www.elsevier.com/locate/jnoncrysol

Journal of Non-Crystalline Solids 353 (2007) 2975–2981

The structures of normal and supercooled liquid silicon metal andSiGe alloy

Shankar Krishnan a,1, Louis Hennet b, Thomas Key a, Benoit Glorieux c,Marie-Louise Saboungi d, David L. Price b,*

a Containerless Research Inc., Evanston, IL 60201, USAb Centre de Recherche sur les Materiaux a Haute Temperature, 45071 Orleans cedex 2, France

c IMP-CNRS, Tecnosud Rambla de la Thermodynamique, 66100 Perpignan, Franced Centre de Recherche sur la Matiere Divisee, 45071 Orleans cedex 2, France

Available online 14 August 2007

Abstract

The atomic structures of liquid Si metal and SiGe alloy in the normal and supercooled liquid states have been measured by X-raydiffraction from aerodynamically levitated and laser heated liquid droplets. The measurements covered a wide range of scattering vectorQ (0.8–20 A�1) and a wide temperature range that extended into the supercooled region. The present results on liquid Si confirm earliermeasurements that showed a decrease in first-shell coordination with increased supercooling. For liquid SiGe, the shoulder on the high-Qside of the first peak in the structure factor S(Q) sharpens with increased supercooling, suggesting an increase in covalent bonding anddevelopment of chemical short-range order.� 2007 Elsevier B.V. All rights reserved.

PACS: 61.10.-i; 61.20.-p; 61.25.Mv; 64.70.Ja

Keywords: Liquid alloys and liquid metals; X-ray diffraction; Medium-range order; Short-range order

1. Introduction

Silicon crystal growth and crystal properties are impor-tant in the semiconductor industry. Silicon is the hostmaterial for the majority of semiconductor applications,and the properties of its crystalline, amorphous and liquidphases are of substantial interest. The atomic structure,electrical, optical and thermophysical properties of theliquid phase are the key factors that determine the qualityof crystals grown from the melt.

Consequently, there have been several investigations ofthe thermophysical properties of the normal and super-cooled liquid phases [1–3]. While some of these have sug-gested anomalous density changes [3], others [1,2] show

0022-3093/$ - see front matter � 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.jnoncrysol.2007.05.176

* Corresponding author.E-mail address: price@cnrs-orleans.fr (D.L. Price).

1 Present Address: KLA-Tencor Corporation, San Jose, CA, USA.

little or no anomalies in the temperature dependence ofthe density vs. behavior in the liquid and supercooledregimes, suggesting effects of container contamination inthe earlier work. Since silicon, germanium and other semi-conductor liquids are known to undergo a semiconductor-metal transition upon melting, their structures have beenstudied extensively using X-ray and neutron scattering.Waseda et al. [4,5] reported some of the first X-ray mea-surements on the liquid and showed that the structure ofliquid silicon resembled that of white tin (A5 structure)with a well-defined shoulder on the high-Q side of the firstpeak in S(Q) and a first-shell coordination of 6. However,these studies were confined to temperatures above the melt-ing point because the experiments were performed on con-tained samples.

A majority of the structural features observed for theliquid were satisfactorily reproduced by the ab initio mole-cular dynamics (MD) simulations of Stich et al. [6,7] using

2976 S. Krishnan et al. / Journal of Non-Crystalline Solids 353 (2007) 2975–2981

the local density approximation (LDA) and the generalizedgradient approximation with the inclusion of Spin (SGGA).This pioneering work established the basic characteristics ofthe nearest neighbor structure and also suggested a meanfirst-shell coordination of 6 at temperatures close just abovethe melting point. Grabow and Gilmer [8] and Angell et al.[9] performed conventional MD calculations using the Stil-linger-Weber potential and their structural results on liquidsilicon were in satisfactory agreement with the experimentalobservations. They further predicted a decrease in the first-shell coordination with supercooling, and found that theliquid underwent a first-order liquid–liquid phase transitionto a tetrahedrally coordinated amorphous semiconductingliquid, with the first-shell coordination dropping discontin-uously from 4.6 to around 4.2. This suggestion receivedsupport from the X-ray diffraction measurements of Ansellet al. [10,11] that extended into the supercooled region andshowed a coordination number and interatomic distancethat decreased with decreasing temperature. However, theseresults were limited to a modest degree (140 K) of superco-oling, considerably smaller than the 340 K that can be typ-ically achieved in the laboratory [12]. Subsequently, Angelland Borick [13] suggested a first-order liquid–liquidtransition temperature of roughly 1345 K, the experimen-tally observed supercooling limit. This idea has gainedsupport from subsequent computer simulations: Sastryand Angell [14] find that the liquid-transition marks achange in the liquid dynamic character from that of a fragileliquid to that of a strong liquid, as recently observedin supercooled water [15], while Mirandi and Antonelli[16] find a weak first-order liquid–liquid transition at1135 K and a continuous liquid-amorphous transition at843 K.

Recently, Kimura et al. [17] performed energy-dispersiveX-ray diffraction measurements on electromagneticallylevitated liquid Si and reported structure factor and paircorrelation functions that qualitatively confirmed thepredominant features observed in the previous measure-ments. However, they obtained values of the first-shellcoordination number that were less than 5 at high temper-atures in the liquid and approached 6 as the liquidapproached 1400 K. This trend in the temperature depen-dence of the coordination number is opposite that reportedby Ansell et al. [10], and the value at elevated temperatures(4.9) is in considerable disagreement with those obtained inprevious experimental studies and simulations, which arearound 6 or higher.

In this paper, we describe results from new experimentalmeasurements on normal and supercooled liquid silicon,spanning a temperature range from 1767 K in the normalliquid to 1458 K (a supercooling of 227 K). These newstudies involved the use of a new experimental setup atthe advanced photon source (APS), measurements overan extended Q range and a substantially refined data anal-ysis procedure. The results confirm our earlier finding of adecrease in coordination number on supercooling. Theobserved temperature dependence of the coordination

number also agrees extremely well with a new ab initiomolecular dynamics (AIMD) simulation by Jakse andPasturel [18].

We also report the first measurements of the atomicstructure of equiatomic liquid Si0.5Ge0.5 alloy and contrastand compare its structure of this alloy with the end mem-bers of the SiGe system.

2. Experimental

This work was performed with the combination of con-ical nozzle levitation (CNL) of laser-heated liquids andsynchrotron X-ray diffraction. The basic principles of theexperimental methods and data analysis procedures aredescribed in our review article [19]. A brief summary andkey modifications incorporated in the new experimentalsetup at APS are given below.

The conical nozzle levitation apparatus was used toposition the specimens at the center of a Huber six-circleX-ray diffractometer. The levitation system was enclosedin an environmentally controlled chamber equipped withBe windows for transmission of the incident and scatteredX-rays. The chamber included several ports that providedaccess for optical pyrometry, video imaging and laser beamheating of the specimens. Most experiments were con-ducted at a chamber pressure of 600 mbar, with a levitationgas flow rate of about 350 cm3/min of pure argon. A keymodification to the apparatus was the use of a titanium-getter furnace to further purify the incoming gas; the oxy-gen and nitrogen content of the gas was estimated to be<0.01 ppm.

A 270-W CO2 laser was employed as the heat source toachieve liquid temperatures in the range 1200–1800 K forSi and SiGe. Another modification was to include a secondCO2 laser (40 W of laser power) to provide additional heat-ing of the specimen from below through the opening in thenozzle. At the lowest temperatures, the power delivered tothe specimen from below was roughly equal to that deliv-ered from above, a key factor in achieving high levels ofsupercooling. We estimate temperature gradients to be lessthan 4 K over the region irradiated by the X-ray beam.

Temperature measurements were performed with the aidof two separate pyrometers whose operating wavelengthswere 0.650 and 2.0 lm, respectively. The two pyrometerswere calibrated prior to the X-ray studies with the aid ofa NIST-traceable calibration lamp source. Absolute tem-perature measurements were obtained by measuring theradiance temperature at the known melting temperaturesof Si and SiGe, computing the spectral emissivities at thetwo wavelengths from the measured radiance temperaturesat the known melting temperatures. The spectral emissivi-ties were assumed to be independent of temperature. The2.0 lm pyrometer was used to measure temperatures inthe lower temperature range, while the 0.65 lm pyrometerwas predominantly used in the higher temperature range.Temperature uncertainties using this single-color pyrome-ter approach were estimated at ±5 K at the melting point

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 5 10 15 20Q (Å-1)

1767K 1667K

1543K 1458K

Fig. 1. Structure factor for liquid Si at four temperatures including thedeeply supercooled state. Successive curves are displaced upwards, inorder of decreasing temperature, by 0.5 units for clarity.

S. Krishnan et al. / Journal of Non-Crystalline Solids 353 (2007) 2975–2981 2977

of Si. Specimens were maintained at each temperature fordurations of up to 60 min in order to achieve high statisticsin the X-ray measurements.

The X-ray measurements were performed at the 12-ID-B beam line at APS using a monochromatic beam withenergy range 25 keV. Scattered X-rays were detected usinga solid-state detector with 300 eV resolution over a 2h

range of 2–110�, corresponding to a Q range of 0.8–

21 A�1. The background scattering and attenuation ofthe incident X-rays by the ambient gas at the operatingpressure in the experiment chamber were measuredindependently.

3. Data analysis

The scattering data were analyzed with an interactivePC-based system developed at Orleans and based on themethod of Wagner [20]. The background scattering wasremoved from the measured intensity using a fittedLorentzian function. Multiple scattering also contributesto the level of a few percent and this was subtracted analyt-ically using the procedure of Warren and Mozzi [21]. Theatomic scattering factors were calculated using values fromWassmaier and Kirfel [22] and the anomalous dispersionwas taken from the Henke [23] tables. The coherent scat-tered intensity Icoh(Q) is given by

ISðQÞI0ðQÞ

¼ AcohðQÞI cohðQÞ þ AincohðQÞI incohðQÞ; ð1Þ

where Is(Q) is the corrected measured intensity, I0(Q) isthe intensity of the incident beam measured with an ioniza-tion chamber, and Acoh(Q) and Aincoh(Q) are attenuationfactors determined using numerical integration of the opti-cal path of the X-ray beam over the irradiated volume ofthe sample. For this calculation step, absorption coeffi-cients were approximated by the X-ray cross sections com-piled by McMaster et al. [24]. The incoherent scatteringintensity Iincoh(Q) was calculated using data from Balyuzi[25].

The dimensionless structure factor S(Q) was derivedfrom Icoh(Q) by the relation

SðQÞ ¼ ðI cohðQÞ � hjf ðQÞj2iÞjhf ðQÞij2

þ 1; ð2Þ

where hf(Q)i and hf(Q)2i are the mean and mean squaredscattering amplitudes. In the case of a two-component sys-tem like SiGe, S(Q) is a weighted average of the partialstructure factors for each element pair.

The pair correlation function was obtained from S(Q)by the usual Fourier transform

gðrÞ ¼ 1þ 1

2p2q0

Z Qmax

0

Q½SðQÞ � 1� sin Qrr

MðQÞdQ; ð3Þ

where M(Q) is the Lorch modification function used to re-duce truncation effects. The number density q0 was taken

0.054 A�3 for Si, based on the measurements of Egry[26], and 0.049 A�3 for SiGe, derived from the average den-sities of liquid Si [26] and Ge [27].

4. Results

The results for S(Q) for liquid Si at temperatures of1767, 1667, 1543 and 1458 K, respectively 82 K aboveand 18, 142 and 227 K below the equilibrium melting pointof 1685 K, are shown in Fig. 1. The shoulder observed onthe high-Q side of the first peak is well defined and sharp-ens considerably with supercooling. This peak – the highestone in amorphous Si [30] – can be viewed as a signature ofthe tetrahedral structure. A similar behavior was previouslyobserved by Ansell et al. [10] and by Kimura et al. [17].There are two further well-defined peaks followed by rapiddamping of the structure at higher Q.

The corresponding results for g(r) are shown in Fig. 2.The g(r) is characterized by three well defined peaks at2.46, 3.9, and 5.7 A. Table 1 lists the principal characteris-tics of the S(Q) and g(r) obtained in this study togetherwith a comparison with other experimental studies. Thefirst nearest neighbor distance over the full temperaturerange is around 2.48 A, with no significant dependenceon temperature. This result differs from the trend reportedAnsell et al. [10] and is probably due to the much larger Q

range of the current study that leads to pair correlationfunctions of higher precision.

The first-shell coordination number, obtained by inte-gration of the radial distribution function n(r) = 4pqr2g(r)over the limits of the first peak, has values close to 6 at hightemperature and close to 5 at the lowest temperaturesinvestigated. An absolute uncertainty of 0.5 is associatedwith the coordination numbers obtained in this study,but the relative differences in coordination are measuredwith a substantially greater precision.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1 2 3 4 5 6 7 8r (A)

1767K1667K1543K1458K

Fig. 2. Pair correlation functions for liquid Si at four temperatures,including the deeply supercooled state. Successive curves are displacedupwards, in order of decreasing temperature, by 0.5 units for clarity.

2978 S. Krishnan et al. / Journal of Non-Crystalline Solids 353 (2007) 2975–2981

Fig. 3 shows the X-ray weighted average structure factorS(Q) for SiGe for four temperatures in the range 1450–1650 K; the liquidus temperature at this composition is1553 K. The liquid appears to be more disordered at hightemperature than at the lower ones where the shoulderon the high-Q side of the first peak becomes better defined,suggesting an increase in covalent bonding and develop-ment of chemical short-range order.

The X-ray weighted average pair correlation functionsg(r) for liquid SiGe are shown in Fig. 4 for the samefour temperatures. The peak positions are substantiallyshifted to larger r as expected from the size differencebetween Si and Ge. At lower temperatures, some struc-

Table 1Structural properties of liquid silicon, SiGe and germanium

Temperature (K), ±5 K Q1 (A�1), ±0.02 Qshoulder (A�1)

Liquid silicon, this work

1767 2.64 3.361667 2.67 3.301543 2.64 3.271458 2.58 3.33

Liquid SiGe, this work

1551 2.49 3.371523 2.46 3.421453 2.52 3.421433 2.49 3.24

Liquid Si, Ansell et al. [10]1829 2.45 3.551542 2.65 3.65

Liquid Si, Kimura et al. [17]1893 2.61 3.331403 2.51 3.44

Liquid Si, Waseda et al. [4,5]1793 2.76 3.35

Liquid Si, Jakse et al. [18]1767 2.65 3.60

Liquid Si, Stich et al. [6,7] 2.63 3.54

Liquid Ge, Waseda [27] 2.55 3.2

tural evolution appears to occur in the region betweenthe two coordination shells. There is also a shift to lowerr in the second peak of g(r). The similarities between Siand SiGe in the S(Q) and g(r) suggest that the structureof liquid SiGe is not unlike that of pure Si or Ge; how-ever, it is not clear whether the distribution of atomswithin the first shell is truly random, as may be expectedfrom the phase diagram, or if clustering occurs. Anoma-lous X-ray scattering measurements at the Ge K absorp-tion edge are needed to establish if clustering occurs inthese liquids.

Table 1 also lists the principal structural characteristicsfor liquid SiGe. The values of the first-shell coordinationnumber over the full temperature range are roughly 6, withno observable trend. It should be noted, however, that thepresent measurements on SiGe span a relatively modesttemperature range, and that measurements at higher super-cooling are needed to establish if there is a behavior similarto liquid Si. Also included in Table 1 are literature valuesfor liquid Si and Ge from previous experimental and MDsimulations.

5. Discussion

Figs. 5 and 6 compare previous and MD results in theliterature for S(Q) and g(r), respectively, of liquid Si withthe present results. The overall agreement for S(Q) is good,but that for g(r) is poorer, particularly in the regionbetween the two coordination shells, perhaps due to insuf-ficient Q ranges for some of the studies.

Q2 (A�1), ±0.05 R1 (A), ±0.02 Coordination number, ±0.5

5.55 2.49 5.975.58 2.49 5.725.57 2.48 5.565.54 2.48 5.46

5.28 2.66 5.965.22 2.66 6.045.16 2.68 6.115.19 2.68 6.07

5.45 2.46 6.45.65 2.41 5.6

5.62 2.445 4.95.64 2.438 6.1

5.60 2.45 5.8

5.61 2.52 6.0

5.68 2.47 6.2

5.1 2.7 6.1

-1.25

-0.75

-0.25

0.25

0.75

1.25

1.75

2.25

0 5 10 15 20

Q (Å )

S (Q

)

1551K 1523K

1453K 1433K

-1

Fig. 3. X-ray weighted average structure factor for liquid SiGe (equi-atomic) at four temperatures (see legend), including the supercooled state.Successive curves are displaced upwards, in order of decreasing temper-ature, by 0.5 units for clarity.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 2 4 6 8r (A)

1551K 1523K

1453K 1433K

Fig. 4. Pair correlation functions for liquid SiGe at four temperatures,including the supercooled state. Successive curves are displaced upwards,in order of decreasing temperature, by 0.5 units for clarity.

-1

-0.5

0

0.5

1

1.5

2

0.0 2.0 4.0 6.0 8.0 10.0Q (Å-1)

S(Q

)

Ansell et al, 1829KWaseda et al , 1793K

Present Work, 1767KJakse et al (AIMD), 1767K

Fig. 5. Comparison of the S(Q) results for liquid Si near the melting pointwith experimental results from Ansell et al. [10] and Waseda et al. [5], andab initio MD results of Jakse et al. [18]. Successive curves are identified inthe legend and displaced for clarity.

-1.5

-0.5

0.5

1.5

2.5

3.5

4.5

5.5

1 2 3 4 5 6 7 8r (Å)

g(r)

Stich et al, 1690K, MDWaseda et al, 1793KAnsell, et al 1829KPresent work, 1767KJakse, et al, AIMD, 1767K

Fig. 6. Comparison of the g(r) results for liquid Si near the melting pointwith experimental results from Ansell et al. [10] and Waseda et al. [5], andab initio MD results of Jakse et al. [18] and Stich et al. [6,7]. Successivecurves are identified in the legend and displaced for clarity.

S. Krishnan et al. / Journal of Non-Crystalline Solids 353 (2007) 2975–2981 2979

Fig. 7 compares the coordination numbers for liquid sil-icon as a function of temperature obtained by differentinvestigators. It can be seen that the present results are inagreement with the earlier study of Ansell et al. [10]; theslight differences in coordination number are well withinthe stated uncertainties. They also agree extremely wellwith the AIMD results of Jakse and Pasturel, as reportedpreviously [18]. It is clear that the results of Kimura et al.[17] differ substantially from the other two measurementsat or above the melting point, and show a considerably dif-ferent trend with temperature.

In the present study, measurements were obtainedat temperatures of up to 227 K below the equilibrium melt-ing temperature. The change in the coordination numberwith temperature and the magnitude of the coordinationnumber near the supercooling limit are in good agreement

4.75

5

5.25

5.5

5.75

6

6.25

6.5

1300 1400 1500 1600 1700 1800 1900Temperature, K

Coo

rdin

atio

n nu

mbe

r, at

oms

Present workAnsell et al,Waseda et alKimura et al, 2001MD, SGGAJakse, et al

Fig. 7. First shell mean coordination numbers for liquid Si obtained in thestudy compared to experimental results from Ansell et al. [10], Wasedaet al. [5] and Kimura et al. [17], and ab initio MD results of Jakse et al. [18]and Stich et al. (SGGA) [6,7]. The arrow on the x-axis marks the meltingpoint of 1685 K.

0

0.5

1

1.5

2

2.5

3

3.5

1 2 3 4 5 6 7 8r ( )

Si, T=1767SiGe, T=1433KGe, T=1253K

Fig. 9. Pair correlation functions for liquid Si and liquid SiGe obtained inthis study together with that for pure Ge [27]. Note the shift in the positionof the primary peak to larger r with increasing Ge concentration.Successive curves are displaced by 0.5 units for clarity.

2980 S. Krishnan et al. / Journal of Non-Crystalline Solids 353 (2007) 2975–2981

with the predictions of Angell and Borick [8]. The resultsprovide substantial support to their concept of a liquid–liquid transition in the deeply supercooled region.

Since this paper was originally submitted (January2005), further X-ray measurements on the structure of nor-mal and supercooled Si have been reported. Higuchi et al.[28] used electromagnetic levitation, like Kimura et al. [17],and obtained coordination numbers between 5.0 and 5.2with no systematic dependence on temperature, whileKim et al. [29] used electrostatic levitation and obtainedan essentially constant value of 6.0 over the temperaturerange studied, 1400–1800 K. The reason for the very differ-ent behaviors observed in the five measurements is notclear at this time. In addition to the three different levita-tion techniques employed, there are differences in X-rayenergies and Q ranges used in the present work and Refs.[10,28,29], while Kimura et al. [17] used an energy-disper-sive technique. Support for the reliability of the results ofthe present work is provided by the good agreement withthe earlier measurements at NSLS [10,11], in which entirelydifferent X-ray energy, experimental setup and analysisprograms were employed, and agreement with two sets ofcomputer simulations: the AIMD results of Jakse andPasturel [18] and the conventional MD of Angell and co-workers [8,9,13,14] with the Stillinger-Weber potential.Furthermore, if the development of the shoulder on thefirst peak of S(Q), observed in the other experimental workas well as our own, is indeed associated with the develop-ment of tetrahedral order, it is hard to understand how thatcan not be associated with a change in nearest-neighborcoordination. (It should be noted that in none of the mea-surements discussed is the real-space resolution adequate toresolve the first- and second-neighbor distances in thewhite-tin structure).

Lastly, Figs. 8 and 9 compare the S(Q) and g(r) for thethree liquids, Si, Ge, and SiGe. The results in Figs. 8 and 9correspond to liquids close to their respective melting

-1.5

-1

-0.5

0

0.5

1

1.5

0 2 4 6 8 10Q (Å-1)

S (Q

)

Si, T=1767SiGe, T=1433KGe, T=1253K

Fig. 8. X-ray weighted average structure factor for liquid Si and liquidSiGe obtained in the present work together with that for pure Ge [27], attemperatures identified in the legend. Note the shift in the position of thesecond peak in S(Q). Successive curves are displaced by 0.5 units forclarity.

points or liquidus temperatures. The results for Ge weretaken from Waseda et al. [29] and correspond to a temper-ature of 1253 K. The progression in the structure can bereadily seen, particularly in the first and second nearestneighbor distances.

6. Conclusions

We have presented results from a new series of X-raydiffraction experiments performed on normal and deeplysupercooled liquid silicon. The measured structure factorfor silicon shows a primary peak at Q � 2.7 A�1 and a welldefined shoulder on the right side of this peak. The shoul-der becomes very pronounced with increased supercooling,and becomes a very distinct feature near the supercoolinglimit. No abrupt changes in the structure were observedover the entire liquid range. In addition, we have presentedthe first results on equiatomic liquid SiGe alloy. The pres-ent results for liquid Si are in excellent agreement with thepreviously reported measurements of Ansell et al. [10], andindicate that the first shell coordination of silicon decreasescontinuously with increased supercooling. The X-rayresults are in good agreement with recent ab initio MDsimulations of Jakse and Pasturel [18], which show anincrease in the amplitude of the maximum in the bond-angle distribution close to the tetrahedral angle on superco-oling. Together with the decrease in coordination numberand evolution of the shoulder on the first peak of the struc-ture factor, this supports the conjecture of Angell and Bor-ick [13] of a first-order liquid–liquid transition at atemperature close to the experimentally observed superco-oling limit, and its further development by Sastry andAngell [14] and Mirandi and Antonelli [16].

Acknowledgments

The authors thank Dr Mark Beno and Dr Jennifer Lin-ton of the APS for their help with the experiments, MrJames Rix for his work on the experimental hardware and

S. Krishnan et al. / Journal of Non-Crystalline Solids 353 (2007) 2975–2981 2981

Drs Austen Angell, Noel Jakse, Paul Nordine and AlainPasturel for useful discussions. The work was supportedin part by a Grant from the NASA Microgravity Sciencesand Applications Division, NASA Grant No. NAS8-00122. Work at the Advanced Photon Source is supportedby the US Department of Energy, Office of Science, Officeof Basic Energy Sciences, under Contract No. W-31-109-ENG-38.

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