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Measurement of small diffusion coefficients using ion-beam-sputtering as a microsectioning technique
Journal of Nuclear Materials 69 & 70 (1978) 545-548 0 North-Holland Publishing Company
MEASUREMENTOFSMALLDIFFUSIONCOEFFICIENTSUSINGION-BEAM-SPUTTERING ASAM~CROSECT~ONIN~TECHNI~UE H. MEHRER, K. MAIER, G. HETTICH, H.J. MAYER and G. REIN Institut fi’ir theoretische und angewandte Physik der Universitiit Stuttgart and Max-Planck-lnstitut fiir Metallforschung, Institut fiir Physik, Stuttgart, W. Germany
1. Introduction The most precise diffusion measurements in solids are commonly made using a radiotracer method in combination with an appropriate serial sectioning technique which profiles the tracer redistribution within the host lattice. When mechanical sectioning techniques are used the measurements are restricted to diffusion coefficients R Z 10-r* cm*/s and hence to temperatures not too far below the melting temperature. However, diffusion in low-temperature phases of metals, in non-polymorphic metals at low temperatures, and in elementary and compound semiconductors, for example, may imply smaller diffusivities. Reliable data in these cases would be extremely desirable from scientific and tec~olo~c~ considerations. Such measurements necessitate serial sectioning techniques on a submicron level. For some materials chemical or electrochemical techniques are available and have been applied successfully to various diffusion studies in metals (see, e.g. [l--S]). However, their main disadvantage is that they are specific to certain materials. Fortunately, in recent years sputtering methods, which had been already used for me~urements of implantation profiles (see, e.g. [6]), have been adopted to tracer diffusion studies in solids * . They permit material removal from almost all materials including metals, alloys and semiconductors. Two variants of the sputter-sectioning methods for depth-profiling have been developed. Gupta (see, e.g. [8]) utilizes radiofrequency Ar-bac~puttering in a glow discharge whereas
* In the early 1950s 171it was proposed that sputtering could be used in diffusion studies. However, only the recent improvements of the experimental technique permitted successful applications.
Maier and Schtile [9] use a separate ion-in. The latter method permits sputtering under well-controlled conditions with respect to ion energy and angle of incidence. It has already been used for self-diffusion studies in Cu [lo] and Ni [ 1 l] with good success. We developed a sputtering apparatus which is an improved version of the one described in [9]. Its main features are discussed in section 2. Some results of diffusion studies obtained with the ion-beam sputter sectioning technique are reported in section 3.
2. Microsectioning
by ion-beam-sputtering
A schematic representation of the ion-beam-sputtering apparatus is shown in fig. 1. The whole assembly is inside a vacuum chamber not shown in the figure. The ion-gun is a modified duoplasmatron [i 21 which is operated with argon. It produces a fairly in-
I specimen holder frotatingl
collec
tiffs -device
Fig. 1. Arrangement of ion-gun, specimen and collector-device in the ion-beam-sputtering apparatus. 545
546
H. Mehrer et al. / measurement
tense beam of Ar-ions when a fairly low acceleration voltage is applied between specimen and gun. Typically the beam current is about 1 mA for a voltage of SO0 V. The beam hits the specimen at an oblique angle which is equal to the angle of maximum sputtering yield [ 131. The specimen itself is rotated in order to prevent it from developing a surface relief during the sputtering process. The off-sputtered material is preferentially emitted in the forward direction. A constant fraction (about 80%) is collected on a collector foil which can be moved within the collector device like a fnm in a camera. Serial sectioning of the whole profile is performed in one pump-down. One section is taken by sputtering for a certain period - typically a few minutes. By moving the collector foil step by step without interruption of the ion-beam section after sectin can be collected. The section thicknesses are determined from the sputtering-rate and from the individual sputtering times. The sputtering-rate is kept constant by controlling the beam current and beam voltage. In each experiment the sputterin~rate is obtained from the total sputtering time and the total removed thickness. The latter is measured with the help of interferometric microscopy by analysing the step in an interference pattern which occurs between a protected and a sectioned part of the diffusion surface. Typical sputtering-rates are between 30 and 300 A/min depending on the beam parameters and on the material. A successful serial sectioning experiment demands that the layers removed are parallel to the initial surface. The requirement of constant sputtering-rate over the whole diffusion surface has been checked and was found to be satisfacto~.
3. Applications
of small ~if~~s~on coefficients
Fig. 2. Penetration profiles for iron self-diffusion. Each division on the abscissa is: Temperature [“Cl 144 744 744 694 664.5 625 625 597
Value of one division
[A21 -_-______ 1.9 11.5 11.5 6.2 1.1 8.6 1.0 4.0
x x x x x x x x
lo6 lo6 io6 10’ lo6 lo5 lo6 lo5
3.1, Selfidiffusion in ferromagnetic iron From the viewpoint of classical diffusion studies ferromagnetic iron constitutes a “low-temperature” phase, since at the Curie-temperature (!Z’c= 770°C) the self-diffusion coefficient is about IO-r2 cm2is. However, diffusion me~urements can be extended to L)values as low as 10-i’ cm2 /s within reasonable diffusion times when sputter-se~tion~g is used. In fig. 2 diffusion profiles which we obtained for diffusion of
59 Fe in pure iron are shown in a plot of In A versus X2 (A = activity, X = distance from the initial surface). In favourable cases the profiles are gaussian over more than three orders of magnitude in activity drop. The diffusion coefficients deduced from these profiles are plotted in fig. 3 together with previous studies of elf-diffusion in a-iron [14-l 6f. The temperature dependence of the self-diffusion coefficient in ferromagnetic iron does not obey an Arrhenius law. The devia-
H. Mehrer et al. /Measurement 800
YlU
10‘” -
7#
Tc
I
10”
Tc=770
of small diffusion
T PCI-
I
I
Self-diffusion “4
500
600
’
?% k
in a- iron 0 Borgand Birchenall
(1966) Buffington, Hirano and Cahcn(l961) Walter and Peterson 11968) Mrhrer. Maier, Hcttich, Mayrr and Rein (1976)
0
1
0 I
I
.
1
1
para= +--I magnetic I-
10-l
lo-‘8
547
coefficients
ferromagnetic
.
I
:
I
9
I I
. I
I
I
10
11
12 -
lo’/
T
I l
13
IL
CK’I
Fig. 3. Arrhenius plot of self-diffusion in or-iron.
tions from an Arrhenius equation are correlated to the spontaneous magnetization in a way which is in reasonable agreement with an equation proposed in [ 171. A detailed discussion is given in [26].
3.3. Diffusion in platinum Preliminary results for the diffusion of 19’Pt and ‘99Au in platinum have been obtained between 750
Self-diffusion in a valence crystal like silicon is a much slower process than self-diffusion in metals. The diffusivity at the melting point of Si is only about lO_” cm’/s. Consequently a microsectioning technique is a prerequisite for radiotracer measurements even in the high-temperature region. We used our method, which also permits fairly rapid microprofiling, in combination with the only easily obtainable isotope 31 Si with a half-life of 2.6 h. The data obtained for intrinsic silicon are plotted in fig. 4 in an Arrhenius diagram. A comparison with literature data of silicon self-diffusion [ 18-201 shows that our data cover the widest temperature range so far investigated in a unique study. For a discussion we refer to
WI
r,= 1~10OC,300 I 8
lo.”
3.2. Self-diffusion in silicon
I -l ?
0
10-12_
TlOCl 1200
Reart(1966) v Ghoshtagorefl9661 0 Masters (1.Fairfield _ f 1967) + Sandem 0. Dobson (1974) Mayer, Mehrer and Maier 11976) -
0 * 0 “a
I
I
0
“*
5 lo-= ,L. I0
1000
1100
I
l
0 e %A 8
10-14-
(1 D = 1460exp(-5~$m%-1 kT
’ \
Ki’S-
+
+ +
X+66-
I 0.6 Fig. 4. Arrhenius
,
I
,
1
0.8 0.75 lo’/ T CK-'I plot of silicon self-diffusion. 0,65
0.7
_
H. Mehrer et al. /Measurement
548 TPCI +
1200
1500
1000
a-
t
g
10-g
lo-,l_
lo-‘J-
I
4 %
%
x
1
8
(Au- impurjty dilfuston Mrhrrr, Mairr, Hettich, and Rein 119761 t
01 Mayer
Q 0
.
0
l.
0 0 .*O .O
10J5-
.
0
0
l*.
lo-‘6lo-‘7
600
in platinum
Diffusion
* x *
Self -diffusron 8 o KIdson and Ross (19581 8 x Cattoneo. Grrmognol, and 8 Grasso 119621 0 Million and Kucrro 119731 l
lo-‘d-
900
“”
loqo 10‘”
800
I
5
6
7
8
9 -
Fig. 5. Arrhenius
plot of diffusion
cl
10 10L/T
11
IK”]
in platinum.
and 900°C. The data are shown in fig. 5 together with previous high-temperature studies of platinum selfdiffusion [23-251. Wheu an Arrhenius equation is fitted to our self-diffusion data a pre-exponential factor Do = 0.05 cm’/s and an activation energy Q = 2.67 eV can be derived. A full account of the results on platinum will be given in [27].
of small diffusion coefficients [3] N.Q. Lam, S.J. Rothman, H. Mehrer and L.J. Nowicki, Phys. Status Solidi 57 (1973) 225. [4] J.G.E.M. Backus, H. Bakker and H. Mehrer, Phys Status Solidi (b) 64 (1974) 151. (51 J. Pelleg, Phil. Mag. 29 (1974) 383. (61 H. Lutz and R. Sizmann, Z. Naturforsch. 19a (1964) 1079. [7] T.F. Fisher and C.E. Weber, J. Appl. Phys. 23 (1952) 181. [8] D. Gupta, Thin Solid Films 25 (1975) 231. [9] K. Maier and W. Schiile, Euratom Report EUR 5234 d (1974). [lo] K. Maier, C. Bassani, and W. Schiile, Phys. Lett. A44 (1973) 539. K. Maier, Phys. Status Solidi, in press. [ 1 l] K. Maier, H. Mehrer, E. Lessmann, and W. Schiile, Phys. Status Solidi (b) 78 (1976) 689. (121 K.L. Chopra and M.R. Randlett, Rev. Sci. Instrum. 38 (1967) 8. [13] H. Oechsner, Z. Phys. 261 (1973) 37. [14] F.S. Buffington, K. Hirano and M. Cohen, Acta Met. 9 (1961) 434. [15] R.J. Borg and C.E. Birchenall, Trans. Met. Sot. AIME 218 (1960) 980. [16] C.M. Walter and N.L. Peterson, Phys. Rev. 178 (1969) 178. [17] L. Ruth, D.R. Sain, H.L. Yeh, and L.A. Girifalco, J. Phys. Chem. Solids 37 (1976) 649. [18] R.F. Peart, Phys. Status Solidi 15 (1966) K 119. [19] J.M. Fairfield and B.J. Masters, J. Appl. Phys. 38 (1967) 3148. [20] R.N. Ghoshtagore, Phys. Rev. Lett. 16 (1966) 890. [21]
I.R. Sanders
and P.S. Dobson,
J. Mater. Sci. 9 (1974)
1987.
Acknowledgements
[ 221 H.J. Mayer, H. Mehrer and K. Maier, in: Radiation
This work has been supported by the Deutsche Forschungsgemeinschaft. Support from the GfK Karlsruhe which produced the isotopes 31Si and 197Pt by neutron-activation is also acknowledged.
[23]
Effects in Semiconductors 1976, Eds. N.B. Urli and J.W. Corbett (Institute of Physics Conf. Series No. 31, Bristol and London, 1977) p. 186. G.V. Kidson and R. Ross, Proc. Int. Conf. on Radioisotopes gamon
[24]
References [I] R.E. Pawel and T.S. Lundy, Acta Met. 13 (1965) 345. [2] W. Rupp, U. Ermert and R. Sizmann, Solidi 33 (1969) 509.
Phys. Status
in Science
F. Cattaneo, (1962)
Research,
Paris, vol. 1 (Oxford,
Per-
Press, 1958) p. 185. E. Germagnoli
and F. Grasso,
Phil. Mag. 7
1373.
[25] B. Million and J. Kucera, Kovove Mater. 11 (1973) 300. [ 261 G. Hettich, H. Mehrer and K. Maier, Scripta Metallurgica 11 (1977) 795. [27] G. Rein, H. Mehrer, and K. Maier, Phys. Status Solidi, in press.
MEASUREMENTOFSMALLDIFFUSIONCOEFFICIENTSUSINGION-BEAM-SPUTTERING ASAM~CROSECT~ONIN~TECHNI~UE H. MEHRER, K. MAIER, G. HETTICH, H.J. MAYER and G. REIN Institut fi’ir theoretische und angewandte Physik der Universitiit Stuttgart and Max-Planck-lnstitut fiir Metallforschung, Institut fiir Physik, Stuttgart, W. Germany
1. Introduction The most precise diffusion measurements in solids are commonly made using a radiotracer method in combination with an appropriate serial sectioning technique which profiles the tracer redistribution within the host lattice. When mechanical sectioning techniques are used the measurements are restricted to diffusion coefficients R Z 10-r* cm*/s and hence to temperatures not too far below the melting temperature. However, diffusion in low-temperature phases of metals, in non-polymorphic metals at low temperatures, and in elementary and compound semiconductors, for example, may imply smaller diffusivities. Reliable data in these cases would be extremely desirable from scientific and tec~olo~c~ considerations. Such measurements necessitate serial sectioning techniques on a submicron level. For some materials chemical or electrochemical techniques are available and have been applied successfully to various diffusion studies in metals (see, e.g. [l--S]). However, their main disadvantage is that they are specific to certain materials. Fortunately, in recent years sputtering methods, which had been already used for me~urements of implantation profiles (see, e.g. [6]), have been adopted to tracer diffusion studies in solids * . They permit material removal from almost all materials including metals, alloys and semiconductors. Two variants of the sputter-sectioning methods for depth-profiling have been developed. Gupta (see, e.g. [8]) utilizes radiofrequency Ar-bac~puttering in a glow discharge whereas
* In the early 1950s 171it was proposed that sputtering could be used in diffusion studies. However, only the recent improvements of the experimental technique permitted successful applications.
Maier and Schtile [9] use a separate ion-in. The latter method permits sputtering under well-controlled conditions with respect to ion energy and angle of incidence. It has already been used for self-diffusion studies in Cu [lo] and Ni [ 1 l] with good success. We developed a sputtering apparatus which is an improved version of the one described in [9]. Its main features are discussed in section 2. Some results of diffusion studies obtained with the ion-beam sputter sectioning technique are reported in section 3.
2. Microsectioning
by ion-beam-sputtering
A schematic representation of the ion-beam-sputtering apparatus is shown in fig. 1. The whole assembly is inside a vacuum chamber not shown in the figure. The ion-gun is a modified duoplasmatron [i 21 which is operated with argon. It produces a fairly in-
I specimen holder frotatingl
collec
tiffs -device
Fig. 1. Arrangement of ion-gun, specimen and collector-device in the ion-beam-sputtering apparatus. 545
546
H. Mehrer et al. / measurement
tense beam of Ar-ions when a fairly low acceleration voltage is applied between specimen and gun. Typically the beam current is about 1 mA for a voltage of SO0 V. The beam hits the specimen at an oblique angle which is equal to the angle of maximum sputtering yield [ 131. The specimen itself is rotated in order to prevent it from developing a surface relief during the sputtering process. The off-sputtered material is preferentially emitted in the forward direction. A constant fraction (about 80%) is collected on a collector foil which can be moved within the collector device like a fnm in a camera. Serial sectioning of the whole profile is performed in one pump-down. One section is taken by sputtering for a certain period - typically a few minutes. By moving the collector foil step by step without interruption of the ion-beam section after sectin can be collected. The section thicknesses are determined from the sputtering-rate and from the individual sputtering times. The sputtering-rate is kept constant by controlling the beam current and beam voltage. In each experiment the sputterin~rate is obtained from the total sputtering time and the total removed thickness. The latter is measured with the help of interferometric microscopy by analysing the step in an interference pattern which occurs between a protected and a sectioned part of the diffusion surface. Typical sputtering-rates are between 30 and 300 A/min depending on the beam parameters and on the material. A successful serial sectioning experiment demands that the layers removed are parallel to the initial surface. The requirement of constant sputtering-rate over the whole diffusion surface has been checked and was found to be satisfacto~.
3. Applications
of small ~if~~s~on coefficients
Fig. 2. Penetration profiles for iron self-diffusion. Each division on the abscissa is: Temperature [“Cl 144 744 744 694 664.5 625 625 597
Value of one division
[A21 -_-______ 1.9 11.5 11.5 6.2 1.1 8.6 1.0 4.0
x x x x x x x x
lo6 lo6 io6 10’ lo6 lo5 lo6 lo5
3.1, Selfidiffusion in ferromagnetic iron From the viewpoint of classical diffusion studies ferromagnetic iron constitutes a “low-temperature” phase, since at the Curie-temperature (!Z’c= 770°C) the self-diffusion coefficient is about IO-r2 cm2is. However, diffusion me~urements can be extended to L)values as low as 10-i’ cm2 /s within reasonable diffusion times when sputter-se~tion~g is used. In fig. 2 diffusion profiles which we obtained for diffusion of
59 Fe in pure iron are shown in a plot of In A versus X2 (A = activity, X = distance from the initial surface). In favourable cases the profiles are gaussian over more than three orders of magnitude in activity drop. The diffusion coefficients deduced from these profiles are plotted in fig. 3 together with previous studies of elf-diffusion in a-iron [14-l 6f. The temperature dependence of the self-diffusion coefficient in ferromagnetic iron does not obey an Arrhenius law. The devia-
H. Mehrer et al. /Measurement 800
YlU
10‘” -
7#
Tc
I
10”
Tc=770
of small diffusion
T PCI-
I
I
Self-diffusion “4
500
600
’
?% k
in a- iron 0 Borgand Birchenall
(1966) Buffington, Hirano and Cahcn(l961) Walter and Peterson 11968) Mrhrer. Maier, Hcttich, Mayrr and Rein (1976)
0
1
0 I
I
.
1
1
para= +--I magnetic I-
10-l
lo-‘8
547
coefficients
ferromagnetic
.
I
:
I
9
I I
. I
I
I
10
11
12 -
lo’/
T
I l
13
IL
CK’I
Fig. 3. Arrhenius plot of self-diffusion in or-iron.
tions from an Arrhenius equation are correlated to the spontaneous magnetization in a way which is in reasonable agreement with an equation proposed in [ 171. A detailed discussion is given in [26].
3.3. Diffusion in platinum Preliminary results for the diffusion of 19’Pt and ‘99Au in platinum have been obtained between 750
Self-diffusion in a valence crystal like silicon is a much slower process than self-diffusion in metals. The diffusivity at the melting point of Si is only about lO_” cm’/s. Consequently a microsectioning technique is a prerequisite for radiotracer measurements even in the high-temperature region. We used our method, which also permits fairly rapid microprofiling, in combination with the only easily obtainable isotope 31 Si with a half-life of 2.6 h. The data obtained for intrinsic silicon are plotted in fig. 4 in an Arrhenius diagram. A comparison with literature data of silicon self-diffusion [ 18-201 shows that our data cover the widest temperature range so far investigated in a unique study. For a discussion we refer to
WI
r,= 1~10OC,300 I 8
lo.”
3.2. Self-diffusion in silicon
I -l ?
0
10-12_
TlOCl 1200
Reart(1966) v Ghoshtagorefl9661 0 Masters (1.Fairfield _ f 1967) + Sandem 0. Dobson (1974) Mayer, Mehrer and Maier 11976) -
0 * 0 “a
I
I
0
“*
5 lo-= ,L. I0
1000
1100
I
l
0 e %A 8
10-14-
(1 D = 1460exp(-5~$m%-1 kT
’ \
Ki’S-
+
+ +
X+66-
I 0.6 Fig. 4. Arrhenius
,
I
,
1
0.8 0.75 lo’/ T CK-'I plot of silicon self-diffusion. 0,65
0.7
_
H. Mehrer et al. /Measurement
548 TPCI +
1200
1500
1000
a-
t
g
10-g
lo-,l_
lo-‘J-
I
4 %
%
x
1
8
(Au- impurjty dilfuston Mrhrrr, Mairr, Hettich, and Rein 119761 t
01 Mayer
Q 0
.
0
l.
0 0 .*O .O
10J5-
.
0
0
l*.
lo-‘6lo-‘7
600
in platinum
Diffusion
* x *
Self -diffusron 8 o KIdson and Ross (19581 8 x Cattoneo. Grrmognol, and 8 Grasso 119621 0 Million and Kucrro 119731 l
lo-‘d-
900
“”
loqo 10‘”
800
I
5
6
7
8
9 -
Fig. 5. Arrhenius
plot of diffusion
cl
10 10L/T
11
IK”]
in platinum.
and 900°C. The data are shown in fig. 5 together with previous high-temperature studies of platinum selfdiffusion [23-251. Wheu an Arrhenius equation is fitted to our self-diffusion data a pre-exponential factor Do = 0.05 cm’/s and an activation energy Q = 2.67 eV can be derived. A full account of the results on platinum will be given in [27].
of small diffusion coefficients [3] N.Q. Lam, S.J. Rothman, H. Mehrer and L.J. Nowicki, Phys. Status Solidi 57 (1973) 225. [4] J.G.E.M. Backus, H. Bakker and H. Mehrer, Phys Status Solidi (b) 64 (1974) 151. (51 J. Pelleg, Phil. Mag. 29 (1974) 383. (61 H. Lutz and R. Sizmann, Z. Naturforsch. 19a (1964) 1079. [7] T.F. Fisher and C.E. Weber, J. Appl. Phys. 23 (1952) 181. [8] D. Gupta, Thin Solid Films 25 (1975) 231. [9] K. Maier and W. Schiile, Euratom Report EUR 5234 d (1974). [lo] K. Maier, C. Bassani, and W. Schiile, Phys. Lett. A44 (1973) 539. K. Maier, Phys. Status Solidi, in press. [ 1 l] K. Maier, H. Mehrer, E. Lessmann, and W. Schiile, Phys. Status Solidi (b) 78 (1976) 689. (121 K.L. Chopra and M.R. Randlett, Rev. Sci. Instrum. 38 (1967) 8. [13] H. Oechsner, Z. Phys. 261 (1973) 37. [14] F.S. Buffington, K. Hirano and M. Cohen, Acta Met. 9 (1961) 434. [15] R.J. Borg and C.E. Birchenall, Trans. Met. Sot. AIME 218 (1960) 980. [16] C.M. Walter and N.L. Peterson, Phys. Rev. 178 (1969) 178. [17] L. Ruth, D.R. Sain, H.L. Yeh, and L.A. Girifalco, J. Phys. Chem. Solids 37 (1976) 649. [18] R.F. Peart, Phys. Status Solidi 15 (1966) K 119. [19] J.M. Fairfield and B.J. Masters, J. Appl. Phys. 38 (1967) 3148. [20] R.N. Ghoshtagore, Phys. Rev. Lett. 16 (1966) 890. [21]
I.R. Sanders
and P.S. Dobson,
J. Mater. Sci. 9 (1974)
1987.
Acknowledgements
[ 221 H.J. Mayer, H. Mehrer and K. Maier, in: Radiation
This work has been supported by the Deutsche Forschungsgemeinschaft. Support from the GfK Karlsruhe which produced the isotopes 31Si and 197Pt by neutron-activation is also acknowledged.
[23]
Effects in Semiconductors 1976, Eds. N.B. Urli and J.W. Corbett (Institute of Physics Conf. Series No. 31, Bristol and London, 1977) p. 186. G.V. Kidson and R. Ross, Proc. Int. Conf. on Radioisotopes gamon
[24]
References [I] R.E. Pawel and T.S. Lundy, Acta Met. 13 (1965) 345. [2] W. Rupp, U. Ermert and R. Sizmann, Solidi 33 (1969) 509.
Phys. Status
in Science
F. Cattaneo, (1962)
Research,
Paris, vol. 1 (Oxford,
Per-
Press, 1958) p. 185. E. Germagnoli
and F. Grasso,
Phil. Mag. 7
1373.
[25] B. Million and J. Kucera, Kovove Mater. 11 (1973) 300. [ 261 G. Hettich, H. Mehrer and K. Maier, Scripta Metallurgica 11 (1977) 795. [27] G. Rein, H. Mehrer, and K. Maier, Phys. Status Solidi, in press.