The Optical Constants of Sputtered U and a‑Si at 30.4 and 58.4 nm.

M. B. Squires, David D. Allred and R. Steven Turley

Department of Physics and Astronomy, Brigham Young University, Provo, UT.

 

Figure 1. Example of a multilayer with a uranium oxide cap.

Introduction

Optical constants are used to compute the response of a material to light. Previously published optical constants for uranium and a‑Si over portions of the extreme ultraviolet (EUV) are questionable. The optical constants of a‑Si from peer-reviewed literature1,2 are not consistent with optical constants calculated from the atomic scattering factors of crystalline Si3. The optical constants for uranium and silicon predicted reflectivities higher than we measured. Therefore, we have fit the optical constants of sputtered uranium and amorphous silicon using reflectance measurements.

Optical constants are important in the design of optical devices that may be used in multilayer optics, plasma diagnostics, lithography, and space optics. Specifically, we were involved in the design and fabrication of space flight mirrors for the IMAGE4 explorer satellite. The proper design of these devices depends on reliably knowing the optical properties of many materials. It is also possible to learn about the basic electronic properties of a material by measuring its optical properties.

We used the optical constants of many materials to design multilayer mirror coatings for three cameras which were part of the IMAGE mission satellite. An iterative process was used to select the materials and design the multilayer coating because the optical constants were not well known. The multilayer samples that were made were used to obtain the optical constants of a‑Si and U at 30.4 and 58.4 nm. We were not certain if the individual optical properties of a‑Si and uranium could be distinguished in a multilayer, but we were partially successful in the determination of the optical constants of a‑Si and uranium in the EUV. Many different multilayers were prepared to understand the reflective properties of a‑Si and uranium; we will only report on multilayers that have an a‑Si/U G of 0.70.03 and have a uranium oxide overcoat. Here G is the ratio of the thickness of the top layer to the D-spacing.

Interaction of Light and Matter

When light interacts with matter it is primarily the electrons and their energies that determine the optical properties of the material. Classically, the interaction of light and matter is described by the dielectric constant, e, of the material. It describes how an electric field is modified in the presence a material. The dielectric constant depends on the material's electronic structure and the frequency of the incident light. In most materials, e depends on the cumulative effect of several electrons. In the lower energy portion of the spectrum (visible, IR, microwave, etc.) e is principally determined by the energies of the valence electrons that form chemical bonds. In the higher energy portion of the spectrum (x ray, etc.) e depends on the energies of the core electrons. When high-energy radiation interacts with a compound e depends on the densities and stoichiometric ratios of the core electrons in the material, and depends very little on the bonding properties.

The wavelengths of light used in this paper fall between these two extremes. The bonding of the valence electrons and the properties of the core electrons are both factors in determining the optical properties of a material. It is not completely understood how low and high energy effects combine in the medium energy region (vacuum ultraviolet, EUV). This paper will report the optical properties of two materials, with specifics on how the materials were deposited and characterized.

The refractive index, n, and the attenuation factor, k, will be reported instead of e, because n, k are used in existing optical software, have readily apparent physical interpretation, and are proportional to atomic scattering factors. The relationship between e and n, k is e1=n2‑k2, e2=2nk. A full development of the relationship between n, k and e is found in reference 7. Commonly, n determines the wavelength of light in a material. At higher energies (δ=1‑n) is reported instead of n, because n differs little from unity at higher energies. The attenuation factor, k, is used to calculate the percentage of light that is absorbed per unit length. These optical constants are used in the Fresnel equations5 to calculate the reflectance from an interface of two materials.

 

Deposition and Characterization with x rays

The optical properties of uranium and a‑Si were calculated from single angle (14.5o from normal) reflectance measurements of multilayer mirrors deposited via sputtering. Sputtering is used to deposit thin coatings of materials onto substrates. Sputtering is usually done in a medium vacuum, 1x10‑1 to 1x10‑3 torr (750 torr =1 Bar). At these pressures the mean free path between molecules in the chamber is comparable to the distance between the sputtering target and the substrate. This allows for better sputter rates, coverage, density, and adhesion of the sputtered material. Before sputtering begins, the deposition chamber is evacuated to about 10‑6 torr to remove nitrogen, oxygen, and water vapor. This diminishes the incorporation of impurities in the deposited film that will change the optical properties of the materials being deposited. The partial pressures of water and nitrogen in the system are typically less than 10‑6 torr before deposition. The partial pressures of all the gases in the deposition chamber are measured using a quadrupole residual gas analyzer (RGA). (Ferran Scientific)

Deposition can begin after the base pressure in the chamber is 3 x 10‑6 torr or lower. After the base pressure has been reached the entrance to the vacuum pump is mostly blocked or throttled. The pressure in the deposition chamber rises to 3‑7 x 10‑6 torr after the entrance is throttled. Ultrahigh purity argon (99.999% pure) is then flowed into the system until the steady state pressure of about 103 torr is reached. The argon (Ar) pressure is maintained by mass flow controllers and is measured by the RGA. Nobel gases are commonly used for sputtering because they do not form compounds with other materials. Ar is used to create a plasma for sputtering because it is least expensive of the noble gases, has a large enough mass to efficiently eject material from the surface of the target, and readily forms a plasma.

After the Ar gas is ionized in the chamber, the positively charged Ar ions are accelerated toward the negatively charged target. When an Ar ion strikes the surface of the target material there is a significant probability it will eject one or more atoms of the target material from the target surface. The surface of the 4" diameter target does not sputter uniformly because magnets below the target confine the plasma in a broad ring that is about 2/3 the diameter of the target. Because of this confinement the center and rim of the target tend to sputter at a lower rate than where the plasma is confined. The substrates are rotated over the target to increase the uniformity of the deposited material on the sample. Parts of the target are blocked off or "masked" to increase the uniformity of the material on the sample. The shape and size of the masks are determined by an iterative process of measuring the spatial uniformity and then changing the masks. The thickness of the deposited material is controlled by the time the substrate is over the target. Because the materials are deposited a few atoms at a time the thickness can be controlled to atomic dimensions.

The thickness of the multilayer mirrors is determined by x‑ray diffraction. X‑ray diffraction involves reflecting x rays off a sample into a detector at varying angles. As the angle is scanned, the path length of the x rays inside the multilayer changes. The detector sees a series of narrow, bright lines in a dim background that come from constructive and deconstructive interference of the light reflecting from the layers of the multilayer. After the data has been saved it is compared to a model. By varying the thickness of the layers in the model the bright and dim lines can be used to fit the reflectance data to the actual thicknesses of the layers in the multilayer. The spatial uniformity is also determined by measuring the thickness of a multilayer coating at various places on a sample. The ratio of the top layer thickness to the thickness of the d‑spacing is Γ. For the multilayers used in this paper a‑Si is the top layer. The presence of the uranium oxide overcoat does not change the Γ of the a‑Si/U multilayer.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Figure 2. Chamber 1

The top layer of our multilayer mirrors is uranium, which readily oxidizes, 1.5 nm oxidizes in a few minutes when exposed to air.11 We found that having uranium oxide on the top of the multilayer increases the reflectance at 30.4 nm and decreases the reflectance at 58.4 nm. The apparent thicknesses of the uranium oxide layers are not the same for all of the multilayers. Many multilayers were made to determine the optimal thickness of the uranium capping layer, 1.7 nm. The approximate thickness of the uranium oxide layer was calculated by knowing the thickness of the pure uranium layer deposited in vacuum and then calculating the change of volume of the uranium when it oxidized in air, based on the density. Uranium expands by a ratio of 1.97:1 and 3.2:1 in volume when oxidized to UO2 and UO3. (Ref. 11 p 65). Auger studies suggest the oxygen/uranium ratio in the surface oxide is 4:1. This is not out of the question since UO2(OH)2 is known and has this ratio of oxygen to uranium.

 

 

Reflectivity Measurements and Analysis

We use a McPherson, model 225, 1‑meter scanning VUV monochromator to isolate one wavelength of light created in a plasma lamp. The light from the monochromator can be reflected off a mirror and into a detector, or the light can be directly measured to monitor the intensity of the plasma lamp. The system is evacuated by a vacuum pump mounted directly behind the diffraction grating, because vacuum ultraviolet (VUV) and EUV light is strongly absorbed in air. The channeltron detector operates at a high electrical potential and would be destroyed by electrical arcing if operated above 1x10‑4 torr. The detection chamber is pumped by a Varian 550 turbo molecular pump mounted directly behind the diffraction grating. The detector chambers are evacuated through the exit slits and by a separate Varian 300 turbo molecular pump to assure the detectors could be operated safely.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Figure 3. Chamber 2

A McPherson, model 629, hollow cathode plasma lamp is used to produce EUV light. The plasma is made by flowing a gas in a region of high potential difference. The pressure in the plasma lamp is on the order of 0.1 torr, about ten thousand times less then atmospheric pressure. EUV light is created by collisions of gas atoms with electrons or other ionized gas atoms. These collisions cause electrons to be excited to a higher energy level in the atom. Because there is a vacancy in a lower energy level the electron may decay to the lower energy, and emit light that corresponds to the energy that was lost by the electron.

Helium gas is used to produce light at 58.4 and 30.4 nm. Neutral helium has two electrons in the 1s shell. When an electron is excited to the 2p state and decays to the 1s state it will radiate light at 58.4 nm. This is a very intense spectral line because it does not need much energy, compared to the 30.4 nm, to be excited, the helium atom does not have to be ionized, and the 2p→1s is a probable transition. The 30.4 nm line is created by the 2p→1s transition in a singly‑ionized helium atom. This spectral line is not as bright as 58.4 nm because of the optical efficiency of the monochromator and detector are less at 30.4 nm. It also depends on the percent ionization of the helium gas. The hollow cathode source was run in series with a 2000S ballast resistor to limit the current in the lamp.

The McPherson scanning monochromator is used to select a specific spectral wavelength of light. The McPherson monochromator can also scan smoothly through many wavelengths making it possible to measure the reflectivity of a sample over a range of frequencies of light. The monochromator can isolate light from about 30.0 to 100.0 nm, and select with an accuracy of about 0.05 nm. Our platinum‑coated grating reflects about 12% of the light between 30.00 and 60.0 nm.

The principally unpolarized beam of light reaching the sample is defined by adjustable entrance and exit slits. The vertical slits are 50‑300 microns depending on the intensity of the light. The horizontal slits are normally 0.5 centimeter in width, and were infrequently changed.

 

Measurement Chambers

Two chambers (Fig. 2 and 3) were used to measure the reflectivities of multilayer coatings. Chamber 1 was used to measure absolute reflectivity. It can only measure the reflectivity of one mirror coating at a time. Chamber 2 can be used to measure the reflectivity of three mirrors relative to a known reference mirror. Using Chamber 2, we could make reflectance measurements significantly faster than using Chamber 1. Both chambers were designed to measure the reflectance of mirrors at 14.5o relative to normal to satisfy the requirements for the IMAGE mission mirrors.

Absolute reflectivities can be measured using Chamber 1 because the intensity of the source and the intensity of the light coming off a mirror can be measured by the same detector. The distance from the exit slits to the back of chamber is the same as the total distance from the exit slits to the mirror to the side of the chamber. These two distances are important because the light coming from the exit slit diverges. Measurements are made by attaching the detector to the back of chamber 1and measuring the intensity of light. The detector is then moved to the side of Chamber 1 and a mirror is put in the center of the beam. The intensity of the light reflected from the mirror is measured. The mirror is removed, and the detector is put on the back again to check the stability of the source. This process is repeated several times because the source changes with time.

Chamber 2 was designed to measure the reflectivity of the curved mirrors for the IMAGE mission. The reflectivity of flat samples could be measured with a special holder that was designed to hold four flat mirrors at the same angle and position as a curved mirror would be in Chamber 2. Because of the design it is very easy to measure the reflectivities of the other three mirrors relative to reference mirror of a known reflectivity. Only one sample needs to be aligned because the mirror holder was machined from one piece of aluminum and the sample positions are fixed. The relative alignment of the sample positions has been verified and is not a significant source of error.

 

Detectors

During different phases of research either one of two detectors was used to measure the intensity of the light coming from the monochromator and reflecting off the mirrors. A CCD camera is used to image the spatial variations in the plasma source and to check the alignment of the mirrors in the chambers. A channeltron detector is used in the majority of the measurements because it is more sensitive than the CCD camera.

The CCD camera is a Princeton Instruments back‑thinned CCD camera with 512x512 pixels in a 1.25 cm square active surface optimized for detection in the EUV. The benefit of using a CCD camera is its ability to produce an image. This is important because the plasma source discharge is not spatially uniform and it is important to know the shape of the plasma at different wavelengths. There are, however, some disadvantages in using the CCD camera: the camera is not as sensitive as the channeltron, the camera must be cooled to ‑50o C, and the chip surface is very delicate.

Figure 4. Calculated vs. Measured Reflectance at 30.4 nm

 

The channeltron detector is an AmpTek model MD‑501. The channeltron detector has a background count of less than a half count per second. This background is ignored in all measurements because usual measurements average several thousand counts a second. The channeltron is used for the majority of the measurements because the data collection is significantly faster than the CCD camera, there is a small background, and the detector does not need to be cooled. The main disadvantages of using the channeltron detector are that it must be operated below 10‑4 torr and it does not image.

 

Measurements and Data Analysis

Most of the measurements were made using Chamber 2 by aligning a molybdenum reference mirror (measured with Chamber 1) so the greatest amount of light was reflected from the mirror at a given wavelength. The intensity reflecting from the reference mirror was recorded two or three times to monitor the stability of the plasma lamp. The other samples were then moved into the beam and the intensities of the three samples were recorded two or three times. The reference mirror was measured again to monitor the long‑term stability. This process was repeated several times to record the variations in the source, but did not give a measure of the time variations of the source.

The raw data taken from the mirrors gave a range of reflectivities for each mirror. There were normal statistical variations because the detectors counted a certain number of photons in a

 

Figure 5. Calculated vs. Measured Reflectance at 58.4 nm

fixed time. There were variations in the deposition of the multilayer mirror coatings and the thickness of the uranium oxide, making each coating slightly different. Also, the reflectance is sensitive to surface contaminants. There were variations in the measurement of the reflectivities. The plasma lamp may have been somewhat unstable and each mirror may have been aligned slightly differently.

These variations can be classified as statistical and experimental error6. The majority of the error was experimental, because of the limitations inherent in the measurement chambers. The statistical error was a small factor in the error. The statistical error was reduced by lengthening the exposure time until the statistical error was about 1%. The statistical methods used in the data reduction are furthered explained in reference 4.

Data at 30.4 and 58.4 nm

All the mirror coatings consisted of seven periods of a-Si on uranium with =0.70.03 over a range of d‑spacings from 15.0‑27.0 nm. These multilayers had a uranium oxide overcoat on top of the seven periods of a-Si and uranium bilayers. All the mirrors were measured at 14.5o from normal. All the mirrors were measured multiple times, but some measurements were more reliable than others and were so weighted. The error bars (Figures 4,5) were calculated by the methods explained in reference 7.

 

 

Calculated Reflectance is Different than Measured Reflectance

At 30.4 nm (Figure 4) the measured reflectivity peak position, relative to the calculated peak, is shifted 0.5 nm towards a higher layer thickness. The calculated refractive indices of uranium and a‑Si are both closer to unity (Table 1). The shift in the peak position and the shift in the fitted optical constants are self-consistent. We are investigating the interdiffusion of the uranium and a‑Si layers and the oxidation of uranium and a‑Si to explain differences in the reflectivities of these multilayer mirrors.

At 58.4 nm (Figure 5), the shape of the reflectivity versus period curve can be approximated by a straight line. This is not unexpected because the multilayers were designed to have a broad minimum around 58.4 nm, however the reflectivity is significantly lower than the calculated reflectivity. Both roughness and surface oxidation can lower reflectance. However, the reflectance is much lower than could be expected if roughness were the only factor affecting the reflectivity. Longer wavelength light (i.e. 58.4 nm) is scattered less by roughness than shorter wavelength light (i.e. 30.4 nm). It is well known that the effect of roughness is to decrease the reflectance of a surface at shorter wavelengths more than at longer wavelengths. Thus, even if the roughness in the multilayers was more than seen in TEM8 in our calculations it would have lowered the reflectivity at 30.4 nm much more than at 58.4 nm. This is not seen. Multilayers capped with uranium oxide are between 1/2 to 1/3 less reflecting at 58.4 nm than would be expected for stacks capped with silicon rather than uranium oxide. No decrease is seen in the reflectance at 30.4 nm, but an increase is seen in the reflectance as a result of the presence uranium oxide layer on top of the last a‑Si layer. We conclude that the lowering of the reflectance at 58.4 nm is caused by the presence of the uranium oxide layer, rather than roughness or a deviation from the published optical constants of a‑Si and uranium at 58.4 nm7.

The relative difference between measurement and modeled reflectivities at 58.4 nm is more pronounced than at 30.4 nm. This shows the current understanding of optical constants of a‑Si, uranium, and compounds like uranium oxide in the lower to middle EUV may be deficient. This might be expected because 58.4 nm (21eV) is a lower energy then 30.4 nm (41eV), and would be more affected by the atomic bonding of the materials in a multilayer. The typical energy of chemical bonds is a few eV. The closer the energy of the light is to the energy of the bonds in the material the stronger the effect on the optical constants.

 

Calculated Optical Constants


The measured reflectivities were used to calculate the optical constants of uranium and a‑Si by fitting a model of the multilayer to the measured data points. IMD10 was used to fit the optical constants to the measured data. IMD used CURVEFIT and the Marquardt method of non‑linear least squares fitting5. The surface and interfacial roughness was set to 0.5 nm based on other measurements8.

To fit the optical constants with IMD, a model of the multilayer mirror, initial values of the parameter to be fit, and the measured data are entered into IMD. The number of fitting parameters that can be chosen depends on the number of data points. More fitting parameters can be used if there are more data points, but experience has shown that care must be taken to avoid over‑fitting a physical feature with extraneous nonphysical parameters. IMD can be used calculate the confidence interval over a user‑defined grid space to determine the goodness of the fit.

We chose the initial values of δ and k for silicon to be close to the values of crystalline silicon, and the values of uranium close to those reported in reference9. The confidence integral was not conclusive for the fit optical constants of uranium, so the error bars of these fits are not reported. The literature values and the best fits to date are shown in Table 1.

 

 

30.4 nm

58.4 nm

 

Material

δ

n

k

δ

n

Literature Values (approx. original values)

c-Si1

0.063

0.937

0.009

0.373

0.627

 

U9

0.322

0.678

0.279

0.41

0.59

Fit Values

Sputtered Si

0.039 0.025

0.961 0.025

0.037 0.015

Not Fit

Not Fit

 

Sputtered U

0.306

0.694

0.067

0.51

0.49

Literature Values

a-Si1

0.027

0.973

0.0314

0.215

0.785

Table 1. Optical Constants from literature and as fit for uranium and silicon.

The magnitude and direction of the shifts in δ and k for a‑Si and uranium are noteworthy at both 30.4 and 58.4 nm. The largest changes are in k. The k of a‑Si increased about four times, while the k of uranium decreased about four times. The δ of uranium changes little while the δ of sputtered Si is about half that of crystalline Si. It is instructive to compare the fit optical constants of silicon with the published values of a‑Si (bottom row of Table 1). The fit δ and k are closer to the literature values of a‑Si than to the literature values of crystalline silicon. This supports the need to measure the optical properties of sputtered silicon, but leaves open the basic question. Why do the optical properties of crystalline and amorphous Si differ at all? The observed differences are much larger than can be accounted for on the differences in density of the two materials. The major difference is atomic packing, that is, the density of the material. The standard model for calculating optical constants, at or near x‑ray energies, weights each by the ratio of the density of the material in the multilayer to its standard density. This ratio is about 0.8 for room temperature sputtered amorphous silicon. The fact that the optical constants of a‑Si differ so much from the optical constants of c‑Si demonstrates the inadequacy of this model in the EUV. But why the model fails in not clear.

 

Conclusions

We have determined the optical constants of uranium and a‑Si and 30.4 and 58.4 nm using reflectance measurements of multilayer mirror coatings. The change in k at 30.4 nm is large and is significant. The changes in δ are smaller, but are still significant. The changes in the optical constants at 58.4 nm are probably significant but the data does not support strong conclusions. The large differences between the measured and calculated reflectance is noteworthy. The top layer of uranium oxide plays a stronger role in the reflective properties at 58.4 than anticipated. The effects of the oxide layer might be eliminated by an ultrahigh vacuum system that is capable of deposition and measurement without exposure to water vapor, oxygen and nitrogen. Measuring the optical constants of uranium oxide in the EUV also has merit.

Our effort to determine optical constants based on multilayer reflectance was only partially successful. A greater span of Γs, and angles of measurement would have helped. Independent measurements of layer interdiffusion, roughness, and material composition would help set limits of what the optical constants of a material are. It would be helpful to measure the reflectivity of a single film or layer pair to obtain the optical constants of a material to isolate better the properties of one material.

We are building a chamber that will measure reflectivity of a sample as a function of angle; ultimately we expect to be able to do in situ deposition of thin films. An EUV ellipsometer is being developed at BYU and will provide another means to measure the optical properties of materials in the EUV. The development of a more robust fitting algorithm will also be an important step to accurately determine the optical constants of materials in the EUV.

 

Acknowledgments

We would like to thank Greg Harris and Dean Barnett for the design of Chamber 1 and Chamber 2, Adam Fennimore for sputtering and rates calculations, Spencer Olson for data acquisition software development, Sterling Cornaby and Aaron Fox for designing and building the substrate holder for sputtering, and the Department of Physics and Astronomy at Brigham Young University for supporting the work during Summer 1998. We would like to thank Wayne Anderson, David Balogh, Shannon Lunt, James Reno, Erroll Robison, Ross Robison, and C. Edward Whitney for the general tasks of sputtering, sample preparation and characterization, XRD, and sundry technical support. This work was supported by contract 83818 from Southwest Research Institute, a subcontract under contract GSFC‑410‑MIDEX‑001, Rev. A and GSFC‑410‑MIDEX‑002 from Goddard Space Flight Center.

 

1. Edward D. Palik ed. Handbook of Optical Constants of Solids, Academic Press Handbook Series, 1985.

 

2. Edward D. Palik ed. Handbook of Optical Constants of Solids II, Academic Press Handbook Series, 1991.

 

3. B.L. Henke, E.M. Gullickson, and J.C. Davis. X‑ray interactions: photoabsorption, scattering, transmission, and reflection at E=50‑30,000 eV, Z=1‑92, Atomic Data and Nuclear Data Tables, July 1993, 54,(no.2):181‑342.

 

4. 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, David D. Allred, R. Steven Turley, D. L. Gallagher, AThe Extreme Ultraviolet Imager Investigation for the IMAGE Mission,@ Space Science Reviews 91, 197-242 (2000).

 

5. Max Born and Emil Wolf. Principles of Optics, Pergamon Press, 1965.

 

6. Philip R. Bevington. Data Reduction and Error Analysis for the Physical Sciences, McGraw‑Hill Book Co., 1969.

 

7. Matthew B. Squires. The EUV Optical Constants of Sputtered U and a‑Si, Honors Thesis, Brigham Young University, April 1999.

 

8. Adam M. Fennimore. Morphology and oxidation of U/Al and UN/Al multilayer mirrors, Honors Thesis, Brigham Young University, February 1998.

 

9. A. Faldt and P.O. Nilsson. "Optical properties of uranium in the range 0.6‑25 eV," Journal of Physical F: Metal Physics, Received April 24, 1980.

 

10. David L. Windt. IMD Version 4.1, Bell Laboratories, Lucent Technologies, December 1998.

 

11. David Oliphant, Characterization of Uranium, uranium oxide and silicon multilayer thin films, Master thesis, Brigham Young University, April 2000.

 

Submitted to the Utah Academy of Arts and Sciences, 1999. To be published in the 1999 J of the Utah Academy.