Anal. Chem. 1966, 58, 1282-1285
1282
Absorption Correction in Electron Probe X-ray Microanalysis of Thin Samples A. A. Markowicz,' H.M. Storms, and R.E. Van Grieken* Department of Chemistry, University of Antwerp (LJIA),B-2610 Antwerp- Wilrijk, Belgium
A new expression for the X-ray absorption correction factor In electron probe X-ray microanalysis of thin foils Is proposed and thoroughly evaluated. It Is based on the simple assumption of a uniform X-ray production within the foil. Its evaluation showed that the results are satisfactory for a wide range of elemental composition, X-ray energy, and foil thickness. I n all cases, accuracy is better than for the Yakowltr-Newbury method of absorption correction, which is commonly used in this context.
Evaluation of the absorption correction factor is of prime significance in quantitative electron probe X-ray microanalysis (EPXMA). The problem exists not only in the quantitative characterization of bulk specimens, but also in the analysis of specimens such as thin films, small particles, and biological sections whose dimensions are smaller than that of the region in which X-rays of a given energy are excited in a bulk sample. Yakowitz and Newbury ( 1 ) have developed an empirical approach for the analysis of thin homogeneous layers of uniform thickness (either films or self-supportingfoils). Their absorption correction factor, fY-N,is expressed as ( 1 , 2 ) fY-N
= 1 + (pt/dxH)[f(X) - 11
(1)
where pt = mass thickness of the thin specimen, mg cm-2;pdxH = depth of X-ray excitation, defined below, mg cm-2; and f(x) = absorption correction factor for bulk specimen of the same composition. In the Yakowitz-Newbury procedure the depth of X-ray generation, pdxH,is given by Heinrich's expression (2):
pdxH = 0.007 (Eo1'66 -
(2)
where Eo,E , = energy of incident electrons and critical excitation energy of the measured X-ray line, respectively, keV, while the bulk absorption correction factor, f(x), is given by (2) f(x) = 1 / [ 1
+ (1.2 X 10-6)(Eo1.66- E
c
)XI2
ground. In this case the critical excitation energy, E,, in the equations should be substituted by the energy of continuum photons under consideration. The Y-N procedure could also be used for the calculation of the absorption correction factor for particles (3-5). However, Goldstein et al. (2)have pointed out that the Y-N approach has only a limited applicability and cannot be used for strongly absorbing systems. The possibility of making the assumption of a uniform X-ray production within the foil is evident, particularly for relatively thin specimens. The only problem that arises is how to define the limiting depth of X-ray generation. Bishop and Poole (6) have proposed a method for calculating the absorption correction in thin films assuming that X-ray production is constant as a function of depth up to a value defined by the ratio of two integrals of the X-ray depth distribution function calculated for the thin-film thickness and a bulk specimen. Using this definition of the limiting depth of X-ray generation can result in higher values of the absorption correction factor than the expected ones, particularly for films that are not very thin. Also Tixier (7) has proposed a similar expression for the absorption correction in thin films, but no evaluation of the applicability and limitations of the approach has been made. In the present work an alternative procedure is proposed for calculating the absorption correction factor for thin films, for any X-ray energy. It is also based on the simple assumption of a homogeneous X-ray production within the foil, but the evaluation of its relative advantages and limitations will fully justify this apparently daring assumption for a realistic application range.
THEORY The most exact formula, in fact the rigorous definition, for the calculation of the adsorption correction factor, it,,, is given by ( 2 )
(3)
where x = ~ ( c s I c) ),with = the mass absorption coefficient of the specimen for characteristic X-rays of the element of interest, cm2 g-l, and t+h = takeoff angle for detected X-rays. The need for the calculation of the absorption correction factor also arises when the continuum Bremsstrahlung radiation has to be described. In that case the absorption correction factor has to be calculated for a large number of X-ray energies in the whole continuum energy range including very low energies. Therefore a relatively simple yet accurate procedure for the calculation of the absorption correction factor is necessary. The Yakowitz-Newbury method (denoted by Y-N below) can supposedly also be used as the absorption correction procedure in the description of continuum back'On leave from the Institute of Physics and Nuclear Techniques, Academy of Mining and Metallurgy, Cracow, Poland. 0003-2700/86/0358-1282$01.50/0
where qb(pz) = x-ray depth distribution function. The only problem that arises when applying eq 4 for thin specimens ( p t is then the limit of the integral) is how to define the + ( p z ) function for thin films. It appears that although the +(pz) functions are different for thin and bulk specimens (2),their shapes are quite similar and this justifies making the following approximation: $thin f o ~ ( p z= ) constant +bdk(pz). If the approximation can be used, the absorption correction factor, ftrue, for thin films can be simply calculated by using the $ ( p z ) function developed for bulk specimen. Moreover, when eq 4 is applied to X-ray continuum radiation, it must be assumed that the continuum X-ray depth distribution function can be described by that proposed for characteristic X-rays, which appeared to be justified (8, 9). Obviously calculations of the absorption correction factor via eq 4 are not straightforward because the integrations are time-con0 1986 Amerlcan Chemical Society
ANALYTICAL CHEMISTRY, VOL. 58, NO. 7, JUNE 1986
ftne
I
I
5
10 E [keVr
Figure 1. Absorption correction factors (eq 4) vs. X-ray energy for Fe and Cu foils.
suming. Also the X-ray depth distribution function I$(pz) has to be known. These I$(pz) functions for bulk specimen have been assessed theoretically and experimentally (IO). Inspection of a large number of I$(pz) curves showed that they are similar for all elements and, moreover, can be approximated by a rectangular function, a t least for very thin specimens relative to the depth of the X-ray generation. When such a uniform X-ray production is assumed within the considered thin film, Le., r$(pz) is assumed to be constant, eq 4 obviously transforms into the following simple formula for a new approximate absorption correction factor, fnew: 1 - exp(-ppt csc $1 (5) fnew = PPt CSC $ The questions that then arise are, of course, how accurate such an absorption correction via eq 5 can be in EPXMA of thin films and in which film thickness range it can be applied advantageously. First it is important to examine the influence of the X-ray energy on the accuracy of the proposed procedure. Second, the dependence of the accuracy on the foil thickness should be considered. Af
1283
A priori, it can of course be stated that the absorption correction in a thin film can never exceed that in a bulk specimen of the same composition. In a recent paper (11)it was shown that the absorption correction in a bulk sample can, within certain limits, advantageously and accurately be expressed on the basis of an effective depth down to which all X-ray production is assumed to take place in a uniform way. This effective depth was expressed as a fraction, lz, of the X-ray excitation depth given by Whelan's expression (12). When now for a film, the thickness p t exceeds this effective depth, obviously the absorption correction factor will always be overestimated via eq 5. Therefore, the following restriction has to be introduced for practical application of eq 5: pt
< kpdxW
(6)
where k = fraction of the X-ray excitation depth, yielding the effective depth in bulk specimen (11);pdXW= the depth of X-ray excitation given by Whelan's expression (12), in g ern++, and pdXW= 0.033 (A/Z)(E01.69- E,1.69) ( 6 4 with 2, A = average atomic number and atomic mass, respectively, of the specimen. For thin foils of thickness larger than that defined by eq 6 the bulk absorption correction factor, presented elsewhere (11),should be preferred over eq 5. As will be seen below the proposed new procedure for the calculation of the absorption correction factor in EPXMA of thin foils, although based only on rough approximations without any rigorous theoretical base, gives acceptable results.
RESULTS AND DISCUSSION To give some idea about the magnitude of the absorption correction factor for thin foils, Figure 1 shows the calculated ftrUe factor vs. X-ray energy for Fe and Cu foils. Even for a thickness of 0.5 hm, the correction can be significant.
Af
I%I
[%I
m 025pm
@ 4
100
AY-N
0.25 pm
Y-N New *Y-N
A
OEpm A Y - N
A
05pm 10
0
I
New oY-N New
4
OS pm
.
50
:
0 -in
'"I
E lkeV1
E IkeV]
Af [%I
II/
@
E lkeV1
g' il
103-
Au
0.Epm
E IkeVl
AY-N A New
h
0
4
0 -10
0
- 10
Figure 2. Relative error on the absorption correction factors, calculated via the Yakowitz-Newbury method (eq 1) and the proposed new procedure (eq 5) as a function of the X-ray energy, for foils of (a) AI, (b) Fe, (c) Cu, (d) Ag, (e) Au, (f) AgBr, and (9)FeB.
1284
ANALYTICAL CHEMISTRY, VOL. 58, NO. 7, JUNE 1986
I
/
@ 0
Y-N
I
AI 2 5 p m Y-N New 0
0 -10
-10
Flgwe 3. Relative error on the absorption comection factors, calculated via the Yakowitz-Newbury method (eq 1) and the new procedure (eq 5 with pt = kpdXw)as a function of the X-ray energy, for foils of (a) Cu and (b) AI whose thickness exceeds the effective X-ray generation depth.
The new expression, eq 5 , has been applied for the calculation of the absorption correction factor for thin foils of Al, Fe, Cu, Ag, Au, AgBr, and FeB. First, in order to take the restriction in eq 6 into account, the depths of X-ray excitation have been calculated according to Whelan’s expression,eq 6a. By assuming an electron beam energy of 20 keV, the following pdxW ranges were obtained for X-ray energies from 10 to 1keV 2.76-3.98 pm in Al, 0.98-1.41 pm in Fe, 0.88-1.27 pm in Cu, 0.79-1.13 pm in Ag, 0.46-0.67 pm in Au, 1.27-1.83 pm in AgBr, and 1.08-1.55 pm in FeB. (These values differ from those obtained by Heinrich’s expression, eq 2, by only a few percent.) The values of the factor k in eq 6 ranged from 0.46 for A1 to 0.70 for Au, without any strong influence of the X-ray energy (11). Hence, the limitation expressed by eq 6 means that in case of films thicker than, e.g., 1.3-1.8 pm for A1 and 0.3-0.5 pm for Au, the pt value in eq 5 should be substituted by kpdxW;i.e., the bulk sample procedure (11) should be preferred. Figure 2 shows the relative errors, Af(%), for the Yakowitz-Newbury method and for the newly proposed procedure. These errors were expressed as
f - ftrue
Af(%) = 100 -
(7)
ftrue
where f = fY-N (eq 1) or f = f,,, (eq 5 ) , respectively. For the computation of ftrU,, the 4 ( p z ) function of Brown and Packwood (10) was dsed. It can be seen that for the considered sample, the accuracy of the new procedure, which is based on an oversimplified assumption, is much better than that of the Y-N method, particularly for the low X-ray energy region. In fact the Y-N method only gives acceptable results for the higher X-ray f’
@
energies (2). The new procedure applied for very thin foils gives practically the same results as those obtained via the rigorous expression, eq 4. To check the applicability of the proposed new procedure for thin foils of thickness larger than that defined by eq 6, the calculations have been carried out for 0.75- and 2.5-1m foils of Cu and Al, respectively. For such foils the absorption correction factor can be expressed by use of the procedure recently proposed for bulk samples (11). Figure 3 shows the relationship between the relative errors obtained from eq 7 for the Y-N method (eq 1) as well as for this new procedure, i.e., employing pt = kpdxW in eq 5. As before the accuracy of the new procedure is better than that of the Y-N approach, particularly for the low X-ray energy region. Finally the dependence of the accuracy of both absorption correction methods on the foil thickness will be considered. The calculations have been carried out for Cu foil and for three different energies of X-rays: 1,2.5, and 5 keV. Figure 4 shows the relationship between the absorption correction factor calculated via eq 4 (ftru8), eq 1 (fY-N) as well as eq 5 , as a function of the foil thickness normalized to the X-ray generation depth, pdxH. It can be seen that the values of the absorption correction fator predicted by the new expressions are in very good agreement with those obtained from the exact formula, eq 4,for the whole thickness range. The Y-N procedure predicts erroneous results for very low X-ray energies except for the very narrow range of foil thickness just around the depth of X-ray excitation. For higher energies all functions for the absorption correction factor, considered above, give practically the same results. As can be seen the values for the ft, factor as well as for the f,, factor are nearly the same for foil thickness range between 0.5 pdxH and pdxH regardless of the X-ray energy.
CONCLUSIONS The results presented above confirm the potential of the new procedure, which in fact, was based on the rough approximation assuming a uniform X-ray generation within thin foils. In all considered cases, which cover a wide range of elemental composition, X-ray energy, and foil thickness, the accuracy of the new procedure is better than that of the Yakowitz-Newbury method. Particularly good results have been obtained for very thin foils within the whole X-ray energy range (starting from 1.0 keV upward). The new procedure gives adequate results for the whole range of foil thickness, while the Yakowitz-Newbury method of absorption correction is of limited applicability and can be accepted only for very thin or relatively thick foils and only for higher X-ray energies. Because of its simplicity and accuracy, the new procedure can also be used for the calculation of the absorption correction X = Zca)cm2g’(25W)
10
f‘ 10-
~
t 5-
5
@
X = 3 0 0 c m 2 g ’ (5keVl fY-H
fNev I
\
L
r
Anal. Chem. 1986, 58,1285-1290
1285
factor for continuum Bremstrahlung radiation over the whole continuum X-ray energy range. Registry No. AgBr, 7785-23-1;FeB, 12006-847;Al, 7429-90-5; Fe, 7439-89-6; Cu, 7440-50-8; Ag, 7440-22-4;Au, 7440-57-5.
(7) Tixier, R. J. Microsc. Specfrosc. Electron. 1979, 4 , 295-304. (8) Statham, P. J. X-Ray Spectrom. 1976, 5 , 154-168. (9) Markowicz, A. A,; Storms, H. M.; Van Grieken, R. E. Anal. Chem. 1965, 57, 2885-2889. (10) Brown, J. D.; Packwood, R. H.X-Ray Spectrom. 1982, 11, 187-193. (11) Markowicz, A.; Stroms, H.; Van Grleken, R. X-Ray Spectrom., in
LITERATURE CITED
(12) Armstrong, J. T. Ph.D. Dissertatlon, Arizona State University, Tempe, AZ, 1978.
(1) Yakowitz, H.; Newbury, D. E. Scannlng Electron Microsc. 1976, I , (2) Goldstein, J. I.; Newbury, D. E.; Echlin, P.; Joy, D. C.; Fiori, Ch.; Lifshin, E. “Scanning Electron Microscopy and X-ray Microanalysis”; Plenum: New York and London, 1981. (3) Barbi, N. C.; Giles, M. A,; Skinner, D. P. Scanning Electron Microsc. 1978, I , 193-200. (4) Small, J. A. Scanning Electron Mlcrosc. 1981, 2 , 447-481. (5) Aden, G. D.; Buseck, P. R. R O C . Annu. COnf. Microbeam Anal. SOC. 1983, 18, 195-201. (6) Bishop, H. E.; Pooie, D. M. J . Phys. D . 1973, 6 , 1142-1158.
press.
RECEIVED for review February 13, 1985. Resubmitted December 30, 1985. Accepted December 30, 1985. We acknowledge partial financial support by the Belgian Ministry of Science Policy under Contract 80-85/10 and 84-89/69 and a sabbatical research grantfrom the ~ ~~ ~ tl iF ~ ~~ a ~li dation for Scientific Research to A.A.M.
Analysis of Polymer Surface Structure by Low-Energy Ion Scattering Spectroscopy Thomas J. Hook, Robert L. Schmitt, and Joseph A. Gardella, Jr.* Department of Chemistry, State University of New York at Buffalo, Buffalo,New York 14214
Lawrence Salvati, Jr. Perkin-Elmer Physical Electronics Laboratories, 5 Progress Street, Edison, New Jersey 08820
Roland L. Chin Buffalo Research Laboratory, Allied Chemical Corporation, 20 Peabody Street, Buffalo, New York 14210
Low-energy Ion scattering spectroscopy (LEIS or ISS) Is used to complement angle-resolved X-ray photoelectron (ARESCA or ARXPS) data for various polymer surfaces. ISS analysis of poly(dlmethylslloxane) (DMS), poly( methylphenylslloxane) (MPS), and poly( dlphenylslloxane) (DPS) showed a nonlinear Increase In C/O ratlo with bulk carbon content, lndlcatlve of the shadowlng by bulky phenyl rlngs. The series of stereoregular poly(methy1 methacrylates) (PMMA) and atactlc PMMA Is Investigated to Illustrate the unlque ablllty of ISS to detect tactlclty vla dlfferences In functional group shadowlng In polymer surface structure. A series of poly( methyl methacrylate)/poly(methacryllc) acld (PMMA/PMAA) random copolymers are lnvestlgated to Illustrate capabllltles to detect composltlonal changes In polymer surface structure. ESCA data that show no dlfferences In composltlon or qualltatlve peak shlfts for these systems are also presented. ISS data from siloxane copolymers and blends are Investigated to Illustrate the effects of surface orlentatlon and mlcrostructure of near-surfacereglons. ESCA data are used for both systems to be complemented or contrasted by ISS data In the elucldatlon of surface mlcrostructure, especially for block copolymers and blends of DMS and blsphenol A polycarbonate (BPAC).
Low-energy ion scattering spectroscopy (LEIS or ISS) has been used extensively for surface analysis and is often said to yield no “chemical” information (1). This is not strictly true, however, since indirect chemical information can be obtained from “shadowing”effects ( 2 , 3 )of atoms above other atoms and oscillatory ion yields due to neutralization phe0003-2700/86/0358-1285$01.50/0
nomena ( 4 , 5 ) . In the present work we endeavor to illustrate from the analysis of polymer structure at surface that indirect chemical information due to shadowing from different bonding situations of functional groups oriented at the interface (and different compositions) is accessible from ISS measurements. As Baun has pointed out in previous work (6, 7), the chief advantage of the ISS experiment lies in its high sensitivity for the first atomic layer. This occurs since a large scattering cross section and strong neutralization occur following ion penetration into the solid. The resultant high sensitivity and selectivity allow for fewer corrections than most techniques as observed by Smith (2, 3). The ISS technique also can provide semiquantitative elemental analysis and/or profiling capability with depth (8). ISS can also be operated in the so-called “static” mode (9, IO). With lower ion beam energy and ion beam current density to obtain minimal sputtering, sample damage is minimized in “static” or “low-damage” primary ion conditions. Inherent in the ISS experiment are analytical limitations that must be monitored to minimize their effect on the data. The limitation of primary concern is the poor peak resolution with overlapping the rule rather than the exception. Another spectral limitation that occurs is the tendancy for many elements to scatter light ions to produce broad peaks with high levels of background (7). This problem can be compounded by a rapidly changing or uncertain background. Baun has also pointed out a fundamental limitation to quantitative analysis, that of relating the intensity of scattered ions to the number of ions originally incident upon the sample surface. .Polymeric analysis via ISS can provide a good example of the advantages of the technique to extract surface-sensitive structural information. For instance, in comparison to ESCA (which is used extensivelyfor the analysis of polymer surfaces), 0 1986 American Chemical Society
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