Backscattering analysis for oxygen profiling using 16O(α, α)16O 3.05 MeV resonance parameters

335

Nuclear Instruments and Methods in Physics Research B36 (1989) 335-339 North-Holland, Amsterdam

BACKSCATTERING ANALYSIS RESONANCE PARAMETERS P. BERNING

and R.E.

FOR OXYGEN PROFILING USING 160( 01,CY)‘~O3.05 MeV

BENENSON

Physics Department, State University of New York at Albany, 1400 Washington Avenue, Albany, NY 12222, USA Received 9 September 1988 and in revised form 30 October 1988

The well-known 160(a, (w)160 scattering resonance near 3.05 MeV permits oxygen to be identified in the presence of heavy elements being analyzed by Rutherford backscattering. We investigate explicit use of published resonance parameters and the best presently available stopping powers to make computer simulations of backscattering energy spectra in order to make quantitative measurements of near surface oxygen profiles in bulk oxides and thin films. Simulations of bulk Al,O,, Y203, YBa,Cu,O,_,, and thin films of ZrO, on silicon are compared with actual data, and found to be generally in excellent agreement.

1. Introduction Ion beam techniques such as Rutherford backscattering spectrometry (RBS) have long been used to study the elemental stoichiometry of materials and so have naturally played a role in the analysis of high T, superconducting oxides. RBS offers a rapid, quantitative method for determining the composition of oxides including superconductors such as Y,Ba,Cu,O,_,; however for purely Coulomb scattering, the oxygen spectrum does not stand out sufficiently for adequate analysis of oxygen content. The structural, electrical, and superconductivity properties of these compounds are extremely sensitive to oxygen content [1,2], which has led to a search for more sensitive methods of measuring oxygen concentration [3,4]. The familiar 160( OL,01)160 elastic nuclear resonance near 3.05 MeV offers an attractive means of extending RBS techniques to the study of oxygen concentrations in oxides. This is an isolated resonance with a backscattering cross-section near the resonance energy as much as 25 times greater than the Rutherford cross-section. Although the “O(p, y)19F and i’O(p, a)15N reactions offer better depth resolution because of narrower resonances [5], the detection of naturally occurring oxygen can be very advantageous. The simulation calculation described in this paper is based on Cameron’s [6] extensive measurement and analysis of 160( (Y, 0()‘~0 cross-sections up to incident energies of 4 MeV which provide parameters describing the 3.05 MeV resonance. The actual fitting of backscattering spectra then combines these cross-sections with, for the heavier elements of a compound, Rutherford cross-sections and the best available stopping powers. The 160(~, a)i60 0168-583X/89/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

cross-sections are calculated using the methods of partial wave theory for laboratory energies up to 4 MeV. This method is particularly flexible, since resonant cross-sections can be updated by simply adjusting one or two parameters. Programs were written to simulate backscattering spectra from four different oxides. Simulations and data for the relatively simple cases of bulk Al,O, and bulk Y,O, are compared in order to demonstrate the accuracy of the cross-sections. Simulations of thin film ZrO, and bulk Y,Ba,Cu,O,_, are compared to actual data as a test of the usefulness of the technique in more complicated situations.

2. Simulation of backscattering energy spectra 2.1. 160((u, a)160 cross-section calculations The differential ing of two spinless do _=_ dQ

cross-section for the elastic scatterparticles is expressed by refs. [6,7]:

e 1 - &csc2-exp k2 2 +x(21+

l)P,(cos

in In csc*19) sin(8,)

e 2 exp(i8,)

2 x exp(io,)

,

where do/d9 is the differential cross-section, where p is the reduced mass and v is velocity, 17= ZZ’/fiv, where Z and Z’ are of the colliding particles, 8 is the scattering the Ith order Legendre polynomial, and S,

k = pv/h, the relative the charges angle, P, is is the phase

336

P. Beming, R.E. Benenson / Backscattering analysis for oxygen profiling

Table 1 160( a, (u)‘~Oresonance parameters for laboratory energies up to 4 MeV (ref. [6]). Partial waveno.

I=0

I=3

I=0

1=2

I=2

E, (MeV) lab. r (MeV) lab.

2.490 0.024

3.045 0.010

3.090 0.005

3.380 0.010

3.885 0.003

1.0

7%

E

G. c % =

shift of the partial wave with orbital angular momentum Zh. The Coulomb phase shifts 01, are given by:

0.5

r ”

0 2.4

and exp(icu,) = 1. All of the above is in terms of the center-of-mass coordinate system. In the case of elastic scattering and when resonances associated with a given partial wave are well separated, the phase shift 6, can be approximated by: S,= -$/+

tan-’

[2&-E)]

where F is the experimental width of the resonance and E, is the resonant energy. The potential phase shift #J[ is given by: Gr = tan-‘(WG,)

I T=ai)

where FI and G, are the regular and irregular Coulomb wave functions, respectively, and a is the interaction radius. Five resonances were found between 2.5 and 4.0 MeV [6], and the values of E, and F are listed in table 1. The values are based on an interaction radius of 5.75 x lo-l3cm, which results in good fits at these and at higher energies [7]. Potential phase shifts were interpolated from published tables [8] of the Coulomb wave functions, and values of +[( E,,,) were fitted with fourth degree polynomials over the range 1.8 to 4.1 MeV. Below 1.8 MeV the potential phase shifts are all effectively zero. Our FORTRAN subroutine XSECT, using these polynomial fits of $J~ and the resonance parameters of ref. [6], then calculates the CM differential cross-section up to a lab energy of 4 MeV as described above, and includes coordinate system conversions so that the laboratory energy and scattering angle are input, and the laboratory cross-section is output. Values of CM cross-sections generated by this program are compared to data by Cameron in fig. 1. The quality of the fit is essentially the same as the one shown by Cameron, with the possible exception of the top of the 3.05 MeV resonance, which is not displayed by Cameron. The fit is poor above 3.8 MeV, probably due to broad

2.6

3.2

ELAB (MeV)

3.6

4.0

Fig. 1. 160(cq cy)160 CM differential cross-sections vs laboratory energy for a CM scattering angle of 168 O. Circles are data taken from graph in ref. [6]; solid line represents values calculated by our program XSECT.

resonances above 4 MeV [7,9], but is in good agreement with more recent data [lo] up to this energy. 2.2. Simulation

techniques

Computer simulations of backscattering spectra were performed using methods described elsewhere [11,12]. Individual stopping powers were calculated using Ziegler’s S,,, - Slow formula and associated parameters [13], and stopping powers for compounds were calculated using Bragg’s rule [12]. The energy of the alpha particles EHe(x) at a given depth x were calculated from

EH, = EH, (0) -

Lxs( EH,) dx

using numerical integration. As a check, calculated ranges were found to be in good agreement with published values. The effects due to detector energy resolution and energy straggling using the Bohr model were also included. Linear additivity [12] was assumed in the calculation of straggling in compound targets. The effect of finite detector area was not included in the simulations. In order to compare with experiment, the four simulations generated were for bulk Al *03, bulk Y203, bulk YBa,Cu,O,_,, and thin films of ZrO, on silicon substrates. The densities of Al,O,, Y203, ZrO, and silicon were assumed to be the same as previously published values [14], and the density of the high temperature superconductor YBa,Cu,O,_, was calculated from the size of the unit cell as determined by high resolution X-ray and neutron diffraction studies [15,16]. The su-

P. Berning, R. E. Benenson

/ Backscattering

337

analysis for oxygen profiling

perconductor simulation program was written so that the composition could be adjusted slightly, but the density was not varied.

3. Experimental method and sample preparation Data were taken using standard RBS techniques at the SUNY Albany 4 MV Dynamitron accelerator. Previous experiments suggest that this accelerator should have a beam energy spread of between 1 and 3 keV FWHM for 3 MeV alpha particles. The sample holder was a 2-axis goniometer with secondary electron suppression. The detector was a 95 mm2 area surface barrier detector, which was placed at an angle of 162.4 f 0.3’ relative to the beam direction and covered a 5.2” range of scattering angles. Since the resonant cross-section can vary as much as 3% per degree in backscattering geometries, the detector angle had to be known accurately. The energy resolution of the detector was typically 25 keV FWHM. The accelerator energy setting had to be calibrated before each run by measuring the 160(a, a)160 (3.05 MeV) yield from the natural oxide layer present on a piece of aluminum. As illustrated in fig. 2, the integrated number of counts from the oxygen peak was obtained for several energy settings, after a quadratic fit to the underlying Al part of the spectrum was subtracted. The energy scale of the multichannel analyzer used to record data was then calibrated using this corrected energy and the positions in the RBS spectra of the leading edges for several standards. The width of the curve in fig. 2 can also be used to estimate the energy spread of the beam. The total width of the curve (12 keV FWHM) is related to the width of the resonance (10 keV FWHM), but is also affected by energy loss and straggling in the target and beam energy spread. It is difficult to separate the effects of each of

6000

-

4000

-

2000

-

+

+-P

P-+ +G+

1

/

#

&A* 0

3.02

““I”.‘,.

y+ 3.03

3.04

3.05

ENERGY SETTING (MeV) Fig. 2. Total oxygen yield due to the natural oxide layer on aluminum vs accelerator energy setting (6 pC per point). The solid line is a guide for the eye. This curve indicates an offset of 6.4 + 1 keV from the true energy, and also suggests a beam spread of = 3 keV FWHM.

\

I 01

100

t 200

300

400

500

I

600

CHANNEL Fig. 3. Backscattering spectrum for sapphire, with an incident energy of 3.052 MeV. The solid line is our simulation, which overestimates the stoichiometric oxygen yield by 8.0%.

these factors [17], but a calculation in which the resonance is assumed to have a Lorentzian shape and all other factors enter as Gaussians suggests that the beam energy spread is actually around 3 keV FWHM. The Al,O, sample was a single crystal of commercial sapphire with 300 A of gold evaporated on the surface to avoid charging of the sample when exposed to the beam. The Y203 sample consisted of 99.9% pure yttria powder pressed into a half-inch pellet, again with an evaporated 330 A layer of gold. The ZrO, sample was made by e-beam evaporation of 99% pure zirconia onto a single crystal of Si at room temperature; no gold layer was used. The superconducting sample was prepared using method similar to those described elsewhere [18]. It consisted of a sintered pellet of pressed powder, with an expected composition of roughly Y,Ba,Cu,O,_,, where c = 0.05.

4. Experimental results and discussion A comparison of a simulation and an actual sapphire spectrum are plotted in fig. 3, showing a very satisfactory agreement. In order to compensate for the extra energy loss and straggling that occurs in the gold layer, these quantities were carefully calculated and their effects incorporated into the simulation. All spectrum parameters were predetermined; no adjustments were made. Care was taken to avoid channeling effects in the crystal. After subtracting a linear fit to the underlying Al spectrum, the total oxygen yield in the simulation proved to be about 8.0 f 1.4% higher than that of the data. Data taken using the Y203 sample and the corresponding simulation are shown in fig. 4, again with good agreement. Here the integral under the oxygen peak was about 7.8% higher in the simulation. The simulation of a 500 A thick film of ZrO, on Si and data are compared in fig. 5. Clearly the simulation underestimates the oxygen content in this film, by an

338

P. Berning, R.E. Benenson

/ Backscattering

analysis for oxygen profiling

1000 -

0 100

300

500

700

1.

9-00

CHANNEL

CHANNEL Fig. 4. Backscattering spectrum for yttria, with incident energy of 3.061 MeV. The simulation (solid line) overestimates the oxygen yield by 7.8%.

average of 8.3% over several energies. The composition of the film is suspect, however, since films prepared this way are known to be very porous and tend to absorb large quantities of water [19]. The hydrogen content of this film was later measured using the i5N nuclear reaction technique [5] and the hydrogen to zirconium ratio was found to be 0.31. If one assumes that the hydrogen was present entirely in the form of water, then the simulation would be underestimating the oxygen content of pure ZrO, by less than 1%. The thin-film sample can be used to demonstrate the ability to profile by varying the incident energy. Fig. 6 illustrates the qualitative similarity of simulated and actual oxygen peaks for this film at various energies. Data and a corresponding simulation of Y,Ba,Cu,O, are compared in fig. 7; the divergence between the simulation and data can most likely be attributed to poor knowledge of the energy loss in this compound. Actually, some difference in the slopes of data and simulations is evident in the binary systems; the larger number of components magnifies the effect in this case. The high energy parts of the spectra show an almost

CHANNEL

Fig. 6. Simulated and actual oxygen peaks for a 500 A thick ZrOs film on silicon for energies between 3.03 MeV and 3.07 MeV. The relative peak sizes are similar, however the absolute oxygen yields in the simulations are an average of 8.3% too low, probably the result of absorption of water in the film.

linear decrease of count rate with alpha energy, so once again linear fits can be subtracted in order to compare the oxygen peaks. The results of this operation are also shown in fig. 7; here the oxygen yield in the simulation is about 4.8% higher than the data. The use of this method for profiling at large depths is hampered by energy straggling. Bohr straggling is sufficient to describe the behavior at the depths illustrated above (= 500 A), but it becomes inadequate past depths of about 1500 A. As in the case of high temperature superconductors, subtracting a polynomial fit to the non-oxygen parts of the spectrum and integrating under the oxygen peak may allow a sufficiently accurate determination of oxygen content at greater depths. Alternately, an empirical fit to the actual amount of straggling at various energies could be included in the simulation.

----

I

I

$ ;;;:p

2000

...........&

..... . .... ~

P 5 =:

iooo _I

,000

CHANNEL 0

CHANNEL Fig. 5. Backscattering spectrum for a 500 A thick ZrO, film on silicon. Here the simulation underestimates the oxygen yield, probably due to impurities in the film.

Fig. 7. Backscattering spectrum and simulation for Y,Ba,Cu,O,. The poor agreement for the heavy elements is most likely due to uncertainties in the stopping powers used in the simulation. After linear fits to the metallic parts of the spectra are subtracted, the simulation’s oxygen yield is found to be 4.8% higher than that of the data.

P. Beming, R.E. Benenson / Backscattering analysisfor oxygen profiling

5. Conclusion At the present level of development this technique can measure oxygen concentrations to better than 10% accuracy. Simulations based on these nuclear resonance parameters have a tendency to overestimate the oxygen yield slightly. The fact that the predicted oxygen yield is 8% high for our two best-characterized samples (AlzO, and Y203) suggests that an adjustment of less than 1 keV in the resonance width would solve this problem. This adjustment would be within the resolution of Cameron’s measurement. Aside from this difficulty, this technique would be very advantageous when studying the composition of oxides such as the new class of high temperature superconductors, since the complete composition can be determined with one measurement. The 3.05 MeV resonance is sufficiently narrow to study individual depths directly, by varying the incident energy, with a depth resolution of about 100 A. This could prove useful in oxygen transport or surface degradation studies. It has all the advantages of RBS with the additional benefit of high sensitivity to oxygen. We would like to thank Dr. William Lanford, Dr. Walter Gibson, and Arthur Haberl for valuable discussions, and Wayne Skala for his technical assistance. Note added in proof: After the submission of this article we became aware of the article by B. Blanpain et al. [20].

References [l] J.D. Jorgenson,

B.W. Veal, W.K. Kwok, G.W. Crabtree, A. Umezawa, L.J. Nowicki, and A.P. Paulikas, Phys. Rev. B36 (1987) 5731.

PI J.M. Tarascon,

339

W.R. McKinnon, L.H. Greene, G.W. Hull, and E.M. Vogel, Phys. Rev. B36 (1987) 226. J. Keinonen, and R. Jarvinen, Appl. Phys. [31 E. Rauhala, Lett. 52 (1988) 1520. [41 J.A. Martin, M. Nastasi, J.R. Tesmer, and C.J. Maggiore, Appl. Phys. Lett. 52 (1988) 2177. 151G. Amsel and W.A. Lanford, Ann. Rev. Nucl. Part. Sci. 34 (1984) 435. 161J.R. Cameron, Phys. Rev. 90 (1953) 839. K.W. Jones, H. Smotrich, and R.E. [71 L.C. McDermott, Benenson, Phys. Rev. 118 (1960) 175. in: Handbook of Mathematical FuncVI M. Abramowitz, tions, eds. M. Abramowitz and I.A. Stegun (Dover, New York, 1965) p. 538. Nucl. Phys. A300 (1978) 165. [91 F. Ajzenberg-Selove, WI J.A. Lea&t, P. Stoss, D.B. Cooper, J.L. Seerveld, L.C. McIntyre Jr., R.E. Davis, S. Gutierrez, and T.M. Reith, Nucl. Instr. and Meth. B15 (1986) 296. P11 R.E. Benenson, L.S. Wielunski and W.A. Lanford, Nucl. Instr. and Meth. B15 (1986) 453. [121 W.-K. Chu, J.W. Mayer and M.A. Nicolet, Backscattering Spectrometry (Academic Press, New York, 1978). [I31 J.F. Ziegler, Helium Stopping Powers and Ranges in All Elements (Pergamon, New York, 1977). of Chemistry and Physics, eds. R.C. [I41 CRC Handbook Weast, M.J. Astle, and W.H. Beyer (CRC Press, Boca Raton, 1985). [I51 R.M. Hazen, L.W. Finger, R.J. Angel, C.T. Prewitt, N.L. Ross, H.K. Mao, C.G. Hadidiacos, P.H. Hor, R.L. Meng, and C.W. Chu, Phys. Rev. B35 (1987). [I61 Q.W. Yan, P.L. Zhang, Z.G. Shen, J.K. Zhao, Y. Ren, Y.N. Wei, T.D. Mao, C.X. Liu, T.S. Ning, K. Sun, and Q.S. Yang, Phys. Rev. B36 (1987) 5599. [I71 G. Amsel and B. Maurel, Nucl Instr. and Meth. 218 (1983) 183. and R.E. BenenWI P. Berning, J. Collazo, A. Mashayekhi, son, Mater. Res. Sot. Symp. Proc. 99 (1988) 939. W.G. Sainty, G.J. Clark, [I91 P.J. Martin, R.P. Netterfield, W.A. Lanford, and S. Sie, Appl. Phys. Lett. 43 (1984) 711. B. Blanpain, P. Revesz, L.R. Doolittle, K.H. Purser and J.W. Mayer, Nucl. Instr. and Meth. B34 (1988) 459.