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Physica B 374–375 (2006) 376–378

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Muonium hyperfine parameters in Si1�xGex alloys

Philip Kinga,�, Roger Lichtib, Stephen Cottrella, Ichiro Yonenagac

aISIS Facility, Rutherford Appleton Laboratory, Chilton, Oxfordshire OX11 0QX, UKbPhysics Department, Texas Tech University, Lubbock, TX 79409-1051, USA

cInstitute for Materials Research, Tohoku University, Japan

Abstract

We present studies of muonium behaviour in bulk, Czochralski-grown Si1�xGex alloy material, focusing in particular on the hyperfine

parameter of the tetrahedral muonium species. In contrast to the bond-centred species, the hyperfine parameter of the tetrahedral-site

muonium centre (MuT) appears to vary non-linearly with alloy composition. The temperature dependence of the MuT hyperfine

parameter observed in low-Ge alloy material is compared with that seen in pure Si, and previous models of the MuT behaviour in Si are

discussed in the light of results from Si1�xGex alloys.

r 2005 Elsevier B.V. All rights reserved.

PACS: 61.72.Tt; 61.72.Ji; 76.75.+i

Keywords: Muonium; Si1�xGex alloys; Hyperfine parameters

1. Introduction

Muonium studies in the elemental materials Si and Gehave enabled very detailed models of hydrogen sites,charge states and dynamics to be built up (for example,[1]). Similar muonium states are formed in both elements:an immobile, axially symmetric, bond-centred speciesMuBC and a rapidly moving, isotropic cage-centred stateMuT. However, whilst Si and Ge have identical crystalstructures and lattice parameters which differ by only 4%,the behaviour of the muonium species varies significantlybetween them, in terms of relative formation probabilities,ionisation temperatures and dynamics. In particular, whilstthe MuBC species is the more energetically stable in Si, MuTbeing metastable, the state stabilities are much closer in Gewith MuT possibly being the more stable. In Si, MuBCionises at around 150K; in Ge signals from bothparamagnetic centres disappear around 100K, possiblyowing to the onset of site interchange rather than

front matter r 2005 Elsevier B.V. All rights reserved.

ysb.2005.11.105

ng author. Fax: +44 1235 445720.

ss: p.j.c.king@rl.ac.uk (P. King).

ionisation due to the smaller energy difference betweenthe two states [2].It is therefore of interest to study muonium behaviour in

crystalline alloys of Si and Ge across the composition rangebetween the pure elements. Si1�xGex alloys are oftechnological interest due to their applications instrained-layer systems for transistor manufacture or foroptoelectronic components [3]. Bulk alloy material can beproduced using the Czochralski growth method [4],enabling investigation of a wide variety of properties ofthe unstrained alloy together with allowing exploration ofpotential applications for radiation detectors [5]. Studies ofimpurity behaviour in the bulk alloy, particularly thosewhich span the composition range, are quite limited,however. With regard to hydrogen, infrared absorption[6] and DLTS [7] studies have focused on observations ofbond-centred hydrogen properties in dilute alloys at eitherend of the composition range; theoretical studies haveenabled local vibrational modes of this species to bemodelled for similar compositions [8]. In these cases,modified properties of the bond-centred species have beenobserved owing to altered local bonding environments dueto the presence of near-by impurity atoms. Other impurity

ARTICLE IN PRESSP. King et al. / Physica B 374–375 (2006) 376–378 377

species—for e.g., iron [9], oxygen [10], and carbon [11]—have also been studied, primarily in low-Ge alloy material.

Here we report on muonium investigations across thealloy composition range in bulk Si1�xGex material, aimedat providing models for isolated hydrogen behaviour. Thiswork builds on earlier studies [12,13], aspects of which aredescribed in detail in Ref. [14]. In particular, we focus hereon the hyperfine parameters of the muonium species,including both temperature and composition dependence.

2. Experimental

Si1�xGex alloys were grown by the Czochralski methodat the University of Tohoku [4]. Single crystals withx ¼ 0:09, 0.2, 0.45, 0.6, 0.77 were available as [1 0 0]-oriented wafers varying in size from 5 to 20mm across. Asingle alloy sample with x ¼ 0:11 produced by VirginiaSemiconductor by the Czochralski method was alsoavailable.

Muon studies were performed at the TRIUMF contin-uous muon facility and at the ISIS-pulsed muon source. AtTRIUMF, the M15 beamline was used for high (3T)transverse field (TF) measurements. In this case, observa-tion of muonium precession lines enabled direct calculationof muonium hyperfine parameters. At ISIS, radiofrequency(RF) mSR was used to determine muonium hyperfineconstants. In this method, RF radiation at a knownfrequency (500MHz was used) is applied to the sampleduring the time when muons are present, together with aconstant magnetic field parallel to the initial muonpolarisation direction. As the constant field is sweptthrough a resonance condition for a transition betweenthe energy levels of a muonium species at the RFfrequency, a dip in the time-averaged muon polarisationis observed due to muon precession. The field at which theresonance occurs allows calculation of the hyperfine

520 530 540 550 560 570 580-0.016

-0.012

-0.008

-0.004

0.000

RF

asy

mm

etry

Field (G)

26 K

99 K

Fig. 1. RF-mSR resonance curves (ISIS data) for the MuT n12 transition

taken from the Si0.91Ge0.09 sample at 26 and 99K. The position of the

centre of the curves allows the hyperfine parameter for the MuT species to

be deduced.

parameter of the muonium species. Whereas TF-mSRrequires a promptly formed muonium state, RF-mSR canbe used to observe muonium whose formation is delayed,perhaps the result of conversion from another species. ForISIS RF measurements, samples were wrapped in thinKapton tape to prevent the RF coil shorting; the coil itselfwas produced by winding thin copper-conducting tapearound a sample. The Kapton and copper tapes were thinenough so as not to stop the implanted muons. Measure-ments were performed in ‘fly past’ mode [15] to reduce thebackground from muons not stopped in the sample.Examples of RF-resonance curves are given in Fig. 1.The MuT n12 line was used for RF measurements, as itsstrength increases with applied field and its position isrelatively sensitive to hyperfine parameter changes at thefields used here.

3. Results

MuBC signals were observable in all alloys studied. Forthe [1 0 0]-oriented crystals used here, the separation of theMuBC n12 and n23 lines measured in high TF is a directmeasure of the isotropic component of the MuBC hyperfineparameter. This hyperfine parameter component is shownin Fig. 3 versus alloy composition, calculated from theaverage of several low-temperature runs for each alloycomposition (the MuBC hyperfine parameter is relativelytemperature independent below around 100K). As can beseen, the hyperfine parameter component is a linearfunction of composition. It is interesting to note that,within bulk Si1�xGex alloys, there is a random siteoccupancy of Si and Ge atoms with no preferentialordering. Also, the Ge–Ge, Ge–Si and Si–Si bond lengthsare distinct and each varies linearly with alloy composition[16]. Implanted muons adopting an immobile, bond-centred position therefore experience a random selectionof bonding environments from those possible within agiven alloy which leads to an overall linear variation ofhyperfine parameter with alloy composition.MuT signals were only strongly observable by either RF-

mSR or high-TF mSR in samples with x ¼ 0:09, 0.11 and0.20. Faint signals were visible in other alloy compositionswhich allowed limited hyperfine parameter measurementson these samples. For samples showing strong MuT signals,the hyperfine parameter was found to be stronglytemperature dependent, and examples are shown in Fig.3. Also shown in Fig. 3 is the hyperfine parameter for MuTin pure Si, taken from Ref. [17]. Firstly, it can be seen thatthe MuT hyperfine parameters in the Si1�xGex alloys arelower than that found in Si over the temperature rangemeasured. If the MuT parameter varied linearly with alloycomposition, as found for the MuBC isotropic component,then alloy values should be higher than those found in pureSi, as the MuT hyperfine parameter in Ge is 16% higherthan that found in Si (at 100K). The lower values shown inFig. 3 suggest a non-linear temperature dependence as isshown in Fig. 2, where measured MuT values for various

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0.0 0.2 0.4 0.6 0.8 1.060

65

70

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80

85

90

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100

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2000

2050

2100

2150

2200

2250

2300

2350

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Mu T

hyp

erfin

e pa

ram

eter

(M

Hz)

Mu B

C h

yper

fine

para

met

er (

MH

z)

Ge content

MuBC

MuT

Fig. 2. Variation with alloy composition of the MuBC isotropic hyperfine

parameter component and the MuT hyperfine parameter. Values for MuBCare averages of several measurements below 110K; values for MuT are for

50K (except x ¼ 0:45 and 0:77 which are for 70 and 75K, respectively).

0 50 100 150 200 250 300

1940

1950

1960

1970

1980

1990

2000

2010

Hyp

erfin

e P

aram

eter

(M

Hz)

Temperature (K)

Pure Si, Ref. [17]

Si0.91Ge0.09, ISIS RF

Si0.80Ge0.20, ISIS and TRIUMF

Fig. 3. Measured temperature dependence of the MuT hyperfine

parameter in alloys with x ¼ 0:09 and 0:20. x ¼ 0:09 data are from ISIS

RF measurements; x ¼ 0:20 data are from both ISIS RF (6–26K) and

TRIUMF high-TF measurements (15–200K). Also shown is the MuThyperfine parameter variation for pure Si taken from Ref. [17].

P. King et al. / Physica B 374–375 (2006) 376–378378

alloy compositions are given, together with values found inthe pure elements. It can be seen that the MuT hyperfineparameter appears to stay low over a large part of the alloycomposition range.

The temperature dependence of the MuT hyperfineparameter in alloy material is also of interest. It can beseen that, above around 100K, it follows a form similar asthat found in pure Si—an increasing value as thetemperature decreases leading to a maximum and adecrease towards lower temperatures. However, in addi-tion, both alloys shown in Fig. 3 show a further turningpoint around 25K leading to an upturn at low tempera-tures. In Ref. [17], a model of the Si parameter temperaturedependence is given based on MuT coupling to the Debyespectrum of acoustic phonons. This model accounts wellfor the temperature dependence at temperatures above the

70K maximum; to describe the low-temperature fall-off, anenhancement of the model was made which assumed twoMuT sites with slightly different hyperfine parameters. Thedata in Fig. 3 show that this model alone would not beenough to describe the MuT parameter behaviour in theSi1�xGex alloys measured here, as the upturn below 40Kwould not be accounted for. In addition, there is someevidence of an upturn in the MuT hyperfine parameter inpure Si [18] below 15K which is not shown in Ref. [17]. Amore complete model than that given in Ref. [17] istherefore needed to fully describe the MuT hyperfineparameter temperature dependence in the Si1�xGex alloysand probably also in Si. Such a model is likely to involvethe coupling of MuT to lattice phonon modes as suggestedin Ref. [17], but a more complete modelling of the Siphonon modes is likely to be needed than has been used todate. For example, there is a strong similarity between theMuT temperature dependence and that shown by the Silinear coefficient of thermal expansion [14], particularlywith regard to where both parameters have turning pointsas a function of temperature. This suggests that MuT isinfluenced by the transverse acoustic phonon modes whichlead to Si showing negative thermal expansion in the15–70K region. If this observation for Si is also true forx ¼ 0:09 and x ¼ 0:20 Si1�xGex alloys shown in Fig. 3,then the MuT hyperfine parameter temperature dependencefor these alloys would predict that they will show negativethermal expansion behaviour in the temperature region ofroughly 25–100K. This measurement, together with themore detailed modelling of MuT interaction with latticephonon modes, are suggestions for future work.

Acknowledgements

PJCK and SPC would like to thank the EPSRC (grantsGR/N64977/01 and GR/R53067/01) for support for thiswork, and RLL would like to thank the US NSF (grantDMR-0102862) and the Robert A Welch Foundation(grant D-1321).

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