Determination of concentration profile in thin metallic films: Applications and limitations of He+ backscattering

Determination of concentration profile in thin metallic films: Applications and limitations of He+ backscattering

Thin Solid Films, 25 (1975) 431-440 © Elsevier Sequoia S.A., Lausanne--Printed in Switzerland 431 DETERMINATION OF CONCENTRATION PROFILE IN THIN MET...

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Thin Solid Films, 25 (1975) 431-440 © Elsevier Sequoia S.A., Lausanne--Printed in Switzerland

431

DETERMINATION OF CONCENTRATION PROFILE IN THIN METALLIC FILMS: APPLICATIONS AND LIMITATIONS OF He + BACKSCATTERING *

S. U. CAMPISANO, G. FOTI, F. GRASSO AND E. RIMINI Istituto di Struttura della Materia dell'Universitgt, Corso Italia, 57-195 129 Catania (Italy)

(Received October 10, 1974)

Backscattering of energetic He + ions has been applied to study the thermal behavior of metallic thin film couples. A description of the methods used to determine the surface concentration and concentration profiles of interdiffusing species is given. As applications, the activation energy and diffusion coefficient of Cu dissolved in Au thin films have been measured. The Matano surface for interdiffusing Au and Cu has been determined. This surface practically coincides with the initial Au--Cu interface. Errors in the determination of the surface concentration of mixed metallic couples have been evaluated from both a theoretical and an experimental point of view. An example of the limitations of backscattering is given in the analysis of a laterally non-uniform target.

1. INTRODUCTION

The backscattering technique has been extensively applied as an analyzing tool to investigate the kinetics of phase formation 1, the thermal behavior of metallic contacts on semiconductor substrates 2 and thin metallic film couples 3. Such extended applications have been made because the energy of backscattered particles depends on both the mass of the scattering atoms and the depth from which the backscattering event occurs 4. Mass perception is a result of recoil energy loss, similar to the well-known billiard ball problem. The depth perception results from the ion projectile energy loss in traversing the thin film. A particle of initial energy Eo, after traversing a path length t normal to the target surface, is detected at an angle 0 with an energy E1 given by t

EI(Eo,t)=KM(Eo-NSedx)-N o

t/cos 0

~ edx

(1)

o

where KM is the kinematic factor, e the stopping cross section and N the atomic density of the target atoms.

* Paper presented at the International Conference on Low Temperature Diffusion and Applications to Thin Films, Yorktown Heights, New York, U.S.A., August 12-14, 1974.

432

s . u . CAMPISANOet al.

For a very thin target the depth is simply related to the measured energy width AE1 by A E 1 = N t {KMe(Eo)+ sec 0 e(KMEo)} = tN[e]

(2)

For a mixture of atoms A and B let us define the stopping cross section per atom in the mixture as eAB= eANAB/N~Bt + eBNAB/NtAoBt

(3)

where N AB and N AB are respectively the atomic densities o f A and B atoms in the target, whose total atomic density is N'tAot B = N~AB+ N~AB. Then [e]As and [elAB will measure the energy width of the spectrum due to backscattering on A and B atoms, respectively, in a thin target o f uniform composition. The backscattering spectrum height for scattering near the surface of a pure A target is given by HA = Q aA ~1 mEII[SIAA

(4)

where SEt is the energy per channel o f the detecting system, Q the total number of incident particles, a , the Rutherford cross section and f2 the solid angle subtended by the detector. For samples containing A and B atoms the spectrum height due to backscattering on A atoms on the target surface is then given by HA s = Q aA f2 NABhE,/[S] AB = Q a A f2 NABfE1/NtAoBt[elAB

(5)

A complete derivation o f these formulae has already been described by Chu et al. in ref. 5. 2.

EVALUATION OF SURFACE CONCENTRATION

The relative atomic concentration CA = NAB/NABt of element A in a mixed A + B sample can be determined at the target surface by three different methods involving the ratio o f the spectrum heights: (a) from the ratio of the height H As o f element A to that H AB o f element B in the mixture, HA~

AB NA AB aAEe]B

°AEe]A B CA

HAB

O.B[~]AB A NBAB

( 1 _ CA)trBre]AB

(6a)

(b) from the ratio between the spectrum heights due to backscattering on A atoms in an A + B mixture and on A atoms in a pure A sample, HABI/-, 1L1A A

CA[e]A/[e] AB

(6b)

(c) from the ratio between the spectrum heights due to backscattering on B atoms in an A + B mixture and on B atoms in a pure B sample, HAB/I-I~a = ( 1 - CA) [e]~/[e]AB

(6c)

433

CONCENTRATION PROFILES IN THIN METALLIC FILMS

The first ratio for the elements in the mixture is plotted in Fig. 1 for the Cu-Au system and for two different analyzing beam energies. This ratio is a linear function ."f" . . .AIAuCulAIAuCu A, /''Cu because the ratio r^lAueutr^lAuCu t~Jcu /tgJAu does not depend on the validity of Bragg's rule (eqn. (3)). In fact an uncertainty of _ 10~o in Bragg's rule gives rise to an indetermination of __+0.1 ~o in this ratio. The second ratio HA A"cu/um is plotted in Fig. 2 for the same Cu-Au system and for three analyzing u /JaAu beam energies. This ratio depends on the validity of the assumption of Bragg's rule. In fact an uncertainty of + 5 % in eqn. (3) gives rise to an indetermination of 0.09, 0.06 and 0.03 in the gold concentration obtained for Au relative concentrations of the order of 0.75, 0.50 and 0.25 respectively. 50

I

l

I

I

I

I

I

J.O

I

I

I

I

I

I

I

~

40

x,

O.E AuCu

Hcu

20 0.4

0.2

I 0

I 2

1

/ 4

I

N,. Ncu

/

0.8

3O

1 6

I

I 8

/ '

I I0

o;j

o!2

2 0 - 2 . 5 MeV

'

d,

'

&

'

o'.~

'

AuCu Au CONCENTRATION = " AAuCu u Ntotat

Fig. 1. Calculated ratio between A u and Cu spectra heights vs. atomic density ratio NA~C"/NAc~cu. The calculated curve for 2.5 MeV He + coincides with the curve marked 2.0 MeV. Fig. 2. Calculated ratio between the gold spectrum for an Au--Cu target and a pure gold spectrum vs. gold concentration. (Energies of the incident He + ions are 1.0, 2.0 and 2.5 MeV.)

For scattering from large depths inside the target, eqn. (5) must be corrected by using the Rutherford cross section calculated for the energy just before scattering. The" local "[8], i.e. the [8] value calculated for energies just before scattering, must also be used. The energy width ~(KME) just after scattering from a layer 8t inside the target is different from the revealed energy width 6E 1. Thus another correction term arises from this factor. However, for depth profiling we use ratios between heights, so the ratio between these two 6(KME) factors is, for all practical purposes, equal to unity 6. 3. APPLICATIONS As an appfication of the above method we determined the diffusion coefficient and the activation energy for copper diffusion in gold thin films. The experiment

434

s . u . CAMPISANOet al.

was performed by evaporation, in a vacuum of 10- 6 torr, of 700 ]k of Au onto a Cu substrate. The migration of Cu atoms dissolving in Au was detected by 2.5 MeV He ÷ backscattering. From measurements of the area under the spectrum due to migrating copper atoms we measured the equivalent thickness of diffused copper for different annealing times and temperatures. The results are summarized in Fig. 3. The left-hand side shows that the amount of dissolved Cu increases linearly with the square root of the annealing time. The slope of these curves increases with increasing annealing temperature. The right-hand side shows the Arrhenius plot of these results and the resultant straight-line fit. The measured value for the activation energy is 1.05 eV and it corresponds to about one-half of that for bulk diffusion. This result confirms that thermal processes in thin films require temperatures lower than those necessary for the same reaction in a bulk sample 7, suggesting a grain boundary diffusion mechanism as the dominant process occurring in the dissolution of bulk copper in a gold thin film.

~zx~ m/280"C

Z

/.

"

~o w

10-m

1'o T IM E(rnin~)

,'s

1.8

20 22 l/r (10-3"K~)

Fig. 3. Left-hand side: thickness of dissolved Cu in an Au thin film v s . the square root of time for different annealing temperatures. Right-hand side: Arrhenius plot of these data and the straight-line fit.

Another application of backscattering is the determination of the interdiffusion coefficient from a knowledge of the concentration profile and the consequent identification of the Matano surface 8. One of the methods previously used for the determination of concentration profiles consists of the activation by neutron irradiation of one of the constituents of the couple. Subsequently layers are stripped and the residual activity measured. This method, besides being a destructive one, requires the capability to strip layers by chemical, electrochemical or mechanical means. Moreover its application requires a good calibration to measure the thickness of the stripped layer. However, backscattering requires only the know-

CONCENTRATION PROFILES IN THIN METALLIC FILMS

435

ledge of the energy loss experienced by the incident particle. Figure 4 shows the backscattering spectrum of 2.5 MeV He + incident on a Cu-Au couple before and after 30 min annealing at 230 °C. The energy spectrum after annealing shows that Cu migrates into Au and vice versa. The concentration profile obtained by using eqn. 6(a) is shown in Fig. 5. The initial Cu-Au interface practically coincides with that identified by the equation C2

(7)

t dC = 0 Cz

where C is the atomic concentration. The identification of this plane allows us to calculate the interdiffusion coefficient through C

1 (dCl -1I

tdC

(8)

C~

where h is the annealing time. Equations (7) and (8) are the well-known MatanoBoltzmann solution of the diffusion equation for interdiffusing species with a concentration-dependent diffusion coefficient s. For this case the interdiffusion coefficient does not depend on the Au concentration, at least in the concentration range shown by the experimental points of Fig. 5 and within the limits of the approximation involved in assuming eqn. (8) to be valid for the case under investigation. 4. EVALUATION OF ERRORS

The surface concentration of an element A in a mixture can be evaluated with an accuracy which depends mainly on the experimental conditions. From a theoretical point of view the indetermination in surface concentration depends on the concentration itself and on the accuracy in the measured experimental

2.~ ~

25M~V-He at 230°¢

i__

7

z

7

": Au

"

".1

::D

1

O U

J

i

i

: l

i il

i

'

'I

t

f""

J

CHANNELS

'

!

J

Fig. 4. Backscattering energy spectra for 2.5 MeV He + incident on a C u - A u sample: left-hand side, unannealed; fight-hand side, after 30 min annealing at 230 °C.

436

s . u . CAMPISANO et al.

heights. Let us call r and r' the height ratios of eqns. 6(a) and 6(b) respectively. Taking the derivative of the logarithm of these ratios we obtain AC A

Ar C---~-= (1 - CA) --r

ACA--{CAA1

(9a)

CA[KA(gA--eB)E°'4-secO(13A--gB)K^E°]t-I[/3] AB X Ar'r__;_

(9b)

where ACA/CA is the uncertainty in the obtained concentration due to an uncertainty Ar/r or Ar'/r'in the measured experimental ratio. The ratios (ACA/CA)/(Ar/r) and (ACA/CA)/(Ar'/r') are shown in Fig. 6 for 2.0 MeV He + impinging on a C u + A u mixed sample. The relative uncertainty in the obtained concentration is equal to the uncertainty in the measured height ratio for zero gold concentration and it decreases or increases with increasing Au concentration for the ratios 6(a) and 6(b), respectively. There are several possible sources of experimental error in the measured height ratio which depend on the case under investigation. Typical spectra are shown in Fig. 7 for the Cu-Au system with an Au relative concentration of the order of 0.5. The upper part shows the spectrum obtained by backscattering 1.0 MeV He + ions. In this case there is an overlap between the signals due to backscattering on the Cu and Au atoms and the height of the Cu spectrum must be obtained as a difference between the extrapolated Au signal and the extrapolated signal due to overlap between the Au and Cu spectra. Because of the difference in the Rutherford cross sections, the small Cu spectrum height is determined from the difference between two large numbers. This procedure can lead to serious errors. An error of 1 ~ in the slope of the fit of the

W

AC

2.5 l~eV- He" after ~ m i n

at 230°C:

o Cu profile

z o

AAu

profile

o

[]

i- 1 <[ Q:

o

n

II

Cu

Ld

U Z 0 (..)







• I

0

Au I I

THICKNESS

(108A)

50 Au (%)

100

Fig. 5. Concentration profile for the data of Fig. 4 obtained using eqn. 6(a). The Matano surface coincides with the original Au-Cu interface. Fig. 6. Relative uncertainty in concentration for unity uncertainty in the measured height ratios Au concentration in the Cu-Au system. (2.0 MeV He ÷ .)

vs.

CONCENTRATION PROFILES IN THIN METALLIC FILMS r

1.0 MeV- He+

Co~ 0

800

I

437

i

""....... " " -

. . . . . . . ('

5~

".~.

4OO

~•..oo•..o•.~o.-~o°*

:::L

260

' 2.5

300

460

I

MeV - He"

"~

I

4OO x5 200

0

.....1

300

, ""-"'("

J

400

,

CHANNEL

Fig. 7. Energy spectra obtained by backscattering of 1.0 MeV (upper part) and 2.5 MeV (lower part) He + ions. The target is a C u - A u evaporated thin film with CAu = 0.55.

plateaux causes an error of 10~ in the measured height of the Cu spectrum. The lower part of Fig. 7 shows the spectrum of the same target but obtained with 2.5 MeV He ÷ ions. In this case, because of the lower energy loss experienced by the incident particles, the Cu and Au signals are well separated. Errors can arise from the evaluation of the tail in the energy range between the high energy edge of the Cu signal and the low energy edge of the Au signal. In the evaluation of errors which can affect the measure of the ratio HAB/H~,, one should pay attention also to differences in dead time and in secondary electron emission during the two different measurements• An experimental determination of surface concentration, with relative errors, is shown in Fig. 8. Targets were prepared by simultaneous evaporation, under 10-6 torr vacuum, of mixtures of copper and gold whose relative weights were chosen to get relative atomic concentrations of gold of the order of 0.25, 0.50 and 0.75. The samples were then annealed in an argon atmosphere for 30 min at 300 °C to avoid concentration gradients. Analysis was performed using 1.0, 2.0 and 2.5 MeV He ÷ backscattering. The experimental error decreases with increasing beam energy, in agreement with the considerations described above. The absolute errors for the 2.0 MeV analysis range from 0.01 to 0.06 in relative atomic concentration of gold. These errors have been evaluated through eqns. (9a) and (9b), considering experimental uncertainties. 5. LIMITATIONS IN APPLICATION

Limitations in the application of the backscattering technique to analyze mixed samples are essentially twofold. They arise from the difficulty in resolving spectra due to backscattering on atoms whose atomic masses are close to each other and from the lack of lateral resolution•

438

s.u. CAMPISANOet al. i

+ He - Au + Cu

HA~c~

i system

A~

0.85

A

- -

{ t;{

HAw H AuCu A. •

o

0.75

A.c~ Hcu A~c~ H c. - cu

Hc u

I

i

0.6C z

2

~0.5C ,,.) Z o

I

i

i

l

o~c

0,2C [

z'o

LO

BEAM

ENERGY

3.0

[MeV]

Fig. 8. Experimental determination of the Au surface concentration in Au-Cu evaporated thin films for three different gold concentrations and analyzing He + beam energies. Error bars have been calculated through eqns. (9a) and (9b) and by evaluation of experimental uncertainties.

If the target under investigation is composed of two atomic species whose atomic masses are close to each other, the difference in the kinematic factors for He + backscattering is very small. It is practically impossible to distinguish between signals due to backscattering on these two different atoms. One could increase the difference in kinematic factors by increasing the mass of the ion projectile, e.g. by using a carbon beam. Heavy ion accelerators, however, are not available in most laboratories. For the second limitation, a misinterpretation of backscattering spectra can arise from the analysis of laterally non-uniform targets. An example is shown in Fig. 9. This target was prepared by vacuum deposition of a Pb layer onto a silicon substrate, followed by annealing for 10 min at 275 °C. The scanning electron microscope image of Fig. 9 shows that after annealing the Pb layer condenses in small islands, leaving free a large portion of underlying silicon. The corresponding backscattering spectrum is shown in Fig. 10. The spectrum obtained with 2.0 MeV He ÷ backscattering from the unannealed sample shows a well-defined peak due to Pb atoms and a plateau due to the thick silicon substrate. The spectrum after annealing shows a strong decrease in the Pb yield, which now overlaps the Si spectrum. This occurs because a fraction of the beam hits the Pb atoms while the remaining beam hits the silicon atoms on the surface. If one supposes that the sample is laterally uniform and hence that this spectrum

CONCENTRATION PROFILES IN THIN METALLIC FILMS

439

d

.T.2 ¢." , ' - - . . , -.'..D

.° d,

t

"~

-

.~ .~

.

"..'.we6a Fig. 9. Scanning electron micrograph o f a Pb layer on a Si substrate after 10 min annealing at 275 °C. The average lateral dimension of the Pb islands is 2 ~tm.

is due to the diffusion of Pb in Si one can obtain a fictitious concentration profile. The "profile" can be obtained to very large depths by analyzing with a particle which experiences a lower energy loss than s-particles. Figure 11 shows the spectrum obtained with 1.0 MeV H + incident on the same target. The broken line represents the calculation of the spectrum height as given in ref. 6. Triangles show the obtained yield due to Pb atoms. By using eqns. (6) this yield can be reduced to a concentration "profile ", and this "profile" fits very well the function 2 C(t)

l+ t

~0 = erf ( ~ ) +

I- t

erf(~)

(lo)

which is the concentration profile after an annealing time h of a diffusion layer with initial thickness l. This agreement with the theoretical curve can give rise to a misunderstanding of the true composition of the target, i.e. lateral non-uniformities (in this case island formation) can give a false impression of diffusion profiles. 6.

SUMMARY AND CONCLUSIONS

Backscattering has been applied to obtain concentration profiles, enabling us to measure the activation energy and the diffusion coefficient of copper in a gold thin film. The Matano surface for interdiffusing Cu and Au thin films has been identified. The uncertainty in the measured surface concentration has been estimated from both a theoretical and an experimental point of view. For the Au--Cu system this uncertainty ranges from 0.01 to 0.06 in relative atomic concentration. A limitation in the application of the backscattering technique due to laterally non-uniform targets has been described. In conclusion, backscattering is a powerful tool to investigate thermal processes in thin film metallurgy. Its application is simpler than earlier methods used to

al.

S. U. CAMPISANO et

440 i

i

S~.Pb - 2,0 MeV - He* "'~.%. "-.,%. after lOmin at 275%

,._.~h x

l

~Si

r

x101

• Si. Pb

H ° 1.0 MeV

Pb y ed

vcalcula ed

c~

~'•"~'.'~'-'--~.,.,...,,.~

uJ 10 ~

li li

~,0

.d

>-

4

4

,~iF"

• V

--

I

v

>v

i~rg~ n

,

451

Ill

CHANNE

.,~-

LS

I

v vv

v v .-t v • I 0.6

I L

ENERGY

~u t.0 (MeV)

Fig. 10. Backscatteringenergyspectraf~rthesamp~esh~wninFig.9bef~re~)andafter~)annea~ing. After annealing the Pb yield is decreased by a factor 10 and the high energy edge of the Si spectrum is shifted to the energy corresponding to surface backscattering. Fig. 11. Energy spectrum obtained by 1.0 MeV H ÷ backscattering on the same sample as that shown in Fig. 9. Triangles show the Pb contribution to the spectrum calculated using eqns. (6a) and (6b), modified for depth profiling.

study concentration profiles and its results can reach an acceptable degree of accuracy. A complementary technique, such as scanning electron microscopy, must be used to avoid the misinterpretation which can arise from analysis of laterally non-uniform targets. ACKNOWLEDGMENTS

The authors are particularly indebted to Professor J. W. Mayer for clarifying discussions and comments. Thanks are due to J. M. Harris who performed the SEM observations. REFERENCES

1 S.U. Campisano, G. Foti, F. Grasso, J. W. Mayer and E. Rimini, in T. S. Picraux, E. P. EerNisse and F. L. Vook (eds.), Application of Ion Beams to Metals, Plenum Press, New York, 1974, p. 159. 2 H. Kraiitle, M.-A. Nicolet and J. W. Mayer, J. Appl. Phys., 44 (1973) 3851. 3 S.U. Campisano, G. Foti, F. Grasso and E. Rimini, Thin Solid Films, 19 (1973) 339. 4 W . K . Chu, J. W. Mayer, M.-A. Nicolet, T. M. Buck, G. Amsel and F. Eisen, Thin Solid Films, 17 (1973) 1. 5 W . K . Chu, J. W. Mayer, S. U. Campisano and E. Rimini, in J. W. Mayer and E. Rimini (eds.), Catania Working Data, Backscattering Analysis, to be published. 6 D.K. Brice, Thin Solid Films, 19 (1973) 121. 7 J.W. Mayer and K. N. Tu, J. Vac. Sci. Technol., 11 (1974) 86. 8 Y. Adda and J. Philibert, La Diffusion dans les Solides, Vol. I, Presses Universitaires de France, Paris, 1966, p. 17.