anode distance is L = 2 mm. The edges of the circularly symmetrical hole are indicated by vertical dashed lines. The r positions of the rays were multiplied by 3/2 to remove the demagnification of the anode aperture as discussed in Kennedy et al.21 The horizontal solid lines are the positions of the projected image plane for the images in Fig. 2.

FIG. 3.

Simulated electron ray path positions projected onto the resist, having reflected from a caustic mirror of a surface hole in GaAs, for defocus Δf which is controlled by the objective lens current. A line caustic is formed at the region marked ‘a,’ a fold caustic at the region marked ‘b,’ these caustics are regions of strongly enhanced electron intensity. The mirror or cathode surface is held at a potential of V = −20000.4, the electron energy is U = 20 keV, and the cathode–anode distance is L = 2 mm. The edges of the circularly symmetrical hole are indicated by vertical dashed lines. The r positions of the rays were multiplied by 3/2 to remove the demagnification of the anode aperture as discussed in Kennedy et al.21 The horizontal solid lines are the positions of the projected image plane for the images in Fig. 2.

Close modal

In order to create line elements in a lithographic pattern, consider a raised ridge or wire on the mirror surface as depicted in cross section in Fig. 4(a). Simulated MEM images indicate that this mirror surface produces both double and single fold caustics, producing lines in the projected image (Fig. 4(b) and 4(c) respectively), with the type, position and intensity of the caustics varying with the electron optics of the MEM system. These caustic features are similar to those experimentally obtained from a nanowire on a planar surface.23 

The use of a CAM in place of a conventional mask in ECL has a number of advantages. All surfaces are potentially CAM candidates and specific mirrors can be tailored by conventional lithography techniques such as top–down direct write EBL techniques.4–6,24–26 It may also be feasible to utilize self–assembled nanostructures on surfaces, such as quantum dots, as the basis of CAMs for niche applications. Caustics are commonly produced when focusing an optical beam, and they are typically stable to perturbations19 such as imperfections on the mirror surface, and aberrations in the optical system including an electron energy spread.3,8,12 Thus a variety of caustics should be readily formed from a vast range of mirror surfaces, including curved lines and junctions, with contributions from both surface topography and potential variations, such as differences in material work function. Caustic features can typically be focused to finer dimensions than the surface structures or variations producing them, improving resolution of lithographic patterns. For example, bright spots of diameter 100 nm are shown in Fig. 2(b) and were produced from microholes of diameter 600 nm, and a raised line of width 400 nm produced a simulated line caustic of width less than 100 nm. Caustic features are by definition very bright, which increases the electron dose to the desired region of the resist, which in combination with the fine focusing of features increases the contrast between exposed and underexposed regions of the resist.

In REBL, the role of the mask is played by the digital pattern generator (DPG) developed by Petric et al.,12,13 which is a sophisticated array of electrostatic mirrors that create the pixels of the image projected onto the resist. As a logical extension, the flexibility of ECL could be improved by adopting a DPG with every individually controllable pixel ‘on,’ i.e. reflecting every electron with a variable but consistently negative potential, creating a flexible CAM. While this decreases the ease of use compared to a static CAM, with no ‘off’ pixels of the CAM DPG, few electrons would be absorbed, increasing electron current and efficiency. By further controlling the electron optics i.e. the defocus of the projected image, a single pattern in the CAM DPG could produce a range of caustic features, such as the examples in Figs. 2 and 4.

FIG. 2.

Experimental and simulated MEM images of a grid of circular microholes in a GaAs surface of diameter 600 nm and depth 200 nm, formed by focused ion beam (FIB) techniques. The experimental images are taken with varying objective lens current i.e. defocus providing a through–focus sequence of images. The electron energy is U = 20 keV, the specimen voltage is V = −20000.4 V, and the anode–cathode separation is L = 2 mm so that the electron beam turns approximately 40 nm above the surface. The objective lens current is (a) 1670 mA, (b) 1650 mA, (c) 1640 mA, and the defocus for the simulated images is (d) −20 μm, (e) 10 μm, and (f) 50 μm.

FIG. 2.

Experimental and simulated MEM images of a grid of circular microholes in a GaAs surface of diameter 600 nm and depth 200 nm, formed by focused ion beam (FIB) techniques. The experimental images are taken with varying objective lens current i.e. defocus providing a through–focus sequence of images. The electron energy is U = 20 keV, the specimen voltage is V = −20000.4 V, and the anode–cathode separation is L = 2 mm so that the electron beam turns approximately 40 nm above the surface. The objective lens current is (a) 1670 mA, (b) 1650 mA, (c) 1640 mA, and the defocus for the simulated images is (d) −20 μm, (e) 10 μm, and (f) 50 μm.

Close modal
FIG. 4.

(a) Equipotential surfaces above a raised ridge (dark region) on a CAM substrate with height profile H(x) and potential −20000.4 V. The potential difference between each surface is 0.3 V. (b) Simulated MEM image an infinitely long raised line at negative defocus, demonstrating that two line caustics can be formed. (c) Simulated MEM image of the same raised line at positive defocus, demonstrating that the same surface feature can produce a single line caustic.

FIG. 4.

(a) Equipotential surfaces above a raised ridge (dark region) on a CAM substrate with height profile H(x) and potential −20000.4 V. The potential difference between each surface is 0.3 V. (b) Simulated MEM image an infinitely long raised line at negative defocus, demonstrating that two line caustics can be formed. (c) Simulated MEM image of the same raised line at positive defocus, demonstrating that the same surface feature can produce a single line caustic.

Close modal

Finally we consider throughput, which is a major consideration confronting EBL. As mentioned earlier, the throughput of serial scanning techniques is inherently limited. Simply increasing beam current to increase throughput creates the issue of space–charge effects which tend to blur image features.6,8,9 However, ECL is a parallel illumination method which can simultaneously illuminate large areas of the resist, ameliorating the requirements for large beam currents.8,10 In addition, dual beam LEEM methods have been shown to reduce the effect of the electron beam on the mirror itself, which causes some mirror surfaces to change potential and distort the outgoing electron beam.10 ECL is entirely compatible with a multiple column architecture which can, in principle, reduce the required beam current in any one column, and realise several tens of wafers per hour.13 Further improvements are likely in throughput for reflective electron beam lithography systems and ECL will also benefit from such developments.

In summary, we have outlined a new approach to EBL, ECL, which utilises the reflection of an electron beam from an electrostatic mirror to produce caustics in the demagnified image projected onto the resist. By varying the electron optics both the type and dimensions of the caustic features may be controlled, producing a range of bright tightly focused image features which form the building blocks of a lithographic pattern. The potential exists to apply DPG technology to ECL, providing a more flexible CAM and a complementary mode of REBL.

We are grateful to Rod Mackie for technical support. S.M.K., W.X.T., D.M.P. and D.E.J. acknowledge funding from the Australian Research Council via the Discovery–Projects programme. This work was performed in part at the Melbourne Centre for Nanofabrication, an initiative partly funded by the Commonwealth of Australia and the Victorian Government.

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