PHYSICAL REVIEW B VOLUME 21, NUMBER 8

Physical studies of Au„Si, „amoryhous alloys

15 APRIL 1980

Ph. Mangin, G. Marchal, C. Mourey, and Chr. JanotLaboratoire de Physique du Solide, Laboratoire associe au Centre National de la Recherche Scientifique No. 155, Uniuersite de Nancy-I,

Case Officielle 140, 54037 Nancy Cedex, France

(Received 24 July 1979)

Amorphous films of the system Au„Si, „have been prepared by vapor deposition over a wide

compositional range (0&x &0.8). Their physical properties, their stability in the amorphous state, and the

crystallization mechanisms have been investigated by electronic microscopy and diffraction, electrical-

resistivity and mass-density measurements. The results are compared with those obtained in the liquid

alloys, liquid quenched glasses, and getter sputtered films of the same system. Some similarities in short-

range orders of all these materials are suggested especially near the eutectic composition. The present study

would also suggest that Au-rich alloys near the Au, Si composition (a-p, phase) have a close-packed metallic

structure, while the alloys of the Si-rich end exhibit a more open continuous-random-network-like structure

with Au atoms in interstitial sites {a-Si phase), amorphous alloys in the intermediate-composition range

being an intricated mixture of both a-p, and a-Si phases. Before reaching the equilibrium dissociation into

crystalline Au and Si, crystallization occurs via a diffusionless transformation into a crystalline c-p, phase

(alone or with silicon) whose short-range order is compared with that of the a-p, phase. Electrical properties

and stability are discussed within the framework of this model.

I. INTRODUCTION

The existence of a deep eutectic in the equili-brium phase diagram has been long suspected asa crucial factor in obtaining an amorphous ma-terial by quenching a liquid. Large viscosity atrelatively low temperature in the liquid eutecticis indeed favorable to solidification withoutcrystallization. '

This rule has been verified for several systems,especially for Au„Si, , alloys" for which the eu-tectic is so deep that the melting point is 370'Cat x=0.81,' and reaches 600'C for differences ofabout +0.05 in composition. In addition, this bin-ary system has a very simple phase diagram with

miscibility gap in the solid state over the wholerange of composition. ' This is probably the rea-son why Au, Si, , glasses near the eutectic con-centration have been prepared and studied for along time." Since then, amorphous Au„Si, „al-loys have been obtained over a wider concentra-tion range than liquid quenched glasses (g-Au, Si, „)either by getter sputtering (s-Au, Si, ,) (Ref. 6) orvapor deposition (v-Au„si, J."

As we have been able to extend the composi-tional range of stability for this amorphous alloyfrom pure silicon to x =0.80 and as both investi-gation techniques and ideas have largely gonethrough evolutions, one would like to proposesome sort of balance sheet regarding the follow-ing properties:

Stability as a function of composition, tempera-ture, and preparation method.

Structural description as obtained from dif-fraction traces and mass-density measurements.

Electrical properties in relation with short-range and long-range structure near the eutecticcomposition and towards Si-rich composition(metal- nonmetal transition).

Crystallization via a series of both diffusion-less and diffusion-controlled transformation.

In this paper data collected in the present workwill be critically compared to previous resultsand a structural model will be proposed as asynthesis.

II. OBTAINMENT CONDlTIONS FOR Au„SilAMORPHOUS ALLOYS

A. Experimental procedures

As the preparation technique may influence thestructure oi the obtained amorphous material itis of importance to describe briefly the variousprocedures that have been used, mainly quenchingfrom the liquid, ' vapor quenching after sputter-ing, ' or evaporation. " As described by Hauseret al. alloy films were getter sputtered with anargon pressure of about 3 &&10 ' Torr onto sap-phire substrates held at 7'7 K. The sputteringtargets were prepared by inductively melting goldand silicon in the proper proportion.

In the work of Hiraki et al. ' and Kishimotoet al.' evaporations from a single crucible havebeen carried out by electron beam bombardmentin a vacuum which is claimed to be better than10 ' (Ref. '7) or 2 X 10 Torr. s' Substrates weretantalum or glass plates whose temperature hasnot been reported. In both sets of methods theactual composition of the alloys has to be post-determined by the atomic absorption spectro-

3047 1980 The American Physical Society

3048 PH. MANGIN, G. MARCHAL, C. MOUREY, AND CHR. JANOT 21

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LIOUI D NITROGEN

photometry or with the help of x-ray fluorescence.In the present work samples were prepared in

an ultrahigh-vacuum chamber by simultaneouscondensation on cooled substrates (77 K) of goldand silicon evaporated from separate electronbeam crucibles. The pressure was better than3 X10 ' Torr during the evaporation process, theultimate vacuum of the apparatus being 10 ' Torr.The evaporation rates of the two components weremeasured and controlled by two quartz monitor-ing systems (QMS) whose vibration period is alinear function of the deposited mass. Thus al-loy composition can be determined after calibra-tion using aluminum evaporated films (Fig. 1).Substrates were simple glass plates with goldelectrodes for resistivity measurements, opti-cally polished glass plates for thickness data,and carbon coated grids for electron microscopyinves tigations.

B. Compositional range of existence

Results are summarized in Fig. 2 according tothe preparation method. Quenching from the li-quid" gives rise to amorphous Au„Si, „alloys if0.60&x &0.83. On the Au-richer side quenchedmaterials are crystallized and Si-richer alloyshave too high a liquidus temperature.

Getter sputtered amorphous films have beenobtained from x = 0.60 to x = 0.87 (Ref. 6). InHefs. 7 and 8 Au„Si, „obtained by the evaporationtechnique have been presumed amorphous overthe range 0&x &0.30 without proper physicalchecking (resistivity transition or diffractiontrace). In the present work the evaporation de-posited films have been found amorphous in elec-tron diffraction and resistivity over the eomposi-

...... crystallineatllorphoUs

evaporation

sputtering

splat cool+grrzxr

0.5

FIG. 2. Sketchy representation of the stability rangeof the Au„Si& „amorphous alloys obtained by variousmethods.

tion range 0&x&0.8; x&0.80 results in a quenchedcrystallized alloy.

C. Temperature dependence of stability

The crystallization temperatures of Au, Si, ,amorphous alloys have been scarcely measuredand are shown in Fig. 3. g-Au, Si, , (Refs. 2, 3,and 10) is transformed into crystalline materialat room temperature within a few hours.s-Au+i, , starts to crystallize above 373 K andtransformation is completed within 20 min at550 K. As described in Sec. IV of this paper,we have measured the crystallization tempera-ture T, of the v-Au„Si, , (see the curve in Fig. 3).Starting from room temperature for x =0.80, T,exhibits a sharp increase over the ranges 0.6&x&0.8 and 0&x &0.30 with an obvious smallerslope in the intermediate compositions,

Thus g- and v-Au„Si, „near the eutectic compo-sition crystallize at the same temperature (-roomtemperature). The apparent greater stability ofthe s films, according to Hauser himself, isundoubtedly caused by the incorporation of argon(-1%) during deposition.

[aao

Y+ 400-

S2

3000 0.5

FIG. 1. Evaporation arrangement. QMS1, QMS2:quartz monitoring systems; S1: gold source, $2:silicon source; F: Au„Si, „ film; Fl, F2: pure gold andpure silicon films.

FIG. 3. Compositon dependence of the crystallizationtemperature.

PHYSICAL STUDIES OF Au~8&g ~ AMORPHOUS ALLOYS

III. STRUCTURAL APPROACH

Again, structural studies of the Au, Si, , amor-phous systems have been mainly restricted tosummary diffraction traces near the eutecticcomposition and down to x = 0.5. In this sectionelectron diffraction profiles and mass-densitymeasurements will be reported and analyzed indetail.

A. Diffraction traces and interference functions

1. g A uxSi I-x

According to Chen and Turnbull' the x-raydiffraction patterns show a broad peak charac-teristic of an amorphous structure at the diffu-sion vector k =2.76 A '. Dixmier and Guinierdata" are in qualitative agreement with the pre-vious authors. It is worth noting that there is no

splitting (or shouldering) of the second maximum,contrary to that found in many amorphous metal-

llmetalloid alloys near the eutectic composition.%ithout going into detail, it is mentioned in Ref . 10that enrichment with silicon results in a broaden-ing of the first ring.

2. s-Au Si&„(Ref. 6)

Hauser et al.' have restricted their publisheddata to the recorded intensity around the firstring of their diffraction patterns. This first peakculminates at k =2.76 A' if x —0.87 is not sensi-bly shifted down to x = 0.69, at which a significantbroadening can be observed especially on the shortwave vector side, and finally splits into twomaxima situated at k~= 2.9 A ' and k~™2.25 A 'for x =0.5. The authors claim that this broaden-ing and, finally, splitting is caused by the pro-gressive occurrence of more and more covalennttetrahedral bondings among silicon atoms.

3. v-Au Si& ~ (present ~ork)

The interference functions have been obtainedfor amorphous alloys (from x = 0 to x =0.80),using electron diffraction traces as previouslydescribed ' Compared to x-ray or neutrontechniques this method suffers from basic in-accuracy in the absolute intensities, but givesa correct description of shapes and positions ofthe diffraction rings.

Experimental data are shown in Fig. 4. For thealloys of the gold-rich side the interference func-tions have a sharp maximum at k~=2.78 A ' witha weaker unsplit maximum at k~=4.9 A '. En-richment with silicon results first in broadeningand then in the progressive appearance of twosatellite peaks, situated on each side of k~, at k,=2.10 A ', and k, =3.60 A '. Near pure amorphoussilicon, k, has been completely erased and (k„k,)

2 3 4 5 6

k(A )

FIG. 4. Interferences functions J(k) obtained withv —Aug' t

are the remaining major maxima of the interfer-ence functions of pure silicon. "

Thus the main features as pointed out in Sec.IIIA are the following:

(a) Near the eutectic composition the interf ere ncefunction has a broad maximum at k~=2.75 A 'whatever the preparation method used and, whenreported, the second maximum is unsplit.

(b) Again in the three cases, enrichment by 10-15 /g

silicon has no drastic consequences except forbroadening of the peak bottom.

(c) Upon further enrichment with silicon the in-terference functions as reported in the presentwork transform themselves into a sort of weightedsuperposition of two partial patterns that can berespectively ascribed to "amorphous eutectic, "referred as a-p, phase in the following, and basi-cally amorphous silicon-like material.

15On the other hand %aghorne et al. have mea-sured diffraction traces in Auo, »Si, „,liquidalloy and have found a first maximum at k~=2.75 A ', and a second unsplit one at k~=4.8 A ';this is very similar to that observed in amorphousmaterials near the eutectic composition. Theseauthors have calculated a radial distribution func-tion and have interpreted their results in a close-packed model with more than ten nearest neigh-bors.

B. Mass density measurements

To our knowledge any mass-density measure-ments have not been reported before in Au Si, ,

3050 PH. MANGIN, C. MARCHAL, C. MOUREY, AND CHR. JANOT 21

TABLE I. Experimental data for density and atomicdensity of Au Si& amorphous alloys (a-Au Slf ),crystalline gold (c-Au), crystalline silicon (c-Si), andliquid silicon (l -Si) at the melting point.

density N(atomic moles cm-3)

c-Au

a-Au Si&,

c-Sil-Si (Ref. 37)

0.800.750.700.6350.530.330.190.090.050-00

19.315.4314.9813.7312.9410.76

7.585.273.752.902.20

2.32

2.51

0.0979

0.09470.09640.09380.09540.09170.09000.08700.08370.07980.0785

0.0826

0.0893

amorphous alloys. It is well known that such anaccurate investigation suffers from drastic ex-perimental difficulties. Density measurementson amorphous films require the determination ofboth thickness e and mass m of unit area sam-ples.

Thicknesses e were about 2000-2500 A anddirectly determined by multiple beam interfero-metry" with an error less than +15 A. Carefulmass" calibration of both QMS (used as balances)were carried out by scaling the QMS indicationswith the mass of deposited aluminum films whichcan be calculated from measured thickness valuesand the Al density considered as being the samefor evaporated films and bulk material (data fromRef. 18 modified by conclusions of Ref. 17). Totest this calibration procedure, the density ofpure gold films has been measured and found tobe the same as in bulk material (with differenceless than lfo). Moreover, to ascertain the massof the amorphous Au+i, , alloys with a greaterprecision and in particular to do away with timeshift or statistical fluctuations of the regulationsystem, pure gold (El) and pure silicon (F2)films were simultaneously deposited on two sub-sidiary substrates; the directly measured thick-nesses of these pure films have been used as apermanent control of the @MS indications (seeFig. 1).

In Table I are reported the density data mea-sured at room temperature and the number & ofatomic moles per cm' which is easily calculatedfrom the density. In Fig. 5 are shown the compo-sitional dependence of ~ in the amorphous alloysalong with the N values in pure crystalline gold,pure crystalline silicon, and pure liquid silicon

0100

CO

ECP d ~ Cr«IO

C 0090~v-:E- Si

E r~ .

- Si

0.080a-Si' "

c-Au

gl ~

FIG. 5. Compositional dependence of the atomic den-sity: measured in v —Au„Si~ „alloys (full line and ~ ).Calculated for a mixture of (a) crystalline gold and sili-con (dashed line): for a mixture of c-Au and a-Sifdashed (b) line); for a mixture of c-Au and liquid Si[dashed (c) line]. Expected from purely interstitialsolution of Au in a-Si fdotted (d) line].

at the melting point; hypothetical dashed lineshave been drawn to picture the expected composi-tion dependences of N in a mixture of crystallinegold and crystalline silicon (a curve), in a mix-ture of crystalline gold and amorphous silicon(b curve), and in a mixture of crystalline goldand liquid silicon at its melting point (c curve).

If we look at our data with a "semiconductorpoint of view, " meaning at the Si-rich end ofFig. 5, the most prominent features are the fol-lowing:

(1) According to N values in pure silicon, thepacking fraction is only 5%less in amorphousthan in crystalline material which is very closeto the calculated value from the continuous-ran-dom-network (CRN) model" and in good agree-ment with recent experimental data." The highpacking of the material obtained here can cer-tainly be ascribed to the preparation conditions(a slow evaporation rate &10 A sec ' and a goodvacuum).

(2) Alloying gold to silicon in the amorphousstate up to x =0.1 results in an increase of theatomic density larger than expected from mixingcrystalline gold and amorphous silicon (b curve)and not too far from values calculated for a pureinterstitial model (dotted d curve) in which goldatoms would simply fill the holes of the CRNstructure. Thus, growth of small noble-metalcrystallites in the amorphous silicon matrix dur-ing quenching can be denied. "

On the metal-rich side, quite a different be-havior can be pointed out. The atomic densityN=0.095 atomic moles cm ' remains practicallythe same as the Si content varies from 20-40%.

21 PHYSICAL STUDIES OF Au~Sil ~ AMORPHOUS ALLOYS 3051

This N value is about 3 /o less than in pure crystal-lized gold as expected from the packing fractionof the relaxed dense random packing of hardspheres (DRPHS) model" and very consistentwith data in. metallic glasses materials. " Thusit can be stated that the gold-rich Au, Si, , amor-phous alloys have a close-packed structure up toa concentration of 40-at.% Si and that, contrari-wise to the semiconductor end, the addition ofsilicon in the amorphous metallic alloy is mostlysubstitutional. Looking again at Fig. 5, it can besuggested that crystallization of the amorphousmetallic phase into gold and silicon would resultin a volume expansion of a few percent which isjust the estimated volume expansion on solidifica-tion of the Aup 8y5Sip F85 liquid alloy. " This couldsupport the idea of some resemblance betweenthe amorphous phase and the liquid state. Suchan analysis of the density data is well supportedby the evolution of the interference functions asdescribed in the preceding section.

IV. ELECTRICAL PROPERTIES

The main ideas in measuring the electricalresistivity have been to give evidences of ametal- nonmetal transition on the silicon-richside and to test the Ziman model on the otherside [resistivity maximum and negative tempera-ture coefficient of the resistivity (TCR} 1/pdp/dTnear the eutectic composition]. As previous simi-lar studies have been restricted to a more narrowcompositional range and have been claimed bytheir authors to suffer a great experimental un-certainty a detailed investigation will be reportedhere. Resistivity of the as-quenched samples and

resistivity changes during aging were monitoredwith a four-point probe accurate to 0.01%.

Typical experimental resistivity behaviors arepictured in Fig. 6. Label 0 applied to as-quenchedstate; one-way irreversible behaviors 0-1,1-3 correspond to relaxation of the amorphousmaterial towards a more stable, still amorphous,state; two-way reversible sequences 1=2,3=4. . . are linear if x&0.3 [Figs. 6(a) and 6(b)]and then give the TCR for each partially relaxedamorphous state but show thermally activatedphenomena on the other compositional side(x&0.3) [Fig. 6(c}].

For a particular temperature T, there is anabrupt irreversible decrease 3-5 in the resis-tivity which corresponds to crystallization (seeFig. 3} into a metastable phase whose TCR canbe measured on 5= 6. Upon further warming upto T„a second transformation results in anadditional resistivity irreversible change 5-7[Figs. 6(a)-6(c)]. For alloy with x &0.5 [Fig. 6(a)]

(a)

150 ~

FQ 100-CL

50-

80 100 200 300 400 500 600

(bj

7

1000

700-'-EQ

650Q

600 .

550 .

0 100 200 300 400 500 600

r(v}

(c)

3-

EV

C2

O

CL

Tc

0 100 200 300 400 500 600

FIG. 6. Typical resistivity behavior in v -Au Si& ~..(a) @=0.715, (b) @=0.36, (c) @=0.174.

this resistivity recovery is a decrease and apositive TCR in the state labeled 7 can be mea-sured along f = 8. On the other side (x & 0.5)[Figs. 6(b} and 6(c)] this second resistivity changeis an increase and the result is typical of ther-

3052 PH. MANGIN, G. MARCHAL, C. MOUREY, AND CHR. JANOT 21

TABLE D. Resistivity behavior with respect to composition.

0.1 0.3 0.5 0.8

Structural relaxation in the amorphous phase

Thermally activated processes in (1/p) dp/dT &0 and constant vs Tstabilized amorphous states in stabilized amorphous states.

Crystallizationis not observedin resistivity

Evidence of crystallization via an abrupt irrevers-ible decrease in resistivity

Second transition withincrease in resistivityand stabilization into astate exhibiting therm-ally activated process-es

Second transition with de-crease in resistivityandstabilization into a statewith linear pP') andTCR greater than 0

m ally activated processes.All these experimental data are summarized in

Table II and pictured in Fig. 7 which gives the as-quenched resistivity versus composition pp(x) alongwith s-Au, Si, „data and resistivity in liquid,in Fig. 8 which gives the TCR for the amorphousstate stabilized at 300 K (which in fact is stillvalid whatever the annealing temperature), andin Fig. 9 which duplicates Fig. 7 in the logarithmcoordinate to allow drawing over the whole com-position range and compares the present datawith those of Kishimoto et a/. ' The activationenergies calculated in the range x &0.3 are shownin Fig. 10 along with those given in Ref. S. InTable III are reported the calculated activationenergies at 77 and 300 K for alloys annealed upto 300 K. A reasonable agreement between litera-

ture data and the present work can be observedif consideration is given to the difference inpr eparation method. "'"

V. CRYSTALLIZATION OF THE AuxSi~ ~ AMORPHOUSALLOYS

Crystalli ation of our v-Au, Si, „compared tothat of g-Au+i, , near the eutectic compositionhas been the subject of a detailed paper. " Themain results are summarized in Table IV and thecomposition dependence of the crystallizationtemperature T, as obtained in resistivity mea-surements is given in Fig. 3. The first trans-formation at 1; results into a metastable phase,referred to as c- p, phase, which can appear alonearound the composition Au, Si or in a mixture withsilicon. This c-p, phase would have an orthorhom-

300.

E

C

~ fWux Sii-x~s-Aux Slq-x~v-Aux S|,-x

4

.s-A2-

~v-A'I

(a » 3

0 02 OA cL6 a.8 1

X 0 a2 a4 as as

FIG. 7. Composition dependence of the as-quenchedresistivity in Au„Si& „alloys: ~ present work, a Hef.6, a in the liquid system.

FIG. 8. Temperature coefficient of the resistivityaccording to Fig. 7.

PHYSICiAL STUDIES OF Au Si~ AMORPHOUS ALLOYS $053

10 =10 '.-

105

E

C10 =

10

O

3lLI

10

10 =10 0 01 02 0.3

2 I I ~ I

0 02 0.4 (L6 G8 1

FIG. 10. Composition dependence of the activationenergy in resistivity regime below x & 0.3: ~ presentwork, Q Ref. 8.

FIG. 9. ln p(~) over the whole range of composition:y present work, O Ref. 8.

bic structure with a = 12.9, b = 7.45, and c = 11.6A, similar to the ~ phase of Andersen et al. ,~and which can be described in terms of distortedgold-like sub-cell structures. The so-called c-p.

phase, a-p phase (see Sec. IIA), and the eutecticliquid have a similar silver-like color whateverthe preparation method, and have comparablemass densities larger than the one of a gold-sili-con mixture in the same proportion. '~ A se-cond transformation at higher temperaturecorresponds to the dissociation into crystallinegold and silicon as foreseen by the equilibriumphase diagram.

VI. INTERPRETATION AND DISCUSSION

A. Description of the proposed model

In this section one would like to describestructure, electrical properties, and crystalliza-tion of the Au+i, „amorphous alloys in theframework of a model based on the assumptionthat the a-p. and c-p. phases as well as the li-quid near the eutectic composition are charac-terized by the same short-range order (SRO).This SRO would correspond to favorable stabilityconditions and consequently the three phaseswould have a local minimum of their free energyfor this composition.

In the liquid phase, adding gold or silicon tothe p. eutectic liquid would not change the SRQ,since pure liquid silicon has still a close-packedmetallic structure, but results in a drastic in-crease of the free energy, which is consistentwith the existence of a deep eutectic in the phasediagram. Contrariwise, silicon would have astrong tendency to become tetrahedrally coor-

dinated for high silicon concentration in amor-phous alloys and free energy can be gained by"dissociation" into a- p. and amorphous silicon-like (s-Si) phases, the latter including goldatoms in interstitial positions. The existence ofthese two amorphous phases must be ratherregarded as local fluctuation in structure andcomposition without true phase interf aces.Such a dissociation into two precursor amorphousphases (a- p and a-Si) could be explained by thefast diffusion of gold in both amorphous and crys-talline silicon even at relatively low tempera-ture. ' Thus the free-energy diagram of thesystem would be that pictured in Fig. 11. Abso-lute minima in the free energy correspond ofcourse to crystalline materials c-Si and c-Au.%e would like to use this model to interpret theexperimental results as given in the precedingsections.

8. Interpretation of the crystallization mechanism

According to the free-energy diagram of Fig. 11,the a- p. and a-Si phases are supposed to crystallizeseparately into metastable c-p, and c-Si phaseswithout long-range diffusion. Thus the crystal-lization occurs in place and the c-p, +c-Si ma-terial interfaces are as poorly defined as in theamorphous alloy. However, this first trans-formation results in a decrease in resistivitybecause of ordering inside the p. phase.

The second transformation, which is the disso-ciation into gold and silicon, must be controlledby long-range diffusion and results in more sep-arated phases. On the gold-rich side (x& 0.5),silicon islands are disseminated in a gold sea andthe second transformation naturally involves adecrease in resistivity. On the other side (x& 0.5), the second transformation makes goldclusters in a silicon matrix whose electrical con-

3054 PH. MANGIN, G. MARCHAL, C. MOUREY, AND CHR. JANOT 21

TABLE III. Measured values of the activation energy in v-Au„Si& „alloys.

Compositionat. % Au 0.05 0.086 0.10 0.174 0.20 0.265

Eat300 K(eV) p.12 0.11 0.06 6.7x 1p-2 2.5x ].0-' 1.5x 10-~ 7.4x 10-3

E at 77K(eV) p.p35 0.0]6 ].9x1p- 4.9x10- 3.6xlp- 8 x10

duction is ruled by thermally activated pheno-mena with large resistivity (see Table II). Themeasured atomic composition border x = 0.5 be-tween the two regimes corresponds to 45% goldand 55/p silicon of the total volume. This resultis very similar to that measured in the aluminum-germanium system. "

C. Structural description (interference functions and

mass density data)

Assuming the diagram of Fig. 11 to be truewould result in amorphous material made ofmainly the a-p, phase on one side, the a-Si phaseon the other side, and a mixture of both phasesin the intermediate composition range. Indeedthis is well supported by data obtained from dif-fraction traces and density measurements.

On the gold-rich side the interference functionsare very similar between them and with that ofthe liquid eutectic; mass-density data show thatatomic density is fairly constant over the compo-sition range 0.6&x& 0.8. This should be the exis-tence range of the a-p. phase, whose structurelooks very close packed. Contrariwise to dataobtained with Fe„Si, , amorphous alloys, ""en-richment of the a-Au„Si, „ films does not resultin a continuous homogeneous transformation ofthe interference function but involves the ap-

pearance of an amorphous Si-like phase. Thissecond phase progressively replaces the a- p,

phase and seems to be alone when x&0.1. Theatomic density increases with gold content whichcould be due to gold atoms in interstitial positionof a CHN structure. Thus the assumption of goldcrystallites into a silicon matrix can be de-ceiving.

D. Electronic transport properties

In the Ziman model" the resistivity of amor-phous material reaches a maximum when thediameter 2k~ of the Fermi surface is equal to thediffusion vector k~ of the interference functionfirst peak. The TCH is negative when 2k~ =k~,and becomes positive for 2k~ sensitively largeror smaller than k~." This model has been qual-itatively verified in a recent study devoted toFe,Sn, , amorphous alloy, "and seems to be rel-evant for Au„Si, „liquid alloys down to x =0.5,~addition of silicon involving only a shift of theFermi level. Looking at the free-energy dia-gram (Fig. 11) on the gold side shows that thea- p. phase is as homogeneous as the liquid andthe Ziman model should be valid. Contrariwise,on the silicon side of the a- p, phase liquid isstill homogeneous while the amorphous materialis not anymore and applying a Ziman model

TABLE IV. Crystallization processes of the A~it ~ amorphous alloys.

annealingtemperatu 0.2 0.7 0.8

below &c(RT)

just above~C

after 2ndtransfo rma-tion in re-sistivity

Amorphous material

Crystalline silicon c-Si+ c-p phasec-Si+ c-p (small crystals) (large crys-a-p phase ('P) tais)

Crystalline gold

crystalline silicon

Quenched al-loys are al-ready crys-tallized

21 P H Y S I C A L S T U 0 I E S 0 F A u z S i ] z A M 0 R P H 0 U S A L L 0 & S 3055

TABLE V. Calculated 2&z values versus composition.

0.80

2.78

0.75 0.70 0.635

2.88 2.935 3.05

tion was one of the suggested ideas of Hauser et al.6

who had presumed the appearance of tetrahedrallycoordinated silicon atoms without proposing dis-soci.ation, into two amorphous phases.

According to Kishimoto et al. ,""the composi-

tion range x&0.30 should be subdivided into twoconductivity regimes on each side of x = 0.14: (i)hopping regime at low gold concentration, and (ii)appearance of a gold narrow band in the silicongap for x&0.14.

FIG. 11. Hypothetical free-energy diagram for theAu„Si& „systems.

would not be sensitive. Indeed the resistivitytrend is to increase (Fig. 7} with a negative de-creasing TCR (Fig. 8} in the composition rangex &0.70.

Calculated values of 2k„ in the assumption thatgold contributes one and silicon four electrons tothe conduction band and using density data (TableI) are reported in Table V. 2k+ =k~=2.75 A ' isreached near the eutectic composition. On theother hand, the resistivity does not decrease onthe silicon-rich side and the TCR fails to reacha minimum. Over the composition range 0.3 &x&0.7, the electrical conductivity is due to thepercolating a- p, phase whose effective crosssection decreases upon silicon enrichment. Thusthe overall resistivity increases but has mainlythe negative TCR of the p. phase. Below x=0.3,the a- p, phase does not percolate anymore andconductivity should be mainly ruled by the a-Siphase. Thus the resistivity increases drasticallywith an obviously different regime behavior sincethe mean TCR is -16x10 for x=0.25 comparedto TCR = -6x 10 for x= 0.34. Suchaninterpreta-

E. Thermal stability of the amorphous alloys

As shown in. Fig. 3 Au„Si, alloys are more andmore stable in the amorphous state upon additionof silicon. The T, (x) curve has a particularlylarge slope when x&0.7 and x&0.3. The improvedstability between x =0.8 and 0.7 might be inter-preted in terms of the nearly free electron modelof Nagel and Tauc" which foretells the best sta-bility when 2 k r -—k~. On the other side (x &0.3),the increasing prominence of covalent bondingsin a percolating a-Si phase is indeed in favor of agreat stability. In the intermediate concentrationrange (0.3& x& 0.7), changes in the total stabilitymay be a compromise between constant stabilityof the percolation a- p, phase and the appearanceof more stable a-Si islands. However, it is notclear why the p. -phase small islands fail to crys-tallize along with silicon above T,; it might re-sult from a size effect or kinetic problems. Notean apparent slight discrepancy between densitydata, which show the a- p phase between x =0.6and x= 0.8, and resistivity measurements whichlimit the composition range down to x= 0.7. Infact, electrical resistivity is well known as beingvery sensitive to the least transformation and

may probe changes in the a -p. phase structure be-fore the mass density does.

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