Rutherford back-scattering measurements of antimony diffusion in nanocrystalline copper

Nan&ruchucd Mataids. Vol. 8, No. 1. pp. 374.1997 Elsevies Science Ltd Copyright Ib 1997 Acta Metallurgica Inc. Printed in the USA. All ri@s resend 0965-9773197 $17.00 + .oo

Pergamon

PII SO9659773(97)00063-9

RUTHERFORD BACK-SCATTERING MEASUREMENTS OF ANTIMONY DIFFUSION IN NANOCRYSTALLINE COPPER I.L. Balandin’ , B.S. Bokstein’, V.K Egorov*, P.V.Kurkin’ lMoscow Steel and Alloys Institute, Leninsky Pr., 4.117936 Moscow, Russia *Institute for Problems of Microelectronics Technology and Superpure Materials, RAS, 142432 Chemogolovka, Moscow District, Russia (Accepted October 1996) Abstract--Antimony diffusion in nanocrystalline copper with average grain size about 50 nm and porosity75% of theoretical value was studied at the temperature range 50-100°C using Rutherford backscattering spectrometry. Based on the metallographic data, a diffusion cluster model is proposed. According to this model, dtrusion occurs along cluster boundariesfollowing by nanograins boundaries diffusion. Both grain and cluster boundary dtrision coefficients of Sb in n-Cu were calculatedfrom this model. Obtained activation energy values for Sb d@ision along grain (0.39 eV) and cluster (0.41 eV) boundaries are close to each other, and more probably describe surface mass transport than grain boundary.

INTRODUCTION Nanocrystals are relatively new class of materials. They are characterized by grain or particles size below 100 nm and significant number of the atoms are situated at the inner surfaces (up to 30%). There are few works devoted to diffusion studies in nanccrystals that demonstrated special and interesting properties. The small number of the papers in this field is due to experimental difficulties arising from low temperature (less 0.3 T,,,, where Tm is melting point of the matrix) that is necessary to avoid recrystallization and grain growth. From (l-4) it follows that at these temperatures only grain boundary diffusion takes place. In our paper we present the experimental data on antimony diffusion in nanocrystalline copper. EXPERIMENTAL Ultrafine copper powder-was produced by evaporation-condensation technique in high purity Ar flow. By compacting Cu powder under pressure -1 GPa cylinder shaped specimens of 5 mm in diameter and 2-3 mm thick have been prepared. Density measurements using Archimedes principle yieldedadensity 75% relative to theoretical. Theaveragecrystal size of the nanocrystalline copper (n-C@ samples was 50 nm. The sample faces were mechanically polished on emery-paper of 5 pm grade and finally with diamond paste of 1 pm grade, then they were cleaned in organic solvents (acetone, ethanol). 37

38

IL BALANDIN.

BS

BOKSTEIN,

VK Eemov

AND

PV

KUAKlN

Figure 1. Micrograph of the nanocrystalline copper sample. Metallographic study revealed that the nanograins are agglomerated into clusters with average size about 50 pm. A micrograph of n-Cu samples is shown in Figure 1. The authors (5) have obtained similar results during embrittlement experiments with n-Ni in the presence of liquid mercury. Antimony was deposited by thermal evaporation technique (the residual gas pressure in vacuum chamber was 2.6 10e3 Pa). Thickness of Sb layer was 50-60 nm. The samples were annealed in glass ampoules with residual gas pressure less then 6 . 10” Pa at 50,80 and 100 “C ((0.24-0.28) Tm, where Tm is copper melting point) for 194, 96 and 48 hours respectively. Calorimetric study revealed no transformation of n-Cu at the temperatures below 110°C. Sb diffusion in n-Cu was studied using Rutherford backscattering spectrometry (RBS) of He+ ions with standard scattering geometry. Energy of incident He+ beam was 1.305 MeV, the scattering angle was 157”, the ion beam diameter was about 1 mm and total charge collected was -10 PC. Experimental procedure is described in detail elsewhere (6). RBS spectra were obtained both before and after annealing. Conversion of RBS spectra to concentration profiles was performed by means of the simulation program RUMP (7).

RESULTS The typical RBS spectra of the sample n-Cu/Sb are shown in Figure 2 and corresponding concentration profiles (composition c(y) vs. the 615 power of penetration depth) are presented in Figure 3. These profiles are described by two distinct linear segments, the first one adjacent to the initial interface Cu/Sb is characterized by sharp decreasing of the Sb concentration, and the second one remote from the interface demonstrates the smooth reduction of Sb concentration and deep

39

FIBS OF ANTIMONYDIFFUSIONIN NANOCRYSTALLINE C&PEA

450

490

530

570

CHILVNELNUMBER

Figure 2. RBS spectra for Sb/n-Cu sample before (circles) and after annealing at 100 “C for 48 hours (squares).

penetration of antimony into n-Cu. Such non-uniform distribution of diffusing species was already obtained in nanocrystals (3,8) but, however, the diffusion parameters were calculated only for the second segment. It is worthwhile to note that similar penetration profiles are usually observed in polycrystals under the kinetic regime “B” (9) when fast grain boundary diffusion with simultaneous volume diffusion from the boundary into the crystal takes place (in these cases the first region is attributed to the direct volume diffusion from the surface and the second one is due to the grain boundary diffusion). Obviously, at the experimental temperatures the lattice diffusion is negligible because of the diffusion path (~DL . t)llL (DL is lattice diffusivity (10) and t denotes annealing time) does not exceed lo4 nm. In our opinion, observed Sb penetration profiles can be explained in terms of simultaneous diffusion of antimony via nanocrystalline grain boundaries (NB) and cluster boundaries (CB) (4). Let us propose the model reminiscent of Fisher’s model (11). The difference is that in Fisher’s model diffusant leaks from the GB to the volume, but in ours, the single opportunity is to move from the CB along the NB’s because DL is very close to zero. The model resembles that in (4), but in (4) the analysis was semiqualitative. Hence, the CB is treated as a high-diffusivity, semi-infinitive isotropic slab of uniform width 6’, embedded in a polycrystalline specimen composed of cubic nanocrystalline grains forming a 90”crossed network of NB. Let DCB be the cluster boundary diffusion coefficient, and DM the diffusion coefficient along NB and S - NB width (Figure 4).

IL BAUNDIN,BS BOKSTEIN, VK

1

EGOROVANDPV

KURKIN

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, 0

10

20

30

DEPTH, nm Figure 3. Concentration profiles of antimony in n-Cu before (circles) and after annealing at 100°C for 48 hours (squares) as derived from spectra in Figure 2.

Figure 4. Diffusion cluster model in nanocrystalline materials. Applying the Whipple solution (12) (in our case the NB diffusion is analogous for volume diffusion and CB diffusion is analogous for the grain boundary diffusion), one may write the exact solution in a condensed form as cNB (59 q1,P>= ml)

+ c2(5,

“rl, P>.

111

FIBS OF hnrdow

DIFFUSIONIN NANOCRYSTALLINE COPPER

41

where CNB is the concentration of diffusant in NB and dimensionless parameters defined as follows:

h is the NB length per unit area (h is equal to 2/d for a system of cubic grains of edge d). In equation [I] the first term ct = coerfc(~l/2) (where co = c&x, 0, t)) represents the contribution due to direct diffusion along NB from a constant source in the y-direction. The average concentration c is determined as (13)

G = Uico erfc(q@),

PI

The second term in eq. [l] represents the contribution from the CB. For the proposed model, the parameters of diffusion along cluster boundaries may be expressed as:

The gradient -

ahc 6,5

for p > 10 has a constant value of about 0.78 independent of p (14).

a(tlp-1’2) The resulting equation can be written as:

The diffusion coefficients (DNB)of antimony in nanocrystalline copper were extracted from complementary error function solution [2] in the regions closest to the original interface. In our experiments, the value of L&c was 5.5 * 0.5 at.%. Assuming 6 = 1 nm and d = 50 nm we can evaluate co > 100%. However, if we take into account the porosity of the experimental samples (-25%) and assume the free volume located on the NB and CB, we can propose the effective value of 6 may exceed the crystallographic value of grain boundary width (0.5+1.0 nm). For 100% solubility of Sb in copper NBS the evaluations show the NB width yields the reliable value of 1.5 nm. The temperature dependence of NB diffusion of Sb in n-Cu is sketched in Figure 5 and parameters of GB diffusion are computed to be DNEI= 1.0 x lo-l3 exp(-0.33 eV / kT), cm2/s

42

IL BUNDIN, BS

BOKSTEIN,VK

EGCMOVAND PV

KURKIN

Parameter ~‘DcB~& for diffusion of Sb along CB was calculated by means of equation [4]. Temperature dependence of G’&&& is listed in Figure 5, yielding

G’DcB~ = 4.9 X lo-l7 exp(-0.41 eV / kT), cm3/s

Note, the parameter fi =

in our experiments was of 24 + 32.

DISCUSSION If we assume that 6’ z 6 the value of DCB can be fiily estimated as 7.6 x lo-l7 cm2/s for 5O”C, 3.3 x lo-l6 cm2/s for 8O’C and 5.2 x lo-l6 cm2/s for 100°C. Sb diffusion coefficients along CBS are of 2 orders of magnitude higher as compared with the diffusion coefficients along NBS in n-Cu. It is interesting that calculated activation energies for Sb diffusion along the copper NBS and CBS are close to each other (Em = 0.33 and Ecu = 0.4 1 eV) within the experimental error (k 0.04 ev). The previous investigations of self-diffusion in nano-Ni with the density about 94% (4) revealed the activation energy for GBs to be close to the activation energy of self grain boundary diffusion in polycrystalline Ni, but the activation energy along CBS in nano-Ni was comparable with the value for the surface self-diffusion (one third of the bulk diffusion activation energy). In our opinion, such lower values of activation energies for NB diffusion in our experiments are attributed to porosity of the samples investigated. In (4) it was found that the free volume was localized at the CBS of nanocrystalline specimens. Ourexperiments were carried out with the non-sir&red samples of n-Cu; porosity was up to 25%. Therefore, we assume that free volume is concentrated both at CBS and NBS, and most probably the obtained results describe the surface diffusion rather than grain boundary diffusion. In Table 1, the nanoboundary and cluster boundary diffusion activation energies obtained in our work are compared with data for copper self-diffusion and antimony heterodiffusion in copper.

TABLE 1 Activation Energies for Copper Self-diffusion and Antimony Heterodiffusion in Copper System

Cu

SbinCu

SbinCu

Shin

lattice

grain boundary

n-Cu NB

Sb in n-Cu CB

0.64

1.82

0.87

0.33

0.41

(1)

(10)

(18,191

this work

this work

CU grain boundary

cu surface

n-Cu

lattice

Q, eV

2.04

0.88

0.69

Ref.

(1%

(16)

(17)

43

RBS OFANTWMNV DIFFUSION INNANOCRYSTALLINE COPPER

2

lE-22 t 7 6 5 4 3

% 9\ “9 g _;;w

2

2.6

2.8

3.0

lE-23 3.2

1000/T, K-* Figure 5. Temperature dependencies for NB diffusion (circles) and CB diffusion (squares) parameters of antimony in n-Cu.

As seen in Table 1, a similar result was obtained in the case of self-diffusion in n-Cu. Diffusion coefficients for grain boundary diffusion of Sb in n-Cu are of 7 orders lower than the extrapolated values of K&Dt,,for Sb grain boundary diffusion in copper bicrystals (18), where K is the segregation factor. Note such a difference can be connected with the following circumstances: the first, the author of (18) realized the experiments at temperatures in excess of the Sb melting point, so the wide extrapolation (from 700°C) is needed to compare the results, and secondly, from (20) it follows that K = 100-700 at 4OO-800°C. As a rule, K increases with a decrease in temperature. Note, the Sb diffusion coefficients for CBS in n-Cu calculated in our work are close to the grain boundary diffusion coefficients of Bi in n-Cu calculated in (3) for the “tail” region of concentration curves.

ACKNOWLEDGMENTS The authors are grateful to T. Khvostantceva for preparing the specimens. The investigation described in this publication was made possible in part by Grant No. M3B300 from ISF and Grants No. al275,259p from ISSEP.

44

IL BALANDIN.BS BOKSTEIN,VK EGOROV AND PV KURKIN

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

Horvath, J., Birringer, R., and Gleiter, H., Solid State Communication, 1987,62, 319. Schumacher, S., Birringer, R., Strauss, R., and Gleiter, H., Acta Metallurgica, 1989,37,2485. Hofler, H.J.,Averback, R.S., Hahn, H., and Gleiter, H.,JournalofAppliedPhysics, 1993,74,3832. Bokstein, B.S., B&e, H.D., Khvostantceva, T.P., and Trusov, L.I., Nunostructured Materials, 1995,6,873. Igoshev, V., Rogova, L., Trusov, L. and Khvostantseva, T., JournalofMaterials Science, 1994,29. 1569. Aleshin, A.N., Bokstein, B.S., Egorov, V.K., and Kurkin, PV., Thin Solid Films, 1993,223, 51. Doolittle, L.R., Nuclear Instruments Methods, 1985, B9,344. Hofler, H.J., Averback, R.S., and Hahn, H., Defect and Diffusion Forum, 1991.75, 195. Harrison, L.G., Transactions Furudq Society, 1961,53, 1191. Inman, M., and Barr, L., Acta Metallurgica, 1960.8, 112 . Fisher, J.C., Journal of Applied Physics, 1951,22,74. Whipple, R.T.P., Philosophical Magazine, 1954,45, 1225 . Kaur, I., and Gust, W., Fundamentals of Grain and Interphase Boundary D@ision, Ziegler, Stuttgart, 1988, p. 422. Le Claire, A.D., British Journal of Applied Physics, 1963, 14, 35 1. Mayer, K., Physica Status Solidi, 1977, B44,567. Surholt, T., Mishin, Yu.M., and Hetzig, Chr., Physics Review B, 1994,50,3577. Cousty, J., Peix, R., and Peraillon, B., St&ace Science, 1981, 107,586. Balandin, I.L., and Bokstein, B.S., DefectandDiffusion Forum (Proceeding of DIMAT-96). (to be published). Kaur, I., Gust, W., and Kozma, L., Handbook of Grain and Interphase Boundary Diffusion Data, Ziegler, Stuttgart, 1989, p. 426. Bokstein, B.S., Nikolsky, G.S., and Smimov, A.N., Fiz. Met. Metalloved., 1991, N8, 140 (in Russian).