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Diffusion of gold in relaxed Si–Ge epi-layers
Physica B 273}274 (1999) 598}602
Di!usion of gold in relaxed Si}Ge epi-layers Roland Fischer!, Werner F.J. Frank!,*, Klara Lyutovich" !Max-Planck-Institut fu( r Metallforschung, Heisenbergstra}e 1, D-70569 Stuttgart, Germany "Universita( t Stuttgart, Institut fu( r Halbleitertechnik, Stuttgart, Germany
Abstract The di!usion of implanted 195Au in relaxed, low-dislocation-density Si Ge epi-layers has been measured as a 1~y y function of temperature (700}9503C) and composition (0)y)0.24) by means of a radiotracer technique, where serial sectioning was done by precision grinding. In all cases, the di!usion takes place by the kick-out mechanism, which is self-interstitial-controlled at low Ge contents, low temperatures, or close to the epi-layer surface, but gold-interstitialcontrolled otherwise. An interpretation is presented in which a novel mechanism of alloy-retarded substitutional} interstitial di!usion plays a major ro( le. ( 1999 Elsevier Science B.V. All rights reserved. Keywords: Si}Ge epi-layers; Di!usion of gold; Radiotracer technique; Kick-out mechanism
1. Introduction Nowadays it is generally accepted that germanium and silicon di!er considerably with respect to intrinsicpoint-defect-mediated di!usion [1]. In Ge, the native point defects dominating under thermal-equilibrium conditions at all solid-state temperatures accessible in di!usion experiments are vacancies, and therefore Ge self-di!usion is vacancy-controlled. The same holds for the di!usion of substitutional solutes in Ge, particularly for dopants of the groups III and V of the periodic table. In Si, by contrast, self-interstitials and vacancies coexist in thermal equilibrium. Whereas in the most thoroughly investigated temperature regime above about 10003C Si self-di!usion is self-interstitial-controlled, it is vacancycontrolled at lower temperatures. Under these circumstances it is not surprising that the di!usion behaviour of groups-III and V dopants in Si is quite sophisticated due to the di!erent electrostatic and elastic interactions of these atoms with self-interstitials and vacancies. On the other hand, the group-IV element Ge has been found to di!use in Si almost like Si, and therefore the radiotracer
* Corresponding author. Tel.: #49-711-689-1940; fax: #49711-689-1932. E-mail address: [email protected] (W.F.J. Frank)
71Ge may be used as a Si substitute permitting the simulation of Si self-di!usion by 71Ge di!usion in Si. McVay and DuCharme [2] have made use of this possibility by measuring the 71Ge (self-) di!usion in Si Ge 1~y y alloys over the entire composition range 0)y)1. In fact, they observed a changeover in the di!usion mechanism at y"0.35 in accordance with the expected transition from the interstitialcy mechanism in Si to the vacancy mechanism in Ge. Whereas the indirect (i.e. intrinsic-defect-mediated) di!usion of self-atoms or substitutional solutes * sometimes referred to as `slow di!usersa * re#ects the properties of the dominating thermal-equilibrium defect species, this is obviously not the case for the `fasta direct interstitial di!usion of transition metals not involving native defects as di!usion vehicles (e.g., Fe in Si). However, there are `intermediate di!usersa * Au [1], Pt [1], or Zn [3] in Si and Cu [4] or Au [5}7] in Ge * which during di!usion repeatedly change from interstitial to substitutional sites, and vice versa, with the aid of intrinsic point defects. The fact that Au is an intermediate di!user in both Si and Ge has prompted us to study the di!usion of Au in Si Ge alloys as a function of com1~y y position in order to search for the changeover from Si-type self-interstitial-controlled to Ge-type vacancycontrolled interstitial}substitutional Au di!usion. This paper reports on our "rst results concerning the composition range 0)y)0.24.
0921-4526/99/$ - see front matter ( 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 0 5 8 2 - 7
R. Fischer et al. / Physica B 273}274 (1999) 598}602
2. Interstitial}substitutional di4usion mechanisms Intermediate di!usivity in Si or Ge arises from the hybrid nature of the corresponding element, say, Au, i.e. its capability to occupy both interstitial (Au ) and substi* tutional (Au ) sites. While the interstitial di!usivity (D ) of 4 * a hybrid is high compared to its substitutional di!usivity (D +0), the opposite is true for the corresponding 4 solubilities (C%2;C%2), so that C%2 is practically identical * 4 4 with the measured total solubility. Depending on whether self-interstitials (I) or vacancies (V) dominate in thermal equilibrium, the site exchange required in interstitial}substitutional hybrid di!usion occurs either by the kick-out mechanism [8] (Si case), Au ÁAu #I, * 4
(1)
or the dissociative mechanism [9] (Ge case), Au #VÁAu . * 4
(2)
In specimens containing internal sinks and sources for intrinsic point defects (e.g., dislocated specimens), in which the equilibrium concentrations C%2 of self-interstitials (l"I) or vacancies (l"V) may rapidly be established, the e!ective di!usivity D of the substitutional 4,%&& hybrid component is Au -controlled and given by * D "DH,D (C%2/C%2), 4,%&& * * * 4
(3)
irrespective of which of the two interstitial}substitutional di!usion mechanisms is operative. In the absence of internal sinks and sources for point defects, the expressions for D are di!erent for the two 4,%&& interstitial}substitutional di!usion mechanisms: (i) In the case of kick-out di!usion, D is controlled by the #ux 4,%&& D C%2 of the self-interstitials produced via the reaction (1) I I to the specimen surface and given by D "DH[C%2/C (x, t)]2 4,%&& I 4 4
(4a)
with DH,D C%2/C%2 I I I 4
(4b)
(D "di!usion coe$cient of self-interstitials). It is I noteworthy that, via the local, instantaneous Au concen4 tration C (x, t), the preceding expression for D is 4 4,%&& space-coordinate (x)- and time (t)-dependent. For this reason, self-interstitial-controlled kick-out di!usion produces di!usion pro"les of extraordinary shapes. (ii) In the case of dissociative di!usion, D is controlled by the 4,%&& #ux D C%2 of vacancies from the surface to the interior of V V the specimens, where they are consumed by reaction (2). In this case D "DH ,D C%2/C%2 4,%&& V V V 4 (D "di!usion coe$cient of vacancies). V
(5)
599
Now, the attention is to be focused on two interesting features of interstitial}substitutional di!usion, which will play a ro( le in the interpretation of our data (Section 4): (a) In the Au -controlled case, a distinction between the * kick-out mechanism and the dissociative mechanism is not possible, since for both mechanisms D is the same 4,%&& [Eq. (3)]. (b) In in-di!usion experiments, in which C%2/C '1, self-interstitial-controlled kick-out di!usion 4 4 tends to predominate over vacancy-controlled dissociative di!usion. This follows from Eqs. (4) and (5), according to which D for kick-out di!usion exceeds that for 4,%&& dissociative di!usion by a factor of (C%2/C )2 for 4 4 D C%2"D C%2. The opposite is true for out-di!usion I I V V experiments (C%2/C (1). 4 4 In this section, the discussion of the interstitial}substitutional di!usion mechanisms has been restricted to limiting cases in order to bring out the physical base. However, the data evaluation (Section 4) has been done numerically by means of the computer program ZOMBIE [10] which is based on the theories of kick-out and dissociative di!usion in their general versions.
3. Experimental The specimens used in the present investigations were 5]5 mm2 square platelets sawn out from about 10 lm thick, relaxed, monocrystalline Si Ge layers (0)y) 1~y y 0.24), which had been grown epitaxially from the vapour phase (H , SiCl , GeCl ) on dislocation-free, 440 lm 2 4 4 thick silicon substrates at 11003C at the Institute of Electronics of the Academy of Sciences of Uzbekistan in Tashkent. The thicknesses of the Si}Ge epi-layers were determined from raster electron micrographs of the cross-sections of cleft specimens or by means of spreading-resistance measurements across these cross-sections. The Ge contents of the layers were measured by means of energy dispersive X-ray spectroscopy. The dislocation densities in the layers were estimated by counting the etch pit densities on optical micrographs of Secco-etched layer surfaces. For instance, in Si Ge the dis0.947 0.053 location density was found to be 2.4]1010 m~2. As revealed by transmission electron microscopy, the interfaces between the Si substrates and the Si}Ge epi-layers contain ladder-type networks of mis"t dislocations, whose densities exceed the dislocation densities inside the epi-layers by several orders of magnitude. The di!usion studies were performed by means of a modi"ed radiotracer technique, in which radioactive 195Hg and 195.Hg ions were implanted with an energy of 60 keV into the Si}Ge epi-layers to depths of about 20 nm at the on-line isotope separator (ISOLDE) of the European Nuclear Research Centre (CERN) in Geneva, Switzerland. The decay of these implants via electron capture with half-lives of 10 and 41 h, respectively,
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R. Fischer et al. / Physica B 273}274 (1999) 598}602
produces 195Au atoms, which, due to their suitable halflife of 186 d, may serve as Au radiotracers in the subsequent di!usion experiments. Isothermal di!usion anneals were performed in the temperature regime 700}9503C. Their durations t lay in the regime 10 s)t)18 d. The short-time anneals ()240 s) were done in a computer-controlled rapidannealing facility, in which for heating the light of two xenon arc lamps was focused on the specimens by means of mirrors and light-conducting glass rods [11]. After the di!usion annealing of a specimen, the Au distribution in the Si}Ge epi-layer and, in many cases, also in the adjacent part of the Si substrate was measured along the `depth coordinatea x perpendicular to the epi-layer surface x"0. To this end, the specimen was serially sectioned by precision grinding, where the minimum thickness of the removed layers was about 0.5 lm. By layerwise counting the 195Au atoms in the taken-o! material, which was achieved in a liquid-scintillation counter by detecting the electrons emitted after the radioactive decay of 195Au, it was possible to `constructa the Au concentration pro"le C(x) in a di!usion-annealed specimen (C"total 195Au concentration).
Fig. 1. Temperature dependence of the e!ective di!usion coef"cient DH [Eq. (4b)] of 195Au in Si Ge epi-layers (* y"0, full I 1~y y symbols 0(y)0.09 [j y"0.013, m y"0.039, v y"0.053, . y"0.09], empty symbols 0.09(y)0.24 [h y"0.102, £ y"0.132, n y"0.196, L y"0.239]) and dislocation-free bulk Si (solid line) [12].
4. Results and interpretation In order to test our measuring technique and, in particular, to "nd out whether the di!usion in thin epi-layers may be compared to bulk di!usion, the 195Au di!usion in (Ge-free) Si epi-layers was investigated. The di!usion pro"les show the typical features of I-controlled kick-out di!usion into thick, dislocation-free Si specimens [12]. The DH values extracted from those pro"les (Fig. 1, *) I follow reasonably well the Arrhenius law DH"9.1]10~3 exp (!2.94 eV/k¹) m2s~1 I
(6)
(k"Boltzmann's constant, ¹"di!usion temperature) for Au di!usion in dislocation-free bulk Si [12] (Fig. 1, solid line). As expected for Si epi-layers perfectly grown on Si substrates, there is no interface e!ect on the shapes of the pro"les. In Si}Ge epi-layers with 0(y)0.09, 195Au di!usion occurs via the I-controlled kick-out mechanism, too. An example is the U pro"le for y"0.013, ¹"8003C, and t"240 s (Fig. 2, m), to which a solid curve was "tted by means of the computer program ZOMBIE (Section 2). From such "ts, for 0(y)0.09 the DH values were found I which are represented in Fig. 1 "lled symbols. In accordance with what one expects in the case of low Ge contents for the low-dislocation-density epi-layers used in our investigations and in agreement with previous "ndings on bulk Si}Ge specimens of the same kind [13], these values are quite close to those for dislocation-free Si, though, in spite of their scatter, on the average a devi-
Fig. 2. 195Au di!usion pro"les C(x) in Si Ge epi-layers for 1~y y 240 s anneals at 8003C (m y"0.013, v y"0.239) and a 60 s anneal at 9503C (j y"0.239). The data points on the righthand sides of the dashed vertical lines refer to the Si substrates.
ation to lower values is recognizable. In contrast to Si epi-layers, Si Ge layers with y)0.09 show a distinct 1~y y increase of C(x) in the vicinity of the interface (e.g., Fig. 2, m), particularly at low temperatures. In some cases, at the interface C even exceeds C%2 for Si. This 4 increase in part arises from a local acceleration of the Au PAu transformation [Eq. (1)] due to the absorp* 4 tion of self-interstitials at the mis"t-dislocation network in the interface (Section 3); however, conventional segregation of Au at the interface also contributes to this phenomenon. In the regime 0(y)0.09, at a given temperature DH decreases to a value DH(0.09(y)0.24) which is * * considerably smaller than that in Si and y-independent for 0.09(y)0.24. At 9003C, for instance, DH(0.09( * y)0.24) is by more than two orders of magnitude smaller than DH(y"0) (Fig. 3). As a consequence, in Si}Ge *
R. Fischer et al. / Physica B 273}274 (1999) 598}602
Fig. 3. Dependence of the e!ective di!usion coe$cient DH [Eq. * (3)] of 195Au at 9003C on the Ge content y for Si Ge epi1~y y layers in the regime 0.09(y)0.24 (v). The empty triangles are lower limits of DH(9003C) for 0(y)0.09. Also included are the * DH(9003C) values for dislocated bulk Si [14] (m) and disloca* tion-free bulk Ge [6] (v).
epi-layers with 0.09(y)0.24, under certain circumstances to be speci"ed at once, the 195Au di!usion pro"les show a transition from `I-controlleda to `Au * controlleda. Whereas close to the epi-layer surface even after short annealing times the Au concentration has * reached its saturation value C%2 and thus, at any rate, the * in-di!usion of 195Au is I-controlled, in greater depth it may be Au -controlled. For instance, this is the case for * y"0.239, ¹"8003C, and t"240 s (Fig. 2, v). One realizes that in this case the in-di!usion rate is considerably lower than for y"0.013 and otherwise identical conditions (Fig. 2, m) where the di!usion is I-controlled over the entire epi-layer thickness. It should be noted, however, that the moderate increase of the Au concentration close to the interface in the pro"le for y"0.239, ¹"8003C, and t"240 s (Fig. 2, v) cannot be due to a locally enhanced absorption of I, but must be a segregation e!ect, since that part of the pro"le is Au -controlled. * At 7003C, the lowest di!usion temperature in our investigations, 195Au di!usion takes place via the I-controlled kick-out mechanism over the entire thickness of the epi-layers even for 0.09(y)0.24. This is only partly due to the extremely long duration (3d) of the anneals performed at this temperature. Rather for 0.9(y)0.24, where DH (Fig. 4, v) obeys the Arrhenius * equation DH"4]10~9 exp (!1.3 eV/k¹) m2s~1 (7) * (solid line in Fig. 4), I-controlled kick-out di!usion is also favoured by low temperatures, since, decreasing the temperature, DH(C%2/C )2 (Fig. 1) "nally drops below DH. By I 4 4 * contrast, at high temperatures DH(C%2/C )2 exceeds DH, I 4 4 * and thus 195Au di!usion becomes Au -controlled except * near the surface. In these cases the interface leaves the pro"le shape una!ected, as shown in Fig. 2 (j) for y"0.239, ¹"9503C, and t"60 s. The DH values exI
601
tracted from the I-controlled pro"les or pro"le parts in the composition regime 0.09(y)0.24 (Fig. 1, empty symbols) scatter considerably, but lie preferentially below the solid Arrhenius line for pure Si like those for 0(y)0.09 (Fig. 1, "lled symbols). In the entire composition regime investigated (0(y)0.24), a systematic dependence of DH on y cannot be revealed. I An interpretation of the results reported above may be based on the dependences of DH on composition (Fig. 3) * and temperature (Fig. 4). In addition to the DH(9003C) * data in the regime 0.09(y)0.24, the DH(9003C) values * for Si and Ge from the literature have been included in Fig. 3. Whereas the Si value refers to highly dislocated materials, in which Au undergoes Au -controlled kick* out di!usion [14], the Ge value has been measured on both dislocated and virtually dislocation-free crystals, in which the Au -controlled dissociative mechanism is oper* ative [6,7]. For 0(y)0.09 the kick-out pro"les are I-controlled (see above), so that in this regime only lower limits of DH can be determined. At "rst sight, one may * speculate that alloying of Ge to Si, or vice versa, introduces sites at which the Au atoms may temporarily be * trapped and that this leads to a reduction of D which, * according to Eq. (3), is re#ected by the small DH values in * the Si}Ge alloys with 0.09(y)0.24 documented in Fig. 3. However, a closer inspection of the theory of trap-retarded di!usion shows that this kind of D reduc* tion would involve an increase of the pre-exponential factor of D which is overcompensated by a simultaneous * increase of the activation enthalpy entering D [15]. This * is in contradiction to the "nding that for Si}Ge both the pre-exponential factor and the activation enthalpy of DH are smaller than for Si or Ge (Fig. 4). Hence, the small * DH values in Si}Ge must arise from a reduction of the * ratio C%2/C%2 in comparison to Si or Ge, for instance, by * 4 a decrease of C%2 as a result of the lattice distortions * induced by Ge additions. At least in part, the reduction of C%2/C%2 may also be achieved by an increase of C%2. In * 4 4 fact, according to Eq. (4b) the preferential location of the DH values for Si}Ge below the Si line (Fig. 1) is in I accordance with an enhancement of C%2 in Si}Ge in 4 comparison to Si. Such an enhancement is very likely, since the Au solubility is much greater in Ge [6] than in Si [12]. Presumably, this is related to the increase of the lattice parameter from Si to Ge [16]. The decrease of DH as a result of a reduction of C%2/C%2, * * 4 which has been postulated above, is an interesting phenomenon that leads to a retardation of the di!usivity of hybrid di!users, which can exist in both a `sessilea and `mobilea con"guration. This kind of di!usion retardation is a collective property of the matrix, in which the mobile fraction of the di!users is lowered by alloying. It di!ers conceptually from conventional trapping [15] in which the reduction of the di!usivity results from a temporary immobilization of the di!users at localized traps.
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R. Fischer et al. / Physica B 273}274 (1999) 598}602
ness, though the likelihood that vacancies predominate over self-interstitials is expected to increase with decreasing temperature (Section 1). Hence, we conclude that in Si Ge of the composition range 0)y)0.24 the in1~y y di!usion of Au occurs via I- or Au -controlled kick-out * di!usion. This does not necessarily mean that in all our experiments D C%2 has exceeded D C%2. In in-di!usion I I V V experiments, a predominance of the kick-out mechanism over the dissociative mechanism may also occur due to its `(C%2/C )2 advantagea (Section 1). The physical cause 4 4 of this is the need for vacancies for the Au PAu trans* 4 formation in the dissociative mechanism [Eq. (2)] which has no analogue in the kick-out mechanism [Eq. (1)]. Fig. 4. Temperature dependence of the e!ective di!usion coef"cient DH [Eq. (3)] of 195Au in a Si Ge epi-layer (v). * 0.761 0.239 The straight lines represent Arrhenius laws for DH in the * Si Ge epi-layer (solid line [Eq. (7)]), in dislocated bulk 0.761 0.293 Si [14] (dashed line), and in dislocation-free bulk Ge [6] (dashed}dotted line).
5. Final remarks The experimental data on the di!usion of Au in Si}Ge alloys presented in this paper have been discussed in terms of the kick-out mechanism, which * depending on the Ge content, the di!usion temperature, the annealing duration, and/or the location in the specimens * is either I- or Au -controlled. Whereas the assignment of di!usion * pro"les to the I-controlled kick-out mechanism is possible without any unambiguity, from di!usion data alone a discrimination between Au -controlled kick-out dif* fusion and Au -controlled dissociative di!usion is, in * principle, not possible (Section 1). However, there is no physical reason why in the Au -controlled case the * Au PAu transformation should be dominated by reac* 4 tion (2), whereas in the I-controlled case the rate of reaction (1) obviously exceeds that of reaction (2). This view is con"rmed by the fact that at 7003C, the lowest temperature in the present investigations, all di!usion pro"les are I-controlled over the entire epi-layer thick-
Acknowledgements We are grateful to W. JuK ngling and his collaborators for putting the computer program ZOMBIE at our disposal and to the ISOLDE Collaboration for the assistance in the implantation experiments.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]
W. Frank, Def. Di!. Forum 75 (1991) 121. G.L. McVay, A.R. DuCharme, Phys. Rev. B 9 (1974) 627. N.A. Stolwijk et al., Def. Di!. Forum 59 (1988) 79. N.A. Stolwijk et al., J. Appl. Phys. 57 (1985) 5211. A. Almazouzi et al., J. Appl. Phys. 70 (1991) 1345. H. Bracht et al., Phys. Rev. B 43 (1991) 14 465. A. Strohm, Diplomarbeit, UniversitaK t Stuttgart, 1999. U. GoK sele et al., Appl. Phys. A 23 (1980) 361. F.C. Frank, D. Turnbull, Phys. Rev. 104 (1956) 617. W. JuK ngling et al., IEEE Trans. Electron. Dev. ED-32 (1985) 156. C. Rank, Vakuum Praxis 2 (1990) 286. N.A. Stolwijk et al., Physica 116 B (1983) 335. A. Giese et al., Verhandl. DPG 5 (1997) 722. B. KuK hn, Dr. rer. nat. Thesis, UniversitaK t Stuttgart, 1991. M. Koiwa, Acta Metall. 22 (1974) 1259. J.P. Dismukes et al., J. Phys. Chem. 68 (1964) 3021.
Di!usion of gold in relaxed Si}Ge epi-layers Roland Fischer!, Werner F.J. Frank!,*, Klara Lyutovich" !Max-Planck-Institut fu( r Metallforschung, Heisenbergstra}e 1, D-70569 Stuttgart, Germany "Universita( t Stuttgart, Institut fu( r Halbleitertechnik, Stuttgart, Germany
Abstract The di!usion of implanted 195Au in relaxed, low-dislocation-density Si Ge epi-layers has been measured as a 1~y y function of temperature (700}9503C) and composition (0)y)0.24) by means of a radiotracer technique, where serial sectioning was done by precision grinding. In all cases, the di!usion takes place by the kick-out mechanism, which is self-interstitial-controlled at low Ge contents, low temperatures, or close to the epi-layer surface, but gold-interstitialcontrolled otherwise. An interpretation is presented in which a novel mechanism of alloy-retarded substitutional} interstitial di!usion plays a major ro( le. ( 1999 Elsevier Science B.V. All rights reserved. Keywords: Si}Ge epi-layers; Di!usion of gold; Radiotracer technique; Kick-out mechanism
1. Introduction Nowadays it is generally accepted that germanium and silicon di!er considerably with respect to intrinsicpoint-defect-mediated di!usion [1]. In Ge, the native point defects dominating under thermal-equilibrium conditions at all solid-state temperatures accessible in di!usion experiments are vacancies, and therefore Ge self-di!usion is vacancy-controlled. The same holds for the di!usion of substitutional solutes in Ge, particularly for dopants of the groups III and V of the periodic table. In Si, by contrast, self-interstitials and vacancies coexist in thermal equilibrium. Whereas in the most thoroughly investigated temperature regime above about 10003C Si self-di!usion is self-interstitial-controlled, it is vacancycontrolled at lower temperatures. Under these circumstances it is not surprising that the di!usion behaviour of groups-III and V dopants in Si is quite sophisticated due to the di!erent electrostatic and elastic interactions of these atoms with self-interstitials and vacancies. On the other hand, the group-IV element Ge has been found to di!use in Si almost like Si, and therefore the radiotracer
* Corresponding author. Tel.: #49-711-689-1940; fax: #49711-689-1932. E-mail address: [email protected] (W.F.J. Frank)
71Ge may be used as a Si substitute permitting the simulation of Si self-di!usion by 71Ge di!usion in Si. McVay and DuCharme [2] have made use of this possibility by measuring the 71Ge (self-) di!usion in Si Ge 1~y y alloys over the entire composition range 0)y)1. In fact, they observed a changeover in the di!usion mechanism at y"0.35 in accordance with the expected transition from the interstitialcy mechanism in Si to the vacancy mechanism in Ge. Whereas the indirect (i.e. intrinsic-defect-mediated) di!usion of self-atoms or substitutional solutes * sometimes referred to as `slow di!usersa * re#ects the properties of the dominating thermal-equilibrium defect species, this is obviously not the case for the `fasta direct interstitial di!usion of transition metals not involving native defects as di!usion vehicles (e.g., Fe in Si). However, there are `intermediate di!usersa * Au [1], Pt [1], or Zn [3] in Si and Cu [4] or Au [5}7] in Ge * which during di!usion repeatedly change from interstitial to substitutional sites, and vice versa, with the aid of intrinsic point defects. The fact that Au is an intermediate di!user in both Si and Ge has prompted us to study the di!usion of Au in Si Ge alloys as a function of com1~y y position in order to search for the changeover from Si-type self-interstitial-controlled to Ge-type vacancycontrolled interstitial}substitutional Au di!usion. This paper reports on our "rst results concerning the composition range 0)y)0.24.
0921-4526/99/$ - see front matter ( 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 0 5 8 2 - 7
R. Fischer et al. / Physica B 273}274 (1999) 598}602
2. Interstitial}substitutional di4usion mechanisms Intermediate di!usivity in Si or Ge arises from the hybrid nature of the corresponding element, say, Au, i.e. its capability to occupy both interstitial (Au ) and substi* tutional (Au ) sites. While the interstitial di!usivity (D ) of 4 * a hybrid is high compared to its substitutional di!usivity (D +0), the opposite is true for the corresponding 4 solubilities (C%2;C%2), so that C%2 is practically identical * 4 4 with the measured total solubility. Depending on whether self-interstitials (I) or vacancies (V) dominate in thermal equilibrium, the site exchange required in interstitial}substitutional hybrid di!usion occurs either by the kick-out mechanism [8] (Si case), Au ÁAu #I, * 4
(1)
or the dissociative mechanism [9] (Ge case), Au #VÁAu . * 4
(2)
In specimens containing internal sinks and sources for intrinsic point defects (e.g., dislocated specimens), in which the equilibrium concentrations C%2 of self-interstitials (l"I) or vacancies (l"V) may rapidly be established, the e!ective di!usivity D of the substitutional 4,%&& hybrid component is Au -controlled and given by * D "DH,D (C%2/C%2), 4,%&& * * * 4
(3)
irrespective of which of the two interstitial}substitutional di!usion mechanisms is operative. In the absence of internal sinks and sources for point defects, the expressions for D are di!erent for the two 4,%&& interstitial}substitutional di!usion mechanisms: (i) In the case of kick-out di!usion, D is controlled by the #ux 4,%&& D C%2 of the self-interstitials produced via the reaction (1) I I to the specimen surface and given by D "DH[C%2/C (x, t)]2 4,%&& I 4 4
(4a)
with DH,D C%2/C%2 I I I 4
(4b)
(D "di!usion coe$cient of self-interstitials). It is I noteworthy that, via the local, instantaneous Au concen4 tration C (x, t), the preceding expression for D is 4 4,%&& space-coordinate (x)- and time (t)-dependent. For this reason, self-interstitial-controlled kick-out di!usion produces di!usion pro"les of extraordinary shapes. (ii) In the case of dissociative di!usion, D is controlled by the 4,%&& #ux D C%2 of vacancies from the surface to the interior of V V the specimens, where they are consumed by reaction (2). In this case D "DH ,D C%2/C%2 4,%&& V V V 4 (D "di!usion coe$cient of vacancies). V
(5)
599
Now, the attention is to be focused on two interesting features of interstitial}substitutional di!usion, which will play a ro( le in the interpretation of our data (Section 4): (a) In the Au -controlled case, a distinction between the * kick-out mechanism and the dissociative mechanism is not possible, since for both mechanisms D is the same 4,%&& [Eq. (3)]. (b) In in-di!usion experiments, in which C%2/C '1, self-interstitial-controlled kick-out di!usion 4 4 tends to predominate over vacancy-controlled dissociative di!usion. This follows from Eqs. (4) and (5), according to which D for kick-out di!usion exceeds that for 4,%&& dissociative di!usion by a factor of (C%2/C )2 for 4 4 D C%2"D C%2. The opposite is true for out-di!usion I I V V experiments (C%2/C (1). 4 4 In this section, the discussion of the interstitial}substitutional di!usion mechanisms has been restricted to limiting cases in order to bring out the physical base. However, the data evaluation (Section 4) has been done numerically by means of the computer program ZOMBIE [10] which is based on the theories of kick-out and dissociative di!usion in their general versions.
3. Experimental The specimens used in the present investigations were 5]5 mm2 square platelets sawn out from about 10 lm thick, relaxed, monocrystalline Si Ge layers (0)y) 1~y y 0.24), which had been grown epitaxially from the vapour phase (H , SiCl , GeCl ) on dislocation-free, 440 lm 2 4 4 thick silicon substrates at 11003C at the Institute of Electronics of the Academy of Sciences of Uzbekistan in Tashkent. The thicknesses of the Si}Ge epi-layers were determined from raster electron micrographs of the cross-sections of cleft specimens or by means of spreading-resistance measurements across these cross-sections. The Ge contents of the layers were measured by means of energy dispersive X-ray spectroscopy. The dislocation densities in the layers were estimated by counting the etch pit densities on optical micrographs of Secco-etched layer surfaces. For instance, in Si Ge the dis0.947 0.053 location density was found to be 2.4]1010 m~2. As revealed by transmission electron microscopy, the interfaces between the Si substrates and the Si}Ge epi-layers contain ladder-type networks of mis"t dislocations, whose densities exceed the dislocation densities inside the epi-layers by several orders of magnitude. The di!usion studies were performed by means of a modi"ed radiotracer technique, in which radioactive 195Hg and 195.Hg ions were implanted with an energy of 60 keV into the Si}Ge epi-layers to depths of about 20 nm at the on-line isotope separator (ISOLDE) of the European Nuclear Research Centre (CERN) in Geneva, Switzerland. The decay of these implants via electron capture with half-lives of 10 and 41 h, respectively,
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produces 195Au atoms, which, due to their suitable halflife of 186 d, may serve as Au radiotracers in the subsequent di!usion experiments. Isothermal di!usion anneals were performed in the temperature regime 700}9503C. Their durations t lay in the regime 10 s)t)18 d. The short-time anneals ()240 s) were done in a computer-controlled rapidannealing facility, in which for heating the light of two xenon arc lamps was focused on the specimens by means of mirrors and light-conducting glass rods [11]. After the di!usion annealing of a specimen, the Au distribution in the Si}Ge epi-layer and, in many cases, also in the adjacent part of the Si substrate was measured along the `depth coordinatea x perpendicular to the epi-layer surface x"0. To this end, the specimen was serially sectioned by precision grinding, where the minimum thickness of the removed layers was about 0.5 lm. By layerwise counting the 195Au atoms in the taken-o! material, which was achieved in a liquid-scintillation counter by detecting the electrons emitted after the radioactive decay of 195Au, it was possible to `constructa the Au concentration pro"le C(x) in a di!usion-annealed specimen (C"total 195Au concentration).
Fig. 1. Temperature dependence of the e!ective di!usion coef"cient DH [Eq. (4b)] of 195Au in Si Ge epi-layers (* y"0, full I 1~y y symbols 0(y)0.09 [j y"0.013, m y"0.039, v y"0.053, . y"0.09], empty symbols 0.09(y)0.24 [h y"0.102, £ y"0.132, n y"0.196, L y"0.239]) and dislocation-free bulk Si (solid line) [12].
4. Results and interpretation In order to test our measuring technique and, in particular, to "nd out whether the di!usion in thin epi-layers may be compared to bulk di!usion, the 195Au di!usion in (Ge-free) Si epi-layers was investigated. The di!usion pro"les show the typical features of I-controlled kick-out di!usion into thick, dislocation-free Si specimens [12]. The DH values extracted from those pro"les (Fig. 1, *) I follow reasonably well the Arrhenius law DH"9.1]10~3 exp (!2.94 eV/k¹) m2s~1 I
(6)
(k"Boltzmann's constant, ¹"di!usion temperature) for Au di!usion in dislocation-free bulk Si [12] (Fig. 1, solid line). As expected for Si epi-layers perfectly grown on Si substrates, there is no interface e!ect on the shapes of the pro"les. In Si}Ge epi-layers with 0(y)0.09, 195Au di!usion occurs via the I-controlled kick-out mechanism, too. An example is the U pro"le for y"0.013, ¹"8003C, and t"240 s (Fig. 2, m), to which a solid curve was "tted by means of the computer program ZOMBIE (Section 2). From such "ts, for 0(y)0.09 the DH values were found I which are represented in Fig. 1 "lled symbols. In accordance with what one expects in the case of low Ge contents for the low-dislocation-density epi-layers used in our investigations and in agreement with previous "ndings on bulk Si}Ge specimens of the same kind [13], these values are quite close to those for dislocation-free Si, though, in spite of their scatter, on the average a devi-
Fig. 2. 195Au di!usion pro"les C(x) in Si Ge epi-layers for 1~y y 240 s anneals at 8003C (m y"0.013, v y"0.239) and a 60 s anneal at 9503C (j y"0.239). The data points on the righthand sides of the dashed vertical lines refer to the Si substrates.
ation to lower values is recognizable. In contrast to Si epi-layers, Si Ge layers with y)0.09 show a distinct 1~y y increase of C(x) in the vicinity of the interface (e.g., Fig. 2, m), particularly at low temperatures. In some cases, at the interface C even exceeds C%2 for Si. This 4 increase in part arises from a local acceleration of the Au PAu transformation [Eq. (1)] due to the absorp* 4 tion of self-interstitials at the mis"t-dislocation network in the interface (Section 3); however, conventional segregation of Au at the interface also contributes to this phenomenon. In the regime 0(y)0.09, at a given temperature DH decreases to a value DH(0.09(y)0.24) which is * * considerably smaller than that in Si and y-independent for 0.09(y)0.24. At 9003C, for instance, DH(0.09( * y)0.24) is by more than two orders of magnitude smaller than DH(y"0) (Fig. 3). As a consequence, in Si}Ge *
R. Fischer et al. / Physica B 273}274 (1999) 598}602
Fig. 3. Dependence of the e!ective di!usion coe$cient DH [Eq. * (3)] of 195Au at 9003C on the Ge content y for Si Ge epi1~y y layers in the regime 0.09(y)0.24 (v). The empty triangles are lower limits of DH(9003C) for 0(y)0.09. Also included are the * DH(9003C) values for dislocated bulk Si [14] (m) and disloca* tion-free bulk Ge [6] (v).
epi-layers with 0.09(y)0.24, under certain circumstances to be speci"ed at once, the 195Au di!usion pro"les show a transition from `I-controlleda to `Au * controlleda. Whereas close to the epi-layer surface even after short annealing times the Au concentration has * reached its saturation value C%2 and thus, at any rate, the * in-di!usion of 195Au is I-controlled, in greater depth it may be Au -controlled. For instance, this is the case for * y"0.239, ¹"8003C, and t"240 s (Fig. 2, v). One realizes that in this case the in-di!usion rate is considerably lower than for y"0.013 and otherwise identical conditions (Fig. 2, m) where the di!usion is I-controlled over the entire epi-layer thickness. It should be noted, however, that the moderate increase of the Au concentration close to the interface in the pro"le for y"0.239, ¹"8003C, and t"240 s (Fig. 2, v) cannot be due to a locally enhanced absorption of I, but must be a segregation e!ect, since that part of the pro"le is Au -controlled. * At 7003C, the lowest di!usion temperature in our investigations, 195Au di!usion takes place via the I-controlled kick-out mechanism over the entire thickness of the epi-layers even for 0.09(y)0.24. This is only partly due to the extremely long duration (3d) of the anneals performed at this temperature. Rather for 0.9(y)0.24, where DH (Fig. 4, v) obeys the Arrhenius * equation DH"4]10~9 exp (!1.3 eV/k¹) m2s~1 (7) * (solid line in Fig. 4), I-controlled kick-out di!usion is also favoured by low temperatures, since, decreasing the temperature, DH(C%2/C )2 (Fig. 1) "nally drops below DH. By I 4 4 * contrast, at high temperatures DH(C%2/C )2 exceeds DH, I 4 4 * and thus 195Au di!usion becomes Au -controlled except * near the surface. In these cases the interface leaves the pro"le shape una!ected, as shown in Fig. 2 (j) for y"0.239, ¹"9503C, and t"60 s. The DH values exI
601
tracted from the I-controlled pro"les or pro"le parts in the composition regime 0.09(y)0.24 (Fig. 1, empty symbols) scatter considerably, but lie preferentially below the solid Arrhenius line for pure Si like those for 0(y)0.09 (Fig. 1, "lled symbols). In the entire composition regime investigated (0(y)0.24), a systematic dependence of DH on y cannot be revealed. I An interpretation of the results reported above may be based on the dependences of DH on composition (Fig. 3) * and temperature (Fig. 4). In addition to the DH(9003C) * data in the regime 0.09(y)0.24, the DH(9003C) values * for Si and Ge from the literature have been included in Fig. 3. Whereas the Si value refers to highly dislocated materials, in which Au undergoes Au -controlled kick* out di!usion [14], the Ge value has been measured on both dislocated and virtually dislocation-free crystals, in which the Au -controlled dissociative mechanism is oper* ative [6,7]. For 0(y)0.09 the kick-out pro"les are I-controlled (see above), so that in this regime only lower limits of DH can be determined. At "rst sight, one may * speculate that alloying of Ge to Si, or vice versa, introduces sites at which the Au atoms may temporarily be * trapped and that this leads to a reduction of D which, * according to Eq. (3), is re#ected by the small DH values in * the Si}Ge alloys with 0.09(y)0.24 documented in Fig. 3. However, a closer inspection of the theory of trap-retarded di!usion shows that this kind of D reduc* tion would involve an increase of the pre-exponential factor of D which is overcompensated by a simultaneous * increase of the activation enthalpy entering D [15]. This * is in contradiction to the "nding that for Si}Ge both the pre-exponential factor and the activation enthalpy of DH are smaller than for Si or Ge (Fig. 4). Hence, the small * DH values in Si}Ge must arise from a reduction of the * ratio C%2/C%2 in comparison to Si or Ge, for instance, by * 4 a decrease of C%2 as a result of the lattice distortions * induced by Ge additions. At least in part, the reduction of C%2/C%2 may also be achieved by an increase of C%2. In * 4 4 fact, according to Eq. (4b) the preferential location of the DH values for Si}Ge below the Si line (Fig. 1) is in I accordance with an enhancement of C%2 in Si}Ge in 4 comparison to Si. Such an enhancement is very likely, since the Au solubility is much greater in Ge [6] than in Si [12]. Presumably, this is related to the increase of the lattice parameter from Si to Ge [16]. The decrease of DH as a result of a reduction of C%2/C%2, * * 4 which has been postulated above, is an interesting phenomenon that leads to a retardation of the di!usivity of hybrid di!users, which can exist in both a `sessilea and `mobilea con"guration. This kind of di!usion retardation is a collective property of the matrix, in which the mobile fraction of the di!users is lowered by alloying. It di!ers conceptually from conventional trapping [15] in which the reduction of the di!usivity results from a temporary immobilization of the di!users at localized traps.
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ness, though the likelihood that vacancies predominate over self-interstitials is expected to increase with decreasing temperature (Section 1). Hence, we conclude that in Si Ge of the composition range 0)y)0.24 the in1~y y di!usion of Au occurs via I- or Au -controlled kick-out * di!usion. This does not necessarily mean that in all our experiments D C%2 has exceeded D C%2. In in-di!usion I I V V experiments, a predominance of the kick-out mechanism over the dissociative mechanism may also occur due to its `(C%2/C )2 advantagea (Section 1). The physical cause 4 4 of this is the need for vacancies for the Au PAu trans* 4 formation in the dissociative mechanism [Eq. (2)] which has no analogue in the kick-out mechanism [Eq. (1)]. Fig. 4. Temperature dependence of the e!ective di!usion coef"cient DH [Eq. (3)] of 195Au in a Si Ge epi-layer (v). * 0.761 0.239 The straight lines represent Arrhenius laws for DH in the * Si Ge epi-layer (solid line [Eq. (7)]), in dislocated bulk 0.761 0.293 Si [14] (dashed line), and in dislocation-free bulk Ge [6] (dashed}dotted line).
5. Final remarks The experimental data on the di!usion of Au in Si}Ge alloys presented in this paper have been discussed in terms of the kick-out mechanism, which * depending on the Ge content, the di!usion temperature, the annealing duration, and/or the location in the specimens * is either I- or Au -controlled. Whereas the assignment of di!usion * pro"les to the I-controlled kick-out mechanism is possible without any unambiguity, from di!usion data alone a discrimination between Au -controlled kick-out dif* fusion and Au -controlled dissociative di!usion is, in * principle, not possible (Section 1). However, there is no physical reason why in the Au -controlled case the * Au PAu transformation should be dominated by reac* 4 tion (2), whereas in the I-controlled case the rate of reaction (1) obviously exceeds that of reaction (2). This view is con"rmed by the fact that at 7003C, the lowest temperature in the present investigations, all di!usion pro"les are I-controlled over the entire epi-layer thick-
Acknowledgements We are grateful to W. JuK ngling and his collaborators for putting the computer program ZOMBIE at our disposal and to the ISOLDE Collaboration for the assistance in the implantation experiments.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]
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