-Eu-i -'El--

'~AD-AL16 028 ARMY ELECTRONICS RESEARCH AND DEVELOP14ENT COMMAND FO--ETC F/6 20/12L. INUCLEAR TRACER MEASUREMENTS OF LOW TEMPERATURE WATER DIFFUSION -ETC(U)

JU 8 R L PFFFER

UNCLASSIFIEO DELET-TR-24 ML

*Mouunuuson uu-EEEEEEEI-'El...---Eu....-i- - ENDII

iiiii, 10 ,

'121 111-.* 36

IIII

111111L25 11 ____

MICROCOPY RESOLUITION TST CHARi

RESEARCH AND DEVELOPMENT TECHNICAL REPORT

DELET-TR-82-4

0 NUCLEAR TRACER MEASUREMENTS OF LOW TEMPERATURE

* WATER DIFFUSION IN SILICON DIOXIDE (S1O 2) THIN

FILMS

ROBERT L. PFEFFERELECTRONICS TECHNOLOGY & DEVICES LABORATORY

JUNE 1982

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I - ERADCOM AUS ARMY ELECTRONICS RESEARCH & DEVELOPMENT COMMANDFORT MONMOUTH, NEW JERSEY 07703

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NUCLFAR TRACER MEASUREMENTS OF LOW TEMPERATUREWATER DIFFUSION IN SILICON DIOXIDE (SiO2 ) 6 PERFORMING ORG. REPORT NUMBER

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7. AUTHOR(e) 5. CONTRACT OR GRANT NUMBER(s)

Robert L. Pfeffer

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IS. SUPPLEMENTARY NOTES

A condensed report of the research described herein has been publishedin J.Appl,Phys,52 (2), 777 (Feb 81).

19. KEY WORDS (Continue on reverse aide if necessary and identify by block number)

OxidationDiffusion in Solids

ABSTR ACT (Crant wiw. rvrse idb Itf n s:esear md ident ,t by block number)

As part of an investigation of the physical basis underlying aspects of MOSprocessing technology, we have studied the transport mechanism by which waterdiffuses through thin SiO 2 films, This process is responsible for the formationof oxide layers on silicon wafers by means of thermal steam oxidation, which isfrequently employed in the manufacture of integrated circuit devices. We haveperformed tracer diffusion measurements involving network 18(;,demonstrating theimportance of oxygen exchange between the SiO 2 network and molecularly dissolved

(cont'd on reverse side)

W I JA " 1473 ETIO N OF IOV 6 IS OSOLETE UNCLASSIFIED

SECUFrTV CLASSIFICATION Or TMIS PAGE (Moon Pets Ene.nedI:!

UNCLASSIFIEDSFCLHITY CLASSIFICATION OF THIS PAGE(Whau Data £flte , d)

>3, Abstract (Cont'd)

water. We have foun ithat in the presence of water, bound network oxygendiffuses through SiO 2 as a constituent of molecularly dissolved water. Employingmethods common to state-of-the-art semiconductor technology, the central rggionwithin a thermal oxide layer grown on silicon was enriched with immobile 0 hVion implantation. After heating in atmospheres with different water contents,the extent of 180 diffusion was determined by observing changes in the concen-tration profile (i.e. the chemical concentration as a function of depth) ofimplanted 180 by means of nuclear resonance profiling. In this technique, high-

energy protons from a Van De Graaff accelerator lose e~rgy in their passagethrough the oxide until their energy falls to a resonant energy of the180(p,c)I5N reaction. High-energy alpha particles, emitted in this inelastic

reaction from the 180 which is located at that depth, are detected afterescaping from the surface. The observed thermal broadening of ion-implant,strihutions permitted bulk diffusivity to be measured conveniently at temper--ires or gas-phase concentrations much lower than previously possible. Dif-...'Ons conducted in steam at 1 atm (at temperatures as low as 250C) showed an:'v;,tion energy of about 17 kcal/mol, which is close to that originally

-'w,,isured for water permeation in SiO 2 . Diffusions in both air and dry nitropenY hwed a similar activation energy, with respective ore-exponential factors two

three orders of magnitude below the steam value. Diffusions in low presF:urc-'r vapor showel a clearly linear dependence on gas phase water concentr.atitn

to 80 ppm, in contrast to thermal oxidation results reported by othersThe results of this study are consistent with a recently proposed model of:'ter diffusion in Si02,in which the diffusion mechanism is the interstitial-nnlsport of dissolved molecular water accompanied by a reversible reaction with

'con-oxygen bonds in the network.

NASI

UNCLASSIFIED

CONTENTS

Page

INTRODUCTION I

Background 1

Molecular Structure of SiO 2 2

Ion Implantation and Its Effect on SiO2 5

Transport of 02 and H20 in SiO 2 8

Nuclear Profiling Techniques 20

EXrERIMENTAL PROCEDURE 25

Materials-r a&- ----- * -25

Thermal Treatments 25

Nuclear Resonance Profiling 31

RESULTS 40

DATA ANALYSIS 46

Method of Determining Tracer Diffusivity 46

Temperature and Pressure Dependence of Tracer Diffusivity 52

DISCUSSION

Absence of Ion Bombardment Induced Damage in SiO 2 Network 57180 Tracer Diffusion 58

Water Permeation Kinetics 60

CONCLUSIONS 65

ACKNOWLEDGMENTS 66

APPENDICES

A. Evolution of 180 Distribution 67

B. Evolution of Alpha Particle Yield 70

C. Proton Energy Straggling Distribution 77

D. Nonequilibrium Permeation Kinetics 81

Bibliography 84TABLES

1. ACCELERATOR ENERGY CALIBRATION REACTIONS 37

2. SUMMARY OF THERMAL TREATMENTS AND RESULTS 41 & 42

3. COMPARISON OF METHODS FOR OBTAINING TRACER DIFFUSIVITY 56

FIGURES

1. Schematic diagram of a two-dimensional structure of SiO 2. 4

Aft

(KEY TO FIGURE, p 12) Temperature Dependence of Deff:H 13

and Do02 in S'02: previous permeation results.

3. (KEY TO FIGURE, p 18) Previous measurements of parabolic rate 19

constants for thermal oxidation of Si in 07 and steam.

4. Principle of nuclear resonance profiling. 21

5. Analysis of residual gas in ion implantation apparatus 26

6. Apparatus for thermal treatments in steam. 29

7. Apparatus for thermal treatments at low pressure. 30

M. (KEY TO FIGURE, p 32) Van de Graaff accelerator: experimental 33

area.

9. (KEY TO FIGURE, p 32) Van de Graaff accelerator: operating 34

console.

: n&chamber. 36

7. 27Al(p' )2 Si gamma ray yield curve near 991 keV resonance 39for thick target.

'?;i, h, c. (KEY TO FIGURES, p 40)

a. Observed alpha particle yield curves for selected samples. 43

b. Observed alpha particle yield curves for annealed samples. 44

c. Observed alpha particle yield curves for low D*t samples. 45

o Theoretical 180 concentration profiles in SiO 2 layer after thermal 48

treatments.

14. Theoretical alpha particle yield curves (labels indicate n). 49

5. Time behavior of theoretically derived peak alpha yield. 50

Observed temperature dependence of 180 tracer diffusivity at 53 & 54

I atm.

Pressure dependence of tracer diffusivity at 820 C. Labels 55

indicate P in fractions of 1 atm.

increment in the parabolic rate constant upon addition of H2 0 to 63oxygen atmosphere, as percent of BH 2 0 in pure water vapor.

ii

NUCLEAR ','RACI'I( .EAHURE z 1,NOF LOW TEMPERATURE, WA EIR DIFFUSION

IN SiO2 THIN FILMS

INTRODU CT [ON

&ackgro und

The formation of thin insulating films on the surface of semiconductormaterials is an important part of modern integrated circuit technology, which

nas assumed a central role in the production of Army control, communications,

raidar and data processing systems. The Ehin film can serve in integrated

circuits as a dopant mask, surface protector, primary passivation coating,

component isolator, and as gate insulacor in MOS structures (1). Other

applications of current interest include solar cells and power transistors.

Because of their military and commercial importance, various means of film

growth have been intensively studied, especially for high-quality gate

_insujators on silicon surfaces. For that application a more or less standard

practice therma 1

A properly made thermal oxide film must have a high dielectric strength and

immunity Lo electrical breakdown, contain an acceptably low amount of trapped

charge (particularly at the oxide-silioon interface), be uniform in thickness,

bond intimately to the semiconductor sUbstrate, and resist chemical or mechan-

ical degradation. These requirements are well satisfied by present thermal

oxid,tion methods However, as integrated circuit devices become more

complex a7a opor.,te at higher speeds, they require smaller and more closely

packed component structures. The scale of sizes being contemplated has now

reached a point where basic changes will soon be required in manufacturingmethods. For example, the need is foreseen to hold temperatures in all steps

of a proce3si'ng sequence low enough to prevent significant migration of

dopants. This has spurred work on low-temperature, high-pressure thermal

oxidation (2,3).

As might be expected, these low-temperature processing techniques may

offer enougih advantages over present high-temperature processing to supplantit in the manufacturing technology of future integrated circuit devices.

ThLse techaiques may well produce devices having electrical characteristics,ucimes cand reiiabilities surpassing any previously attainable. The ubi-

cjuity of SiO2 films oh semiconductor materials has been accompanied by a

vast :esearch effort - a recent bibliography (4) lists 560 references.

included are many studies of film formation, particularly thermal oxidation,

i. A. S. Grove, Phyics and Technology of Semiconductor Devices(Wiley, 1967)

2. R. .. Zeto, C. C;. Thornton, E. ifrvckowian and C. 1). 13osco, J ElectrochemSoc 122, 1411 (1975)

3. 1.. 1". K Zz an,, ;,. I F. H!owelis, .1 Elcctrochem Soc 126, 1822 (1979)

. . Ag' i,, anfn, Sol St Tech 19, 3 (1977). I

.:raaLy all of this work has been device-oriented. Physical models of theOxidation process have received little attention; only now are models being

tested with sufficient care to generate a consensus of acceptance. Through-out the device-oriented literature, one encouiiters a virtually unanimous

lack of appreciation of both the nature and the consequences of the water-

i02 reaction. The lack of reproducibility in thermal growth kinetics datacnused by the presence of water, even in trace amounts, has lately been

corructed through careful control of conditions (5). For the future, arater understanding of the mechanism responsible for oxidation in the

,)res'1ce of water is imperative, especially in the new low-temperature regime,

where it now appears that processing of the coming generation of devices will

place.

he purpose of this investigation was threefold:

* clarify the mechanism of Si0 2 film growth in atmospheres contain-S, .:hrouh its determination of the kinetics of network oxygen. .. .. . .. . .. .. . . .. . -7 -:.... .. --.. . . .-... . . ..---.-... . . . .- . . . . . . ..-. y- l--

f, thils work provides the irtdrect experimentaT -emonstration orol a recently proposed model of the oxidation process,, Accord-

- this model, growth proceeds by inward interstitial diffusion of'Ved iolecular water, which simultaneousiv reacts with the Sio, network

;.mrobile reaction products.

V,) ;ipply the technique of ion implantotion to measure tr.i'cer oxygen.' , i, Si0 2 . The observation of tracer distribution broadening both

.-s surface effects and enhances the sensitivity of diffusion measure-... ...... tt tracer diffusion measurements can be carried out at considera-

".:tji. temperatures,

To provide a framework for resolving several long-standing discrepan-,tween measurements involving water and oxygen diffusion in SiO 2.

ir -t id d d i V -rIer os i1 -oxygen dii. I fus ivi ties observed in pe rmea-.-.,ri ments, as we[ as in measurements involving the pressure depend-

, the growth kinetics of thermal silicon oxidation, This work demon-_hat these can be resolved through a proper understanding of water

- io, in the oxides.

" Structure of SiO.

'" ' basic building block of vitreous silica, the amorphous form of Si0 2 ,'tr"hedron of oxygen ions around a central silicon ion. According to*'-a[y accepted model originated by Zachariasen (6), each tetrahedronlic to Four others by silicon-oxyg, en bonds at Its corners in a con-''ire,' - ',mensional random network lacking any symmetry or periodicitv.

S, Mav,, nd W.H. Evans, "Development of Hydrogen and Hvdroxvl Contamina-tion in Thin Silicon Dioxide Films" NBSIR 78-1558 (NBS, March 1979)

6. W. H. Zachariasen, .1 Am Chem Sot 54 3841 (1932)

2

;is iIlu.trated in Fi' r i. The Si-() WLertoILc disLaMcC is 1.62 A; the

0-O distance is 2 65 A. The distribution of Si-O-Si bond angles ranges from1zO ° Co 1800; it is skewed toward the smaller angles and has a single maximum

located at 1440 (7). It is narrow corpared to a fully random distribution,

so that the structure is quite uniform over several tetrahedra (although

not beyond that). "here is a good deal of experimental evidence supporting

this model which is quoted by Doremus, pp. 24-28 (8), including X-ray diffrac-

tion studies in terms of pair distribution functions, transmission electronmicroscopy and atomic vibrational spectroscopy via infrared absorption, Raman

enmission and inelastic neutron scattering. Beside this work are studies

involving X-ray diffraction (9, 10), inelasLic neutron scattering (1i), and

,-_lectron diffraction and infrared absorption (12).

Several recent experiments (i3, 1, 15) support closely related but com-

peting models based on a collection of distorted microcrystallites such as

cry--tobalice, ech conr::ining only a few tetrahedra. All viable models,

however, share the esSential picture of vitreous silica as a loosely packed

m aterial in wich ,-avities or interstices are surrounded by walls of more or

less intact SiC, tutraedr, Shackelford and Masaryk (15) give the mean

diameter of the interstices as 1.96 X,

Ther-e is mu'h evidencc that zhy:I=ermal oxide' layers formed on silicon

surfaces liav: Ltte same St rcture as vitreouS :ilica X-ray diffraction

exper Dt. t 1 '.n :" t W. aide layers to n)e amorphous (16). The density of

e ay, r , t, :o tn< of fused silica (17), as are the changes in

den.ay . e ionizing radiation (18). The optical properties are

esscntiIlly -iL .ia1 (19), as are the Si-O-Si bond angles obtained from

electron Jiffraction and TA absorption experiments (12).

. .ozz and ,. L. W'ar ret , .i A,.pl Crvst 2, 164 (1969)

8. R. IH. 0occ2ms, ( ass 4 'e,-e (Wiley, 1973)

9. j. ii. r\onnert and ,. Kare, Acta Cryst A 29, 702 (1973)

10. A. ii. Nartc-, .I Chem Pnys 5h, 1905 (1972)

11. A. 1. Leadbetter and M. W. Stringfelliow, "Neutron Inelastic Scattering,"

Proc Grenoble Conf (IAEA, Vienna, 1972) p. 501

2. N. Nagasima, Japan J Appl Phys _9, 879 (1970)

13. G. firatter, (;. iioden, A. Ba ogh iid A. Andreeff, Appi PlIvs 16, 2l

.14. P. i. (;ask, ll, 1). W. Johnson, I. Nuncr'.vst SoI 20, I/1 ( 19/b)

15. J1. F. Shacke1ford and .1. '. M:isas vk, Noncrvst So] 30, 127 (1978)

16. M. B. Brodsky, 1). Cubicciotti, J Am Chem Soc 73, 3497 (1951)

17. R. :1I. Doremus, ,1 Phys Chem 80, 1773 (1976)

18. 1". P. EerNisse, J Appi Phys 45, 167 (1974)

19. A. N. Knopp and R. Stickler, Electrochem Technology 5, 37 (1967)

3

1.r Set diagram ....

[,;

Xiremus (8)). The oxygen atoms (larger circles) act as bridges betweentetraliedrai. Note the large size of the interstices.

* , R. H, Doremus, Glass Science, p 27 (Wiley, 1973)

4

I on Inm- I Li u L,1ot ,i , l I t'iL'S L I t S o n ,

The implantation of heavy ions in the tens Lo hundreds of keV range isby now a routine aspect of semiconductor processing (20). The implantation

of dopant elements directly into desired regions in the interior of semi-

conductor materials has eliminated the need for high-temperature diffusions

to induce their migration from the surface, allowing much greater controlover material properties. In regular lattice structures, the ions produceheavy damage, and a significant fraction of them remain interstitial. Whenappropriate arnealing procedures are employed, the damage is healed virtually

completely and the dopant ions assume desired substitutional sites (21).

There have been many studies of ionizing radiation effects on SiO 2 as

well, One motivation for these is nuclear vulnerability assessment formilitary applications; another comes from the frequent practice of implan-tation into silicon through previously grown SiO 2 layers. Many differenteffects have been observed, including radiation compaction (22, 23, 24, 25,

18), enhancement of HF etch rate (26, 27), accumulation of thermal energy(28), changes in Raman and IR spectra (29, 30), change in refractive index

20. J. W. Mayer, L. Erikssoa and J. A. Davies, Ion Implantation in Semi-

conductors (Academic, 1970)

21. J. R. Gibbons, Proc IEEE 60, 1062 (1972)

22. W. Crimak, J Appi Phys 43, 2745 (1972)

23. J. E, Shelby, J Appl Phys 50, 3702 (1979)

24. C. B Norris and E. P. EerNisse, J Appl Phys 45, 3876 (1974)

25. E. P. EerNisse and C. B. Norris, J Appl Phys 45, 5196 (1974)

26 W. Kratschmer, "Effects of Heavy Ion Radiation on Quartz Glass,"

ru,, _. lit_._ IuI) . NzcI Phot iriphy - iynl. '.rk lDhl,,ctl4 r

(bucharest [972) quoted in Antoniii (1978)

27, A, onfret and J. Bernard, "Chemical and Electrical Behavior of Ion

implanted Si0 2 Films" in Proc. 2nd Int. Conf. Ion Implantation in

Semiconductors, I Ruge and J. Graul, eds. (Springer-Verlag, 1971).

28. V. Antonini, A. Manara and P. Lensi, "Ion Irradiation and Stored Energy

in Vitreous Silica, in Pantelides (1978), p. 316

29. J. B. BaLes, R W. Hen.dricks and L B. Shaffer, J Chem Phys 61, 4163

(t974)

530. C. K. Fritzcn~e an'. W, Rotherniund, J Electrochem Soc 119, 1243 (1972)

(bid), thermoluminescence (31), and generation of deep electron traps, 33, 34) and color centers (35, 36, 37).

The mechanisms responsible for these effects fall into three roughcategories, which are separable to some extent by choice of appropriateprojectile and by studying the annealing behavior of the defects created.The first is bond breaking resulting from ionization reactions, exemplified

by dangling bonds and oxygen vacancies. These are produced by X- and g;l.naradiation and electrons, and are largely annealed out by heating to 400 C;some remain until 700 C (25). The second is formation of new bonds between

implanted heavy ions and the network, These do not anneal out but remain asteatures of an altered network (34). The third, structural alterationscaused by atomic displacement, is associated with heavy ion bombardment,These may be produced by direct nuclear knock-on reactions causing displace-

I It (If recoils, ;s we II as Lhlrough abso rp)tion of suff icient vitr;t tloma I-i.,rgy to reconfigure strained bond structures. Their importance increses

.ihincreasing ion mass and decreasing velocity, being especially signifiJ-'it: near the end of the ion paths; most displacement damage is confined

'hut region (38, 39). An additional effect peculiar to the presence ,_hus recently been identified by Shelby (23) as dilatation or

,-'. '- o network, possibly caused by a radiation-inducec increase"- an icr if binding sites for SiOH and SiH. Irene and Ghez (40) hav-

! ',cuJa)ed that this dilatation may contribute to the pronounced effect ofameunts of water in the network.

\s "_n the case of silicon, inert-atmosphere heating has been observed to.'.o out tie various radiation-induced alterations to the SiO 2 network.

'. Shelby, J Appl Phys 50, 3702 (1979)

E. P. Ee-Nisse and C. B. Norris, J Appl Phys 45, 5196 (1974)

G'. . W. Arnold, "Thermoluminescence in Ion-Implanted SO2," in Chernowet al (1977)

'. ',.tic'van and M. Simons, ' Appl Phbs 43, 2897 (1972)

" .. !,hrsoi, W. C. Johnson and M. A. Lampert, J Appl Phys 46, 1216

. . M)i~lria, 1). R. Young, W. R. Hunter and C. M. Serrano, IBM J Res

2-2, 2L-;9 (1978)

* . . Arnold, IEEE Trans Nucl Sci NS-20, 220 (1973)

\rnol d, "Vibrational ind L!,:tronic Spectroscopy of Ton-lmpIlanti-1-In,,,,ed )efects in Fiused Silica and Crystalline Quart:, . in

.K H. M :ce! , !r., !;. I). Evans, R. J. Ginther, U.. 1. Friebele, D. L.rscom and ,. '-k. NRI. Memo Rpt No. 2934 (NRL, 1974)

38. 1). K. Brice, Radiation Eff (GB) 6, 77 (1970)

39. K. B. Winterbon, Ion Implantation Ran e and Energy Depositions, Vol 2(1'lenum, 1975)

40. E. A. Irene and R. Ghez, J EIectrochem Soc 124, 1757 (iq77)

6

.ALLoa c~c aL 2o obse rved that too thirm~ih Le 2 iaring)momardment with MeV alph , partic-e:s w i r .:.:, upoO heating to about

470] C, whiu that ac:uCIulated during Ioa me t W L1, '6.5 XV Ni+6 ions was

relelscu in two stages: partly at 450 C and tile r0st aL about 610 C.

Motifret and Bernard (27) reported that radiaition eo nement ,f the HF etch

rate largely disappeared after a 20 rain anneal at (00 C (totally after

000 C), Wang et al (41) reported zne changes (ialiced by 50 keV Al ion

,'I),'.nation) in iV absorption in the 7.5 eV band to be 75% gone with a

500 ' anneal (totally after 900 C), and that the amplitude of a similarly

du.c SR resonance (with g = 2.0037) decreased with increasing tempera-

tui--!, Jisap)pearing by 500 C. Eernisse and Norris (25) in their thorough

,ompaction annealing, reported a relatively sharp return to initial

den ity temperatures increased beyond 650 C after bombardment by either

.27 -eV electrons or 250 keV protons, and a gradual return between 300 C

and 900 C after 500 keV4 0 Ar + bombardment. In sum, and as indicated by

Sigel (42), all scudies of radiation camage in ,iC), indicate that a 900 C

anneal is sufficient co completely restore the network to its pre-irradiation

"Ie Obu-:av OL of the implanted ions at tfie end of their range in the net-

8,ork ca:; cce i-: -sin> a m-,od f ion-network interactions propounded by:'rim,,' 1971 (22' I mak "9'h, .. -iji .Tis is a refinement of

it e C I.m Q- El i{ Jly pco osed h, So- z (44), in which heavyions c:rstcr Cr,, t network v. to c c ,, isions, causing a large

amna.rK[ vibcto-' I citotio, Subsecun. rapid refreezing leads to

refrocmatin ot . Is With the implanted ions in substitional sites. Evi-

,oencre this comes from SIMS measurements by H. Hughes (quoted in Johnson

e- al (3S)), who found that 30-min. anneals in N2 at 900 C failed to alter

the concentraticn profiies of Al implanted in Si02 ; a similar result was

obtained by zitaria et al (34) at 1050 C.

22. . Primak, J Appi Phys 43, 2745 (1972)

. .] . derNisse ana C. B. Norris, j App! Phys 45, 5196 (1974)

.7. a.nre and J. Bernard, "Chemical and Electrical Behavior of Ion

.planted Si0 2 Films" in Proc. 2nd Int. Conf. Ion Implantation in

Semiconductors, I. Ruge and J. Graul, eds. (Springer-Verlag, 1971)

2b. V. A.ntonini, A. Manara and P. Lensi, "Ion Irradiation and Stored Energy

rn Vitreous Silica,"in Pantelides, p 316 (1978)

33. N. M, Johnson, W. C, Johnson and M. A. Lampert, J Appl Phys 46, 1216

34. D. J. biMaria, D. R. Young, W. R. Hunter and C. M. Serrano, IBM J Res

Devel, 22, 289 (1978)

41. S. Wang, T. Russell and B. S. H. Royce "Annea]ing Studies of Al+

Implanted ,'i0 2 Thin Films." PSSL 300874 (Princeton U., 1974)

42. G;. H. Sigel, private communication (1.979)

43. W., .'rimak, Coi.pacted Status of Vitreous Silica (Gordon and Breach, 1975)

44..:,itz, Disc faraday Soc. 5, 271 (1949)

7

ran -p-ort of 0_and H20 in SiO

Definitions of Solubility

The solubility generally found in the literature is the saturation

concentration of gas dissolved in the solidPdissolved(sat) (in units of

,'Iecules/cm3 ) at standard temperature and pressure. A related quantity,

*:a. solubility ratio, also frequently appears in the literature. This

quantity is defined as thesteadv state ratio.Odissolved(sat)/ gas phaseS,,ven temperature and pressure. This is a dimensionless quantity. It

..........Piltnlf of atth Nl c a'ipl.l prw, o: I r VIdJed Ill hi M 1i.i~~ I;zi

., ,,e rved both outside and inside the oxide (I.e, in thv absence of"

: ocLation). Its temperature dependence - generally very weak - arises

- ossible temperature dependence in the activation onergy of molecular

)_'4 5)

!'C dt:'.usse shortly, the d.sqol 't :on f water it "U), Ln 1c!'e .

rt, cactcicn with the network, in w!:.h L 'I mo 1 ecul arlv (1 so lvel water

-:Les to form two OH units with thc, additional 0 ion being provided bv

* , etwork (46, 45). This reversible re.action

F2(0 + Si-O-S'. SiOll (1)

equilibrium concentrations of reaction products which are large

i ' that of molecularly dissolved water. The equilibrium concentra-

'- related by the law of detailed balance

K 2 =:OH * (2)

oC K2 (including any temperature dependence) is gotten from the

.. lities of molecular and "reacted" water (i.e. SiOH groups). It

* ,'n eered that the di. sociation of H2 0 leads to a reacted water

1': "hich is dependent on the concentration of vapor phase water.

t~,. Ko F. Shackelford and I. S. Masaryk, J Noncryst Sol 21. 55 (1976)

46. R. H. Doremus, in React vit of Solids, Mitchell, de Vries,

Roberts and Cannon, Eds., (riev, 1Q60) p. 667

Definitiuns oj jiffusiVitV

fherc are three diflerent diffusion coe:ficiens which arc involved inthe transport of tracer 18u. The firsL of these., Jeff, is that quantitynormally measured in permeation exper.'.ents. The basic method of determiningLiis effoc~ive diffusivity is by obsrving the steady-state flux J of gaspassing Lhrou,,h a m.bm')rane of thicknc, X, whisL- Lwo? -.urfaces are main-ained at differenIt pressures. From the b.sic equation J = -Df 1issolved

we have

XeD .. . 0 (3)D) _ = - -____ ~elt Ad ld steady-std te

where . - - , the differnce in concentrations at the two surfaces, isknown through independent r.oasurement of the solubility. The temperaturedependence of D) is generaliy expressed via the Arrhenius equation

Sr\ I Ea (4)

wlht.re .\ tJ ar the universal. gs constant (in uni;ts of kcal/mol/ K andeV / r rc ,<7iv ,IY) .:c (Q a a are twa tIct ,- ioc energy of diffusion (inunits c. i :m: a 'a \es ,ectively). De'f can aLso be measured dynami-

:i, . ,arv-;~ evolution of a mbient gas pressures in the early stages

oC e-tr perMeaion or" desorption in membranes, filaments or powders in anencluse,, vci '. m .see, for example, Doremus, pp. 128-130 (8)). It should benote". LaaL cff will be independent of ambient gas-phase concentration onlyif ti, fluxes of both the emerging particles and the dissolved species havetoe sac-,e pressure dependence. Such is not the case for water diffusion,where D,-,- is the apparent aiffusivity of reacted water.

S,,, transporL of the actual mooile species is described by the micro-eoplc diffusiv:tv D. It is influenced only by the interactions of individ-

. iffusing iolecuies wiL. the network. For a dilute gas (i.e. one with-otL ticant interaction between diffusing molecules) in a spatially

.aLiforr network, D is independent of ambient gas phase concentration,:,xiriel Location and dissolved gas concentration - it depends only on temper-atur . -or oxygen diffusion in SiO 2 , which proceeds without any appreciabledi suciation or reaction with the network, Deff and D have the same value.

howevec, for water diffusion, they are related by the equation

D = i) 2°') (5)

eff H 20 -jj OH

t1he traction represents the fraction of time that any particular OH groupfinds itseLf mcvia.; as part of a iifusing water molecule. The factor of 2appeajrs .5-ause eoah water molecule removes two OH groups from the network.

.Ii. , r,, , (:1.,-; Sci.,n'. (Wilov, 107)

9

i. third diffusion coefficient, D*, describes the apparent diffusion of

t::lcer L80. As will be discussed shortly, the mechanism responsible for the

,i ,r,ition of network 180 observed in this study is the exchange between

d1 Iluinlg water and network oxygen. The reaction between dissolved molecular

wa!iter and the SiO 2 network described by equation (1) acts to remove 180 from

its network site and to convert it instead to a constituent of diffusing

nolecu, l r water:

H2160 + Si- 180Si - SiI6 Ol+ Si 18 H 0 H2180 + Si- 160-Si .

the presence of free exchange, the tracer diffusivity D* is related to thu

;u,,Yivity of molecularly dissolved water by the equation

___ _ __ (6)

D* =D ___ _

f2,SiO 2 +fH 2l"O +fo()

., tion is the fraction of time that an 0 finds itself being carried

i diffusing water molecule. The factor of 2 accounts for the two.'-, per SiO2 molecule.

Mechanisms of 02 and H20 Diffusion

.r! on the observations to be discussed shortly, the mechanism of

S" ,,'-oxyen or water diffusion has been taken to be the interstitial trans-

dissolved molecular oxygen or water respectively. In neither case

', diffusion pro,:ess involve direct bonding between the diffusing

- .,(! the 5 i02 network. ilather it involves the transport of nonreacting

through the interstices or cavities in the network. This inter-

* odel was first proposed by Anderson and Stuart (47); they calculatedV,,:tion energy for diffusion as the elostic energy required to deform

, by en'argng the circular doorways between interstices enough for

isiing soecies to pass. An essential feature of this model is a lack

:* *ical binding between the diffusing species and the network (Milberg

.* . Although the model is simplistic, the functional dependence of activa-

,eigy upon molecular diameter agrees well with activation energies

for molecular diffusion of various gases in fused silica (Doremus,

( )) . it is also con-,isteiit with the !inear dependence of diffusivity..!'t pressure observed by Norton (49) for oxygen, whose diffusion is

,aiiied by any significant reactions with the SiO2 network.

":. ),-rem(us, Class Science (Wiley, 1973).Anderson and D. A. Stuart, J Am Ceram Soc 37, 573 (1964)

16. M. E. Milberg, "Diffusion in Glass," in Fast Ion Transport in Solids,

W. Van Gool ed. (lorth IUol.:nd 1973) p. 37S

49. F. o1. Norton, Natuie 191, 701 (1961)

10'4.A

This was demonstrated recently in a trdcvr experimenL cunuucLed by Rosencherot al (50) in which thermal oxide films which were first grown in natural

oxygen were further grown in 1 80-enriched gas. Almost all additional 180

was observed to collec: in a layer at the Si-SiO 2 interface, while less than

0.3% remained in the previously grown region. Great care was taken to

eliminate any water in this experiment.

The mechanism for water diffusion tarough SiO 2 is similariy thought toinvolve the interstitial transport of dissoived mohc(4uiar water (Doremus(46)). The transport of the diffusing species, dissolved molecular water, is

.- aiin postulated to involve no direct reaction with the network. However, asiiaicated in equation (i), a strong reaction occurs with silicon-oxygen bonds

in tne network, accounting for its high solubility as well as the square root

.:ependence of the reacted water concentration on ambient water vapor pressure.S:he reaction products (i.e. SiOH groups) are postulated to be immobile, while

t.e irolecuiarly dissolved wter diffuses with a difiusivity D, as discussedabove.

0? Solub~lity, Diffusivity: Previous Permeation Measurements

Prevous experimental values for oxygen diifusivity in SiOC were deter-mined using variants of the basic technique mentioned anve. By mass

spectrom,-ry. Norton (4)' measured the evolution of (160)2 gas insideevacLr0 ;411C1J bulbs waich were subjected for a time to a known oxygen

pressure cutside. haul and Dumbgen (51) and Sucov 52) introduced measured

quantities of 180 gas into chambers containing silica fibers, then observed

the decrease in Lbo:160 mole fractions with a mass spectrometer; Williams

(53) did the same for both bulbs and fibers. Their results (as they appear

in the works cited) nave here been compiled as an Arrhenius plot in Figure 2,

and are considered at length in the Discussion; it may be remarked here that

the three secs of very low oxygen diffusivities were all measured by means of

tracer 18 0 (to be discussed later) while the other was measured with natural

d2. Norton (49) a.so determined the 02 solubility ratio to be 1.9(10)- 3

, 2.3(10)-3 (at 950 C) and observed that the rate of permeation

, to th. fi:9st power of the ambient oxygen pressure. None of

works presents an explicit value of the 0? solubility ratio.

4'. RK. H. Doremus, in Reactivity of Solids, Mitchell, de Vries, Robertsand Cannon, Eds. (Wiley, 1969) p. 667

49. F. J. Norton, Nature 191, 701 (1961)

50. E. Rosencher, A. Straboni, S. Rigo and G. Amsel, AppI Phys Lett 34,

254 (1979)

51. R. haul and G. Dumbgen, Z Ele-trochem 6, 636 (1962)

52. E. W. Sucov, J Am Ceram Soc 46, 14 (1963)

33. f.. I. Williams, .J Am Ceram Soc 48, 190 (1965)

II

t i.jurj 2. (Following Page) Temperature dependence of D el:H20 and Do2

S;io2: previous permeation results.

KEY TC FIGURE

SvfMBOL SOURCE D0 (cm2 Is) Q (kcal/mol)

* Norton (49) 2.9(10)- 4 27.0

Haul and Dumbgen (51) 1.2(10) - 5 56.0

as quoted in Terai andHjyami (92)

Sucov (52) 1.5(10)-2 71.2

o A Williams (53) 2.0(10) -9 29.0

Moulson and Roberts (54) 1.0(10)- 6 18.3

Norton, Nature 191, 701 (1961)

)umbgen, 7 Flectrochem 66, 636 (1962)

Suctv, .1 AP Ceran.i Soc 46, 14 (1963)

-'. 1. Williams, .I Am Ceram Soc 4R, 110 (1965)

5A. J. Moulson and J. P. Roberts, Trans Faraday Soc 57, 1208 (1961)

2. IR. C. Weast, Handbook of Chemistry and Physics, 55th ed (CRC Press,

1974)

12

1t

TEMPERATURE - C

13001200 1100 1000 900 800 700 600

-8Ktn

I-

C

' -10 "1

u

-12 L \

000

11 6o

-14 -73CC

-JJ

-1i t -- j. _-

6 7 8 910 11 12*,-1041/ K

13

, . '

I 1' So I ub iI itv, N if f usivitv: Previous Permeation Measurements

In the case of water, Moulson and Roberts (54) measured the effectiveIulk (11i.fusivLty in vitreous silica slabs by observing permeation-inducedChaiW'es in optical density of the OH infrared absorption peak at 2.7 urn. Byt!s t.'hnique they also determined the number of hydroxyl groups per Si02

.. o : range from 6 x 10- 3 (9600 () to 3 x 100 (@1200 C) at 1 atmosphere, rvd it to vary as the square root of the ambient water vapor

.heir solubility results were confirmed by Shackelford et al (55). similar technique. Shackelford and Masaryk (45) later analyzed thisi,, a slightly temperature-dependent activation energy for OH-group

'The observed pressure dependence of Y1oH(Sat), as well as its largev! • i ase,. by the strung reaction of water with SiO2 , as noted.

cr, 'LLon of dissolved molecular waiter is inaccessible to direct

,, nhrh sma '1r -than -(Sat) rnth<r it must beamong known solubil ;tv ratios of nonreactive gases

ts mciec,':r size. Doremus (17),taking the molecular diameterS.is viscu,_es at 700 C) to be 3.3 . (Doreums, P. 133 (Fi), con-

t ', ,,!'_ ty ratio of molecular water is 0.01. Using Grove's

_ SiO 2 = 2.25(10)2 2 (cm- ) (7)

.t. Lict the results of Moulson and Roberts (54), and Doremus (17)

H (Sat)I2 894 (@ 600 C)0OH (Sat) = P(atm) x (8)

581 (@ 1200 C)

'r 's, . a._...cience (Wiley, 1971)

1i. :) oremus, J Phvs<' Ch-m 80. 1771 (1976)

45. . F. Shackelford and .1. S. Masaryk, J1 Noncryst Sol 21, 55 (1976)

54. J. Moulson and J. P. Roberts, Trans Faraday Soc 57, 1208 (1961)

55. J. F. Shackelford, R. L. Studt and R. M. Fulrath, J Appl Phys 43, 1619(1972)

14

The values oi Deff which were measured for h,0 diffusion in SiO 2 by

Moulson and Roberts (54) appear in Figure 2. If these are taken in conjunc-

tion with their measured values forPOH(Sat), values for the diffusivitv of

molecular water can be calculated by use of equations (5) and (8)j namely

.9(10)9 (@ 600 C)

D = cm/s. (9)

5,2(10)- 7 (@1200 C)

Finally, the tracer diffusivity may be calculated on the basis of free

exchange. Using equation (6) and the inequalities PSiO2>"POH >,> fH 2 0

we find that D* is related to Deff by

(TD-) (Sat) fi5(0) -4 0 600 C (10)free exchange - 7.5(10)- @1200 C

The value of P oi P 2 has been taken from the solubility measurements of

Moulsoi. and Robert-.

0., and 11,,L Diffusior through SiO Films: Thermal Oxidation Kinetics

e diffusion .n 1120 through SJO 2 is intimately involved in thecirmua. oxidacion f 1i . hen silicon is iai ntained at an elevated

e.rer w'e in .fn ax; .i tiasphere :iuch :. oxvgL-n e r stta.m, .i layer of, ;c ed c. " t r:ac , rfhi'h 11"s c , u ilai y in the presence of the

Vricu c ac" r-xeri -ants cited Ln Deal and urove (56) have estab-IL. t oxidaI i - , Us :zy the inward transport of oxygen through the

'yur 5s a cnstiLt .r, 01 rolecularly dissolved oxygen or water. The sil icons-bctr-,,.e is converted to new oxide by the incorporation of atomic oxygen atthe .x de-silicon int ,rface after molecular dissociation. The layer thickens

by formation of aew oxide underneath the existing layer.

As discussed previously, the dissociation products also react stronglywith the SiC 2 network only in tht. case of H20 oxidation (46); for oxygen,

the atomic oxygen reacts significantly only with the silicon at the interface

(50). In that case, as was pointed out by Blanc (57), an equilibrium exists,t ihe interface; atomic oxygen can either form new SiO2 or recombine into;,)Iecular oxygen. larcn was able to deduce equilibrium constants for these

:-fac~ions so as to produce a very impressive match to a large body of data ontie rizal growth kinetics, and disprove the existence of a hypothetical space-

charge iayer which Deal and Grove (56) introduced to reconcile the data to

, neir linear-parabolic model (discussed later).

46. R. H. Doremus, in Reactivity of Solids, Mitchell, de Vries, Roberts

and Cannon, Eds. (Wiley, 1969) p. 667

50. E. Rosencher, A. Straboni, S. Rigo and G. Amsel, Appl Phys Lett 34,

?54 (1979)

54. .. Mou3 son and .1. P. Roberts, Trans Faraday Soc 57, 1208 (1961)

A . B. E. D; aIvu A. S. Grove, J Appl Phys 36, 3770 (1965)

'. J. Banc, App] Phys Lett 33, 424 (1978)

15

It may be mentioned that oLher competing models for the thermal oxidati.iprocess also exist, including transport of charged interstitial oxygen andholes (58), transport of 0-, 0 = and 027 ions through a nonstoichiometrih:interphase region beneath the oxide layer (59), and transport of excessoxygen and silicon centers (60). None of these provides an acceptable fitto the experimental data. A model of interfacial dissociation/recombinationsimilar to Blanc's was proposed by Ghez and Van der Meulen (61); thisinvolved the incorporation of both atomic and molecular oxygen.

The growth kinetics of thermal oxide films provide an independent muthodof measuring oxygen and water diffusion in SiO 2 . By equating the steady-state fluxes of oxidant entering the oxide layer, diffusing through it, andforming new oxide at the interface, Deal and Grove (56) were able to sh-wthat the thickness of the growing oxide layer obeys a linear-paraboli, oqa-tion of the form

2xo + Ax ° B(t

V:'1wre xo is the thickness of the layer at time t. Their equation (12b)! ing 1,e :arabolic rate constant B with the effective diffusivity of th -

oxidizing species appears in our notation as

Bo = 0 D (Sat) S (12)

2D (Sat) (13)

02 0 2 02 fSIO2.

Deal and Grove measured the parabolic rate constant B to have activationenergies of 28.3 and 16.3 kcal/mol for 02 and H20 oxidation; by combiningtheir measurements of B with the values for Deff found by Norton andMoulson (49) and Roberts (54) respectively, they found thatRP0 H(Sat) and

a L) agreed with the permeation values ta within about 10%. They foundi,_)e .!inearly proportional to ambient gas p)ressure in both cases. Thi s is

1%e exoected from the observed square-root dependence of both Deff and_'11- (ct,) on pressure for water and their linear dependence for oxygen, as

pointedj out by Doremus (17).

7, R,. H. Doremus, J Phys Chem 80, 1773 (1976)

.. Norton, Nature 191, 701 (1961)

)4. .. Moulson and J. P. Roberts, Trans Faraday Soc 57, 1208 (1961)

E. Deal and A. S. Crove, j Appl Phys 36, 3770 (1965)

,R. F. M. Fowkes and F. H. Hielscher, Electrochem Soc Abstract #182,Spring Meeting, Sec ttle (21. May 1978)

59. A. Lora-Tomayo, E. Dominquez, E. Lora-Tamayo and J. Llabres,

Appl Phys 17, 79 (1978)

60. R. J. Maier, "A Study of Si02 Growth Mechanism," AFWL-TR-76-228

(US Air Force, Kirtland AFB, NM, 1977)

61. R. Ghez and Y. J. Van der Meulen, J Electrochem Soc 119, 1100 (1972)

16

Since the work of Deal and Grove, a car gc number of other experiments onthe growth kinetics of thermal oxides have been conducted. Among these aremeaisurements in oxygen at I atm (62, 6), 6. , 65, 40, 66, (67, 68) and steam(69, 70); the activation energies reported by all these investigators arein good agreement with Deal and Grove. Some of this data is displayed inFigure 3, where it may be compared to the permeation measurements shown inFigure 2.

in addition to these, a number of studies have been made of the depen-dence of B on tne partial pressure of ambient water. Ota and Butler (71)found a linear dependence at 1230 C for H20 partial pressures between 0.1 andI atm, using water vapor either alone or in mixtures with H2 and Ar. Dealand k;roV also found this dependence between 0.02 and 0.2 atm at 1100 C with0, and Ehara et al (68) between 0.02 and I atm at 1100 C with 07. Katz andHowells (3) found B to be twice that expected at 20 atm at 725 C using pureH90. Irene, however, (64, 40) has found that B increases sharply with thefirst traces of li20 in 02 up to 125 ppm followed by a smaller rate ofincrease for H20 concentrations from 0.001 to 0.02 atm. The measurementsperformed in this study contradict those of Irene - they imply a purelylinear pressire ependence down to 80 ppm. A likely explanation for thediscrepant! and ;uggestions ,or its resolution are put forth at length inthe Discussion section.

3. ,. E. Katz and B. F. ,K 'els, J El,ctrochem Soc 126, 1822 (1979)

40. E. A. Irene and R. Ghez, J Electrochem Soc 124. 1757 (1977)

62. A. G. Revesz and R. J. Evans, J Phys Chem Solids, 30, 551 (1969)

63. M. A. Hopper, R. A. Clarke and L. Young, J Electrochem Soc 122, 1216(1975)

64. E. A. Irene, J Electrochem Soc 121, 1613 (1974)

65. E. A. Irene and Y. J. Van der Meulen, J Electrochem Soc 123, 1384 (1976)66. B. F. Deal, J Electrochem Soc 125, 576 (1978)

1!/. 1). . it'i D. W. Ife;S , .1. 1). Iliimi r ;ind C. 13. Ilo, .1 lectrochem Soc

125, 339 (1978)

68. E. Lhara, K. Sakuma and K. Ohwada, J Electrochem Soc 126, 2249 (1979)

69. T. Nakayama and F. C. Collins, J [Clectrochem Soc 113, 706 (1966)

70. . A. Pliskfn, IBM J Res Dev 10, 198 (1966)

71. Y. Ota and S. R. Butlr, 1 Electrochem Soc 121, 1107 (1974)

L17

Figure 3. (Next page) Previous measurements of parabolic rate

constants for thermal oxidation of Si in 02 and steam. The valuesare those given by authors for oxidation at 1 atm. Whure necess-it,the quoted values were adjusted to 1 atm by assuming that B was

linearly proportional to gas pressure.

KEY TO FI;URE 3

- , LSOURCE

*B. E. Deal & A. S. Grove, J Appl Tlovs 36, 3770 (1965)

.4.. E Rosencher, A. Straboni, S. Rigo & G. Amsel, Appl

Phys Lett 34, 23/, (1979)

E. A. Irene, J Electrochem Soc 121, 1613 (1974)

E. A. Irene & G. Ghez, J Electrochem Soc 124, 1757 (1977)

E. Ehara, K. Sakuma & K. Ohwada, J Electrochem Soc 126,2249 (1979)

* 1 M. A. Hopper, R. A. Clarke & L. Young, J Electrochem

Soc 122, 1216 (1975)

Y. Ota & S, R. Butler, J Electrochem Soc 121, 1107 (1974)

B E. Deal, D W. Hess, J. D. Plummer & C. P Ho,

J I'lectrochem Soc 125, 339 (1978)

MA. G. Revesz & R. J. Evans, J Phys Chem Solids, 30,

55! (1969)

I,18

TEMPERATURE - C

1400 300 1200 1100 1000 900 800 700-1 ---- -----

-12

A. I-

<U

-13jI

) -1 , •

-14

Al&

6 7 8 9 10

104 /K

u', .lvv . r .i trn~ent s Of p.I abo 1ic rate constants for thermal

, in , Si ii .,d steam. Uppe.- group all involve water vapor;

',, .., , . ,.v..-n N Lt! sit miiaritv of activation cuersv to nermeati n val] ns.

1'

....... ..... . ... t s. .

nr-srtace chemical analysis using ion beams is by now a common practice.. -ials research; see, for example, Thomas and Cachard (72), >laver and. (U3) and Meyer et a! (74). The technique most often employed is

L .r)ord hackscattering Spectrometry (RBS) (75), in which low-Z i>,ns (at a, ed energy somewhere below 10 HeV) are directed at .a saip ; L'. After

ve I arge-ang-!e nuclear (Rutherford) scattering at stamc degth within

t:,, the ions themselves are detected by a detector capa ,t :inra'vz-.r energy. Since the ions lose energy throughout their path in the

e,, L nergy which remains upon their emergence (at a given sctter-,, i yesv to indicate the depth at which the scatterin ,,,urrc

, ',v ect rum of backscattered ions indicates the distribution tO

I t s auld be noted that since the elastic seat teni n, c ross-! Ii t a towlv varyin, tunction of energy, the probablitv ; tt -i .

T, mcrion o, depth (For near-surface events). 'hS in('- a. n n determining distrihutions of high-Z impur-

ih a'ee ,f erenco in scattered ion energ ,y -1 ie r "'vents malkes tho two ypes 0, scatt(erj -;

Jependence of the Rutherford cross ;e.- ' ' t.ow-X matrIx.

. I , , I t ion ' stnil ,t l05, h|iW t I, thc' I I

to tI, s Study was that of nuLIClear resonance profIliu, (uc 7i

1 que, as anptied -o 180 profiling, is illustrated in Fiure 4. Ai:ed beam 01 protons from a Van de Graaf electrostatic acce) cratrc.'XJie layer after being energy analyzed. The cross section 'or

. (,:action 180(p, n ) "N between the protons and the i()0, naimely

p 4 180 15N 4- 3 .980 MeV

i• ,,,er narrow resonance at a proton energy of 629 keV (.'ayer d. (73)). Protons enter at a higher energv than thait- and lose

'homas and A. Cachard, Material Characterization Psing Ion Beams

1978)

.,?ver and E. Rimini, ids., Ion Beam Handbook for Materials,V (.cd(Iemic, 1977)

Linker and F. Kappeter, Ion Beam Surface Laer Analysis

, 976)

K . ,. Chu, J. W. Mayer, and M, A, Nicolet, Backscattering Spectrometry

(Academic, 1978)

K. I,. Dunning & H. L. Hughes, IEEE Trans Nucl Sci. NS-19, 6, 243 (1972)

ii. C. Amsel, .1. P. Nadal, E. D)'Artemaire, 1). David, F. Girard and .. Moulin,

1,;ti . Trist Meth 92, 491 (1971)

. t..

SENSITIVE EGION

SILICON SiO 2

192 eV/channel

soIo

Ep, K.Vz

0 100 2M So0 400 500

CHANNELS

Figure 4. Principle of nuclear resonance profiling. The graph shows thecross section vs incident proton energy at 8 lab = 1500 for 18 0(p,X)15Nreaction. The peak energy is at 629 keV; protons enter with slightly higherenergy. The sensitive region is located at the depth where the proton energyhas fallen to that value. Alpha particles, emitted with an energy of3.4 MeV, easily escape. (From Mayer and Rimini, p 163 (73))

21

'I'

energy continuously along their path in the layer until they reach theresonance energy, at which depth the reaction occurs. (The reaction can, ofcourse, occur at any other depth, but with much less likelihood.) Alphaparticles produced via the reaction escape from the surface and are detected;their yield (relative to the proton fluence) indicates the 180 concentrationat that depth. By systematically varying the energy of the proton beam andobserving the alpha particle yield, the NO concentration profile can bedetermined.

In order to determine an unknown 180 concentration profile by the tech-nique of nuclear resonance profiling, one observes the yield of alpha parti-cles (per steradian per incident proton) from the reaction of protons with180 distributed within the oxide layer. A general expression for the alphaparticle yield (vs. proton beam energy) is

=Xx 0 o E i d (

Y(Eb) dxO(x) dEtg(Eb, Ei) dE -(E) f(E, Ei, x) (14)

where

Eb is the mean energy of the incident proton beam,

E is the energy of the reacting protons,

Ei is the actual energy of protons incident on the surface of the layer,

is the thickness of the oxide layer,

x !s the depth at which the reaction occurs,

} (x) is the 180 concentration profile (i.e. atoms per unit volume at depthx),

do is the differential cross section of the 1800p, 15N reaction,

'"(Eb, Ei)dEi is the fraction of protons in the beam which have an incident-irgy between Ei and Ei + dEi,

'E, Ei, x)dE is the probability that a proton which has started with energy"Ind arrived at depth x will have an energy between E and E + dE.

if the functions g(Eb, Ei), f(E, Ei, x) and da(E) are all previously knownand the yield Y(Eb) is observed, then the functionP(x) can in principle bedetermined by inversion of the integral equation.

22

lad

An enlightening discussion of this matter apears in Dunning et al (78), in

which a similar calculation (involving the Al(p, y )28Si reaction) appears.

It should be noted that the energy of the emerging alpha particles is(a) considerably greater than that of the incident protons, and (b) almostequal to the Q-value of this inelastic reaction. They lose at most about40 keV (having been emitted with 2.4 MeV) in traveising the 2000 X thickSi02 layers in this study (Mayer and Rimini, p. 16 (73)).

Applications of nuclear resonance profiling of 180 have included oxygendiffusion in Zr0 2 (79), silicon (80), GaP (81), Ti0 2 (82), Ti0 2 and Cr203(83), and water diffusion in Ta oxide (84).

Nuclear resonance profiling contrasts with RBS in several importantrespects. First, since the depth at which the reaction occurs is determinedsolely by the incident particles' energy, the detection system need not pro-vide energy analysis for the reaction product (except to screen out productsof competing reactions). Second, the specificity of the reaction allows thedetection of minute quantities of an isotope in the presence of any othermaterial (subject to the non-interference of other reactions). This makes itespecially valuable for detection of low-Z materials, whose resonant reac-tions tend to be readily distinguishable. Third, and most important, narrowresonances provide high resolution in depth - the 2.1 keV width of the 629keV 180 resonance corresponds to a depth spread of 350 X (as is discussed ingreater detail later).

73. J. W. Mayer and E. Rimini, Eds, Ion Beam Handbook for MaterialsAnalysis (Academic, 1977)

78. K. L. Dunning, G. K. Hubler, J. Comas, W. H. Lucke and H. L. Hughes,Thin Solid Films 19, 145 (1973)

79. G. Ainsel, G. Beranger, B. deGelas and P. Lacombe, J Appl Phys 39,2246 (1968)

80. J. E. Gass, H. H. Muller, H. Schmied, L. Jorissen and G. Ziffermayer,Nucl Inst Meth 106, 109 (1973)

81. J. L. Whitton, I. V. Mitchell and K. B. Winterbon, Can J Pbys 49,1225 (1971)

82. J. M. Calvert, D. J. Derry and D. G. Lees, J Phys D: Appl Phys 7, 940(1974)

83. D. J. Neild, P. J. Wise and D. G. Barnes, J Phys D: Appl Phys 5,2292 (1972)

84. S. Rigo, B. Maurel, and G. Amsel, Electrochem Soc Abstract #182,Spring Meeting, Seattle (21 May 1978)

23

It is important to distinguish nuclear resonance profiling from the other

principal profiling technique based on direct observation of nuclear reac-

tions (85, 86). That technique, pioneered by Amsel (1963), uses reactionsin an energy domain where the reaction cross section is a slowly varyingfunction of energy. As in RBE, the energies of the emerging reactionproducts are analyzed; the depth distribution of reacting material is

provided by the resulting energy spectrum. This technique has been employed

in a number of studies involving oxygen, including 160 diffusion in Alpha-

zirconium (87, 88), 170 diffusion in zirconium oxide (89), 180 diffusion in

quartz (90), and determination of 160 concentration profiles in Si0 2 films

(91).

I

45. E. Ligeon and A. Bontemps, J. Radioanal Chem 12, 335 (1972)

86. G. Amsel and D. Samuel, Anal Chem 39, 1689 (1967)

87. D. David, G. Amsel, P. Boisot and G. Beranger, J Electrochem Soc 122,

388 (1975)

A. G. Amsel, G. Beranger, B. deGelas and P. Lacombe, J Appl Phys 39,

2246 (1968)

-9. R. W. Ollerhead, El Almqvist and J. Kuehner, J Appl Phys 37, 2440 (1966)

90. A. Choudhury, D. W. Palmer, G. Amsel, H. Curien and P. Baruch, Sol St

Comm, 3, 119 (1965)

91. A. Turos, L. Wielunski, A. Barcz and J. Olenski, J Radioanal Chem 16,

627 (1973)

24

EXPERIMENTAL PROCEDURE

Materials Preparation

Single-crystal silicon wafers (2" diam) were obtained from MonsantoCorp. They were of (100) orientation, with one face polished; their resis-tivity was 4 ohm-cm (n-type). They were first degreased in boiling trichlor-ethylene, cleaned in both H2SO4 (at 90 CA and HF, and rinsed in deionizedwater. They were then oxidized to 2000 A in flowing dry oxygen at I atm at1200 C in a commercial 3-zone tubular furnace (Thermco) which was lined witha quartz diffusion tube. Both the sample preparation and oxidation proce-dures are standard in the semiconductor processing industry.

Following the oxidation, 180 was implanted into the Si0 2 films. TheJ80 was in the form of isotopically enriched gas (70 atom %, obtained from

ProChem Isotopes), a lecture cylinder of which was mounted in a commercialion accelerator (at RCA Laboratories, Princeton, N. J.). This device ionizedthe gas, then electrostatically accelerated the ions to the desired energythrough a mass analyzer which accepted only ions of the desired atomic weight.The implantation was accomplished by raster-scanning the ion beam across thepolished faces of the wafers to provide a uniform fluence of 3(10)15 ions/cm 2 .To avoid H2

160 contamination, the mass analyzer was set 1t36 AMU rather than18 AMU, so that the projectile ions were actually (180- 0)+ . To reach thedesired depth, the molecular energy was set at 80 keV per nucleus). A massanalysis of the residual gas within the ion implantation apparatus which ap-pers as :igure 5, showed the major contaminants to be (5N 2 and0Ar, in quantities insufficient to affect the fluence measurement signifi-cantly. The wafers received no immediate post-implant treatment.

Finally, samples were prepared by cleaving the oxidized and implantedwafers into 5mm x 10mm sections which had been individually labeled to indi-cate their original locations on the wafers.

Thermal Treatments

The general procedure involved heating samples in atmospheres containingvarious water vapor concentrations. In each atmosphere, samples were heatedat a number of temperatures in order to determine the activation energy ofdiffusion in equation (3). Comparison of the pre-exponential factors Do* ob-tained in different atmospheres at a single temperature provided the means ofdetermining the pressure dependence of D*. The extent of 180 diffusion as afunction of heating time at a fixed temperature and atmosphere was observedin order to determine reaction rates involved in water permeation.

Temperature Dependence

The first set of thermal treatments was carried out in room air. .Theroom was maintained at a temperature of 21 C and a relative humidity of ap-proximately 50%. Samples were placed in a horizontal 3-zone tubular alloyingfurnace, (Pacesetter II, Thermco Products Corp.) lined with a 6.4 cm ID X 91cm long fused quartz diffusion tube, open at one end. The furnace wasequipped with a proportional temperature controller (Ana-Lock Series 321,Thermco Products Corp.) for each of its three integral Type K (Ni-Cr/Ni-Al)thermocouples. Sample temperatures were monitored by means of a separate

type R (Pt/Pt-13%Rh) thermocouple which was inserted in the diffusion tube.

25

.. :. - . .. j .7 . ..7

[4,

LK- .

--7

7- . . ... . - i--- -TT

, - 7 - .. . .. . . . . . ... . .. . K - - -

; ... .i; .-.. - 2 -... 755- .1 ;--. i i t--' .. 7....

* 4 ~ ----- ,-- -A ~ ---- -.-f---.--- ..... -----

.. . . . . . ..-- ;--_.. : .-- --- -_ - : -

. . . . . .. - ": .. .. , -

,p -~ . L . - .t t - I .. :- - -, - 4-- - _', -i . . , .-lt

-i

I i , l" ; I .1 I

.7 - ..F - - -- -- - L +;, . . i-?__ . - ! ;

• - -- .7 -: . [ .. _-. _ _ _- ___, 1 < I __ _ _ __4 .___77177 71T7Z

Figure 5. Analysis of residual gas in ion implantation apparatus. Thehorizontal scale indicates molecular weight of detected species; the ver-

tical scale their relative abundance. 3 02 the accelerated ion, is off

scale vertically.

26

The thermocouple wires were fixed within a 91 cm long X 0.6 cm OD quartztube; the hot junction was located near its closed end. The thermocoupleindicator (Model DS-350, Doric Scientific Corp.) had been factory-calibratedfor a type R thermocouple; it had a digital display with a resolution of0.1 C. The furnace controls were adjusted while monitoring the temperatureat various points so that an 8 cm long "flat-zone" was obtained near thecenter. Diffusions were carried out by loading a batch of samples on a 4.1cm X 15 cm plate-type slotted carrier made of fused quartz (obtained fromQuartz International Corp.) which had been preheated for at least 45 minutesat the center of the furnace. The carrier was pulled out to the mouth of thediffusion tube using a hooked quartz rod, the samples were loaded quickly andthe carrier returned to a position such that the samples were within the flatzone; the thermocouple was then inserted adjacent to the samples. Sampleplacement and/or removal involved withdrawing the carrier from the furnacefor no more than half a minute per operation. Samples were transferred to aroom-temperature pyrex surface where they cooled rapidly. Samples were al-ways placed with the implanted face up. Timing was done with a quartz-cry-stal digital wrist watch.

The next set of thermal treatments was carried out in dry nitrogen atI atm. The same furnace controller, thermocouple and diffusion tube wereused. A fused quartz diffusion-type end cap was placed on the gas supplyend of tho diffusion tube; the other end was left open. Gas was obtained viaboiloff of liauid nitrogen; flow was maintained using a tube flowmeter (Sho-Rate, Brooks InsLrument Company) at 500 cc/min (equivalent at 700 F, I atm).

A similar procedure was followed for thermal treatments in steam atI atm. in this case, however, the furnace at first was a horizontal single-zone tubular resistance furnace (Model 54233, Lindberg/General Signal), linedwith a 5.1 cm ID x 91 cm long fused quartz diffusion tube. The furnace wasequipped with an integral proportional temperature controller (Model 59544,Lindberg/General Signal) for the furnace's integral thermocouple. After atime, the furnace and controller were replaced with a horizontal single-zonetubuiar resistance furnace (Model 1127, Marshall Furnace Co.) lined with a3.8 cm II) x 117 cm long fused quartz diffusion tube. Furnace temperature wascentrolld using a proportirnal controller (Eurotherm Model 901-2075, MarshallFurnc Co.) and a type K taermocouple whose junction was located at the cen-Ler of a small tube bored parallel to the furnace tube. Sample temperatureswere monitored by means of a separate type K thermocouple whose hot )unctionwas lrated uLear the closed end of a 91 cm long x 0.95 cm OD quartz tube,wiich was inserted in the diffusion tube. The thermocouple EMF was read outon the 200 mV scale of a 3-1/2 digit multimeter (Model 8020A, John FlukeCorp.), and converted to temperature with the aid of appropriate tables(Omt-ga, 1979). The readings were compensated for cold junctio, temperatureby means of an electronic cold-junction compensator (Model MCJ-K, Omega En-gineering Corp.). The type K and R thermocouples were cross-checked by put-ting both into the furnace at various temperatures between 550 C and 600 C.

The type K thermocouple was calibrated by separating the two wire endsand bridging them with a small horizontal strip of silver foil whose surfaceshad been cleaned by abrasion. The ends of the silver strip were crimped onto

27

thc wires, which were then heated under high vacuum. The last DMM reading be-Iore the strip melted corresponded to a temperature of 958 C, which is with-

in 4 C of the melting point of silver (1). This discrepancy was judged to bewithin the error of reading on the digital multimeter, especially since the

temperature was still increasing at the time of the last reading, so that themeter readings were taken as indicating the true temperature.

The steam was generated by boiling deionized water in a stoppered 2-liter'>i~ing flask, as shown in Figure 6. The boiling rate was governed by a vari-ihie autotransformer supplying power to a hemispherical heating mantle aroundt! 'sk. Steam was conducted to the diffusion tube through a horizontal py-

Litme emerging from the neck of the flask; this was joined to the narrowed, i the diffusion tube via a tapered ground joint. The entire length of

h., tita.! tubing and the neck of the flask were wrapped in fiberglass heat-and maintained at a temperature of 120 C to avoid condensation there.-perature was monitored with a Type T (copper-constantan) thermo-.Aii :nti-backstreaming plug, formed by a wad of fiberglass tape, was

tie thermocouple tube. When inserted into the diffusion tube, itI hah: positive pressure to be maintained in the furnace. Sample

, a procedure which took approximately 15 seconds, was delayed until' bec!,een replaced by steam and the furnace temperature had stabilized.'L .ls rested on a 2 cm x 6.5cm quartz boat which was inserted to theS t the furnace with a hooked steel rod.

Pressure Dependence

!: ii~y, a set of thermal treatments was carried out in pure water vaporc, pressures. These were performed within the 46 cm diameter x 79 cm

,,Ii jir of a vacuum evaporation station (Model VS-400, Veeco Corp.), asii Figure 7. The samples were placed inside a 17.6 cm long section of'i) quartz tubing. A double-hole ceramic rod with a type K thermocouple

at one end was also inserted in the tubing so that the junction was-,u11ple location. The tubing was then inserted into a 1.35 cm ID x 10.5*iulular resistance furnace so as to put the sample at its center. The:.'met, a small pedestal, rested on the 61 cm diam stainless steel

o f the evaporation station. Electric power for the furnace was sup-variable autotransformer through feedthroughs in the baseplate;

t, W w-is required to maintain a sample temperature of 800 C. The ther-, , wires were likewise connected to electrical feedthrough in the base-.Water vapor was supplied by deionized water in a stoppered vacuumi ..sting on a thermostatic hotplate to maintain a constant water temper-

'l'i e vapor was conducted through a length of copper tubing to a varia-.v'lve (micrometer type), and entered the vacuum chamber through the7;mmlte valve. A continuous flow was maintained by exhausting the.roiigh a choked-down roughing valve to a mechanical forepump (Model

i. ' ,ent-Welch Scientific Co.). Chamber pressure was monitored by a ca-" . manometer (Baratron Pressure Meter Type 220-2A3-10, MKS Instruments,

Tr. wmose sensing tube entered the chamber through a port in the baseplate.S ,lals from both the manometer and the thermocouple were read via digitalmultimeters and recorded on strip chart recorders (Model 680, Hewlett-PackardCorp.).

1. R. C. Weast, Handbook of Chemistry and Physics, 55th ed (CRC Press, 1974)

28

(n 0

~ Er:LI

U- 0

-- J

I.-j

zz

Er--

LLI-

-LU

Lo

LUL

LUL

UU

LU 3

-j >

0l:

CLa

U) 41

c->

030ctL

The thermal treatments were carried out by first oaiuing the samplus andthermocouple in the furnace. The bell ar was then lowered and the systemevacuated by the forepumip through the diffusion pump backing line. For this,,peration, the high-vacuum valve, the backing valve and the air admittance,,iLve were all. fuiV open, while the roughing valve, the mechanical pump vent-ini valve and the variab[C' leak vi:y,_ were all shut. The latter was thenopened to evacuate the air fro-, the water supply flask and tube and to degastht. water, hien shut to re-evacuate the system. Next, water vapor was admit-rt'ki oV .idusting tue variable leak valve until the observed rate of pressure

',,r, i* y; such that the pressure reached its desired value in 5 min. At" ,i:a, rehinc valve was "cracked" open to maintain that value stably.. -:-'.i s '.i1:n evacuated, this time through the hacking valve, and the

w", '<ought up to temperature. No difficulty was encountered in keep-,, t2,Qprat,.irk constant to within about +3C by manuallv adjusting the

, r:r oltaee. The pressure was then brought up to its presentthr,- s~u;-off o I t)e backing valve. On short runs, pressure excur-

,S anre rLneu throuih manual adiustment of the variable leak valve; on,, -. , t v :-unted to something like +2n' of the average value.

JI Loling

18-oterjne thle ex ,nt of 0 di ffusion induced by the thermal

-a :arr i e vold curves were taken usinp, the method of nuclearvi .srV describe. in the irtroduct ion. A proton beam, Van de' raa- ff electrostatic accelerator (Model A, Nigh

Vo 7 r ). A portion of the accelerator, as well as the an-- shown in Figures 8 and 9; prominent features are indi-

-tr i ng kev.

was -,7itrolled bv adjusting the field strength of a"- . :-, t . The current to the magnet coils was supplied

, revulate o rnwer supplv. The magnetic field strength wasa n \'Y l c'us-moeter (Model ' 2, Nuclear Magnetics Corp./

wnos.L, ;rocbe element was fixed between the flat faces of,,e o,,ussmetoc modulated the local magnetic field at the

a oi 'iaal Helmholtz coils. The RE oscillator was set, a. -pr,,a in to the desired beam energy, and the beam energy

the ..a.tnet current until the N4'MR signal dip centered_ n current. An oscillator frequency of 12.050 kfHz

.iewli -P,,ckara Model 5243L digital frequency counter) cor-a jocan (nerv of 630 keV. Excursions in the magnetic field were

::" i , ' imit beam energy variations to under +40 eV dur-

,' i -- Iration alpha particle count.

31

KEY TO PHOTOGRAPHS OF NUCLEAR PROFILING APPARATUS (pp 33, 34)

A, VAN DE GRAAFF VERTICAL DRIFT TUBE: Protons travel downward.

'RVF OF ANALYZING MAGNET (Coils are in dark area below): Protons

i=duergo qPO deflection with 38 cm radius of curvature, then emerge

',,ward right.

K;ATTERING CHAMBER: D-shaped, multiport. On its rear plate is a

rizontallv translatable stage upon whose rotatable center is

* "t, the sample holder. Protons enter a front port, housing

in,,tor, which is attached to the horizontal beam tube.

...rt ',d vacuum gauge, electrical feedthroughs, vacuum

vtoew nd viewing window.) Excending through the top

.. i rotatable feedthrough for changing detector ang'e

.. "L' OtsQ. Kevond it stands a switchable microammeter,itc to t -e cl mator sectors for beam ,lig Tm,.en

'.,t;'- SENSTTIVE PREAMP: Mounted on rotatable feedthrough holding

V tOr.

TILLATION DETECTOR. NaI(TI) crystal/photomultiplier tube

,,-blv and plug-in preamp, shielded with lead bricks, for gamma

alibration of beam energy. It should be noted that theter "E" in the upper right corner is a wall plaque denoting

_t" rather than a label for this diagram.

'P MN: Spectroscopy and DDL amplifiers. Below this is the

i-ower supply for the photomultiplier.

, ?rA'OR UNIT: For NMR gaussmeter, connected by a short cable

nrohe mounted in magnet gap on far side. Immediately to its

is a digital counter to facilitate setting frequency; to its

t is an RF amplifier for oscillator signal.

,1.ILLOSCOPE: Used to display NMR signal. To its left (not shown)

magnet current controller, NMR power supply (modified to include

'ira(tor for remote trimming of oscillator frequency) and digital

'a" c ounter.

'S CONSOLF FOR VAN DE GRAAFF ACCELERATOR.

!'cANNEIL PULSE HEICHT ANALvZER.

. 'ARGET CURRENT INTEGRATOR.

32

I. Fr

4;'

I -4

I-

I. C;

U

V V

U

F'

a

I'

r0

-'h

These served to al low passage Of on y those protons with the set energv, aswell as to provide a feedback signal I-Cr closed-loop fine control of beamenergy. Beyond these lay the horizontal beam tube, at the end of which wasa stainless steel multiport scatterino, chamber, shown schematically in Figure

I This ,used a sample holder and a particle detector. The sample holder4.a cm diamweter stainless steel disc with a shallow ;zroeve milled -"

cross its face; batches of samples stood side by side in the groove :,nd were.d in -ice b% small clips extending over its edoes. Each batch included a

o;Ice asample that had been 18 0-implanted but not thermallv treated. Then. ]ier was mortared with its face normal to the proton beam and biasLd

, to col lect secondary electrons; it was movable from outside the;nbc.r, -,s was chn detector mount. The detector was a silicon surface bar-

,evice 13 mn area, 100 um depletion depth, Ortec) located 17 m. from,ampie -it , anlt 0f )0- to the beam direction. It was shielded by a

;,~i,. t r i n whose k or i .... ) to the bem -cm -

, ss of .g-m was sufficient to prevent any

,-tcks,, ,ttere, )rotons fro, reaching it while allowing nenetration o' the 3.-', . h ,ttor pulses, ater bein, amplified (by a >hdel

,, - L j 'e Pre ;:p iand Model 1417 Spectroscopy Ampl if er, both.',,. , .,-d on a 2048-channel pulse height analyzer

75,i", -,or-N rtiern Corp.), which performed a "region-of-interest". 'c,,t SP ye.: ve,i mo ing total of paises accumulated in the alpha-

::-,zen by a sipna] lren a current integrator (Model:ji, ting that the proton fluence on the sample had

ceac, - w7e (typically 50 uC). The "region of interest" was an

u ddLinkO the alpha particle energy; it was set on the PHA so astho a]pna particles registered in the narrow, well-defined

Background counts were negligible. Alpha particle counts(aP O 5000 per 50 aaC run; beam current was held to n.5 uA to

"'vo 1 1 I,, g ra Ie' . samp i es (ace Discussion for clarification rf this point)i :,, i i.a- t no rv setting, the sample holder was translated to place each

consecutivelv in the I mm-diameter beam. The range of beam- . spann,- was typically 13 keV on either side of the energ\" at

,vie u .'s i:,x'mum. This corresponded to a projected range-r si. , Cie locatipn of the distribution peak - enough to

., tii entire 2000 A thickness of the oxide layer.

:i p-.A .'i'I curves were taken, a calibration was performed on

. f acc. eiator in order to functionally relate the proton beam:.11ac, bsnrved .:,f oscillator frequency. This was done also by means

rbut with (p)' rather than (p,o) reactions., c re;ctions used.) A thick target containing a uniform con-

";it 1(I Of cippriate nucl ide was placed in the proton beam, whose energys;vstia t i,ilv varied. The yield of gamma rays was plotted as a function,::'IR frequencv. As the NMR frequency (and thus the proton energy) was svs-

cc ',:r, ia;lv incrosed, the yield increised relatively slowly as long as the

i,,t,)n ,,n(.r,,v re memo ,. below the, relev;nt resonant energy. (These gammaSa : ,"orn i muit itude of smali resonances in the (p, ) cross section.)

'va- c ar -rcan i t tao pcot on energy reached the main resonant energy, the

* e'o,, ; ,, s,,.t, v, reflecting the increased number of interactions at

,; i i, proton energy was further increased, the yield resumed

, 0, rc! icit hi' tie slow variation in the reaction cross section.

,.io', e f ;; iick-target gamma-ray yield curve is shown in Figure 11

35

MULTICHANNELLOGIC PULSE HEIGHTGATE

ANALYZER

SPECTROSCOPY

CURRENT AMPLIFIER

INTEGRATOR

CHARGE SENSITIVE

j PREAMP

!I*j .ROTATABLE DETECTOR HOLDER

- COLLIMATOR

ATABLE iAM

'ARGET -

HOLDER

TRANSLATABLE

BACK SAMPLE \-DETECTOR

: ure L0. Nuclear scattering chamber. Successive samples are irradiatedhv horizontally translating the back. Target current is collected by aslip ring to allow rotation. See KEY TO PHOTOGRAPHS for more description.

36

I

TABLE 1. ACCELERATOR ENERGY CALIBRATION REACTIONS

I

Observed

Reaction Kp (keV) r (keV) E (MeV) 0-(mb) -n (MHz)

19F(p, c )16 0 340.5 2.4 6.13 160 8.930

7Li(p, )8Be 441.4 12.2 17.64 6 10.230

i9F(p,C )6 0 872.1 4.7 6.13, 6.92 540 14.200

2 7 Al (p, )28Si 991.9 0.10 12.54 - 15.086

Reference: Mayer and Rimini (2)

. 4. W. Mayer and E. Rimini, Eds., Ion Beam Handbook for Materials Analysis

(Academic, 1977), pp 207, 281

37

llie calibration proceeded as follows: A target thick compared to aI MeV proton range was prepared. In the case of Al this was a small block of1/8" stock; in the cases of Li and F it was a layer of LiF formed by fusing1,iF crystals on a copper disk. The target was placed on the sample holderarid a scintillation detector (a 5"x5" NaI(TI) crystal attached to a 5" photo-multiplier tube) was placed on the scattering chamber nearby. Lead brickswere positioned upstream to shield the crystal from gamma rays coming fromvarfous beam stops. As before, an NMR frequency was selected, and detector

i ses were displayed on a multichannel pulse height analyzer, where those in31i appropriate energy range were accumulated until a preset target charge hadle-en reached. The appropriate gamma ray energy range was selected on thei 's of a detector-analyzer system calibration (using 6 0Co and 1 37Cs stan-I rd reference sources) to include the principal gamma rays emitted in the-- ctions listed in Table I. The resulting thick-target gamma ray yield was

, and the accelerator energy was calibrated by Identification of the! .uency at which the step in the yield curve occurred (i.e., the last

S .. able T) as the proton energy corresponding to the resonance.

-Jnce MR frequency is proportional to the analyzing magnet's fieldtand the magnetic force is equal to the centrifugal force on the

S. the proton energy is proportional to the square of the NMR frequency.- 'ound to be approximately

E (keV) = 4.36 v2 (MHb z

" . cause of inaccuracy is the nonuniformity of the field over the di-

os of the iron pole pieces: the probe, being of necessity located near- iinge, could not accurately reflect conditions along the beam path. It.. bd he stressed, however, that this experiment is self-calibrating - the--- w width of the 18 0(p,0)1 5 N reaction allows the reference sample (im-

p red but unheated) to provide an energy calibration for every other sample

hamber.

l e beam was not purely monoenergic: due to differences in trajectorieswas a distribution of incident proton energies, This was determined

gamma ray yield calibration curve for the Al (p,y) 8Si reaction,',ijure II. Noticeably, the step is not sharp, but has a

L width (here on the order of 1 keV). Since the reaction width is less~i', 0.1 keV, this deviation is almost entirely attributable to the energy

( of the beam.

38

x UCD-

LC) ~ -

N >

C))1

acc

X LU

*J >

XO Ux ux

C/)0

0

CD

4)

o

U')J

00'.4

C))

CM CM -

Jfl 13d SINI1oo Av83 vwwvE

39

The thermal treatments given to all the processed samples, and the 9u-Clear resonance profiling data reflecting the resultant changes in the 0distributions, are summarized in Table II and Figures 12a - 12c. Table ITlists the thermal treatments; for each sample it shows the temperature, dura-tion and type of atmosphere employed. It also shows some nuclear profilingresults - the yield of alpha particles (per 50 uC of incident protons) re-ccdd at the proton beam energy for which this was maximum. (The signifi-Cli:i!e of this quantity, as well as that of other information in the table, is

1 i -'ied in the following section.) In addition, a representative set of' :Ve experimental alpha particle yield curves is shown in Figures 12a -. ,It should be noted that the yield curves are all plotted on a semilo -

a- " scale; this was done to facilitate visual cross-comparison as well"'hasi-e the importance of the lower-lying points on the wings. Super-

:1 the experimental points are theoretical yield curves which were"'Cording to a procedure described in the following section.

KEY TO FIGURES 12a, b, c (pp 43, 44, 45)

Observed alpha particle yield curves. All pointsshown are recorded data for the samples which areidentified at left. (Different symbols are usedfor ease of distinguishing nearby curves.) How-ever, for the lower curves (Samples 606,827, A824and 802) the counting time was doubled to obtainsufficient statistical accuracy. The pointsplotted for those curves are half the recordedcounts. The statistical errors (not shown) arethe square roots of the observed counts; for thelower curves they should be reduced accordingly.Also shown with each observed curve is a theore-tically derived curve (the continuous curve be-tween the data points); these were selected onthe basis of best fit, as described in the text.

40

TABLE 2. SUMMARY OF THERMAL TREATMENTS AND RESULTS

THERMAL TREATMENT PROFILING RESULT ANALYSIS

Sample Temp Duration Atmos- Peak . Fraction n D

# (0C) (s) phere Count of Ref. (by peak frac) (cm2 /s)

304 413 71640 air 3800 0.970 1.105 1.23(10)- 17

308 627 22500 air 13674 0.863 1.49 2.1 -16

309 627 230805 air 6491 0.410 4.85 3.90, -16

311 788 68521 air 2992 0.473 3.88 8.20(10)- 16

313 789 12600 air 5068 0.801 1.73 6.27(10)- 16

316 106 30630 air 5144 0.665 2.32 5.72(10)-16

J16 707 3540 air 7304 0.965 1.120 2.87(10)- 16

401 563 1799210 N2 4882 0.822 1.65 3.79(10)- 18

402 548 619400 N2 5155 0.834 1.58 9.66(10)- 18

404 543 244900 N2 5634 0.917 1.295 1.11(10)- 17

606 609 8520 steam 3005 0.250 8.10 3.03(10)- 14

612 609 3111 steam 3111 0.541 3.12 1.88(10)- 14

627 1160 11400 N2 4346 0.785 1.79 7.73(10)- 16

o31 690 230700 HV 10909 1 1 0

631 1150 10980 N2 4353 0.812 1.68 6.64(10)- 16

632 815 582240 HV 5087 1 1 0

707 805 7200 H20 3473 0.721 2.07 1.82(10)- 15

(8.9 torr)716 828 253800 H20 10805 0.719 2.08 5.27(10)17

(0.24 torr)

717 740 75900 H20 12781 0.851 1.54 7.22(10) -17

(0.80 torr)1*1 819 16800 H20 8244 0.865 1.49 2.87(10)16

(2.65 torr)

41

TABLE 2. SUMMARY OF THERMAL TREATMENTS AND RESULTS (contd.)

THERMAL TREATMENT PROFILING RESULT ANALYSIS

Sample Temp Duration Atmos- Peak Fraction n D(0 ) (s) phere Count of Ref. (by peak frac) (cm Is)

722 842 609000 H20 7621 0.800 1.73 1.30(10)-17

(0.062 torr)726 514 2700 steam 7593 0.812 1.68 2.70(10)-15

i28 423 5280 steam 7498 0.786 1.79 1.67(10)-15

-7' 331 23640 steam 17589 0.940 1.213 7.80(10)

263 85440 steam 7573 0.794 1.75 9.66(10)-l7

Y2 476 22380 steam 5828 0.410 4.80 3.94(10)-15

81,6 476 2775 steam 8899 0.817 1.66 2.53(10)-15

-7 476 7420 steam 9858 0.706 2.14 1.92(10)-15

-16g12 345 25200 steam 11860 0.850 1.61 2.53(10)

V 15 473 7620 steam 12175 0.901 1.35 4.36(10)-16

816 473 7620 steam 9108 0.674 2.28 2.20(10) -15

k820 475 22770 steam 4905 0.743 1.97 5.06(10) -16

23 619 1290 steam 7919 0.569 2.90 2.30(10)14

616 16260 steam 5844 0.455 4.12 3.93(10)-15

619 1290 steam 11246 0.817 1.66 5.44(10)- 1 5

827 616 16260 steam 2419 0.188 11.80 3.40(10)-14

Prefix "A" signifies prior high-vacuum (HV) annel: 1 hr @ 900 C.

42

8000 ---- I-

7000

60002

5000

00

0 00

cl 000 316 0

~ 2000LJ 0

L

I-

0

-j 800

000

5 00

LL SILTRFRQEC ~

I-igir 800 Osre lh aril il uvsfo eetdsmls

<4

8000

7000

6000

7 5000

Juu

- 3000

#A818

#A826-2000 0

)<_

10 0

O0

900

300

1.950 12.000 12.050 12.100 12.10

NMR OSCILLATOR FREQUENCY - MHz

Figure 12b. Observed alpha particle yield curves for annealed samples.

44

8000

7000

Z

o 6000o

- 5000

U

w

L 4000 F- -

o

:3 3000 -

#811

#820 0ou 2000

0

4823

a-a0-802

1000

11.950 12.000 12.050 12.100 12.150

NMR OSCILLATOR FREQUENCY - MHz

Figure 12c. observed i',ha particle yield curves ior low D*t samples.

-A ANAYS I S

'.Itthod of Determining Tracer Diffusivitv

'!it, tracer diffusivity D* was extracted from the data in the context ofr (IIf f usion model discussed in the Introduction. According to this

>j.,the exchange of network oxygen with molecular water dissolved in theis solely responsible for any observed change in the distribution of im-

0~. The dependence of D* on thermal treatment parameters is a diag--fthe mechanism of water diffusion in SI0 2) lavers ,and a test of the

this model. The extent of change in the distribution 1s in r-utrm! ,ab] e I1w inversion of the integral ecua tion ('. ) whliich gives tC

;e' vield observed by nuclear resonance Profilinc.. Tr practice,,-i" compl icatcd procedure entailinag large currors Whose propa-

-I otraIck.

1_8

-1.-ilone the initial 18) distribution Is determined, its subseauentrigta eI Doug sci diffusion theor, rovided theI

-us tr e medium are correctly perceived and the apropri.-te ounarya , r d ,upion I ed. A full mathematical treatment o the macroscopic dif-

',.ss gsoverning the evolution of an imlanted distribution ap-.... !A. .t is shown there that when a sample is maintained For. a fixed temperature, the resulting distr ution ,t) Is o tUno-

ingle parameter - name the product ditt. The characteristics"i. process are embodied in this parameter. ror example, its

,-' v id pressure dependence reflect the activation energ and identi-,i r iudsported species. Its position or time dependence indicate non-i.t in, the medium (see the Discussion). For the case of diffusion,

Sthe problem of determining (%,t) is really that of evaluating

,I v, rather than parametrizing the distribution with D*t, which hasI -'0 , dimensionless parameter was chosen for clarity of presen-

5 o~ram'te , dnotedin can be thought of as a natural time unit,, td extent of diffusion in terms of the amount of broadening

"-n v firi tut iil thuss inn distribution. Its applicab l , itv to thisS ' * rt ile ver close similarity of the implanted 180 concentration

i poce adistrebution. It is well known that a Gaussian distri-t, in itisr varinnce i broadens with time in an infinite homo-ir ortd in e to the relation

20*t Cy(t) -

i - s hv;irianou O the distribution at time t. c he definedt i(, ~ c., the extent of profile broadening of a Gaussian dis-

ion for the partiulr case of an infinite homogeneou medium. However,n in k Ilsed to index the broadening of a ;aer sslan imp nt for any other

iii ondr deoeit ions. The corresponding value of D*t Is then expressed in termsof n , .ord ingn to t* e rel)tion

46

provided l)* is independent of and t . fr o thekr au i.a rv N, ndi t ins n aosesits meaning Lis the ratio of widths, but still serves as a single index forthe product D*t.

To dietermine thc- proper value of r to be associatedI With a particoulaorthermal trteatment, a set of lpossib'e d iscrete values for n wais selected. Forea~h member of this set, a distinct distribution o(%,t) was calculated usin 'the methodl described in Appendix A. Based on this distribution, a predictedalpha particle yield curve Y(Eb) was calcu-Lated using the method described1i Apperwiy P. T1he resulting family of yield curves, -parametrized '1v n, wascompared to .lhe experimental yield curve resullting. from that thermal treat-

rot he appropriate value of n was taken as that which indexed the calcu-'ited yield curve most closely matching the experimental yield curve. Th is

4OCcea,,ure all owed -,he extraction of the relevant inform-,ation on difffus ionwithoult r3eSaIrting to inversion of the integral equation. A representativefamily of 0v~d ( concentration profiles calc :Iated -in this manner isshown in Figure i3, wille a family of calculated alpha particle yield curvescorresponding to these distributions is illustrated in Figure IL.

it sou' .;;ot ii~athat a number of7 prolimi nary computat ions, we reave ved a a on. the viel d Curves. Those involvye(; determining 1

tle. Corrt - v'ai'p-- (-) ILt.. 'Iata T,)pearing, in the Formula,, for the reac-t 1on_ Cv ,C .a h nencr, ad ~ ,lc init ialI 1' 0l d ist ribult io n

%a Ae- o ao yitova -tes of the co)nstants were,,Va1 1 I ' T e 17 u !!!e Ctc, there, tbc p'at valuies were iett.rmined hx'fioing -'.t ~ete' ;OF the calculated initial yiel d curve (topmost curveireateObseredns ofyit canre odg bn pinecbtio ofethie to-

treatec "'h 4,osere yfi canrve of nmpned b uetio oertie ton-milst curve in o' ,re 12.1

[2'to rootil'e, tiIC prodlre: doeterminin.a the value of r% corres-ad ( 1. en t e rnma r tr m tin* conis isted of taking an e xperimental

vie]. ,I r' imaLrLn o t c the <i !v of prec1cuio11a ted y ield curves,-, t henli'', rraio La 1l a1d I Ist"ed( a o1)tain1 a S oedC a ma tc i; as possibl e.

a; Il icul t ton dettrne n wit an ac c ura cy, silf i c int fonrr g v est a i a. h procedure proved unwiel dv, when h i gher ac-

Ics red, espuc jalv for sm~Ivailues of M, when the relativea;. c ~ o..'iron errors in n grew very Iar (e. As can he seen by

i'fr' t'ig equation (15), the rel ative crror in i* is

t, * 2nf An. (16)

:ror irge '7tu of n, the relative error in T)* is twice that in nl. As 11ileercases, howevcr, it becomes much larger; for fl < 1.4 the ratio of relativeeryrors is '.In addition, the shape of the yield curves changed relativelyIi jtle for ,,mall nl, making the determination of fl difficult.

a 'yVIr.(iM In 110',te pr'i'i' eMIs, in a1t I (e rna t e procedure was adopted for roti-1m ne met, rLeMent, (I.f ioP . lbis prowedure, based on the rate of decav of the

p~eak a n. .art ict vifl d , proved especial lv useful in the regime of small n.1:, -'ci ', -r r1.1~ tilet fail of ield curves in Figure 14 that the peak

-e 'h 'adli rt icits is, a monotonical lv decreasing function of T1. kTb is:n- t-o ji e shown in Figure 19.3 To determine the value of r? using this

47

C:) J)

C)4

C

c'F

CDC

C

C

c) CDW

o< r-4-)

C)c

CL

-j

(cz

CDC:)E

0 E

C-.4 4~j

C)

>11

4Sj

80001111

7000 A6000 1.

50002

400 3

3000

X-

200 .

900

700,

600

600

11.950 12.000 12.050 12.100 12.150

NMR OSCILLATOR FREQUENCY - MHz

Figure 14. Theoretical alpha particle yield curves (labels indicate n).

49

~O 0

4 -j 0 r-s.

Z- Uo 41tu m 0 m

c :)w m

*~ > OD~ ~

-

- W C)

>~4-

m~ cu -H

0t- 4-j u$.4 0 >

cz U

> t

a~C) P A

4- ) 4-

W -4 W 0. r_'.4 0t a 0

=tU- U)W

4-i 0 '

0. 0 .0 0 -

co c)~

.., 0

LA -, CO 0. CO)-4 wj t .,4

c.0 t.0 L

C.) WC. Ct,4 0 0

SII~~~~~nC -viu 13AVdVNVduuD

50C~

function, it was necessary to measure an alpha particle yield curve for asample only in the vicinity of its peak, so as to determine the peak yield.This quantity was then normalized to that of an implanted but untreated re-ference sample located nearby on the wafer. The appropriate value of n wasthen found simply by locating the resulting peak yield ratio on a graph ofthat function (Figure 15). This procedure had several advantages. First, itgreatly shortened the time spent in nuclear profiling. Second, it allowedshorter thermal treatments. This can be seen from Figures 14 and 15. Forrelatively small n (i.e. short treatments), the shape of the yield curve isinsensitive to changes in n, so that comparison of shapes is a poor means ofdetermining n. However, the maximum slope of the peak yield ratio occurs injust that situation, so that its use is most advantageous there. Third, itallowed errors in D* to be estimated directly.

To demonstrate this, consider the statistical error in D* obtained bythis means for the case of small n. Let the number of alpha particles countedbe denoted N and N for the treated and untreated samples, respectively. Thepeak yield ratio, denoted R, is then

R=N.R-No

A0

The statistical error in R is gotten from the statistical errors in N and%N o taken in quadrature, namely

2 22(AR) = ( R AN) + ( R AN )2 (17)

N aN0

The errors in those quantities are just their square roots. If these aresubstituted in equation (17), we find that AR is given by

AR (I + R) .(18)

* According to Figure 15, the initial functional dependence of R upon n is ap-proximately

R = I 4.1

This is now differentiated to get An in terms of AR, which in turn is givenby equation (18). By substituting the resulting expression for AV in equa-tion (16), the relative error in D* is found to be AD* = 8.2k R(l+R) (19)

D* -N N

With N = 5000, AD* is about 20% for A=1.5, decreasing to 10, for n=-2.5.D*

The calculation of error propagation can be easily extended to includeother sources. For example, lateral nonuniformities in implanted 180 dosecan be represented by including another term In equation (17). (In thisstudy, the practice of using nearby samples reduced the magnitude of thiserror to below the level of statistical uncertainty.) Errors in temperaturemeasurement are represented bv including (in quadrature) the additional termEa AT in equation (19).kT TThe errors in reading temperature were about 2 C. For the range of tempera-tures used (610 C to 263 C in steam) this represented a contribution rangingfrom 5% to 25%.

51

i'.nature and Pressure Dependence of Tracer Diffusivity

'ie temperature dependence of D* was determined as follows. First, D* was cal-

-.d from the observed data using the method of peak yield decay described inthe previous section. The results of these calculations all appear in the lastcolumn of Table II. For each of the three atmospheres (i.e. steam at 1 atm, room,ir and flowing dry nitrogen) the values of D* were fit by an equation of theArrhenius type

D* = D* et-( Q

wLth a temperature-independent pre-exponential factor Do. The values of D* weretaken as measured: they were not adjusted for the temperature variation of gaswiSe concentration. The fit was carried out by the method of unweighted linear

.,'-4 squares using I and as the independent and dependent variables,

--:ectively. The results, which appear in Figure 16, along with the individualof D*, are

10+= 2.7 ( .IO+40 - (16.9 1.3 kca]/m) 10)

steam RT 2

)* 1.3 (10) -12+.34 - (15.5 + 1.4 kcal/mol) (211)room air RT Cm-/1

'dry N 2 1.8 (10)13 - (15.7 kcal/mol) (22).r v N 2 "2 2

RT an-/s

-iicated errors are derived solely from the variances of the fitting param-S,-, (, and take no account of the sources of error mentioned in the previous

S. .The standard deviations in the fits for log D* are 0.232 and 0.135 for"Ind room air respectively, which imply relative errors of 171% and 136% for

dry nitrogen data points fell fortuitously close; their error was notwed. The three fitted lines shown in Figure 16 are almost parallel; at

t wi:t representing D* r lies a factor of 93 below D* s whileroom air steam'

lies a factor of 8.1 below that. Also shown in the figure are: ! t rogen

steam for a few samples that had been vacuum annealed prior to thermal

mvnt. These values (the square symbols in the figure) lie a factor of 5.0those for unannealed samples. The reasons for this will be discussed shortly.

i)ressure dependence of D* was determined by calculating D* in a similar,r the samples heated at low pressure (#707, 716, 717, 718 and 722). As-e tfn heated at slightly different temperatures, their values of D* wereto a common temperature (of 820 C) by assuming a temperature dependenceseen for steam. The resulting values of D* (per unit pressure) are dis-rn Figure 17. Also shown is D*steam at I atm which was calculated using

.. 20). The indicated errors are those arising from counting statistics.,mplpe (#632) was maintained at 815 C for 579600 s at a pressure of (l0)- 6 torr;

1. W. Mendenhall and R. L Scheaffer, Mathematical Statistics and Applications(Duxbury 1973) pp. 391-393.

52

no difference could be discerned between the yield obtained from that sample andthat from an untreated reference sample: at that pressure, D* was below the limitof measurement. Another sample (#631) had its alpha garticle yield measir r-wice.After being maintained at 690 C for 230400 s at (0)-9 torr, the yield w,; aparedto that of a reference sample: no difference could be detected. It was thea main-tained for 10980 s at 1150 C in flowing dry nitrogen at I atm and the yield wasagain compared to that of the reference sample. This time the results implied avalue of D* close to that of a sample (#627) which had undergone a similar treat-ment in dry nitrogen but-had no prior vacuum treatment.

The alternate method of determining D*, comparing the shapes of obser-ed andcalculated alpha particle yield curves, is illustrated in Figures 12a-c. Accom-panying each observed yield curve in the figures is a calculated curve, a member ofthe family depicted in Figure 14. The basis for selection was visual judgmentrather than numerical computation. A number of points concerning the observationsand results must be mentioned. First, the alpha particle counts indicated in thefigure are either the actual observations or (for #606, 827, A824 and 802) half therecorded counts. The corresponding statistical errors in the counts are between1% and 2.5%; as they can be calculated directly, they did not seem wortv indicatingexplicitly. Second, some variation in overall normalization was encountered. Thiswas caused by lateral nonuniformities in implanted dose and by slightly difterentsettings of detector angle on different runs. The maximum variation was on theorder of 10%.

The values of n associated with each of the theoretical curves in Figures 12a-c, as well as the resulting estimates for D*, are listed in Table III. The listedvalues of D* for the samples shown in Figure 12a are comparable to those obtainedby the method of peak yield decay listed in order of magnitude. The origin of thisdiscrepancy is addressed in the Discussion section which follows.

Figure 16. (Next page) Observed temperature dependence of180 tracer diffusivity at I atm. The solid lines represent

linear least squares fits to the data shown; the resultingpre-exponential factors and activation energies are indicated

below.

KEY TO FIGURE

SYMBOL ATMOSPHERE Do*(cm2/s) Q (kcal/mol)

X Steam 2.7(10)- 1 0 16.9

+ Room Air 1.3(1O)-1 2 15.5

O Dry N2 1.8(10)- 1 3 15.7

NOTE: 0 represents steam measurements of samples that

had previously undergone a high-vacuum anneal.

53

1I~ T T i0

',

.~~~~- . ......------

c:C

f 1 n0-4x C

C -

-4

a)

S zW:) - *aC 90 "1

54

77

00

C)C

cc~

L -O

0 0

K C

Z 9L-

AIV U)(55

IP

TABLE 3. COMPARISON OF METHODS FOR OBTAINING TRACER DIFFUSIVITY

YIELD CURVE SHAPE PEAK YIELD RATIO

Figure Sample n D* (cm 2 /s) n D* (cm 2 /s)

12a 316 1.75 2.7(10)-]6 2.32 5.7(10) - 1 6

612 2.5 1.1(10)- 14 3.12 1.9(10) - 14

606 15 5.5(10)14 8.1 3.0(10)14

12b A826 1.08 5.2(10)- 16 1.66 5.4(10)- 15

A824 1.5 3.1(10)- 16 4.1 3.9(10)- 15

12c 821 1.2 2.4(10)- 16 1.69 1.0(10)- 15

823 1.5 3.9(10)-15 2,9 2,3(10)-14

802 1.5 2.2(10)-16 4.8 3.9(10)- 1 5

56

DISCUSSION

Absence of Ion Bombardment Induced Damage in S10 2 Network

The measurements of tracer diffusivity performed in this study can becompared to others made in Si0 2 films and membranes only if the properties ofthe material used here match those others. In view of the well-known ten-dency of ion implantation to induce lattice damage in crystals, it may besuspected that the 180 implantation altered the structure or properties ofthe Si02 network. However, a good deal of evidence was collected during thecourse of this study which indicates that the implantation process does notproduce enough network damage to appreciably alter the oxide's properties, atleast as far as 180 tracer diffusion is concerned.

First, the amount of 180 implanted was small enough to avoid gross mor-

phological changes brought about by its incorporation, such as blister or

bubble formation. (None were seen.) The additional oxygen implanted in the

network amounted to, at most, 1.9% of the normal concentration. This can be

seen from equation (A4), which shows the peak concentration of implanted 180

in the initial distribution to be

421r

where 9 is the fluence of implantedl8 0O ions. As this was 3(10)15

ions/cm 2 and (Z*-? was 0.0283 um, Ppeak was 4.2(10)20 molecules/cm3 . This

was 1.9% of the concentration of 02 in Si0 2 , which is given in equation (7)

as 2.25(10)22 molecules/cm 3 .

Second, the shape of every alpha particle yield curve could be wellmatched to one or another of the set of theoretical curves; these were calcu-ILated on the basis of a dilute homogeneous medium. There was, therefore, no

indica.tion ever observed of a region of anomalous diffusivitv.

Third, iimilar thermal treatments were performed on two sample., On( oewhich had previously undergone a high-vacuum aiineai at 690 C for 23nno0O s.The 180 tracer diffusivity was found to be unaffected by this anneal. Theseobservations can be interpreted in the context of previous investifations of

annealing of radiation damage in Si02 discussed in the Introduction. Fromthese studies it may be concluded that whatever damage is produced in Sin) isentirely removed by a suitable high-temperature anneal. Tt is reasonable toconclude that the thermal treatments performed to induce is0 diffusion them-selves served to anneal out any damage induced by the implantation.

Next, there is the question of whether the proton bombardment involvedin the nuclear resonance rofiling caused any alteration of the network orinduced any diffusion of Y0. To answer this, alpha particle yield curveswere collected in implanted but otherwise untreated reference samples bothbefore and after lengthy proton bombardments (about 2000 uC, at a current of

0., ) A). No difference could be detected.

57

Final II v, to( dererine whether thfit impl ant ed I ic t uai I!v rep] aced' cxY.it htI, oxvijen ini the nettwo rk ,or rem;ai intn! inr-crs- it iai' ;tt( 'ret, to miierate,, otn

',,I ia pa rt-h>! yic ld curve wa's tatkeni for in tintreatevd refter-nc< -sanile ' laI t tA h i i-vacuum anneal at 1 5 C for 570(-nO( s. T '7an :intprec jatb) e amount c-im-

nI an)t edi~ hadl rena ire(' mobf !te thenl it wol U hlavc Udi ~e nIn ~i 0d W ith a d di f 'Ius"i Vi t V wh i 11 wa' lhara]Ct L r ist ; c o 4 dss i i ',,I! ole 10IcCIla r % VCTn;It th a t t emok ra t 't 't , nlare ! V ,m 1s (s) )-~ '.r 2 , (e ,o '~ r 2

itiusion n kmre f )irrespu)ndIinP to( thos;e valuecs of j)* andI t cri1 ted(I(- si it ,(!:iit on fI) ! to ico i.'0 implvinp tht, escalne_ of virtuazl v 171>>iI ic 8 t 1ir ou 'h t- tit o x ideit suir Iacte. However , the observed v i e t k, curve ,1

1, 1 i -I ishah IIi 'InI that 0f ain untreated utnannealed ref erence - vl.d i a'it in no 1, l ISIIi ft in hetlk in1 i t i A1 1'( T C~ c One t ra I ion prof i , . lit)t I Ic(u1r Ve

I* t -a, t mt h. t he t ;o-ret ical* IlIv pred ic ted curve for saicli an in m'nIIt.n: i r: ' ,nt i ai (Ilist r ihut i on o f 180 f ormed 1)y the imn - i, i

- in. no wor oxgen; an insignifiat>otcnon is i n accord wi;th' the t' -

K I,, !luvhes (Johnson et ;1. 32));i .. ~.~ro.ilct ion, It is also in acco'rd-----------

-. i,,v ion energy I ;,whichJ rCdi'; n

i- . i i peak temper-. S of I15W Q *-1'1n1, on atimo? scale of (h s .*'~.

- ~''Innconcentration of implanted e"ts* ....- ouIt ration. The subsequent "' ,-

teincorparit ino

>-ossedi the previous section, tle i Pl'latI1 on l-is n.oxygen as,. a constitlien, 0_ the ;if() ?'WV 1tV ~

t i- was t I n d t o h)e t ota IIv, i mro!hi !e at tekI'teraIt i ra Ieq xcednL 800C'~.v, n te )rcsence oif water it was, obsertved (! to v i\ . ,ara oss

.'Io :' With dIiSSOlved no) I e-iar W'" r ;11 . ; : ' scn di ~1- 'nst ;tulent of that s'pec is. II)er-t aire 'out.rltL~ cv; hence

ti is cunl us ion:

a observed linear dependence of the J~) tracer ( fus' v Vi t V uponvi, -r phase concentrat ion is identicail to thait expect ed "or !iq (I olved

* I water. This linear dependence was seen to hol I ivir 4 orders )'-tc:! (s ee FiC'rure 17) , fr atm to 79 ppm (of 1 it-,) . Thiese meaisuro-

its were rnde in pure water vapor - no carr ier ea,;ses were emiloved. VNhen- " was used Ias a carrier gas, the observed raceI-Lr d tfus -;vi tv conformed

;11 near dependence, but depended upon the part iai tpressure oif tmo-cr vap)or. This can he seen from Figure 16( whecre " he Measured raitio

D* steam 9T 7room air

33. N. M. Iohnson, W. C. Johnson and M. A. Lampert, I APnol Ph%,s 146,1216 (1975).

34. D. J. DiMaria, D. R. Young, W. R. Hunter and C. M. Serrano, lB'l J ResDevel, 22, 289 (1978)

93. W. Primak, J. Appl Phys 43, 2745 (1972)

58

is close tc the ratic o: water .,,, :,,rtial pressures for these atmospheres,namely 87 (92) oslumin,! ro(,, air At .OC and 507 rel hum. And when the sam-ples were treated in high vacuum, no 180 diffusion could be detected evenafter 6.7 days at 815C.

(2) The temperature dependence of D* -team showed an activation energyof 16.9 + 1.3 kcal/mol, which is indistinguishab], From those observed forwater diffusion by all previous investigators (s, 'igures 2, 3, and 16).Previously determined activation energies range from 16 to 18 kcal/mol. Thisvalue is clearlv inconsistent with those previously observed for oxygen dif-fusi- , the most reliable of which are about 28 kcal/mol.

(3) The magnitude of D* is close to that expected for free exchanpv re-tween network oxven and dissolved water. In the presence of free exchanee,D* is related to ')ei , the experimentally measured diffusivitv of water, a-cording to equation (10) hv

7 Deff/ free excnalg. e 7. 10 )-4 ;2(jC

This ratio, w",ose valuc is derived irom thc wat, r s--,,l ,i' it'. -eastremerat- t b

Moulson and Roberts (54) can aso be evajte: by as in, the results o'

D*steam obtained in this study (see [i-:ur,, In). This is

-*steam (this work) o .12 o)-'O(

Deff (Moulson-Roberts) 4(i0)- v1o0

The magnitude of D* ,team is thus seen to le consistent with free exchange atboth tremperat'trps meta,,red by Mnilson and Roberts to within a factor of 2-3,which is within the limits of accuracy obtained for the D* measurements inthis SfIidv.

(4) In the presence of atmospheric oxygen, the activation energy forD*room air remained that of water (roughly 16 kcal/mol, as indicated inequation 21), rather than revertinp to that of oxygen (28 kcal/mol). Thiswas true even at 800 C, where D02 exceeds (DefO)H20 bv an order of magnitude,and even though the concentration of atmospheric oxygen was 17 times that ofwater vapor (20% of 760 torr vs. 50% of 18 torr). This implied the absenceof exchange between atmospheric and network oxygen, in agreement with similarrecent findings by Rosencher et al.(50). As discussed in the Introduction,these authors observed the failure of diffusing 1802 to replace existingnetwork 160 during thermal growth of oxide films on silicon in dry 180 at-mospheres.

92. R. C. Weast, Handbook of Chemistry and Physics, 55th ed (CRC Press, 1974)p. D-159

54. J. Moulson and J. P. Roberts, Trans Faraday Soc 57, 1208 (1961)

50. E. Rosencher, A. Straboni, S. Rigo and C. Amsel, Appl Phys Lett 34,254 (1979)

59

Waiter Pereation Kinetics

The vaOlues of D* which appear in Fipgure 16, although conforming closelynoulh to an Arrhenius relation to support the conclusions reached in the

irvous sect ion, nonetheless show a significiint i-oulnt o17 scatter. Thi S i sei etfrom the large standard deviations to the fts, o'_ enuat ions, (2) and,

(2 1), wih ar t times larger than would h)e exp-ected on tilt I';As thleIi,-cusslun of eqiuat ion (19). "'he scat ter in the I)* va lties, ap:nea -rs t ',L svo-on!!At c rather than random: the smallest va1lues,'- of IL- L t i e It' o e Sso _ te

wi h the short est thermal treatments (i .(. small () n)'. I. wts , tl IsW, a hrr1-TIauck of aI hig-v;cium anneal prior to thcrmail t r,, t rio t a, 0 1l,

- rhe ,the amount of vie] d curve broiadening in t ht-u t <ist- i on ma11a om pa rd to( the d~ecay in peak %viel (! (See Vi Vures p'

I V'. - , -; et Lhla t a n r LV 1f)U 1. 1 uns ;U peted ' t-

a .~ e ei~natio Kr the !L Lt ' '

in ~~I%,1 ('rN OYf e ser is rlce 'i a 1. ~ '~~<

't er vapT)o, m o ecula 1r wa; o i tr,,; 'r'

t dsri te '-,jt~"' o t ,

nains its saturation \':I !!w. A t , I t tthat enul ibr;III- 1-'etweon dlai 1'e, "oi- ui r waiI(tr inc4' one, rk is also quiickly ost.Wisi2,1ha r. 1'

n so rapid 1v at ta ins its sat 1 %r n il 'oey1r*'a-oiiil ibriumn is not rapid "Ind the oxide laver is i la l ~1 r' ' 'av wi

( av observed inr 1, O d if fus ion ount i t he reac ted watI-er wi c ' ceS!o ts transport has reached a sim'ni ficant: level . Th e nno"a' oiiF'

"a val ues observed here after short thermal treatments and vacuumn desic-4 ,!rlton, especially for the lower temperature steam treatments, suggest that* ,ese conditions occur.

In order to properly asseqs !-he effects or nonequil1ibrium. Permeat ion'itionq on the evolution of 18 distributions,i a thorough theoretical nni

etlstudy is needed. Although a complete study is beyond the sconiearo, a introductory developmient appears here in Appendix TD, where

rtridifferential enn ations governing 110 dil~usion (a formidable setvcoupled nonlinear equations) are presented. They are solved here

'-vopr two special cases, both of which involve rapid saturation o-f thevile with dissolved molecular water. one of them, involving rarid estab-1;qnment of equilibrium, is the case which was thorouphly treated in the body

this study. For the other case, the content of reacted water remains Uni-

't'a troughout the oxide but varies with time. For times on the order of ,i

'u-oristwtime ~it is far lower than its saturat ion value, causinp the.nit-tal diepression in ()*.

rt is interesting that this same phenomrenoin seemns to have been ol-serve,'

both Will iams(53) and Haul and Dumhgen (51) in their eairlystdispermeation in SiPN fibers and membranes. As discussed in) the nrout o

3. R. H. IDoremus, Glass Science (Wilev, 19)73) p. 128

53. F. 1_ Williams, JT Am Ceram Soc LA, 190 (1965)

51. R. Haul and G. Dumbgen, Z Flectrochem 66, 636 (1962)

60

these authors employed mass spectrometers to measure atmospheric oxygen iso-topic ratios in containers with limited amounts of 180-enriched oxygenWilliams, observing that the values of diffusivity at short times were muchlower than those evaluated at long times, particularly for low-temperaturediffusions, invoked this effect to account for the very high activation ener-gies found earlier by Haul and Dumbgen and by Sucov (52), whose observationsall involved short times. By not carrying out long enough diffusions, theyobserved erroneously small D values at lower temperatures, leading to anoverestimate of the activation energy. The activation energy he found(29 kcal/mol) was close to that measured by 'Norton (49) as well as to thethermal oxidation B values for dry oxygen. The magnitudes of the diffusivitvmeasured in the early 180 permeation experiments, however, were on the orderof those measured in this study rather than those of Norton and the thermal

* oxidation experiments. This suggests that they were observing some sort ofexchange of diffusing 180 with network oxygen. Both Meek (94) -and Schaeffer

*and Muehlenbachs (95) explained the six order of magnitude dif4:ference on thebasis of a direct exchange. However, in view of the lack of exchange ()I-served both by Rosencher et al. (50) and in this study for IFndiffusion indry SiO? films, their explanations must 1be douibted. Tf anyv exchanget occurs,it is more likely mediated byv reacted water in the oxide. It is certa-inl%the case that significant qujatities ot_ waiter were present in hNill ians ' ex-perinent oboth in the oxides and in the atmosnhere. lie studiec' its infilenceOn his I di ffusivi rv byVacu V, esM J-i c-tion o-* the Si O-) and found that thisprocedure oinc reasec the in it ia, del a, and lowered the limit ini va illicthle " di s %,i t v. The influenrce of water was app)arent lv not apreciated,!the other early invest icator's,' who seem not to have taken pains eithe-r toeliminate. -or control it. The actual me, anis.: oi exchance (lif it exi-sts "ttween di -using no lecil ar o)XVc!er. and reacted water rema ins obscuire; an(! tuetprocess hsnot bheen obnserved in thermal oxidat ion experiments which haive

invoI ved oxygen , ns~rsontai~ning control led fract ions of water arThe paral cl iC coe Mt' I S I asTLeI bo th by Deal et al (67) and bv Ot a in,:Butler (71) aret- sitn with independent diffusion of water an, 4 1 k,

Ove'r A caeCt ~s~rlfae concentrations from 2" to 1007,1,%,\o~nThis cc. ts wi-t. t,, rvatin of Irene and C'hez (40), that atMOSPIher~.water roncentrratiz as 25 ppm (in 09) markedly increased the )arabo2 ic

c oet' i c eUn t

bO. . Rlsea~cA. t rnoni ,S. Rigo and C. Amsel , AppI Phivs Lttt

52. E. V. uc'.', : A:,,Cram Soc 46, 14 (1963)

49 . i.. N or o ,' .;it ,rk, I , 7D () 1 1961)

94. R. I.. I Ark , An ram Soc 56 , 142 (107))

95. 11. A. Schaeffer and K. Miiehlenbachs, I Mat Is V~i Ill ITh

67. B. E. Deal , 1). l. ess, .. 1). P1 innmer and C. P. i' I Ie etroc hen7 SOc1215, 339 (19"8)

71. Y. flta .ind S . Ix. Butler, 1 Fle trocher; So, I21,11-

40. E. A. ]rent? and B. CGiez, I Electrochem SoL ., ~

The analysis of these authors yielded systematically different values of Bfrom those of other investigators (see Figure 3, particularly their values ofBO9 at 780 C and of BH2 0 at 893 C). In addition, the dependence of theirparabolic coefficients upon the crystallographic orientation of the Si sub-strate supgests a nonstandard definition of B, which is normallv taken tu in-volve pure bulk diffusion rather than interface effects. Tt may be noted.that although Deal et al (67) also report a large increase in B with the addi-tion of trace amounts of H2j based on data plotted in their Figure 3, a re-plotting of that figure with (Bobserved - BO2) replacing Bobserved as ordinate(plotted against volume % H2 0 in 02) shows this quantitv to depend strictlylinearlv upon water concentration, as was found in this study. Figur- 18here shows their data plotted in such a manner, with the ordinate show11 tsieroent of R in pure water vapor in order to compensate for the tempcratir,-o4,nendence of BH,)O. The linear dependence is evident.

Another example of the strong influence that water exerts on diffusion"iO occurs when silicon wafers are thermally oxidizecd in resistance-- 2 'urnacs. The evolution of water from the wal s o- tho si b ,i2 i-

t tues caused a reat deal of variation in tariv resu2 ts on therma.l ,i!;i-Ion kinetics, as was noted by Revesz and Evans (62). These authors elir-

-ted the wall contribution by rf heating their samnl]s in a co-l-wal edn)aco. Subsenuent investigators, realizing the signi+-icance of this ffect,

'oved various means to inhibit water vapor evolution. For exam. ,, I V;, o

E, -vans ( 5) used polysilicon diffusion tubes: the film of SiP" whichr'-ed ~n the inner wall acted to getter any water vapor present in the at--ihere. The extent to which silica furnace walls contrihute to atm(sp!eric,or vapor content can be seen from the work of Nakavama and Collins (69),,easured oxidation rates for silicon in dry argon corresponding to water

* i,,r p)ressures of 0.22 torr at 850 C and n.35 torr at 1000 C. The same ef-.t ('b he seen from the values of D*drv N2 observed in this study. These

vre consistently a factor of only 8 below those of D*room air as mentionedthe Data Analysis, corresponding to water vapor pressures of about ] torr.

...kstreaming of room air through the open exhaust end of the diffusion tube15s() have contributed to the large value of D*dr v, N2. As no quantitative

,rences were drawn from that data, this possibility was not investigatedher.

* .' B. F. Deal, D. W. Hess, J. D. Plummer and C. P. Ho, J Electrochem Soc!25, 339 (1978)

A. 1;. Revesz and R. J. Evans, J Phvs Chem Solids, 30, 551 (1969)

. Vavo and W. H. Evans, "Development of Hydrogen and Hvdroxvl Contamin-'on in Thin Silicon Dioxide Films" NBSIR 79-1559 (NBS, March 1q70)

N;ikayama ;ind F. C. Collins, J Electrochem Soc 111, 706 (1966)

62

1II' I I I --

10-

85

6 6

4 =900 C

2O 1000 C

2 o 1100 C

0

0 2 468 10VOL % H20 IN 02

Figure 18. Increment in the parabolic rate constant upon addition of H20 to

oxygen atmosphere, as percent of BH 2 0 in pure water vapor. All data pointsare from Deal et al. (67); values of BH 2 0 in pure water vapor (used for nor-malization) are from Deal and Grove (56), adjusted to 100 vol % water vapor.

67. B. E. Deal, 1). W. Hess, J. D. Plummer and C. P. Ho, J Electrochem Soc

125, 339 (1978)

56 . B. E. Deal and A. S. Grove, J Appl Phys 36, 3770 (1965)

63

An independent confirmation of the time variation in 180 tracer dif-fusivity resulting from nonequilibrium permeation conditions has recentlybeen provided by Rigo et al.(96). Using procedures similar to that ofRosencher et al.(50),the¥ measured the permeation of 180 into Si0 2 films uponthermal treatment in H2180 atmospheres. They found that the 180 profileswere consistent with a time-varying D*, especially for temperatures nearthose employed in this study.4

5

T.:. -osencher, A. Straboni, S. Rigo and G. Amsel, Appl Phys Lett 34254 (1979)

j6. S. Rigo, F. Rochet and A. Straboni, "An 180 Study of the Oxygen Exchangein Si0 2 Films During Thermal Treatment in Water Vapor," Presentation,1980 International Conference on the Physics of MOS Insulators,Raleigh, NC 17-20 June 1980.

64

CONCLUSIONS

The results of the 180 tracer diffusion measurements performed in thisstudy clearly demonstrate that water diffusion in Si0 2 films proceeds by thetransport of molecular water and that it is accompanied by a strong reversi-ble reaction between molecular water and network oxygen. The observed lineardependence of tracer diffusivity upon partial pressure of atmospheric watervapor, for pressures ranging from 1 atm to as little as 0.06 torr, indicatesthat network oxygen is exchanged with molecular water. The activation energy

* of tracer diffusion remained about 16 kcal/mol, characteristic of water dif-fusion, over a range of temperatures from 1150 C to 260 C. Further, the mag-nitude of the tracer diffusivity was consistent with the presence of free ex-

* change between network oxygen and diffusing water. The extent of tracer dif-fusion proved to be unaffected by the presence of atmospheric oxygen, indi-cating the absence of exchange with that species. The results obtained hereagreed with corresponding results obtained by most other investigators usingdifferent means. They are in complete agreement with recently proposed mo-dels of oxygen and water diffusion in Si0o,, in which the diffusion Droceedsby transport of the molecular species thrbugh interstices in the networkwithout any direct reaction between the molecular species and the SiO 2. (Thestrong exchange reaction accompanying water diffusion is mediated by immobileOH groups which are dissociation products of the molecular water.)

The process employed for introducing tracer 180 into the network, thatof ion implantation, was shown to produce a region within the oxide in whichthe 180 was fully incorporated in the network: no18 0 diffusion was observedin high vacuum,even after 161 hrs at 815 C. The properties of the networkremained otherwise unaltered, at least as far as diffusion was concerned.This was demonstrated both by the data's close match to theoretical predic-tions based on a dilute homogeneous medium as well as by the absence of anyeffect on diffusion of a high-temperature treatment which was sufficient to

anneal out any implantation-induced damaee. These findings indicate that thethermal treatments performed to induce 180 diffusion were themselves suffi-cient to anneal out any damage.

The technique of nuclear resonance profiling pro-ed to be a convenient,nondestructive and sensitive method of measuring 0 diffusivities as low as1(10) - 17 cm2 /s at temperatures as low as 260 C.

-in addition to supporting the above conclusions concerning the mecha-nical water diffusion in Si0 2 , the measurements made in this study providedevidence indicating that chemical equilibrium between water dissolved inSi0 2 films and its reaction products often had not been attained over thetime spans of the thermal treatments. The time variation of the reactedwater concentration, leading to a time variation in 180 tracer diffusivity,suggests a series of 180 diffusion measurements which would form a naturalfollow-up to this study. Thermal oxide films could be grown on a set ofsilicon samples in dry oxygen, each of which would contain a thin layer en-riched with 180 (formed either by a short oxidation inl 80 or by a low-energyimplant). Although the total thicknesses and the enriched-layer thicknesseswould all be identical, the depth of the enriched layer would be differentfor different samples. After the set of samples received a thermal treatmentin water vapor, the concentration profile of reacted water in the oxide could

65

be determined by measurement of D* near each enriched laver by nuclear re-sonance profiling. Successive concentration profiles could be determinedfrom a series of thermal treatments, providing a complete experimental deter-mination of nonequilibrium water permeation kinetics.

Such a study could be of great benefit in the manufacture of future

high-reliability integrated circuit :evices. The absorption of moisture isknown to seriously degrade the breakdcwn resistance of MOS gate oxides,

leading to premature device failure. Detailed observations of permeationkinetics would be a valuable tool in the investigation of new methods toiOibit water permeation in oxide films.

*WKNOWLEDGMENTS

author wishes to express sincere gratitude to Dr. S. Kronenberg and

i. Kohn for their persistent encouragement and support, to Dr. G. Brucker"!r-. F. Kolondra of RCA Labs, Princeton for performing the ion implanta-, to Mr. E. AhIstrom for preparing the thermal oxides, and to Mr. A.

Rager and Mr. J. Freeman for glass and thermocouple fabrication; particularlyt, his colleagues, Dr. H. Berkowitz, for his advice on theoretical physics

. on programming, and Dr. R. Lux for his invaluable and generously provided-. eration both in the nuclear profiling and in many discussions of physical

eclanisms.

66

.. 8

APPENDIX A - Evolution of 180 Distribution

Suppose an Si02 layer containing implanted 180 is heated for a time t underconditions which produce a tracer diffusivity D* which is independent of x and t,where x is depth in the layer. Then the distribution of excess 180 in the oxide(i.e.,in excess of the natural background level of 0,02% isotopic fraction) willchange with time so as to satisfy the diffusion equation

a2(x,t) = D* Jo(xt) (Al)

under boundary conditions appropriate for the experimental case. The generalsolution to this equation is

;i _ 2~(x~t ~ + ~+ Ce n D t [Acsczv~+ B sin a~c. (A2)

18Remember that 0 is transported only as a constituent of molecularly dissolved

water. The boundary conditions are therefore determined by considering thebehavior of this substance at the boundaries:

(a.) At the oxide surface, equilibrium between the outside atmosphere and water

dissolved in the oxide occurs rapidly: surface absorption and reactions are not

involved (1). This implies the conditionfP(O,t) = 0.

(b) At the oxide-silicon interface, the boundary condition is temperaturedependent. This can be seen from the analysis of steady-state steam oxidation

performed by Deal and Grove (2). (Steady-state means V-J = 0 within the oxide).According to their equations (6) and (7), the ratio of molecularly dissolvedwater concentration at the interface to that at the outer surface is given by

Ci 1C 0 + ko/Deff (A3)

where k, the interface rate constant, is determined through observations of thelinear and parabolic rate constants A and B and the equilibrium solubility C*(X is the layer thickness.) Deal and Grove give a value of

k = 1.8 (10) 3 um/hr

at 1000 C with an activation energy of 45.3 kcal/mol. Using this in conjuction

with Moulson & Roberts' (3) equation

Deff = (10) -6 exp (-18.3(kcal/mol)/RT) (cm 2/sec),

A-I. R. H. Doremus, Glass Science (Wiley, 1973), p. 128

A4. B. E. Deal and A. S. Grove, J Appl Phys 36, 3770 (1965)

A-3. J. Moulson and J. P. Roberts, Trans Faraday Soc 57, 1208 (1961)

67

C iLie temperature dependence of -- is seen to be the following:

0

T(C) o/ eff 0il

250 3.1(10) - 7

-4475 7.7(10) 1

600 0.011 0.989

1000 1.4 0.417

1200 5.9 0.145

C.1Lemperatures encountered in this work, the ratio - is more than 98,. The

Cate boundary condition is therefore o

0.18

, or sufficiently long times all the excess 0 will eventually disappear,

A 'r through surface leakage or interface incorporation of diffusing molecularimplying the condition 'O(xoo) = 0.

S( The initial distribution was taken to be that implantation profile given by

LiLb~uzs,et al (4) for the appropriate experimental conditions. This was an Edge-

wo'-th -:itribution (the product of a Gaussian and a polynomial); explicitly, it

ja(x0)~ Fluence 1 /1W2wo aimp e 2 L

( 6 E 6 2 + 3) __ 6 4 + 452 15 (A4)

72 72 )

XXimp

Ui o imp

Yimp = 00768 Am

aimp 0.0283 um

-- - 0.164

A-4. J. F. Gibbons, W. S. Johnson and S. W. Mylrole, Projected Range Statistics,

2nd Edn. (Academic, 1975)

68

Conditions (a), (b), and (c) imply

A = B = A = 0 (all n)

B = 0 (n even)n

_ni

O n 2 7 -°

The solution to the diffusion equation is then straightforward, being

=(~ )B2- sin " 2- X (A5)

n=I 0

with

Bk = 2 dx sin (- X)P(X,0) . (A6)

The numerical evaluation of.P(%,t) was performed with an Interdata 832 Computerlocated at Fort Monmouth, N.J. The programs were straightforward. Representative

k results appear in Figure 13.

69

APPENDIX B - Evolution of Alpha Particle Yield

The yield of alpha particles from the 180(p, )IN reaction is given by

the integral equation

Y(b),xo df t)J Ht) dEi g(Eb' EE i dr-E )f(E,Ei,x) (RT)

where

Eb is the mean energy of the incident proton beam,

E is the energy of reacting protons,

Ei is the actual energy of protons incident on the surface ol

the layer,

xo is the thickness of the oxide layer,

x is the depth at which the reaction occurs,

,P(x,t) is the 180 concentration profile (i.e. atoms per unit volumeat depth x at time t),

do is the differential cross section of the 180(p, i )I5reaction,

g(EbEi)dEi is the fraction of protons in the beam which have an incident

energy between Ei and Ei + dEi,

f(E,Eix)dE is the probability that a proton which has started with

energy Ei and arrived at depth x will have an energy betweenE and E + dE.

This also appears in the Introduction as equation (14). Once the functions

-do(x,t), g(Eb,Ei), f(E,Ei,x) and-7(E) are established, then the yield isobtained by integration. A means of calculating is given in Appendix A.For the remaining functions, we proceed as follows:

g(Eb,Ei):

The distribution of energies in the incident beam was found experimen-

tally through analysis of the thick-target Al(p,V')2 8 Si excitation curve

(see Procedure). As the energy spread amounted to less than 1 keV, the

details of its shape are relatively unimportant; for ease in calculation it

can be taken to be a Gaussian with ab1l keV, i.e.,

( 1 -(Eb-Ei) 2 (B2)g(EbEi) r b 202

70

f(E,Ei,x):

If the proton energy loss were strictly deterministic, then f would be given

by &(E-{E dxt T}), where ToE is the specific energy loss of protons in.'fo dX, dxi dE

Si0 2. At an Eb of 629 keV the value of -E is 61 keV/um (1). Since the

layer is only 02 um thick, the protons lose 12.2 keV in a complete traver-dE

sal; throughout this region j-ois constant to within 1%. Thus

However, the random nature of the independent scattering events by whichprotons lose energy in materials implies that their energy at a givenprojected range is not uniquely determined by their initial energy. The

effect of this energy straggling is to broaden the delta function to a

distribution f(x,A), where x is the projected pathlength and A= Ei-E(x).Vavilov () found that this function may be closely approximated by one of

three expressions, the choice depending on the magnitude of x. (A review

of Vavilov's work appears in Appendix C.) Upon performing detailed calcula-

tions based on that work, it was found that for the particular conditions

of this experiment, the distribution could be approximated by

f(XA)- (B3)v/ 2xks) - e xPksx I

where ks = 17.75 (keV2 um- )

dr(E):

Highly accurate measurements of the differential cross section for the18 0(PCa )15 aN reaction at 0lab = 1500 have recently been performed by Asel,

Maurel and Nadaf (3J. la

B-L E. Bonderup and P. Hvelplund, Phys Rev A4, 562 (1971)

1-2. P. V. Vavilov, Soviet Phys JETP 5, 749 (1957)

6-3. J. W. Mayer and E. Rimini, Eds., Ion Beam Handbook for Materials Analysis(Academic, 1977) p 163

71

A very close fit to their data in the region of the 629 keV resonanci ha-;

been found to be a sum of two interfering Lorentzians plus an exponential

background. Explicitly, this was

2 E-EresU'res ,116

do 4 (12.78-K) - (E-Eres) 4.7e, E-Eresd- (E) 2 2 + Ke 58 (mb/ste)

(E-Eres) + res' (A4)

where

k 2 (E <Eres)

S=1.75 (E >Eres)

E 629 keV

res

With all the constituents of the yield established, its evaluation wa iscarried out numerically by first substituting equations (B2) and (B3) in

equation (BI). Because of the strong damping of the exponential functionE(xA,) in the range of 7 where +(x,t) was appreciable, the limits In the E

integral could be extended to ±00 without ignificantly changing the result.Similarly, the strong damping of the exponential function g(Eb,Ei>, allowed

the lower limit on the Ei integral to be extended to -0. The order ofintegration was then interchanged, enabling the yield to be written

Y(Eb ) dx (x, t dE -(E) d~i 4 b k

do

( r(E -Eb) 2 (Er- EEIexp~( i + k" (B5)

The Ei integral could then be performed using the convolution identity

iL t (5-0 - 2 " 2 +o 2 (136)- 2 - l Z+ 012001 c1

-',0

72

, j'

with

t Ei-Eb, S = E-Eb+Cx, CvI G 2= V2ksx.

The yield is ixo /2.x (E-E +ex)2

Y(Eb) = do (xt) dE (E) e b (B7)0 2i~a~+~x)2(c ~ + x)

4 1 E- (E b -E)

Using the substitution E E.'E 2 , this was rewritten as2( b2 + ksX)

40 412

Y(E dx , dE /2 E b + ksX) + Eb -c 7XJX ,Jc ~ ~ 2~ k ) +(B8)

This was the appropriate form for evaluation by Hermite integration (4):K+ JdE e-IZf(El) Y W f (E'j).

j=-J

The evaluation of equation (B8) was performed using the weight factors and- do

and abscissas appropriate for a 20-point Hermite integration over E with

given by equation (B4), and a 50-point Simpson integration over x, with

AO(x,t) given by the sum of equation (A5) plus a constant background). A

listing of the program appears on the next three pages; it was run on an

Interdata 832 computer located at Fort Monmouth, N.J. Representative resultsappear in Figure 13.

B-4.M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 924

(US Government Printing Office, 1964)

73

i.U-1

K 'LL 1ii IONf C1Th HLFI-.rm (IE; D FFLTP INLHITIIL):NDF: I - I H E F:i17 FH [ F ELI IL F I F FII IE I ir 1

F!

-4 I PiLHi t~ I i- TJM 1, 1;'g T. Hi T1L 9>

T I E1 P- D 11 m P 411-

-- $ 1' '' Lll [ I . -D iDYLFFF ' 'f L [i F iFI' 2 F IL~ T _, J l-

: F F O F[Jrir ,' -,: F ) - ESH r . rEK I~ m i- F F I! I.T p .,

S- 1i 1- - irE - i

1 H ILL FEFI F HM 21 2 1 I rT r"Y .' F P P 1 L C C TO

. p P ,r P' . L I -'\. - - T'l i -I 5 i'F- I E M.-,I01 M

1 -HLL FREFFM , ' rIliM'

NB Ti:* D2 1

I T .L T .1. I T

r, T- NT *HT 1- 7 11 1- P. p I I -; I. M *

IF I TE i ( i l 4S€'D T II I Ei ' , I , 41

11.I:F~M+11. :4 11

E .' PF: DLHr ' 41 v- *- E FF-

-1-, BE7i'T1 " Im I). IF i - p M F- 1 E,CN IfUE

' P I T E (,1 04 ' i

.i .'<, #I1 G }'iD - I ' - . . + i•'-.' 0

1(1- F. E PN H "-1X - 'Ei. PFF F I , I : IG-PMI (I" Fl0 IT, R T.1: :- ,EN N F P T -ll-1 i .- N0 P N FFIH T, 0R

::: ,' iI F E 'MT I E

F 0 ,. H T 1::-A LPH i TELD FqP tiH FREC = 1:: 1UTT H iI I 1 . _'4 MH .

IlFKI

,.,r 7lE

illr! i N F-,F I P,[lr<H '1 [i ,:~ 'I NN *,P'I *L-"FA: ,* F I 1 , - *L!"F ,F ,. -7 1 - ,-

" ~ I I.' ,Er. ,-. h . , r.1 ..- ,bl In' - '* F K T

LI '.

- " 1 _I, *. ,- . ,:. P,, i-i -,: -: , ,

";'. IF ' ' .i.; *.-: Ii -, r- . "].i :li. , '317] IL) 1 '

-V"ll [] 1 IN LFi-& 'P H I.IF *- ---

:F F-+F - I, - '. .:74

74

4C4 FL FI- U'S

-'I- EriE51 :TE T

-3 FIrIf ii- I I LIN F f'

FEL HC,4 _ 'i T[31 Pi* I F ,P'F . I MP. IG I mF .Pti ID, TF,-]

SE I ELT<.F'E TS1E :1FPCI-FIT,

I_ r~55 <Sri>: 7 *F F:E FIt Ti

_%- F TL P R G Pr D I- ---

r. 1 L T JP3 _ IirI iiil _1=-II II

.:, IF J. Ei-'. "1 T ] 1'l

DE IF i. LT. + , -A

n-E: I IF N:E. T. I. E: 1l.75

, ,*.-iE IE+FF*FF-v +

1 _A EX , I' .- ..-:

' . 1 1 vT:I rT _ 1+1,1, I I I, F:IlN," • 1 0 LtiT I ''F-' ~F : i fi [ 9 .1 3. 7 4 -'1 3 . 3 1.-" 7-h-' U-"- . E.. **F i

_1 . . .F- _,.T_*E F

T FE 1 f.F t

F-I T

~'75

- i' ~~ -iF'T

ii 1 '..... . .'1 , i ' r Y +4 F ? -- L

' - 1'. *5 I ;- I F+ ;.

91 F l i,

: -' t'.l [iv p IIf: i -

4'. -njf I', I J5 + , -;4, I *,F'Th'.I , 1-5i . ]Ci-,Pr'I[' t:I-., KJFFC"' i 1! V TIt . F . * F , 3l- . fr • Fth. I Ih - I ,

75

4 : f' . I . -4 1 .-

.4~ ~~ ~~~ 4. 1.,lfh t -r ~ 4~.,''

S . : , I .1 4 :-

* ~4 .F -'• 4 , :' 4,.-.,

- .4

, It

L: . , 4 1if . " I' ti f j , I7 c P - I-4 -1

HI . I , 44 ' LF'' 1 Fi I - I r-

1 44- 1 1HA1

, . . . ] . , ~ ~ ~ ~~ .1 : . . Il -]_4 ;- ;;4

4 . .lI* 'i., " i. , 4 _,. . . .; ;

. ... - .z ' 1 . , ,.,] -4 :- _] -I , f . ' ., ' : ";

Ir, -l.L i If;,,;. EVE. _I._' WE? lE D I I '' -

* :-:] F.:. IR: .7I. I _iSF T.14 7 ( (-

141.H Hq " i rCq 1F1,cTr

* (,C.I oI

4 . • ff -.' ., 4 I-

APPENDIX C - Proton Energy Straggling Distribution

If a proton with initial energy Ei passes through a medium, its energyE decreases by an amount A = Ei-E(x) where x is the projected pathlength.Because of the random nature of the independent scattering events by whichprotons lose energy in materials, the proton energy at a given projectedpathlength is not a unique function of E1 . Rather, the proton energy loss ischaracterized by a distribution f(x,A). f(x,A)dA is the probability thata proton traversing a path of length x will suffer an energy loss between Aand A +dA . This distribution was studied by Vavilov (1), who found that itis closely approximated by one of three expressions, the choice depending onthe magnitude of x. (The equations given by Vavilov will be denoted hereinby the prefix "V".)

For x- 1 um, the expression for f(x,A) given in equation (V15) is

equivalent to

f(x,A) exp - 2k x (Cl)L S

2 4wish kx X B 4, zZe Nx

where 2B = Bohr straggling parameter (Bohr (2) as quoted by Fano (3))

z = proton atomic number

Z = Si02 atomic number

e = charge of the electron

N = number density of Si02 atoms

t < < Ic 1000 A - x - I um, f(x,A) is given in equation (V13) as

(x ,t- a 3 ) Ai(t) • (C2)

"iis i-r s ioin can be evaluated as follows:

A:rd to 1 , to .:ventional notation of special relativity, the protons'velocity (re' tive to the speed of light) is

2. (c3)- 2(0MC

-I. P. V. Vilov, Soviet Phys JETP 5, 749 (1957)

C-?. ?. Bohr, .dat. Fys. Medd. Dan. Vid. Selsk 18 (8) (1948)

o ino, Aiim Rev Nuct Sci. 13, 1 (1963)

77

where M proton mass and E = proton energy. From equation (V5) we have

2meC2 2 small 4meC2 4Emax __2 ? 1836 F (C4)

where me = electron mass,

And also from equation (V5)

2 me2M2m e C z M c2 M (C 5

*=0,300 x - - = 0.075 x

P2 A E

2where x depth within layer, in g/cm, and z/A = 1/2

I- ween (V5) and (V6), and using equations (CL) and (C5), we have

22TheC 'IC (

" ~K = =311.4 x rn M2(C6)

F. £max E2

I Prom equation (V12), and using equation (C6)

= 2 ~ 2L 1/3 sml 12Ci/3 = .9 ~ \j'1/3

(C7)

Also from equation (V12), and using equations (C5) and C7)

--'1/3,.

.1(1-32il/3 small _ 2 = 0.00464 L c2MC2 1/3.

1 iIrssing x in urn, with p=2.27 g/m3 for Si0 2 (4) and approximat fng F by

V :ros b 29 keV, we have

0.01298 x (MeV) (C9)

Kf= 9.472 x (dimensionless) (C]1)

'/3a, 2.666 x (dimens i onlless) (CII)

;llid T = 1.826 x (keV). 'CI 2)

C-4. A. S. Grove, Physics and Technology of Semiconductor Devices (Wiley, 1967)

78

Using equations (CII) and (C12) and = 61 keV/um (5) in equation (V12),

we have

(A-x)+ a (C13)

The distribution given in equation (V13) can then be written as

f(x1) /0.309 exp(l.46A- 96.43x) Ai + 7.108x 2/ 3 (C14)x 1.826x 1/ 3

*where Ai is the Airy function (6).

The following give an excellent fit to all values of Ai(x) listed in

Table 10.11 of Reference 6:

|x-- /4(0.3975cos + 0.4003 sinC), (x< -2.5)

1 3 4 6 28 90.35503 (1 + W x + -- x +328--- x

'A + X + 362880 x

Ai / 2 4 10 7 80 100.25882 x + 5040 x + x o, (-2.5<x< 1)

1 x1/4 {0.00481(1.5 - + 0.01756(1.5 - -)+ 0.5 27C3j2 '

(1< x) (C15)

2 3/2where 3 x|

For x<1000 , f(x,A) is given by equation (V16):

f(x,A) -1 Ke I+ dy eif ' cos(y I + Kf 2 ) (C16)

0

C-5. E. Bonderup and P. Hvelplund, Phys Rev A4, 562 (1971)

C-6. A. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 446(US Government Printing Office, 1964)

79

where

c = 0.577 .... (Euler's constant)

f,= J2 [in y - Ci(y)] - cos y - y Si(y)

f 2 = y fin y - Ci(y)] + sin y + 2Si(y)

X, KX +IklnK

A -EX 2- - - ,8+ C - In

and where Ci and Si are the cosine and sine integral functions respective!%.

Although later calculations of f(x,A) exist (see, for example Biche]and Saxon (7) and references cited therein), recent straggling experients

involving 0-2 MeV protons in thin films of silicon (8) lvivc ccnfirmed tbl'validity of Vavilov's expressions.

C-7. H. Bichsel and P. Saxon, Phys Rev All, 1286 (1975)

C-8. J. Baglin, private communication (1979)

80

APPENDIX D - Nonequilibrium Permeation Kinetics

180

To fully describe the evolution of the tracer 0 distribution in theSiOi films, it must be realized that 180 can be a constituent of either dis-

solved molecular water, reacted water or network oxide. Let the respective

concentrations of the various species be denoted

j f (x,L) = [H 2 1 6 0 (dissolved water)

Jor (x, t) i [16OHJ (reacted water)

Pr(xt) [Si OR]

'A (x,t) j [Si1 6 020 (network oxide)

;. ( " t) [Si 180_-16 0 •'1080

(The stars indicate the presence of tracer 180.) We may assume that

a. the amount of 180 is everywhere small compared to the amount of 160,

and thus neglect any terms involving J&09.

b. fO,(xt) = fSiO2, independent of x and t, i.e. a uniform oxide.

Under these conditions the equations governing the tracer distributions are

_. : : v p; (pr-)

dfr9/ I( A"/

?*-2 - ))(D)

k. Z: (D3)

2. w(D4)

81

The first term in equations (Dl) and (D4) describes the transport of dis-

solved molecular water; the quantity VP is the flux of thaJt species. The

other tterms in the equations describe the formation and disappearance uf the-

vairious species through the processes of recombination and dissoCiat ion;

:terms involving products of concentrations describe hinary (ollisions. The

"at ttS Z can be thought of as the lifetime o! a dissol vvd water -iolecul,,

.>'oslsy to the charge carrier lifetime which appeo rs in tht, equ;ations

t escribilg electron and hole diffusion in solids (I). Lt she'ujdIii ntod

,tLi qi:antLtv measured by means of nucleir resonance pyT Yuii',[, ' 4 I7

!' rohem of solving the ful set of equat ios wi" noLt he iddressed

some approximations will be made which ii'ow treut n ff-t T ,- vn iditv ,of the approxir,,ati,.n may tO- (',urse !)c 1:1,- t ,.i' d

: t- ali* it can he seern that by adding equa.t ions (D ) throuhteio (ci

jIppoxma io

is ma: e, then f'.., can be found by finding solutions to equations (D1) and

05), which thus decouple from the first three.

These latter equations can be seen to revert to the equations generally

'en to describe water permeation, which assume both that f'> bt equilibrium 's established quickly between and 5 . Under those

itions _adding eqietions (D4) and (05) results in

+ f~ A + J 7-

,.ln~'n the inequa.lity as weil as the equilibrium condition given as equa-

:o.n (6) in the test, this reduces to

[]-I. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt Rinehart, 1976)

p 603

82

which is the equation that both Doremus (2) and Wagner (1) have.

An interesting case occurs in the limit thLat 'Vis so large that the meanfree path between water dissociations is large compared to the SiO2 filmthickness. Under those conditions Ro approaches its saturation value while

JPr is still negligible. The buildup of Pr can then be described by setting

10t z /0 (3) in equation (D5). That equation then decouples from equa-

tion (D4) as well; its solution is

./. t~ (&+ -,4 20 oi (-C

indepenJent of x.

Since the exchange of an individual 180 between the network and dissolvedmolecular water depends on the recombination of 0H, the value of tracer dif-

fusivity D* at any time is proportional to the value of O-L at that time.Under these conditions, the apparent value of D*t at any time is related toits limiting value (i.e. when equilibrium has been established by the equation

This equation can be integrated to give

(V D~~~ -- -t jere- Zt4,

'D~ , 6

It can hu seen that the quantity [D*tlapparent is small for short times; it

reaches hlif ;',-symptotic value at t = 1. Using equation (8) in the text,R

this time is approximately 900 b at 600 C. The actual value of r at any tem-perature can be determined through measurement of the time behavior of[. apparent.

D-2. R. H. Deremus, J Phys Chem 80, 1773 (1976)

D-3. C. Wagner, .1 Chem Phys 18, 1229 (1950)

83

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Apendix A

K. H, Doremus, Glass Science (Wiley, 1973), p. 128

- ? . ? ea' ,nd P. S. Grove, J Appl Phys 36, 3770 (1965)

.,j ,I t. ( ;. P. Roberts, Trans Faraday Soc .5_7, 1208 (1961)

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ipendix B

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Apoe ndix C

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* S. Grove, Physics and Technology of Semiconduct-or Devices (Wiley, 1967

. !onder-un and D. Hvelplund, Phys Rev A4, 562 (1971)

. Abra!, owitz and I. A. Stegun, Handbook of Mathematical Functions, U6",. Government Printing Office, - ....

Plichsel and P. Saxon, Phys Rev All, 1286 (lq75)

*. a,1in, orivate communication (1979)

Append ix 0

N. W. Ashcroft and N. 0. Mermin, Solid State Physics (lio!* Rinehart, 1976,

)-?. R. H. Doremus, J Phys Chem 80, 1773 (1976)

-3. C. Wagner, J Chem Phys 18, 1229 (1950)

82 HI SA- FM- 1330-82