Inreflectance: a new function for the optimization of multilayers with absorbing materials

A new magnitude is unveiled from the fact that a multilayer can be optimized for the largest reflectance in a layer-by-layer sequence: This magnitude has been named inreflectance. Inreflectance equals the modulus of the complex reflectance once elevated to the inverse of the complex refractive index of the next outer layer, including the inclination term. The maximization of inreflectance at every internal layer, proceeding sequentially starting with the innermost layer, results in a multilayer with the largest reflectance. At a given layer in the multilayer, inreflectance is different from reflectance when the next outer material absorbs radiation, whereas the two magnitudes are coincident when the next outer layer is transparent. The outermost layer of the multilayer is intrinsically different from the internal layers, and its optimization is performed through reflectance and not through inreflectance. Every maximum of inreflectance is found at a layer thickness that is larger than that for the reflectance maximum. The new magnitude is illustrated with some examples in the extreme ultraviolet, a spectral range in which all materials absorb radiation. Inreflectance can also be used to design multilayers in which some layers have fixed thicknesses and the rest of the layers have to be optimized taking into account the fixed layers.     

General theory of sub-quarterwave multilayers with highly absorbing materials

A general theory of multilayers with enhanced reflectance has been developed based on the superposition of sub-quarterwave layers of various highly radiation-absorbing materials. The theory has been developed by second-order expansion of the multilayer reflectance with respect to the optical-constant differences between the materials in the multilayer. The current paper completes and improves the theory that was developed in a previous paper [J. Opt. Soc. Am. A 18, 1406 (2001)] by including the case of nonnormal incidence and general radiation polarization and by providing more-accurate film thickness values of the optimized multilayer than with the previous theory. The theory provides an accurate approach to the design of a new concept of multilayer coatings with more than two materials. The new multilayers are adequate to enhance the reflectance of the materials particularly in the far and the extreme ultraviolet.     

Can multilayers be optimized sequentially when radiation is partially polarized?

For radiation-absorbing materials and nonnormal incidence, multilayers with the largest reflectance at a desired wavelength are here demonstrated to require nonsequential optimization when radiation is partially polarized. The thicknesses of multilayers with the largest possible reflectance at a desired wavelength can be calculated sequentially either for s- or p-polarized radiation or for normal incidence and any polarization. The equations that impose the condition of maximum reflectance in the general case of partial polarization do not allow for the simplification that is performed when radiation is s or p polarized, which implies that multilayer optimization for partially polarized radiation is not sequential. An example is given in which the importance of nonsequential optimization is displayed. In contrast to the case of s- or p-polarized radiation, when radiation is partially polarized extra maxima may be found within an optical path difference of much less than half a wavelength.     

Mo/Si multilayers for EUV lithography by ion beam sputter deposition

Mo/Si multilayers for applications in extreme ultraviolet (EUV) lithography have been prepared on Si wafer substrates using ion beam deposition. The multilayers were characterised by transmission electron microscopy, secondary ion mass spectroscopy, atomic force microscopy, photoelectron spectroscopy, X-ray reflectometry at grazing incidence, and EUV-reflectivity measurements at nearly normal incidence. The surface and the interfaces of the multilayers are rather smooth with only small roughness. The material properties of the layers are characterised by some intermixing and silicide formation at the Mo-Si interfaces and a polycrystalline grain structure of the Mo layers, which is in agreement with prior studies. Appearance of multilayer diffraction spots, well-resolved Kiessig fringes and other diffraction evidence indicate very good coherence of the wave fields and in this manner a good reproducibility of the multilayer period of 6.7 nm. Normal incidence peak reflectivities of 64-65% in the EUV spectral range were routinely obtained at 13.4 nm wavelength. This reflectivity value and the formation of an EUV standing wave field are confirmed using photoelectron spectroscopy, and an application for defect particle analysis is proposed. The obtained results are discussed in comparison to literature data of multilayers prepared by other deposition techniques and considering new attempts of interface engineering.     

Interfacial properties and characterization of Sc/Si multilayers

We investigate the intermixing of layers in Sc/Si and Sc/B₄C/Si/B₄C multilayers using electron and synchrotron excited soft X-ray emission and absorption spectroscopy. The multilayers are annealed at 100, 200, 300, 400 and 500 °C after preparation by magnetron sputtering. Silicon K_β emission and reflectivity measurements verify that the non-annealed multilayer systems are composed of distinct layers with only a minor interdiffusion in Sc/Si samples whereas annealing Sc/Si multilayers at 400 °C leads to a degradation of the multilayer structure and the formation of intermittent scandium silicide, ScSi. The presence of B₄C barriers in Sc/B₄C/Si/B₄C hinders this degradation from developing for the entire temperature range considered. The barrier layers continue to be effective for the entire temperature range even after an extended shelf-life.     

New layer-by-layer multilayer design method

A new layer-by-layer multilayer design method is presented. The method is demonstrated mathematically and makes possible the optimization of the multilayer for the highest possible reflectance either at normal incidence or at nonnormal incidence for s- or p-polarized radiation. With the current method multilayers can be designed regardless of the number of different materials used. The optimum layer thickness is determined by means of functions suitable for implementation in a computer code. The new multilayer design method is fast and accurate.     

Effects of ion-assisted growth on the layer definition in Cr/Sc multilayers

Nano-structural evolution of layer morphology and interfacial roughness in Cr/Sc metal multilayers grown with ion assistance during magnetron sputter deposition has been investigated by high resolution transmission electron microscopy and hard X-ray reflectivity. Calculations based on a binary collision model predict an ion-assisted growth window for optimized Cr/Sc multilayer interface sharpness, within the ion energy range of 21 eV to 37 eV and an ion flux of ∼ 10 ions per deposited atom. Multilayers with nominal modulation periods in the range of 1.6 nm to 10.2 nm, grown with these conditions, exhibit a well-defined layer structure with an improved flattening and abruptness of the interfaces. It is shown that multilayers with a modulation period smaller than 3.4 nm have clear benefit from the reduced intermixing obtained by utilizing a two-stage ion energy modulation for each individual layer. The amorphization of Sc and Cr layers, below certain thicknesses, is found to be independent of the low energy ion-assistance. It is also shown that the Cr/Sc multilayers, containing periods less than ∼ 2 nm are ‘self healing’ i.e. they re-gain abrupt interfaces and flat layers after morphological disturbances during ion assisted growth. In comparison, multilayers grown without ion-assistance exhibited severe roughness and layer distortions.     

Reflectance enhancement with sub-quarterwave multilayers of highly absorbing materials

A new theory of multilayers with enhanced normal reflectance has been developed based on the superposition of a few layers of various different radiation-absorbing materials. Every layer in the multilayer had a subquarterwave optical thickness. The theory was developed for materials with small refractive-index differences, although it is also valid in some cases for materials with large refractive-index differences. Reflectance enhancements were obtained in a very broad band and over a wide range of incidence angles. The theory is particularly suited to designing multilayers with enhanced reflectance in the extreme ultraviolet for wavelengths above 50 nm. In this spectral region the reflectance of single layers of all materials is relatively low, and standard multilayers are not possible because of the high absorption of materials.     

Experimental comparison of extreme-ultraviolet multilayers for solar physics

We compare the reflectance and stability of multilayers comprising either Si/Mo, Si/Mo2C, Si/B4C, Si/C, or Si/SiC bilayers, designed for use as extreme-ultraviolet (EUV) reflective coatings. The films were deposited by using magnetron sputtering and characterized by both x-ray and EUV reflectometry. We find that the new Si/SiC multilayer offers the greatest spectral selectivity at the longer wavelengths, as well as the greatest thermal stability. We also describe the optimization of multilayers designed for the Solar-B EIS instrument. Finally, we compare experimental reflectance data with calculations and conclude that currently available optical constants cannot be used to adequately model the performance of many of these multilayers.     

Thermal and stress studies of normal incidence Mo/B4C multilayers for a 6.7 nm wavelength

Wavelength, reflectance, and stress stability of Mo/B(4)C multilayers were studied as a function of postdeposition annealing up to 900 °C. These multilayers are of interest as normal incidence coatings for wavelengths above the boron K-absorption edge. Mo/B(4)C multilayers deposited at low sputtering pressure have high compressive stress. Zero stress can be achieved at 360 °C-370 °C, but annealing at <200 °C is sufficient to reduce stress by ～40%. This stress relaxation is accompanied with a multilayer period expansion of ～0.02 nm and a <0.5% decrease in normal incidence reflectivity. The multilayer period remains stable up to ～600 °C, while intrinsic stress changes from compressive to tensile. A four-layer model with amorphous molybdenum and boron carbide layers separated by amorphous layers of molybdenum borides (Mo(x)B(y)) is presented. These interlayers are present already in the as-deposited state and continue to grow with increasing temperature. Their presence lowers the optical contrast and the achievable reflectivity. However, they also increase multilayer thermal stability. At temperatures >600 °C, a noticeable decrease in reflectivity associated with the phase transition from amorphous to crystalline molybdenum boride is observed. This is accompanied with an increase in interface and surface roughness and a change in stress as a function of temperature.     

W/SiC x-ray multilayers optimized for use above 100 keV

We have developed a new depth-graded multilayer system comprising W and SiC layers, suitable for use as hard x-ray reflective coatings operating in the energy range 100-200 keV. Grazing-incidence x-ray reflectance at E = 8 keV was used to characterize the interface widths, as well as the temporal and thermal stability in both periodic and depth-graded W/SiC structures, whereas synchrotron radiation was used to measure the hard x-ray reflectance of a depth-graded multilayer designed specifically for use in the range E approximately 150-170 keV. We have modeled the hard x-ray reflectance using newly derived optical constants, which we determined from reflectance versus incidence angle measurements also made using synchrotron radiation, in the range E = 120-180 keV. We describe our experimental investigation in detail compare the new W/SiC multilayers with both W/Si and W/B4C films that have been studied previously, and discuss the significance of these results with regard to the eventual development of a hard x-ray nuclear line telescope.     

Reflectance enhancement in the extreme ultraviolet and soft x rays by means of multilayers with more than two materials

Sub-quarterwave multilayer coatings with more than two different materials are shown to provide a reflectance enhancement compared with the standard two-material multilayer coatings when reflectance is limited by material absorption. A remarkable reflectance enhancement is obtained when the materials in the multilayer are moderately absorbing. A simple rule based on the material optical constants is provided to select the most suitable materials for the multilayer and to arrange the materials in the correct sequence in order to obtain the highest possible reflectance. It is shown that sub-quarterwave multilayers generalize the concept of multilayers, of which the standard two-material multilayers are a particular case. Various examples illustrate the benefit of sub-quarter-wave multilayer coatings for highest reflectance in the extreme ultraviolet. Applications for sub-quarterwave multilayer coatings are envisaged for astronomy in the extreme ultraviolet (EUV) and soft x rays and also for future EUY lithography.     

Epitaxial growth of MgO/TiN multilayers on Cu

The growth of epitaxial MgO/TiN multilayer films on (001) Cu has been investigated. In particular, epitaxial structures were grown on (001) Cu layers that were epitaxial on (001) SrTiO₃. X-ray diffraction and reflection high-energy electron diffraction indicate that the multilayer structures are epitaxial on the (001) Cu surface. The motivation is the use of crystalline MgO/TiN multilayers as a diffusion barrier to both copper and oxygen. MgO/TiN multilayers are potentially useful as diffusion barriers for Cu interconnects on semiconductors as well as for superconducting wires based on the epitaxial growth of cuprate superconductors on biaxially textured copper.     

Residual stress characterization of Al/SiC nanoscale multilayers using X-ray synchrotron radiation

Nanolayered composites are used in a variety of applications such as wear resistant coatings, thermal barrier coatings, optical and magnetic thin films, and biological coatings. Residual stresses produced in these materials during processing play an important role in controlling their microstructure and properties. In this paper, we have studied the residual stresses in model metal-ceramic Al/SiC nanoscale multilayers produced by physical vapor deposition (magnetron sputtering). X-ray synchrotron radiation was used to measure stresses in the multilayers using the sin²Ψ technique. The stresses were evaluated as a function of layer thicknesses of Al and SiC and also as a function of the number of layers. The stress state of Al in the multilayer was largely compressive, compared to single layer Al stresses. This is attributed to a peening mechanism due to bombardment of the Al layers by SiC and Ar neutrals during deposition. The stress evolution was numerically modeled by a simplified peening process to qualitatively explain the Al thickness-dependent residual stresses.     

Mechanically responding nanovalves based on polyelectrolyte multilayers

The alternate deposition of exponentially and linearly growing polyelectrolyte multilayers leads to the formation of multicompartment films. In this study, a new system consisting in nanometer-sized multilayer barriers deposited on or between multilayer compartments was designed to respond to mechanical stimuli and to act as nanovalves. The diffusion of polyelectrolytes through the barrier from one compartment to another can be switched on/off by tuning the mechanical stretching and thereby opening or closing nanopores in the barrier. This work represents a first step toward the design of chemically or biologically active films responding to mechanical stresses.     

Cr /sc multilayers for the soft-x-ray range

We have systematically investigated ultrathin Cr/Sc multilayers (nanolayers), using tunable soft-x-ray synchrotron radiation. The multilayers were optimized for use either in normal incidence or at 45 degrees at photon energies around the 2p-absorption edges of Sc (399 eV) and Cr (574 eV), respectively. They were sputter deposited on Si wafers or on thin Si(3)N(4)-membrane support structures for use in reflection and in transmission, respectively, as polarizing and phase-retarding elements in a polarimeter. The performance theoretically expected with respect to reflection/transmission and energy resolution has been confirmed experimentally: A value of 7% for the normal-incidence peak reflectance at 395 eV was measured as well as a pronounced minimum in transmission for certain incidence angles and energies below the respective absorption edges, indicating significant phase-shifting effects.     

Carbon/Titanium multilayers as soft-x-ray mirrors for the water window

C/Ti multilayers with a period thickness of 2.1-2.7 nm were produced by electron-beam evaporation in ultrahigh vacuum as soft-x-ray mirrors in the water window (lambda = 2.3-4.4 nm). For smoothing the individual interfaces and thus enhancing the total reflectance, each layer was ion polished with an Ar(+) ion beam after deposition. For a multilayer of 85 bilayers, a reflectance of approximately 11% at an angle of incidence of 59 degrees (with respect to the surface normal) by use of s-polarized radiation at a wavelength of 2.77 nm was achieved.     

Metal-substituted organic Cd-arachidate multilayers as soft-x-ray mirrors

Multilayers for soft x rays, lambda > 4.5 nm, have been made with Cd arachidate, a metal-substituted fatty acid. The multilayer period is found to be 5.53 nm, double the normal length of a Cd-arachidate molecule. The interfaces have a low roughness value of < 0.3 nm, which does not reduce the long-wavelength reflectance significantly. The soft-x-ray reflectance at 3.0 nm has been measured to be 0.13% for this prototypical multilayer that has 12 bilayers. The theoretical reflectance of these multilayers determined at a wavelength of 10.0 nm, suitable for x-ray lithography, is found to saturate at approximately 43% for approximately 150 bilayers.     

Interface engineered ultrashort period Cr-Ti multilayers as high reflectance mirrors and polarizers for soft x rays of lambda = 2.74 nm wavelength

Cr-Ti multilayers with ultrashort periods of 1.39-2.04 nm have been grown for the first time as highly reflective, soft-x-ray multilayer, near-normal incidence mirrors for transition radiation and Cherenkov radiation x-ray sources based on the Ti-2p absorption edge at E = 452 eV (lambda = 2.74 nm). Hard, as well as soft, x-ay reflectivity and transmission electron microscopy were used to characterize the nanostructure of the mirrors. To achieve minimal accumulated roughness, improved interface flatness, and to avoid intermixing at the interfaces, each individual layer was engineered by use of a two-stage ion assistance process during magnetron sputter deposition: The first 0.3 nm of each Ti and Cr layer was grown without ion assistance, and the remaining 0.39-0.72 nm of the layers were grown with high ion-neutral flux ratios phi (phiTi = 3.3, phiCr = 2.2) and a low energy Eion (ETi = 23.7 and ECr = 21.2), ion assistance. A maximum soft-x-ray reflectivity of R = 2.1% at near-normal incidence (approximately 78.8 degrees) was achieved for a multilayer mirror containing 100 bilayers with a modulation period of 1.379 nm and a layer thickness ratio of tau = 0.5. For a polarizing multilayer mirror with 150 bilayers designed for operation at the Brewster angle, 45 degrees, an extinction ratio, Rs/Rp, of 266 was achieved with an absolute reflectivity of R = 4.3%.     

Synthesis and investigation of π-conjugated azomethine self-assembled multilayers by layer-by-layer growth

Layer-by-layer formation for π-conjugated azomethine multilayers bonded on substrates was investigated. The multilayers were synthesized using ethanol (EtOH) and dichloromethane (DCM) as reaction solvents. The multilayer characteristics were analyzed using UV-vis absorption spectroscopy, ellipsometric thickness, and atomic force microscopy. The absorption spectra and ellipsometric thicknesses of multilayers formed using EtOH and DCM were compared. The results indicate that EtOH is more suitable than DCM for such layer-by-layer formation. In addition, bandgaps estimated from the absorption edge of multilayers were investigated. The results indicate that the bandgap decreases as the number of benzene rings contained in the molecular chain of the multilayer increases. Also, a multilayer with four benzene rings bonded on a substrate had a bandgap close to that of a polymer with a similar chemical structure.