Nanolaminates built from ultra-thin, ultra-smooth films of amorphous metals, and solution-processed oxides represent a new platform for dispersion engineering. Materials exhibiting anisotropic elliptical dispersion and hyperbolic dispersion with positive refraction are realized through choice of amorphous metal and laminate design. Transmission electron microscopy (TEM), X-ray photoelectron spectroscopy (XPS), polarized reflectance measurements, and effective medium theory are combined to demonstrate the precision and predictability of the fabrication techniques and optical properties from ultra-violet to infra-red frequencies.
Engineering anisotropic dielectric response through amorphous laminate structures.
Dispersion engineering is defined in the context of this contribution as the control of electromagnetic radiation through material dielectric properties. The dawn of dispersion engineering can be traced to early attempts to focus electromagnetic radiation in the optical frequency range. Indeed, evidence exists suggesting crystalline lenses were fabricated by ancient Egyptians 1. A significant advance in dispersion engineering occurred in 13th century Italy with the development of spectacles, greatly expanding the reach of the printed word 2.
In modern times, interest in dispersion engineering has been renewed around the concept of negative refraction through isotropic dispersion 3. The mathematical treatment of electromagnetic radiation through Maxwell's equations provided evidence that negative refraction could, e.g., produce a perfect lens if a suitable material could be fabricated. The turn of the 20th century saw the mathematics describing negative refraction modernized 4, which in turn catalyzed intense efforts to fabricate new materials and measure negative refraction. Most of these studies have been focused on materials structures with a high degree of fabrication complexity. Recognition of laminate material anisotropy provided the breakthrough concept necessary to fabricate materials exhibiting anomalous dispersion 5, 6 and to produce precisely measurable dispersion effects. Recent dispersion engineering literature describing anisotropic materials systems exhibiting anomalous dispersion of incident light has increased dramatically since 2002 7–13.
In this contribution, we address dispersion engineering through fabrication and study of new nanolaminates containing thin amorphous-metal and solution-processed-oxide films. We have recently described the materials properties and film interfacial chemistry of these highly regular laminated structures 14. The smooth and pristine interfaces between the amorphous metal and oxide have also enabled the realization of high-performance metal–insulator–metal diodes 15. These findings have prompted us to examine their behavior as a new type of anisotropic dielectric medium.
To appreciate the advances in dispersion engineering enabled by these amorphous composite materials, we first describe the differences between isotropic and anisotropic dispersion. The following discussion of dispersion is focused on non-magnetic materials (µ = 1). Additionally, the materials described are planar in nature and are represented by an abrupt change in index of refraction in the z direction as light passes into the plane of the material. In planar structures with small out of plane scattering, momentum is conserved to a single plane represented by two dimensions. The mathematics used to describe the dispersion effects observed in planar structures are, therefore, presented in two dimensions.
The dielectric response, ε, of a planar isotropic material that does not exhibit directional dependence is described as
where kxy is the light's momentum component in the plane of the material, kz the momentum component orthogonal to the material interfaces, n the material's index of refraction, ω the angular frequency of the light, and c is the speed of light in vacuum. The engineered dispersion of incident light is accomplished solely through the modulation of ε, which is a complex number varying with the frequency of the incident light. As light encounters a change in ε, as it passes from free space (ε = 1) to a material with ε ≠ 1, the direction of the light's momentum (K) changes due to a magnitude change in the z component of the light's momentum (kz). The Poynting vector (S) represents the direction of energy flux, and is coincident with K in an isotropic dielectric material. Figure 1(a) illustrates the response of light as it passes into an isotropic dielectric material from air. The described dispersive effect, through the use of isotropic dielectric materials with ε ≠ 1, is the means through which light was manipulated via dispersion engineering by the ancient Egyptians 1.
The dielectric response of layered, anisotropic, dielectric materials has two components; εxy in the plane of the material interfaces and εz orthogonal to the plane of the material interfaces. Anisotropic dispersion is exhibited only with TM polarized light. TM polarization stipulates that the magnetic field vector is parallel to the material plane as shown in Fig. 1(b) and (c). The electric field in TM polarized light is influenced by both components of the material dielectric response. Two dielectric response components lead to a dispersion equation
where εz is the dielectric response orthogonal to the material plane and εxy is the dielectric response in the material plane. A condition of anisotropic dispersion is that εz ≠ εxy. Isotropic and anisotropic materials may possess dielectric responses with real components being either positive or negative polarity. A negative real component of a dielectric response is typically indicative of a metallic material in which electromagnetic waves decay due to the fast rearrangement of free charge.
The mathematics describing an anisotropic material possessing two distinct dielectric responses, εz and εxy, allow for three distinct dispersion effects based on the polarity of Re(εz) and Re(εxy). Figure 1(b) illustrates anisotropic, elliptical dispersion which occurs when both Re(εz) and Re(εxy) are positive. Anisotropic, elliptical dispersion separates K and S as light propagates in the anisotropic material. Anisotropic, hyperbolic dispersion, presented in Fig. 1(c), occurs when Re(εz) and Re(εxy) possess opposite signs. Negative refraction occurs when Re(εz) < 0 and Re(εxy) > 0, whereas hyperbolic dispersion with positive refraction occurs when Re(εz) > 0 and Re(εxy) < 0. Anisotropic materials fabricated in this research possess measured reflectance characteristic of both anisotropic, elliptical dispersion, and hyperbolic dispersion with positive refraction.
The amorphous metal thin films were deposited using three-inch vacuum-arc-melted multi-component metal targets purchased from Kamis Inc. with stoichiometric compositions of Zr40Cu35Al15Ni10 and Ti25Al75. DC magnetron sputtering was employed at a power of 60 W, a pressure of 3 mTorr, and a 20 sccm flow of Ar gas. To investigate the lower thickness limit of deposited amorphous metal films below 10 nm, the deposition power was lowered to 30 W with the remaining parameters held constant.
AlPO solution precursors for the amorphous oxide layers were prepared as previously described by Meyers et al. 17 to a 0.1 M concentration of aluminum with nitric acid as the strong acid. An aluminum to phosphate ratio of 5:3 was chosen for all films. The solution was spin-coated onto the AMMF at a speed of 3000 RPM for a duration of 30 s, followed by a treatment at <300 °C for 1 min on a hotplate under ambient atmospheric conditions. All samples were prepared on 1 inch × 1 inch coupons of thermally oxidized silicon prepared by Hewlett Packard's campus in Corvallis.
XPS measurements were performed in a Physical Electrons Quantera Scanning ESCA Microprobe with a focused monochromatic Al Kα X-ray (1486.7 eV) source for excitation. The X-ray beam used was a 40 W, 200 µm X-ray beam spot at the sample. The sputter depth profile data were acquired at grazing incidence with the samples at <20° relative to the detector. The binding energy (BE) scale was calibrated using the Cu 2p3/2 feature at 932.62 ± 0.05 eV and Au 4f at 83.96 ± 0.05 eV. The ion gun used in this system was a standard Quantera ion gun, and the sputter depth profiles were acquired using a 1 keV argon-ion beam rastered over a 3 mm × 3 mm area. To minimize charging artifacts, the XPS data were collected with 1 eV, 20 µA electrons and low-energy Ar+ ions. The XPS data were reduced using a linear least squares procedure to differentiate the oxidation states of the materials 18. The atomic concentrations were calculated using relative sensitivity factors that were not corrected to reflect any preferential sputtering of the materials during the analysis.
The samples for TEM analysis were coated with carbon (vacuum evaporator, 30 s) and iridium (sputtered, 2.5 min) as protective masks. Cross-section samples were then prepared using a standard focused ion beam (FIB) in situ lift out process in an FEI DualBeam 235 system. The FIB preparation involved patterning of a 1 µm thick membrane using a 30 kV Ga+ ion beam after which the sample was transferred to a copper-grid using a micromanipulator inside the FIB system. Once attached to the copper grid, the membrane was further milled to an electron transparent thickness (<100 nm). The preparation was completed by milling both sides of the sample with a 5 kV Ga+ ion beam at a glancing angle of 6°. TEM and electron diffraction analysis was performed in a JEOL JEM2500SE analytical TEM/STEM employing a 200 kV accelerating voltage.
The artistic overlays onto TEM images were completed by utilizing raw image files from the JEOL JEM25500SE TEM. The scale bars from the raw image files were copied and separated from the original images into separate layers using Adobe Photoshop. Image cropping and rotation was then performed with the copied scale bar remaining unchanged. XPS data was then overlaid upon the images and relatively sized for effect. The data was intuitively overlaid to clearly demonstrate the congruency of the measurements taken. Added dimension bars were measured by calibrating pixel dimensions using the copied original scale bar.
Polarized reflectance measurements were performed using a J.A. Woollam variable angle spectroscopic ellipsometer (VASE). Incident light was generated by a wide spectrum xenon light source, and polarized to TE and TM polarizations using a linear polarizer. Reflectance measurements of both TE and TM incident light were recorded at wavelengths between 300 and 1500 nm and incident angles between 20° and 80° at 5° increments. A baseline (straight-through) reference scan was collected at the beginning of the measurement, as there is no reference beam in this experimental setup. The dielectric responses of optically thick samples were calculated using a non-linear least squares fit of the reflectance data at each wavelength across the 13 unique angular measurements.
3 Results and discussion
To assess the optical dielectric properties of the amorphous metal/oxide laminates, structures containing ten bilayers were fabricated. Two amorphous metals, ZrCuAlNi and TiAl3, and amorphous aluminum phosphate oxide (AlPO) were used to fabricate the stacks. The use of two different amorphous metals allows us to attribute differences in dielectric properties to the effects of the amorphous metals.
Materials analysis data for a ten bilayer TiAl3/AlPO laminate structure are given in Fig. 2. As seen in Fig. 2(a), highly ordered structures and well-defined interfaces are realized with a bilayer thickness of 16 nm. During the transmission electron microscopy (TEM) imaging, the extent of the TEM sample was inspected for defects. No defects were revealed. Therefore, the image is representative of the laminate across a larger area than shown in the figure. Our overall experience with the laminates indicates that they are homogeneous over the surface of the substrate. Diffuse rings are observed in the diffraction pattern of Fig. 2(b), providing evidence that the laminate is amorphous. X-ray photoelectron spectroscopy (XPS) depth profiling was performed through a laminate fabricated concurrently with the laminate presented in Fig. 2(a) to generate the overlaid XPS data shown in Fig. 2(c). The image reveals that the bilayer composition profile is faithfully repeated through the structure. The same high level of bilayer material repeatability is observed in ZrCuAlNi/AlPO laminates, as has been previously reported 14. Existing examples of dispersion engineering at optical frequencies via amorphous materials (glass lenses) have been successful, in part, because of the ease and reproducibility of amorphous material systems. The extension of dispersion engineering through amorphous laminate materials benefits from the same amorphous fabrication advantages. Precisely repeated bilayer thicknesses and stoichiometries are essential for the realization of high quality metamaterials.
Amorphous metal films, as presented in Fig. 3, have been deposited via DC magnetron sputtering as ultra-smooth, homogenous films with a minimum thickness of 2 nm. Oxidation of an amorphous metal film deposited via sputtering occurs at interfaces above and below the film 14. Below the film, the energy of sputter deposition supplies the driving force of oxidation, creating the sputter oxide shown in Fig. 3. The native oxide, on top of the deposited film, occurs when the film is exposed to ambient oxygen as substrates are processed using the solution deposition of amorphous oxide films. Both the sputter oxide and native oxide of amorphous metal films are repeatable in thickness, when deposition process conditions are consistent, as revealed via the XPS profile shown Fig. 2(c). Repeatable oxidation leads to repeatable thin film thicknesses, which allows for the use of amorphous metal films in anisotropic dielectric laminate materials. Amorphous oxide films, deposited via solution processing, have minimum thicknesses less than 3 nm 16. The minimum bilayer thickness (i.e., thickness of amorphous metal and amorphous oxide films) is limited by the oxidation of the amorphous metal, and is on the order of 10 nm. Laminates fabricated with bilayers of 10 nm thickness satisfy the quasi-static condition for light in the deep UV regime, i.e., ≤193 nm.
Effective medium theory predicts spatially averaged values of a laminate structure's dielectric response when the bilayer thickness of the laminate is significantly smaller than the wavelength of incident light 9. Under this condition of bilayer thickness, a quasi-static state is established, where the incident light is affected by the average dielectric responses of the laminate material. The spatial averaging of distinct, isotropic dielectric responses of amorphous metals and oxides into two anisotropic dielectric responses defines εz and εxy for TM polarized light as
εm and dm are the dielectric response and film thickness, respectively, of the amorphous metal layer, and εo and do are the dielectric response and film thickness, respectively, of the amorphous oxide layer.
Effective medium theory modeling of ZrCuAlNi/AlPO and TiAl3/AlPO laminates reveals the anisotropic dielectric responses, εz and εxy, of the two laminate materials. Effective medium modeling employs dielectric responses calculated through the use of polarized reflectance data collected from bulk amorphous metal and AlPO films. The polarized reflectance data are gathered using linearly polarized TM light of wavelengths between 300 and 1500 nm and incident angles between 20° and 80° at 5° increments. The dielectric responses of optically thick amorphous metal samples and AlPO films are calculated using a nonlinear least squares fit of the reflectance data at each wavelength across the 13 unique angular measurements. The resulting dielectric responses were verified through a comparison to spectroscopic ellipsometry measurements on the same bulk films. Both measurement techniques, polarized reflectance and spectroscopic ellipsometry, produced the same dielectric responses. The thickness of each layer is also input into the model. The calculated anisotropic dielectric responses of the laminates, as well as the calculated isotropic dielectric responses of the amorphous metals and oxide are presented in Fig. 4. The shaded yellow region above 600 nm in Fig. 4(a) and below 350 nm in Fig. 4(b) are frequency ranges where TM polarized incident light exhibits anisotropic hyperbolic dispersion with positive refraction. The remainder of the measured frequencies exhibit anisotropic elliptical dispersion.
The real components of the bulk, isotropic dielectric responses from optically thick ZrCuAlNi and TiAl3 provide insight into the flexibility of the described amorphous dispersion engineering materials platform. Re(εm) decreases from −1 to −6 for ZrCuAlNi, whereas the dielectric response of TiAl3 increases from −7 to −3 across the identical wavelength range between 300 and 1500 nm. The dissimilar dielectric responses of optically thick ZrCuAlNi and TiAl3 films are input into effective medium mathematics (Eqs. (3) and (4)) to produce two distinct dielectric responses. The resulting anisotropic dielectric response of TiAl3/AlPO exhibits hyperbolic dispersion below a distinct frequency, i.e., a lowpass filter with a corner frequency wavelength of 350 nm, while the anisotropic dielectric response of ZrCuAlNi/AlPO exhibits hyperbolic dispersion above a distinct frequency, i.e., a highpass filter with a corner frequency wavelength of 590 nm. The distinct, anisotropic dielectric responses of the two amorphous metal/oxide laminates illustrates the ability to engineer dispersion characteristics based on the bulk dielectric responses of the individual layers. Through investigations into the dielectric responses of different amorphous layer materials, a toolbox of material components is created. Increased diversity of the available toolbox materials will directly increase the breadth of performance achievable with anisotropic dispersion materials.
The impact of the laminate metal/dielectric thickness ratio on Re(εxy) is illustrated in Fig. 4. Equation (4) reveals the magnitude of Re(εxy) to be thickness scaled values of Re(εm) and Re(εo). Decrease of the metal/dielectric thickness ratio moves Re(εxy) in a positive direction, i.e., shifts Re(εxy) up. Conversely, an increase of the metal/dielectric thickness ratio will move Re(εxy) in a negative direction, i.e., shift Re(εxy) down.
The data presented in Fig. 4 illustrate the described modulation of Re(εxy) through the use of different metal/dielectric ratios. The metal/dielectric thickness ratio in the measured ZrCuAlNi/AlPO laminate is 1:1. As expected from Eq. (4), Re(εxy) is seen to be the arithmetical mean of εm and εo. The ratio of metal-to-dielectric thickness in the measured TiAl3/AlPO laminate is lower, i.e., less metal. Therefore, Fig. 4(b) places Re(εxy) closer to the dielectric response of AlPO than to the dielectric response of TiAl3. Modulating Re(εxy) at a specific wavelength is accomplished through simply changing the layer thickness to change the metal/dielectric ratio. Therefore, anisotropic dispersion materials can be engineered to possess specific dispersion characteristics as required by targeted applications.
The control of Re(εz) is not as simple as the control of Re(εxy). Equation (3) contains the multiplication of two complex responses, εm and εo. Therefore, modulation of Re(εz) is influenced by the imaginary components of the bulk material dielectric response as well as layer thickness. Re(εz) is modulated in a negative direction by minimizing the amorphous metal loss and/or increasing the real component of the oxide dielectric response. The selection of amorphous materials and the scaling of layer thicknesses, therefore, enables precise control of the anisotropic dielectric responses, Re(εxy) and Re(εz), of amorphous laminate structures.
Alignment between measured and modeled reflectance data from a laminate structure provides an assessment of laminate structure metal/dielectric thickness ratio. The inputs into the laminate structure reflectance model, as described by Eqs. (3) and (4), are the dielectric response and thickness of the laminate component layers and the silicon/silicon dioxide substrate layers. These values are employed in a transfer matrix calculation to model the reflectance expected from the air/laminate interface. The polarized reflectance of the laminate structures is also measured at wavelengths between 300 and 1500 nm and at angles of incidence between 20° and 80° at 5° increments. The calculated anisotropic dielectric response of the laminate structure is determined with the bulk dielectric responses and the layer thicknesses via Eq. (4). The alignment between the measured and modeled data is used as a confirmation of the metal-to-dielectric thickness ratio, and therefore serves as a metrology tool for the fabrication of laminates exhibiting anisotropic dielectric response. The metric through which measurement-to-model alignment is evaluated is defined as
where Rmeas is the measured reflectance value and Rmodel is the modeled reflectance value at a specific wavelength. The normalized error metric provides a single value across all wavelengths (300–1500 nm) at each angle of incidence.
By changing the metal and dielectric thicknesses input to Eq. (4), the modeled reflectance is changed, which, in turn, changes the normalized error. The change in normalized error with respect to metal/dielectric ratio is presented in Fig. 5. The metal/dielectric ratio at which the normalized error data is equal to zero is the convergence point of the model and measurement data, and represents the best estimate of actual metal/dielectric ratio. Figure 5(a) is comprised of data from a ZrCuAlNi/AlPO laminate, while Fig. 5(b) is comprised of data from a TiAl3/AlPO laminate. Normalized error data from both laminate structures behave similarly with respect to metal/dielectric ratio. For dielectric rich ratios, the modeled reflectance data are of lesser magnitude (less predicted reflectance) than the measurements suggest. Therefore, the normalized error metric is positive for dielectric-rich metal/dielectric ratios. Conversely, for metal-rich ratios, the model data predict more reflectance than measured, leading to a negative normalized error. Both conditions are consistent with expected higher reflection from metals and lower reflection from oxide dielectrics.
As noted above, the processing steps lead to oxidation of the amorphous-metal film, which diminishes the effective thickness of the metal. The normalized error analysis, combined with the XPS profile data through the laminate structures, provides insight into the un-oxidized elemental metal content required for an amorphous metal film to behave as a metal. At un-oxidized metal content equal to or greater than the level determined through effective medium modeling, the amorphous metal film possesses the measured bulk metallic dielectric response. An XPS depth profile for a ZrCuAlNi/AlPO laminate structure is represented in Fig. 6(a). The horizontal green and black lines, representing metal and oxide film thickness, respectively, are exactly the same length. The normalized error zero crossing predicts a 1:1 thickness ratio of metal to dielectric. The total metal content is approximated by adding the atomic concentration of the four metal constituent XPS signals (Zr 3d, Cu 2p3, Al 2p, and Ni 2p3) at the interfacial location determined by the equivalently scaled horizontal lines. Using this methodology, the total metal content is estimated as 20%. The ZrCuAlNi film behaves as a metal when 20% of the elemental components remain unoxidized.
The initial analysis of XPS data collected from the ten bilayer TiAl3/AlPO laminate revealed metal-to-oxide ratios that were not in alignment with the expected ratios based on deposition rate characterization. The amorphous metal depositions had targeted thicknesses of 8 nm, which would have produced 16 nm bilayers with equal proportions of metal and oxide similar to the ZrCuAlNi/AlPO laminate. The XPS analysis presented in Fig. 6(b) shows the unoxidized metal to be 31% of bilayer thickness instead of 50%. TEM analysis confirms that the XPS profiles provided an accurate metal/oxide thickness ratio in the laminate, as illustrated by the overlay of XPS and TEM data in Fig. 2(c). The observed reduction of un-oxidized metal thickness is consistent with observations across a variety of amorphous metal/oxide laminates. As discussed, oxidation of the amorphous metal occurs at interfaces on both sides of the amorphous metal layers. The interface created through the deposition of amorphous metal onto the AlPO layer contains oxides of Ti4+ and Al3+ created with the energy supplied from the sputter deposition. The interface on top of the amorphous metal layers contains a native oxide comprised of Ti4+ and Al3+ which is formed through the exposure of the amorphous metal layers to air during sample transport from the sputter tool to the spin coater. The TiAl3 formed a thicker native oxide layer than the ZrCuAlNi native oxide, which reduced the metal/dielectric ratio of the laminate bilayers.
The ability to precisely measure a material's relevant characteristics is a requirement for a materials platform to be suitable for high volume manufacturing. Whereas the material analysis presented in Fig. 2 is precise, the use of TEM imaging and XPS depth profiling is not an ideal metrology tool in high volume manufacturing due to the complexity of the analysis. An investigation into polarized reflectance as a precise dispersion measurement technique for amorphous metal/oxide laminates shows that reflectance data easily evaluates anisotropic dispersion, and serves as the basis for effective medium theory based modeling. The characterization of thin-film amorphous metal/oxide laminates through polarized reflectance measurements, materials analysis, i.e., XPS and TEM, and effective medium modeling provides a robust picture of the predicted anisotropic optical dielectric response of amorphous metal/oxide laminates.
In summary, we have demonstrated the ability to precisely control and measure the anisotropic dispersion characteristics of amorphous metal/oxide laminate materials. Through the modulation of the individual layer bulk dielectric responses and thicknesses, we are able to predict the anisotropic dispersion responses with respect to incident light wavelength and angle through the use of effective medium modeling. The alignment between material analysis and polarized reflectance measurements taken on fabricated laminate composites comprised of TiAl3 or ZrCuAlNi amorphous metal and amorphous AlPO dielectric bilayers confirm that polarized reflectance is a sensitive metrology tool able to monitor metal/dielectric ratio. Precise control of a laminate metal/dielectric ratio coupled with the differing dispersion responses of the two materials allows the resulting anisotropic dispersion to be engineered. The use of simple fabrication techniques, DC magnetron sputtering and aqueous solution deposition, illustrates the utility of amorphous metal/oxide laminates as a dispersion engineering platform that may be employed in large-area, low-temperature applications. Further development of the reported dispersion engineering platform will expedite the achievement of widespread anisotropic dispersion applications.
This material is based upon work supported by the National Science Foundation under Grants No. CHE-0847970 and CHE-1102637. The authors would like to thank Professor Brady Gibbons at Oregon State University for ellipsometry and reflectance measurements, Peter Eschbach of Hewlett Packard ADL Labs for TEM support, and CAMCOR for the TEM image used in Fig. 1(c).