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Geometric considerations relevant to hydrogen depth profiling by reflection elastic recoil detection analysis
Nuclear Instruments and Methods in Physics Research B 183 (2001) 391±400
www.elsevier.com/locate/nimb
Geometric considerations relevant to hydrogen depth pro®ling by re¯ection elastic recoil detection analysis R.D. Verda a
a,*
, J.R. Tesmer a, C.J. Maggiore a, M. Nastasi a, R.W. Bower
b
Los Alamos National Laboratory, Mail Stop G755, Los Alamos, NM 87545, USA b University of California, Davis, CA 95616, USA Received 20 November 2000; received in revised form 21 March 2001
Abstract This work addresses geometric considerations relevant to the accuracy of depth pro®ling by re¯ection elastic recoil detection analysis, which becomes an issue when many samples are compared over time or a single sample is repeatedly analyzed following a sequence of processing steps. In such cases, accurate and reproducible geometric alignment and incident beam energy calibration must be performed over time, and are addressed here. Our analysis and experiments show that geometric deviations in the sample tilt angle and incident particle beam steering, as well as deviations from the sample eucentric position, can result in signi®cant errors in depth pro®ling. As a result, a recommended degree of accuracy is stated for each of these geometric components; techniques are presented to attain this accuracy, or better. The most notable of these techniques is a laser alignment of the sample tilt angle, which has a reproducible accuracy of 0.04°. Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 61.18.Bn; 61.43.Bn; 61.72.Ss; 61.72.Tt Keywords: Geometry; Energy calibration; Simulations; Depth pro®ling
1. Introduction Elastic recoil detection analysis (ERDA) is a well-known and widely used ion beam analysis technique whereby information about sample composition can be obtained by detecting light target nuclei recoiling from heavier bombarding
*
Corresponding author. Tel.: +1-505-665-6685; fax: +1-505667-8021. E-mail address: [email protected] (R.D. Verda).
ions [1±3]. The accuracy of depth pro®ling by re¯ection ERDA is subject to a number of factors including, but not limited to, multiple scattering [4], the accuracy of the cross-sections and stopping factors [5], energy straggling [6], system resolution [7], and also experimental geometry and energy considerations. The issue of accurate and reproducible depth pro®ling becomes most important when materials analysis requires comparison of data from many samples over time or from a sample that is repeatedly analyzed following a sequence of processing steps. Especially in such
0168-583X/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 1 ) 0 0 6 3 4 - 6
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cases, the experimental techniques used must ensure that accurate and reproducible geometric alignment and energy calibration can be performed over an arbitrary time period. Re¯ection ERDA, typically performed at grazing incidence [8], is highly sensitive to changes in the experimental geometry. Thus, an accurate transformation of the data into a depth pro®le will require precise knowledge of the geometry [9,10]. The purpose of this work is to systematically examine certain geometric components of re¯ection ERDA, namely the tilt angle, eucentric position, and incident particle beam steering in order to determine how deviations with respect to these components aect depth pro®ling. Simple mathematical expressions are given to show the eects of geometric deviations and data are presented which show the characteristic changes expected in the ERDA spectra for these deviations. Based on the experiments and analysis, a recommended degree of accuracy is stated for each geometric component, and techniques are presented to attain this accuracy, or better. The most notable of these techniques is a laser alignment of the sample tilt angle, which has a reproducible accuracy of 0.04°. 2. Experimental details The accelerator used for these experiments was a National Electrostatics Corporation 3 MV tandem. All energies reported are described with respect to the laboratory system. To ensure that the experimental observations were independent of energy variations, all experiments were performed at the 16 O a; a 16 O resonance energy of 3.036 MeV, which has a full width at half maximum of 8 keV [11]. Incident 4 He particles at this energy are well below the Coulomb barrier of silicon, so no primary nuclear reactions take place when irradiating silicon samples or standards. This resonance energy was tuned by maximizing the counts in the 16 O peak of the Rutherford backscattering spectroscopy (RBS) spectrum of a substrate having a thin native oxide; the narrow width of the oxygen resonance allows the energy to be determined accurately and precisely. The beam spot size at
normal incidence on a target was approximately 1 mm 2 mm (horizontal vertical). Surface contamination during irradiation was minimized by the use of a liquid nitrogen cold trap, which resulted in a chamber pressure of about 5 10 7 Torr. The ERDA detector was oriented such that the plane formed by the incident and recoiled beams was perpendicular to the tilt axis of the target; the detector was located approximately 20 cm from the target at a nominal recoil angle of 30°. RBS was performed simultaneously with the ERDA; computer simulations of the RBS spectra were used to determine the incident particle dose. The RBS detector was oriented such that the plane formed by the incident and backscattered beams contained the tilt axis of the target; the detector was located approximately 7 cm from the target at a scattering angle of 167°. The channel-energy conversion for both detectors was approximately 5.3 keV/channel. The distance from the target to the nearest collimator was approximately 53 cm. The variation in the recoil hydrogen yield per unit beam particle dose was small for the beam doses used to acquire spectra. The sample mounting system used in these experiments consisted of a sample holder mounted on a goniometer that can be manipulated with six degrees of freedom: three translational movements along each of the three mutually orthogonal axes and three rotational movements about the same axes. The most critical manipulation in this work is the tilt angle rotation, which can move in increments of 0.01°, with a stepping motor backlash less than this amount. A depth calibration standard was synthesized for these experiments using sputter deposition techniques. The standard was prepared on a single crystal silicon (c-Si) substrate by depositing a zirconium + hydrogen layer containing approximately 64 1015 at./cm2 (both species, approximately 50 at.% each), followed by an overlayer of approximately 1400 1015 at./cm2 of amorphous silicon (a-Si). The areal densities were determined by ERDA, RBS, and secondary ion mass spectroscopy (SIMS). A more complete description of the standard and its synthesis and measurement is described in [12].
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3. Geometric considerations 3.1. Re¯ection ERDA experimental geometry The setup and geometry of a typical re¯ection ERDA experiment is presented in Fig. 1(a). All angles are described with respect to the laboratory system. The angle h1 , the tilt angle, is the angle of the incident particle beam onto the sample, and h2 , the exit angle, is the angle of the recoiled particle from the sample to the detector; both angles are measured with respect to the surface normal of the sample. The angle /, the recoil angle, lies between the path of the recoiled particle to the detector and the continuation of the path of the incident beam. The sample, sample holder and goniometer are oriented such that the sample surface plane contains the tilt axis of the goniometer, and the inci-
393
dent particle beam impinges the sample at the tilt axis location. Typically, the tilt axis and the position of the ERDA detector are ®xed; once the tilt angle is chosen, the exit and recoil angles are automatically determined provided the incident beam strikes the sample at the tilt axis. Deviations in the experimental geometry result principally from variations in sample mounting and manipulation, but also from variations in the steering of the incident particle beam. Geometric errors can be described as a combination of three types of independent misalignment: (1) misalignment in the tilt and exit angles, (2) the misalignment that results if the sample surface plane does not contain the tilt axis of the goniometer, de®ned to be a deviation from the eucentric position, and (3) variations in the incident particle beam steering. These will be discussed in turn.
(b)
(a) Fig. 1. Schematics of (a) the experimental arrangement; (b) tilt angle geometry with deviation Dh.
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3.2. Tilt angle To accurately convert an ERDA spectrum into a depth pro®le requires an accurate knowledge of the angles h1 and h2 . In our apparatus, choosing the tilt angle h1 automatically determines the exit angle h2 . These angles determine the path lengths traveled by the incident and recoiled particles; an uncertainty in h1 or h2 will lead to an uncertainty in the energy lost by the incident or recoiled particle, respectively. The eect of deviations in the tilt and exit angles on path length can be simply examined by considering a change from the symmetric condition where h1 h2 h0 to an asymmetric condition where h1 6 h2 , Fig. 1(b). Under these conditions the deviation from the original path length r of the symmetric geometry for each leg is given by Dr cos h0 r cos h0 Dh
1;
(a)
1
(b)
where Dr =r is the fractional increase/decrease in a single leg of the path length, and Dh is the deviation from h0 . It is important to note that while the magnitudes of the increase and decrease in the path length are similar (but not equal) for small deviations, the electronic stopping cross-sections of the incident and recoiled particles in the sample material are not necessarily equal. Then in general, there is no ``canceling eect'' for small deviations from the symmetric geometry when considering the ®nal energy of the recoil.
(c)
3.3. Eucentric position Fig. 2(a) represents a deviation from the eucentric position. The angle /0 is the recoil angle of the sample in the symmetric geometry without a deviation from the eucentric position; D/ is the deviation in the recoil angle resulting from a sample surface displacement d. A deviation from the eucentric position is de®ned to be positive (negative) if the distance of the incident beam must travel before encountering the standard is greater (less) than for the proper alignment. A deviation in the recoil angle will result in two eects, the ®rst being a deviation in the recoil path
Fig. 2. (a) Schematic of the deviation from eucentric position d. (b) Schematic of the beam steering deviation Da. (c) Figure illustrating the method for determining the incident particle beam steering deviation.
length. If the deviation in the recoil angle is known, the deviation in the recoil path length can be calculated using Eq. (1) by substituting D/ for Dh. The second eect resulting from a deviation in the recoil angle is a change in the initial energy of the recoil. Using the recoil kinematic factor [13], an equation can be derived for the deviation expected in the recoil energy as a function of the deviation D/, DE cos2 /0 D/ cos2 /0 E
1;
2
where DE =E is the fractional increase/decrease of the initial energy of the recoil. Typically, the distance from the target to the detector D will be large compared to the deviation from the eucentric
R.D. Verda et al. / Nucl. Instr. and Meth. in Phys. Res. B 183 (2001) 391±400
position d, thus the deviation in the recoil angle D/ can be accurately estimated using a small angle approximation as D/
2d / cos 0 : D 2
3
3.4. Beam steering A beam steering deviation is shown in Fig. 2(b). For demonstration purposes in Fig. 2(b) we have chosen the apex for beam steering deviation to be at the collimator, while in practice the apex could also be located further away, say, at the nearest steering magnet. However, in our experiments the horizontal separation between the collimator slits was set to 1.20 mm, slightly more than the horizontal extent of the incident particle beam, which in fact positioned the apex for beam steering deviation at the collimator. We de®ne Da to be the angular deviation in the incident particle beam steering and Db to be the resulting change in the angle at which the recoil enters the detector (not to be confused with the change in the recoil angle). For calculation purposes a beam steering deviation is de®ned to be positive (negative) if it leads to an increase (a decrease) in the angle of incidence. Fig. 2(b) shows that the eects of beam steering are twofold: deviations in the incident and recoil angles and deviations in the respective path lengths. The deviation in the incident or recoil path length is calculated using Eq. (1) by substituting Da or Db, respectively, for Dh. The remainder of the section discusses determining deviations in the incident and recoil angles. From geometry it can be shown that the change in the recoil angle D/ that results from a beam steering deviation can be written as D/ Db
Da;
4
where Db carries the same sign as Da. The approximation Db C ; Da D
5
where C and D are the respective distances from the last collimator and detector to the target is very
395
accurate if the beam steering deviation Da is small and the distances are large. By rotating the sample such that it is normal to the incident beam, the angular deviation Da can be estimated from the deviation in the location of the beam spot at the sample, Fig. 2(c). The beam steering deviation can be estimated using the small angle approximation Da
Dx ; C
6
where Dx is the deviation in the location of the beam spot at the sample at normal incidence and C is the distance from the last collimator to the sample. Because C is positive, Dx carries the same sign as Da. In cases where Eqs. (5) and (6) apply, these can be substituted into Eq. (4) to give 1 1 D/ Dx ; 7 D C which estimates the change in the recoil angle from beam steering deviations in terms of the deviation of the beam spot at normal incidence and the respective distances from the detector and collimator to the target. Notice that for small beam steering deviations, D/ vanishes if D C.
4. Results 4.1. Eucentric position The eects of deviations from the eucentric position on ERDA spectra were examined with the sample in the symmetric geometry at a nominal tilt angle of 75° and subsequently misaligned with 2:00 mm and )1.00 mm deviations. For the 2:00 mm deviation, Fig. 3, there was a shift in the entire spectrum to lower energy with a measured decrease of 32 keV in the hydrogen distribution centroid location. Fig. 2(a) shows that a positive deviation from the eucentric position results in a reduced recoil path length, and an increased recoil angle. The reduced recoil path length will contribute to an increase in the ®nal energy of the recoil, whereas an increase in the recoil angle will contribute to an
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R.D. Verda et al. / Nucl. Instr. and Meth. in Phys. Res. B 183 (2001) 391±400
Fig. 3. ERDA spectra of the depth calibration standard illustrating deviations from the eucentric position.
Fig. 4. ERDA spectra of the depth calibration standard illustrating a beam steering deviation.
energy decrease. Using d 2:00 mm as the deviation from eucentric position, /0 29:46° as the ideal recoil angle and D 20 cm as the distance from the detector to the standard in Eq. (3) gives a change in the recoil angle of D/ 1:1°. Using D/ 1:1° in Eqs. (1) and (2), along with calculations of the initial energy of the recoil and its energy loss on the outbound path results in a net decrease in the recoiled particle energy of 28 keV, attributed almost entirely to the change in the recoil angle. The calculation compares well with the observed energy decrease of 32 keV from Fig. 3, where the underestimate by the calculation is due to the broadening of the ERDA spectrum when an absorber foil is used, as explained in Section 5.
gives a net decrease in the recoiled particle energy of 13 keV, attributed almost entirely to the change in the recoil angle. The calculation compares well with the observed energy decrease of 15 keV from Fig. 4, the discrepancy explained by the use of the absorber foil.
4.2. Beam steering The eect of beam steering deviation was examined for misalignment of Da 0:2°, at a nominal tilt angle of 75°, resulting in a decrease in the location of bulk hydrogen centroid of 15 keV, Fig. 4. The beam steering deviation was calculated using Dx 2 mm, Fig 2(c), in Eq. (6). From Eq. (7) the change in the recoil angle was D/ 0:4°. Using D/ 0:4° in an analysis similar to that done for the deviation from eucentric position
4.3. Tilt angle deviations The eect of tilt angle deviation was examined for 1:00° misalignments from the symmetric geometry at a nominal tilt angle of 75°, Fig. 5. An increase in the tilt angle of 1.00° was accompanied by a decrease in the bulk hydrogen centroid location of 8 keV, while the decrease in the tilt angle was accompanied by a similar increase in the bulk centroid location. A negligible change in the location of the surface contamination peak was observed for either deviation. These observations are consistent with the appropriate calculations: the ratio of the He to H electronic stopping crosssections at the appropriate energies is eHe =eH 6. By Eq. (1), positive tilt angle deviations produce longer incident and shorter recoil path lengths, and vice versa for negative deviations. Accordingly, positive tilt angle deviations should result in a lower ®nal recoil energy and vice versa for negative, which was observed. The surface peaks
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397
5. Discussion
Fig. 5. ERDA spectra of the depth calibration standard illustrating tilt angle deviations.
showed negligible change because there was no change in the recoil angle. A summary of the previously treated experimental geometric deviations and the associated calculated deviations is presented in Table 1.
The results of the experiments and analysis, summarized in Table 1, have shown in detail how intentional changes in experimental geometry in¯uence ERDA data: a + 2.00 mm deviation from the eucentric position results in a change of )32 keV in the bulk centroid of the ERDA spectrum. Likewise a + 0.2° beam steering deviation results in a change of )15 keV, while + 1.00° tilt angle deviation results in a change of )8 keV. For these spectra, 5 keV is equal to one channel, and represents approximately 10 nm in depth. These results show that a depth pro®ling scheme based only on the location of the bulk signal is prone to large errors if substantial geometric deviations occur. The simulator in the RUMP [14] ion beam analysis program was used to compare the depths of the hydrogen distributions for the proper geometries to those for the deviations listed in Table 1. The PERT [14] subroutine was used to ®t each spectrum in the same fashion to insure that the simulations were as objective as possible. This comparison was performed by ®rst simulating the
Table 1 Summary of experimental geometric deviations, associated calculated deviations, observed and simulated changes, and recommended accuracy
a
Type of geometric deviation
Amount of experimental deviation
Calculated deviation in path length(s)a
Calculated deviation in initial recoil energyb
Observed change in bulk centroid energy (keV)c
Simulation change in bulk centroid depth (nm)d
Recommended accuracy to keep error 6 5 keV (6 10 nm)
Eucentric position
+ 2.00 mme (+ 1.1° recoil angle)
)7% recoil only
)2%
)32
)16
6 0:3 mm
Beam steering
+ 0.2°f (+ 0.4° recoil angle)
+ 1% incident, )4% recoil
0.8%
)15
0
6 0:07°
Tilt angle
+ 1.00°g
+ 7% incident, )6% recoil
0%
)8
+ 16
6 0:6°
Eq. (1). Eq. (2). c Figs. 3±5. d Figs. 3±5; ignores geometric errors, readjusts absorber thickness. e Positive value corresponds to greater distance incident beam must travel before encountering sample. f Positive value corresponds to increase in angle of incidence. g Positive value corresponds to increase in angle between detector and sample normal. b
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spectra of the proper geometries with Gaussian hydrogen distributions, ignoring the zirconium in the sample, and recording the depth to the peak of the simulation's distribution. Then simulations were performed of the spectra with the deviant geometries as follows: the geometries used in the active ®les were the same as those of the proper geometries, the simulations' absorber foil thicknesses were readjusted in order to register the surface peaks, new Gaussian hydrogen distributions were determined, and the changes in hydrogen distribution depths were noted. From the results of the two sets of simulations, the changes in the depths for the deviation from the eucentric position, and beam steering and tilt angle deviations were found to be )16, 0 and + 16 nm, respectively, and are listed in Table 1. It was necessary to substantially increase the absorber thickness in the simulations for the deviation from the eucentric position and beam steering deviation. These deviations caused a signi®cant change in the recoil angle, which in turn caused a shift in the entire ERDA spectrum to lower energy. If the same absorber foil is used when collecting all spectra, as was the case here, substantially readjusting the simulation's absorber foil thickness for each spectrum in order to account for an energy shift due to the change in the recoil angle is unphysical and can lead to depth pro®ling errors. To illustrate this, inspection of the energy difference between the surface and bulk centroids of 249 keV for the spectrum of the symmetric geometry in Fig. 4 shows it is greater than the energy dierence of 173 keV for the symmetric geometries in Figs. 3 and 5. The spectra of the symmetric geometries in these three ®gures are all of the same standard, and all experimental parameters are identical, the only dierence being that the absorber foil used for the spectrum in Fig. 4 was 70% thicker than that used for the others. Notice the identical surface peak and bulk signal locations for the symmetric geometries in Figs. 3 and 5, as expected if all geometric and energy parameters are identical. The comparison of Fig. 4 with Figs. 3 and 5 shows that a thicker foil will lead to a broadening of the ERDA spectrum of a given hydrogen distribution. The RUMP simulator also follows this trend, i.e., for a given simulated dis-
tribution, increasing the foil thickness increases the separation between the surface and bulk centroids. It is clear that a geometric misalignment causing a deviation in the recoil angle will shift the ERDA spectrum with respect to energy. Compensating for this shift by erroneously changing the simulation's absorber thickness will lead to an underestimate or overestimate of the depth determined by the simulation because of the arti®cial broadening or narrowing, respectively, of the simulation spectrum. For example, in Fig. 4 the simulated hydrogen distribution used to ®t the spectrum of the symmetric geometry was broadened by 5 keV, 10 nm, when its absorber thickness was increased to that of the absorber needed to ®t the spectrum of the deviant geometry. Then using this simulated spectrum to ®t data would underestimate the depth. From the results of the simulations, an interpretation of the changes in the depths for the deviation from the eucentric position, and beam steering and tilt angle deviations, )16, 0 and + 16 nm, respectively, can be given on the basis of the changes in path length, recoil angle and absorber thickness: the positive tilt angle deviation caused no change in the recoil angle so there was no shift in the surface peak and consequently no need to adjust the absorber thickness; the decrease in the energy of the bulk signal arose from the changes in the path length described previously and the simulation erroneously predicted an increased depth of 16 nm. The positive deviation from the eucentric position caused an increase in the recoil angle, shifting the entire spectrum to lower energy; erroneously increasing the absorber thickness to compensate for the energy shift caused the simulated distribution to be arti®cially broadened; the increase in the recoil angle caused a decrease in the recoil path length, leading to an increase in the energy location of the bulk signal; the simulation erroneously predicted a decreased depth of 16 nm because of the underestimate of the depth from broadening the simulation spectrum and the increase in the energy location of the bulk signal. Finally, the positive beam steering deviation caused an increase in the recoil angle, shifting the entire spectrum to lower energy; erroneously increasing the absorber thickness to compensate for
R.D. Verda et al. / Nucl. Instr. and Meth. in Phys. Res. B 183 (2001) 391±400
the energy shift caused the simulated distribution to be arti®cially broadened; the positive beam steering deviation causes a small increase in the incident path length compared to a larger decrease in the recoil path length; because the electronic stopping cross-section for the inbound helium is much higher than that for the outbound hydrogen, the net energy change for the path length deviations resulted in a decrease in the energy location of the bulk; the underestimate of the depth from broadening the simulation spectrum opposes the decrease of the bulk energy location resulting in essentially no change in depth predicted by the simulation, although for erroneous reasons. This explanation of the simulations shows that our characterization of the geometric deviations and the consequences of erroneously changing the absorber thickness are accurate predictors of the associated depth pro®ling errors. From the results obtained in this work a level of accuracy needed in each geometric component can be estimated in order to maintain the error in the ERDA spectra to 6 5 keV, 6 10 nm. This constraint requires that the deviation from the eucentric position, and the beam steering deviation be controlled such that the deviation in the recoil angle is 6 0:1°. This means the deviation from the eucentric position should be 6 0:3 mm, and the beam steering deviation should be 6 0:07°. Likewise, the deviation in the tilt angle should be 6 0:6°. These recommendations are listed in Table 1. In an experimental setup where the incident particle beam energy can be reproducibly controlled, shifts in the ERDA surface contamination peak can be used as an indicator of geometric misalignment of the sample. These shifts will not be caused by deviations in the incident beam energy if the oxygen resonance energy calibration technique is used, which ®xes the beam energy to within 2 keV of the 3.036 MeV resonance energy. Consequently, a shift in the surface peak is an indication that there are deviations in the recoil energy, which in turn indicates a deviation from the eucentric position and/or a deviation in beam steering. Furthermore, we found that beam steering deviations could be kept below 0.05° by adjusting the horizontal separation in the collimator slits to 1.20 mm, slightly greater than the hori-
399
zontal extent of the incident particle beam. Then the only remaining cause for a substantial shift in the surface peak would be a deviation from the eucentric position, which can be prevented by careful sample mounting. Our sample mounting technique results in negligible deviations from the eucentric position based on observations of the shift in the surface peak for many spectra. But because of the nonstandard nature of sample mounting systems in practice, the technique will not be described here. While monitoring the surface contamination peak centroid provides an excellent indicator of a deviation from the eucentric position and/or beam steering deviation, this technique is unable to monitor tilt angle deviations. Fortunately, a laser alignment technique was developed to ensure accurate and reproducible tilt angle manipulation. But in order to achieve the proper laser alignment of the sample tilt angle, the tilt angle of the goniometer must ®rst be accurately calibrated. Calibrating the tilt angle was performed with a HeNe laser beam coincident with the path taken by the incident particle beam and directed into the scattering chamber, Fig. 1(a). In the absence of the incident particle beam, a Mylar ®lm was positioned near a sample in the goniometer and directly in the path of the incoming laser beam. The laser beam passed through the ®lm, was re¯ected from the sample, and passed back through the ®lm. Adjusting the sample orientation so that the re¯ected laser spot was coincident with the ®xed, incident spot on the ®lm positioned the goniometer in its tilt angle origin. This process was repeated many times, reloading the sample and recording the tilt angle each time. The average tilt angle of 0.05° was taken as the calibration, while the standard deviation of 0.02° was taken as the error. Afterwards, the ®lm was removed. With the tilt angle properly calibrated, the same HeNe laser beam was then used to reproducibly orient the sample in the symmetric geometry, in situ, immediately prior to collecting the ERDA spectrum for each sample. In the absence of the incident particle beam, the alignment was performed by directing the laser onto the sample while adjusting the sample tilt angle such that the re¯ected beam entered the aperture of the ERDA
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detector, Fig. 1(a). Once the alignment was performed the laser beam was shut o so that it did not interfere with collecting the ERDA spectrum. In our scattering chamber this laser alignment technique has a resolution of 0.03° for the reproducibility of the tilt angle. This resolution along with the error of 0.02° in calibrating the tilt angle allows the tilt angle to be determined (resolution and calibration error summed in quadrature) to within 0.04°, which is signi®cantly less than the recommended tilt angle deviation of 6 0:6° needed to keep the tilt-related error in the ERDA data 6 5 keV. In conclusion, the laser alignment of the sample tilt angle, along with the incident particle beam energy calibration and the close adjustment of the collimator slits to reduce the beam steering deviation are very accurate geometric alignment techniques. It only remains for samples to be carefully mounted, minimizing the deviation from the eucentric position, in order to achieve an accurate and reproducible setup of the ERDA geometry. Using the geometric and energy techniques presented here, and from summing all geometric and energy errors in quadrature, we have determined that our ERDA spectra are accurate to 6 2 keV, or approximately 6 4 nm, when taken over time. 6. Conclusion This work discussed certain geometric deviations that can introduce errors in depth pro®ling by re¯ection ERDA, namely tilt angle and beam steering deviations, and deviations from the eucentric position. A level of accuracy was recommended for the individual components of the experimental geometry, with deviation from the eucentric position being 0.3 mm or less, beam steering deviation being 0.07° or less, and tilt angle deviation being 0.6° or less. A laser alignment technique was described that allows the tilt angle to be determined to within 0.04°. Monitoring the location of the ERDA surface contamination peak centroid characterizes deviations from the eucentric position, and deviations in beam steering, whereas the laser alignment technique accurately ®xes the tilt angle geometry. The use of the two
techniques, along with a reproducible and absolutely determined energy calibration, results in an accurate and reproducible determination of the ERDA experimental setup, thus making it possible to accurately compare depth pro®les from spectra acquired over time. Acknowledgements We gratefully acknowledge excellent technical support, advice and contributions from Caleb Evans, Mark Hollander and Chris Wetteland. This work was supported by the Department of Energy, Oce of Basic Energy Sciences, Division of Materials Science. References [1] J. L'Ecuyer, C. Brassard, C. Cardinal, J. Chabbal, L. Deschenes, J.P. Labrie, B. Terrult, J.G. Martel, R.St. Jaques, J. Appl. Phys. 47 (1976) 881. [2] J.C. Barbour, B.L. Doyle, in: J.R. Tesmer, M. Nastasi (Eds.), Handbook of Modern Ion Beam Materials Analysis, Materials Research Society, Pittsburgh PA, 1995, p. 85. [3] J. Tirira, Y. Serruys, P. Trocellier, in: Forward Recoil Spectrometry, Plenum, New York, NY, 1996, p. 1. [4] J. Tirira, Y. Serruys, P. Trocellier, in: Forward Recoil Spectrometry, Plenum, New York, NY, 1996, p. 42. [5] J. Tirira, Y. Serruys, P. Trocellier, in: Forward Recoil Spectrometry, Plenum, New York, NY, 1996, p. 108. [6] J. Tirira, Y. Serruys, P. Trocellier, in: Forward Recoil Spectrometry, Plenum, New York, NY, 1996, p. 99,103. [7] J. Tirira, Y. Serruys, P. Trocellier, in: Forward Recoil Spectrometry, Plenum, New York, NY, 1996, p. 101. [8] F. Paszti, E. Szilagyi, E. Kotai, Nucl. Instr. and Meth. B 54 (1991) 507. [9] J.C. Barbour, in: J.R. Tesmer, M. Nastasi (Eds.), Handbook of Modern Ion Beam Materials Analysis, Materials Research Society, Pittsburgh, PA, 1995, p. 99. [10] J. Tirira, Y. Serruys, P. Trocellier, in: Forward Recoil Spectrometry, Plenum, New York, NY, 1996, p. 250. [11] J.R. Tesmer, in: J.R. Tesmer, M. Nastasi (Eds.), Handbook of Modern Ion Beam Materials Analysis, Materials Research Society, Pittsburgh, PA, 1995, p. 687. [12] R.D. Verda, C.J. Maggiore, J.R. Tesmer, A. Misra, T. Hoechbauer, M. Nastasi, R.W. Bower, Nucl. Instr. and Meth. B 179 (2001) 401. [13] J.C. Barbour, in: J.R. Tesmer, M. Nastasi (Eds.), Handbook of Modern Ion Beam Materials Analysis, Materials Research Society, Pittsburgh, PA, 1995, p. 90. [14] L.R. Doolittle, Nucl. Instr. and Meth. B 9 (1985) 344.
www.elsevier.com/locate/nimb
Geometric considerations relevant to hydrogen depth pro®ling by re¯ection elastic recoil detection analysis R.D. Verda a
a,*
, J.R. Tesmer a, C.J. Maggiore a, M. Nastasi a, R.W. Bower
b
Los Alamos National Laboratory, Mail Stop G755, Los Alamos, NM 87545, USA b University of California, Davis, CA 95616, USA Received 20 November 2000; received in revised form 21 March 2001
Abstract This work addresses geometric considerations relevant to the accuracy of depth pro®ling by re¯ection elastic recoil detection analysis, which becomes an issue when many samples are compared over time or a single sample is repeatedly analyzed following a sequence of processing steps. In such cases, accurate and reproducible geometric alignment and incident beam energy calibration must be performed over time, and are addressed here. Our analysis and experiments show that geometric deviations in the sample tilt angle and incident particle beam steering, as well as deviations from the sample eucentric position, can result in signi®cant errors in depth pro®ling. As a result, a recommended degree of accuracy is stated for each of these geometric components; techniques are presented to attain this accuracy, or better. The most notable of these techniques is a laser alignment of the sample tilt angle, which has a reproducible accuracy of 0.04°. Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 61.18.Bn; 61.43.Bn; 61.72.Ss; 61.72.Tt Keywords: Geometry; Energy calibration; Simulations; Depth pro®ling
1. Introduction Elastic recoil detection analysis (ERDA) is a well-known and widely used ion beam analysis technique whereby information about sample composition can be obtained by detecting light target nuclei recoiling from heavier bombarding
*
Corresponding author. Tel.: +1-505-665-6685; fax: +1-505667-8021. E-mail address: [email protected] (R.D. Verda).
ions [1±3]. The accuracy of depth pro®ling by re¯ection ERDA is subject to a number of factors including, but not limited to, multiple scattering [4], the accuracy of the cross-sections and stopping factors [5], energy straggling [6], system resolution [7], and also experimental geometry and energy considerations. The issue of accurate and reproducible depth pro®ling becomes most important when materials analysis requires comparison of data from many samples over time or from a sample that is repeatedly analyzed following a sequence of processing steps. Especially in such
0168-583X/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 1 ) 0 0 6 3 4 - 6
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cases, the experimental techniques used must ensure that accurate and reproducible geometric alignment and energy calibration can be performed over an arbitrary time period. Re¯ection ERDA, typically performed at grazing incidence [8], is highly sensitive to changes in the experimental geometry. Thus, an accurate transformation of the data into a depth pro®le will require precise knowledge of the geometry [9,10]. The purpose of this work is to systematically examine certain geometric components of re¯ection ERDA, namely the tilt angle, eucentric position, and incident particle beam steering in order to determine how deviations with respect to these components aect depth pro®ling. Simple mathematical expressions are given to show the eects of geometric deviations and data are presented which show the characteristic changes expected in the ERDA spectra for these deviations. Based on the experiments and analysis, a recommended degree of accuracy is stated for each geometric component, and techniques are presented to attain this accuracy, or better. The most notable of these techniques is a laser alignment of the sample tilt angle, which has a reproducible accuracy of 0.04°. 2. Experimental details The accelerator used for these experiments was a National Electrostatics Corporation 3 MV tandem. All energies reported are described with respect to the laboratory system. To ensure that the experimental observations were independent of energy variations, all experiments were performed at the 16 O a; a 16 O resonance energy of 3.036 MeV, which has a full width at half maximum of 8 keV [11]. Incident 4 He particles at this energy are well below the Coulomb barrier of silicon, so no primary nuclear reactions take place when irradiating silicon samples or standards. This resonance energy was tuned by maximizing the counts in the 16 O peak of the Rutherford backscattering spectroscopy (RBS) spectrum of a substrate having a thin native oxide; the narrow width of the oxygen resonance allows the energy to be determined accurately and precisely. The beam spot size at
normal incidence on a target was approximately 1 mm 2 mm (horizontal vertical). Surface contamination during irradiation was minimized by the use of a liquid nitrogen cold trap, which resulted in a chamber pressure of about 5 10 7 Torr. The ERDA detector was oriented such that the plane formed by the incident and recoiled beams was perpendicular to the tilt axis of the target; the detector was located approximately 20 cm from the target at a nominal recoil angle of 30°. RBS was performed simultaneously with the ERDA; computer simulations of the RBS spectra were used to determine the incident particle dose. The RBS detector was oriented such that the plane formed by the incident and backscattered beams contained the tilt axis of the target; the detector was located approximately 7 cm from the target at a scattering angle of 167°. The channel-energy conversion for both detectors was approximately 5.3 keV/channel. The distance from the target to the nearest collimator was approximately 53 cm. The variation in the recoil hydrogen yield per unit beam particle dose was small for the beam doses used to acquire spectra. The sample mounting system used in these experiments consisted of a sample holder mounted on a goniometer that can be manipulated with six degrees of freedom: three translational movements along each of the three mutually orthogonal axes and three rotational movements about the same axes. The most critical manipulation in this work is the tilt angle rotation, which can move in increments of 0.01°, with a stepping motor backlash less than this amount. A depth calibration standard was synthesized for these experiments using sputter deposition techniques. The standard was prepared on a single crystal silicon (c-Si) substrate by depositing a zirconium + hydrogen layer containing approximately 64 1015 at./cm2 (both species, approximately 50 at.% each), followed by an overlayer of approximately 1400 1015 at./cm2 of amorphous silicon (a-Si). The areal densities were determined by ERDA, RBS, and secondary ion mass spectroscopy (SIMS). A more complete description of the standard and its synthesis and measurement is described in [12].
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3. Geometric considerations 3.1. Re¯ection ERDA experimental geometry The setup and geometry of a typical re¯ection ERDA experiment is presented in Fig. 1(a). All angles are described with respect to the laboratory system. The angle h1 , the tilt angle, is the angle of the incident particle beam onto the sample, and h2 , the exit angle, is the angle of the recoiled particle from the sample to the detector; both angles are measured with respect to the surface normal of the sample. The angle /, the recoil angle, lies between the path of the recoiled particle to the detector and the continuation of the path of the incident beam. The sample, sample holder and goniometer are oriented such that the sample surface plane contains the tilt axis of the goniometer, and the inci-
393
dent particle beam impinges the sample at the tilt axis location. Typically, the tilt axis and the position of the ERDA detector are ®xed; once the tilt angle is chosen, the exit and recoil angles are automatically determined provided the incident beam strikes the sample at the tilt axis. Deviations in the experimental geometry result principally from variations in sample mounting and manipulation, but also from variations in the steering of the incident particle beam. Geometric errors can be described as a combination of three types of independent misalignment: (1) misalignment in the tilt and exit angles, (2) the misalignment that results if the sample surface plane does not contain the tilt axis of the goniometer, de®ned to be a deviation from the eucentric position, and (3) variations in the incident particle beam steering. These will be discussed in turn.
(b)
(a) Fig. 1. Schematics of (a) the experimental arrangement; (b) tilt angle geometry with deviation Dh.
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3.2. Tilt angle To accurately convert an ERDA spectrum into a depth pro®le requires an accurate knowledge of the angles h1 and h2 . In our apparatus, choosing the tilt angle h1 automatically determines the exit angle h2 . These angles determine the path lengths traveled by the incident and recoiled particles; an uncertainty in h1 or h2 will lead to an uncertainty in the energy lost by the incident or recoiled particle, respectively. The eect of deviations in the tilt and exit angles on path length can be simply examined by considering a change from the symmetric condition where h1 h2 h0 to an asymmetric condition where h1 6 h2 , Fig. 1(b). Under these conditions the deviation from the original path length r of the symmetric geometry for each leg is given by Dr cos h0 r cos h0 Dh
1;
(a)
1
(b)
where Dr =r is the fractional increase/decrease in a single leg of the path length, and Dh is the deviation from h0 . It is important to note that while the magnitudes of the increase and decrease in the path length are similar (but not equal) for small deviations, the electronic stopping cross-sections of the incident and recoiled particles in the sample material are not necessarily equal. Then in general, there is no ``canceling eect'' for small deviations from the symmetric geometry when considering the ®nal energy of the recoil.
(c)
3.3. Eucentric position Fig. 2(a) represents a deviation from the eucentric position. The angle /0 is the recoil angle of the sample in the symmetric geometry without a deviation from the eucentric position; D/ is the deviation in the recoil angle resulting from a sample surface displacement d. A deviation from the eucentric position is de®ned to be positive (negative) if the distance of the incident beam must travel before encountering the standard is greater (less) than for the proper alignment. A deviation in the recoil angle will result in two eects, the ®rst being a deviation in the recoil path
Fig. 2. (a) Schematic of the deviation from eucentric position d. (b) Schematic of the beam steering deviation Da. (c) Figure illustrating the method for determining the incident particle beam steering deviation.
length. If the deviation in the recoil angle is known, the deviation in the recoil path length can be calculated using Eq. (1) by substituting D/ for Dh. The second eect resulting from a deviation in the recoil angle is a change in the initial energy of the recoil. Using the recoil kinematic factor [13], an equation can be derived for the deviation expected in the recoil energy as a function of the deviation D/, DE cos2 /0 D/ cos2 /0 E
1;
2
where DE =E is the fractional increase/decrease of the initial energy of the recoil. Typically, the distance from the target to the detector D will be large compared to the deviation from the eucentric
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position d, thus the deviation in the recoil angle D/ can be accurately estimated using a small angle approximation as D/
2d / cos 0 : D 2
3
3.4. Beam steering A beam steering deviation is shown in Fig. 2(b). For demonstration purposes in Fig. 2(b) we have chosen the apex for beam steering deviation to be at the collimator, while in practice the apex could also be located further away, say, at the nearest steering magnet. However, in our experiments the horizontal separation between the collimator slits was set to 1.20 mm, slightly more than the horizontal extent of the incident particle beam, which in fact positioned the apex for beam steering deviation at the collimator. We de®ne Da to be the angular deviation in the incident particle beam steering and Db to be the resulting change in the angle at which the recoil enters the detector (not to be confused with the change in the recoil angle). For calculation purposes a beam steering deviation is de®ned to be positive (negative) if it leads to an increase (a decrease) in the angle of incidence. Fig. 2(b) shows that the eects of beam steering are twofold: deviations in the incident and recoil angles and deviations in the respective path lengths. The deviation in the incident or recoil path length is calculated using Eq. (1) by substituting Da or Db, respectively, for Dh. The remainder of the section discusses determining deviations in the incident and recoil angles. From geometry it can be shown that the change in the recoil angle D/ that results from a beam steering deviation can be written as D/ Db
Da;
4
where Db carries the same sign as Da. The approximation Db C ; Da D
5
where C and D are the respective distances from the last collimator and detector to the target is very
395
accurate if the beam steering deviation Da is small and the distances are large. By rotating the sample such that it is normal to the incident beam, the angular deviation Da can be estimated from the deviation in the location of the beam spot at the sample, Fig. 2(c). The beam steering deviation can be estimated using the small angle approximation Da
Dx ; C
6
where Dx is the deviation in the location of the beam spot at the sample at normal incidence and C is the distance from the last collimator to the sample. Because C is positive, Dx carries the same sign as Da. In cases where Eqs. (5) and (6) apply, these can be substituted into Eq. (4) to give 1 1 D/ Dx ; 7 D C which estimates the change in the recoil angle from beam steering deviations in terms of the deviation of the beam spot at normal incidence and the respective distances from the detector and collimator to the target. Notice that for small beam steering deviations, D/ vanishes if D C.
4. Results 4.1. Eucentric position The eects of deviations from the eucentric position on ERDA spectra were examined with the sample in the symmetric geometry at a nominal tilt angle of 75° and subsequently misaligned with 2:00 mm and )1.00 mm deviations. For the 2:00 mm deviation, Fig. 3, there was a shift in the entire spectrum to lower energy with a measured decrease of 32 keV in the hydrogen distribution centroid location. Fig. 2(a) shows that a positive deviation from the eucentric position results in a reduced recoil path length, and an increased recoil angle. The reduced recoil path length will contribute to an increase in the ®nal energy of the recoil, whereas an increase in the recoil angle will contribute to an
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Fig. 3. ERDA spectra of the depth calibration standard illustrating deviations from the eucentric position.
Fig. 4. ERDA spectra of the depth calibration standard illustrating a beam steering deviation.
energy decrease. Using d 2:00 mm as the deviation from eucentric position, /0 29:46° as the ideal recoil angle and D 20 cm as the distance from the detector to the standard in Eq. (3) gives a change in the recoil angle of D/ 1:1°. Using D/ 1:1° in Eqs. (1) and (2), along with calculations of the initial energy of the recoil and its energy loss on the outbound path results in a net decrease in the recoiled particle energy of 28 keV, attributed almost entirely to the change in the recoil angle. The calculation compares well with the observed energy decrease of 32 keV from Fig. 3, where the underestimate by the calculation is due to the broadening of the ERDA spectrum when an absorber foil is used, as explained in Section 5.
gives a net decrease in the recoiled particle energy of 13 keV, attributed almost entirely to the change in the recoil angle. The calculation compares well with the observed energy decrease of 15 keV from Fig. 4, the discrepancy explained by the use of the absorber foil.
4.2. Beam steering The eect of beam steering deviation was examined for misalignment of Da 0:2°, at a nominal tilt angle of 75°, resulting in a decrease in the location of bulk hydrogen centroid of 15 keV, Fig. 4. The beam steering deviation was calculated using Dx 2 mm, Fig 2(c), in Eq. (6). From Eq. (7) the change in the recoil angle was D/ 0:4°. Using D/ 0:4° in an analysis similar to that done for the deviation from eucentric position
4.3. Tilt angle deviations The eect of tilt angle deviation was examined for 1:00° misalignments from the symmetric geometry at a nominal tilt angle of 75°, Fig. 5. An increase in the tilt angle of 1.00° was accompanied by a decrease in the bulk hydrogen centroid location of 8 keV, while the decrease in the tilt angle was accompanied by a similar increase in the bulk centroid location. A negligible change in the location of the surface contamination peak was observed for either deviation. These observations are consistent with the appropriate calculations: the ratio of the He to H electronic stopping crosssections at the appropriate energies is eHe =eH 6. By Eq. (1), positive tilt angle deviations produce longer incident and shorter recoil path lengths, and vice versa for negative deviations. Accordingly, positive tilt angle deviations should result in a lower ®nal recoil energy and vice versa for negative, which was observed. The surface peaks
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5. Discussion
Fig. 5. ERDA spectra of the depth calibration standard illustrating tilt angle deviations.
showed negligible change because there was no change in the recoil angle. A summary of the previously treated experimental geometric deviations and the associated calculated deviations is presented in Table 1.
The results of the experiments and analysis, summarized in Table 1, have shown in detail how intentional changes in experimental geometry in¯uence ERDA data: a + 2.00 mm deviation from the eucentric position results in a change of )32 keV in the bulk centroid of the ERDA spectrum. Likewise a + 0.2° beam steering deviation results in a change of )15 keV, while + 1.00° tilt angle deviation results in a change of )8 keV. For these spectra, 5 keV is equal to one channel, and represents approximately 10 nm in depth. These results show that a depth pro®ling scheme based only on the location of the bulk signal is prone to large errors if substantial geometric deviations occur. The simulator in the RUMP [14] ion beam analysis program was used to compare the depths of the hydrogen distributions for the proper geometries to those for the deviations listed in Table 1. The PERT [14] subroutine was used to ®t each spectrum in the same fashion to insure that the simulations were as objective as possible. This comparison was performed by ®rst simulating the
Table 1 Summary of experimental geometric deviations, associated calculated deviations, observed and simulated changes, and recommended accuracy
a
Type of geometric deviation
Amount of experimental deviation
Calculated deviation in path length(s)a
Calculated deviation in initial recoil energyb
Observed change in bulk centroid energy (keV)c
Simulation change in bulk centroid depth (nm)d
Recommended accuracy to keep error 6 5 keV (6 10 nm)
Eucentric position
+ 2.00 mme (+ 1.1° recoil angle)
)7% recoil only
)2%
)32
)16
6 0:3 mm
Beam steering
+ 0.2°f (+ 0.4° recoil angle)
+ 1% incident, )4% recoil
0.8%
)15
0
6 0:07°
Tilt angle
+ 1.00°g
+ 7% incident, )6% recoil
0%
)8
+ 16
6 0:6°
Eq. (1). Eq. (2). c Figs. 3±5. d Figs. 3±5; ignores geometric errors, readjusts absorber thickness. e Positive value corresponds to greater distance incident beam must travel before encountering sample. f Positive value corresponds to increase in angle of incidence. g Positive value corresponds to increase in angle between detector and sample normal. b
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spectra of the proper geometries with Gaussian hydrogen distributions, ignoring the zirconium in the sample, and recording the depth to the peak of the simulation's distribution. Then simulations were performed of the spectra with the deviant geometries as follows: the geometries used in the active ®les were the same as those of the proper geometries, the simulations' absorber foil thicknesses were readjusted in order to register the surface peaks, new Gaussian hydrogen distributions were determined, and the changes in hydrogen distribution depths were noted. From the results of the two sets of simulations, the changes in the depths for the deviation from the eucentric position, and beam steering and tilt angle deviations were found to be )16, 0 and + 16 nm, respectively, and are listed in Table 1. It was necessary to substantially increase the absorber thickness in the simulations for the deviation from the eucentric position and beam steering deviation. These deviations caused a signi®cant change in the recoil angle, which in turn caused a shift in the entire ERDA spectrum to lower energy. If the same absorber foil is used when collecting all spectra, as was the case here, substantially readjusting the simulation's absorber foil thickness for each spectrum in order to account for an energy shift due to the change in the recoil angle is unphysical and can lead to depth pro®ling errors. To illustrate this, inspection of the energy difference between the surface and bulk centroids of 249 keV for the spectrum of the symmetric geometry in Fig. 4 shows it is greater than the energy dierence of 173 keV for the symmetric geometries in Figs. 3 and 5. The spectra of the symmetric geometries in these three ®gures are all of the same standard, and all experimental parameters are identical, the only dierence being that the absorber foil used for the spectrum in Fig. 4 was 70% thicker than that used for the others. Notice the identical surface peak and bulk signal locations for the symmetric geometries in Figs. 3 and 5, as expected if all geometric and energy parameters are identical. The comparison of Fig. 4 with Figs. 3 and 5 shows that a thicker foil will lead to a broadening of the ERDA spectrum of a given hydrogen distribution. The RUMP simulator also follows this trend, i.e., for a given simulated dis-
tribution, increasing the foil thickness increases the separation between the surface and bulk centroids. It is clear that a geometric misalignment causing a deviation in the recoil angle will shift the ERDA spectrum with respect to energy. Compensating for this shift by erroneously changing the simulation's absorber thickness will lead to an underestimate or overestimate of the depth determined by the simulation because of the arti®cial broadening or narrowing, respectively, of the simulation spectrum. For example, in Fig. 4 the simulated hydrogen distribution used to ®t the spectrum of the symmetric geometry was broadened by 5 keV, 10 nm, when its absorber thickness was increased to that of the absorber needed to ®t the spectrum of the deviant geometry. Then using this simulated spectrum to ®t data would underestimate the depth. From the results of the simulations, an interpretation of the changes in the depths for the deviation from the eucentric position, and beam steering and tilt angle deviations, )16, 0 and + 16 nm, respectively, can be given on the basis of the changes in path length, recoil angle and absorber thickness: the positive tilt angle deviation caused no change in the recoil angle so there was no shift in the surface peak and consequently no need to adjust the absorber thickness; the decrease in the energy of the bulk signal arose from the changes in the path length described previously and the simulation erroneously predicted an increased depth of 16 nm. The positive deviation from the eucentric position caused an increase in the recoil angle, shifting the entire spectrum to lower energy; erroneously increasing the absorber thickness to compensate for the energy shift caused the simulated distribution to be arti®cially broadened; the increase in the recoil angle caused a decrease in the recoil path length, leading to an increase in the energy location of the bulk signal; the simulation erroneously predicted a decreased depth of 16 nm because of the underestimate of the depth from broadening the simulation spectrum and the increase in the energy location of the bulk signal. Finally, the positive beam steering deviation caused an increase in the recoil angle, shifting the entire spectrum to lower energy; erroneously increasing the absorber thickness to compensate for
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the energy shift caused the simulated distribution to be arti®cially broadened; the positive beam steering deviation causes a small increase in the incident path length compared to a larger decrease in the recoil path length; because the electronic stopping cross-section for the inbound helium is much higher than that for the outbound hydrogen, the net energy change for the path length deviations resulted in a decrease in the energy location of the bulk; the underestimate of the depth from broadening the simulation spectrum opposes the decrease of the bulk energy location resulting in essentially no change in depth predicted by the simulation, although for erroneous reasons. This explanation of the simulations shows that our characterization of the geometric deviations and the consequences of erroneously changing the absorber thickness are accurate predictors of the associated depth pro®ling errors. From the results obtained in this work a level of accuracy needed in each geometric component can be estimated in order to maintain the error in the ERDA spectra to 6 5 keV, 6 10 nm. This constraint requires that the deviation from the eucentric position, and the beam steering deviation be controlled such that the deviation in the recoil angle is 6 0:1°. This means the deviation from the eucentric position should be 6 0:3 mm, and the beam steering deviation should be 6 0:07°. Likewise, the deviation in the tilt angle should be 6 0:6°. These recommendations are listed in Table 1. In an experimental setup where the incident particle beam energy can be reproducibly controlled, shifts in the ERDA surface contamination peak can be used as an indicator of geometric misalignment of the sample. These shifts will not be caused by deviations in the incident beam energy if the oxygen resonance energy calibration technique is used, which ®xes the beam energy to within 2 keV of the 3.036 MeV resonance energy. Consequently, a shift in the surface peak is an indication that there are deviations in the recoil energy, which in turn indicates a deviation from the eucentric position and/or a deviation in beam steering. Furthermore, we found that beam steering deviations could be kept below 0.05° by adjusting the horizontal separation in the collimator slits to 1.20 mm, slightly greater than the hori-
399
zontal extent of the incident particle beam. Then the only remaining cause for a substantial shift in the surface peak would be a deviation from the eucentric position, which can be prevented by careful sample mounting. Our sample mounting technique results in negligible deviations from the eucentric position based on observations of the shift in the surface peak for many spectra. But because of the nonstandard nature of sample mounting systems in practice, the technique will not be described here. While monitoring the surface contamination peak centroid provides an excellent indicator of a deviation from the eucentric position and/or beam steering deviation, this technique is unable to monitor tilt angle deviations. Fortunately, a laser alignment technique was developed to ensure accurate and reproducible tilt angle manipulation. But in order to achieve the proper laser alignment of the sample tilt angle, the tilt angle of the goniometer must ®rst be accurately calibrated. Calibrating the tilt angle was performed with a HeNe laser beam coincident with the path taken by the incident particle beam and directed into the scattering chamber, Fig. 1(a). In the absence of the incident particle beam, a Mylar ®lm was positioned near a sample in the goniometer and directly in the path of the incoming laser beam. The laser beam passed through the ®lm, was re¯ected from the sample, and passed back through the ®lm. Adjusting the sample orientation so that the re¯ected laser spot was coincident with the ®xed, incident spot on the ®lm positioned the goniometer in its tilt angle origin. This process was repeated many times, reloading the sample and recording the tilt angle each time. The average tilt angle of 0.05° was taken as the calibration, while the standard deviation of 0.02° was taken as the error. Afterwards, the ®lm was removed. With the tilt angle properly calibrated, the same HeNe laser beam was then used to reproducibly orient the sample in the symmetric geometry, in situ, immediately prior to collecting the ERDA spectrum for each sample. In the absence of the incident particle beam, the alignment was performed by directing the laser onto the sample while adjusting the sample tilt angle such that the re¯ected beam entered the aperture of the ERDA
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detector, Fig. 1(a). Once the alignment was performed the laser beam was shut o so that it did not interfere with collecting the ERDA spectrum. In our scattering chamber this laser alignment technique has a resolution of 0.03° for the reproducibility of the tilt angle. This resolution along with the error of 0.02° in calibrating the tilt angle allows the tilt angle to be determined (resolution and calibration error summed in quadrature) to within 0.04°, which is signi®cantly less than the recommended tilt angle deviation of 6 0:6° needed to keep the tilt-related error in the ERDA data 6 5 keV. In conclusion, the laser alignment of the sample tilt angle, along with the incident particle beam energy calibration and the close adjustment of the collimator slits to reduce the beam steering deviation are very accurate geometric alignment techniques. It only remains for samples to be carefully mounted, minimizing the deviation from the eucentric position, in order to achieve an accurate and reproducible setup of the ERDA geometry. Using the geometric and energy techniques presented here, and from summing all geometric and energy errors in quadrature, we have determined that our ERDA spectra are accurate to 6 2 keV, or approximately 6 4 nm, when taken over time. 6. Conclusion This work discussed certain geometric deviations that can introduce errors in depth pro®ling by re¯ection ERDA, namely tilt angle and beam steering deviations, and deviations from the eucentric position. A level of accuracy was recommended for the individual components of the experimental geometry, with deviation from the eucentric position being 0.3 mm or less, beam steering deviation being 0.07° or less, and tilt angle deviation being 0.6° or less. A laser alignment technique was described that allows the tilt angle to be determined to within 0.04°. Monitoring the location of the ERDA surface contamination peak centroid characterizes deviations from the eucentric position, and deviations in beam steering, whereas the laser alignment technique accurately ®xes the tilt angle geometry. The use of the two
techniques, along with a reproducible and absolutely determined energy calibration, results in an accurate and reproducible determination of the ERDA experimental setup, thus making it possible to accurately compare depth pro®les from spectra acquired over time. Acknowledgements We gratefully acknowledge excellent technical support, advice and contributions from Caleb Evans, Mark Hollander and Chris Wetteland. This work was supported by the Department of Energy, Oce of Basic Energy Sciences, Division of Materials Science. References [1] J. L'Ecuyer, C. Brassard, C. Cardinal, J. Chabbal, L. Deschenes, J.P. Labrie, B. Terrult, J.G. Martel, R.St. Jaques, J. Appl. Phys. 47 (1976) 881. [2] J.C. Barbour, B.L. Doyle, in: J.R. Tesmer, M. Nastasi (Eds.), Handbook of Modern Ion Beam Materials Analysis, Materials Research Society, Pittsburgh PA, 1995, p. 85. [3] J. Tirira, Y. Serruys, P. Trocellier, in: Forward Recoil Spectrometry, Plenum, New York, NY, 1996, p. 1. [4] J. Tirira, Y. Serruys, P. Trocellier, in: Forward Recoil Spectrometry, Plenum, New York, NY, 1996, p. 42. [5] J. Tirira, Y. Serruys, P. Trocellier, in: Forward Recoil Spectrometry, Plenum, New York, NY, 1996, p. 108. [6] J. Tirira, Y. Serruys, P. Trocellier, in: Forward Recoil Spectrometry, Plenum, New York, NY, 1996, p. 99,103. [7] J. Tirira, Y. Serruys, P. Trocellier, in: Forward Recoil Spectrometry, Plenum, New York, NY, 1996, p. 101. [8] F. Paszti, E. Szilagyi, E. Kotai, Nucl. Instr. and Meth. B 54 (1991) 507. [9] J.C. Barbour, in: J.R. Tesmer, M. Nastasi (Eds.), Handbook of Modern Ion Beam Materials Analysis, Materials Research Society, Pittsburgh, PA, 1995, p. 99. [10] J. Tirira, Y. Serruys, P. Trocellier, in: Forward Recoil Spectrometry, Plenum, New York, NY, 1996, p. 250. [11] J.R. Tesmer, in: J.R. Tesmer, M. Nastasi (Eds.), Handbook of Modern Ion Beam Materials Analysis, Materials Research Society, Pittsburgh, PA, 1995, p. 687. [12] R.D. Verda, C.J. Maggiore, J.R. Tesmer, A. Misra, T. Hoechbauer, M. Nastasi, R.W. Bower, Nucl. Instr. and Meth. B 179 (2001) 401. [13] J.C. Barbour, in: J.R. Tesmer, M. Nastasi (Eds.), Handbook of Modern Ion Beam Materials Analysis, Materials Research Society, Pittsburgh, PA, 1995, p. 90. [14] L.R. Doolittle, Nucl. Instr. and Meth. B 9 (1985) 344.