IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII Will/ll fill/Ill”?llllllllllllIll/ll! ll 0575 3904 LIBRARY Michigan State University This is to certify that the thesis entitled THE OPTICAL PROPERTIES OF ULTRATHIN SILVER FILMS presented by John Willet Oeschger has been accepted towards fulfillment of the requirements for M.S . deg“. in Physics Mates; Major professor Date LOW / I q 8 2 0.7539 Msu is an Affirmative Action/Equal Opportunity Innitution PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or betore date due. = DATE DUE DATE DUE DATE DUE __ ___..__l MSU Is An Affirmative Action/Equal Opportunity Inetitutlon THE OPTICAL PROPERTIES OF ULTRATHIN SILVER FILMS By John Willet Oeschger A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Physics and Astronomy 1988 [9270-207 W ABSTRACT THE OPTICAL PROPERTIES OF ULTRATHIN SILVER FILMS BY John Willet Oeschger The optical properties of multilayered silver-silicon films deposited on sapphire subsrates were studied. The thicknesses ftn~ the :silver and silicon films were 75 A and 50 A, respectively. An optical system was built to measure the reflectivity and transmission. By comparing the reflectance and transmission measurements to expected values for ideal multilayer stacks, no changes from the bulk values of the optical constants of silver could be determined. ACKNOHLEDGMENTS I wish to thank Professor Paul Parker and Professor Michael Harrison for their contributions to this thesis. I am also grateful to Pam Deiter for her ideas and suggestions. I also wish to acknowledge, and express, my appreciation for the work which Peggy Andrews so graciously did. Most of all I would like to thank Professor Carl Foiles for his guidance, support, and encouragement throughout my graduate work. iii TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES INTRODUCTION CHAPTER 1 METHODS A. Theoretical B. Experimental 1. Spectrophotometer 2. Hatbox 3. Multilayer Preparation and Characterization CHAPTER 2 RESULTS AND ANALYSIS A. Reflectivity versus Energy B. Transmission versus Energy CONCLUSION LIST OF REFERENCES iv Page vi 1O 10 10 11 11 12 17 22 22 23 “7 55 56 Table 2.1 Theoretical results for bulk Ag; Ag on outer surface 2.2 Theoretical results for bulk Ag; Si on outer surface 2.3 Theoretical results for film Ag; Ag on outer surface 2.A Theoretical results for film Ag; Si on outer surface 2.5 Experimental results for Ag on outer surface; hatbox 2.6 Experimental results for Si on outer surface; hatbox 2.7 Experimental results for Ag on outer surface; spectrophotometer 2.8 Experimental results for Si on outer LIST OF TABLES surface; spectrophotometer Page 2“ 25 26 27 28 29 30 31 2.10 2.11 2.12 LIST OF FIGURES Typical film behavior Top view of hatbox R vs E for 1,000 A Ag with 50 A Si R T VS VS VS VS VS VS VS VS VS VS VS VS VS VS VS VS E E for for for for for for for for for for for for for for for for 1,000 A 51 1,000 A Si three periods, bulk Ag, hb three periods, film Ag, hb three periods, bulk Ag, sp three periods, film Ag, sp four periods, bulk four four four five five five five periods, periods, periods, periods, periods, periods, periods, film bulk film bulk film bulk film A8. A3. A8. A8. A8. A3. A3. A8. hb hb sp 3P hb hb SP SP six periods, bulk Ag, hb six periods, film Ag, hb vi Page 13 18 19 20 32 32 311 311 35 3‘3 36 36 38 38 140 110 111 111 .15 .16 .17 .18 .19 .20 .21 .22 .23 .2” .25 .26 .27 .28 .29 .30 .31 .32 .33 .314 .35 .36 VS V3 V8 V8 V8 V3 V8 VS VS VS V8 V8 V8 VS VS V8 V5 V8 VS VS VS VS for for for for for for for for for for for for for for for for for for for for for for six periods, bulk Ag, sp six periods, film Ag, sp eight periods, bulk Ag, hb eight periods, film Ag, hb eight periods, bulk Ag, sp eight periods, film Ag, sp twelve periods, bulk Ag, hb twelve periods, film Ag, hb twelve periods, bulk Ag, sp twelve periods, film Ag, sp three periods, bulk Ag three periods, film Ag four periods, bulk Ag four periods, film Ag five periods, bulk Ag five periods, film Ag six periods, bulk Ag six periods, film Ag eight periods, bulk Ag eight periods, film Ag twelve periods, bulk Ag twelve periods, film Ag vii 112 112 113 113 1111 1114 115 115 146 146 “9 119 50 50 51 51 52 52 53 53 514 511 INTRODUCTION The interest in studying the optical properties of thin silver films arises from a suggested anomaly in the complex index of refraction, (where the complex index of refraction, hm-ik). This anomaly is believed to be due to a geometrical quantization in the thin films. That is to say, when the transverse dimension of the film becomes very small, on the order of 11% or less of the wavelength of light being used, the optical constants begin to change with that dimension. Hereafter this anomaly will be called the film effect. Various authors have researched this phenomenon and have arrived at differing conclusions. Thus a brief historical review is in order. In 1960 0.3. Heavens wrote a report on the optical properties of thin films‘. In his review he cited the work done by Krautkr'a'mer, Philip and Trompette, Clegg, and others. The results of these researchers seemed to indicate a marked dependence of the optical constants on the film thickness. This film effect was observed in silver and in other metals such as gold and copper. The film effect can be characterized by a slight increase (from its bulk value) in the index of absorption before it begins to fall off with decreasing film thickness. The index of refraction is found to increase substantially (from its bulk value) before it begins to decrease with decreasing film thickness. Figure 1.1 shows the "typical" film behavior of the optical constants of silver as a function of film thickness, at a wavelength of light at 5H6 nm1. Measurements taken by different authors cited by Heavens show large differences, albeit similar trends, in the complex index of refraction. In an effort to isolate the varying factors during film deposition, Clegg looked at thin (10 to 350 A) films of silver, gold, tin and indiumz. He found that the optical properties depended upon the evaporation rate, the temperature of the substrate and the cleanliness of the substrate. Furthermore, below a certain film lfluickness, his experimental findings strongly disagreed with expected values. To rectify this discrepancy, Clegg applied the Maxwell Garnett theory to thin metallic films. The Maxwell Garnett theory assumes one has small metallic spheres embedded in a dielectric medium; thus one is no longer dealing with a continuous film, but with an islet type structure. The Maxwell Garnett theory (MGT) modifies the applied electric field by considering the effects due to the dipole fields of the metallic islets. It is a simple theory, beginning with the Clausius-Mossotti equation and ending with an equation which gives the "effective" optical constants of the islet type structure in terms of the bulk optical constants of the metal, and a number "q", which is the volume fraction ratio of the metallic islets to the film volume3. By choosing a suitable q, Clegg was able to show qualitative agreement between MGT predictions and experimental results. This prompted him to say that, "...this implies that by far the most 4.00 LLIALILIIILLII $888888 m'm'm'cu'ééca' xuou Figure 1.1 Typical Film Behavior 150 200 250 300 Thickness in X 100 50 important factor which alters the optical constants of thin films from those of bulk material is their aggregated structure" (p. 781). However, as Heavens pointed out, the assumption that the islets are spherical and that the optical constants of the islets are equal to those of the bulk material casts considerable doubt on the results1. "Also the q-values are found to vary appreciably for different wavelengths although there seems no obvious reason why they should do 30"3 (p. 183). Clegg was aware of the fact that the topography of the substrate might influence the form of the deposited film. He therefore checked the optical properties of films made on different types of glass substrates and found no difference among them. However since that time it has been noted that films formed on glass substrates are of the discontinuous, islet type structure, up to a thickness of 80 to 90 A“. In 1970, Shklyarevskii and Korneeva reported on their studies of thin (50 to 150 A) silver filmsS. They prepared their samples on quartz substrates. By measuring the reflectivity from the film side and from the substrate side and measuring the transmission, they were able to calculate a 6. Their results supported a film effect in the complex index of refraction. The study the extent of the islet type structure they took pictures of the films with an electron microscope, and observed that beginning with film thicknesses of 70—80 A, "...the images of the film granules lose their disk like shapes and form a complex mosaic" (p. 1““). Even so, their values for 3 beyond a film thickness of 80 A still resembled those of the film effect. However the study of Shklyarevskii and Korneeva suffered from one disadvantage not encountered by Clegg. Throughout Clegg's experiment, he was able to make his optical measurements in the same vacuum in which the deposition occurred, thereby minimizing the chance of atmospheric contamination. Heavens noted that the large discrepancy between different10bservers' results may be due to the great reactivity of the metal1. In fact, in looking at studies where people investigated the homogeneity of evaporated silver films by measuring the phase change of light upon reflection, he found that at some wavelengths the phase change had an abrupt Jump of 211, while at other wavelengths no Jump was found. This prompted Dumontet et al. to suggest that a contamination surface layer might be responsible for the anomalies1. The study of thin films has many implications in the field of optical coatings. This naturally leads to multilayer films. In 1980 MadJid and Abu El-Haija reported on the optical properties of thin multilayer films7. In their study they considered multilayer films composed of silver and silicon monoxide and measured the reflectivity and transmission as a function of wavelength, and compared their findings to their theoretical calculations. The theory which they developed took into consideration boundary layers which might exist between the silver and silicon monoxide layers, and possible thickness variations in each layer. They combined these ideas with the transfer matrix technique to arrive at expressions for the reflectivity and the transmission in terms of the relevant geometrical and optical parameters. The optical constants for the silver layer of thickness 60 A, were found by measuring the reflectivity from the film side and the substrate side, and measuring the transmission, and using the computational method published by Holter8. The optical constants 1u1ich they calculated for the silver are seen to show somewhat of the film effect, albeit not as drastic as those reported by Shklyarevskii and Korneeva. MaJid and Abu El-Haija used substrates of quartz or glass. It is not certain which substrate they used for which measurements. They were able to measure the thickness of one period (one silver layer combined with one silicon monoxide layer) by small angle x-ray diffraction and by an interferometric technique, which gave close agreement. Their multilayer stacks were only made in one order. For example, Si-Ag as opposed to Ag-Si. Their results are in general agreement with theory although at times the agreements were weak. The discrepancies suggest that perhaps the optical constants of the silver layers formed in vacuum might be different from those found by the individual layer in air, or that the theory needs to include a boundary layer between the element and the substrate. Theoretical work in thin films and granular films has progressed since the time of the Maxwell Garnett theory for spherical metallic particles embedded in a dielectric medium. Beginning with 9 Schopper , who extended the Maxwell Garnett theory by considering ". ..a model based on a two-dimensional distribution of particles in the shape of rotation ellipsoids," (p. 188)3 to Cohen et al. who further refined this approach10. The study by Cohen et al. investigated the optical properties of granular silver and gold films as the volume fractnn1retio of the silicon dioxide was varied. From their results they concluded that ". . .metal particles as small as 20 A have optical constants that do not differ significantly from those of the bulk metals" (p. 3689). This conclusion was based on a generalized Maxwell Garnett theory. More recently, papers presented by Wood and Ashcroft11 and by Dryzek and Czapla“ have advanced the theory of quantum size effects in optical properties of small particles and thin metal films. The motivation for pursuing a quantum treatment of small particles as given by Wood and Ashcroft is "...within the single particle approximation, one could imagine solving for the eigenstates of free electrons subject only to the constraint that they remain within a finite volume. The energy levels of such a small particle will then be discrete and the small energy difference between the highest occupied level and the lowest unoccupied level will mean that, ha pndnciple, the particle as a whole will behave as a large atom"11 (p. 6258). With this idea in mind they were able to arrive at an expression giving the real and imaginary parts of the dielectric function for small cubic metallic particles. A similar expression was also arrived at by Dryzek and Czapla who applied the result to thin metallic films. The result of Dryzek and Czapla predicts oscillations in the infrared region for the reflectivity and transmission for films up to 20 A in thickness. However these oscillations in some cases are small, and the film quality and thickness would be hard to control“. At this point, the results of Clegg, Shklyarevskii and Korneeva, and MadJid and Abu El-HaiJa appear to be a consequence of film quality rather than the quantum size effect (at least not in a large part due to film thickness, or region of spectrum covered). It should be noted that these researchers used the evaporation method to form their films. MGT replaces the idea of a continuous film with that of an islet type structure. For the evaporated films in which some form of MGT was applied, much better agreement between experiment and theory was found. These two facts leave open the possibility that thin films formed by evaporation may not be films at all. This leaves open the question of the optical properties of films formed by the sputtering method. In an effort to determine whether or not the bulk optical constants of silver can be maintained in thin films formed by the sputtering method, we propose to study the optical properties of sputtered silver silicon multilayers. The thickness of the silver layers will be 75 A, (it is near this thickness where the complex index of refraction for silver has been reported to have its most radical departure from bulk values). This study will also determine to some extent, if the optical properties are found to be bulk-like, the quality of the thin silver film and to a lesser extent, the compatibility of the sapphire substrate with the silver film. A preliminary test using glass substrates produced easily damaged multilayers whose quality was questionable. Thus, the substrates to be used will be double polished sapphire, so that the film growth will not be subject to the same problems as those formed on glass substrates. The fact that we will be dealing with multilayers will help minimize the chance of oxidation on the silver layers, albeit boundary layers may be germane to this study. The ordering of the stacks will be of the ABAB....AB type as well as the BABA....BA type. Transmission (T), and reflectivity (R), measurements will be made of the various samples at different wavelengths. This will allow us to compare the R, and T measurements on the effect of multilayer arrangement as a function of wavelength; and at each wavelength, to compare this effect as a function of layers. These results will then be compared with theoretical predictions for a multilayer sample consisting of two primary layers. Each primary layered pair (A8 or BA) will be called one period. The theoretical calculations will be based on two types of behavior for the complex index of refraction of silver. The first type will be referred to as the bulk optical constants, the second type will be called the film optical constants. The bulk optical constants for silver are the commonly accepted values for bulk silver. The film optical constants to be used will be those given by Shklyarevskii and Korneeva12. Therefore by using these two different properties of silver in the multilayer calculations, we should be able to determine whether bulk optical constants of silver are appropriate for our films in two multilayer sequences. CHAPTER 1 METHODS Theoretical In order to calculate the expected reflectivities and transmissions from a periodic multilayer system, a program was used which was developed and written by C.L. Foiles. The program was designed for a multilayer having a periodicity of two primary layers. The R and T calculations are made by using the "characteristic matrix" method for multilayer films. This characteristic matrix relates the electric and magnetic fields of one medium to an adjacent medium. The related fields are found by applying the appropriate boundary conditions for E and H. By introducing more layers, one may apply the same procedure, for all boundaries. The relationship between the fields in the first layer and the third layer may then be found by multiplying the characteristic matrix of the first boundary by that of the second boundary. By continuing this process one ends with a final characteristic matrix with which the reflectivity and transmission may be calculateda. A more formal treatment of the matrix method may be found in Hecht and Zajac13. aIt should be noted that light of normal incidence is assumed for the calculations made using this program. 10 11 Experimental In this section we will discuss the methods used and developed to determine the optical properties. A major part of this thesis was the construction and testing of a system which would be capable measuring R and T simultaneously. This optical system will be called the "hatbox". A spectrophotometer was used as a complementary method of obtaining data. Spectrophotometer The spectrophotometer used was a Beckman DB-GT Grating Spectrophotometer. It was used in the double beam mode. The double beam mode sends one beam of light to a reference plate in an integrating sphere. The second light beam, sent alternately with the first light beam, is directed to the sample plate inside the same integrating sphere. The detection system then measures the amount of light reflected from the reference and compares that with the amount of light reflected by the sample. By assigning the light measured from the reference to be 1001, the spectrophotometer can then give a readout of the reflectivity of the sample in per cent. The spectrophotometer is also capable of measuring the diffuse light from the sample by throwing away the specular light, thus giving an estimate of the surface roughness of the sample. One limitation of spectrophotometer is its limited spectral range; it only covers wavelengths from 388 to 729 nm. Another drawback is its inability to measure the optical transmission. Thus, there was the need for a new system. 12 Hatbox As the name might suggest, a hatbox was instrumental in the design of‘the new system. The goal was to design and set up a system where the reflectivity and transmission could be measured simultaneously. As a result, a hatbox was used as the "optical chamber", where R and T could be measured. Figure 1.1 gives a top view of the system. The scheme is straightforward. Light is focused from the source by a lens to a collimating mirror. The mirror then reflects this light to the "front" side of the monochromator. As the desired wavelength of light leaves the "back" side of the monochromator it passes through an aperture before entering the optical chamber (or hatbox). Once inside the hatbox, part of the light is reflected by the sample to a photomultiplier, where the amount of reflected light is measured by the output voltage of the photomultiplier. If the sample is neither completely reflecting nor absorbing, part of the light will be transmitted through the sample. This light is then measured as the transmitted light in the same manner as the reflected light. In order to obtain the true reflectivity and transmission one has to calibrate the reflected and transmitted light relative to the incoming light. Bylinspection of figure 1.1, the calibration for the transmitted light is obvious. Indeed, with the sample mount empty, the light is free to pass through, unobstructed, to the T detector, thus giving the T calibration. The task of calibrating the R detector is somewhat more challenging than that of the T detector. Originally, it was thought 13 T detector /\ / filter / \ R detector ope rture / \ monochromator light source F L. . l \ I \ lens / mirror Figure 1.1 Top View of Hat Box 11-1 that an easy calibrating method of the R detector would be to simply interchange the two detectors. However the hatbox system proved to be too unstable, at that time, to handle such a disturbance (with the results of the next paragraph, this method might still be possible). An alternate procedure of reflecting light from a sample which has a known reflectivity was used to determine the incident light relative to the R detector. This procedure was accomplished by using a special mirror that has a known reflectivity; however, even this calibration method was not without its problems. After finding large discrepancies between different experimental runs of the same samples, reproducibility soon became a major goal. Various factors in the hatbox setup were found to have played an important role in the calibration problem. However, it wasn't until the photomultipliers were tested for position sensitivities that the biggest stumbling block was located. To determine the position sensitivities of the detectors, i.e. , the effect of light entering the photomultiplier apertures at different positions, a 2 mm by 20 mm beam of light was scanned across the face of each photomultiplier tube. The photomultipliers were held in a horizontal position during the first pass and then in a vertical position for the second pass. The results indicated that one of the detectors being used was extremely position sensitive, while the other was marginally acceptable for this experiment. Suitable changes were made with the problematic detectors, as well as a procedural change in getting a reliable calibration. The most important factor involved in getting a reproducible result was being certain that the light entering the detector fell in the region 15 of the photomultiplier which gave acceptable limits of error for R and T measurements. With this final adjustment, the hatbox system was ready for use. The interior of the hatbox itself was covered with black paint. This was used to minimize the effect of stray light. The port holes were made to fit snugly around the two detectors and aperture. Black tape was used around these boundaries to eliminate any outside light from entering the system. A black wall was placed along the diameter of the hatbox with a port hole large enough to allow the light beam to the sample but not so small that it obstructed the reflected light. This was done to minimize the chance of "optical talking" between the detectors. As best as could be'd'etermined, the hatbox was light tight for these measurements. The amount of incoming light could be adjusted to suit most demands. At the front and back sides of the monochrometer are grooves where interchangeable varying slits may be placed. Once one determines the reduction factors of each slit over the working spectrum, one may choose the slits to optimize an output measurement without destroying the calibration. The monochromator is capable of easily covering a wide range of the spectrum by using any one of three mounted diffraction gratings at the flip of a switch. Unfortunately the detectors used for this project do not cover the same range, and thus data are limited tn) the ‘visible range. Finally, after the light leaves the monochromator but before it reaches the sample, it passes through an order sorting filter. This filter is used to eliminate higher order reflections from the diffraction grating. 16 System checks were made by testing bulk samples and comparing the results to those from the spectrophotometer and multilayer calculations as well. The samples used for this test were a 1,000 A Ag film with a 50 A Si overlayer, and a 1,000 A Si film. All samples were made on double polished sapphire substrates. Figure 1.2 gives R as a function of photon energy for the 1000 A Ag film with a 50 A Si overcoat. Excellent agreement between the theoretical curve (-) and the measurements made by the hatbox system (0) are obtained up to an energy of 2.9 eV. At 3.0 eV the reflectivity measurements begin to tail up off of the curve. Unfortunately, the measurements made by the spectrophotometer (+) fall short of the calculated and hatbox results between 1.7 and 2.11 eV. Above 2.11 eV there is good agreement between the spectrophotometer data and theory. Figure 1.3 gives similar data for a 1,000 A Si film on a sapphire substrate. Both experimental systems show qualitative agreement. However in this case the range of good agreement for the spectrophotometer data with theory is from 2.1 to 2.7 eV. The close but offset trace of the hatbox results suggest a systematic calibration problem, and beyond 2.7 eV the hatbox gave a somewhat. higher reading for the reflectivity. At this point a broader context is needed. If these two sets of data were from different investigators then they would be comparable to much of the data in the literature. Differences of 10% are not uncommon and suggestions of surface problems such as roughness, contamination, etc. are typical. Since the "anomalous film effect" of interest involves differences of > 101 and systematic trends, we 17 believe that the two optical measurement systems are adequate for the task at hand. However, the differences in absolute values for these two systems are worthy of further study. Figure 1.1-1 shows the transmission for the 1000 A Si sample as found by the hatbox. From 2.11 to 1.9 eV, the hatbox begins to fall off of the expected values for this sample. At 1.7 eV, the hatbox shows the T going to 0%, while the calculation gives 50%. Further investigations suggest that this is not a systematic problem with the hatbox. Multilayer Preparation and Characterization For the purposes of this thesis the Ag-Si multilayers should be viewed as independently supplied and well characterized samples. The multilayers were prepared by sputtering Ag and Si onto polished sapphire substrates at ambient temperature. The sputtering was done in a 2.5 mtorr atmosphere of pure, dry Argon gas; the sputtering rates were 2 A/s and 15.11 A/s for Si and Ag, respectively. The positioning of substrate relative to target necessary for layering and the monitoring of sputtering parameters were done automatically by an IBM PC. The sapphire substrates were 13 x 13 x 1 mm in size. The final samples were characterized by x-ray diffraction studies. Bragg peaks at low angles determined the compositional period. This period was within 6% of its nominal preparation value. At higher angles there were no Bragg lines from Si but the (111) Bragg line for Ag was observed. The linewidth of this Ag (111) line indicated a coherence length that was less than the compositional 18 + spectrophotometer __ theory 0 hatbox 3 3.0 2 . O O V 30 O O O 1\ L0 L0 90 BO % U1 AltAtnoaIIau Figure 1.2 R vs E for 1,000 A Ag with 50 A Si 20 10 1 Energy in eV 19 m. >m :fl >memcm o.mu mw.m cmumsouocaocuomam + xooumc o >Lomcg I1 .fi om cm on om om % UI AAIAIAUBIJBH Figure 1.3 R vs E for 1,000 A Si 20 __ theory 0 hatbox l rhlrnn_41\ ‘r‘vvvv % UT UOTSSTUJSUEJL Figure 1." T vs E for 1,000 A Si 3.5 3.0 Energy in ev 21 period but was comparable with the Ag layer thickness. These data are consistent with isolated, crystalline Ag layers separated by amorphous Si layers. CHAPTER 2 RESULTS AND ANALYSIS In this chapter we will report the experimental findings and compare them to the calculated results, for multilayer behavior. These results will be presented in tables. Graphs of selected information will then follow to facilitate the identification of systematic trends. These trends are the basis for judging the agreement between theory and experiment. The multilayers are made by repeating a basic bilayer unit of 50 A amorphous Si, and 75.3 A Ag; the Si layer is amorphous and the Ag layer is crystalline. Uncertainty in the thickness of one period, i.e. one bilayer unit, was 6%. If one assumes an uncertainty of 10% for the thicknesses in the multilayer calculations, one finds an uncertainty of only 2 to 3 1 in the reflectivity and transmission calculations. This error is less than experimental error and thus the multilayers can be viewed as well characterized for optical studies. Table 2.1 gives the calculated results for the samples made with Si first on the substrate and silver on the outer surface. These calculations used the bulk optical constants for Ag. Table 3.2 uses the same parameters as Table 2.1 except now Ag is next to the substrate and the Si is on the outer surface. Tables 2.3 and 2.11 present results equivalent to Tables 2.1 and 2.2, respectively, when the film values of optical constants for Ag replace the bulk values. Tables 2.5 to 2.8 give the experimental findings from the hatbox and 22 23 the spectrophotometer. The term hatbox denotes the optical system constructed with the hatbox, and capable of measuring R and T; hereafter it will be abbreviated by "hb". The term spectrophotometer denotes the Beckman spectrophotometer, which incorporates an integrating sphere; it will be abbreviated by "sp". Reflectivity versus Energy Figure 2.1 shows the reflectivity versus the energy of a three period multilayer. The broken line is the calculated reflectivity for silver on the outer surface and silicon first on the substrate. The solid line is the calculated reflectivity when the silver film 115 the first material on the substrate and the silicon layer is on the outer surface. For the purpose of this thesis, the letters "ofs" denote the words "on front surface" and the word "theory" will be denoted by "thy". The down triangles represent measurements taken by the hatbox for Ag ofs. The up triangles are measurements taken by the hatbox for Si ofs. Considering the case when Si is the outer film, the agreement is good, both qualitatively and in magnitude, between the reflectivity measured by the hatbox and the calculated reflectivity. The uncertainty in the hatbox measurements is never greater than one per cent, however this assumes all uncertainties are independent and random. That assumption is likely to be in error, since repeated measurements indicate that reproducibility of results is i 5 to 10%. When Ag is the outer film, the hatbox gives less reflectivity than that predicted by theory. 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CE 20 - —l 10 l g L l L I A l 1 l L A l l l j l 1 L 1.5 2.0 2.5 3.0 3.5 Energy in ev Figure 2.1 R versus E for three periods,'bulk silver, hb. 55 I I I I I I I I I I I I I I I I I I I 3Q ,,/ """""" z.-. 45 " A “/o \ """ \ -‘ 5 v1/’ v '5 x/e v , >~ ' /' V A ‘J 117/ 4' P"- -H - W. V 35 - ' ‘V ‘V VV‘V 1A — .3. // v v 4.) U I- A A .1 m A F‘ A ‘3; 25 '- A v :9 ole -‘ II A A All on 1- A A A -.o- tn, " 0“ .1 -0.- th’ 3‘ 0". l I l l l l l L l l l A l l A L l I l 1:5.5 2.0 2.5 3.0 3.5 Figure 2.2 Energy in eV R versus E for three periods, film silver, hb. 33 deviation from theory in the infrared region. In figure 2.2 the calculated results are for the film optical constants of silver. A much different behavior is expected for film Ag for this three period stack. After reaching a maximum at 2.5 eV, the reflectivity is expected to decrease as the infrared region is approached. The hatbox data do the opposite. It reaches its minimum at 2.5 eV, and begins to increase on both sides of this point. The difference in magnitude is considerable for both sets of samples and approaches 20% with Si on the front surface near the 2.5 eV region. Results from the spectrophotometer for the three period sample are shown in figures 2.3 and 2.14. Once again, the data in the infrared region are significantly lower than calculated for the case of bulk Ag. When Ag is the front surface film, these data appear to give better agreement with theory for the case of bulk silver than the hatbox data in figure 2.1. These data for Si on the front surface give a poorer fit to theory than the hatbox data. By comparing figure 2.3 to 2.“, one immediately observes the experimental trends favor bulk Ag, rather than the dissimilar behavior predicted for film Ag. The qualitative agreement between theory and experiment is generally poorer when Si is on the outer surface. All the data give significant discrepancies in the infrared region. Figures 2.5 through 2.8 give the results of R versus E for a four period stack. Bulk Ag again predicts high R in the infrared region, decreasing to a minimum at 2.3 eV and slightly increasing into the ultraviolet region. The hatbox data, (figures 2.5 and 2.6), show very little front surface distinction except in the infrared region. This Reflectivity in % Reflectivity in % 3h I I I I I I I I I lfi I' I I I I I . 7 — \ .. O 9A9 at! - \ E] u on ‘ 60 - \ "’ -thy M on ‘ . 0 \ "" My 3. of. .. 50 - 4 40 - - 30 - A 20 - — 10 l 1 l l l l k 1 l l l l l L l A l J A 1.5 2.0 2.5 3.0 3.5 Energy in eV Figure 2.3 R versus E for three periods, bulk Ag, sp. 55 I 6 I I I I I I I l I' I I I l I I I I 0 - C] 6’ . ,z’ """""" 2.-- 45 "' a 0,.V' \ """ \ ‘1 :z’ o /’ °‘o - /. E] 0 0 0 0 0 2._ d ./'—"_"\./"l 35 - l/W"a - /’ . E] E] [3 [3 .. C] a 0‘3 25 '- [3 E] D On an ._. Bu on - -.o—th’ ‘9 0‘. " curd—thy 3‘ 0" 15 1 l l A l l L l l l l 1 l l 1 l l L l 1.5 2.0 2.5 3.0 3.5 Figure Energy in eV 2.“ R versus E for three periods, film ag, sp. Reflectivity in % Reflectivity in % 35 I I I I I I I I I I I I I I I I so — \\ r \ V" on 4 70 _ Au on _ _ \ .. ..tlw M at. q 60 _ A \ . --'uw u on _ '- 1 50 - - 40 - — 30 - — 20 - _ 10 L l l 1 l A 1 l l l l l l A L 1_ 1 1.5 2 0 2.5 3 0 Energy in eV Figure 2.5 R versus E for four periods, bulk Ag, hb. I I I I I I I I I I I I I I I I I 80 - ' v A. m d 70 "’ A“ on ‘ _ ..a— thy A9 “i - 50 _ A .. " ’“A— ----- \_-.___ A . 4° - ’2. . “7:? - a. ‘ " fi'?“‘“‘---:ér7' '- _ _ V 3 X Z X X . 20 - — I l I l l l A l l I l l l l l l l 101 5 2.0 2.5 3.0 Figure 2.6 R versus E for four periods, film Ag, hb. Energy in eV Reflectivity in % Reflectivity in % 36 i f I I I I I I I I r r r I I I I I I so - \\ . \ On at: 70 _ a 'I 0!! .. \ — ’thy M on 50 "' E1 \ "'7 II on 50 '- 40 - 30 *- 20 '- 10 I L I I l I I L j l I L L l I I I I L 1 5 2 0 2.5 3 0 Energy in eV Figure 2.7 R versus E for four periods, bulk Ag, sp. I I I l I I I I I I I I I I T I I I 80 - ' 0" on 70 "' Bu on .. -.._thy M on so .- E] coo-CH, ,I 0!. . o a 50 '- 0 El . °_ _____ I“, 0 N---"\ 40 — 0 o "M - /-’—'~B-—-3.i° ° Lifi—a ...._- El E] 30 ' a a . BIJEJCIB 2O '- L L l I l I L L I J I I l L l l l I I 101.5 2.0 2.5 3.0 Energy in eV Figure 2.8 R versus E for four periods, flim Ag, sp. 37 lack of distinction makes the quantitative discrepancy between theory and experiment particularly large when Ag is the front surface. However, in figure 2.7, the sp data do show a surface distinction for this four layer stack. This type of discrepancy between these experimental data requires further study. Qualitatively, figures 2.5 and 2.6 suggest bulk-like behavior in the infrared and ultraviolet regions of the spectrum. Although between 2.2 and 2.8 eV one might argue that the change in magnitude of the hatbox data supports film-like behavior over bulk. For example, at 2.5 eV bulk silver gives a 120% increase in the reflectivity when going from Si to Ag on the outer surface, film Ag predicts a 26% increase, and the hatbox finds an increase of 12%. However it would be more difficult to support film behavior as opposed to bulk behavior when considering the systematic trends for the entire range of energies. Figures 2.7 and 2.8 show R versus E for a four period stack using experimental data from the spectrophotometer. Here the surface distinction is clear but not as large as bulk Ag would predict. One anomaly in these figures is the apparent flip-flop of the reflectivity in the infrared region. It is not predicted by either the bulk Ag or the film Ag. Thus, although a number of clear discrepancies occur, the overall trends are more consistent with bulk Ag behavior. For figures 2.9 and 2.10, where R versus E is given for a five period stack using the hatbox data, the same problems exist here as for the hatbox data of the four period stack given in figures 2.5 and 2.6. The hatbox does not find a surface distinction, although there are hints of it in the infrared and ultraviolet. The surface 90 80 70 60 50 40 3O Reflectivity in % 2O 10 Figure 90 80 7O 60 50 40 30 Reflettivity in % 20 10 1 Figure 38 r I I I I I I I I I I I fi D \ .1 — V" on _ _ \ Au on g _ \ - -"W A. on _ _ \ —'thy u on . - J r- I1 L I I L l I I I I 1 LI LIL I I J I L 5 2.0 2.5 3.0 3.5 Energy in eV 2.9 R versus 8 for five periods, bulk Ag, hb. Energy in ev 2.10 R versus E for five periods, film Ag, hb. I I I I I I I I I I I I I I If I I I _ 7 Ag all _ h A II on d .— Inco- ‘h’ l. ..a J .- —-—thy 3. ”I, 1 — A -1 I- -4 n v A q _ _--V-é‘oo—~.-‘ ........... /--.A_% A _ “""37%~—«~_ user/”5’ _ n A A V ‘i b A v _ Xaevvv q - I I I I l I I I L l I I I I l I I J I . 5 2 . 0 2 . 5 3 . 0 3 .5 39 distinction is clearly found for the five period stack by the spectrophotometer, in figures 2.11 and 2.12. Even more exciting is the very good agreement between the bulk Ag predictions for both surfaces and sp data (except for the infrared region where the measured reflectivities fall short of prediction again). And by comparing figure 2.11 to 2.12 we see that bulk behavior is definitely favored. Analysis of the six period stack from figures 2.13 to 2.16 confirms again the bulk behavior of our Ag-Si films. The hatbox data, in figure 2.13, this time do find a surface distinction, although in this case there appears a flip-flop in the infrared region. And again, for Ag on the front surface, the reflectivity is lower than expected by bulk Ag. But in figure 2.15, the sp data for Ag on the surface have higher R than the hatbox, and fit well with the bulk Ag curve. For tflue eight period stack the hatbox data find no surface distinction except in the infrared where the R flip-flops from bulk Ag (and film Ag) prediction, figure 2.17. However there is qualitative agreement between the sample with Si on the surface and bulk Ag prediction. The sp data for the eight period stack do find a surface distinction, but not as large as bulk Ag predicts, figure 2.19. There is a hint of the dip in the sp data, but not as large as that found by the hatbox. Overall, the tendencies seem to favor bulk Ag. The experimental data from both the hatbox and the sp on the twelve period stack do not find a surface distinction, figures 2.21 to 2.2“». And in both cases the reflectivity flip-flops in the infrared. In figure 2.21, the hatbox gives good agreement with bulk Ag for Si on Reflectivity in % Reflectivity in % NO go I I I I I I r I I I I I l I l I l I 1— . \ 4 BO - \ 0M 0!: .1 .. Q 81 on ., 70 '- \ — -thy Aq on - ’ 0 \ "" "it at .g, ., 50 _ E] 0 \ q “’ '3 o 0 \. ‘ 50 '- 0 o\ - °\ \ / \ _ I 40 - <> 0 — - . 0 0 0 o .. 30 - .. 20 - .. 10 r. g I 1 I I I L I I I L I I 1 I I L L 1 I 1.5 2.0 2.5 3.0 3.5 Energy in eV Figure 2.11 R versus 3 for five periods, bulk Ag, sp. 90 I I I I I I I I I I I I I I I I I I I 30 "' 089 at! ... - E181 on ‘ 70 ... --._thy A9 on .. F’ 0 —-—thy 81 on .. 50 ,— 0 0 .— - E] 0 .. .. 0 _ 50 E] 0 . o .1 40 r- —---—-El~ ----- ‘0 ___ Q E .— ..... "l B " . "6"0 0 0 e . 30 r- “..E'" 'fl‘m -1 . EJBEJEIB . 20 r- d 10 I L I L L I I I I l I I L I l I I I L 1 5 2 O 2.5 3 O 3.5 Energy in eV Figure 2.12 R versus E for five periods, film Ag, sp. H1 Figure 2.1” Energy in eV R versus E for six periods, film Ag, hb. 90 I \I I I I I I I I I I I I I I | I so — \ _ V" on N ,. \ A II on ' C 70 L- \ .. ..a: A. on " 'F‘ £5 \\\ --tny II can ‘ 4-) I- q -H >1 50 - 1 -H 44 ’ . L) 40 .. _ a) H " . H- 0.1 30 — -« CI: ~ 1 20 - - F «I 10 I I I 1.5 3.5 Energy in ev Figure 2.13 R versus E for six periods, bulk Ag, hb. go I I I I I I I I I l I I I I I I I I I 80 L— - N ’ - v I. do .1 70 _. A“ on _ c '- --.- ‘h’ ‘. .‘i .H A —o— III] 3. ”I. ‘ 4-J - 9 cl -H >1 50 - - -H 4a ' E: :K ' m \--‘ ..... ’-,’—V' " r-I ' “\AE """" V . ‘ .2 V'V Viv ,éwv' g 30 '- \“-\__&_-—,LV—A—'Z’A - h A A n 20 __ 15 A» _ 10 I I I I I I I I I I1 I I I I LJ I I III 1.5 2.0 2.5 3.0 3.5 Reflectivity in % 112 90 r I . 1 I I I I I I 1 I I I I _ \ ‘ l so - \\ _ . \ 0A1 oh ‘ 70 _. <9 \ E] u on .1 . 0 - -thy IQ of. I 50 " E] 0 \ "— thy 3' a“ —1 . [3 0 \ . 50 - E] o \ .. .. o . 40 "' °\G\° “’ - _ El vo’é'VO 0 .1 30 - - 2O - - 10 I L I I I I L I I I I I I I I I I I 1.5 2.0 2.5 3.0 3.5 Energy in eV Figure 2.15 R versus E for six periods, bulk Ag, sp. go I I r I I I I I I I I I I I I I I I I 80 _ ON; on _ " Bu 0!! .1 N 70 P- ...-‘h’ M 0.. ‘1 C o ..a—any u on .fl -- 0 a 3:. - D o . '3 40 - a o °‘ 50 - - 4.1 .- d -r-4 >- 50 - _ .H .- .- 4.) c: 40 - _ o: H " a :5 30 t- n a: - 1 20 - d r - ‘ 10 L I I I L I I I I I I I PI L I I 1.5 2.0 2.5 3.0 3.5 Energy in ev Figure 2.17 R versus 8 for eight periods, bulk Ag, hb. 90 I I I I I I I j I I I I I I I T I I- 4 80 - — _ v M on d __ A" on 70 --a-III t", I. 0“ -‘ I. A ..a—dim ’I '3‘. " 60 *- - l. .. A. 50 - V' — ' v 9 ‘ 40 — A .__ A,“§L~ - . v /“’- 9-0—.- I 30 F" _"’-‘ , /.I'_"-FV -+ . —_-_"/‘ x x x ., X x X 20 .. _ 10 I I I I l I I I J I I I I I l I I d 1.5 2.0 2.5 3.0 3.5 Figure 2.18 R versus E for eight periods, film Ag, hb. Energy in eV ill} go 1 I\I I I I I I I I I I I I l I I I I 80 h \ ‘ . \\ <>Aq at: 4 R 70 _ \ El 3' on _ S . Q \ _ -thy A9 on 4 4-) .- . 4-! >. 50 - _ ..-1 _ .1 4) OJ r-I ’ - u. m so - — m " d 20 - q 10 P 4 J L I l L I I _I l I I I I l I I I I 1 5 2 O 2.5 3 O 3 5 Energy in eV Figure 2.19 R versus 8 for eight periods, bulk Ag, sp. 90 I I I I j I I I I I I I I I I I r I I 30 r- -1 N .. ON on - 70 {- Uu on "‘ E '- "'"-"'Y *9 on 4 > 60 - g a —-—Ihy 3' of: _ 4.) .- .4 .H 4 +4 ' [3‘° 8 40 - o 9""r I ''''' - F. ‘ ,Ela” <9 °.o ”Angfg ‘ II- _.."‘ -___’--’ B _ m 30 I. ‘9‘, a B a m . _-—”/ a B a d - I I I I l I I I I l L I L I l I L L 105 5 2 O 2.5 3 0 3.5 Energy in eV Figure 2.20 R versus E for eight periods, film ag, sp. . Reflectivity in % Reflectivity in % NS go I I\I I j I I I I l I I I I I I I I I- \ 4 30 - \ - ' V" on ‘ 70 L— \\ Quito!- _ .- \ --‘h’”... 4 50 _. A ——:M u m _ .J 50 L -+ 40 - -+ 30 - - " '1 20 '- _ 10 I I I I I I I I I I I L I I I I I L I d 1 5 2 0 2.5 3 0 3 5 .Energy in eV Figure 2.21 R versus E for twelve periods, bulk Ag, hb. go I I f I l I I I I I I I I I I I I fiI 80 *- _ . v A9 a“ ' . 7o _ A" on _ _ ...... thy A. “I q --—thy 3| on so - A — - J so-— A - . V' e: l 40 '- v A ____ ____ 12" "J :- "/--"-'_’ r .p- .4 30 '- / 'f..Y_A._—v— x‘r -‘ .. / V 9 X x .. 20 - £113 ~ . J I L I- I I I I I I I PI L L I L I I I 191 5 2 0 2.5 3 0 3 5 Energy in eV Figure 2.22 R versus 3 for twelve periods, film Ag, hb. Reflectivity in % 90 I I \I I—I I I I I I I I I I I I I I r \\ - 80 I. \ 0A9 ols '- ' Q It on " 70 I. \ "" ”guy he on I 60 :_ E] \\ '-"¢hrst¢us J 50 "' ..q 40 '- -1 F J 30 - .. 20 - _. 1o 4 I I L I I I I L I I I I I I I I I I 1.5 2.0 2.5 3.0 3.5 Energy in eV Figure 2.23 R versus E for twelve periods, bulk Ag, sp. Reflectivity in % Figure 2.2a R versus E for twelve periods, film Ag, so 80 70 so so 40 so 20 10 1 I I 7 I T I I I I 1 I 1 1 I ' r T 1 - _4 " 0“ on . " Bu cu _ ----"'Y M on - D —--—Ihr SI of. j .- D ‘ _. o E! - .. 0 d -— j..a’ ........ --"" -------- ’- ----- j " a —/‘T:T'" / — -—- - _ _ D a _ ' ”/— fr-e'l‘iielral5l5:>'<><><><9 _ I I I I I I I I I I P l I I I I I I L 5 2.0 2.5 3.0 3,5 Energy in eV u? the surface, except in the ultraviolet where the reflectivity rises above that predicted by theory. In summary, although a number of varying discrepancies between theoretical predictions and experimental results occur, the experimental results appear to be more consistent with bulk optical constants for the Ag films. It should be noted that the hatbox data, data that gave the more significant deviation between theory and experiment, always followed the general shape of the bulk Ag curve and gave a strong dip at 2.11 eV. This tendency should be contrasted with the behavior for film Ag, where the reflectivity remains relatively constant across the spectrum, and in fact slightly lowers when approaching the infrared, when bulk Ag and experimental data increase drastically. The discrepancies between hatbox and spectrophotometer data do not alter the choice between "bulk" or "film" behavior; however, these discrepancies are disturbing since the hatbox system requires specular reflections to be accurate while the spectrophotometer does not, the quality of the sample surfaces and/or the Ag-Si interfaces need further study. Initial tests are in process. Transmission versus Energy In figure 2.25, T versus E: is given for the three period stack. The bulk optical constants of Ag were used to calculate T. The features of this graph would seem to indicate fair agreement beween theory and experiment. However, theory predicts that the stack with Si on the outer surface should have a higher transmission than the stack with Ag on the surface, whereas the exact opposite is found 148 experimentally. If one calculates the change in magnitude at 2.2 eV upon reversing the order of the stack, we get a 1&1 change with tnUJc Ag, a 51 change with film Ag, and a 1% change in the other direction experimentally. A sufficient explanation for this anomaly has yet to be developed. In comparing figure 2.25 with 2.26, we find that the theoretical differences between bulk and film Ag are quite large. In the case of film Ag, theory gives a steadily decreasing transmission as the energy increases, and also predicts little to no change when the order of the stack is reversed. On the other hand, bulk Ag predicts that the transmission will increase until it reaches a maximum near 2.1 eV where it then begins to decrease with increasing energy. A small.tnit significant surface distinction is predicted. The energy dependence‘ of'the transmission is more consistent with bulk Ag behavior. In figures 2.27 through 2.36 there is general agreement between calculations for bulk Ag with Ag on the front surface and the hatbox data but these experimental data give a larger surface distinction than is calculated. The data generally disagree with calculations for film Ag. In summary, the transmission data has an energy dependence that is more consistent with behavior predicted for bulk Ag. Transmission in % Transmission in % N9 40 t I t I ‘ I I T r I 1 y 1 r I f U 1 .. V” on 4 A It all 30 _ .. ..thy A. on ..1 "fihr H on 20 _ ‘ 10 P 3 .q k J l 1 19 L l L l I L l J L L l A 1.5 2.0 2.5 3.0 Energy in eV Figure 2.25 T versus 8 for three periods, bulk Ag. 40 I 1 I I I I I I I I I I I I I I I - v lg on " A" on \\‘ é...— tlw M a“ 30 - \\ —o—th1 3! oils - \. “VL. Vvv VNAV 20 - A_A \\~ Asg - A ‘:§. X‘v .. ‘\_. AX .. A X 10 - . :Z:g; _ llLllllllIllllllll 1.5 2.0 2.5 3.0 Energy in eV Figure 2.26 T versus 8 for three periods, film Ag. Transmission in % Transmission in % 50 30 I I I I I I I I I rI I I I I I , VM on . A u on .. ..thy M on """Ny II on 20 - 2L5 Energy in eV Figure 2.27 T versus 8 for four periods, bulk Ag. 30 I I I I I I I I I I I r I I ! F fi V 89 all " \\ AI. 9“ ‘§ ----— thy A. oll' ‘:\ —-—thy 3| 0!! 20 "" \CKV V V‘\3 V .§‘ V . ‘~§‘ V ‘~§. v V a A.A.A '\\ v 10 - ‘3 A. A.2§‘. APQZ.V' A\‘V - A $2 A \s LW’. 1 l 1 n 1 .L l A A L L I l 1 Energy in eV Figure 2.28 T versus E for four periods, film Ag. Transmission in % Transmission in X 51 20 r I I r r I I I I l r I I I l T I ' V“! on A u on _ -thy M on —"thy II on 10 - 1.5 Energy in eV Figure 2.29 T versus E for five periods, bulk Ag. v A, on A" on ..a—0 May A1 016 ..a—thy QI 0", Energy in ev Figure 2.30 T versus E for five periods, film Ag. Transmission in % Transmission in % 52 7‘1 on A u on _ ..tlw M on "‘1“ It on 10- o W l l I l I l l l L l l l 1.5 2.0 ans 3:0 . Energy in eV Figure 2.31 T versus E for six periods, bulk Ag. 20 I I I I I I I I I l I I I I r I I \‘ v A. on \ A II on .- \ -00- "If M O“ \. —-—u.y u on Energy in eV Figure 2.32 T versus E for six periods, film Ag. Transmission in % Transmission in % 53 20 I I I r I I I I I I I I I I I I rIfi VI, 0!. " A II on " .. ..tlw A. on —"thy II on 10 - _ Energy in eV Figure 2.33 T versus E for eight periods, bulk Ag. 20 I I I I I I I I I Ifi I I I I I I I I 7 lg all . A II on ..s-.- thy A1 9“ —-—thy II or“ . \. . \. \. VVfinHy figéélllélfhm 1.5 2 0 2.5 3.0 3.5 Energy in eV Figure 2.3A T versus E for eight periods, film Ag. Transmission in % Transmission in x 5H 10 I I I I I I I I I I I I I I 1 q" etc A II ole .. ..uv n 0“ ‘1“, .‘ 0'. .A-i 1.5 2. Energy in ev Figure 2.35 T versus E for twelve periods, bulk Ag. o 245 ‘6? ‘axr 3.5 10 I I I I l I I I I I Ii I I I V A, all A" a“ ..a-- I“, ‘Q 0... —.- thy ,I 0" \\ \\ \I\-.\ Energy in ev Figure 2.36 T versus E for twelve periods, film Ag. 3.5 CONCLUSION The object of this thesis was to construct a system that measures reflectance and transmission and subsequently use this system to determine if multilayers involving ultrathin Ag layers have optical properties of bulk Ag. Based upon the analysis of the results to date we conclude the following: 1. Our multilayers formed by sputtering have optical properties more consistent with bulk optical constants for silver, than with anomalous film optical constants. Since our sputtered multilayers show bulk—like behavior, we conclude that silver films made by sputtering form a continuous film (as opposed to those made by evaporation referred to earlier in this thesis) and the limiting continuous film thickness remains to be determined. 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