PHYSICAL REViEW B VOLUME 24, NUMBER 8 15 OCTOBER 1981

Structural and vibrational properties of amorphous phosphorus

B.V. Shanabrook* and J. S. LanninDepartment of Physics, The Pennsyluania State Uniuersity, Uniuersity Park, Pennsyluania 16802

(Received 17 February 1981)

Thin films of amorphous P, prepared by rf sputter deposition under conditions of vari-able substrate temperature, have been studied using x-ray diffraction and Raman scatter-

0

ing methods. The low-angle x-ray spectra indicate a peak at k™1.1 A ', whose half-

width and relative intensity are a continuous function of deposition temperature. The dif-

fraction spectra provide evidence for continuously variable intermediate-range order as afunction of deposition temperature. The polarized and depolarized Raman componentsindicate substantial changes with deposition temperature associated with the developmentof a number of high-frequency spectral features. Modifications of the depolarized Ramanspectra, as well as differences between the phonon density of states and depolarized bulk

spectra, provide additional evidence for intermediate-range order. The x-ray and Ramanspectra imply structural and dynamical correlations in amorphous solids of intermediate

range and further suggest that such correlations are continuously variable. The experi-mental results are discussed in terms of a layerlike model with variable intralayer and in-

terlayer correlations. As in crystalline solids, it appears that structural correlations are aprerequisite for dynamical correlations for optical-like modes.

INTRODUCTION

In crystalline solids the presence of periodicity,which leads to Bloch's theorem, results in physicalproperties that are appreciably influenced by spa-tial and temporal correlations. Thus long-range or-der in finite temperature or dilute impurity latticesresults in spatial and temporal correlations of thewave functions for electrons as well as phonons. Incontrast to crystalline solids, it has often been as-sumed that amorphous solids have limited spatialcorrelations, so that temporal correlations beyondthose associated with short-range order are not sig-nificant. It is, however, of interest to inquire ifnonperiodic solids may be prepared in a state ofintermediate-range order and whether, by analogywith periodic systems, correlation effects will occurin the phonon and electron wave functions overthis range. A related important point is the ques-tion of whether structural and dynamical correla-tions in nonperiodic solids may be continuouslyvariable.

Information about intermediate-range order andthe question of correlations in phonon and electronstates may in principle be obtained by elastic aswell as inelastic scattering experiments. In anumber of elemental amorphous semiconductors, aswell as in bulk binary chalcogenide glasses andliquids, ' x-ray-diffraction measurements yield a

peak at low scattering vectors, —l A '. While thegeneral structural conditions for the observation ofthis "anomolous" peak are unclear, it is generallybelieved' that it is a manifestation of structural .

correlations over an intermediate range. In con-trast to diffraction studies, Raman scattering mea-surements may provide information about dynami-cal correlations that arise from phonon inducedfluctuations in electronic polarizability. Intuitively,the existence of intermediate-range order is expect-ed to modify the phase relation of atomic displace-ments and thus the Raman scattering spectra rela-tive to that of a system with only short-range or-der.

In thin-film and bulk amorphous (a-) As it hasbeen suggested that large variations in the Ramanspectra and specific heat arise from changes inintermediate-range order. ' Neutron scatteringstudies also suggest coherency effects in a-As asso-ciated with intermediate-range order. Selected vi-brational modes in the bulk binary chalcogenide '

and oxide glasses have also been interpreted asmanifesting order beyond short range. The evi-dence to date for intermediate-range order based onvibrational probes has not, however, been con-clusive. A recent theoretical study has consideredthe role of structural correlations on the Ramanscattering response for the polarized and depolar-ized spectral components. This work has indicated

24 4771 1981 The American Physical Society

4772 B.V. SHANABROOK AND J. S. LANNIN

that the depolarized component will tend to mani-fest the general form of the phonon density ofstates unless intermediate-range order is present. Ifsuch order exists, however, then it is possible thatcertain vibrational states may yield dynamicalcorrelations that result in a depolarized spectrummodified from that of the phonon density of states.This theory was applied to a binary AX2tetrahedral glass of GeG2, for which it was deter-mined that intermediate-range order was absent. Itis therefore useful to determine if other amorphoussolids may indicate the presence ofintermediate-range order based on the above cri-terion. In contrast to binary systems, elemental

amorphous materials allow for an improved test ofthis theory as a reasonable estimate of the phonondensity of states may be obtained, unencumbered

by differences in neutron cross sections.In the present study, complementary x-ray dif-

fraction and Raman scattering measurements havebeen performed on thin-film elemental a-Pprepared by rf sputtering. In bulk form, a-P indi-

cates the aforementioned low-angle diffractionpeak' '" as well as considerable detail in the Ra-man" and infrared-absorption' spectra that aresuggestive of intermediate-range order. The results

presented below represent the first systematic com-parison of the structural and vibrational propertiesof an amorphous solid which allow information tobe obtained about correlation effects and their vari-

ability. The experimental results in a-P indicatethat, as in periodic systems, structural correlationsare a general necessary condition for dynamicalcorrelations, for high-frequency, optical-like modes.

EXPERIMENT

A commercial Material Research Corporationsputtering system was employed for thin-film

preparation. Thin films of a-P of -20-pm thick-ness were prepared by rf sputtering at an argonpressure of 60 pm and a power of 100 W. Thetarget-to-substrate distance was -5 cm. Since thesputtering parameters of pressure, power, substratedistance, and geometry all affect the energy distri-bution of the incoming sputtered species and resul-tant film properties, it is necessary tq carefully con-trol the sputtering parameters. The properties ofthe films were varied by independently changingonly the substrate temperature via a heater. Accu-rate surface temperature measurements were at-tained with Ag-Al thin-film thermocouples' depo-sited on polished Si wafers. The rather large

sputtering gas pressure results in a mean free pathof sputtered atoms of -0.2 cm. Stirling and West-wood' estimated that thermal equilibrium betweenthe sputtered atoms and the sputtering gas occursafter —10 collisions. As the target-to-substrate dis-tance is -25 mean free paths, the sputtered atomsare essentially thermalized when condensed on thesubstrate. Under these conditions, the substratetemperature should be an important parameter inthe film formation process. Raman scattering, in-

frared absorption, and x-ray diffraction measure-ments were performed on thin a-P films preparedat substrate temperatures between 0—177'C. Thelarge vapor pressure of P films at temperaturesgreater than 200'C limited the preparation ofhigher temperature films, while the rf sputteringsystem design prevented films from being formedbelow O'C.

The film thermocouples were used to directlymonitor the surface temperature of the substrateimmediately after deposition, as differences in po-tential in the sputtering chamber due to rf induc-tion effects result in inaccurate temperature mea-surements during deposition. However, the use ofa calibrated thin film amorphous Ge resistanceprobe' indicated temperature readings duringsputtering which were negligibly different fromthose immediately after sputtering.

RESULTS

In Fig. 1 the x-ray diffraction spectra of selectedrf sputtered films are shown for substrate tempera-tures T, of 0, 94, and 177'C. The spectra are simi-lar in form for scattering vectors k =4m sin8/A,

0

greater than 1.5 A ' and have thus been normal-ized to the intensity I2 shown. As the peak at 2.3A ' as well as higher peaks are primarily deter-mined by the nearest-neighbor distance, this nor-malization procedure is a useful first approxima-tion for determining the relative intensity of thelow-angle peak I~. Additional contributions to thescattering which determine the actual intensityabove background are assumed to be relatively con-stant. A more detailed determination of changes inthe scattering function' F(k) with T, are, howev-

er, prohibitively difficult for a-P given its small x-ray absorption cross section and the requirementfor rather thick films.

With increasing substrate temperature, Fig. 1

qualitatively indicates a rise in the ratio I& /I2 aswell as a narrowing of the lowest diffraction peak

0

at 1.08 A '. The latter peak is, however, observed

STRIIClllBAL AND VIBRATIONAL FROFBRTIBS OF. . . 4773

k &5-~l

FIG. 1. Selected x-ray diffraction spectra of rf sput-

tered a-P films for the substrate temperatures shown.

to occur at the same k value for films depositedunder conditions of fixed sputtering geometry,pressure, and cathode voltage. The position of thispeak occurs somewhat above the k =1.04 Avalue of bulk a-P prepared by polymerization ofliquid P. Figure 2 indicates in a more quantitativemanner the substrate temperature variation ofIi/I2 as well as the inverse width of the low-angle

peak; the width corresponds to the full width athalf maximum. As Fig. 2 indicates, the inversewidth of the low-angle peak is observed to varyessentially linearly with T, . In contrast, the inten-

sity ratio I~ /I2 indicates a weak variation at low

T, with a more rapid increase ensuing atT, 75'C. At high T, this ratio appears to satu-rate to a value of I~/I2 2.8. The position of thelow scattering vector peak k& has been indicated asan inverse measure of a quasiperiodic structural re-

peat distance. ' Fourier inversion suggests that thisdistance is of order 2m/ki. For the data of Fig. 2this yields 2m/k& ——5.8 A. The inverse half-width

of the low-k peak has similarly been attributed toan 'associated structural correlation length, l, . Onerough estimation procedure for l, uses the Debye-Scherrer equation derived for small crystallites ofmean dimension D =2m'/Lk, where hk is thepeak width in A ' and c is a nuinerical factor be-

tween 0.9—1.4.' If l, is equated to D, then forc =0.9, l, =29 A for the highest temperature film.

In contrast, for the O'C film this value decreases by30%. Though no theoretical justification has beengiven for extending the Debye-Scherrer equation toamorphous solids, it is reasonable to expect that ityields, within most likely a factor of -2, an esti-mate of the structural correlation length. Indepen-dent of the precise values of l, it is reasonable toassume that the inverse half-width variation of30% for the films studied in Fig. 2 is a quantitativemeasure of the relative change in structural corre-lation length with T, . For a layerlike model, dis-cussed below, l, may be associated with an inter-layerlike correlation length. '

Figure 2 indicates that I&/I2 has a differentvariation than the inverse width and as such is asecond measure of structural order. In crystallinesolids the effect of "phonon disorder, " associatedwith finite temperatures, is to reduce diffractionpeak intensities by the Debye-Wailer factor, whilepreserving the width of the peaks. The ratio I&/I2is thus an alternative means of viewing the role ofdisorder in amorphous solids and has a somewhatmore intuitive justification than the area, e.g., ofthe lowest peak. While no detailed theoretical in-

terpretation has been presented for this ratio,Bishop and Shevchik' have suggested that for alayerlike model it is a relative measure of the "frac-tion of material in the layer structure. " For thefilms of Fig. 2, I&/I2 is found to increase by 55%between the lowest and highest T, values. In con-trast to the peak position and a half-width in bulk

Z.o ,

2.6-C4

2.2-

C3

0 50 IOO I50 200SUBSTRATE TEMPERATURE (OC)

5.2 -'

4.8—

«I—4.4—(b)

~.o-|' I I

0 50 l00 l50 200SUBSTRATE TEMPERATURE ( C)

FIG. 2. Variation of the x-ray diffraction intensity

ratio, I~/I2 (a) and low-angle peak width, 1/hk (b) as afunction of substrate temperature.

4774 B.V. SHANABROOK AND J. S. I.ANNIN

HH

I-CQlK

3M

oG

a-P, which are similar to that of the highest T,film, this is not the case for I i /I2. In bulk a-Pthis ratio is 2.3, or -20% lower than the value forthe highest T, film.

The HH Raman scattering spectra of the rf sput-tered films prepared between 0—177'C are shown

in Fig. 3. These spectra exhibit rather strikingdifferences as a function of increasing T, for amor-

phous solids. This is noted both in the evolution

of peaks in the range between 200—300 cm ' and

at higher frequencies. In addition, various spectralminima are enhanced at higher T, values. Specifi-

cally, the features indicated by the arrows in Fig. 3

at 210, 280, 350, 380, and 500 cm ' of the HHspectra become more prominent in the higher T,films. The minima or pseudogaps at -165 cmalso become deeper for the higher T, films. Acomparison of these sputtered results with those ofbulk a-red-p, also shown in Fig. 3, indicates anumber of similarities. This is particularly thecase for the film prepared at 177'C. Although thebulk and 177'C film spectra are similar, some

differences are noted in the relative intensities offeatures at 210, 280, 300, 380, and 500 cm '. Avery weak feature occurs at -300 cm ' in thesputtered data, in contrast to a stronger feature in

the bulk a-P. This weak peak, which is not visibleon Fig. 3, is —

30 the intensity of the 500 cm

feature. This intensity ratio is rather constant forall of the HH Raman spectra of the rf sputteredfilms, in which the 300 cm ' peak could be ob-served within. signal-to-noise ratio.

Shown in Fig. 4 is an analysis of the T, depen-dence of the relative intensity of the major featureobserved at 350 cm '. As the measurement of theabsolute intensity is sensitive to the absorptioncoefficient, which is itself a function of T„' andalignment of the sample, the ratio of the intensitiesat 350 and 440 cm ', RHH(350), is shown in Fig.4. This ratio appears to be a reasonable normaliza-tion procedure, as the intensity variation at -440cm ' is relatively weak and exhibits the leastamount of relative change in shape for tne higheroptical band as a function of T,. As Fig. 4 indi-cates, this ratio increases by -90% between T,values of 0 and 177'C, and indicates the increasingprominence of the peak at 350 cm '. The intensi-ties of features occurring at -380 and 500 cmare observed to exhibit similar behavior with in-

creasing T„as they vary proportional to the peakat 350 cm

The sharp Raman features in bulk a-As at 165and 280 cm ' which correspond to those at 300and 500 cm ' have been attributed to bondingcoordination defects. ' ' %e have observed thatthe Raman scattering features in a-P films becomelarger with increasing T, . Furthermore, the Ra-man intensities at 300, 350, 380, and 500 cm ' ap-pear interrelated. As the concentration of bonding

2 2

600

I.S-E

0

* l.4—X

K

FIG. 3. A comparison of the 80-K HH Raman spec-tra of rf sputtered a-P films prepared at the indicatedT,. The arrows indicate features exhibiting largechanges. The Raman spectrum of bulk a-red-P is alsoshown. The HH designation corresponds to incidentand scattering fields within the scattering plane.

IP I

0 50 IOO 150 200SUBSTRATE TEMPERATURE ( C)

FIG. 4. The T, behavior of the Raman ratio,RHH(350 cm '), where RHH(3SOcm ')=IHH(3SOcm ')/IHH(440 cm ').

4775L PROPERTIES OF ~ ~ ~AND VIBRATIONALURAL A24

e ex ected to becomecoordination eT fl s and since the Ra-smaller for the ig '

300 and 500 cm —ap-man intensity

f normally coordinah th d'f"t 'd'1

features of a norma-P network, we sugg h test that t e

VH Raman scattering p

odification.s ectra ofThe depolarized V a

t ehe rf sputtered filmss are shown inistinct features at 160 210, 280,cm ' become more

films. The lowes-dt d

' f' is also observe otoThis eak is observedis increase . is

occur at —12 cmm and — c

'b tio'

th 177 C77 and 0 C, respective y.

the larger backg round contri u iin the appearancefilm could result in

nc eak, the larges pt possible shift ish'1'" f-12 cm . T p

p p

k Raman coupling"' "'"'"""u'"'"'"1dg f hot si nificanty i e

ims,'

1 a shi ofilms, the spectra imp y

high ef T mensity of states o -

d HH spectra ofA compariso n of the VH anthe features at -28o,5 indicates that t e eaFigs. 3 and

—i are rather polarized350, 380, and 500changes observed inAlthough stil m

'1 measurable, the c ang

correspondinglya~ager than thoae '

H'

yH) Of selectedzed Rama Pi Fi

film.380, and 500 cmt -375 Cma sin le pea at-latter indicates g

d h t such po]arized92' have note1

everal authors ''

tors where locaced for eigenvecsca emodulated in p ase.

ttering js enhanceh geeman andnd lengths are Io

tall Polarized spec

with the spectra p-

h her optical-bandthree distinct, goccurrence o5~ m

—' in H»f tures at -350 380, andeaspectra may no,t however, beand totally polari

1 of pyramidal„ndom coup»gexplained by a ra' ' t eaks at 350 and

~ 22 absence of distinc PThe ald rise due to a380 Cm of the 0 oC film cou

~

le broad peakf these ~odes i tobroadening o

K

6)

II

77oC

500cu (cm ')

600

rison of the 80-K VH Raman spec-fi ed at the indi tedfilms prepar atra o p

s ectrum of bulk a-re-co p d t incident and scat-

S'

The VH designation co ptered fields perpendicular and paral e opa, ' 1.plane, respective y.

500I

300 400~ ~c~-'&

'son of the totally polarize'zed Ramand h drf s uttered a-P films preparespectra of rf spu e

ed T~.

4776 B. V. SHANABROOK AND J. S. LANNIN 24

I

oE 1.8OFO

1.4—X

IO' I I

1.8 2.2 2.6I)/Ip

(o)

I

2.8

2.2 I

I

E 1.8—OtO

1.4—K

1CI1.040 4.4 4.8 S.2

I/ak ()l)FIG. 7. The interrelationships of the Raman ratio,

RHH(350 cm ') and the x-ray-di6raction results for (a)the I~/I2 ratio and (b) )/ilk values.

at 375 cm '. This broadening could result due toadditional disorder relative to the higher T, films.The larger Lk and smaller Ii /I2 ratio of the O'C

film are consistent with this suggestion.We have previously shown in Figs. 1, 3, and 5

that marked modi6cations occur in the Raman andx-ray diffraction spectra as a function of T, . InFig. 7 we examine the correspondence between

changes in these static and dynamic probes. InFig. 7(a), the interrelationship of RHH(350) and

I&/I2 is shown, while the correspondence between

RHH(350) and 1/b, k is shown in Fig. 7(b). In bothcases, as the HH Raman intensity of the feature at-350 cm ' increases, the I~/I2 and 1/b, k values

also become larger. As the intensities at 350, 380,and 500 cm ' exhibit similar T, behaviors, thefeatures at 380 and 500 cm ' are similarly relatedto the low-angle diffraction parameters. This indi-

cates that the structural correlations, which areprobed by the x-ray diffraction measurements, arerelated to the polarizability correlations examinedwith Ra'man scattering. Figure 7(a) indicates anapproximate linear variation between RHH(350)and I&/I2. In contrast, RHH(350) is a weak func-tion of 1/Ak at lower values of the latter, while athigher T, values both RHH(350) and 1/bk in-

crease. These results suggest that the Raman spec-tra are more directly correlated with variations inthe intensity of the low-angle diffraction peak rath-er than the width of this peak for the sputteringconditions employed here.

2 2 l

DISCUSSION

A recent theoretical Raman study has em-phasized the role of correlated first-neighborstretching motions in AX2 glasses in a one parame-ter, central force model. Such motions lead to arelatively polarized high-frequency band-edge modein this system and a depolarized VH Raman spec-trum that is of the form of the phonon density ofstates. This study also indicates that ifintermediate-range order is present in the amor-phous network, then the VH spectra will notresemble the phonon density of states, but may beenhanced for selected modes. While the a-PRaman spectra differ from these AX2 glasses andindicate a more detailed vibrational spectrum, cer-tain qualitative general conclusions of the theorymay be applicable.

A comparison of the VH Raman spectra of bulka-P with a neutron scattering experiment indi-cates differences between the VH spectrum and thedensity of states that are consistent with thegrowth of dynamical correlations associated withintermediate-range order. The similarity of thehigh-T, films and bulk a-P-, shown in Fig. 5, implythat intermediate-range order is present in thesefilms. These results indicate the first experimentalevidence of intermediate-range order consistentwith the theory of Martin and Galeener. Such or-der may also, within the general theoretical Ramanframework, modify the polarized Raman com-ponent. In contrast to the depolarized spectrum,however, the polarized component is sensitive toboth correlations. within the first coordinationsphere as well as those of longer range.

In Fig. 8 the background subtracted, higher op-tic band, VH results are shown. The full width athalf maximum of these bands, as denoted by thearrows, is observed to increase for the higher T,films. This is somewhat surprising as the phonondensity of states might be expected to become nar-rower for the more correlated, higher T, films. Inaddition, the experimentally determined phonondensity of states of bulk a-red-P exhibits a nar-rower bandwidth than the VH Raman spectra ofthe bulk material or any of the rf sputtered resultspresented here. This apparent inconsistency is at-tributed to the presence of intermediate-range orderin the bulk material as well as the a-P films. Anincreased coupling to the modes at 350 cm ' ofthe VH spectra, due to intermediate-range polariza-bility correlations, could result in an increase in thehigher optical bandwidth relative to the phonondensity of states.

24 STRUCTURAL AND VIBRATIONAL PROPERTIES OF. . . 4777

I

l77oQ

I

300I

500

FIG. 8. A comparison of the high-frequency VH Ra-man spectra of the rf sputtered a-P films prepared at theindicated T, . The arrows indicate the full widths at halfmaximum of the bands.

Although some modifications in local bond-anglefluctuations may occur and lead to a broadening ofthe high-frequency VH band at lower T, values,the growth of selected high-frequency features areattributed to increased intermediate-range polariza-bility correlations. This is reasonable, since a-Asfilms prepared at two temperature extremes indi-cate similar bond-angle variations, for differencesin I

& /I2 of -30%. The increase narrowing oflower frequency peaks and minima in the Ramanspectra of Figs. 3 and 5 may also be a consequenceon increasing intermediate-range order. This mayalso apply to the low-frequency Raman peak,below 100 cm ', which narrows and shifts tolower frequencies with increasing T, .

The comparison of diffraction and Ramanscattering measurements in Fig. 7 indicates thatdynamical correlation effects appear to be relatedto the growth of structural correlations. Similar,less detailed evidence exists in the case of a-As. '

In the limiting case of a-Sb, low-angle x-ray-dif-fraction measurements in sputtered films with

T, 100 K indicate a very weak peak at k 1.1

A ', with Ii/I2 0.1, while the Raman spectraare relatively structureless, as is the depolarization

ratio. In order to discuss correlations in more de-tail it is necessary to consider various structuralmodels for amorphous group-V systems. Moststructural models have considered that these sys-tems m.ay be locally viewed as being quasi-two-dimensional in character. An exception to this isthe tubular model of Krebs and Gruber' whichsuggests that linear tubular arrays similar to thosein Hittorfs P may be present. This model does not,however, yield reasonable agreement with the radi-al distribution function (rdA of a-P and would re-

quire further study of intertubular arrangements todetermine if improved agreement with experimentis possible. Other models vary in the extent towhich the quasi-two-dimensional systems exhibitinterlayer and intralayer structural correlations.The two limiting cases are (a) the random networkmodel for a-As of Greaves, Elliot, and Davis,which has a relatively random dihedral angle dis-tribution with little interlayerlike correlations, and

(b) microcrystallitelike models ' ' in whichparalle1, relatively ordered, layers are present. In-termediate to these structures are layer modelssuch as that suggested for a-As in which a mixtureof staggered and eclipsed dihedral bonding anglesare present. Additional layer models have beenconsidered for a-As by Beeman and Alben ' andPopescu. All of the above models are assumed tocorrespond to a given structure of a-As, that ofpresumed lowest energy, given the relaxation pro-cedures employed. These models do not, for exam-

ple, .consider that variations in structure are possible,Such variations are quite graphically indicated bythe present a-P results as well as those in a- As. '

While the random network and layerlike modelsare similar in terms of locally two-dimensionalcharacter of the structure they differ in the extentto which the layers are ordered within, a well asbetween, themselves. Beeman has recently calculat-ed I(k) for a-P using the a-As, Greaves-Davismodel relaxed to the 102' average bond angle of a-P. His results yield a much smaller low-angle peakthan that of bulk a-P or any of the sputtered filmsreported here. As the Greaves-Davis model exhi-bits little layer parallelicity locally, this suggeststhat a less random, more layerlike model may bemore appropriate to a-P. If it is assumed, as is

reasonable for the P system, that interlayer interac-tions are relatively weak, then Raman scatteringprimarily probes dynamic correlations in'polariza-bility within such individual layerlike regions. TheRaman spectra will then depend on intralayerlikecorrelation functions that are in general a function

4778 B. V. SHANABROOK AND J. S. LANNIN 24

of both structure and atomic displacements. Sim-

ple structural and dynamical correlation lengthsthus may be difHcult to obtain directly from exper-iment, except in the low-frequency Debye-type re-

gime. ' In contrast, regular structural features ei-ther within or between local layerlike regions arerequired to obtain a diffraction peak. In layerlikemodels it is assumed that the low-angle difFraction

peak is a consequence of interlayer correlations,where various degrees of disorder or "buckling"within the layers are assumed. In this type ofmodel the width of the low-angle diffraction peakis a statistical measure of the average interlayercorrelation length. In contrast, the relative intensi-

ty of this peak wiH depend both on intralayer andinterlayer correlations. Thus, I~/I2 might be in-

terpreted as the fraction of material in which locallayers tend, on average, to be parallel. ' As such,I

~ fI2 would then depend on both intralayer andinterlayer correlations.

In bulk a-P the I& /I2 ratio of 2.3 is significantlylarger than the value of -0.4 observed in bulk a-As, while the widths of the low-angle peaks aresimilar. Within a layerlike model this implies agreater degree of intralayer structural correlationsin bulk a-P. The rdf of bulk a-P indicates -8atoms in the second coordination sphere, while a-As has -10 atoms. The larger number of atomsin the second coordination sphere of a-As indicatesa trend toward increased back-bonding interac-tions. This trend is consistent with increased co-valency" of a-P as indicated by a static bondcharge in a-P that is larger than that of a-As by-a factor of 1.8. In addition, a-P has a narrowerbond-angle variation, (b,8)=4.3' versus 7. 1' in a-As. ' ' The decreased fluctuations in a-P from themean bond angle would result in increasing in-

tralayer order, relative to a-As.An additional indication of increased structural

correlations in a-P is exhibited by the Raman spec-tra of bulk a-P and a-As shown in Fig. 9. Thespectra have been scaled by the relation

coA, ——0.56cop, so as to yield the maximumcorrespondence of spectra features in the two sys-tems. The scaling factor of 0.56 agrees with thatobtained for the corresponding crystalline, layerlikeorthorhombic forms of P and As. As Fig. 9 indi-cates, there is a considerable similarity in the formof the two spectra, suggesting related microscopicstructures. The a-P data indicate, however, a fargreater degree of resolvable features. While thiswill in part reflect smaller variations in bond angle,it is also a consequence of increased dynamical

0)

3

K

COK

0i60-

i20-E

80-3& 4o-

'o

(b)

I I I I

200 400 600m(cm ')

CO

4-

K 2-IXIK

30

320

240-EO= i60-3

80-

lOO 200cu(cm ')

300

correlations that arise from enhanced intralayerstructural correlations. This is also consistent with

the greater similarity of the VH Raman componentand neutron scattering spectra ' in a-As than a-P.In a-As an increase in metallicity results in in-

creased bond-angle fluctuations and back-bondinginteractions, both of which tend to reduce dynami-

cal correlations. In contrast, the greater covalencyof a-P allows for the potential of a more ordered

layerlike structure with reduced interlayer cou-

pling.

CONCLUSIONS

The observed changes in the Raman and x-raydifFraction spectra with T„ for fixed sputteringconditions, have been suggested to arise from

dynamic and static correlations in atomic displace-ments and positions. The experimental results,

FIG. 9. Comparison of the Raman spectra (a) and in-frared absorption coefficients (b) of bulk a-red-P with theRaman spectra (c) and absorption coefficient (d) of bulka-As.

STRUCTURAL AND VIBRATIONAL PROPERTIES OF. . . 4779

along with recent theoretical work, provide, we be-

lieve, the strongest evidence to date forintermediate-range order and related dynamicalcorrelations in amorphous solids. A possibledescription in terms of a generalized layerlikemodel in which intralayer- and interlayerlike corre-lations in structure and interlayer dynamical corre-lations is suggested. Within this model the growthof intralayerlike correlations with T, could accountfor the substantial changes in the high-frequencyRaman spectra. In addition, the shift of the low-

frequency Raman peak may also be a consequenceof increasing the layerlike character of the vibra-tional modes. 'Modifications of intermediate-rangeorder may, for example, arise from variations indihedral angle distribution, ring statistics, or moreextended network geometrical factors. Furthertheoretical work is needed to determine if such alayerlike model may account in detail for the dif-fraction and Raman spectra and their variation.The intense low-angle peak in a-P clearly placesimportant constraints on such models. In contrastto most studies in amorphous solids, this work em-

phasizes the nonuniqueness of the amorphous stateand the need for a range of structural models for

a-P. This is also the case for the related a-As anda-Sb systems where structural and dynamicalcorrelations are also suggested. In contrast tothese systems, where weak back-bonding interac-tions play an increasingly important structural role,a-P is more covalent in character. This impliesthat dominant interlayer van der Waals couplingallows in both the structure and dynamics for amore correlated amorphous solid. As is intuitivelyreasonable from crystalline solids, structural corre-lations appear to be a requirement for the high-frequency dynamical correlations. The experimen-tal results in a-P further -indicate that such correla-tions appear to be continuously variable.

ACKNO%'LEDGMENTS

We wish to thank Dr. Dorn of the firm ofHoechst for the black P sputtering material, R.Messier and J. C. Phillips for stimulating discus-sions, and D. Beeman for communicating unpub-lished structural results and for useful discussions.This work was supported by NSF Grant No.DMR7908 390.

'Present address: Naval Research Laboratory,Washington, D.C.

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