Three-dimensional nuclear microanalysis in materials science

Nuclear Instruments North-Holland

and Methods

in Physics Research

NOMB

B77 (1993) 312-319

Beam Interactions with Materials & Atoms

Three-dimensional

nuclear microanalysis in materials science

Guy Demortier and Serge Mathot LAW-ISIS,Facult& Universitaires Notre-Dame

de la Paix, 22 Rue Muzet, B-5000 Namur, Belgium

The quantitative analysis of silicon in gold is performed in three dimensions by the spectroscopy of protons emitted from various depths by scanning a microbeam of monoenergetic deuterons. Owing to the high Coulomb repulsion of incident deuterons by heavy nuclei, proton emission can only be induced on light elements. The spatial resolution in the three dimensions of space lies around 3 pm. Application is made to the study of a eutectic gold-silicon alloy formed in situ in gold foils (lo-20 pm thick). This alloy can be used for the soldering of gold pieces at a low temperature (400°C).

1. Introduction

around 400°C [5,6], slightly higher than the eutectic temperature (363°C). Deuteron induced X-ray emission (DIXE) and nuclear reactions (NR) induced by a deuteron microbeam have been simultaneously used to characterize the gold-silicon alloy formed by the diffusion of silicon into gold foils. These measurements are completed by metallographic observations with optical and electron microscopes. The performance and limitations of these ion beam techniques (DIXE and NR) are discussed in terms of sensitivity, matrix effects, spatial resolution and depth resolution in an optimum experimental assembly.

Due to low cross sections of nuclear reactions by comparison with PIXE cross sections, high energy ion microprobes are scarcely used as true nuclear microprobes. The applications of various atomic and nuclear techniques to materials characterization published during the meetings on high energy ion microprobes held in Namur [l], Oxford [2], Melbourne [3] and the present meeting in Uppsala [4] are clear in that respect (table 1). Nuclear reaction analysis with microbeams is only applicable to light elements present in major concentration in materials. Silicon and gold are usual “partners” in electronic industry and the analysis of silicon in gold may be of great interest for the study of electronic materials. Silicon alloyed with gold may form a eutectic alloy (19 at.% Si) which can be used as a low melting point solder. We have experimented with a process of gold soldering involving two steps: (a) the formation of a microscopic gold-silicon eutectic alloy during silicon diffusion through polycrystalline gold foils along their grain boundaries, and (b) the redistribution of a part of this eutectic alloy for the joining with a second piece of gold. Both steps are performed at a low temperature:

Table 1 Number of papers giving elemental high energy ion microprobes

results by various

Conference

PIXE

PIGE

Namur, 1981 [l] Oxford, 1987 [2] Melbourne, 1990 [3] Uppsala, 1992 [4]

6 23 20 35

1 2 2 2

0168-583X/93/$06.00

0 1993 - Elsevier

Science

2. Sample preparation

Pure polycrystalline gold foils are rolled at room temperature down to thicknesses ranging from 10 to 20 km. A film of silicon is then deposited through a mask on a part of these foils with an electron gun. The deposition is performed at a pressure lower than lop6 Torr to obtain silicon films up to 1 urn thick on gold foils maintained at 400°C during the silicon deposition. At this temperature a liquid Au-Si mixture

ion beam techniques

Publishers

and diffusion process

with particle

microbeams

during the four conferences

RBS

NRA

STIM

Damage

3 9 13

2 4 5 6

3 10 7

2 10 1

B.V. All rights reserved

on

313

G. Demortier, S. Mathot / Three-dimensional nuclear microanalysis

Fig. 1. (a) Optical micrography at the rear of a 12 urn thick polycrystalline gold foil after diffusion during 1 h at 400°C. (b) SEM micrography of the front face in the neighbouring of the deposited Si film (top) showing leaf shaped migration of the eutectic alloy along the grain boundaries (bottom).

diffuses during the deposition procedure in the gold foils -along well defined paths: the gold grain boundaries. Figs. la and lb clearly indicate that a gold-silicon alloy has diffused on the surface of the foil by forming characteristic leaf shaped decorations starting from the boundaries of the gold grains flattened by the rolling procedure. One can understand that several of these flattened grains may occupy the whole thickness of the foil. The diffusion of a liquid phase can then take place through the whole thickness, as observed in fig. la, where one identifies the typical ramifications of the eutectic structure at the back side of the foil: the side opposite to the one on which was the silicon film deposited. At such a low temperature, nothing else than a liquid phase of gold-silicon eutectic alloy can diffuse. The typical diffusion shown in fig. la is obtained after 60 min of deposition of Si on a 12 km thick gold foil. Such ramifications also appear on the rear of foils up to 150 pm thick. At high magnification (fig. lb) one can identify typical eutectic lamellae starting from the limit of the deposited Si film and extending along the gold grain boundaries.

3. Experimental 3.1. Interaction

conditions for the microanalyses of deuterons

with materials

The actual path of deuterons of energy in the range of 1 to 3 MeV is nearly linear. In table 2 we summarize several parameters related to the mean deuteron energy at various depths below the surface, their mean

angular deviation, the uncertainty on the energy of these deuterons after each layer of 1 pm below the surface due to nuclear interaction only. The angular deviation after crossing a thickness of 12 pm of gold is still very small and the actual beam size may be considered as constant and equal to 3 pm in all depth profiling experiments. This beam diameter was measured by scanning a tungsten wire of defined size.

Table 2 Deuteron energy, energy and angular straggling for 2.8 MeV incident deuterons in various thicknesses of the Au-Si eutectic alloy [12] Alloy thickness

Deuteron energy

h.4

keV1

Energy straggling

Angular straggling

AJ% (nuclear only)

pdoeg1

keV1 0

2800

_

1 2 3 4 5 6 7 8 9 10 11 12

2707 2615 2519 2422 2323 2223 2117 2013 1900 1783 1675 1553

19 27 34 41 47 53 57 63 69 78 80 91

4.3 4.6 5.4 5.8 6.9 7.3 7.8 8.3 9.4 10.4 10.8 11.7

VII. MATERIALS / SEMICONDUCTOR

G. Demortier, S. Mathot / Three-dimensional nuclear microanalysis

314

(b) : (0)

(a) : DIXE

4----

100pm

----+

Fig. 2. X-ray and proton maps simultaneously obtained by scanning a region of 100 p,rnX 100 pm with a deuteron beam (3 pm in diameter) on the rear face of a 12 pm gold foil treated for Si diffusion during 1 h. (a) DIXE scan. Depth analysed 2 0.5 pm. (b) (d, p,,) reaction analysis of the same region. Depth analysed: 12 Wm.

Deuterons can scarcely hit or graze a light nucleus (like Si) and be stripped, leading to the capture of the neutron and the emission of the residual proton (stripping reaction). This nuclear reaction on silicon is highly exoenergetic (Q = +6.249 MeV). For 2.8 MeV incident deuterons, protons of 9.035 MeV are emitted in the forward direction. The spectroscopy of these protons leads to a possible determination of the depth profile of silicon. By scanning the deuteron beam on the surface of the sample, one obtains, by the measurements of the proton energies, the 3D distribution of Si atoms.

3.2. DIXE

analysti

Particle-induced X-ray emission under deuteron irradiation will be called DIXE. In DIXE analysis, KXrays of silicon and M X-rays of gold are used as analytical signals. The absolute concentration in different regions of the surface of gold foils prepared by silicon diffusion may be measured by comparison with a eutectic gold-silicon alloy (19 at.% Si). Using this

Energy 5733

6236

Pl

Collimator

Sample holder _________. pro*o”s -

Deuterons

\ Surface barrier detector (Depleted depth 700 pm)

Fig. 3. Experimental arrangement for (d, p) reaction analysis at 0 = 0”.

73338

7739

+ PO

Au Absorber

Au-Si Sample

(keV) 6737

+ R

Fig. 4. Part of a typical (d, p) experimental spectrum showing p0 and pi contributions during the bombardment of a 75 pm thick silicon sample. The energy scale takes into account the presence of the 22 pm gold ‘absorber. The simulation (full line) is obtained using SENRAS [9] with our measured cross sections given in fig. 5.

G. Demortier, S. Mathot / Three-dimensional nuclear microanalysis

315

Table 3 Energies of the protons induced by 2.8 MeV deuterons in various depths in a 12 Frn thick Au-Si eutectic foil, outgoing energy of these protons after crossing the full thickness of the eutectic foil and a 22 pm thick gold absorber, calculated energy stragglings AE and corresponding uncertainty At on the thickness determination [12] Proton energy

Depth below the surface bml

keV1

0

Outgoing proton energy [keVl

AE, a nuclear IkeVl

AEb electronic

AE total

h-4

7643 7581 7504 7432 735.5 7288 7204 7129 7048 6959 6862 6784 6684

140 146 140 140 142 125 128 130 126 125 122 110 128

159 159

212 217 215 215 216 208 210 213 212 213 215 210 223

2.2 2.2 2.2 2.2 2.2 2.0 2.0 2.0 2.0 2.0 2.0 2.0 1.8

9035 8940

1 2 3 4 5 6 7 8 9 10 11 12

8847 8750 8652 8552 8450 8342 8121 8001 7891 7766

159 159 159 159 159

159 159

159 159 1.59 159

At

a Monte Carlo calculation [lo]. b Analytical formula [ll].

bulk sample of eutectic gold-silicon as the reference, we have shown that the maximum silicon concentration in the grain boundary is close to the eutectic composition [7]. Contrary to solid solutions in which elements may be mixed at atomic level, the eutectic gold-silicon alloy is composed by the juxtaposition of silicon grains and gold grains. It is then obligatory that the reference sample of eutectic composition used as a reference

Energy 700

1.6

1.8

Deuteron

2.0

2.2

energy

2.4

2.6

2.8

(MeV)

Fig. 5. Cross sections of?d, pO) and (d, pl) nuclear reactions extracted from various spectra like the ones of fig. 4 at different deuteron energiei. Details in ref. [ll].

(keV) 7000

600

50

1.4

6500

B: Au

(12 pm)

+

Channel

Si

number

Fig. 6. Experimental procedure to obtain depth profiling of silicon from the decomposition in nine slices of the p0 contribution: (a) pure 75 pm Si sample; (b) 12 pm thick Au foil processed for silicon diffusion (irradiation of the rear face).

VII. MATERIALS / SEMICONDUCTOR

316

G. Demortier, S. Mathot / Three-dimensional nuclear microanalysis

material contains silicon grains of nearly the same dimension as those observed in the gold-silicon samples prepared by diffusion. In the eutectic alloy, neighbouring atoms of silicon are mainly silicon atoms, neighbou~ng atoms of gold being gold atoms. In a hypothetical solid solution of gold and silicon the neighbours of silicon atoms would mainly be gold atoms. As the difference in the mass absorption coefficients of K, X-rays of silicon in silicon and in gold is very large (328 and 1790 cm’/g respectively), the apparent composition in silicon would appear highly enhanced in the eutectic structure by comparison with the one we would obtain in a solid solution of the same composition. The intensity ratio I..,,,, on Isolidso,ution is highly dependent on the size of the grains. Conventional computer prongs for the treatment of PIXE spectra do not take this situation into account. A typical concentration map of Si obtained by DIXE in the grain boundaries at the back side of a 12 pm thick gold foil prepared for silicon diffusion is given in fig. 2a. The analysed depth of silicon and gold by DIXE involving the detection of K lines of Si and M lines of gold is much less than 1 p,rn below the surface. This analysed depth is mainly limited by the absorption of useful lines of silicon and gold but not by the deuteron range in the sample.

a: O-l .l urn

b: l-l-2.7,um

c: 2.7-4.3 Urn

d: 4.3-5.8 pm

e: 5.8-7.2 pm

f: 7.2-8.5 ym

3.3. Nuclear reaction analysis The nuclear reaction ‘*Si(d, pJ2’Si (leaving the residual ‘9Si nuclei in their fundamental energy level) is mainly governed by a neutron capture invol~ng no exchange of angular momentum (I = 0). As a consequence, the maximum intensity in the proton emission is achieved in the forward direction. The cross section of this nuclear reaction at E, = 2.8 MeV varies from 6 mbsr-i to 1 mbsr-’ when the angle of emission of protons varies from 0 to 35” [8]. We have then chosen to detect the emitted protons in the forward direction. In this special arrangement, the solid angle of the proton detector (situated into the incident deuteron beam) may be as high as 0.3 sr when the detector is put very close to the sample. In our e~erimental arrangement (fig. 31 we have chosen 0.01 sr. A 22 vrn thick absorber of pure gold is inserted between the sample to be studied and the detector, in order to completely stop the incident deuteron beam even when the beam would cross a hole in the gold-silicon sample. The choice of a material containing only a heavy element as absorber prevents any emission of additional protons. On account of the low cross section of nuclear reactions induced by low intensity microbeams (about 100 to 500 pAI, the limit of detection for silicon determination in volumes of 3 x 3 x 2 Km3 lies around 0.5%. In table 3 we give the main kinematical parameters of the products of the nuclear reaction of interest. The quantitative determination of silicon at different depths below the surface is based on the comparison of proton spectra obtained when pure silicon and gold-silicon samples are bombarded in the same geometrical arrangement. The silicon reference materials is a thin foil (75 I;Lrnthick) used in the semiconductor technology (and offered to us by Canbe~a-Olen). The corresponding depths in pure silicon and gold alloys are calculated using the well-known relative stopping powers and the decomposition of the experimental spectrum of fig. 4 gives rise to the cross sections of (d, pa) and (d, pi) reactions as reproduced in fig. 5. The shape of the excitation functions (fig. 5) at 0 = 0” are in agreement with the published values at 0 = 3”

@I. g: 8.5-9.7 pm

i: 10.9-l 2 i.lrn t 8

4, Application to Good-silicon alloys

3

It is expected that the depth distribution of silicon induced by the diffusion of Si in gold would exhibit a sharp decrease starting from the surface on which silicon is deposited and ending at the opposite face. In order to achieve a sufficient statistical accuracy for the quantitative depth profiling of silicon at the rear of the exposed gold foils, the incident deuteron

i Fig. 7. Set of nine maps corresponding to the nine slices of fig. 6. Symbols (a) to (i) refer to the nine layers of the 12 pm thick sample.

G. Dernortier, S. Muthot / Three-dimensionaEnuclear microanalysis

abc’de

317

f

Depth (,um) Fig. 8. (a) Identification of interesting spots on the scans of fig. 7. (b) Scans along the z axis (the beam axis) in the region filled with the Au-4 eutectic alloy. (c) Scan along the z axis showing a classical diffusion process.

of a cavity

VII. MATERIALS ,’ SEMICONDUCTOR

318

G. Demortier, S. Mathot / Three-dimensional nuclear microanalysis

beam of 2.8 MeV is directed on that rear surface. At Ed = 2.8 MeV, the (d, pc) cross section at 0 = 0” is close to its maximum (fig. 5, upper curve). If the deuteron beam hits a gold grain boundary in which the diffusion of the eutectic alloy took place, one may observe a proton spectrum like the one on fig. 6b showing a more important contribution in the medium and the low energy parts of the pa than when it hits a uniform silicon sample (fig. 4). The pi contribution in fig. 6b is narrower due to the fact that the actual variation of the cross section is more rapidly increasing with the proton energy around 2.5 MeV (fig. 5, lower curve). Working at E, = 2.8 MeV and irradiating the rear of the foil one obtains a nearly flat pa spectrum and then a more constant statistical accuracy on the true silicon concentration along the full foil thickness. The map of fig. 2b has been obtained by scanning the microbeam on a gold foil (12 p,rn thick). The 2.8 MeV deuterons are incident on the back side of the foil prepared by silicon diffusion (the side opposite that on which silicon has been deposited). This map corresponds to the total p. information and may be compared to the surface silicon concentration obtained simultaneously by DIXE. The map of fig. 2a concerns a layer of less than 1 km, but the one of fig. 2b concerns the whole foil thickness (12 pm). This total p,, information may be decomposed in slices whose width corresponds to the energy uncertainty due to straggling as

calculated in table 3. The corresponding Si concentrations are then calculated using the decomposition of the pa peak in nine regions (fig. 6) corresponding to nine layers in the full thickness of the gold foil. In the series of maps of fig. 7, the proton counts in each of the 9 parts of the pa information are corrected for the variation of the cross section of the nuclear (d, po) reaction extracted from fig. 5. In this way, one obtains true silicon concentration maps. One observes, in the present case, that the concentration of silicon is far from being constant along the full thickness into the grain boundary (nearly perpendicular to the surface of the foil), but is nearly zero elsewhere except in the last map (i) corresponding to the surface on which the silicon film has been deposited. The map of fig. 7a corresponds to silicon present at the rear part of the prepared gold foil and then in the front of the bombarded surface. The silicon concentration does not exceed a few %, a concentration well below that of the eutectic composition. Map f corresponds to silicon concentrations at a depth situated around 8 pm below the irradiated surface. One observes several black points corresponding to a larger silicon concentration than that observed at the same positions in the neighbouring maps e and g, corresponding to depths of 6.5 and 9 km. Linear scans along the z axis (the beam axis) are reproduced in figs. Sb and 8c. Scans corresponding to

H

H

10 -

H

9 -

E s7 $ 5 s 5 I?

H

H

11 -

F

1

H

12 -

H

H’

H. H

#H

H

8 -+_+ H

H

-H

H

H

HH

H

HHH +-%Hc_I

H

6-

t-~

H

64-

H-H

H

IJ

AtomicweigOht : 6 ‘f 7 ” 9 ” 10 ” 11 ” 12 ” 13 ” 14 ” 15 ” 16 ” 17 ” 18 ” 19 ” 23 ” 24 ” 25 ” 26 ” 27 ” 28 ” 29 Symbol : Li Li Be B B C Nat.Abundance: 7.5 92.5 100 19.8 80.298.9 Fig. 9. Identification

of the proton

energies

C 1.1

N

N

0

0

0

99.6

0.4

99.8

0.04

0.2

emitted

F 1W

Na Mg Mg Mg Al 100

79

10

at 0 = 0” for (d, pi) reactions from top to bottom).

11

100

Si 92.2

” 30 ” 31 ” 32 ” 46 ” 47 ” 48 ” 52

Si

Si

4.7

3.1

induced by 2.8

P

S

Ti

Ti

Ti

100

95

8

7.3

73.8

‘I

Cr 83.8

MeV deuterons (i = 0,1,2, . .

G. Demortier, S. Mathot / Three-dimensional nuclear microanalysis

fig. 8b concern regions represented by points 8, 6, 3, 4, 5, 7 and 9 (see details in fig. 8a). It is clear that the apparent Si enhancement is due to a cavity which was filled with the eutectic alloy. On the contrary, fig. 8c shows a more conventional depth profile of Si: high concentrations at the surface where silicon is deposited (region i) and low concentrations at the rear (region a). The actual eutectic composition (19% of silicon) is only approached at points 14 and 20. In these regions the beam size (3 urn in diameter) and the dimension of the grain boundary (filled with the eutectic alloy) are close to each other. It is obvious that in other regions (where silicon is detected) only a liquid phase with a composition close to that of the eutectic could have been admitted. Each concentration of silicon lower than 19% as observed in the main parts of all maps, can be explained by considering that the size of a grain boundary is much narrower than the incident deuteron beam. Scans like those of figs. 8b and 8c may then be converted in measurements of the width of the grain boundary filled with the eutectic alloy: the ratio of the measured silicon concentration on the eutectic composition being the ratio of the width of the grain boundary on the beam diameter [12].

5. Possible uses of the method for depth profiling of light elements

The spectroscopy of protons emitted under deuteron irradiation may be applied to the majority of light elements. Fig. 9 gives a general presentation of the energies of protons emitted in the forward direction (0 = O”) by (d, p) reactions induced by 2.8 MeV deuterons. For that purpose one needs a Si barrier depleted at least up to 700-800 pm. An up-to-date review of nuclear methods of analysis of light elements may be found in the proceedings of the 3rd International Conference on Chemical Analysis by Charged Particle Bombardment held in Namur in 1991 [13].

6. Conclusion Nonresonant nuclear (d, p) reactions induced by a deuteron microbeam are very useful for the depth profiling of light elements in heavy matrices or for the

319

identification of inclusions in heterogeneous materials. The special experimental arrangement involving a particle detector into the deuteron beam leads to a general use of the technique very similar to STIM. The reduction of the counting rate is not performed by reducing the intensity of the incident beam (like for STIM) but by taking advantage on the low but optimal cross section of exoenergetic stripping reaction.

References [l] G. Demortier (ed.), Microanalysis Using Charged Particle Accelerators, Proc. 2nd Int. Conf. on Microanalysis, Namur, 1981, Nucl. Instr. and Meth. 197 (1982) l-258. [2] G.W. Grime and F. Watt (eds.), Nuclear Microprobe Technology and Applications, Proc. 1st Int. Conf. on Nuclear Microprobe Technology and Applications, Gxford, 1987, Nucl. Instr. and Meth. B30 (1988) 227-506. [3] G.J.F. Legge and D.N. Jamieson (eds.), Nuclear Microprobe Technology and Applications, Proc. 2nd Int. Conf. on Nuclear Microprobe Technology and Applications, Melbourne, 1990, Nucl. Instr. and Meth. B.54 (1991) l-446 [4] U. Lindh (ed.), these Proceedings (3rd Int. Conf. on Nuclear Microprobe Technology and Applications, Uppsala, 1992) Nucl. Instr. and Meth. B77 (1993). [5] S. Mathot and G. Demortier, Proc. Diffusion Bonding 2, ed. D.J. Stephenson (Elsevier, 1991) 302. [6] S. Mathot and G. Demortier, Proc. 15th Precious Metals Conf. and Exhibition, Naples, FL (IPMI, Allentown, 1992) 245. [7] S. Mathot and G. Demortier, Nucl. Instr. and Meth. B49 (1990) 505. [8] U. Strombusch, W. Bakowsky and H. Lacek, Nucl. Phys. Al49 (1970) 605. 191 G. Vizkelethy, Proc. 9th Int. Conf. on Ion Beam Analysis, Kingston, USA, 1989, Nucl. Instr. and Meth. B45 (1990) 1. [lo] J.F. Ziegler, J.P. Biersack and U. Littmark, The Stopping and Ranges of Ions in Matter, vol. 1 (Pergamon, New York, 1985). [ll] G. Deconninck, Introduction to Radioanalytical Physics, Akadtmiai Kiado, Budapest (Elsevier, Amsterdam, 1978). [12] S. Mathot, Ph.D thesis (in French), FUNDP-Namur (1992). [13] G. Demortier (ed.), Microanalysis of Light Elements (Hydrogen to Neon) Using Charged Particle Accelerators, Proc. 3rd Int. Conf. on Chemical Analysis: Microanalysis of Light Elements (Hydrogen to Neon), Namur, 1991, Nucl. Instr. and Meth. B66 (1992) l-309.

VII. MATERIALS / SEMICONDUCTOR