16
Materials ChvzisrrJ, and PkJ,sics, 20 (I 988) 38 1 -396 381 'fin 0;:ide thin films, specially antkony doped tiri oxide iA'l'0) and i'luorine doped tin oxide (FTO) have attracted considerable attention over the past r"e~r years became of their possible ph0toVoitaic applications. The se i"il!r!s a rz transparent as ueil as conducting and in addition, have the abiiity to i'orhl very hi& basriers on silc':z seniconductors as silicon. In the oresent stitdya nodified spray nyroiysis CiC?thOd is ?isci?,ssed 0-y y!:icl~ the 3nO2 2ihs can bs prepared conveniently anL reproduciuiy. tin tile uasis oi the pyroij-sis reaction 03.'LnGl. ii 511*0, s.:1oot1:, transparent and closely ad!iemr,-c r'ii::o 3re 0btaineG m glacs. I;‘rO!Ei tila -4 LL-- *a? uif?raction 5Lude:; the fiims arc found to be polycTystallinc in nature. i?‘he electricai and o$ical propi‘rties oi these f'ims are stuciec: to optkise tr.e uegosition pl;r&haters -'Or acl,ieving tile:naiAmim _'igure of writ i"or solar cel.1ap3lica- tion. .T. i~:aXir:iLl?Il f. igwe 01 ri.L _ vf?rit obtained for A',"0 Pilrn is G.qAO -3 -1 R . The corrcsnonding Kim properties are ;;i Sk! = &O (sheet resistance), ‘i’( 600) -I 337; for the lilns Loped with 3 ~101$ of SbCl 3 and 2000 3 thick. 'Themaximm figme ol^merit obtained 1'01‘ I?TG I'ilni is ?.L@xlo-2L$ (H I Sh = 2O",'cs, T( 600) = Y3 corresponding to a I"ilm. ti:i.ckr.ess ol I$%0 a ;iith 1.2 sit;"b i;h 1 F. +?resent address Orissa (India) : Regionai Research iaooratory, Ljhubaneswar, 0 Elswier S~quoi~/Print~d in The Netherlands

Characterisation of conducting SnO2layers deposited by modified spray pyrolysis technique

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Page 1: Characterisation of conducting SnO2layers deposited by modified spray pyrolysis technique

Materials ChvzisrrJ, and PkJ,sics, 20 (I 988) 38 1 -396 381

'fin 0;:ide thin films, specially antkony doped tiri oxide iA'l'0)

and i'luorine doped tin oxide (FTO) have attracted considerable

attention over the past r"e~r years became of their possible

ph0toVoitaic applications. The se i"il!r!s a rz transparent as ueil

as conducting and in addition, have the abiiity to i'orhl very

hi& basriers on silc':z seniconductors as silicon. In the oresent

stitdy a nodified spray nyroiysis CiC?thOd is ?isci?,ssed 0-y y!:icl~

the 3nO 2 2ihs can bs prepared conveniently anL reproduciuiy.

tin tile uasis oi the pyroij-sis reaction 03.' LnGl. ii 511*0, s.:1oot1:,

transparent and closely ad!iemr,-c r'ii::o 3re 0btaineG m glacs.

I;‘rO!Ei tila -4 LL-- *a? uif?raction 5Lude:; the fiims arc found to be

polycTystallinc in nature. i?‘he electricai and o$ical propi‘rties

oi these f'ims are stuciec: to optkise tr.e uegosition pl;r&haters

-'Or acl,ieving tile :naiAmim _'igure of writ i"or solar cel.1 ap3lica-

tion. .T.

i~:aXir:iLl?Il f. igwe 01 ri.L _ vf?rit obtained for A',"0 Pilrn is G.qAO -3 -1 R .

The corrcsnonding Kim properties are ;;i Sk!

= &O (sheet resistance),

‘i’( 600) -I 337; for the lilns Loped with 3 ~101 $ of SbCl 3

and 2000 3

thick. 'The maximm figme ol^ merit obtained 1'01‘ I?TG I'ilni is

?.L@xlo-2L$ (H I Sh

= 2O",'cs, T( 600) = Y3 corresponding to a

I"ilm. ti:i.ckr.ess ol I$%0 a ;iith 1.2 sit ;"b i;h 1 F.

+?resent address Orissa (India)

: Regionai Research iaooratory, Ljhubaneswar,

0 Elswier S~quoi~/Print~d in The Netherlands

Page 2: Characterisation of conducting SnO2layers deposited by modified spray pyrolysis technique

'Tin oxide is a wide band gsp scrziconductor (9; = 2.3 eii) and

has round widespread use because of its hi@ piectricai conAuctivity

in combination with transparency in the visible anti near inirared

v:avelen@h rafit;es. Its optical and electrical properties can be

tailored to suit the application o? interest by aglropriate doping.

ksearch on transparent COndilCtifig tin oxide filrx kive 'oeen

intensified reccctly o::in:; to their prociicing applications in the

fsbricstion ol" hnterojunction solar cells. Particularly the Sn02/Si

uhotovoltaic system [I ,2,3_5 ::ith weil-known attractiva ie,-itures

iksve dram consitief~ble attention. 'ihe hetarojunction sol::r ceil

offers the possiuility of fabrication ol‘ low cost solar cells rrith

perfor.;!ance characteristics saltable ior l:irge scale terrestrial

applications. One possibility for cost redilction lies in the

clethod of junction fabrication.

There are many techniques, inciudin;; sputterin;; CL+], Tlash

evaporation [L+J, reactive evaporation [5] chemical vapour deposi-

tion [67_ and spray pyrolysis 171 Zor depositing these nlaterials.

ii'lle inZluence of spray conditions on the quality of tile conduct-

ing ?i.l:r, has also been studied [Sl . The spray deposition method -_

is particularly attractive because of its sinlplicity. It is Yast,

inexpensive and does not require a vacuim. The spray p;rrolysis

1)rocess is suitable <or LEIS~ production. Eowever, problems with

uniiorkty and reproducibility are occasiona;ly encountered. On

the other hand, the usual chemical vapour deposition in a standard

tube furnace can 1236 to :aore uniform and reproducible r^ilms. In

the present study, combined snra.7 , and CVD methoGs based on SnCl 4

511,O hydrolysis reactions are used to deposit the r^ilms conveniently

and reprohcibly.

3:peri;iental set-up and r"ilm deposition

The spray pyrolysis of the Sn02 Tilms were carried out in a

specially fabricated spray/C'JD apparatus. Figure l(a) depicts the

schexxtic disgrm or" ti?s r"xrnaW asse!ilbiy. Figure l(b) shows the

spray ci used ior spraTyin&. Spraying was cond.ucted in a quartz

Page 3: Characterisation of conducting SnO2layers deposited by modified spray pyrolysis technique

383

TO VACUUM

f/-- 5.5. TUBE

+-THERMOCOUPLE /If MULLITE TUBE

INSULATING MATERIAL

SPRAY NOZZLE

100 ml CONICA FLASK

Y=

(al FL SPRAY NOZZLE (bl

1.

Pli. 1. \a) hchexatic ui.agra.;l of the spray asse:,ibly.

(b) Spray gm used.

tube kept centrally in the furnace. The smple llolder,rrhicl~ is

a stainless steel tube, was also kept centrally in the qilartz tube.

The sample holder was connected to a vacua line to hold the sa!:iple.

An iron-constantan thermocouple was attached verjr close to the

xu'ostrate to monitor temperature during deposition. The relative

positions of the sample holder, the quartz tube and spray gun

can be varied to optimise the distance or" the s.ubstrate fror;i the

spray nozzle for efficient deposition. The nozzle diaxeter ol" the

spray gun was 1 .mn. An Slice air compressor which delivers dry oil

free air at a pressure or" 1 kg/cm* was used to spray solution on to

the substrate.

To obtain a homogeneo?Ls _'ilm, th Lroplcts ol the spray :;ere

evaporated b,?I'ore reaching th? hexted substrate. By spraying

upward in the tube furnace at a slow rate, all the droplets were

evaporated beYore reaching the substrate.

Page 4: Characterisation of conducting SnO2layers deposited by modified spray pyrolysis technique

384

Prior to deposition, the glass slides (25 .mm x 25 mm) were

treated in a chromic acid bath for 24 hrs to make them grease free.

They xere then ::ashed with distiilcd water and dried. Finally

they were ultrasonically cleaned in acetone.

Different solution mixtures were investigated for the deposition

of Sn02 films. For the deposition of FTO films the spray solution

containing SnLl i;, 5H20 and kdh4F in ethyl alcohol and water was used.

'The concentrations of the SnCl li, 5H,O and XHq? were varied to have

different doping density. Composition of a typical spray solution

containing 1.5 vrt $ NH 4 F was

SnCl 4' 5y - 14.250 &!TlS

NH&F - 0.750 grill

IG0 - 1g.000 gns

c211501i - 15.800 Ems

IICl - 0.200 &!Tl

For AT0 film deposition the

and SbCl 3

in ethyl acetate.

PO deposit films of uniform

spray nozzle and the substrate

spray solution was 0.7X SnCl 4,' 5"*0

thickness the distance between the

was optimized and found to be 21 cm.

Glass substrates were kept in the hot zone of the furnace maintained

at 51;O'C for about 10 minutes before the spraying period (about

I set), followed by a 30 sec. wait to avoid excessive cooling of

the hot substrate during spraying.

Characterisation

Thickness of the films was determined by weighing the substrate

before and after deposition in a ic!ettler balance having a least

count of 0.00001 gym and taking the density of SnO2 as 6.99 gms/c.c.

The A-ray diffraction measurements were performed using a Philips

automatic power diffractometer with Cu and MO target, graphite mono-

chromator autodivergence slit, scatter slit and receiving slit

assembly. The target was operated at 40 KV, 20 mA for Cu-target

Page 5: Characterisation of conducting SnO2layers deposited by modified spray pyrolysis technique

385

‘I?!e Tarticle size ;ras &temi.ned using the debye Sciierrer

equation

ir = iXl.l width at half !naxirn-ml ( Fyl;;Ii4) P h = 0.709 A for i.:oi< cI radiation

= 1.541 a ior LkJ_K~ rakLiation

l;or zindin g out the F;?iki, the peaks ::ere scanned wi'ch a rate o_"

6.25’ 28/iG_n.

Tile eLectrica characteristics of the filr:is sue!1 as conductivity

type and sheet resistance were determined by using hot probe and

four-point probe methods respectively.

The optical properties ol' SnO, fibs Vjere studied by recording ."

the trans!:iission o_' t!!r. iil.r~is dEposited onto t;ILass substrates for

various thichess.

'i'he transmission ratio ior two I'ilrzs 0T different thickne ss

is

where AC! is the difference in the thickness of the two I"ilms.

A kary 17, ;&:ici? is a double beani spectrophotonater rrias used in

this investigation. .4 properly cleaned blank &lass sitbstrate ol

tile sa!;le size was used as reference. 'l'he optical densities of the

different filns with refermce to the blank substrate were recortied

at roozi teztperature in the wavelen@A range 280 m to 750 n:;i. -l':ile

transmissions ol" the di fferent filn thicknesses were carried oilt at

600 nm to find out the figure 0Z !ilerit using a PYE UNiL:Ai*I Uii and

visible spectrophotorneter.

Yoth the conductivity and tranmission ol the fiims si~o~ulc! be as

hi& as po3sibI.e for solar cell applications. However, they are

inversely proportional to each other. Hence the optimm values or"

these two paraEleters shouid be established asing a figure of merit.

Page 6: Characterisation of conducting SnO2layers deposited by modified spray pyrolysis technique

386

The most comonly iXf?d definition of figure 0Z merit $4Tc of a

trai-Lsparent coz&cting fil!:l given by :;aacke [jc] is

$Tc + (31 S!l

where ‘7 is the tranmission at a particular wavelength. 'The trans- . . .

mlsslon 1s a function of T;ravelength,an, ri therefore use of T (average)

lor calculation ol" gTc is inappropriate because the solar flux is

concentrated in a small wavelength range near green. The spectral

response of Sn02/Si has been reported pi] to be !naxi%in near

600 nm. Therefore, the transmission T(bO0) at a wavelength of

600 nm was used to calculate pTc in this study.

RSSULTS Alvll DISCUSSION

Smooth, transparent and closely adherent films of SnO2:F(FTO)

and Sn02:SbtATO) were obtained. Below l+50°G substrate temperature

the fiti appeared to be patchy. Figure 2 shows that the thickness

increases as a linear Cnction 05 the deposition the. it is also

seen from Fig.2 that the growth rate of the Sn02 film at the consi-

dered temperature is independent oZ film thickness. 'T!?ese results

6000- o AT0 Films

A FTO Films

so00 -

4000 -

3000 -

2000 -

lOOO-

I I I I I 4 8 12 16 20 24

NO. OF SPRAY

Fig. 2. Increase of film thickness as a linear function of the deposition time.

Page 7: Characterisation of conducting SnO2layers deposited by modified spray pyrolysis technique

387

i:.licate t,5,Jt th.7 I lil!.i ,;ro?!tl? __ 'i'OCZSS 011 the >nC; 2 surface progess-

ed 'u;Ci>'A;,- ;‘: ;;itl-j ti<,qe ‘_i _ u . T!I 3 3 ~?_Jl’o:~i.mt~2 Lgl‘C:7th rste obtained i^ro!n

li.2. 2 Por AT0 and FTC arc 250 t/spray respectively.

Both AT0 an< FTO fiI!:ls mre f oiind to be polycrystalline in

nature as eviticnt from the dL-r3.~y <iffraction pattems in Pig. 3.

b 50 I

- 40 28 30 i p10

30 2o 28

1

Fig. 3. L-ray diffraction patterns (a) CuK, diffraction pattern of FTO film, (b) MoK, d iffraction pattern of FTO fil!n, and (c) MOK (L diffraction pattern of AT0 film.

It has been observed that the pyrolytic spray nethod induces an

ano:.alous textiu-e as seen in the suppression of (110) and (101)

iines which are norma_Lly strongest. In Sn02 powder, the lines

(IlO), (101) and (211) are the strongest with relative intensities

100, 81 and 63 (131 respectively). These results are only

sli&htly different from those obtained by Karlsson et al. p2] -I_

and by Kohatgi et al. 13 13.

tising Cuba. radiation for undoped Sn02

Page 8: Characterisation of conducting SnO2layers deposited by modified spray pyrolysis technique

388

Zii!:is obtained by a s‘ pray p-,rolj;;is mthod. ~ELohatgi. et al. jj 3-j

Zound the (119) iinz to b- txice as stron- " iis the (211) ,Vrhereas

Karlsson et al.[l21 Zounc! --_ the (211) to be the strongest line

?oll~~wed by (IOI), (110) and (200). in oilr result the (211) line

is observed to be strongest follo?:ed by (200)) (110) and (101) for

FTO I"ilm. For AT0 films the (110) and (211) lines are seen eqilally

strong followed by (101) and (201) lines. This difference in resuit

may be attributec? to higher substrate tenperature Ts=jL+O'i; as com-

pared to Ts=/+OO'i I"or other irorkers.

Particle size corresponding to reflection Irom (110) plane was

calculated. using eqn.(l). As shovm in Fig. L+ particle size increas-

es with thickness. The increase in the residence time of the

3 50

04

23Oc

0 AT0 Films

A FTO Films

THICKNESS 18 1

Fig. I.+.. Variation of particle size with the film thickness both for AT0 and FTO films.

Page 9: Characterisation of conducting SnO2layers deposited by modified spray pyrolysis technique

389

3 )c ;i:!en in ch2 furnace ior t!:n tllicker fiims niight be a re3son

_^.ji' t!!? inc:*o,is2 0P griiri siz3. FTO _'ii::is have larger grain size

compared to the AT0 films. The observed grain size is comparable

with the reported vaiue available in the literature I19

Lath FTO and AT0 f'ilms l::ere found to be n-type as expected l:hen

tested by the hot probe technique.

It has been observed that the sheet resistance (ils,l) decreases I

considerably 3s thz substrate temperature increases jFig.5). This

0 AT0 Films A FTO Films

350 400 450 500 550 600

Ts t°C 1

Fig. 5. Variation of film sheet resistance with the substrate temperature.

decrease in Hsh is owing to the improvement in the crystallinity

oi' the films at higher Ts. Also at low substrate temperature some

SnO and/or Sn30k (which are both highly resistive) may be present

in the film due to incomplete reaction resulting in a relatively

!ligh R sh PI-

Page 10: Characterisation of conducting SnO2layers deposited by modified spray pyrolysis technique

Shr:Tt r?sist,jncl? of both FTC and AT0 films decroxs~ s with

increasing thickness of the iiLxs jFig.6). 'This is due to the

increase in grain size 3,.:ith thickness p 5j whicn is verified from the particle size measurements carried out by I-ray diffraction

methods.

90-

- 80- 0

2 70-

5 60- a _

z so-

2 =; 40- si

ii 30-

L w z zo-

lo-

o AT0 Films

A FTO Films

0 1000 2000 3000 4000 5000 6000 7000

THICKNESS d 1

Cig. 6. iariation of sheet resistance with t!ie thickness of the film.

Sheet resistance vs doping concentration is plotted in Fig. 7(a) -

and Fig. 7(b) for both AT0 and FTO films. As shown in Fig. 7(a)

R sh

initially -decreases, goes to a minimum and then increases

again as the antimony content increases. Lowest sheet resistance

is obtained for 3 mol$ of SbCl 3’

The increase in the carrier

concentration as a result of doping is responsible for the initial

decrease of R,h. However, since the ionic radius of antimony is

Page 11: Characterisation of conducting SnO2layers deposited by modified spray pyrolysis technique

391

70-

(b)

30 -

101 I I I I I _I

0.0 0.5 1.0 1.5 2.0 2.5 3.0

wt (%I

Yi;. 7. Sheet resistance versus dopinE concentration plot (a) for -.-

.+'I0 :ims and (b) I"or P'i'o :ii.:ls, prepared at the substrate temp. 5!!+.ooc; for 8 spray sec;i?ences.

about 1.2 times that of tin, the crystal defects which create the txp

leve.Ls in the forbidden gap also increase with doping [12]. Thus

above a criticai antimony content the trap concentration doxlinstes

the concentration or" donated electrons, and on 5urther dopinz the

nntirnon-y introduces traps rather than donors. Hence 1% Sh

increases

with antimony content above 3 nol,; ol" SbCl . 'this phenomenon ~13s

also observed by other workers [lo] and thz7 sug.C;ested that the

pronounced increase in resistivity at larger dopant concentration

is probably caused by the incrc:ise or" impurity scattering. In case

ol" FTO films the rfiininum sheet resistance is for 1.5 wt.,: M4F and

Page 12: Characterisation of conducting SnO2layers deposited by modified spray pyrolysis technique

392

tic 2 s,l increases very SlOVJl; at higher doping concentration. I

Ti:is decrease in R sh

and its subsequent s:iturstion can be attribut-

cd to ti?s loWsin& of the E;rai.n boundary potential due to incorpora-

tion of F atoms into the grain boundaries PSI. L ,-

The films are alrlost perfectly transparent in the visible region

and the fundamental absorption begins at about 0.3~)rn extending to

a shorter wavelength. For about 1000 A" thickness both FTO and AT0

film show inore than 95;; transniission at 600 nm. As the thickness

of the filn increases, the transparency of AT0 films decreases

drastically (317: for a thickness of 5100 i). For PTO filns the

variation in the transparency (70,; for 4700 dgj is less compared to

ATC ?il:ns.

In both the cases transpasency decreases as the dopins concen-

tration increases. Figares 8(a) and 8(b) show the energy depen-

tiance of CL 2

i'or AT0 and ST0 films respectively. 2

'The piots of iL

a;;ainst h$ have a linear region, and extrapolation of the Stl*aiC;ilt

line to a = 0 gives ti:e direct band gap. EC is 3.875 eti for AT0

and 4.065 eV for FTO filrls. These values of direct band gap are

cozparable with the values reported by Arai 116-J and Bhmradwaj

et al.[Ill . - -_ Figures 9(a) and 9(b) depict the figure of merit of AT0 films

for different film thickness and doping concentrations respectively.

Figure of merits for FTO film are plotted in Fig. IO(a) and Fig.

IO(b).

In case of AT0 films $JTc is almost constant for the film thick-

ness in the range 1000-2000 I: and decreases sharply as the fila

thickness increases. pTc increases rapidly up to the film thick- 0

ness of 1900 A for FTO films and falls rapidly as the film thick-

ness further increases. P, Tc increases initially because the Rsll L

decreases rapidly while T decreases slowly. At higher thickness

beyond 2000 8 Rsh decreases slowly but T decreases rapidly and thus

pTc falls rapidly.

The figure of merit increases slowly for AT0 film up to 3 mol$

of SbCl 3

and rapidly for FTO filns up to 1.5 wt$ of NH F and 4

finally both fall rapidlyy if the doping concentrations are increas-

ed further. R sh initiaily decreases ver:/ rapidly and transmission

Page 13: Characterisation of conducting SnO2layers deposited by modified spray pyrolysis technique

20

16

"E : 12 AT0 Films (D 0 x 8

"ti 4

0 6.20 4.13 3.10 2.40 2.07 1.77 1

PHOTON ENERGY (ev)

J I.55

60

N

E 60 ”

h 0 40

” 20

3 0 6.20 413 3.10 2.48 2.07 1.77 1.55

PHOTON ENERGY IeV I

1000 2000 3000 4000

THICKNESS d I

Fig. '3. variation or" r^igdre or" r3eri.t _'or AT0 iiirns (aj with r^ilm thickness at the &oping cont. concentration : film thickness

3 3ol$ of S'cC$ and (b) with doping = 2000 8.

Page 14: Characterisation of conducting SnO2layers deposited by modified spray pyrolysis technique

394

lo-!

2 - -I4 210

8

lo-5

\ (a) (b)

I I I 01 ’ I I I I

1000 2000 3000 4000 5000 1 2 3 G 5

THICKNESS (i 1 Mel L % I

6-

Fig. IO. Variation of figure of r,lerit for PTO filzs (aj with thickness at the doping concn. oi' 1.5 wt,; oi' XH doping concentrations at the fi.Ln thickness = 1

decreases slowly. Therefore $ITc increases as the doping concentra-

tion increases. However at higher doping concentration RsI1 increa-

ses and the transmission decreases causing vTc to fall rapidly.

14aximuq $JTc obtained for ATO Elm is 6.96x10-3P-". The corres-

ponding film properties are RsII=&O-x/a , T(600) = 88$ ?or 3 mo$

or” jb 1 3

and 2000 1 film thickness. The maximu! fig.llre of merit

obtained for the FTO film is 24.19~10 -3,C--l L-R Sh

= 2o+,, , T(600)

= 93% -7 corresponding to a Film thickness of 1900 2 with 1.2 wt$

NHLF. The results are comparable with those reported in the

literature vlO,12J .

The modi?ied spray pyrolysis technique was adopted to deposit

fluorine-doped and antimony-doped Sn02 conducting films. Growth

Page 15: Characterisation of conducting SnO2layers deposited by modified spray pyrolysis technique

3 A.ijl:aradwaj, IL.S.iialonia, A.Zaza, A.i(.Sllarma, a.X.Gunta and

O.P. O&hot&. Solar Gel13 5 (19S2) 305. *y-3- 4 J.L.wossen, R.C.A. Rev., 22 11971) 289.

5 J. 1 lanifacier, tii.i)eu_wcia, J .?.Filland and S. Yicario, 'Thin

Solid Films, 41 (19771 127. -

6 S. bluranaka,Y.Bands and T.Tskada , Thin solid FilE, 86 (1381) -

Il.

7 3. L!cls!zeirner and 3. Ziegler, Thin Solid Films 109 (19831 72. e..-_~I -

8 T. Karlsson, A. Roos and i;.G. Ribbing, Solar Enerf;Y I;laterials,

11 (lSS5) 469.

9 K. Ishi~uro, T. Sasaki, T, Arai and T. Amai, J.Phys.Soc. Japan,

13 0958) 296.

10 G. Haacke , Appl. Phys. Ls., 3 61976) 622.

I? A. Zlaradwaj, U.K.Gupta, A. Raza, A.K. Sharma and O.P. Ognihotri,

Solar Cells 5 t 1982) 39. _-..-Pf _

12 T. Karlsson, A. Roos and C.G.Ribbing, Physica Scripta, a (19532)

772

13 A. Kohatt;i, T.R. Viverito and L.H. Slack, Rev. Hi&-Temperature

eaterials,m (1976) 139.

IL+ i;i.Srinivas Wr2;hy and S.R.Jawalakar, Thin Solid Films, 102

t 1983) 283.

Page 16: Characterisation of conducting SnO2layers deposited by modified spray pyrolysis technique

396

15 K.L.dhopra and S.Xajor ) Proc.Irlt..r ','orkshop on Thin Solid Film II.- --~_I

Technolo,-,y r;nd Applications, Hex Delhi 19-30 110~. 1964, Tata

XcGraw-Kill Publishing Co., India, p. 224-236.

16 T. Arai, J.Phys.Soc. Japan, 2 (1960) 916. .---