Low-loss metasurface optics down to the deep ultraviolet region

Shrinking conventional optical systems to chip-scale dimensions will benefit custom applications in imaging, displaying, sensing, spectroscopy, and metrology. Towards this goal, metasurfaces—planar arrays of subwavelength electromagnetic structures that collectively mimic the functionality of thicker conventional optical elements—have been exploited at frequencies ranging from the microwave range up to the visible range. Here, we demonstrate high-performance metasurface optical components that operate at ultraviolet wavelengths, including wavelengths down to the record-short deep ultraviolet range, and perform representative wavefront shaping functions, namely, high-numerical-aperture lensing, accelerating beam generation, and hologram projection. The constituent nanostructured elements of the metasurfaces are formed of hafnium oxide—a loss-less, high-refractive-index dielectric material deposited using low-temperature atomic layer deposition and patterned using high-aspect-ratio Damascene lithography. This study opens the way towards low-form factor, multifunctional ultraviolet nanophotonic platforms based on flat optical components, enabling diverse applications including lithography, imaging, spectroscopy, and quantum information processing.

The scarcity of dielectric materials that are characterized by low optical loss at higher frequencies and simultaneously amenable to high-aspect-ratio nanopatterning has impeded the development of metasurfaces for applications in the ultraviolet (UV) range, a technologically important spectral regime hosting diverse applications in lithography, imaging, spectroscopy, time keeping, and quantum information processing [17][18][19] . To date, metasurfaces designed for operation in the near-UV range (UV-A; free-space wavelength range: 315 nm ≤ λ 0 ≤ 380 nm; energy range: 3.26 eV ≤ E 0 ≤ 3.94 eV) have been implemented using niobium pentoxide (Nb 2 O 5 ), down to an operation free-space wavelength of λ 0 = 355 nm 20 . Crystalline Si has been used to realize metasurfaces operating down to λ 0 = 290 nm 21 , a wavelength that falls within the mid-UV range (UV-B; 280 nm ≤ λ 0 ≤ 315 nm; 3.94 eV ≤ E 0 ≤ 4.43 eV), but the device efficiencies remain limited by the severe absorption loss associated with illumination frequencies above the bandgap of Si (E g ≈ 1.1 eV). In both studies, the demonstrated functionalities are limited to hologram generation and beam deflection, while other important wavefront shaping functionalities that can be empowered by optical metasurfaces, such as high-numerical-aperture focusing and structured beam generation, have not yet been achieved. Meanwhile, metasurfaces that can operate at even higher frequencies, such as within the deep-UV range (longer wavelength portion of UV-C; 190 nm ≤ λ 0 ≤ 280 nm; 4.43 eV ≤ E 0 ≤ 6.53 eV), have not been realized due to the challenge of identifying a dielectric material that has a suitably low optical absorption coefficient in that range and can be patterned into high-aspect-ratio nanostructures using the available nanofabrication techniques.
Here, we report high-performance dielectric metasurfaces that operate over a broad UV range, including within the record-short, deep-UV regime, and perform representative wavefront shaping functionalities. The constituent nanostructured elements of the metasurfaces are formed of hafnium oxide (HfO 2 )-a UV-transparent, high-refractive-index dielectric material. Although HfO 2 has been commonly exploited as a high-static-dielectricconstant (high-κ) material in integrated circuit fabrication 22,23 , its applications in photonics have largely been limited to optical coatings based on planar thin films, in particular due to the difficulty of patterning the material into high-aspect-ratio nanostructures. In this work, we overcome this limitation and use HfO 2 , for the first time, to implement meta-devices operating in the UV and deep-UV regimes. We deposit high-quality, UV-transparent HfO 2 films using low-temperature atomic layer deposition (ALD) and pattern the films using a high-aspect ratio, resist-based Damascene lithography technique [24][25][26] . We implement metasurfaces designed for operation at three representative UV wavelengths of 364, 325, and 266 nm, which perform a variety of optical functions, namely, high-numerical-aperture lensing, accelerating beam generation, and hologram projection, including under spin control for the last two applications. This achievement opens the way for low-form-factor and multifunctional photonic systems based on UV flat optics, and suggests promising applications in photolithography, highresolution imaging, UV spectroscopy and quantum information processing.

Material choice and fabrication approach
The implemented metasurface devices consist of HfO 2 nanopillars of either circular or elliptical in-plane crosssections (Fig. 1a), densely arrayed on a transparent UVgrade fused silica substrate with a low refractive index ( Supplementary Information, Fig. S1). The choice of HfO 2 -a material most commonly exploited for its high static dielectric constant as a transistor gate insulator in complementary metal oxide semiconductor (CMOS) integrated circuits-is guided by the promise of both a large refractive index (n > 2.1 for λ 0 < 400 nm) and a wide bandgap E g = 5.7 eV (λ g = 217 nm) located well within the deep-UV range, leading to a negligible extinction coefficient (k ≈ 0) for λ 0 ≥ λ g . Although the requirement of nanopillar dimensions with a wavelength-scale height (several hundred nanometers), a subwavelength-scale inplane circle diameter or ellipse minor axis (few tens of nanometers), and vertical sidewalls suggest that pattern transfer with a directional dry-etching technique such as reactive ion etching would be optimal, we were unable to identify a suitable high-aspect-ratio, dry-etching chemistry for HfO 2 (a material commonly patterned by nondirectional wet chemical etching 27 ). We instead explore the use of Damascene lithography [24][25][26] for HfO 2 metasurface fabrication, a process that involves first patterning resist using electron beam (e-beam) lithography, conformally filling the open volumes of the resist template with HfO 2 using ALD, back-etching the over-coated HfO 2 layer using argon (Ar) ion milling, and finally removing the remaining resist with solvent to form the required highaspect-ratio nanopillars (see "Materials and methods").
The preservation of the physical integrity of the resist template requires the use of a plasma-free thermal ALD process with a process temperature, T p , lower than the glass transition temperature (reflow temperature) of the utilized resist, T g , along with a process chemistry involving by-products that are not corrosive to the resist. Fulfilling both process tolerance requirements rules out the use of common Hf precursors such as Tetrakis (ethylmethylamino)Hafnium (TEMAH) 28 , for which the minimum T p (≈150°C) is significantly higher than the T g of common e-beam resists, or hafnium chloride (HfCl 4 ) 29 , for which the reaction by-product (HCl) attacks the resist. Instead, we investigate Tetrakis(dimethylamino)Hafnium (TDMAH) 30 as an alternative Hf precursor for thermal ALD of high-optical-quality HfO 2 , using a T p below the T g of common e-beam organic resists (such as ZEP, for which T g ≈ 105°C). To avoid the risk of incomplete reaction cycles and the physical condensation of precursors associated with low-temperature ALD (yielding films with defects and voids, and hence, degraded subbandgap optical properties, such as a reduced refractive index n and finite extinction coefficient k), an existing ALD process which uses TDMAH and H 2 O precursors and operates at T p = 200°C is modified (Fig. 1b) by (1) decreasing the process temperature to T p = 95°C; (2) increasing the TDMAH pulsing time, t 1 , from 0.25 to 1 s to enable a complete reaction with the OH monolayer resulting from the previous cycle; and (3) increasing the N 2 purging times, t 2 and t 4 , from 12 to 75 s to ensure full removal of the excessive precursors and reaction byproducts (see "Materials and methods"). As revealed by X-ray diffraction characterization (Supplementary Information, Section II) and spectroscopic ellipsometry measurements ( Fig. 1c and Supplementary Information, Section III), HfO 2 films deposited using the modified low-temperature ALD process are amorphous and characterized by a high refractive index (n > 2.1) and negligible optical loss (k ≈ 0) over a UV wavelength interval 220 nm ≤ λ 0 ≤ 380 nm spanning the full mid-UV and near-UV ranges and more than half of the deep-UV range. The measured wavelength dependences of n and k closely match those of a film grown using the 200°C reference ALD process ( Supplementary Information, Fig. S4), demonstrating that the optical quality of the deposited HfO 2 can be maintained at significantly lower ALD process temperatures with a suitable Hf precursor and a proper adjustment of the pulsing and purging times. Note that the 95°C-ALDdeposited HfO 2 films exhibit a high refractive index (n > 2.0) and zero optical loss (k = 0) in the visible range (380 nm ≤ λ 0 ≤ 800 nm), making the films suitable for the fabrication of low-loss metasurface devices in this wavelength range as well ( Supplementary Information, Fig. S5).
Using ZEP resist for e-beam lithography and the lowtemperature TDMAH-based ALD process for the HfO 2 deposition, the proposed Damascene fabrication process is applied to yield defect-free metasurfaces, each consisting of a large array of densely packed HfO 2 nanopillars on a UV-grade fused silica substrate (Fig. 1f). The nanopillars have uniform heights, circular (Fig. 1d Fig. 1 Implementation of ultraviolet metasurfaces. a Schematic representation of a metasurface unit cell, consisting of a high-aspect-ratio HfO 2 pillar with height H, an elliptical cross-section (principle axis lengths D 1 and D 2 ), and rotation angle θ, arranged on a SiO 2 substrate to form a square lattice with a subwavelength lattice spacing P. Specific optical functions are implemented via the variation in D 1 , D 2 , and θ as a function of the nanopillar position within the lattice. b Schematic representation of the developed low-temperature ALD cycle using the TDMAH precursor, H 2 O reactant, and a process temperature of T p = 95°C. c Refractive index n and extinction coefficient k of the as-deposited HfO 2 film, measured using spectroscopic ellipsometry. The values of n at the three operation wavelengths targeted in this study are denoted by yellow stars. The dashed line indicates the position of the HfO 2 bandgap E g . d Scanning electron microscopy (SEM) image of the details of a fabricated polarization-independent metalens designed for operation at λ 0 = 325 nm, showing a lattice of 500 nm tall, circularly shaped HfO 2 nanopillars with various diameters. The viewing angle is 52°. e SEM image of the details of a fabricated spin-multiplexed metahologram designed for operation at λ 0 = 266 nm, showing a lattice of 480 nm tall, elliptically shaped HfO 2 nanopillars with various in-plane cross-sections and rotation angles. The viewing angle is 52°. The nanopillars are coated with a layer of Au/Pd alloy (≈5 nm thick) to suppress charging during SEM imaging. f Optical micrographs of the full metalens (top panel) and spin-multiplexed metahologram (bottom panel) corresponding to the metasurfaces described in d, e, respectively. Scale bars: 100 µm in-plane cross sections, and are characterized by straight, vertical, and smooth sidewalls (Fig. 1d, e, and Supplementary Information, Figs. S7-S11). The nanopillar rotation angle and two principle axis lengths in the plane of the metasurfaces (θ, D 1 , and D 2 , respectively, where θ = 0 and D 1 = D 2 = D in the case of a circular crosssection) vary as a function of the nanopillar position (with 0 ≤ θ < π and 50 nm ≤ (D 1 , D 2 ) ≤ 160 nm) depending on the optical function implemented by the metasurface. The nanopillar height H varies depending on the operation wavelength of the metasurface (400 nm ≤ H ≤ 550 nm).
We first demonstrate lenses, self-accelerating beam generators, and holograms based on polarizationindependent metasurfaces consisting of nanopillars with in-plane circular cross-sections, that operate at near-UV wavelengths of 364 and 325 nm (corresponding to emission lines of argon-ion and helium-cadmium lasers, respectively) with efficiencies up to 72%. Further exploiting the high patterning fidelity of the Damascene technique and leveraging the negligible optical loss of the as-deposited HfO 2 dielectric material across most of the UV regime, we scale down the metasurface critical dimensions to realize polarization-independent holograms operating at a deep-UV wavelength of 266 nm (corresponding to the emission line of an optical parametric oscillator pumped by a nanosecond Q-switched Nd:YAG laser), with relatively high efficiencies (>60%). Finally, by opening up the design space with the three degrees of freedom provided by elliptically shaped nanopillars (θ, D 1 , and D 2 ), compared to the single degree of freedom provided by circularly shaped nanopillars (D), we realize spin-multiplexed metasurfaces that impart independent phase shift profiles onto light emerging from the device under illumination with left-handed circularly polarized (LCP) or right-handed circularly polarized (RCP) light. The implemented self-accelerating beam generators and spin-multiplexed metaholograms operate at UV wavelengths of 364 and 266 nm, respectively, with efficiencies up to 61%.

Polarization-independent UV metasurfaces
Each polarization-independent metasurface implemented in this study (lens, self-accelerating beam generator, and hologram) consists of a square lattice of HfO 2 cylindrical nanopillars, where the diameter of each pillar varies as a function of its position within the lattice. Each nanopillar acts as a truncated dielectric waveguide with top and bottom interfaces of low reflectivity, through which light propagates with a transmittance and phase shift controlled by the pillar height H, pillar diameter D, and lattice spacing P. For each targeted operation wavelength (λ 0 = 364, 325, and 266 nm), a corresponding pillar height (H = 550, 500, and 400 nm, respectively) and subwavelength lattice spacing (P = 200, 190, and 150 nm, respectively) are chosen, along with a range of pillar diameters that yield phase shifts varying over a full range of 2π, while maintaining a relatively high and constant transmittance ([50, 160 nm], [50, 150 nm], and [50, 110 nm], respectively). The detailed design procedure is elaborated in Supplementary Information, Section VIII.
As a first demonstration of polarization-independent UV metasurfaces, two 500-µm-diameter, polarizationindependent metalens designs, L 364 and L 325 , with an identical numerical aperture of NA = 0.6 (corresponding to a focal length of f = 330 μm), are implemented to focus UV light at respective free-space wavelengths of λ 0 = 364 and 325 nm (Fig. 2a). Singlet-mode focusing of a plane wave can be achieved by implementing the radially symmetric phase shift function φ L ðx; y; λ 0 Þ ¼ modðð2π=λ 0 Þ ðf À ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 2πÞ; where f is the focal distance normal to the plane of the lens (along the z direction), x and y are in-plane distances along orthogonal directions from the center of the lens, and normal incidence is assumed. Each measured intensity distribution at the metalens focal plane (Supplementary Information, Section IX) reveals a circularly symmetric focal spot, characterized by a cross-section that closely matches the intensity distribution theoretically predicted for a diffraction-limited lens with a numerical where J 1 is the Bessel function of the first kind of order one, and A ¼ 2πNAx=λ 0 (Fig. 2b, c). Metalens L 325 exhibits a less-than-ideal focusing profile with larger side lobes, which could be due to fabrication imperfections and a nonideal realization of the required phase shift profile. The focusing efficiencies, defined as the ratio of the optical power of the focused spot to the total power illuminating the metalens, are (55.17 ± 2.56)% (L 364 ) and (56.28 ± 1.37)% (L 325 ). The cited uncertainties represent one standard deviation of the measured data.
Next, we demonstrate polarization-independent metasurfaces that can transform a normally incident plane wave into a diffraction-free output beam propagating along a curved trajectory, i.e., a self-accelerating beam (SAB) [31][32][33] . Two 270-µm-square SAB generator designs, B 364 and B 325 , are implemented for operation at the respective wavelengths of 364 and 325 nm (Fig. 3a). The SAB generator design and operation are conveniently described using a Cartesian coordinate system in which the constituent metasurface is located in the z = 0 plane and the first xy quadrant, with one corner positioned at the origin. The implemented SAB for each targeted freespace wavelength, λ 0 = 364 and 325 nm, is characterized by an L-shaped wave-packet of the main lobe centered on the trajectory y ¼  Supplementary Information, Section X). The experimental SAB generated by each device exhibits diffractionfree characteristics with xy-plane intensity distributions similar to the intensity distributions numerically computed using the angular spectrum representation method 35 , assuming an ideal metasurface realization with both the designed phase shift profile φ B and unity transmittance T (Fig. 3c). The measured efficiencies, defined as the ratio of the total optical power of the SAB in the z = 5 mm plane to the total power illuminating the metasurface, are (46.75 ± 2.31)% (B 364 ) and (67.42 ± 4.43)% (B 325 ). The efficiencies compare favorably to that of a recently reported TiO 2 -based self-accelerating beam generator operating at visible frequencies 36 .
As a final demonstration of polarization-independent UV metasurfaces, we demonstrate three metaholograms, denoted H 364 , H 325 , and H 266 , operating at three respective UV wavelengths λ 0 = 364, 325, and 266 nm (Fig. 4a). Implementing computer-generated holograms with metasurfaces enables high-efficiency and low-noise operation, fine spatial resolution, a compact footprint, and multiplexing capability [37][38][39][40] . Each demonstrated metahologram, which occupies a square area with a side length of 270 µm, is mapped to a Cartesian coordinate system in which the constituent metasurface is located in the z = 0 plane and the first xy quadrant, with one corner positioned at the origin. The Gerchberg-Saxton algorithm 41 is employed to calculate the phase shift profiles, φ H 364 ðx; y; λ 0 Þ, φ H 325 ðx; y; λ 0 Þ, and φ H 266 ðx; y; λ 0 Þ, required to project a holographic "NIST" image located in the z = 40 mm plane, under normal-incidence, plane-wave illumination (Supplementary Information, Section XI). An additional offset of y = −3 mm is added to avoid overlap of the generated holographic image with the residual directly transmitted beam. The images projected by metaholograms H 364 , H 325 , and H 266 are measured (Supplementary Information, Sections XII and XIII) and displayed in the right panel of Fig. 4b. Each of the experimental holographic images faithfully replicates the shape of the corresponding target image (left panel of Fig. 4b), numerically computed assuming an ideal metahologram realization with both the designed phase shift profile φ H for a given operation wavelength and unity transmittance T. In addition, the speckle patterns filling the shapes of the measured images projected by metaholograms H 364 and H 325 exhibit numerous similarities with those of the corresponding target images; the as-measured holographic image projected by metahologram H 366 does not offer the possibility of such a comparison due to the employed fluorescence transduction characterization scheme, which washes out the details of the speckle patterns. The measured efficiencies for metaholograms H 364 and H 325 , defined as the ratio of the total optical power of the holographic image to the total power illuminating the structure, are (62.99 ± 4.14)% and (71.78 ± 2.06)%, respectively. The measured efficiency for metahologram H 266 , defined as the ratio of the total fluorescence power of the holographic image to the fluorescence power of the light illuminating the structure (Supplementary Information, Section XIII), is (60.67 ± 2.60)%. These efficiency values are comparable to those of recently reported TiO 2based metaholograms operating in the visible range 26 .

Spin-multiplexed UV metasurfaces
Metasurfaces have been demonstrated to switch between distinct optical outputs, such as different holographic images or differently oriented beams, under the  control of the fundamental optical state of the input beam, e.g., polarization 42,43 , or a spatial feature of the input beam such as the angle of incidence 44 . Here, we demonstrate, for the first time, spin-multiplexed UV metasurfaces that can switch between distinct outputs depending on the handedness of the input light (left-hand circularly polarized, LCP, or right-hand circularly polarized, RCP). The detailed design procedure is elaborated in Supplementary Information, Section XIV.
As a first demonstration of a polarization-dependent, spin-multiplexed UV metasurface, we implement a selfaccelerating beam generator operating at λ 0 = 364 nm, denoted as B spin 364 , that generates SABs following different trajectories under the control of the handedness of circularly polarized incident light. The spin-multiplexed SAB generator, which occupies a square area with a side length of l = 330 µm, is referenced to a Cartesian coordinate system in which the constituent metasurface is located in the z = 0 plane and the first xy quadrant, with one corner positioned at the origin. Two distinct phase shift profiles, φ LCP x; y; λ 0 ð Þ¼ , are targeted for the device operation to yield SABs exiting the metasurface from opposite corners and following different trajectories, y ¼ x ¼ Àd 1 ¼ À16z 2 and y À l ð Þ¼ x À l ð Þ¼d 2 ¼ 2:25z 2 , under LCP and RCP illuminations, respectively (Fig.  5a, d). The measured lateral displacement values, d 1 (z) and d 2 (z), are observed to closely match, in each case, the calculated values based on the targeted trajectory (Fig. 5c, d). The experimental SAB generated by the device exhibits Next, we demonstrate a spin-controlled metahologram operating at the same near-UV wavelength of 364 nm. The 330-µm-square metahologram, H spin 364 , located in the z = 0 plane, is designed to project a holographic "NIST" image (for LCP illuminating light) and "NJU" image (for RCP illuminating light) at λ 0 = 364 nm, all located in the xy-plane at z = 40 mm with an offset of y = −3 mm (Fig. 6a; the corresponding phase shift profiles are plotted in the Supplementary Information, Fig. S17). Both of the experimentally captured holographic images (Fig. 6b) faithfully replicate the shape of the corresponding targeted image computed from the designed phase profiles, including some fine grain details (Supplementary Information, Fig. S18). The measured efficiencies, defined as the ratio of the total optical power of the holographic image to the total power illuminating the metahologram, are (54.02 ± 2.22)% (under LCP illumination) and (53.76 ± 2.42)% (under RCP illumination), respectively.
Finally, a spin-multiplexed metahologram, H spin 266 , occupying a square area with a side length of 320 µm, is implemented for operation at the deep-UV wavelength of 266 nm. The device, located in the z = 0 plane, is designed to project, at λ 0 = 266 nm, a holographic "deep" image for LCP illumination and a holographic "UV" image for RCP illumination, where both images are located in the z = 40 mm plane with a lateral offset of y = −3 mm (Fig. 6c; the corresponding phase shift profiles are plotted in the Supplementary Information, Fig. S19). Each of the experimental holographic images (Fig. 6d) faithfully replicates the shape of the corresponding target image ( Supplementary Information, Fig. S20), including subtle details of the chosen font, such as the linewidth variation

Discussion
Given the negligible extinction coefficient of the lowtemperature-ALD deposited HfO 2 down to its bandgap (λ 0 ≈ 217 nm) and the high patterning fidelity of the Damascene process, it should be straightforward to push the metasurface operation wavelengths to significantly shorter values than those demonstrated here. In addition, an experimental demonstration of a broader range of device functionalities in the deep-UV regime other than hologram projection should be possible by using a continuous-wave light source and an appropriate direct imaging system. Moreover, the efficiency of HfO 2 -based metasurface devices can be improved by further optimizing the Damascene process or by employing advanced metasurface design strategies, such as topology optimization 45 and the generalized Huygens principle 46,47 .
In conclusion, an assortment of high-performance metasurface components operating in the UV regime, including wavelengths down to the record-short deep-UV range, is demonstrated by using HfO 2 , a CMOS-compatible, widebandgap, and low-loss dielectric material, and an associated fabrication process based on low-temperature ALD and Damascene lithography. This approach paves the way towards further development of "flat" UV optical elements with customized functionalities and their integration into chip-scale nanophotonic systems, enabling applications such as atom trapping, fluorescence imaging, and circular dichroism spectroscopy with a compact form factor.

Metasurface fabrication process
As the first step in the metasurface fabrication process, 500-µm-thick, double-side-polished UV-grade fused silica wafers are vapor-coated (150°C) with an adhesion-enhancing monolayer of hexamethyldisilizane (HMDS). A layer of ZEP 520A resist is spin-coated onto the substrate, followed by baking on a hot plate at 180°C for 10 min. The spin speed is adjusted to yield a resist thickness varying between 400 and 550 nm (as characterized by spectroscopic ellipsometry), depending on the specific metasurface design. To suppress charging during electron beam (e-beam) lithography, a 20-nmthick Al layer is thermally evaporated onto the ZEP layer (deposition rate of 0.1 nm/s). The ZEP-resist template is fabricated using e-beam lithography (accelerating voltage of 100 kV and beam current of 0.2 nA), followed by Al layer removal (AZ 400 K 1:3 developer for 2 min and DI water for 1 min) and resist development (hexyl acetate for 2 min and isopropyl alcohol for 30 s). The deposition of HfO 2 (deposition rate: 0.11 nm/cycle) is then performed using the low-temperature ALD described below. For all of the processed structures, the deposition thickness is chosen to be 200 nm, which not only exceeds the largest radius (or the largest semiminor axis length) of the circular (or elliptical) openings of the exposed resist patterns for all metasurface designs, providing complete filling of the patterns, but also provides a substantial over-coating of the resist, yielding a quasi-planar top surface (Supplementary Information, Section VI). Following the ALD, the HfO 2 layer is back-etched to the resist top surface using argon (Ar) ion milling (HfO 2 mill rate of ≈0.4 nm/s). During the Ar ion milling, a non-patterned, planar HfO 2 sample of the same initial thickness is also back-etched, and its film thickness is periodically monitored by spectroscopic ellipsometry to ensure that a proper milling time is employed. Finally, the remaining resist is removed by soaking in a solvent, yielding circular or elliptical HfO 2 posts with smooth and straight sidewall profiles (due to the resist templating process), heights varying from 400 to 550 nm (depending on the specific metasurface), and aspect ratios varying from ≈3 to ≈11.

Low-temperature TDMAH-based HfO 2 ALD
In step 1 of the ALD cycle, TDMAH vapor (Hf [(CH 3 ) 2 N] 4 ) is pulsed into the ALD chamber for a duration of t 1 = 1 s, reacting with the dangling O-H bonds on the hafnium-coated surface to create a new solid monolayer of Hf ðCH 3 Þ 2 N Â Ã 2 O and generate the gas by-product (CH 3 ) 2 NH (dimethylamine). In step 2, high-purity nitrogen (N 2 ) gas is flowed for a duration of t 2 = 75 s to fully remove any un-reacted TDMAH vapor and dimethylamine by-product from the chamber. In step 3, water vapor is pulsed into the chamber for a duration of t 3 = 60 ms, reacting with the Hf½ðCH 3 Þ 2 N 2 O to create a monolayer of HfO 2 on the surface. Finally, in step 4, the excessive water vapor and the dimethylamine reaction by-product are completely removed from the chamber by N 2 purging for a duration of t 4 = 75 s.