A Multitechnique Approach for Materials Characterization Using X-Ray Diffractometry, Visible Spectroscopy, and Atomic Absorption Analysis to ~etermineThin Metal Film Thickness Alfred T. D'Agostino College of Notre Dame of Maryland, Baltimore, MD 21210 I t is important to provide students taking advanced undermaduate chemistm laboratories with intemated exercises that use a number of instrument-based tGchniques in the solution of one analytical problem. Within such a framework, students can make a direct comparison of results from different protocols and evaluate the accuracy, precision, and physicochemical basis of each method. Moreover, in light of the pronounced interest in the properties of materials, undergraduate chemists should be introduced to topics in materials science and especially to characterization techniques. Composite, ceramic, polymeric, and semi- and supercouducting materials now play a significant role in tecbnologically important processes and applications and have thus become the objects of intense research and development activities. These materials are often used a s thin films. As such thev exhibit uniaue oro~ertiesand structures. I t is not surprising tben thai on;! oithe most sought-after quantities in evaluation of materials is film thickness. In manv cases it must be determined nondestructively. The strategy described in this article features experimental protocols that students can use to determine thicknesses of thin metal films. Three methods-X-ray diffractometry (XRD),transmissiodreflection visible spectroscopy, and flame atomic absorption spectroscopy (AAS-are applied to metal film analysis in a way that demonstrates their relative merits and role in materials characterization. Outline and Theory In the first part of the three-part experiment, direct application of a modified Scherrer equation is made by stu-
892
Journal of Chemical Education
dents in the determination of the mechanical thickness of highly oriented monocrystalline Au films. The equation
is used where: D is the film thickness, h i s the wavelength of the incident X-radiation, 0 is the Bragg diffraction angle, and K is a numerical constant. Arelationship between the corrected width a t half-intensity of an XRD profile and D is used. Accuracy of this approach depends on the success in measuring and obtaining the actual width a t half-intensity B of the diffraction peak and in selecting a n appropriate value of K. Broadening of the Au (111)diffraction profiles observed from highly oriented thin films (100 to 500 A) is appreciable (relative to that observed for bulk Au samples), thereby allowing accurate film thickness to be calculated. In the latter oarts of the experiment, film thicknesses are evaluated by'two ind e ~ e n d e n methods: t transmissionlreflection visible mettr&-copy and flame AAS. Acomparison is tben made of'the results obtained from each of the three methods. Ikaditionally the Scherrer equation has been applied to crystallite-size determinations in powdered samples by interpreting profile broadening. The phenomena of Bragg diffraction broadening from small crystallites was first observed and treated by P. Scherrer in 1918 (1).By a n approximation method he obtained an expression of the form shown above with the valueofKequal to 0.9394. The validity of this equation was supported by Bragg (2)and von Laue (3).Later Murdock ( 4 ) ,Patterson (51,and Stokes and
Wilson (6)made significant contributions to its various applications. The quantity K can assume values from 0.70 to 1.70 (7) depending on a number of factors, including: crystallite shape, (hkl) indices of the reflecting planes, and the particular definitions of D and peak breadth. Schemer proposed that the peak breadth used for calculating D be obtained from the experimentally observed breadth of a diffraction line bv subtractine - from it the breadth of a diffraction line produced under the same geometrical conditions hv material with mstallite sizes that would not contribute to broadening. To compensate for instrumentally induced broadening Jones (8)and Warren (9)made rigorous analyses of the contributing factors and proposed methods and formulas for making appropriate corrections. These procedures included deconvolution and Fourier methods. The Schemer equation is used in this experimental context to calculate the thickness of highly oriented Au films based on the broadening of XRD profiles. Students are offered an opportunity to use the XRD technique in a novel way, that is, a s a nondestructive characterization technique. They record the full width a t half-maximum (FWHM) of the Au (111)diffraction profile using a conventional goniometer, correct it for instrumental broadening, and use it to obtain D. In the second part of the experiment, a visible spectral analysis involving measurement of film absorbances in transmission andlor reflection mode is made. Film thicknesses are calculated from this data using a nonlinear least-squares computer program run on a personal or mainframe computer to solve optical equations. Results, however, may be interpolated from previously prepared tables. Analysis of the films by a flame AAS procedure involves measuring film area, dissolving the film from the substrate, and analyzing the sample solutions. Film thickness may be calculated based on a standard calibration curve, film density, and area. Hazards in the Use of X-Radiatlon Caution:X-rays are an energetic fonn of electromagnetic radiation that can cause ionization and damage in matter with which thev interact. The extent of ionization. absorption, and molecular damage in a material depends on the radiation flux, intensity, and distribution of photon energy. Because human tissue is particularly susceptible to injury by X-rays, protection from excessive exposure is necessary. In particular, safeguards against exposure to ionizing radiation produced by analytical instrumentation should be observed. The high X-ray output level used in XRD equipment can create health risks and cause serious bodily injury if not properly managed and used. X-rays are insidious in that they cannot be detected by ordinary means (sensed by sight or touch), and the symptoms of injury (redness, swelling, burns) they cause do not appear immediately after overexposure. You must warn all operators of X-ray generating equipment about the potential hazards in using such devices. You must advise them on how to protect themselves from undue exposure and bow to maintain and safely operate such equipment. It also important to stress the potential danger created by X-radiation and safety practices with students who will participate in the use of XRD equipment. Some of the practical safety issues will be addressed later in this paper. However, additional information about X-radiation and safety can be found elsewhere (10,ll).
Experimental X-Ray DiffractionAnalysis A collection of Au films. with thicknesses under 600 A. were studied. ~ ~ ( 9 9 . 9 9 9 "was ; thermally evaporated onti elass (Cornme. -. tvoe ". 0211, in vacuum (Keim Precision Mir;or, Burbank, CAI to produce films with nominal thicknesses of 100,250, and 500 A.Adiffraction pattern of each sample was recorded using a Siemans X-ray diffractometer having parafocusing geometry. Ni-filtered Cu K, radiation (1.5418 A, 35 kV, 16 mA)was collimated with sets of Soller slits after the source and before the scintillationcounter detector. The divergence and acceptance slits used were 0.5' and 0.2". To determine the crystallinity and orientation of the films, profiles were obtained over the 20 scattering angle between 35" and 85" a t 2" 28 min-' and the pattern recorded on a strip chart. For the thickness analysis, a scan rate of 0.5" 20 min? was used. Optimum recording conditions were established by studying an approximately 100Au film. The (111)diffraction peak was recorded at various scan rates. sensitivities. and time constants. Shifts in peak positionand variations in peak height and shape could be noted. Patterns of all films were suhseauentlv recorded under, or close to, the best conditions found. ~ i o m plete diffraction pattern was recorded from a polycrystalline Au reference standard (foil) supplied with the diffractometer in order to obtain reference profile widths and togauge instrumental broadening. The (102)and (110) diffraction profiles of a-SiOz powder were also recorded under the same conditions. For each Au-film analysis, a smooth curve was drawn through the (111) profile. Peak heights were measured from the background baseline to the smooth-curve maximum. The 28,, angle was located by bisecting the width of the peak at two-thirds height. The widths at half-intensity were measured similarly and recorded in degrees. The half-height widths were determinable to f0.0002" (being measured with a vernier caliper) and that of the 20,,, to f0.01".
A
Visible Spectroscopy
Two additional methods were used to determine the thickness of each film. First we used a procedure that involved measuring the transmittance and reflectance of each film at wavelengths in the visible region. A Cary 14 visiblelnear-infrared spectrophotometer with an expanded sample compartment was used. Measurements were made in delta absorbance defined by
where X is either reflectance or transmittance with the Au film present on the glass substrate; and X, is the reflectance or transmittance with no Au. Absorbance changes of less than 0.2 were measured using an expanded slidewire. Four absorbance measurements: transmission a t normal incidence, 25" for perpendicular polarization, 25' for parallel polarization, and reflection a t 45" perpendicular polarization were taken and numerically inverted by a nonlinear least-squares computer program (12,131. This treatment allowed an overdetermination of the film thickness and optical constants. The data were taken a t five wavelengths (400,450,500,550, and 600 nm) and the average thickness used as the film thickness for all subsequent work. Tables of AA vs. film thickness for each wavelength were also generated for data acquired using the normal incidence transmission mode. Volume 71 Number 10 October 1994
893
The reflection device used two right-angle prisms. The reflection prism could rotate around a pivot mounted directly underneath its right-hand corner. The sample prism had one leg completely silvered. The other leg was left blank. The sample was attached to the blank leg by optical contact fluid to obtain total internal reflection. Transmission measurements were made by supporting the thin film sample vertically on posts attached to a rotating platform using spring clips (13).The optical device and method used is described in detail elsewhere (14,151. Atomic Absomtion Analvsb
In the third method for determining thickness, the films were analyzed by flameAAS. Eachfilm area was computed from length and width measurements taken from the rectangular film. The film was then dissolved from its glass substrate with a minimum volume of 1:l conc. HCIlconc. HN08 and subsequently diluted volumetrically with water (Milli-Q system) to give concentrations of Au in the range of 3 to 10 pg L-'. A series of standard solutions were prepared from a stock solution of Au (Anderson Laboratories). A standard flame AAanalysis was performed on each solution (including blanks) on a Jarrell-Ash 810 AA spectrometer using an oxidizing airlacetylene flame and Au analytical line a t 242.8 nm. The absorbance measurements were recorded on a strip chart and were analyzed to generate a linear calibration plot. Athickness for each film was derived using film area, density of bulk Au, and data from the AAanalysis. Results Film Orientation and Crystallinity
sewed in some cases and followed expected trends (7) Film Thickness
A summary of the results of the three film thickness determinations is given in the table. X-ray-derived film thicknesses (second column) were calculated with the measured FWHM of the Au (111)diffraction profiles from each sample using the Scherrer equation with K equal to 0.9394. Results of the optical and AA analyses are shown (columns 3 and 4). The relative percent deviation from the mean of the visible and AA film thickness determinations are given in parentheses for each data entry Comparison of optical and AA results reveal excellent agreement. They imply that the effectiveoptical thickness determined from transmission and reflectance measurements is a good representation of the mechanical film thickness. However, there is a significant discrepancy between these results and the X-ray-derived results a t higher thicknesses. The disagreement is due to uncompensated instrumental broadening and therefore gives rise to consistently lower results. The width of diffraction profiles observed from thicker films approach that of bulk reference profile. Thus, instrumental broadening becomes a larger, more significant percentage of the measured width. To adjust for the observed disparity, the measured FWHM's were corrected for instrument broadening using a geometrical-mean formula adapted from Warren (16) and Azaroff (17). Contribution to experimentally induced broadening are minimized by subtracting the known (111) diffraction width of the Au reference standard from the sample profile. The functional form of the correction factor appears in the footnote of the table. Film thicknesses were reialculated (column 5) after applying the correction. Agreement between the calculated X-ray-derived thicknesses and the average of optical and AA-derived thicknesses is improved but are still systematically low. An empirical correction factor was applied to the experimental data to adjust B for uncompensated broadening effects. After a variety of mathematical forms were tested for
All Au films studied were found to be highly oriented with the (111) planes parallel to the glass substrate. The only diffraction maxima observed were those a t about 38.2" and 82.0" for all films, corresponding to the (111)and (222) planes. The (200) and (220) maxima were not observed for any film. The Au reference standard had a measured (111)diffraction ~rofileFWHM of 0.1598" resultine fromAbroadeningcontributions due to inComparison of Au (111) Film Thicknesses (D) Obtained strumental effects alone. This was conby XRD, VIS, and Flame AASa firmed by comparing the widths of (102) and (110) a-Sioz diffraction profiles, xRDb VIS AAS X R D- C ~ XRDFIT~ which flank the Au (111)~rofileswith Film No. 28,,,'s of 33.6" and 35.9", with that of the orofiles were not 1 89.1 (-14) 103.6(0.19) 103.2(-0.19) 75.9(36) 86.7(-16) Au stmdard. Au (111) . broadened relative to the powder profiles, 2 109.3(3.1) 106.6(0.57) 105.3(-0.66) 92.5(-14) 108.9 (2.7) which showed no experimental broaden3 106.2(-4.5) 111.6(0.36) 110.8(-0.36) 95.7(-15 ) 113.3(1.9) ine. However. the FWHM of another D O ~- Y 4 128.410.39) . . 127.814.08) 128.0(0.081 . . 101 .O 1-26.6) 120.4(-5.9) . . crystalline foil was broadened in part due 9 124.8(-7.7) 135.2(0.0) 135.1 (-0.07) 110.3(-23) 133.0(-1.6) to crystallites of about 635 A and was not 7 1282 I 132.6(1.5) I I 114.0(-14) 137.9(5.6) used as a standard. The (I1') 28mm for 8 129.3(-2.9) 134.8 (1.2) 132.8(4.3) 114.6(-16) 138.7(4.1) both bulk Au was 38'21"' The 5 115.01-12) 130.4(0.08) 130.710.311 H5.2 1-13] 139.517.1) (200) and (220) diffraction maxima were observed for both samples as well. The (111)profiles of the thin metal films used were more than sufficiently broadened with respect to the reference sample peak and intense to provide accurate width measurements. For example, the . . . . . . . . (dl11 diffraction profile widths of a 106.218 328.8(-33) 485.0(4.39) 488.8(0.39) 428.4(-14) 483.4(-0.72) A Au film and the reference standard 'Measurements reported in A. Relative percent deviation from mean of D (VIS) and D (AAS) given in were 0.9840" and 0.1598". Broadened Darentheses for all data entries. 'calculated from the Scherrer equation with K = 0.9394 and measured FWHM of the Au ( I l l ) dinranion sample profiles observed assumed a . . Gaussian shape and were symmetrical. profile. %alculated with K = 0.8859 and an adjusted FWHM obtained fmm a geametdcal mean correction factor Deviations from remlar and snnmetrical adapted from Warren (7.5) and Azaroff (17). shapes in the profiles resuiting from s= (6- a& - $II'" change in recording conditions were obBm is the measured FWhHM: B, is the FWHM of bulk Au profile (0.1598"). ~
.
&
~
A
894
Journal of Chemical Education
goodness of fit of the data, a n instrumental broadening correction of the following form was applied to each FWHM.
where B, is the measured FWHM, and a and b are constants. The constants were obtained by performing a linear least-square analysis using the average of the optical and AA-derived thicknesses. This approach is simple, and it circumvents the need to determine and apply cumbersome forms of the instrumental broadening. The thicknesses of each film was recalculated with the empirically corrected widths using K equal to 0.8859. (The origin of this value will be discussed later.) A plot of the average D from the optical and AAfilm thickness versus the inverse of the empirically corrected B values yielded K equal to 0.9118. Recalculated film thicknesses are given (column 6). The correlation among all sets of results using this procedure are now a t their best.
Discussion Theoretical Considerations The value of ~ e a u ato l 0.8859 used in the thickness calculation is a resul
