518 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT December

measures directly the property of a sphere of dielectricin free space. Under this condition, long-range dipole-dipole interaction is eliminated [9], and the conditionsare not strictly comparable to those in a slab of materialbetween electrodes. In most materials, the resultingchange in properties will be small, but a systematicstudy may reveal interesting information on the internalfields in dielectrics.

Considerable work remains to be done on this methodof measurement. The present equipment is currentlybeing modified for use with linear fields so that a morecomplete analysis of the dielectric properties may beobtained at low frequency. Also, a variable-temperaturespecimen holder to work throughout the range fromroom temperature down to liquid nitrogen temperatureis being constructed.To summarize: An apparatus has been developed for

making dielectric loss measurements from the torquegenerated on a spherical sample by a rotating electricfield. The equipment has a frequency range from 0.001c/s to 80 kc/s and is capable of measuring both inter-

mediate- and low-loss materials. "Calibration" measure-ments using PMMA and polystyrene spheres show rea-sonable agreement with bridge measurements on thesame samples, and a reasonable trend for the data atlower frequencies.

REFERENCES[11 Hertz, H., Concerning the distribution of electricity on the sur-

faces of moving conductors, Wied Ann., vol 13, 1881, p 266.[21 Lertes, P., Investigation of the rotation of dielectric liquids in an

electrostatic rotating field, Z. Phys., vol 4, 1921, p 315; and vol 6,1921, p 56.

[31 Kawai, H., and M. Marutake, The dispersion of the dielectricconstant in Rochelle salt at low frequency, J. Phys. Soc. Japan,vol 3, 1948, p 8.

[4] Ogawa, T., Measurement of the electrical conductivity and di-electric constant without contacting electrodes, J. Appl. Phys.,vol 32, 1961, p 585.

[51 Havens, G. G., The magnetic susceptibility of nitrogen oxide,Phys. Rev., vol 41, 1932, p 337.

[61 Havens, G. G., The magnetic susceptibility of some commongases, Phys. Rev., vol 43, 1933, p 992.

[7] Bitter, F., The magnetic susceptibility of gases, (1) Pressure de-pendence, Phys. Rev., vol 35, 1930, p 1572.

[8] Scheiber, D. J., An ultra low frequency bridge for dielectricmeasurements, J. Res. NBS, C (Engineering and Instrumenta-tion), vol 65c, 1961, p 23.

[9] Scaife, B. P. K., Dispersion and fluctuations in dielectrics, Progr.Dielectrics, vol 5, 1963, p 145.

Measurements of Large Dielectric Constantsand Loss Tangents at 55 Gc/s

G. A. BURDICK, T. J. LYON, AND J. E. PIPPIN, SENIOR MEMBER, IEEE

Abstract-Measurements of dielectric constant and loss tangenthave been made on several paraelectric and ferroelectric materialsin the region of 35 Gc/s. The measurement technique is appropriatefor materials with large dielectric constant and large loss tangent;typical values measured are in excess of 1500 for dielectric constantand 0.1 for loss tangent. Preliminary considerations indicate anaccuracy of approximately 5 per cent. Previously reported techniquesare not suitable for making such measurements at 35 Gc/s, and thisaspect is discussed briefly.

The technique consists of measuring insertion loss and phaseshift of a signal upon passing through a slab of the test material fill-ing the cross section of the waveguide. These data are measured as afunction of slab thickness. The insertion loss (in dB) will undulatewith increasing thickness for sufficiently thin samples, but it quicklybecomes proportional to thickness for material having the afore-mentioned properties. In the region of proportionality the equations

Manuscript received October 30, 1964. The work reported in thispaper was sponsored by the U. S. Army Electronics Research andDevelopment Laboratories, Fort Monmouth, N. J., under ContractNo. DA36-039-AMC-03240E.

G. A. Burdick is now with the University of South Florida,Tampa, Fla. He was formerly with Sperry Microwave ElectronicsCompany, Clearwater, Fla.

T. J. Lyon and J. E. Pippin are now with Scientific Atlanta,Atlanta, Georgia. They were formerly with Sperry Microwave Elec-tronics Company, Clearwater, Fla.

relating insertion loss and phase shift to the dielectric constant andloss tangent become rather simple, allowing data to be reducedeasily.

The paper gives a derivation of the equations required for datareduction and also reports measured dielectric constants and losstangents of various barium-strontium titanates at 35 Gc/s. Experi-mental problems are discussed including the very real problem ofmounting the sample within the waveguide so as to eliminate airgaps and erratic data.

INTRODUCTION

f 1HE INVESTIGATION of ferroelectric materialsin their region of nonlinearity necessitates themeasurement of large dielectric constants and loss

tangents. In the case of single crystals of BaTiO3, forexample, these values may exceed 5000 and 0.5, re-spectively. The measurement of such quantities hasproved quite difficult for frequencies in excess of 20Gc/s. In fact, the authors are unaware of any measure-ments on BaTiO3 (single crystals, ceramic, or Ba-Srsolid solutions) between 24 Gc/s and 55 Gc/s. The onlymeasurements on ferroelectrics reported at the highend, i.e., in the millimeter region, are those between

Burdlick, et al.: Dielectric Measurements at 35 Gcls55 Gc/s and 150 Gc/s reported by Johnson [1 ] who tookadvantage of the small wavelengths in this frequencyrange by using an optical-type interferometer. Thistechnique, however, did not permit a determination ofthe loss tangent. There have been two reports on mea-surements at the lower end (24 Gc/s): a paper by Powlesand Jackson [2] and another by Benedict and Durand[3]. Their results, as they relate to work reported here,are briefly discussed.

Determination of dielectric constant and loss tangentfor ferroelectric materials has proved difficult for fre-quencies above 20 Gc/s because of the high VSWRs,high insertion losses, and precise fabrication tolerancesencountered. This paper discusses one way to overcomethese difficulties and reports results of measurements at35 Gc/s on (Bar - Sri-,)TiO3 ceramic samples for valuesof x of 1.0, 0.8, and 0.6.

SAMPLE SIZE CONSIDERATIONS AT HIGH FREQUENCIES

In measurements involving lumped circuit elementsand in many involving perturbation techniques it is re-quired that one or more dimensions of the test materialbe small compared with a wavelength in the material.Since the wavelength Xm within the material is approxi-mately given by

where Xo is the free-space wavelength and Er' the relativedielectric constant, we see that this would require atleast one dimension of the order of 0.0008 inch (0.1 X,m)for a frequency of 35 Gc/s and an er/ of 1600. Dimensionsof this order are extremely difficult to realize withceramics and single crystals. If one were to achieve suchsmall dimensions by some means, there would still re-main the problem of handling without breakage and theproblem of reproducibly placing the sample within awaveguide or other suitable structure. Consequently,the likelihood of accurately measuring the dielectricconstant and loss tangent of ferroelectric materials inthe region apove 35 Gc/s by any procedure requiringdimensions that are small compared with a wavelengthis quite low.Another method frequently employed is that of trans-

mitting an electromagnetic wave through a dielectric(whose dielectric constant and loss tangent are to bedetermined) and utilizing the transmission resonancesas a function of frequency, geometry of sample, ortemperature. The amplitude transmission coefficient fora wave incident on a specimen (dielectric slab) whoseparallel faces are normal to the direction of propagationis given by the well-known equation [4]

tt'e-'YlT-= , (1)

1 -r2e-2y

where t and t' are the interface transmission coefficientsinto and out of the specimen, respectively, r is the inter-face reflection coefficient, y is the product of the imagi-

nary numberj and the complex piropagation constant k,and I is the thickness of the specimen in the direction ofpropagation. Provided losses are not too large, the trans-mission coefficient will have a maximum whenever theelectrical thickness of the specimen is an integral numberof half-wavelengths. The location and separation ofthese peaks as a function of frequency, thickness, and/ortemperature will give the dielectric constant. However,if transmissioin peaks are to be located accurately, it isclear that the maximum signal 1 ransmitted through aspecimen as a function of an a )propriate parameter,e.g., speciinen thickness, must be large compared withthe minimum signal transmitted Since most detectorsare square-law devices, measuremlents are proportionalto T 2 and a reasonable requirement is forTmaxj 2/ min 2 to be greater td-an 10. Using this re-

quirement and (1), it can be shown that to first order theforegoing is equivalent to requirir g

Ire- l >0.7 (2)

or, since I r I-1,e'y1 < 1.4 (3)

It can be shown that (3) is equivalent to requiring

V/E,' tan a1. - < ).34 (4)

and if I is miieasured in unlits of sample wavelength, thatis, I=nXo/\VEr', (4) becomes

n tan a < 0.1: (5)

To observe at least two peaks, n -nust be 2 or greater;thus tan a mllust be less than 0.06. C(onsequently, for losstangents larger than 0.06, mea;urements by trans-mission resonances rapidly becom,- inaccurate.The loss tangent above 20 Gc's of most ferroelectric

materials is too large to utilize transmission resonancetechniques. It is therefore sugge3,ted that the trans-mission equation for high loss conditions be examined.In this region it is assumed that (1) can be approximatedby

T = tt'e-e1. (6)

That is to say, the term r2e-2,y is negligible comparedwith unity.

THE METHODThe primary principle invoked in this work can be

described as adjusting the physical setup so that multi-ple interface reflections can be disregarded. This, ofcourse, is not unique with the authiors, even as appliedto our problem. See, for example, Powles and Jackson[2]. However, certain practical features of applying thisprinciple ancl reclucing the experimental data differ frompreviously reported measurements. For example, Powlesand Jackson measured VSWRs in front of a ferroelectric

1964 P, I9

520 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT December

material to determine the dielectric constant. Since theVSWRs were too large to measure with sufficient accu-racy, this required the use of quarter-wave transformersto reduce the VSWRs to measurable values. Quarter-wave transformers were not found to be necessary forthe work reported here.As is well known, the insertion loss A due to a wave

passing through a sample is given by

A = -20 log T (7)

and the phase of the wave as it leaves the specimen isgiven by

4) =Arg (T) (8)

Using (1) and (7) gives

A =- 20 log lit' + 201(log e) Re (-y)+ 20 log 1- r2e-2-l | (9)

In the region specified by (6), the last term of (9) isnegligible, and

A -20 log Itt'| + 8.681 Re (y) (10)

In this same region the phase is given by

4)- Im (-yl)-2V/ er'_ 1.

xo

at I = 0. From Montgomery [4 ]

tt' = QC - P)1/2[(C - p)1!2 I]- -2l-p lt-p

Using this and the fact that »E1>>l it can be shownthat

Er' 16(1 - p)(t0)Ao/lO (16)

where p= (Xo/X,)2, X0 is the free-space wavelength, X, isthe waveguide cutoff wavelength, and propagation isassumed to be in the TE mode. Equation (16) serves asan independent check of the data reduction. Also from(10) and (11) it is seen that if A is regarded as a func-tion of 4,

1 aAtan 6-

4.34 04(17)

and this equation allows the determination of tan 6without the prior determination of Er'. The equationsgiving er' and [ tan 6 are now grouped together for theconvenience of the reader.

/ Err tan 6 _

(11)\/' r

-

It is seen from (10) and (11) that, for the specifiedregion, A and 4 are linear functions of the sample thick-ness. Using (11) it is easily shown that tan 3-

1 X0 A

4.34 2r 01

X0 04

(14)

(12)2wr 01

1 dA(17)

4.34 04

V/ C-rI .:2_' dlo)2w Ol) (12)

Thus, if all parameters are held constant except forsample thickness, one can obtain el' by measuring theslope of the 4 vs. l curve and using (12). From (10),

aA8.68 Re (y).

dl(13)

But it can be shown that

Er - 16(1 - p)1OAO/10 (16)

Equation (16) serves as an independent check of thedata reduction for (12).The following conditions must be satisfied to ensure

an accuracy of at least 10 per cent for (14), (12), (17),and (16):

n tan 6 > 0.3 (18)

for (16) and (17), and

R() VE' tan 3Re (ay) * r

x0

Therefore,

1 X0 /A/Er' tan 6 2 (14)

Consequently, Er' and tan 6 can be determined frommeasured values of A and 4 and the rather simple ex-pressions of (12) and (14).

It is of interest to note that if one regards I as the in-dependent variable, (10) is the asymptote to the morenearly correct expression given by (9); this asymptoticline has the value

Ao = -20 log | tt'| (15)

n tan 3 > 0.1 (19)

for (12). Here, again, n is the sample thickness expressedin wavelengths within the specimen.

A. Experimental ArrangementThe experimental arrangement used to measure the

needed parameters OAIdl and a4/Ol is the microwavebridge depicted in Fig. 1. The specimen was placed inthe bridge at the position labeled "test holder." Thephase 4 and insertion loss A were then measured as func-tions of sample length 1, and these data were then usedto determine oA /1 and 0/4)1 as described in Section C.Experimental Results. The attenuation (as deternminedby the rotary vane attenuator) required to balance thebridge and the location of one of the null points within

Burdick, et al.: Dielectric Measurements at 35 Gc/s

the slotted line was measured before and after thesample thickness was changed. The difference in thesetwo sets of readings gave AA directly and AO\ by asimple calculation. The attenuation could be measuredto within +2 per cent and the phase to within + 10milliradian. For further discussion see Section B, Speci-men Mount.

In order to obtain reproducible and reliable data,much care must be exercised in mounting the samplewithin the waveguide. It is necessary to fill the cross-sectional dimensions of the waveguide with a slab of thedielectric to be measured. Its faces must be parallel andtheir normal direction aligned with the direction ofpropagation (Fig. 2). This requires that the thicknessof the sample vary not more than about 0.1 Xm, i.e.,approximately 0.001 inch for a frequency of 35 Gc/s anda relative dielectric constant of 1600, and that the sam-ple be placed within the guide to roughly the sametolerance. In addition, the sample must make goodelectrical contact at all points along its edge. As anillustration of the latter problem, a "press-fit" sampleof ferroelectric material gave an insertion loss of 40 dB,whereas a "press-fit" sample of brass of equal size gavean insertion loss of 35 dB. To appreciate the closetolerance problem fully it must be kept in mind thatmeasurements are to be made as a function of length,which requires frequent removal and rather severehandling of the piece, after which it must be reintro-duced into the waveguide. Many mounting techniqueswere tried before a successful one was established. Inshort, machining and mouinting of the specimen arecrucial.

B. Specimen Mount

The mounting problems were eliminated by using the"diaphragm" mount illustrated in Fig. 3. A square tool-steel plate of sufficient thickness (as determined by therestrictions given by the preceding equations) is made,and a rectangular hole is machined to the inside dimen-sions of the waveguide. Clamping and alignment holesare then drilled in the plate to match those previouslyput in oversized flanges located at the adjoining ends oftwo sections of waveguide (Fig. 3). A specimen whosethickness and rectangular cross section are the same asthose of the hole in the plate is epoxied into place asshown. The interior of the rectangular hole is enlargedcarefully by hand until the specimen will just slip intoposition. A snug fit results, with no noticeable relativemovement of specimen or plate. A silver conductiveepoxy is then used to fill all voids between specimen andplate. The resulting bond has proved sufficient to with-stand subsequent grinding and casual handling withoutapparent effect. Furthermore, the plate is ground to auniform thickness which varies no more than +0.0001inch. Consequently, once the oversized flanges have beenpermanently positioned with their faces normal to thedirection of propagation, it follows that the specimen isautomatically aligned each time it is put into position.The plate can be ground simultaneously with thesample, which ensures (because of the grinding toler-ances) that the faces of the sample remain parallel foreach thickness. To change the thickness of the speci-men, the entire plate-specimen assembled is carefullyground to the desired thickness. Once the specimen hasbeen mounted and placed into position, the changes ininsertion loss and phase vs. sample thickness are deter-mined by a rotary vane attenuator and slotted line,

TOOL STEEL"DIAPHRAGM

Fig. 1. Microwave bridge. Block diagram showing essential ele-ments of microwave bridge used to measure insertion loss andphase as functions of specimen thickness.

MONOGRAM SAFETY

Fig. 2. Specimen orientation. Effective positioning of specimenrequired for transmission measurements.

Fig. 3. Specimen mount. Details of specimen mounting used toachieve nonerratic and reproducible measurements of insertionloss and phase.

3211964

322 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT December

respectively (Fig. 1). The initial value of insertion loss isobtained by RF substitution.

C. Experimental Results

A "typical" set of data is illustrated in Fig. 4. Theparameters dA lal and al/dl are the slopes of the A vs. Iand vs I lines, respectively. The parameter OA/laneeded for (17) is given by

aA adA Odz,V-aA( i1 41) (20)

Equation (20) has the form of an equality between ordi-nary derivatives since the same parameters are held con-

stant for each partial derivative. The straight linesdrawn through the experimental points of A vs. I and

vs. I were determined as follows. A best-fit straightline was first drawn through each set of experimental

40-

m35-]A dSLO~~~~~~~~~~~PE-

)

30U-° 10- ) H -f vsj * PHASE

25-

20 OAn=0.3 CO)ESAMPLE TH ICK

-

C~~~~~~~~~~~~~~~~~~~~~~~~C

o f INSERTION

LOSS

o vs. A PHASE

~~~~~~~~~~~~~~~~~~SHIFT0

Lii

Lb

ZI 2 3 4 WAVELENGTHS

0.050 0.100 0.150 CENTIMETERS

SAMPLE THICKNESS

Fig. 4. Experimental data. Graph showing experimentally measured

values of insertion loss and phase as functions of specimen thick-

ness. Straight unbroken lines represent least-square fits; broken

lines on either side lie above and below central line by rms-

deviation of experimental points.

points by eye. These lines were then used to obtain an

estimate of tan 6. This value was subsequently used in(18) and (19) to establish which values of n satisfy theseconditions. Thus, those values of A lying to the right ofthe vertical line labeled "n tan 6 = 0.3" and those valuesof lying to the right of the vertical line labeled"n tan 6=0.1" were used to determine a linear least-mean-square fit for each set of values. These lines are

shown in Figs. 4 and 5. The broken parallel lines aboveand below each best-fit line represent the probable error

as determined by calculating the root-mean-squaredeviation.The values of Er and tan 6 obtained for various speci-

mens by the method just described are tabulated inTable I, together with the per cent probable error foreach value. By probable error is meant that error whichis obtained by allowing the straight-line slopes of A vs. Iand vs. to take on their extreme values when re-

stricted to remain within plus or minus the root-mean-square deviation of the root-mean-square fit. The prob-able error arrived at by this procedure is considered tobe a conservative estimate of the error. The per centdifference between <r, as determined using (12) and Er' as

determined using (16) is also given.

It is seen (Table I) that the reproducibility from one

specimen to the like specimen agrees to within the prob-able error except for (Bao.6-Sro.4) specimens. The prob-able errors for the Er' determined using (12) average lessthan 5 per cent for all specimens measured. Althoughsome of the probable errors for the Er' as determinedusing (16) are as large as 19 per cent, these Er' still serve

as a valuable check of the data reduction. The twovalues for Er' as determined using (11) and (12) agree

within probable error in all cases.

As could be expected, the largest error is encounteredin the determination of tan 6. But even here, the prob-able error averages to approximately 5 per cent for thefirst four entries.Johnson [1] reported that the possible error for his

results at 55 Gc/s was + 10 per cent for Er' and he was

unable to determine loss tangents. Powles and Jackson[2] reported that their possible error was probably+ 10 per cent for e,' and somewhat worse for losstangents. They made specific mention of power "leak-age" around their specimen.

TABLE IEXPERIMENTAL RESULTS AND PROBABLE ERROR

for er' and tan a

Ceramic Specimen (12)* (16)t Difference Between tan 6Cea1 Pe1ert e.r (12 and (16)

BaTiO3: No. 1 497 ±3.4% 570 ±18% 14.7% 0.184 ± 4.9%No. 2 469 ± 1.9% 453 ± 7% 3.4% 0.204 ± 3.0%

(Bao.8-Sro.2)TiO3: No. 1 524 ±4.8% 437 ± 17 % 16.6% 0.230 ± 7.9%No. 2 473 ± 8.7 % 458 ± 8% 3.2 % 0.231 ± 5.8%

(Bao.6-SrO.4)TiO3: No. 1 1920 ± 1.5% 1987 ±19% 3.5% 0.171 ± 16%No. 2 1770±1.9% 1578±19% 10 .9% 0.159±15%

* Equation (12) column gives er' as determined from the slope of the phase vs. thickness curves.t Equation (16) column gives Er' as determined from the zero intercepts of the line asymptotic to the attenuation vs. thickness curves.

1964 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT

CONCLUSIONSA specimen mounting technique appropriate for

measuring the dielectric constant and loss tangent offerroelectric ceramic materials has been developed. Themounting technique allows the sample to be removedfrom the waveguide, ground to a new thickness, and re-

positioned with sufficient accuracy and without dangerof damaging the specimen. This mount has permittedmeasurements of dielectric constant and loss tangent forferroelectric materials in a frequency region (35 Gc/s)where no measurements had previously been reported.The measurements for six separate specimens are re-

ported to illustrate the accuracy, reproducibility, andlack of erratic behavior made possible by the mountingtechnique. It is shown that, for the measurementsreported, multiple interface reflections could be ignoredwithout introducing intolerable error; such measure-

ments are said to be made under conditions of high loss.The equations relating dielectric constant and losstangent to measurements of insertion loss and phaseshift vs. specimen thickness are given for these condi-tions, and an independent relation for dielectric constantis derived which serves as a valuable check of the datareduction.The primary features of the experimental technique

reported are the following:

1) The difficult specimen mounti ng problem is solved.2) The technique utilizes high insertion loss to ad-

vantage.3) The technique provides an inidependent check of

accuracy.

4) The whole procedure is reasoniably convenient.

In conclusion, the new mnount wolild appear to permitmeasurements of dielectric constani: and loss tangent to

an accuracy of 5 per cent in a frequcncy region where no

previous meatsurements were repor-:ed. This has addedsignificance when it is remembered that previously re-

ported measurements made on comn -arable materials at

24 Gc/s and 50 Gc/s had possible errors of at least±10 per cent.

REFERENCES[11 Johnson, D. A., Microwave properties cf ceramic nonlinear di-

electrics, ML Rept 825, Microwave Laboratory, Stanford UTni-versity, Stanford, Calif., Jul 1961.

[2] Powles, J. G., and W. Jackson, The measuirement of the dielectricproperties of high-permittivity materials at centimeter wave-lengths, Proc. IEE, vol 96, 1949, pp 383 fi.

[3] Benedict, T. S., and J. L. Durand, Dielectric properties ofsingle domain crystals of BaTiO3 at micro vave frequencies, Phys.Rev., vol 109, 1958, p 1091.

[43 Montgomery, C. G., Technique of Microwave Measurements, NewYork: McGraw-Hill, 1947, pp 563, 564 if.

Resistivity Measurement of Semiconducting EpitaxialLayers by the Reflection of a Hyperfrequency

Electromagnetic Wave

M. R. E. BICHARA, ASSOCIATE MEMBER, IEEE, ANI) J. P. R. POITEVIIN

Abstract-The aim of this work is to measure nondestructivelythe resistivity of a semiconductor in the form of an epitaxial layer.The method involves the measurements of the attenuation sufferedby an electromagnetic wave reflected by a semiconducting surface.A mathematical discussion leads in the first instance to the establish-ment of a theoretical curve of attenuation vs. resistivity for homo-geneous samples and later, to the family of curves of attenuation vs.

resistivity for various thicknesses of epitaxial layer grown on highlydoped substrate. The apparatus consists of a 70-Gc/s microwavebridge. The measurement is made by comparing the amplitude of thewave reflected by the semiconductor with that reflected by a short

Manuscript received August 21, 1964; revised November 1, 1964.This paper is a part of a dissertation presented in November, 1964,by M. R. E. Bichara before the Faculty of Sciences of the Universityof Paris, France, in partial fulfillment of the requirements for thedegree of Docteur-Ingenieur.

The authors are with the Centre National d'Etudes des Tele-communications, Issy-les-Moulineaux (Seine), France.

circuit. The reflection of the wave takes place at the end of thewaveguide thus avoiding the necessity of cutting the sample for itsinsertion into the waveguide. The experimental results are obtained1) by using a large number of samples of knowni resistivity and withreadings of attenuation accurate down to the hundredth of a decibel,and 2) by the repeated reading on each sample; the small scatter on

these readings indicates a high degree of reading precision. Thetheoretical curves are then compared with the experimental results.A discussion follows on possible sources of errors and the precautionstaken to avoid them.

I INTRODUCTION

N IMPORT'ANT ASPECT in the construction ofsemiconductor devices is the control and mea-

surement of the electrical pr3perties of thematerial.

525