We measured the transmittance and reflectance of two samples in the extreme ultraviolet (XUV) at the Advanced Light Source at Lawrence Berkeley National Laboratory. The samples were prepared with approximately 20 nm of UOx with one reactively sputtered onto a diode, and one allowed to oxidize naturally on an identical diode. Fitting the reflectance data to the Parratt model yielded a more precise thickness of the UOx film. This thickness combined with a simple analysis of the transmission measurements provides estimates for the imaginary part of the index of refraction for UOx at approximately every tenth of a nanometer from about 3 nm to 30 nm with emphasis in the 12- to 13-nm range. Using these values, a first approximation for the real part of the refractive index has also been calculated. These values provide researchers with information for modeling, design, and fabrication of optical systems in the extreme ultraviolet

Allred, David D.

Dumais, Heidi M.

Turley, R. Steven

English

DigitalCommons@USU

1  The Effects of Oxidation on the Refractive Index of Uranium Thin Films in the Extreme Ultraviolet  Heidi M. Dumais, R. Steven Turley, and David D. Allred Brigham Young University, Provo, Utah  We measured the transmittance and reflectance of two samples in the extreme ultraviolet (XUV) at the Advanced Light Source at Lawrence Berkeley National Laboratory. The samples were prepared with approximately 20 nm of UOx with  one reactively sputtered onto a diode, and one allowed to oxidize naturally on an identical diode. Fitting  the reflectance data to the Parratt model yielded a more precise thickness of the UOx film. This thickness combined with a simple analysis of the transmission measurements provides estimates for the imaginary part of the index of refraction for UOx at approximately every tenth of a nanometer from about 3 nm to 30 nm with emphasis in the 12- to 13-nm range. Using these values, a first approximation for the real part of the refractive index has also been calculated. These values provide researchers with information for modeling, design, and fabrication of optical systems in the extreme ultraviolet.   I. INTRODUCTION  The motivation for studying materials in the extreme ultraviolet (XUV) includes integrated circuit applications,1 astrophysical observations,2 planetary physics,2,3 and high-resolution microscopy.4,5 Photolithography techniques for microelectronics involve projecting an image on photo-sensitive materials to etch patterns for integrated circuits. The use of shorter-wavelength light in this process increases the resolution, leading to smaller features and faster circuits.1,6 In astrophysics, energetic processes that emit in the XUV can be studied in greater detail as better optics are developed in that range.2 In planetary science, helium ions trapped in the Earth’s magnetic field radiate in the XUV.3 As a result, images and movies of the Earth’s magnetic field have been made using XUV optics from the IMAGE satellite.7 In optical microscopy, shorter wavelengths improve resolution of smaller samples with less preparation than that of electron microscopy. Understanding the optical properties of materials in the XUV allows for the design and fabrication of optical systems that can be used for all of these applications, in addition to a better understanding of the materials themselves.4,5 Lunt8 predicted that uranium would be a useful element in XUV optical systems. Elemental uranium has been studied for application in thin-film XUV optical systems.9,10,11 However, the formation of oxides on the surfaces of uranium films makes using the pure element difficult. Uranium oxides themselves can be used for similar applications with greater stability. Uranium dioxide has been studied in the visible and infrared12 but not the XUV. The IMAGE satellite implemented uranium thin films in the XUV mirrors, but due to oxidation issues had to include an oxide layer over the elemental uranium.3 The mirrors did not reflect exactly as predicted by the model, suggesting that the optical constants used were not correct. The only published data for the refractive index of uranium oxides in the XUV are predicted (but not measured) using the independent atom approximation (IAA).11 The IAA weights the optical constants of each element by its density in the compound. This approximation is most valid at high energies (x-rays) and away from band edges. This paper builds on previous work done in the area.14, 15, 16 Programs at the Center for X-Ray Optics (CXRO) website typically use the IAA to calculate optical constants for compounds, using elemental data such as that from Henke et al.13 Recent in situ measurements of the absorption coefficient of elemental uranium in the XUV18 conflict with those recorded in that database. The following analysis compares these values with those calculated based on reflectance and transmittance measurements of two samples prepared with uranium oxide thin films. 2  In general, light incident on a material can be transmitted, reflected, or absorbed. An equation for the intensity of light reveals which parts of the index of refraction affect reflection and absorption:  tiieII140    (1) where I and I0 are the measured and incident intensity,  is the vacuum wavelength, t is the distance the light travels, 1- is the real part of the index of refraction, and  is the imaginary part. From Equation (1), the imaginary part of the index of refraction gives rise to an attenuation factor that corresponds to absorption. The intensity of the reflected field is sensitive to the real part of the index of refraction. Both the real and the imaginary parts of the index of refraction depend on the wavelength of light incident on the material. Most materials, including air, strongly absorb XUV light, which ranges from 1 to 60 nm. This range of wavelengths is also highly sensitive to surface roughness and contamination. Additionally, the real part of the index of refraction for materials in this region of the spectrum lies near unity for many materials, resulting in low reflection. This is because the Fresnel coefficients depend on the difference in the refractive index between various layers. Consequently, mirrors for this region must be constructed of layers of thin films with precise thicknesses meant to cause constructive interference between reflected fields from each interface. Figure 1 shows a simplified schematic for light incident on a four layer stack of thin films (on the nanometer scale) with reflectance at each interface. For clarity, Figure 1 does not show the multiple reflections that would occur at each interface. To properly model the reflectance and transmission of a stack of thin films, the recursive Parratt formula,19 which considers the fields traveling up or down in each layer, must be used.  II. BACKGROUND AND CALIBRATION  We measured two multilayer samples at Lawrence Berkeley National Laboratory’s Advanced Light Source (ALS). Both samples were prepared by sputtering uranium onto a silicon diode with a 7.69-nm SiO2 layer. Half of each diode was covered by a  Figure 1: Reflection at thin film interfaces.  shutter to leave it uncoated for comparison; however, the first sample was reactively sputtered (with oxygen), while the other was naturally oxidized after sputtering. After calibration, the reflectance and transmission of the sample at various wavelengths was measured to provide data for the calculation of the index of refraction of the sample material. Measurements of the transmitted intensity are made at a set wavelength by rocking the sample between an incident angle of 60 and 120 degrees. Each successive run had a different wavelength, so that analysis of each run yields the index of refraction at that wavelength. The reflectance runs vary the incident angle from near grazing to near normal for a given wavelength. III. ANALYSIS As a result of measuring the reflected intensity from near normal to near grazing, the curves varied by several orders of magnitude. These curves show peaks and valleys in the reflectance measurement due to interference between fields that were reflected at the various thin film interfaces on the diodes. Figure 1 illustrates the principle behind how light incident on the top surface can be reflected at several interfaces and yield a more intense reflected beam than would be possible with a single material layer. The angles at which the maxima and minima occur depend on the thickness of the layers. It is therefore possible to use the reflectance runs to calculate the thickness of each thin film layer. The samples were prepared to be at least 20 nm thick; however, to find a more precise thickness, the 3  reflectance data were fit to the Parratt recursive formula19 including a Nevot-Croce correction factor for the surface roughness by varying the real and imaginary parts of the index of refraction and the film thickness in Matlab. This formula uses the indices to calculate Fresnel coefficients for each interface. The thickness of the SiO2 layer was held constant at the measured value of 7.69 nm based on ellipsometry performed on the uncoated diodes at the BYU campus. The large changes in reflectance during a single run require a weight function to prevent the optimization program from over- or under-emphasizing any one portion of the data.14 Figure 2 shows a typical reflectance run fit to the Parratt formula including the weight function, the data, and the fit curve. The average thickness of the UOx layer for these runs was 21.8 ± 0.7 nm for the sample allowed to oxidize after sputtering, and 27.4 ± 0.4 nm for the sample that was sputtered with oxygen. Several reflectance runs were performed on the same diode position for each sample at different wavelengths to obtain these average thicknesses and standard deviations. These thicknesses allowed for a first approximation of the imaginary part of the index of refraction based on analysis of the transmission data. Figure 2: Typical reflectance data fit to the Parratt model using a weight function.   Measurement of the transmission as a function of angle at a given wavelength provided the data for the determination of the imaginary part of the index of refraction. The wavelengths measured ranged from 1 to 40 nm in varied step sizes. As a first approximation, the transmission intensity was assumed to be of the form of Equation (1), with the following simplifications: teII   0    (2) where I is the transmitted intensity, I0 is the incident intensity, t is the distance the light travels through the sample, is a factor that includes attenuation due to reflection, surface contamination, and surface roughness. Figure 3 shows a cross-section of the sample illustrating these parameters.  The distance t is given by sin0tt     (3) where  is the angle measured from grazing which assumes perfect sample alignment and t0 is the UOx film thickness. To correct for possible misalignment of the sample, we add another fitting parameter to  and substitute the expression for t into Equation (2) to get 4  )sin(00 teII   (4) where  corrects for the misalignment of the sample. Fitting the measured values to this model by varying the product of t0, , and the product of I0, we arrive at a value of t0 for each transmission run. The value of  was within 0.3 degrees of zero for each run. This indicates that the alignment was very good and that Equation (4) represents the behavior of the data relatively well. The reflectance analysis provided a value for the film thickness, allowing for the isolation of . By comparing the attenuation factor introduced in Equation (2) with that acquired from an expression for the intensity of the field in Equation (1), we can arrive at an equation for  in terms of : 4    (5) Using Matlab, we wrote a program which calculated a value for  at each wavelength according to the preceding analysis. The differences in the imaginary index for these samples indicate the importance of deposition techniques on the structure and in determining the optical properties of thin films.    Figure 3: Geometry of transmission approximation.  IV. RESULTS AND DISCUSSION   Figure 4 compares the values of the imaginary part of the index of refraction predicted by the CXRO database for elemental uranium and various oxides with both samples as a function of wavelength. The peak absorption for the reactively sputtered sample is shifted toward lower energy, while the naturally oxidized sample’s peak lines up with the CXRO peak value for all of the displayed uranium oxides. The IAA used to predict these values can not predict a shift in the absorption edge which has been demonstrated by our samples. The sample oxidized after sputtering qualitatively matches the CXRO values for U3O8. This indicates the possibility that the elemental uranium data in the CXRO database was obtained from an oxide. Figure 5 compares the CXRO elemental uranium values with our two samples and in situ measurements by Brimhall et al.18 Brimhall et al. measured the refractive index of a uranium thin film without breaking vacuum. The peak absorption of their sample as also shifted to the lower energy range, though more dramatically. This pattern contrasts the IAA’s prediction that more oxygen in the sample would just lower the absorption but not shift the peak. Figure 6 shows a comparison between CXRO predictions of the real part of the refractive index and the first approximation for our samples. The respective peaks show that the reactively sputtered sample again had an absorption peak at longer wavelength than the naturally oxidized sample. However, the behavior of the reactively sputtered samples refractive index between 12.2 and 12.35 nm indicates that a more robust analysis should be completed to yield the real index of refraction for these samples. This analysis is underway. 5   Figure 4: Comparison of CXRO predicted beta (imaginary portion of index) with measured values for both diodes    Figure 5: Comparison of beta measurements for CXRO U, and in situ measurements by Brimhall et al.18 6   Figure 6: Comparison of CXRO predictions for the real index with measured values.  VI. CONCLUSION  The complex index of refraction for UOx has been measured for two different sample preparation procedures. The data indicate that the index of elemental uranium does influence the compound’s index, but the IAA cannot fully predict the behavior of the refractive index as a function of wavelength. Future research will refine these results, enable us to draw conclusions about the electronic structure of the samples, and provide better values for both the real and the imaginary parts of the index of refraction for UOx in the XUV range. These values will aid researchers in the modeling of XUV optical systems for application to photolithography, astronomical imaging, planetary science, high-resolution microscopy, and materials characterization.           VII. AKNOWLEDGMENTS   The transmission and reflection measurements were made at beam line 6.3.2 of the Advanced Light Source at the Lawrence Berkeley Laboratory by the authors, Keith Jackson, Zephne Larsen, and Alison Wells with the aid of Eric Gullikson, with beam time granted under user contract # ALS-03197.  The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. This research was funded by the Rocky Mountain NASA Space Grant Consortium and Brigham Young University.  7  REFERENCES  1 U. Stamm, ―Extreme ultraviolet light sources for use in semiconductor lithography—state of the art and future development,‖ J. Phys. D: Appl. Phys. 37, 3244–3253 (2004). 2 See, for example, http://www.ssl.berkeley.edu/euve/sci/EUVE.html and bibliography cited therein. 3 B.R. Sandel, A.L. Broadfoot, J. Chen, C.C. Curtis, R.A. King, T.C. Stone, R.H. Hill, J. Chen, O.H.W. Sigmund, R. Raffanti, D.D. Allred, R.S. Turley, and D.L. Gallagher, ―The extreme ultraviolet imager investigation for the IMAGE mission,‖ Space Science Reviews 91, 197-242 (2000). 4 W. Chao, B.D. Harteneck, J.A. Liddle, E.H. Anderson, and D.T. 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Available online at http://volta.byu.edu/pubs/JosephThesis.pdf 16 N. Brimhall, N. Herrick, D.D. Allred, R.S. Turley, M. Ware, and J. Peatross, ―Measured optical constants of copper from 10 nm to 35 nm,‖ Optics Express, Vol. 17 Issue 26, pp. 23873-23879 (2009). 17 CXRO resources available online at http://henke.lbl.gov/optical_constants/  18 N. Brimhall, N. Herrick, D.D. Allred, R.S. Turley, M. Ware, and J. Peatross, ―Characterization of optical constants for uranium from10 nm to 47 nm,‖ Applied Optics Vol. 49, Iss. 9, pp. 1581–1585 (2010). 19 L.G. Parratt, ―Surface studies of solids by total reflection of X-Rays,‖ Phys. Rev. 95 (1954) 359. 

The Effects of Oxidation on the Refractive Index of Uranium Thin Films in the Extreme Ultraviolet

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The Effects of Oxidation on the Refractive Index of Uranium Thin Films in the Extreme Ultraviolet

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