- Email: [email protected]
A vacancy-related muon species in crystalline silicon
Physb=5928=SN Reddy=Venkatachala=BG
Physica B 289}290 (2000) 511}515
A vacancy-related muon species in crystalline silicon M. Schefzik , R. Scheuermann , L. Schimmele, A. Seeger , D. Herlach, O. Kormann, J. Major *, A. RoK ck Universita( t Stuttgart, Institut fu( r Theoretische und Angewandte Physik, Pfawenwaldring 57, D-70569 Stuttgart, Germany Max-Planck-Institut fu( r Metallforschung, Heisenbergstr. 1, D-70569 Stuttgart, Germany Paul Scherrer Institut, CH-5232 Villigen, Switzerland
Abstract A new muonium centre, termed Mu , with weak hyper"ne interaction has been discovered recently in crystalline 4 silicon in longitudinal "eld quenching lSR (LFQ) experiments (Schefzik et al., Solid State Commun. 107 (1998) 395). The signatures of this species were found in intrinsic, but not in doped samples (dopant concentration larger than 10 cm\). The centre is not formed promptly but results from a reaction in which normal muonium transforms into the novel species. Since from LFQ experiments one can obtain only a rough estimate of the hyper"ne tensor of Mu it is now 4 determined from zero-"eld (ZF) lSR experiments. The hyper"ne interaction is found to be axially symmetric around the 11 1 02 crystallographic axis with small hyper"ne parameters. Properly rescaled it essentially agrees with the hyper"ne tensor of the hydrogen centre VH, which has been discovered recently by Bech Nielsen et al. (Phys. Rev. Lett. 79 (1997) 1507) and which has been attributed to hydrogen trapped in vacancies. Accordingly Mu is interpreted as muonium 4 trapped in a vacancy, in agreement with the interpretation given on the basis of the earlier LFQ data. 2000 Elsevier Science B.V. All rights reserved. PACS: 61.72.!y; 61.72.Tt; 82.55.#e Keywords: Silicon; Hydrogen; Muonium; Vacancy
1. Introduction Hydrogen is present in virtually every step during the processing of silicon. Hence, it may di!use into the semiconductor and alter its electrical and
* Correspondence address: Max-Planck-Institut fuK r Metallforschung, Heisenbergstr.1, D-70569 Stuttgart, Germany. Tel.: #49-711-689-1264; fax: #49-711-689-1932. E-mail address: [email protected] (J. Major). Present address: Muon Science Laboratory, Institute of Physical and Chemical Research (RIKEN), 2-1 Hirosawa, Wako, Saitama 351-0198, Japan.
optical properties. This explains the long-standing interest in understanding the behaviour of hydrogen-related defects in silicon [1}4]. Nevertheless, because of the limited solubility of hydrogen in silicon, there is little direct information on the structure and dynamics of isolated interstitial hydrogen itself from investigations on hydrogenated or proton-implanted silicon. The behaviour of interstitial hydrogen in crystalline silicon may be studied experimentally by means of lSR (muon spin rotation, relaxation, or resonance) [5], since the positive muon behaves in silicon like a proton and may also bind an electron to form the hydrogen-analogue muonium.
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 0 ) 0 0 2 4 0 - 4
Physb=5928=SNR=VVC=BG
512
M. Schefzik et al. / Physica B 289}290 (2000) 511}515
Three di!erent muon species occurring in silicon are known for a long time. These are the normal (tetrahedral location, Mu ) and the anomalous 2 muonium (bond-centre location, Mu , analogous ! to the AA9 or E3 hydrogen centre) as well as diamagnetic muon species l. Low-temperature investigations in crystalline silicon by means of longitudinal "eld quenching lSR (LFQ) provided us with evidence of a novel paramagnetic muon species, termed Mu , with 4 weak, anisotropic hyper"ne interaction [6]. The generally weak signatures of Mu are found in 4 intrinsic but not in doped samples (dopant concentration larger than 10 cm\). LFQ experiments revealed that Mu is not formed promptly. It re4 sults from a reaction in which normal muonium transforms into Mu , with a reaction rate at 4 ¹"10 K of approximately 10 s\ [6]. LFQ may only determine the order of magnitude, but not the exact values of the hyper"ne parameters of the Mu species. In the present work 4 zero-"eld (ZF) lSR experiments have been performed in order to determine the hyper"ne parameters of the species Mu with high accuracy. 4 2. Experimental results ZF lSR experiments are generally very time consuming. In the present case, due to the weak Mu 4 signal [6], runs with extremely high statistics are absolutely necessary. 250 million events per counter have been collected in the experiments
which were carried out at the lE4 decay channel beam line (muon momentum 35 MeV/c) at PSI (Paul Scherrer Institut, Villigen, Switzerland) at the Stuttgart lSR spectrometer [7]. Only intrinsic samples were investigated, since Mu is only pres4 ent in such samples [6]. The sample characteristics are listed in Table 1. In the case of the "rst sample, it was possible to cut samples with three di!erent orientations from the same crystal (see Table 2). In ZF lSR only the precession frequencies of the paramagnetic muon species are observable. The frequency corresponding to Mu is too high to be 2 observed with a standard lSR set-up. The precession frequencies of Mu , which are 92.6, 54.7, ! and 37.9 MHz, are clearly observed. In addition, the precession frequencies listed in Table 2 are observed. However, the asymmetries of these precession signals, which belong to Mu , are only 4 about 3;10\ } 2;10\ and thus the signals are too weak to be detectable in the Fourier power spectrum of the time histograms. Nevertheless, the very good statistics allows us to determine Table 1 Characteristics of the single-crystalline silicon samples (these are all phosphorus doped and #oat-zone grown) Sample
Dopant concentration (cm\)
Oxygen concentration (cm\)
42772/02 47079/6 Si(i)-4
8.15;10 [P] 4.0;10 [P] 3.0;10 [P]
1.4;10 2.7;10 (10
Table 2 Precession frequencies of Mu determined in ZF lSR experiments for di!erent crystallographic orientations of the initial muon spin 4 direction Sample
Orientation
Frequencies (MHz)
42772/02
11 0 02 11 1 02 11112
7.77$0.04 7.88$0.07 7.66$0.1
* 12.0$0.08 *
18.84$0.25 19.97$0.04 *
42772/02-E1
11 0 02
7.85$0.21
*
18.50$0.06
42772/02
11 0 02
7.60$0.02
*
19.16$0.33
Si(i)-4
11 0 02
7.79$0.03
*
*
47079/6
11 1 12
*
*
*
Physb=5928=SNR=VVC=BG
M. Schefzik et al. / Physica B 289}290 (2000) 511}515
precession signals with asymmetries down to about 3;10\ using careful data analysis by weighted least-squares "ts. The obtained damping rates of the precession signals lie between 1 and 2 ls\. The signal asymmetries correspond to about 3}5% $ 2% of the implanted muons contributing to the Mu signal. According to the previous LFQ invest4 igations [6], most of Mu is formed, with a rate of 4 about 10 s\ from the precursor Mu which initially 2 is formed by somewhat more than 50% of the muons. Taking this fraction and the formation rate, a TF lSR signal due to Mu is expected which corres4 ponds to 1% or slightly less of the implanted l>, which is somewhat below the observed fractions but still compatible with the data. Furthermore, the LFQ data give, or are at least compatible with, a &prompt' Mu fraction of 3}5%. 4
513
Table 3 Calculated amplitudes of the zero-"eld precession signals of Mu for di!erent assumed orientations of the symmetry axis 4 (z-axis) of the hyper"ne tensor and for di!erent crystallographic orientations chosen to be parallel to the initial muon spin direction, i.e., muon beam direction Orientation parallel to initial muon spin direction
Precession frequency (MHz)
11 0 02
Precession amplitudes z-axis 11 0 02
11 1 02
11 1 12
7.9 12.0 19.9
0.33 0.17 0.0
0.33 0.17 0.33
0.33 0.17 0.33
11 1 02
7.9 12.0 19.9
0.33 0.17 0.17
0.33 0.17 0.25
0.25 0.17 0.0
11 1 12
7.9 12.0 19.9
0.33 0.17 0.33
0.25 0.17 0.0
0.33 0.125 0.33
3. The hyper5ne tensor of MuV Depending on which crystallographic orientation is chosen to be parallel to the initial muon spin direction, up to three di!erent precession frequencies of Mu have been determined from the present 4 ZF lSR experiments (cf. Table 2). The hyper"ne tensor of Mu must therefore have axial symmetry 4 with two independent hyper"ne parameters, or lower symmetry. In the case of lower symmetry, we do not expect any observable zero-"eld precession because of further line splitting. All three precession frequencies have only been observed together in sample 42772/02 with the crystallographic 11 1 02 axis parallel to the muon beam direction, i.e., parallel to the initial muon spin direction. Since the frequencies observed on the other samples are consistent with those three frequencies (second row in Table 2) we used these values for the determination of hyper"ne parameters of Mu . 4 The nonvanishing elements of an axially symmetric hyper"ne tensor with the z-axis of the Cartesian coordinate system parallel to the symmetry axis, are the diagonal elements A "A , and A . V W X The zero-"eld precession frequencies are given by l "(A #A ), X V l "A , V l "(A !A ). X V
(1)
The hyper"ne parameters of Mu are then deter4 mined from the precession frequencies as A "!12.0 MHz, V A "27.85 MHz, (2) X with standard deviation dA"0.1 MHz. The absolute sign of the hyper"ne parameters cannot be obtained from ZF lSR experiments. It has been chosen to be compatible with that of the hyper"ne parameters of the hydrogen}vacancy complex VH observed by EPR in proton-irradiated silicon [8]. The orientation of the symmetry axis of the hyper"ne tensor has been selected among the 11 0 02, 11 1 02, and 11 1 12 crystallographic orientations on the basis of a comparison between calculated and measured zero-"eld precession amplitudes. The precession amplitudes associated with the three di!erent precession frequencies have been calculated for each of the three considered crystallographic orientations using the hyper"ne parameters from Eq. (2). The results given in Table 3 show that the precession amplitude for the signal with precession frequency 19.9 MHz vanishes for
Physb=5928=SNR=VVC=BG
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M. Schefzik et al. / Physica B 289}290 (2000) 511}515
4. Conclusions The hyper"ne tensor of the muon species Mu 4 determined from the ZF lSR results is axially symmetric about the 11 1 02 crystallographic direction and is given by
0
0
0
!12.0
0
0
0
27.85
A 4" +
Fig. 1. Con"guration of the muon}vacancy complex Mu in 4 silicon (Si: black symbols, l>: light gray symbol).
initial muon spin directions which are parallel to certain speci"c crystallographic orientations. For which of the three considered initial muon spin directions the 19.9 MHz signal must not show up according to the calculations, depends on which assumption is made about the orientation of the symmetry axis of the hyper"ne tensor. A comparison with the experimental results obtained on sample 42772/02, see Table 2, shows that a symmetry axis of the hyper"ne tensor of Mu 4 which is parallel to 11 1 02 is the only choice which is not in contradiction to experiment. Although the 11 1 02 orientation is not a particular and exceptional direction in the diamond crystal structure of silicon, all silicon}silicon bonds are oriented along 11 1 12, an orientation of the rotational symmetry axis of the hyper"ne tensor of Mu along 11 1 02 may be understood if Mu is 4 4 interpreted as a muonium in a silicon vacancy, as suggested in Ref. [6], in analogy to the VH centre [8]. The microscopic picture of the Mu or VH 4 centre presented in Fig. 1 shows that the dangling bond and the l> (or H) in the Mu (VH) centre 4 are arranged such that the vector between the centre of the spin density distribution and the mean l> (H) position is roughly parallel to 11 1 02 and that a roughly axially symmetric hyper"ne tensor may result, particularly if some quantum mechanical averaging over the l> coordinates is considered.
!12.0
MHz
(3)
with standard deviation dA"0.1 MHz. It is closely related to the hyper"ne tensor of the hydrogen centre VH, which was discovered recently by Bech Nielsen et al. [8] in proton-irradiated crystalline silicon samples and which has been attributed to hydrogen trapped in vacancies. Mu is therefore interpreted as muonium trapped 4 in vacancies. This interpretation is also consistent with the LFQ results [6] which suggest that Mu is 4 muonium trapped in vacancies which are created during deceleration of the implanted muon close to the end of its stopping track. The LFQ results say further that Mu cannot be formed in samples 4 containing a su$ciently high concentration of dopants. The interpretation of Mu as muonium} 4 vacancy complex is also consistent with the abovedetermined orientation of the hyper"ne tensor. Acknowledgements The authors are indebted to Dr. W. Zulehner, Wacker Siltronic AG, Burghausen, Germany for kindly providing the samples. The support of the management and sta! of the Paul Scherrer Institut is gratefully acknowledged. This work was funded by the Bundesministerium fuK r Bildung und Forschung, Bonn, Germany under contract nos. 03MA5ST1 and 03-MA5ST2. References [1] S.K. Estreicher, Mater. Sci. Eng. R14 (1995) 319. [2] S.M. Myers, M.I. Baskes, H.K. Birnbaum, J.W. Corbett, G.G. DeLeo, S.K. Estreicher, E.E. Haller, P. Jena, N.M. Johnson, R. Kirchheim, S.J. Pearton, M.J. Stavola, Rev. Mod. Phys. 64 (1992) 559.
Physb=5928=SNR=VVC=BG
M. Schefzik et al. / Physica B 289}290 (2000) 511}515
515
[3] S.J. Pearton, J.W. Corbett, M. Stavola, Hydrogen in Crystalline Semiconductors, Springer, Berlin, 1992. [4] J.I. Pancove, N.M. Johnson, Hydrogen in Semiconductors, Academic Press, Boston, 1991. [5] A. Schenck, Muon Spin Rotation Spectroscopy, Hilger, Bristol, 1985. [6] M. Schefzik, R. Scheuermann, L. Schimmele, J. Schmidl, A. Seeger, D. Herlach, O. Kormann, J. Major, A. RoK ck, Solid State Commun. 107 (1998) 395. [7] R. Scheuermann, J. Schmidl, A. Seeger, Th. Stammler, D. Herlach, J. Major, Hyper"ne Interactions 106 (1997) 295. [8] B. Bech Nielsen, P. Johannesen, P. Stallinga, K. Bonde Nielsen, Phys. Rev. Lett. 79 (1997) 1507.
Storchak: In order to explain the indicated length scale of 1 lm between V and M one has to assume an extremely high muonium hop rate, 2 about 10 hops during l> lifetime (in case of Mu random walk), 2 which has never been observed in any semiconductor (or in insulator). How you explain this discrepancy?
Comments
Vajda: Have you tried to vary the V-concentration, e.g. by quenching the sample, and to see any variation of the Mu -concentration? This 4 would also be cleaner than using electron irradiation.
Kie6: Do you see ZF oscillations due to Mu-V complexes? How is this possible if it takes 1 ls to form the Mu-V complex? Schefzik: The observed ZF oscillations due to Mu possess a relaxation rate 4 of some 10 s\, which is compatible with the formation rate of 10 s\ as well as with the &50% muon polarization loss due to precursor Mu formation. 2 Brewer: Can you explain how you estimated the Mu formation time of 4 about 1 ls? This is dizcult to reconcile with ZF frequencies of 8}20 MHz, which should be almost completely dephased over 1 ls. Schefzik: The Mu PMu transition rate of 10 s\ was obtained from the 2 4 LFQ data xt reported previously in [6]. The present ZF lSR results are consistent with this transition rate.
Schefzik: The typical distance to the last self-generated vacancy is about 0.1 lm. In earlier experiments of Si doped Ge a muonium diwusion coezcient of D "10\ m/s was found. [K.P. Do( ring et al., +2 Hyperxne Interaction 17}19 (1984) 629]. This could easily explain the observed trapping rate. The corresponding hopping rate is of the order of 10 s\.
Schefzik: We tried to change the vacancy concentration only by electron irradiation, however the side ewects of the irradiation did not allow a clear interpretation of the data. Quenched-in vacancies may really give a better opportunity to study this phenomenon. Grynszpan: Did you try to look for the Mu complex above the vacancy 4 migration stage temperature? Schefzik : The Mu species was identixed at 10 K and measurements up to 4 approximately 50 K were performed. Since dynamical processes set in above 50 K, an identixcation of Mu may not be pos4 sible.
Physica B 289}290 (2000) 511}515
A vacancy-related muon species in crystalline silicon M. Schefzik , R. Scheuermann , L. Schimmele, A. Seeger , D. Herlach, O. Kormann, J. Major *, A. RoK ck Universita( t Stuttgart, Institut fu( r Theoretische und Angewandte Physik, Pfawenwaldring 57, D-70569 Stuttgart, Germany Max-Planck-Institut fu( r Metallforschung, Heisenbergstr. 1, D-70569 Stuttgart, Germany Paul Scherrer Institut, CH-5232 Villigen, Switzerland
Abstract A new muonium centre, termed Mu , with weak hyper"ne interaction has been discovered recently in crystalline 4 silicon in longitudinal "eld quenching lSR (LFQ) experiments (Schefzik et al., Solid State Commun. 107 (1998) 395). The signatures of this species were found in intrinsic, but not in doped samples (dopant concentration larger than 10 cm\). The centre is not formed promptly but results from a reaction in which normal muonium transforms into the novel species. Since from LFQ experiments one can obtain only a rough estimate of the hyper"ne tensor of Mu it is now 4 determined from zero-"eld (ZF) lSR experiments. The hyper"ne interaction is found to be axially symmetric around the 11 1 02 crystallographic axis with small hyper"ne parameters. Properly rescaled it essentially agrees with the hyper"ne tensor of the hydrogen centre VH, which has been discovered recently by Bech Nielsen et al. (Phys. Rev. Lett. 79 (1997) 1507) and which has been attributed to hydrogen trapped in vacancies. Accordingly Mu is interpreted as muonium 4 trapped in a vacancy, in agreement with the interpretation given on the basis of the earlier LFQ data. 2000 Elsevier Science B.V. All rights reserved. PACS: 61.72.!y; 61.72.Tt; 82.55.#e Keywords: Silicon; Hydrogen; Muonium; Vacancy
1. Introduction Hydrogen is present in virtually every step during the processing of silicon. Hence, it may di!use into the semiconductor and alter its electrical and
* Correspondence address: Max-Planck-Institut fuK r Metallforschung, Heisenbergstr.1, D-70569 Stuttgart, Germany. Tel.: #49-711-689-1264; fax: #49-711-689-1932. E-mail address: [email protected] (J. Major). Present address: Muon Science Laboratory, Institute of Physical and Chemical Research (RIKEN), 2-1 Hirosawa, Wako, Saitama 351-0198, Japan.
optical properties. This explains the long-standing interest in understanding the behaviour of hydrogen-related defects in silicon [1}4]. Nevertheless, because of the limited solubility of hydrogen in silicon, there is little direct information on the structure and dynamics of isolated interstitial hydrogen itself from investigations on hydrogenated or proton-implanted silicon. The behaviour of interstitial hydrogen in crystalline silicon may be studied experimentally by means of lSR (muon spin rotation, relaxation, or resonance) [5], since the positive muon behaves in silicon like a proton and may also bind an electron to form the hydrogen-analogue muonium.
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 0 ) 0 0 2 4 0 - 4
Physb=5928=SNR=VVC=BG
512
M. Schefzik et al. / Physica B 289}290 (2000) 511}515
Three di!erent muon species occurring in silicon are known for a long time. These are the normal (tetrahedral location, Mu ) and the anomalous 2 muonium (bond-centre location, Mu , analogous ! to the AA9 or E3 hydrogen centre) as well as diamagnetic muon species l. Low-temperature investigations in crystalline silicon by means of longitudinal "eld quenching lSR (LFQ) provided us with evidence of a novel paramagnetic muon species, termed Mu , with 4 weak, anisotropic hyper"ne interaction [6]. The generally weak signatures of Mu are found in 4 intrinsic but not in doped samples (dopant concentration larger than 10 cm\). LFQ experiments revealed that Mu is not formed promptly. It re4 sults from a reaction in which normal muonium transforms into Mu , with a reaction rate at 4 ¹"10 K of approximately 10 s\ [6]. LFQ may only determine the order of magnitude, but not the exact values of the hyper"ne parameters of the Mu species. In the present work 4 zero-"eld (ZF) lSR experiments have been performed in order to determine the hyper"ne parameters of the species Mu with high accuracy. 4 2. Experimental results ZF lSR experiments are generally very time consuming. In the present case, due to the weak Mu 4 signal [6], runs with extremely high statistics are absolutely necessary. 250 million events per counter have been collected in the experiments
which were carried out at the lE4 decay channel beam line (muon momentum 35 MeV/c) at PSI (Paul Scherrer Institut, Villigen, Switzerland) at the Stuttgart lSR spectrometer [7]. Only intrinsic samples were investigated, since Mu is only pres4 ent in such samples [6]. The sample characteristics are listed in Table 1. In the case of the "rst sample, it was possible to cut samples with three di!erent orientations from the same crystal (see Table 2). In ZF lSR only the precession frequencies of the paramagnetic muon species are observable. The frequency corresponding to Mu is too high to be 2 observed with a standard lSR set-up. The precession frequencies of Mu , which are 92.6, 54.7, ! and 37.9 MHz, are clearly observed. In addition, the precession frequencies listed in Table 2 are observed. However, the asymmetries of these precession signals, which belong to Mu , are only 4 about 3;10\ } 2;10\ and thus the signals are too weak to be detectable in the Fourier power spectrum of the time histograms. Nevertheless, the very good statistics allows us to determine Table 1 Characteristics of the single-crystalline silicon samples (these are all phosphorus doped and #oat-zone grown) Sample
Dopant concentration (cm\)
Oxygen concentration (cm\)
42772/02 47079/6 Si(i)-4
8.15;10 [P] 4.0;10 [P] 3.0;10 [P]
1.4;10 2.7;10 (10
Table 2 Precession frequencies of Mu determined in ZF lSR experiments for di!erent crystallographic orientations of the initial muon spin 4 direction Sample
Orientation
Frequencies (MHz)
42772/02
11 0 02 11 1 02 11112
7.77$0.04 7.88$0.07 7.66$0.1
* 12.0$0.08 *
18.84$0.25 19.97$0.04 *
42772/02-E1
11 0 02
7.85$0.21
*
18.50$0.06
42772/02
11 0 02
7.60$0.02
*
19.16$0.33
Si(i)-4
11 0 02
7.79$0.03
*
*
47079/6
11 1 12
*
*
*
Physb=5928=SNR=VVC=BG
M. Schefzik et al. / Physica B 289}290 (2000) 511}515
precession signals with asymmetries down to about 3;10\ using careful data analysis by weighted least-squares "ts. The obtained damping rates of the precession signals lie between 1 and 2 ls\. The signal asymmetries correspond to about 3}5% $ 2% of the implanted muons contributing to the Mu signal. According to the previous LFQ invest4 igations [6], most of Mu is formed, with a rate of 4 about 10 s\ from the precursor Mu which initially 2 is formed by somewhat more than 50% of the muons. Taking this fraction and the formation rate, a TF lSR signal due to Mu is expected which corres4 ponds to 1% or slightly less of the implanted l>, which is somewhat below the observed fractions but still compatible with the data. Furthermore, the LFQ data give, or are at least compatible with, a &prompt' Mu fraction of 3}5%. 4
513
Table 3 Calculated amplitudes of the zero-"eld precession signals of Mu for di!erent assumed orientations of the symmetry axis 4 (z-axis) of the hyper"ne tensor and for di!erent crystallographic orientations chosen to be parallel to the initial muon spin direction, i.e., muon beam direction Orientation parallel to initial muon spin direction
Precession frequency (MHz)
11 0 02
Precession amplitudes z-axis 11 0 02
11 1 02
11 1 12
7.9 12.0 19.9
0.33 0.17 0.0
0.33 0.17 0.33
0.33 0.17 0.33
11 1 02
7.9 12.0 19.9
0.33 0.17 0.17
0.33 0.17 0.25
0.25 0.17 0.0
11 1 12
7.9 12.0 19.9
0.33 0.17 0.33
0.25 0.17 0.0
0.33 0.125 0.33
3. The hyper5ne tensor of MuV Depending on which crystallographic orientation is chosen to be parallel to the initial muon spin direction, up to three di!erent precession frequencies of Mu have been determined from the present 4 ZF lSR experiments (cf. Table 2). The hyper"ne tensor of Mu must therefore have axial symmetry 4 with two independent hyper"ne parameters, or lower symmetry. In the case of lower symmetry, we do not expect any observable zero-"eld precession because of further line splitting. All three precession frequencies have only been observed together in sample 42772/02 with the crystallographic 11 1 02 axis parallel to the muon beam direction, i.e., parallel to the initial muon spin direction. Since the frequencies observed on the other samples are consistent with those three frequencies (second row in Table 2) we used these values for the determination of hyper"ne parameters of Mu . 4 The nonvanishing elements of an axially symmetric hyper"ne tensor with the z-axis of the Cartesian coordinate system parallel to the symmetry axis, are the diagonal elements A "A , and A . V W X The zero-"eld precession frequencies are given by l "(A #A ), X V l "A , V l "(A !A ). X V
(1)
The hyper"ne parameters of Mu are then deter4 mined from the precession frequencies as A "!12.0 MHz, V A "27.85 MHz, (2) X with standard deviation dA"0.1 MHz. The absolute sign of the hyper"ne parameters cannot be obtained from ZF lSR experiments. It has been chosen to be compatible with that of the hyper"ne parameters of the hydrogen}vacancy complex VH observed by EPR in proton-irradiated silicon [8]. The orientation of the symmetry axis of the hyper"ne tensor has been selected among the 11 0 02, 11 1 02, and 11 1 12 crystallographic orientations on the basis of a comparison between calculated and measured zero-"eld precession amplitudes. The precession amplitudes associated with the three di!erent precession frequencies have been calculated for each of the three considered crystallographic orientations using the hyper"ne parameters from Eq. (2). The results given in Table 3 show that the precession amplitude for the signal with precession frequency 19.9 MHz vanishes for
Physb=5928=SNR=VVC=BG
514
M. Schefzik et al. / Physica B 289}290 (2000) 511}515
4. Conclusions The hyper"ne tensor of the muon species Mu 4 determined from the ZF lSR results is axially symmetric about the 11 1 02 crystallographic direction and is given by
0
0
0
!12.0
0
0
0
27.85
A 4" +
Fig. 1. Con"guration of the muon}vacancy complex Mu in 4 silicon (Si: black symbols, l>: light gray symbol).
initial muon spin directions which are parallel to certain speci"c crystallographic orientations. For which of the three considered initial muon spin directions the 19.9 MHz signal must not show up according to the calculations, depends on which assumption is made about the orientation of the symmetry axis of the hyper"ne tensor. A comparison with the experimental results obtained on sample 42772/02, see Table 2, shows that a symmetry axis of the hyper"ne tensor of Mu 4 which is parallel to 11 1 02 is the only choice which is not in contradiction to experiment. Although the 11 1 02 orientation is not a particular and exceptional direction in the diamond crystal structure of silicon, all silicon}silicon bonds are oriented along 11 1 12, an orientation of the rotational symmetry axis of the hyper"ne tensor of Mu along 11 1 02 may be understood if Mu is 4 4 interpreted as a muonium in a silicon vacancy, as suggested in Ref. [6], in analogy to the VH centre [8]. The microscopic picture of the Mu or VH 4 centre presented in Fig. 1 shows that the dangling bond and the l> (or H) in the Mu (VH) centre 4 are arranged such that the vector between the centre of the spin density distribution and the mean l> (H) position is roughly parallel to 11 1 02 and that a roughly axially symmetric hyper"ne tensor may result, particularly if some quantum mechanical averaging over the l> coordinates is considered.
!12.0
MHz
(3)
with standard deviation dA"0.1 MHz. It is closely related to the hyper"ne tensor of the hydrogen centre VH, which was discovered recently by Bech Nielsen et al. [8] in proton-irradiated crystalline silicon samples and which has been attributed to hydrogen trapped in vacancies. Mu is therefore interpreted as muonium trapped 4 in vacancies. This interpretation is also consistent with the LFQ results [6] which suggest that Mu is 4 muonium trapped in vacancies which are created during deceleration of the implanted muon close to the end of its stopping track. The LFQ results say further that Mu cannot be formed in samples 4 containing a su$ciently high concentration of dopants. The interpretation of Mu as muonium} 4 vacancy complex is also consistent with the abovedetermined orientation of the hyper"ne tensor. Acknowledgements The authors are indebted to Dr. W. Zulehner, Wacker Siltronic AG, Burghausen, Germany for kindly providing the samples. The support of the management and sta! of the Paul Scherrer Institut is gratefully acknowledged. This work was funded by the Bundesministerium fuK r Bildung und Forschung, Bonn, Germany under contract nos. 03MA5ST1 and 03-MA5ST2. References [1] S.K. Estreicher, Mater. Sci. Eng. R14 (1995) 319. [2] S.M. Myers, M.I. Baskes, H.K. Birnbaum, J.W. Corbett, G.G. DeLeo, S.K. Estreicher, E.E. Haller, P. Jena, N.M. Johnson, R. Kirchheim, S.J. Pearton, M.J. Stavola, Rev. Mod. Phys. 64 (1992) 559.
Physb=5928=SNR=VVC=BG
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[3] S.J. Pearton, J.W. Corbett, M. Stavola, Hydrogen in Crystalline Semiconductors, Springer, Berlin, 1992. [4] J.I. Pancove, N.M. Johnson, Hydrogen in Semiconductors, Academic Press, Boston, 1991. [5] A. Schenck, Muon Spin Rotation Spectroscopy, Hilger, Bristol, 1985. [6] M. Schefzik, R. Scheuermann, L. Schimmele, J. Schmidl, A. Seeger, D. Herlach, O. Kormann, J. Major, A. RoK ck, Solid State Commun. 107 (1998) 395. [7] R. Scheuermann, J. Schmidl, A. Seeger, Th. Stammler, D. Herlach, J. Major, Hyper"ne Interactions 106 (1997) 295. [8] B. Bech Nielsen, P. Johannesen, P. Stallinga, K. Bonde Nielsen, Phys. Rev. Lett. 79 (1997) 1507.
Storchak: In order to explain the indicated length scale of 1 lm between V and M one has to assume an extremely high muonium hop rate, 2 about 10 hops during l> lifetime (in case of Mu random walk), 2 which has never been observed in any semiconductor (or in insulator). How you explain this discrepancy?
Comments
Vajda: Have you tried to vary the V-concentration, e.g. by quenching the sample, and to see any variation of the Mu -concentration? This 4 would also be cleaner than using electron irradiation.
Kie6: Do you see ZF oscillations due to Mu-V complexes? How is this possible if it takes 1 ls to form the Mu-V complex? Schefzik: The observed ZF oscillations due to Mu possess a relaxation rate 4 of some 10 s\, which is compatible with the formation rate of 10 s\ as well as with the &50% muon polarization loss due to precursor Mu formation. 2 Brewer: Can you explain how you estimated the Mu formation time of 4 about 1 ls? This is dizcult to reconcile with ZF frequencies of 8}20 MHz, which should be almost completely dephased over 1 ls. Schefzik: The Mu PMu transition rate of 10 s\ was obtained from the 2 4 LFQ data xt reported previously in [6]. The present ZF lSR results are consistent with this transition rate.
Schefzik: The typical distance to the last self-generated vacancy is about 0.1 lm. In earlier experiments of Si doped Ge a muonium diwusion coezcient of D "10\ m/s was found. [K.P. Do( ring et al., +2 Hyperxne Interaction 17}19 (1984) 629]. This could easily explain the observed trapping rate. The corresponding hopping rate is of the order of 10 s\.
Schefzik: We tried to change the vacancy concentration only by electron irradiation, however the side ewects of the irradiation did not allow a clear interpretation of the data. Quenched-in vacancies may really give a better opportunity to study this phenomenon. Grynszpan: Did you try to look for the Mu complex above the vacancy 4 migration stage temperature? Schefzik : The Mu species was identixed at 10 K and measurements up to 4 approximately 50 K were performed. Since dynamical processes set in above 50 K, an identixcation of Mu may not be pos4 sible.