Quantitative Elemental Analysis of Substituted Hydrocarbon Monolayers on Platinum by Auger Electron Spectroscopy with Electrochemical Calibration James A. Schoeffel Varian Associates, Vacuum Division, 25 Route 22, Springfield, New Jersey 0708 1
Arthur
T. Hubbard"
Department of Chemistry, University of California, Santa Barbara, California 93 106
Clean, structurally ordered Pt( 100) surfaces were prepared In ultrahlgh vacuum and characterized by means of low energy electron dlff ractlon and Auger electron spectroscopy. The Pt( 100) surfaces were treated wlth ethylene, allylamlne, allylacetic acid, chlorotrifluoroethylene, or thiophene which formed a chemisorbed layer of known stoichiometric composition containing the elements, C, N, 0, F, CI, or S In varlous comblnations. Second harmonic Auger electron spectra of these layers were obtalned In absolute units (A/eV2) and stored In digital form by computer. The spectra were integrated numerically to obtaln the total Auger electron current for each element in the adsorbed layer. The Interfacial concentration of each adsorbed layer was determined by means of thln-layer coulometry. The proportionallty constant relating Auger electron current to adsorbed amount was thus determlned. Equatlons permffllng calculation of Auger electron current were developed and compared wlth experlment. The results Indicate that Auger electron current Is generally rather Insensitive to the chemlcal envlronment of the emlttlng atom. Calculated Intensities correspond to the measured values within 1 0 % In most Instances.
A number of experiments to calibrate Auger electron spectrometers for various applications have been reported (1-8). Each of those studies has furthered the understanding of the quantitative aspects of Auger spectra. In particular, there is a linear relationship between Auger electron emission intensity and coverage, u p to a monolayer (8). There remain several obstacles t o quantitative interpretation of Auger spectra obtained for chemisorbed layers, as pointed out in Ref. 9. Spectral intensities have usually been obtained in terms of arbitrary units, thus preventing quantitative interpretation. T h e d a t a are commonly presented in the form of graphs of second derivative spectra, which cannot be twice integrated quantitatively by the reader. T h e equations employed t o analyze t h e spectral d a t a were generally approximate, incomplete, or incorrect. Methods employed for spectrometer calibration have not been methods noted for absolute analytical accuracy. In the present article these problems are remedied somewhat: Auger electron current is stated in amperes; equations are derived which relate Auger electron current emitted from an adsorbed layer to all variables known to have a n appreciable effect; and calibration is based upon a quantitative technique, thin-layer coulometry. (Previous articles in this series are Ref. 10 and 11.)
EXPERIMENTAL Single-crystal rods of Pt approximately 9 mm in diameter were obtained from the Materials Research Corp., Orangeburg, N.Y. 2330
ANALYTICAL CHEMISTRY, VOL. 4 9 , NO. 14, DECEMBER 1977
10962 (Marz Grade, 99.99% minimum nominal purity). These were polished preliminarily, oriented by means of Lau6 x-ray reflection photography (12-141, and cut into prisms (each face of which had identical crystallographic symmetry) by means of a diamond saw. The disks were mounted in resin and polished with successively finer grades of abrasive, finishing with 0.05 pm alumina (Buehler Ltd., Evanston, Ill. 60204). The finished disks were spot welded onto a pair of 26-gauge Pt wires and etched for 2 min in hot aqua regia. After insertion of the samples, the vacuum system was baked at 250 "C for several days, during which the pressure decreased from 10-' to lo-' Torr; after cooling, the pressure dropped to Torr. The vacuum system for combined electrochemistry and LEED was described in Ref. I O . The Pt sample surface was cleaned (15) by heating in pure O2 (1000 "C at lo-' Torr for 8 h), followed by Ar+ bombardment (10 PA cm-* at 600 eV in 4 X 10-5Torr Ar for 1 h) and annealing (600 "C for 10 min). Auger electron spectra were recorded after sample preparation in order to verify that the surface was clean. The detection limit for C atoms was about 1013 atoms per cm2, based upon the calibration described below. The sensitivity of Auger spectroscopy varies from element to element as indicated in Tables 1-111. A four-grid LEED apparatus was employed as a retarding field electron energy analyzer (Varian Associates, model 981-0127,Palo Alto, Calif. 94303). Transmittance of the grid system was 0.43; the acceptance angles were: maximum, O2 = 60°, and minimum, d1 = 4" (due to the presence of the normal incidence LEED electron gun at the center of the grid system). Electronic control of the analyzer optics was provided by an electrometer and power supply (Varian, 981-2145 and 981-2148) and lock-in amplifier (Princeton Applied Research, modified model 128, Princeton, N.J. 08540). This detection system is functionally equivalent to the design described in Ref. 16. The modulation frequency was 1kHz. Collected electrons were returned to ground through an audiotransformer (Ouncer, UTC 0-26) which converted current of amplitude A, into a voltage V,. The voltage was sensed by a lock-in amplifier, which produced a dc voltage proportional to the ac signal amplitude, Equation 1.
Aj lVjl = lZj I The effective impedance was Z1 = 9.0 X lo4 R at 1 kHz and Z 2 = 2.74 X 10' C2 at 2 kHz 0' 2). This Auger electron signal, IV,l, was sampled once each millisecond by a 12-bit successive A/D converter during a 100-sscan period; the digital data were averaged numerically in groups of 50, and the resulting 2000 average values stored on a disk memory of a digital converter. A technique for analog integration of Auger spectra has been described (17)which would be advantageous if the energy dependence of the background normalization function, &, were known in advance. Every precaution was taken to minimize damage of the adsorbed layer by the incident electron beams: The incident current was 10 PA distributed over a 17" ellipse (minor axis, 1 mm; major axis, 3.4 mm), and was interrupted when not in use; the total duration of irradiation was 100 s. Control experiments were
Table I. Proportionality Constant, G, between Auger Electron Current and Interfacial Coverage. Experimental and Theoretical Values Kinetic energy, r,1OI4 Element eV Compound chemisorbed a toms/ c m * C 268 Ethylene 8.4 i 0.2 C 268 Allylamine 15.9 i 0.5 C 268 Allyacetic acid 9.5 i 0.6 C 268 Thiophene 8.8 5 0.5 C 268 Chlorotrifluoroethylene 3.8 i 0 . 1 N 383 Allylamine 5.3 i 0.2 0 516 Allylacetic acid 3.8 * 0.2 F 659 Chlorotrifluoroethylene 5.8 i 0.2 S 149 Thiophene 2.2 i 0.1 1.92 i 0.05 c1 181 Chlorotrifluoroethylene Experimental conditions: K = 0.43; e , = 4"; e 2 = 60'; E, = 2000 eV; I , Equation 2 was 50 eV, centered o n the Auger electron kinetic energy. Table 11. Calculated Collection Efficiency, oC, of Electron Energy Analyzer for Auger Electrons Emitted from a Chemisorbed Layer. Background Correction Weighting Factor, @ b , from Equation 11 Kinetic Ele- energy Q, ment eV cmz Qr @c ob 3.03 0.43 Li 51.8 0.091 0.568 2.84 0.40 0.092 0.590 Be 103.8 B 168.0 2.26 0.32 0.095 0.656 1.68 0.24 0.098 C 268.0 0.729 N 383 1.30 0.18 0.100 0.789 0.15 0.101 0.821 0 516 1.03 0.12 0.102 0.854 F 659 0.844 0.34 0.094 0.639 S 149 2.42 C1 181 2.17 0.31 0.095 0.665 1.04 0.15 0.101 0.821 I 507 Auger electron kinetic energies from Ref. 4 9 . Scattering cross section, Q, for Auger electrons in hydrocarbon layer calculated by means of Equation 4 with E , = 1 6 eV and n = 6. Parametric values: K = 0.43; e = 4"; e = 60". For the sake of example, r was assumed equal t o 1.4 X 10l5atoms/cm' in calculation of the entries appearing in this Table. Table 111. Calculated Values of Ionization Cross Section, Q, Backscattering Factor, s , and Auger Electron Yield, G , for Chemisorbed Layers o n Pt EleQ , 10-19 s , 10-19 G , 10-l9 mcnt n E,,eV cm2 cm2 cm* 369.0 26.5 279.0 11.4 58.7 97.7 17.7 36.7 B 188 5.57 6.68 17.0 284 3.03 C N 1.73 2.79 8.70 399 4.67 1.008 1.22 0 532 2.53 0.582 0.539 F 682 S 164 20.1 71.3 140.0 97.4 15.2 45.4 c1 201 15.9 I 10 685 3.58 3.66 Parametric values: E , = 2000 eV; K = 0.43; e , = 4": 0 , = 60" ; Bi= 73" from surface normal; @i = 27" from (010) zone; E , values were obtained from Ref. 50. Li Be
2 2 2 2 2 2 2 6 6
55
110
performed, in which the maximum Auger electron intensity was measured a t constant energy, to verify that the signal strength did not vary detectably as a result of irradiation during the recording of these spectra. In our experience, electron analyzers of the cylindrical mirror design (18, 19) give better Auger spectra than the retarding field type, from the same manufacturer; use of the latter for this work, however, allowed LEED patterns to be obtained concurrently. Auger electron emission was stimulated by irradiation of the sample a t grazing incidence (Oi = 73', measured from the surface
I, >
=
G,
G,
experimental,
experimental, calculated, 10-l' A lo-'' cm2 lo-'' cm2 16- 2 195 2 17.0 26i 6 17i 4 17.0 161 2 17i 2 17.0 17i 1 19i 1 17.0 6.0 i 0.5 16t 1 17.0 3.2 = 0.04 6.0 i 0.2 8.7 1.4 i 0.3 3.6 i 0.2 4.7 0.55 3 0.07 0.9 ? 0.1 2.5 20i 3 9 6 t 13 140.0 1 7 i 0.6 93+ 2 97.0 1 0 PA; 8 , = 73". The range of integration of
normal) by means of a precisely focused and deflected electron beam (10 PA at 2000 eV). The electron gun was Varian 981-2454 and control unit 981-2143 plus 981-2127. The substances were introduced onto the sample surface by means of a nozzle beam (20) which permitted sample exposure equivalent to a partial pressure of approximately 10 Torr while maintaining tolerably low pressure (10 Torr) in the remainder of the apparatus, This procedure invariably resulted in saturation of the surface with the strongly chemisorbing substances investigated in this study. Electrochemical analysis of the chemisorbed layer to calibrate the Auger spectrometer was accomplished as follows: A polycrystalline Pt thin-layer electrode such as described in Ref. 21 was exposed for 60 s to argon containing the adsorbing hydrocarbon at partial pressure comparable to that employed in the vacuum. An aliquot of 1 M HCIOj was then introduced into the thin-layer cavity of 0.15 V vs. NaCE (a calomel electrode prepared with 1 M NaC1). The potential was then adjusted to 1.3 V NaCE, with integration of the resulting current (22, 23). Oxidation of the hydrocarbon layer and the Pt surface took place rapidly. The same degree of surface oxidation occurred as when the surface was initially clean (Le.,the change required for electrode reduction was the same in both cases). Therefore, the background correction was determined by repeating the procedure in the absence of adsorbed hydrocarbon and subtracting the resulting coulometric charge, qB,from that obtained with the coated surface, q, Equation 2.
The standard deviation was 10% for eight trials, due primarily to variation of the hydrocarbon coverage. The magnitude of n was determined for allylacetic acid and allylamine as follows: An aliquot of 10 ' M solution of the surfactant in 1 M HC10, was added to the clean thin-layer cell, after which coulometric oxidation was carried out as described above. The magnitude of n was calculated from the Faraday law, Equation 3.
n = ( 4 - qB)/FVCa
(3)
For allylacetic acid and allylamine, n = 10. The same result was obtained by another method in Ref. 24. Although the oxidation products were not isolated, n = 10 implies the following net reactions:
+ 4H20 COZ + + 10" + 10eCH2=CHCH2CH2C02H + 4H2C) C02 + H02CCH2CH2C02H + 10" + 10e-
CH2=CHCH2NH2 HO,CCH,NH,
+
(4)
-+
(5)
The limited solubility of thiophene, ethylene, and chlorotrifluoroethylene precluded preparation of standard solutions necessary for precise determination of n-values. Therefore, it was necessary to make the assumption that these compounds react analogously to Equations 4 and 5, as follows: ANALYTICAL CHEMISTRY, VOL. 49, NO. 14, DECEMBER 1977
2331
CH2=CH2 + 4 H 2 0 12H20
+
-+
2 C 0 2 + 12"
+ 12e-
(6)
4c02+ H 2 S 0 4 +
26" + 26eF,C=CFCl+ 4 H 2 0 2 C 0 2 l/2C12 + 5" + 5e-+
3HF +
R E S U L T S AND DISCUSSION Determination of Auger Electron Current from a Chemisorbed Layer. Quantitative Auger electron spectra were obtained by electron beam excitation of a Pt(100) surface containing a chemisorbed layer of ethylene, I; allylamine, 11; allylacetic acid, 111; chlorotrifluoroethylene, IV; and thiophene,
V. CH,=CHCH,NH,
I
CH,=CHCH,CH,CO,H
I1
i ,c=c
I11 /F F'
CI
IV
0 V
These compounds chemisorb readily and reproducibly on Pt surfaces. T h e resulting adsorbed material is not removed at room temperature by evacuation, rinsing, or electrolysis apart from extremely oxidizing or reducing conditions a t which oxidation or hydrogenation occurs ( 2 4 ) . I t appears that compounds such as these remain structurally intact during chemisorption a t room temperature ( 2 4 ) . The interfacial concentration of adsorbed molecules can be determined by a coulometric method. Compounds I-V thus provide an opportunity to determine the yield of Auger electrons of the elements C, N, 0, F C1, and S present in a n adsorbed layer in a well defined oxidation state at known coverage and relative abundance. T h e resulting data allow the proportionality constant relating Auger electron yield to surface concentration to be estimated and permit the reliability of various experimental equations for Auger yield to be evaluated. T h e potential variability of Auger electron kinetic energy with chemical environment has received attention (8, 9, 12-24, 26-33), but little is known about the corresponding variation in the emitted intensity. Auger electron spectra of compounds I-V are presented in Figure 1. Spectra were recorded in digital form for accuracy and convenience. T h e entire spectrum from 0 to 2020 eV was obtained in each case. Figure 1was obtained by automated replotting of data over intensity a n d energy ranges convenient for making graphs. Other settings were employed when mathematical analysis of the d a t a was the primary objective. Auger electrons constitute only about 0.01% of the electrons emitted by the sample (34). Accordingly, selective amplification of the Auger electron component is a central aspect of experiment design (8,35,36). To that end, advantage has been 2332
ENERGY,
200
2x)
500
350
400
pJ
t
Y
(8)
Le., the terminal adsorbed carbon is oxidized to COz, and the geminal olefinic carbon to carboxylate. Current-potential data concerning adsorption of atomic hydrogen on single-crystal and polycrystalline Pt electrodes (25) indicate that the polycrystalline thin-layer electrode consists of Pt(ll1)facets (55%) and Pt(100) facets (45%). As a result, the polycrystalline surface contains 1.42 X l O I 5 P t atoms per cm2, compared with 1.30 X 10l5 for Pt(100). Values of r obtained with the polycrystalline electrode were normalized for this difference in site density (1.30/1.42 = 0.92) for purposes of comparison with Auger spectra of the Pt(100) surface. The electrolyte does not desorb the chemisorbed alkenes at open circuit (24);in fact, none of the materials would escape detection, even if it were t o desorb, in that all of the reactant in the thin-layer cavity, whether adsorbed or otherwise, undergoes electrolysis.
CH,=CH,
KINETIC
150
-ol -
(7)
+
A,, d e v 2
ANALYTICAL CHEMISTRY, VOL. 49, NO. 14, DECEMBER 1977
450
t/ 100
I50
200
?50
390
I50
200
250
300
Y I
Flgure 1. Auger electron spectra of substituted hydrocarbons chemisorbed on Pt(100). (A) Clean surface. (B) Alvyhmine. (C) Ethylene. (D) Allylacetic acid. (E) Chlorotrifluoroethylene. (F) Thiophene. Experimental conditions: sinusoidal modulation peak amplitude, k = 5 V; frequency, f = 1 kHz; primary beam current, I , = 10 wA; primary beam energy, E, = 2000 eV; time per scan, 90 s; fiker time constant, RC = 0.1 s
taken of the fact that most of the background electron emission occurs with energies below 40 eV where it obscures relatively few Auger transitions and is distributed relatively uniformly from 40 eV up to E , (37-39). Accordingly, the first derivative, N ( E ) A/eV, of the total emitted current, I , exhibits noticeable peaks at energies characteristic of Auger processes, and the second derivative, "(E) A/eV2, displays these features prominently (35). In the present study, "(E) was monitored by detecting the second harmonic amplitude, A 2 , of the emitted current by means of LEED optics (8) noting that A 2 is a measure of " ( E ) (34). Equation 9, relating A 2 to the Auger electron current, I,, was derived by Houston (40)and confirmed experimentally for modulation amplitude, k, from 0.1 t o 25 eV (41).
I, = 4 1 E 2JE A 2 (corrected for background) dE'dE k2
E, El
(9)
Accordingly, the second-harmonic spectra, A', were corrected for contributions due to background and twice integrated automatically by means of a digital computer to obtain the Auger electron current. As pointed out by Houston ( 4 0 , 4 1 ) , this procedure gives the correct result regardless of modulation amplitude, peak shape, or the small energy losses resulting from plasma or valence electronic transitions. T o correct the second harmonic amplitude, A2,of the coated surface for contributions due to background, the corresponding amplitude, A2c,is measured for the clean surface, decreased by a factor & corresponding to the absorptivity of the adsorbed layer toward electrons of the specified energy, and subtracted from A z .
The factor @ b is, in other words, the fraction of electrons emitted from within the substrate in a cosinusoidal distribution ( 4 2 ) , transmitted by a Beer-Lambert absorber and registered by the detector. Exact values of @b cannot be calculated a priori without specifying the geometry and electron scattering characteristics of the adsorbed layer (43).
200 -201
ELECTW ENERGY, ev 220 240 260 280 '
~
200 220
- 20
'
'
'
'
240
260
280
32C
INCIDENCE GUN
n
Flgure 3. Retarding field energy analyzer used for Auger electron spectroscopy
-
- ?40 OI
ELECTRON ENERGY, ev
Integration of an Auger electron spectrum. From top: Second harmonic signal from allylacetic acid on Pt(lOO), A,. Second harmonic signal from clean !=?(loo),A2c. Second harmonic signal after correction for background, A , - 0.77 APc. Integral of net second harmonic signal, S ( A , - 4bAzc)dE' Figure 2.
However, a calculation based upon single scattering by a uniform carbon film does correctly predict the mathematical form of the energy dependence of @b, Equation 11,
r2
2n
lo
e2
+fel
@b=
d0 do//
82
exp(-o sec
cos e sin
e
e )cos 0
sin 0
d0
81
ob=
le ' exp(-o sec e )cos 9 61 (sin2 e2 - sin2 e , )
2
sin
e
de /
gration are illustrated in Figure 2. Values of the Auger electron current, I,, extracted from the experimental data, A 2 and Azc,by means of Equation 1 and 10, appear in Table I. As can be seen from these data, the Auger electron currents from chemisorbed monolayers are on the order of A. The yields differ from element to element by a factor of 40 or more. As a result, the sensitivity of Auger electron spectroscopy to various surface constituents varies widely. Qualitative detection of the Auger electron current and a knowledge of the factor relating current to coverage is thus essential for interpretation of Auger spectra. Experimental Equations f o r Auger Electron C u r r e n t . The current resulting from a given Auger transition occurring in a chemisorbed layer is expected to follow an equation of the form (45-47)
where I , is the primary beam current incident on the sample surface; @c is the collection efficiency of the electron detector; F, atoms cm2, is the interfacial concentration of adsorbed atoms undergoing the specified Auger transitions; and G is a proportionality constant determined empirically and compared with values calculated from first principles in this work. T h e detector employed in this study was a four-grid hemispherical LEED display system, Figure 3, the collection efficiency of which is given by Equation 14.
(11)
where u is the average absorption cross section of the adsorbed layer (about 0.2) and the differential area increment, sin 6' dB d a , is integrated over the hemispherical surface of area 2rr2 encompassing all azimuthal angles, a , and vectorial angles limited by the LEED gun a t center screen and the outer boundary of the hemispherical analyzing grids. In practice, Equation 11 is linear in kinetic energy, with a coefficient of determination of 0.99, over the energy range of a typical Auger peak, about 100 eV, Equation 12.
T h e slope, m, is small, typically eV-', and the intercept, b, is generally in the range from 0.75 to 1.25. Since A2 = &A2? in regions of the electron energy spectrum over which there is a n absence of Auger transitions of the adsorbed layer, the slope and intercept leading to @b in Equation 1 2 were evaluated empirically by linear least squares analysis of A 2 / A 2 , values over a 50-eV range on either side of the given Auger peak. The coefficient of determination was 0.7 or greater in all cases. Background correction assuming @ b = 1 was described in Ref. 44. The accuracy of Equation 12 was verified by comparing calculated and observed variation of the areas of the platinum Auger peaks in the presence of an adsorbed layer. T h e background correction process and double inte-
&
K e / exp[ Qr(1- sec e)]sin Ode
=-
2
e1
(14)
T h a t is, one-half of the Auger electrons are emitted in the direction of the vacuum hemisphere, of which a fraction K (equal to 0.43 in this work) are transmitted by the series of four analyzing grids. T h e angular distribution of Auger electrons emitted from a hydrocarbon monolayer on a molybdenum substrate ( 4 2 ) conforrris rather closely to the function e x p [ Q r ( l - sec S)] for vectorial angles less than about 60' from the normal, as shown in Figure 4. An inelastic scattering coefficient, Q r , of 0.24 gave best fit with the data. Based upon this observation, values of Q r for the systems encountered in the present work were calculated as follows: The scattering cross section, Q cm2,was calculated by means of a procedure derived and tested by Gryzinski (48),Equation 15. The average binding energy, E,, of electrons in the hydrocarbon layer was taken to be 16 eV. Calculation of Q thusly for the situation depicted in Figure 4 implies that r equals 1.42 X 10'j carbon atoms per cm2;the composition of the hydrocarbon layer was not specified in Reference 42 but the implied coverage falls amid those observed in other experiments (24). Evaluation of @? was accomplished by integrating the angular distribution over the hemispherical region between the shadow of the LEED electron gun (0, = ANALYTICAL CHEMISTRY, VOL. 49, NO. 14, DECEMBER 1977
2333
Ns, ua/ev
"
'1 d
Figure 4.
Angular distribution of Auger electrons emitted from a Solid curve: experimental data of Harris chemisorbed layer. (-) (37)for Auger electrons from hydrocarbons adsorbed on a Mo substrate. (. . .) Dotted curve: graph of exp[0.24(1 - sec) 8)]. (---) Dashed curve: graph of cos 0. A"(€) was normalized to unit emission along the surface normal
otr
4 ' ) and the perimeter of the energy analyzer (0, = 60°), Equation 14. Values of C#I~ thus obtained are presented in Table 11. As can be seen from the Table, & varies less than 2% over the energy range (50 eV) of typical Auger processes. Accordingly, & may be treated as a constant for a given Auger process. Since dCdepends upon r, extraction of the magnitude of r from the measured value of I , by means of Equation 13 requires iteration of self-consistency in I?, or use of a working curve, & = f(Qr).Fortunately, the variation of @ c with r is gradual and the solution converges after one or two iterations. As can be seen from Table 11, c $ ~ ranges from 0.091 to 0.102 in the row Li to F. In Ref. 47 a constant value equivalent to & = 0.073 was employed, based upon the approximation that Auger electrons are emitted uniformly with respect to 0. Scattering cross sections, Q, were calculated by means of Equation 15, developed by Gryzinski ( 4 8 ) .
2334
*
ANALYTICAL CHEMISTRY, VOL. 49,
NO. 14,
DECEMBER 1977
2000
ev
I
- "
'
'
'
'
'
'
'
1000
0
When & is the object of the calculation, E , is equal to the energy to ionize the bound electrons in the outermost shell, occupied by n electrons (inner electrons contribute negligibly, as can be seen by substituting their respective values of E,, into Equation 15), and E, is the energy of the Auger electron. T h e values of E , employed were obtained from Ref. 50. Values of Q thus calculated appear in Table 11. Values of G extracted from the experimental data, A 2 and AZc,by means of the above equations are given in Table I. The magnitude of G observed for the element carbon is similar for compounds I-V and corresponds to 1.7 X lo-'* cm2. These data suggest that the Auger electron yield for carbon is not a sensitive function of molecular environment. Reported variations of Auger electron yield with oxidation state ( 4 7 , 5 1 ) may have been due to structural reorganization of the surface region, as noted in Ref. 52. Accordingly, it appears worthwhile to devote further attention to Auger electron spectroscopy as a potential method for quantitative elemental analysis of chemisorbed molecules. Governing Equations for Auger Electron Yield Factor, G. As described below, t h e proportionality constant, G,
- E,
1000
0
I
2000
Q N s , a cm2/ev 20
IO
I
10-27
/ I
T h e quantity ( Q sec Bi + s) describes the probability that a n electron of energy E , incident on the sample a t an angle Bi (measured from the surface normal) will cause ionization of a specific core level, W , whose cross section is Q. Based upon geometric considerations, the path length of the electron through the adsorbed layer varies as sec 0i. (For example, sec Bi = sec 73' = 3.42, corresponds t o a pathlength equivalent to 3.4 molecular layers or approximately 10 A.) Normalization of I , for variation within the layer is not necessary, in the present instance, as can be seen by use of the Beer-Lambert Law, Equation 17,
AI,/I,=
1- exp[-AL(0.693)/L]
=
4%
(17)
in which L is calculated, Equation 18, as described in Ref. 53.
L
=
1 + (E,/150)2 = 1 7 8 A
(18)
Ionization cross section, Q, was calculated by means of Equation 15, in which E, was the kinetic energy of the incident electron and E , was the binding energy of the initially ionized core level. Values of Q thus calculated appear in Table 111. A graph of Q vs. incident electron kinetic energy for the element carbon appears in Figure 5. These values of Q agree with those of Ref. 47 within *3%. T h e back-scattering factor, S , specifies the number of w-level ionization events in the adsorbed layer which result from the flux of scattered electrons. As such, S is t h e ionization cross section, Q ( E ) ,multiplied by the energy distribution of secondary electrons doing the ionizing, N,(E),in-
sn , IO-''
cmZ/bOund electron
t i
l 5 1
0
30
tegrated over all energies in the distribution and normalized by the total flow of scattered electrons (that is, by the primary beam current, I,): =
A j"," 210nJ:i
Q(E)N,(E) sec 0 cos
I,
e
sin 0 d 0 d E
T h e integrand is zero for E outside the range E , 5 E 5 E , because the secondary electron cannot possess energy greater than that of the primary electron [that is, N,(E) = 0 for E > E,] and ionization of the w-level cannot occur when E, < E,, [that is, Q ( E )= 0 when E, < E,]. Integration over an angular distribution is necessary because electrons are scattered by the substrate in a cosinusoidal distribution (421, Figure 6, after which they travel a distance proportional to sec 8 in the adsorbed layer. The secondary electron energy distribution, N , ( E ) ,was determined directly by measurement of the first harmonic of the modulated electron emission current, A , ( E ) , for t h e clean surface, over the entire energy range from 0 to E,. Normalization of A , ( E ) for collection efficiency of the analyzer was done by means of Equation 20,
N , ( E ) / A , ( E )= l / [ k K 1:2 cos 0 sin 0 de] =
-
\
90
60
Figure 6. Angular distribution of Auger electrons emitted from a substrate. (-) Solid curve: experimental data of Harris (37) for Auger electrons from Mo (190 e V ) containing an adsorbed hydrocarbon overlayer. (---) Dashed curve: graph of cos 8. ("(E) was normalized to unit emission along the surface normal
S
\
4/[kK(sin2e 2 - sin' 12.48 k
e,)]
(20)
the derivation of which is analogous to Equations 11 and 14. T h e ionization cross section, Q ( E ) ,was calculated from Equation 15, by setting E, = E. The integral in Equation 19 was evaluated by computerized application of Simpson's rule. T h e calculation procedure is illustrated in Figure 4. Values of S obtained in this manner are listed in Table 111. A graph of calculated S vs. E,, the ionization energy of the w-level, appears in Figure 7 . As can be seen, S is predicted to decrease sharply in magnitude with increasing E,. Secondary electron emission varies by about 1070 with vectorial and azimuthal angles, 8i and ai. Accordingly, the S-values reported in Table I11 are exact only for the angles employed in this work. Some earlier workers resorted to the use of equations developed for electrons in the 10-keV energy range (46) to calculate S (45,52). An iterative, empirical procedure has been suggested (54)which has the drawback that it requires tedious experiments which must be repeated for each combination
Figure 7. Backscattering factor per electron, Sln, for elements present as an adsorbed layer on Pt(100). Parametric quantities are as in Table I and Figure 1 of incident energy, substrate, and adsorbed layer. Equation 19 differs from the expression employed in Ref. 47,
which neglects the angular distribution of secondary electrons (cos 8) and omits one part (sin 8) of the expression for the differential area increment in spherical polar coordinates. The expression employed subsequently by the same authors (52) is equivalent to Equation 11, however. The fraction of ionization events leading to processes other than x-ray emission, & is nearly unity for incident energies less than about 3000 eV, and follows Equation 21 described in Ref. 55,
where 2 is the atomic number of the emitting element, and g = 1.12 X lo6 for K shells and 6.40 X lo7 for L shells. The fraction of Auger processes, I#Ja, leading to an Auger transition of a specific type is denoted by I#Jv For KLL Auger transitions of the first row elements Li through Ne and for LMM transitions of S and C1, the Auger electron kinetic energies are grouped into bands or closely spaced multiplets. Since, for analytical purposes, the intensities due to a given element are lumped together in the process of integrating the spectra, 4t can be set equal to unity for these elements. Introducing Q , S, and & from Equations 15,19, and 21 into Equation 16 yields the calculated values of G listed in Tables I and 111. These calculations indicate that most of the observed differences in Auger electron yield from element to element in a chemisorbed layer are due to differences in ionization cross section, Q. Accordingly, Q should be the focal point of future attempts to refine the theory. Comparison of Data with Theory. Although the data are sparse, it is interesting to compare experimental values of G with those predicted by the equations, within either a relative or an absolute framework. For instance, comparison of the ratios of G values for elements within an adsorbed layer tests the ability of experiment and theory to produce correct relative elemental compositions. Table IV compares observed and calculated G ratios. As can be seen, theory and experiment correlate within the limits imposed by the experimental precision except in the case of fluorine. It is probable that the very low signal level for fluorine, due to its relatively low 1s ionization cross section, thwarted its accurate determination in these experiments; future spectra, in which a 10 keV inANALYTICAL CHEMISTRY, VOL. 49, NO. 14, DECEMBER 1 9 7 7 * 2335
Table IV. Relative Auger Electron Yields
Compound chemisorbed
Experimental ratio
Theoretical ratio
Allylamine G,:G,= 2.8 * 0.6 2.0 Allylacetic acid G c : G o = 4.7 * 0.5 3.6 Chlorotrifluoroethylene G c : G c l = 0.17 * 0.02 0.175 Thiophene
Gc:G,= 1 7 t 3 G c : G s = 0.20 i 0.03
6.8 0.12
Figure 8. Calibration factor, G, for Auger electron emission from atoms present as substituted hydrocarbons chemisorbed on Pt( 100). (-)
Solid curve: theory. (x x x) Individual points: experimental values. Experimental conditions: as in Figure 1 and Table I cident electron gun is employed, should resolve this question. Absolute magnitudes of experimental and theoretical Auger efficiencies, G, are compared in Table I. As can be seen, there is strong qualitative correlation in all cases and agreement to better than f10% is observed in about half of the examples; of the remainder only one pair displays a difference of more than 30%, the probable cause of which was discussed earlier. A graph of experimental and theoretical values of G vs. E , appears in Figure 8. T h e degree to which factors such as valence state and molecular conformation influence Auger electron yield is of interest in this regard and will be the subject of future investigation. However, a t present it appears t h a t the accuracy of the theory is comparable to that of the techniques available to test it, and that with suitable calibration of the spectrometer, elemental analyses accurate to within 10% or better are t o be expected.
ACKNOWLEDGMENT Assistance was provided by Gerald Gulden and Lance Nakamura in computerization of the data handling process. Roy M. Ishikawa prepared the single crystal samples. Mark Green provided valuable assistance with the experiments.
LITERATURE CITED (1) J. V. Florio and W. 0. Robertson, Surf. Sci., 18, 398 (1969). (2) B. J. Pollard, Surf. Sci., 20, 269 (1970).
2336
ANALYTICAL CHEMISTRY, VOL. 49, NO. 14, DECEMBER 1977
(51) (52) (53) (54) (55)
S. Thomas and T. W. Haas, J . Vac. Sci. Technol., 9, 840 (1971). M. Perdereau, Surf. Sci.. 24, 239 (1971). J. W. T. Ridgway and D. Haneman, Surf. Sci., 26, 683 (1971); 24, 451 (1971). D. T. Quinto, V. S. Sundaram, and W. D. Robertson, Surf. Sci., 28, 504 (1971). J. J. Vrakking and F. Meyer, Appl. Phys. Lett., 18, 226 (1971). R. E. Weber and W. T. Peria, J . Appl. Phys., 38, 4355 (1967). J. M. Morabito, Surf. Sci., 49, 318 (1975). R. M. Ishikawa and A. T. Hubbard, J. Electroanal. Chem., 69, 317 (1976). A. T. Hubbard, R. M. Ishikawa, and J. Katekaru, J , Eiectroanal. Chem., in press. C. S. Barrett, "Structure of Metals", 3rd ed.,Mc&aw-Hili. New York, N.Y., 1977. E. Wood, "Crystal Orientation Manual", Columbia University Press, New York, N.Y., 1963. L. L. Levenson et al., J . Vac. Sci. Techno/., 9, 608 (1971). P. W. Paimberg, in "The Structure and Chemistry of Solid Surfaces", G. A. Somorjai, Ed., John Wiley, New York, N.Y., 1979, Article 29. R. Nathan and B. J. Hopkins, J . Phys. E , 8, 1040 (1973). J. T. Grant, M. P. Hooker, and T. W. Haas, Surf. Sci., 46, 672 (1974). H. 2 . Sar-el, Rev. Sci. Instrum., 38, 1210 (1967). H. Hafner, J. A. Simpson, and C. E. Kuyatt, Rev. Sci. Instrum., 39, 33 (1968). A. E. Morgan and G. A. Somorjai, J . Chem. Phys., 51, 3309 (1969). C. N. Lai and A . T. Hubbard, Inorg. Chem., 11, 2081 (1972). A. T. Hubbard, Crit. Rev. Anal. Chem., 3, 201 (1973). A. T. Hubbard and F. C. Anson, Eiectroanal. Chern., 4, 129 (1970). R. F. Lane and A. T. Hubbard. J . Phys. Chem., 77, 1401, 1411 (1973); 79, 809 (1975). R. M. Ishikawa, Ph.D. dissertation, University of Hawaii, 1976. K. Ueda and R. Shimizu, Surf. Sci., 36, 789 (1973). A. M. Horgan and I. Daiins, J . Vac. Sci. Technol., 10, 523 (1973). R. J. Szalkowski and G. A. Somorjai, J , Chem. Phys.. 56, 6097 (1972). H. H. Farrell, Surf. Sci., 34, 405 (1973). T. W. Haas and J. T. Grant, Phys. Lett., 30A. 272 (1969). T. W. Haas, J. T. Grant, and G. J. Dooley 111, J . Appi. Phys., 43, 1853 (1972). D. A. Shirley, Chem. Phys. Lett., 17, 312 (1972). E. N. Sikafus, Surf. Sci., 36, 472 (1973). J. J. Lander, Phys. Rev., 91, 1382 (1953). L. A. Harris, J . Appl. Phys., 39, 1419 (1968). L. N. Tharp and E. J. Scheibner, J . Appl. Phys., 38, 3320 (1967). C. C. Chang, Surf. Sci., 25, 53 (1971). G. A. Somorjai and F. J. Szaikowski, Adv. High Temp. Chem., 4, 137 (1971). N. J. Taylor, Tech. Met. Res., 7, 117 (1971). J. E. Houston, Surf. Sci., 38, 283 (1973). J. T. Grant, T. W. Haas. and J. E. Houston, Surf. Sci., 42, 1 (1974). L. A. Harris, Surf. Sci., 15, 77 (1969). C. C. Chang, Surf. Sci., 48, 9 (1975). J. T. Grant, M. P. Hooker, and T. W. Haas, Surf. Sci., 51, 318 (1975). H. G. Bishop and J. C. Riviere, J . Appl. Phys., 40, 1740 (1969). H. G. Bishop, Br. J . Appl. Phys., 18, 203 (1967). F. Meyer and J. J. Vrakking. Surf. Sci. 33, 271 (1972). M. Gryzinski, Phys. Rev. A, 138, 305, 322, 336 (1965). W. A. Coghlan and'R. E. Clausing, At. Data, 5, 317 (1973). K. Siegbahn et al., ESCA: Atomic, Molecular and Solid State Structure Studies by Means of Electron Spectroscopy", Almqvist-Wikseii Boktryckeri, UoDsala. Sweden. 1967. R: 2; Fohner and'R. G. Musket, Surf. Sci., 28, 339 (1971). J. J. Vrakking and F. Meyer, Surf. Sci., 35, 34 (1973). G. A. Somorjai and H. H. Farreii, Adv. Chem. Phys., 20, 215 (1971). T. E. Gallon, J . Phys. D ,5 , 822 (1972); 7, 151 (1974). E. S. H. Bishop, "The Auger Effect and Other Radiationless Transitions", University Press, Cambridge, England, 1952.
RECEIVED for review August 26, 1977. Accepted October 3, 1977. Acknowledgment is made to the donors of the Petroleum Research Fund administered by t h e American Chemical Society, and to the National Science Foundation for support of this research.
