Determination of target mass from ISS data in the presence of inelastic losses

NIM B Beam Interactions with Materials & Atoms

Nuclear Instruments and Methods in Physics Research B 243 (2006) 193–199 www.elsevier.com/locate/nimb

Determination of target mass from ISS data in the presence of inelastic losses Matthew D. Coventry a

a,*

, Robert Bastasz

b

Plasma-Material Interaction Group, Nuclear, Plasma and Radiological Engineering, University of Illinois at Urbana-Champaign, 103 S. Goodwin Avenue, Urbana 61081, USA b Sandia National Laboratories, Livermore, CA, USA Received 19 April 2005; received in revised form 14 July 2005 Available online 15 September 2005

Abstract Ion scattering spectroscopy (ISS) is often used to identify the masses of surface atoms through measurement of scattered-ion energies. Mass analysis is straightforward when the scattering events can be described by binary elastic collision kinematics. However, inelastic and multiple scattering effects can alter the final energy of the detected particles, complicating the analysis. Here we present a method that uses ISS data collected at two or more observation angles to identify both the mass of the scattering center and any inelastic energy loss. Use of this technique can also allow detection and quantification of certain systematic errors, such as uncertainties in the initial beam energy, detected ion energy and scattering angle. While ion scattering is stressed here, the presented technique works equally well for the analysis of direct recoil ion energies. An example using He+ ISS data recorded on an Al–Ag alloy illustrates the abilities of this method.
2005 Elsevier B.V. All rights reserved. PACS: 03.20; 34.50.S; 34.50.Dy; 61.18.Bn Keywords: ISS; LEIS; DRS; Kinematics; Binary collisions; Circle fitting

1. Introduction Ion scattering spectroscopy (ISS) is a well-established surface analysis method that can provide composition and real-space structure information about the top atomic layers of a material [1–6]. Typical ISS experiments use a low-flux, monoenergetic ion beam in the range 0.1– 10 keV to bombard a surface and an ion-energy analyzer to measure the kinetic energy of ions that scatter from the surface. Measuring the final energies or velocities of scattered particles of mass, m1 at a known laboratory observation angle, h, provides information about the mass of the target atom on the surface, m2, through the use of binary collision kinematics. *

Corresponding author. Tel.: +1 217 333 8385; fax: +1 217 333 2906. E-mail address: [email protected] (M.D. Coventry).

0168-583X/$ - see front matter
2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2005.07.223

A complementary method to ISS is direct-recoil spectroscopy (DRS), which is especially useful for detection of light atoms on surfaces (e.g. the hydrogen isotopes). As ions scatter from the surface, energy is transferred to the surface atoms. Some binary collisions impart enough outward momentum to surface atoms to eject them. A fraction of these direct recoils are ionized and can be detected in the same manner as scattered ions. Their energy distribution can be interpreted using a similar kinematic analysis as used for ISS. Direct recoil ions are distinct from the lower energy secondary ions that are generated by the subsequent collision cascades. The data from ISS experiments are typically plotted in the form of ion energy spectra. Fig. 1 shows the detected ion signal intensity as a function of relative ion energy collected at two angles of observation. It is usually assumed that the main peaks in a spectrum result from single binary

194

M.D. Coventry, R. Bastasz / Nucl. Instr. and Meth. in Phys. Res. B 243 (2006) 193–199 a

1 keV He+ → Al-Ag

1

SIGNAL INTENSITY (a.u.)

bc b

0.8

(a) (b) (c) (d)

0.6

He → Al at 60° He → Al at 30° He → Ag at 60° He → Ag at 30°

c

DRS data and fits a circular arc to them. This type of approach, using various circle-fitting procedures, some originally developed for computer and engineering applications [7–13], improves the mass accuracy of ISS/DRS measurements. The basis for the method has been noted before [14], but its implementation has not, to our knowledge, previously been presented or discussed in the literature in any detail.

d d

30° spectrum

a

0.4 60° spectrum

2. Method

0.2

0.7

0.75

0.8

0.85

0.9

0.95

1

RELATIVE ION ENERGY

Fig. 1. Ion energy spectra of 1 keV He+ scattered from an Al–Ag alloy sample. The dashed and solid curves are ISS data recorded at scattering angles of 30 and 60, respectively. The vertical dashed lines correspond to the energies of purely elastic collisions. Note that the inelastic energy loss for He+ scattering from Al is significantly greater than that for Ag.

collisions. The first-order approximation is to assume that each collision is quasi-elastic and to determine the mass of the target atom from the relations that follow from binary collision theory. It can be found, using the formulations in the following section, that the target to projectile mass ratio, A, is given by pffiffiffiffiffi 1 þ Es
2 Es cos h A¼ for scattered ions ð1Þ 1
Es and A¼

ðcos h 

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 cos2 h
Er Þ Er

for recoil ions;

ð2Þ

where Es and Er represent the ratios of the scattered and recoil ion energies to the initial ion energy, and h is the observation (either scattering or recoiling) angle. Using the above relations, the correct mass is determined only when the inelastic effects are negligible. However, many scattering interactions have an inelastic (e.g., electronic) component that can alter the final energy of the scattered or recoil particle. Inelastic effects typically move the peak positions in a spectrum toward lower energies, sometimes on the order of 10s of eV. This is shown in Fig. 1, where the experimental peaks lag the elastic peak predictions (dashed lines) for both components of an Al– Ag alloy, with scattering from aluminum showing greater shift than that from silver. The actual amount of the inelastic energy loss is difficult to quantify without specific knowledge of the target surface, i.e., target masses, since inelastic losses can vary with different projectile and target atom combinations, along different ion flight paths, and with varying surface stoichiometry or structure. The premise for the method described in the following section is simple: recording ion energy spectra at two or more observation angles provides enough information to evaluate both inelasticity and the target mass. The method we describe takes a geometric representation of the ISS/

The technique developed here improves the accuracy of target-mass determinations from ISS/DRS ion energy spectra by identifying the inelastic contributions to the ion energy loss. Ion energy spectra are recorded at several observation angles. Applying energy and momentum conservation laws, it can be shown that the peak locations in the spectra data will form a circle when the square root of the relative scattered-ion energy is plotted in polar coordinates as a function of the observation angle. By determining the centers and radii of the circles that fit the peak data, the target mass and the magnitude of inelasticity can be determined. The key to this method lies in the kinematic relations of the incident and target particles in the laboratory reference frame. For this formulation and for the sake of generality, it is useful to use a few non-dimensional variables. The variables A, Es, Er and h were defined in the introduction and are depicted in Fig. 2 (often the s and r subscripts on h are suppressed; they are retained for clarity when necessary). The relative inelastic energy loss, Q, is expressed as a fraction of the initial incident ion energy. For a binary collision between a projectile and an initially stationary target atom, conservation of energy and momentum can be written in dimensionless form as 1 ¼ Es þ Er þ Q; pffiffiffiffiffiffiffiffi pffiffiffiffiffi 1 ¼ Es cos hs þ AEr cos hr ; pffiffiffiffiffiffiffiffi pffiffiffiffiffi 0 ¼ Es sin hs
AEr sin hr .

ð3Þ ð4aÞ ð4bÞ

m=1, E=Es θs m=E=1

θr m=A, E=Er Fig. 2. Definitions of various binary collision-event parameters in dimensionless form and in the laboratory reference frame. The incident particle has mass and energy of unity. It scatters from a target atom with mass A at at angle hs, leaving with energy Es. The target atom recoils at energy Er at an angle hr relative to the incident trajectory.

M.D. Coventry, R. Bastasz / Nucl. Instr. and Meth. in Phys. Res. B 243 (2006) 193–199

The cosines of the scattering and recoil angles can be written as [14]: 1 þ A pffiffiffiffiffi 1
Að1
QÞ pffiffiffiffiffi Es þ cos hs ¼ ; ð5aÞ 2 2 Es rffiffiffiffiffi 1 þ A Er Q cos hr ¼ ð5bÞ þ pffiffiffiffiffiffiffiffi . 2 A 2 AEr The motivation for this particular form will soon be apparent. Consider a circle centered at (x0, 0) with radius R. In polar coordinates (r, /), it is specified by the equation: r x 2
R2 . ð6Þ þ 0 2x0 2x0 r pffiffiffiffi Relating E to r and h to /, Eqs. (5) can be written in forms similar to that of Eq. (6) with the x-coordinate of each circle center on the x-axis, x0, given by pffiffiffi A 1 ð7a; bÞ xr ¼ xs ¼ 1þA 1þA cos / ¼

and the radii of the circles by rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi A Qð1 þ AÞ Rs ¼ 1
; 1þA A ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r pffiffiffi A Qð1 þ AÞ Rr ¼ 1
1þA A

ð8a; bÞ

for the scattered and recoiled particles, respectively. The relationship between the observation angle and relative ion energy is depicted graphically in Fig. 3 for the particular case of He incident on an Al–Ag alloy. As shown for purely elastic collisions with stationary targets, the scattering circles pass through the point (1, 0) and the recoil circles pass through the origin. In the case Q > 0, the center of the scatter or recoil circle remains the same, but the radius is reduced. Therefore if sufficient data exist to fit a circle to the peak data accurately and determine its center and

90°

He → Ag

0.5

√E

Al 180°

1

0

Ag

0.5

Ag

Al

Al 0.1

0.5

0

Ag

1

0°

Al

0.2

0.3

0.4

0.5

√E Fig. 3. Elastic scattering and recoiling circles for He collisions with Al and Ag. The radius of the circle is dependent on the inelastic energy loss of the collision event, but the position of the circle center is not, provided that the inelasticity is independent of observation angle. The circle centers lie on the x-axis if the target atom is initially stationary.

195

radius, the mass of the target atom, as well as the inelastic ion energy loss, can be determined. 3. Fitting techniques The first step, following the measurement of ion energy spectra at a variety of observation angles, is to determine pffiffiffiffi which data to analyze; that is, select the set of ð E; hÞ points to which a circle will be fit. Typically, the raw data are in the form of several ion energy spectra, one for each observation angle. We identify an ion energy range of interest, which is scaled with the observation angle, and find the ion signal intensity peak within that range for each observation angle. It must be kept in mind that the signal peaks of interest must be resolvable from their neighbors in each spectrum used for the data analysis. That is, each ion energy range identified must contain exactly one intensity peak. pffiffiffiffi The key task is to fit a circle to the ð E; hÞ data. Three principal methods were used to analyze existing data – that is, fit circles to experimental data sets to obtain good estimations of the circleÕs center location and radius: a least-squares algorithm; and two geometric construction methods, one using unique sets of two data points (our ‘‘2-point’’ method) and the other using three (‘‘3-point’’ method). The least-squares algorithm was used to fit both an ellipse and a circle to the data set constraining the center to lie on the x-axis. The elliptical fit algorithm calculated values of constants c1, c2 and c3 to obtain the best fit, in a least-squares sense, of f ðxÞ ¼ y 2 ¼ c1 þ c2 x þ c3 x2

ð9Þ

to the data. For an ellipse with semiaxes a and b along the x- and y-axes, their ratio is given by c3 =
b2/a2. Using the other fit constants allows one to find the center x0 = c2/2(a2/b2); the semiaxes are found using the relation c1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi = b
x0ffib2/a2. Also, the eccentricity is given by e ¼ q

1
d 2 =c2 , where d and c represent the minor and major semiaxes, respectively. While elliptical curves are expected only at relativistic velocities [15], this approach imposes the fewest constraints on the data fit. Circular fits (e = 0) were obtained by finding similar constants to best fit f ðx; yÞ ¼ y 2 þ x2 ¼ c1 þ c2 x ð10Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 to the data, now with x0 = c2/2 and R ¼ c1 þ x0 , in the least-squares sense. The imposition of the additional constraint of making a perfect circle is valid as the energies encountered in these types of experiments are clearly in the classical regime. The 3-point geometric fit used here employed a centroiding method [10] where all unique combinations of three data points were p used ffiffiffiffi (a total of N3 = n!/[(n
3)!3!] combinations given nð E; hÞ combinations), which we initially believed could help yield better results. This method makes use of the fact that a circle can be uniquely defined by three

196

M.D. Coventry, R. Bastasz / Nucl. Instr. and Meth. in Phys. Res. B 243 (2006) 193–199

(not all collinear) points. Since a circle has a constant radius, the following relations exist [10,11]: 2

2

2

R ¼ ðx1
x0 Þ þ ðy 1
y 0 Þ ¼ ðx2
x0 Þ þ ðy 2
y 0 Þ ¼ ðx3
x0 Þ2 þ ðy 3
y 0 Þ2 .

2

ð11Þ

This can be written in matrix form as two simultaneous equations (an arbitrary choice of two among the three possibilities) and solved for the unknowns. One way of expressing this is [10,11]   x
2½ x1
x2 y 1
y 2 x2
x3 x2
x3  0 y0  2  x þ y 22
ðx21 þ y 21 Þ ¼ 22 . ð12Þ x3 þ y 23
ðx22 þ y 22 Þ Eq. (12) can then be solved by matrix inversion to obtain the N3 circle centers corresponding to each combination of three points. The position of the true center was taken to be the mean of the the N3 centers. While the average, final, center point can have a non-zero y-value, we have found that the resultant y-values for typical ISS data sets

are small; this is expected due to the validity of the stationary target atom approximation. Parts (a) and (b) of Figs. 4 and 5 show the distributions of centers found using the 3point method along the x- and y-axes, respectively, for the Al–Ag alloy sample data. The 2-point method pffiffiffiffiselected each of N2 = n!/[(n
2)!2!] (again for n sets of ð E; hÞ points) unique combinations of two data points and determined where the perpendicular bisector of their chord intersects the x-axis. This intersection provides the x-coordinate of the center; the y-coordinate was fixed at zero. The mean value of the N2 circle centers was taken as the final center. Figs. 4(c) and 5(c) show the distribution of centers found using the 2-point method. While fewer centers were found using this method, in comparison to the 3-point technique, we imposed the additional constraint of having all circles lie on the x-axis. For both the 2- and 3-point methods, improved estimates were generated by weighting the centers with the inverse square of the distance to the mean radius of the unweighted circle. This was motivated by a report that this weighting method improved the accuracy in another

(a) 3-POINT X-VALUES

(b) 3-POINT Y-VALUES

0.14 0.12

Y-VALUE PROBABILITY

X-VALUE PROBABILITY

0.12 MEAN VALUES UNWEIGHTED: 0.155 WEIGHTED: 0.144

0.10 0.08 0.06 0.04

0.08

MEAN VALUES UNWEIGHTED: 0.0241 WEIGHTED: 0.00567

0.06 0.04 0.02

0.02 0.00

0.10

-0.4

-0.2 0.0 0.2 X-VALUE = 1/(A + 1)

0.4

0.00

-0.4

-0.2

0.0

0.2

0.4

Y-VALUES

X-VALUE PROBABILITY

(c) 2-POINT X-VALUES 0.08

0.06

(d) CENTER DISTRIBUTION MEAN VALUES

0.01

UNWEIGHTED: 0.141 WEIGHTED: 0.141

3-POINT 0.005

EXACT 2 -POINT

LS -CIRCLE

0.04

0.13

0.14

0.15

0.02 -0.005 0.00

-0.4

-0.2 0.0 0.2 X-VALUE = 1/(A + 1)

LS -ELLIPSE

0.4 -0.01

Fig. 4. Distribution of scattering circle center x-coordinates (a) and y-coordinates (b) for a test case of He ! Al calculated using the 3-point method. (c) shows the distribution of centers (x-coordinate only as y is set to 0) calculated by the 2-point method from the same data. Only a single center is found by the least-squares fit to the data, so it has no distribution; the eccentricity for an elliptical least-squares fit is 0.0629. Finally, (d) shows the centers as determined by each method for comparison; the weighted centers were used where applicable.

M.D. Coventry, R. Bastasz / Nucl. Instr. and Meth. in Phys. Res. B 243 (2006) 193–199

(a) 3-POINT X-VALUES

197

(b) 3-POINT Y-VALUES

0.025

MEAN VALUES 0.04 UNWEIGHTED: 0.0564 WEIGHTED: 0.0448

Y-VALUE PROBABILITY

X-VALUE PROBABILITY

0.05

0.03 0.02 0.01 0.00

-0.4

-0.2 0.0 0.2 X-VALUE = 1/(A + 1)

0.020

MEAN VALUES UNWEIGHTED: 0.0192 WEIGHTED: 0.00562

0.015 0.010 0.005 0.000

-0.4 -0.2 0.0 0.2 0.4 Y-VALUE FOUND USING 3-POINT METHOD

0.4

(c) 2-POINT X-VALUES

X-VALUE PROBABILITY

MEAN VALUES

0.08

(d) CENTER DISTRIBUTION

UNWEIGHTED: 0.0387 WEIGHTED: 0.0387

0.015 0.01

0.06

3-POINT

0.005

LS CIRCLE

EXACT X = 1/(A + 1)

0.04

0.01

0.02

0.005 0.02

0.03

0.04

0.05

2-POINT

0.01 LS ELLIPSE

0.00

0.015 -0.4

-0.2 0.0 0.2 X-VALUE = 1/(A + 1)

0.4

Fig. 5. Similar to Fig. 4, this figure is for He ! Ag. Distribution of the x-coordinate (a) and y-coordinate (b) of 3276 circle centers found using the 3-point method. (c) shows the distribution along the x-axis of 378 circle centers found using the 2-point method. In spite of the advantage of having almost an order of magnitude (for the case of 28 observation angles) more centers than the 2-point method, the 3-point method almost always provided inferior estimate of the circle center location. This is seen in (d) by noting the proximity of the centers to the correct value.

circle-fitting application [10]; thus the weighting was believed to yield an improved estimate of the target mass. This procedure yielded only a minor improvement so higher-order weighting was considered to be unnecessary.

ratio within 5% of the exact answer (for known target species) without adjusting for systematic experimental error, 90° 120°

60°

4. Results and discussion A survey of ISS data for dozens of beam/target combinations was performed to evaluate the effectiveness of each of the fitting methods and the technique. The data sets examined usually had 500–3000 eV He+ or Ne+ ions scattering from a variety of pure and alloyed metal surfaces in both the solid and liquid phases. Almost all cases showed improvement of the target-mass determination in comparison to determining the mass from data recorded at a single observation angle. It is important to note that the average of the many readings obtained using single-angle formulas is no better than that obtained using one, single-angle measurement. Use of this technique allows one to obtain an improved estimate of the target atom mass, even when given only a handful of data at different observation angles. In fact, more than half of the results yielded a mass

0.75 150°

30°

0.50 √E

0.25

s

θs 0°

180° 1

0.75

0.50

0.25

0

0.25

0.50

0.75

1

25 amu 100 amu

pffiffiffiffiffi Fig. 6. ð Es ; hÞ plot of experimental ion signal intensity peak positions shows the slightly inelastic nature of the scattering events of 1 keV He+ from an Al–Ag alloy sample. The circle centers (and their corresponding masses) and the circular curves are results from a least-squares circular fit. The data points shown are from spectra, such as those in Fig. 1, at 28 observation angles where the ion signal intensity peaks were followed with changing h.

M.D. Coventry, R. Bastasz / Nucl. Instr. and Meth. in Phys. Res. B 243 (2006) 193–199

which will be later shown to have a noticeable effect on the pffiffiffiffi final results. Fig. 6 shows a set of ð E; hÞ data from the example case of 1000 eV He+ scattering from an Al–Ag alloy with circles determined by a circular least-squares fit to theffiffiffiffiffiffiffiffiffiffiffi data. ffi The data clearly show how ion energy peaks (in p Ei =E0 form) map out a circle as a function of observation angle. Significant improvement is noted for both masses in comparison to those determined using the single-angle data in Fig. 1. The least-squares circular fit and the 2-point method proved to be the most accurate for the cases reviewed during this study. This is most likely due to the fact that both techniques fit perfect circles centered on the x-axis, which imposes actual physical constraints. In spite of the apparent statistical advantage of the greater number of combinations using the 3-point fitting technique (N3 = N2 · (n
2)/ 3), the requirement placed on the 2-point data that the centers lie on the x-axis often yielded the best mass estimate. In addition, weighting of the 2-point data with the inverse square of the distance to the mean circle yielded an additional, but marginal, improvement in the mass estimate. However, the discrepancy for an estimate using the 2-point technique, when it proved to be less accurate than the least-squares approach, was typically greater than the discrepancy for the reverse situation. Thus, finding the least-squares fit of a circle to the experimental data is the technique of choice among those analyzed as it is the most accurate about half of the time, and when it is less accurate than the weighted 2-point technique, the discrepancy in predicted masses between the two techniques is marginal. Results for each method are shown in Table 1, along with single-angle results. An additional application of this technique is to use a target with known mass(es) to detect systematic experimental errors. Errors in accurately determining the energy of the incident ion beam, the detected ion energy or the observation angle can change the results noticeably (see Fig. 7). Such errors may arise from a number of sources – poor calibration, misalignment, voltage shifts and the like – and this technique may be of help in identifying them.

Table 1 Target mass, m2, determinations from ISS data using each method described in the text and the difference, Dm, of the known mass and m2 Method

m2 (Al) (amu)

Dm (amu)

Q (eV)

m2 (Ag) (amu)

Dm (amu)

Q (eV)

Best single Pt. Worst single Pt. Average single Pts.

22.9 17.1 20.4


4.1
9.9
6.6

N/A N/A N/A

87.4 48.1 74.6


20.5
59.8
33.3

N/A N/A N/A

3-Point 3-Point, weighted

22.5 23.6


4.5
3.4

40.5 18.0

66.9 85.3


41.0
22.6

23.7 4.00

2-Point 2-Point, weighted

24.3 24.3


2.7
2.7

21.9 21.9

99.6 99.6


8.4
8.3

10.2 10.2

Elliptical LS fit Circular LS fit

24.9 24.5


2.1
2.5

26.7 23.3

80.1 98.1


27.8
9.8


4.46 9.68

The values shown are those results ignoring any systematic errors.

CHANGE IN CALCULATED MASS (AMU)

198

4.0

ERROR IN ENERGY OF DETECTED IONS

ERROR IN INITIAL ION ENERGY

2.0

0.0

ERROR IN SCATTERING ANGLE

SYMBOL

-2.0

PARAMETER E+∆ E0 / (1 + ∆) 10° x ∆

-4.0 -1.0

-0.5

0.0

0.5

1.0

DEVIATION (∆)

Fig. 7. Mass accuracies based on scattering circle calculations depend on the correct calibration of the incident ion energy, detected particle energy and scattering angle. The plot shows the sensitivity of the calculated mass of Al as a function of various measurement errors for the case 1 keV He ! Al at h ranging from 30 to 84.

Ion energy spectra from our example case of 1 keV He+ scattering from an Al–Ag binary alloy were analyzed using the described techniques and a detailed search for small measurement errors of the incident energy, scattered-ion energy and scattering angle was made. This supplementary study yielded information of the techniqueÕs sensitivity to changes in these parameters and is presented in Fig. 7. In this figure, the change in the determined mass as a function of deviation is shown where there are three different types of deviations. A deviation (D) of ±0.1 represents a 0.1 · E0 error in the detected ion energy, a E0/(1  0.1) error the measurement of the incident ion energy or a 1 misalignment of the detector (observation angle). Table 2 shows the results following correction for systematic errors. The results indicate that offsets to the incident ion energy, scattered-ion energy and scattering angle

Table 2 Target mass, m2 determinations from ISS data after correcting for systematic errors and the difference, Dm, of the known mass and m2 Method

m2 (Al) (amu)

Dm (amu)

Q (eV)

m2 (Ag) (amu)

Dm (amu)

Q (eV)

Best single Pt. Worst single Pt. Average of single Pts.

23.2 13.6 20.0


3.8
13.4
7.0

N/A N/A N/A

69.7 28.7 53.0


38.2
79.2
54.9

N/A N/A N/A

3-Point 3-Point, weighted

20.6 24.7


6.4
2.3

103 24.7

68.4 91.8


39.5
16.1

52.6 29.7

2-Point 2-Point, weighted

27.8 27.8

+0.8 +0.8

47.7 47.7

107 107


0.9
0.9

36.4 36.4

Elliptical LS fit Circular LS fit

22.3 27.5


4.7 +0.5


3.32 46.3

84.8 106


23.1
1.9

20.6 35.8

These data correspond to the beam energy being 960 eV instead of exactly 1000 eV, the ion energy measurements having a 10 eV offset and the angle of observation offset by 5. As apparent upon comparison with values in Table 1, significant improvement was realized following the search for systematic error.

M.D. Coventry, R. Bastasz / Nucl. Instr. and Meth. in Phys. Res. B 243 (2006) 193–199

of 40 eV, 10 eV and 5 are needed in this case to give the best agreement with both target masses. Having two known masses for a single set of scans is very advantageous, and one can imagine similar advantages using a tertiary alloy. For that matter, the method could be developed into a way of calibrating a ISS/DRS instrument by using practically any multi-component sample of known composition with resolvable mass species. 5. Conclusions The use of several angles of observation for ISS/DRS measurements and employment of a circle fitting method can improve the mass accuracy obtained with these techniques. This improvement results from the analysis method and is not just a marginal improvement from averaging data. By using this method, one can better estimate surface atom mass and also evaluate collision inelasticity. The technique can be applied to both ISS and DRS data. Acknowledgements The authors would like to thank J.A. Whaley for providing technical expertise and assistance in obtaining the experimental data. This work was supported by the US Department of Energy under contract DE-AC0494AL85000.

199

References [1] H. Niehus, in: D. Briggs, M.P. Seah (Eds.), Ion and Neutral Spectroscopy, Practical Surface Analysis, Vol. 2, Wiley, Chichester, 1992 (Chapter 9). [2] R.S. Williams, in: J.W. Rabalais (Ed.), Low-Energy Ion Surface Interactions, Wiley, Chichester, 1994 (Chapter 1). [3] S.H. Overbury, in: A.T. Hubbard (Ed.), Handbook of Surface Imaging and Visualization, CRC, Boca Raton, 1995 (Chapter 26). [4] E. Taglauer, in: J.C. Vickerman (Ed.), Surface Analysis – The Principal Techniques, Wiley, Chichester, 1997 (Chapter 6). [5] G.B. Hoflund, in: J.C. Riviere, S. Myhra (Eds.), Handbook of Surface and Interface Analysis, Marcel Dekker, New York, 1998 (Chapter 3). [6] J.W. Rabalais, Principles and Applications of Ion Scattering Spectrometry, Wiley, Hoboken, 2003. [7] G. Vandersteen, Y. Rolain, J. Schoukens, A. Verschueren, IEEE Trans. Microwave Theory Tech. 45 (1997) 1027. [8] C.A. Corral, C.S. Lindquist, IEEE Trans. Instr. Meas. 47 (1998) 789. [9] S.D. Phillips, B. Borchardt, W.T. Estler, J. Buttress, Precision Eng. 22 (1998) 87. [10] Y.T. Chan, B.H. Lee, S.M. Thomas, J. Optim. Theory Appl. 106 (2000) 49. [11] Y.T. Chan, Y.Z. Elhalwagy, S.M. Thomas, J. Optim. Theory Appl. 114 (2002) 363. [12] S.J. Ahn, W. Rauh, H.S. Cho, H.-J. Warnecke, IEEE Trans. Pattern Anal. Mach. Intell. 24 (2002) 620. [13] Z. Drezner, S. Steiner, G.O. Wesolowsky, Comput. Oper. Res. 29 (2002) 637. [14] W. Eckstein, R. Bastasz, Nucl. Instr. and Meth. B 29 (1988) 603. [15] R. Bastasz, W. Eckstein, Methods of Materials Research, Wiley, New York, 2000 (Chapter 1).