Demonstration of frequency encoding in neutral atom lithography

We demonstrate a frequency encoding technique for feature placement in atom lithography. Frequency encoding is widely used in MRI, where the frequency distribution of radio waves reveals the position distribution of nuclei in a magnetic gradient. Applied to neutral atom lithography, frequency encoding enables continuously adjustable feature positions and feature densities not limited by the optical wavelength, unlike intensity- or polarization-based patterning. Lines as narrow as 0.9 ± 0.1 μm are fabricated on silicon and gold substrates when exposed to a metastable argon beam through two mask configurations of up to six laser beams.


Introduction
Neutral atom beams patterned with masks of laser light are uniquely well-suited for structured doping [1,2] and for fabrication demanding long-range coherent registration [3,4]. Atom lithography has so far been able to make lines as small as 13 nm [5,6], to fabricate features with aspect ratios greater than 2 : 1 [7,8], and to pattern areas as large as 38 cm 2 [9,10]. However, feature spacings in light masks have been limited by the length scale of the optical wavelength used [11]- [21]. In this work, we demonstrate a technique that could be used to extend light masks to more complex patterns than standing wave interferences and to features more closely spaced than the optical wavelength.
Research in neutral atom lithography has been motivated by several considerations. Neutral atomic beams need only low kinetic energies (50 meV) to have short (<0.1 nm) de Broglie wavelengths, minimizing diffractive resolution limitations. Compared to electrons and ions, neutral atoms are insensitive to stray electric and magnetic fields, and longrange inter-particle interactions are weak. Previous work has included the development of a wealth of atom optics (mirrors, guides, etc), including light masks which, unlike physical masks, do not sag and cannot be clogged or damaged. Laser-accessible internal structure of atoms allows efficient cooling, the storage of internal energy, and complex manipulations. State-sensitive atom lithography with metastable atoms has been demonstrated with both positive-and negative-tone resists capable of sub-10-nm resolution [22,9,23]. Though atom lithography has relatively long exposure times, patterning is a parallel process, and recent work has demonstrated a tenfold acceleration possible with chemical amplification [24].
In this work, we address the difficulty of previous schemes to create arbitrary patterns. We propose the encoding of the desired position distribution using the frequency, instead of the intensity, of a laser beam. 3 In the presence of an appropriate field gradient, the resonant optical frequency of the atom can be position-dependent. Thus each spectral component of a probe laser beam can interact with the atoms at a specific but separate location. The frequency encoding of spatial information is commonly known from MRI, where protons (instead of atoms) are imaged (instead of patterned) in a potential gradient by radio-(instead of optical-) frequency radiation. We will refer to atom lithography with frequency-encoded light masks as atomic resonance lithography (ARL). Previous work by Thomas et al has developed neutral atom measurement techniques based on an analogue to nuclear magnetic resonance techniques [25,26].
Just as sub-100-µm features can be resolved with 100 m wavelength radio waves in MRI, far sub-optical (i.e., sub-micron) features and spacings can be created with ARL [25]- [27]. As shown in [27], arbitrary one-dimensional patterns can be frequency-encoded and generated. Furthermore, ARL can create two-dimensional patterns, just as MRI can image two- [28] or three-dimensional distributions: by superposing a sequence of one-dimensional distributions. Finally, frequency-encoded masks do not demand high transverse coherence of the incident atoms.
In the following sections, we present two masking configurations. The first (section 2) is a simple, single-step process, which we use to demonstrate the flexibility of patterning. After discussion of the resolution of ARL (section 3), we use a more complicated process to pattern 0.9-µm features (section 4). We discuss our results and compare to atom holography, which can also create arbitrary patterns [29]- [31]. Finally, we discuss extensions of the demonstrated lithographic technique (section 5). Figure 1 describes a realization of ARL based on quenching directly within the potential gradient. Firstly, metastable argon atoms are optically pumped to the |J = 2, m J = 2 sublevel of the 4s[3/2] o 2 or 1s 5 state. 4 Next, the atoms pass through a zone of two overlapping beams: a resonant σ + 'shift' beam (S) on the 812 nm |J = 2, m J = 2 → |J = 3, m J = 3 cycling transition overlaps with a σ − 'quench' beam (Q) containing four frequency components, ±δ 1 and ±δ 2 . As shown in figure 2(a), these frequencies are resonant at two Stark shifts (i.e., four positions) in the resonant shift beam. At these four positions, atoms are optically pumped by Q to the true atomic ground state |g , 'quenching' the internal energy. Note that two frequencies (e.g., ±δ 1 ) were required for complete optical pumping at each resonant position because atomic population exists in both the strong-and weak-field-seeking dressed states in the resonant S field. Thus, the detunings δ 1 and δ 2 control where quenching occurs. 3 In this demonstration we do, in fact, use a light beam with an intensity gradient, in addition to the probe laser. However, no information about the pattern is contained in this gradient, i.e., the same gradient could be used for different patterns. More generally, the 'field gradient' mentioned above can be a gradient in a magnetic, electrostatic, or light field. 4 A second metastable state of argon, 4s [1/2] o 0 or 1s 3 , is also produced by our source, but we eliminate those atoms with an earlier optical quenching stage. If unquenched, these 'J = 0' atoms would contribute a background rate of resistance formation. The mechanism by which internal state manipulation creates a lithographic pattern has been discussed elsewhere [8,9,24]. Briefly, the process exploits the internal energy difference between the ground state and the 4s[3/2] o 2 metastable state of argon: atoms in |m release 11.5 eV of internal energy to activate the formation of a resist on the surface, while atoms in |g do not affect the surface. The resist material is not formed out of argon, but instead from physisorbed hydrocarbons released from the diffusion pumps that evacuate the vacuum chamber. Exposure to metastable atoms induces a chemical change that results in the formation of a durable material. This resist material remains on the surface even after exposure to air and/or solution, and can thus be used as a mask for etching.

Experiment and results
A metastable argon (Ar*) beam with a flux density of 3 × 10 12 cm −2 s −1 is incident on a gold substrate for 5 h with the optical configuration of figure 1. The light mask parameters are as follows: The 5.9 mW S beam is cylindrically focused to a profile of 46 µm ×925 µm, creating a maximum Stark shift that was spectroscopically measured to be 150 MHz. Cylindrically symmetric 110 µm-wide quench beams Q 1 and Q 2 each having 70 µW of power, split between the pair of detunings, ±δ 1 = ±2π × 40 MHz and ±δ 2 = ±2π × 110 MHz. After exposure, the substrate is removed from the vacuum system and etched for 7 min in a ferricyanide solution. Figure 2 shows the correspondence between the light mask configuration and the pattern observed on the etched substrate. At positions where either Q 1 or Q 2 was resonant, metastable atoms are quenched, leaving the underlying substrate unprotected against the subsequent gold etch. At all other positions, a resist material is formed, and gold remains on the silicon substrate after etching. A pattern was formed across 2 cm of the substrate. Figure 2(b) was taken in the centre of that pattern, where atoms entered perpendicular to the light mask. We fit the sum of four Lorentzians to the integrated reflectivity profile of the substrate to determine the feature widths and positions. The lower (upper) two lines have a half-width of 10 ± 1 µm (14 ± 1 µm) and a centre-to-centre separation of 26 ± 2 µm (34 ± 2 µm). The asymmetry between the upper and lower set could be explained by aberrations in the cylindrical optics that formed the shift beam. The lower set of lines are within experimental error of the expected line width, 9 µm (as discussed below), and the expected feature separation, 27 µm. 5

Discussion: resolution limitations in ARL
The significance of the result shown in figure 2 is that two lithographic features were created across each monotonic part of the potential. Unlike previous atom lithographic results with light masks, the wavelength of light does not determine the minimum feature separation. Nor are complex potentials necessary for a complex pattern. The ultimate resolution of ARL can be limited by a variety of effects, discussed by Thomas [25] and Olshanii [27], and summarized in the following paragraphs. Note that although in microscopy the resolution is defined as the minimum distinguishable feature spacing, in this and many other lithography experiments, feature size is the only indication of resolution.

Spectroscopic limit
The most fundamental limitation is the spectroscopic precision with which each resonant transfer position is defined, where is the spectroscopic width of the transition, and F is the potential gradient. In these experiments we used laser light to create the potential gradient, but gradients could also be created with magnetic [26] or electric fields. For the realization of ARL discussed above, is the power-broadened and time-broadened quenching transition, with a natural line width = 2π × 5.83 MHz. Experimentally, we measure = 2π × 20 ± 2 MHz. For the gradient F/h = 2π × 2.3 MHz µm −1 at the feature locations in figure 2, we find δx sp = 9 µm. Note that for a Raman transition, as will be considered below, = v L /w 0 = 1/τ, where v L = 850 ± 40 m s −1 is the mean longitudinal velocity of the Ar* atoms, w 0 is the 1/e 2 intensity waist of the Raman beams, and τ is the atom-light interaction time.

Acceleration and diffraction
Atomic motion during the transfer can also limit the resolution. While transferring an atom of mass M to a state with a gradient F , acceleration and diffraction limit the resolution to the order of Fτ 2 /2M, where τ is again the transfer time [25]. However, the numerical factors depend on which states are in a gradient and for how long. In the case where is determined by the interaction time of a Raman transfer, and the pattern is formed by the atoms transferred to the gradient, one can choose an optimal τ to give a resolution of For 40 Ar and F/h = 2π × 1 MHz µm −1 , the optimal size is δx = 100 nm. This limit is not, however, fundamental: Olshanii et al show that an appropriate choice of probe frequency variation during atomic transfer (a 'magic phase') can correct for later evolution, such that the spectroscopic resolution δx sp is recovered [27]. Free flight between the pattern formation and the substrate will allow the atoms to diffract further. Given a free-flight time T FF , the diffraction limit is For instance, for T FF = 30 −1 , this limit is δx dif = 27 nm, smaller than the other limits given here. Note that this is a quantitative restatement of one of the desirable qualities of atoms as a patterning constituent: their short de Broglie wavelength λ dB minimizes the diffraction, ∼ √ λ dB D, where D is the mask-substrate separation.

Transverse coherence
Finally, the collimation of the atomic beam poses a limit on the observable resolution. Given an rms velocity spread v rms , the resolution is limited to Typical parameters for our experiment are τ + T FF = 30 −1 , and v rms = 0.5 m s −1 , and thus features cannot be smaller than δx v = 0.4 µm wide.

Second experiment: sub-micron features
In order to improve our resolution, we performed a second experiment with several experimental modifications. Firstly, we improved the quality of the optics forming the S beam to reduce the waist by a factor of 3. Next, as shown in figure 3, we used a coherent transfer scheme by detuning the S beam by 2.0 GHz and introducing Raman beams. At resonant positions in the light mask, the Raman beams transfer atoms from |m1 to |m2 . In the third interaction zone, only the atoms transferred to |m2 are quenched. 6 With such a scheme, we realized a factor of 10 improvement in resolution, as described below. Furthermore, such a coherent ARL scheme avoids momentum diffusion by spontaneous emission, and can implement further resolution improvements such as the coherent manipulations described in [27].

Two-step light mask
A silicon 100 substrate with a 15 nm oxide layer was exposed for 6 h through the ARL mask depicted in figure 3. The R beam of 25 µm by 103 µm has σ − and σ + components with powers of 65 and 60 µW and detunings of +61.1 and +104.2 MHz, respectively. A 1.3 G quantization field reduces the differential detuning by 5.4 MHz, such that the net Raman detuning is /2π = −37.7 MHz. The shift beam S has 6.9 ± 0.3 mW of power and a profile of 15 ± 1 µm × 250 µm, and is tuned δ S /2π = 2.00 GHz above resonance. The σ + polarized S beam interacts with both |m1 and |m2 , but gives a differential gradient F/h = 2π × 6.4 MHz µm −1 due to the difference in Clebsh-Gordan coefficients: 1 and 2/5, respectively (note that figure 3 shows only the transition |m1 − |e , for simplicity). The third interaction zone has a 350 µW quench beam (Q) with a waist of 210 µm, such that about 12 photons are scattered from atoms in |m2 , sufficient to optically pump to |g . Atoms that have been transferred to the |m2 state are therefore quenched. Atoms in the |m1 state are not quenched by the σ + polarized Q light, since they are in a dark state (|2, +2 ). The latter atoms arrive at the substrate in the metastable state and can therefore activate resist formation. After exposure, the pattern was transferred to the substrate using both dry and wet etches. Firstly, the sample was etched for 35 s in a CHF 3 reactive ion etch with parameters 42 mTorr chamber pressure, 100 W forward power, 10 W reflected power, −842 V self-bias, and 25.0 sccm flow rate. Secondly, the sample was etched for 50 s in 2% HF to prepare an unoxidized silicon face. Finally, the sample was etched for 14 min in 20% KOH at 22 • C [8]. Figure 4 shows a scanning electron micrograph of the etched sample. The features created by ARL are indicated by arrows. Two features are created with a single Raman detuning because the Stark shift is equal to at a location to either side of its maximum. The dark lines against a bright background indicate places at which silicon was preferentially etched. The sample was patterned across several millimetres of length. At the centre, for the run parameters above (gradient F/h = 2π × 6.4 ± 0.5 MHz µm −1 and τ = 29 ± 2 ns), the expected feature separation is 19.0 ± 1.5 µm, and the spectroscopic limit is δx sp = 0.86 ± 0.07 µm. This agrees well with our measurements: a minimum spacing of (20.0 ± 0.4) µm and an rms width of (0.9 ± 0.1) µm.

Results and discussion
It is interesting to compare these results with the features detected in holographic masking experiments for neutral atoms [29]- [31]. Holographic techniques have created intricate, twodimensional patterns, which are detected by a microchannel plate. The demonstrated resolution was 65 µm, though in principle feature size is only limited by the holes in the hologram, which can be less than 100 nm across. By comparison, our technique is a type of contact printing, where diffraction is avoided due to the small de Broglie wavelength of massive particles. Unlike holography, spatial coherence is not required across the entire mask: in fact, with a velocity spread of 0.5 m s −1 , we have a transverse coherence of only 20 nm, for a mask over 10 µm wide. Higher coherence length sources are only available at much lower flux, and thus the patterns observed in [29]- [31] were formed with less than 10 6 atoms across areas of approximately 1 mm 2 , insufficient to pattern a substrate-which typically requires over 10 15 atoms cm −2 . Thus, atom holography has not yet been used for lithography. In contrast, the patterns in figures 2 and 4 were formed after an exposure of approximately 5 × 10 16 atoms cm −2 , sufficient to pattern gold and silicon substrates.
Although µm-scale, the features shown here are still two orders of magnitude larger than the smallest features fabricated with neutral atom lithography [5]- [8]. If the light gradient were to be increased, feature sizes in the second ARL scheme demonstrated would be limited by the velocity spread of the atomic beam, at δx v = 0.4 µm. Therefore, the spectroscopically limited feature size observed in figure 4 is a factor of two above the minimum observable linewidth for the collimation of our atomic beam. By comparison, the resolution limit of an optimized light mask with a gradient of F/h = 2π × 6.4 MHz µm −1 is δx = 54 nm for Ar*.

Conclusions and prospects
In conclusion, we have demonstrated the use of frequency encoding in optical masks for atom lithography. Using a two-photon internal state transfer, we create features in silicon with an rms width of 0.9 ± 0.1 µm. With a mask based on optical pumping, we show that feature position can be chosen continuously throughout monotonic potential gradients.
The potential gradients we have used here were created by near-resonant laser light. However potentials could also be created using a magnetic field, which could be made uniform across a larger area. A magnetic gradient B would give a differential potential energy gradient F = µ B gB , where µ B is the Bohr magneton and g is the Landé g-factor. For example, the states we have been considering in argon have g ≈ 1.5, such that a gradient of 500 G cm −1 would give F/h = 2π × 0.1 MHz µm −1 . Although this gradient is lower than those used in the above experiments, using a magnetic field might be advantageous for a longer interaction time, or a larger patterned area.
We have demonstrated very simple one-dimensional patterning with a single expsoure, but as discussed in [27], arbitrary patterns can be produced up to the resolution limit of the technique. Furthermore, this technique can be extended to two-dimensional patterning with multiple exposures. This extension is similar to medical imaging with MRI, in which the potential gradient is rotated during imaging. As discussed in [28], a series of one-dimensional projections can define a two-dimensional pattern. The requirement of a series of depositions would increase the required exposure time, but not as quickly as would be required for serial writing of a twodimensional pattern: a pattern with N pixels requires writing time that scales as √ N, essentially because the writing process remains a parallel process for a one-dimensional set of pixels. Thus, ARL can be used to form intricate, sub-micron, two-dimensional patterns.
A practical issue for the experiments shown here is the exposure time. Although 5 h exposure times are acceptable for research purposes, lengthier exposures-for instance for more complex patterns-may be impractical. Recent work [24] has shown that doses as small as 3 × 10 14 atoms cm −2 are sufficient to damage self-assembled monolayers, which has been shown to be a resist for neutral atoms [22]. Thus, it may be possible to reduce the exposure time by two orders of magnitude by improving the resist used. Another approach to reducing exposure time would be to use an alkali metal source, which can be much brighter than a metastable noble gas source. Lithography using ARL and similar internal-manipulation schemes could also be extended to alkali atoms by state-selective ionization and deflection. Neutral alkali atoms, like unquenched metastable atoms, would be left to pattern an atom resist (e.g. [32]).