NBSIR 75-768

Reevaluation of the Densities of

the Four NBS Silicon Crystal

Standards

H. A. Bowman

R. M. Schoonover

C. L Carroll

Institute for Basic Standards

National Bureau of Standards

Washington, D. C. 20234

August 1975

Final

Prepared for Mechanics Division

Institute for Basic Standards

Washington, D. C. 20234

NBSIR 75-768

REEVALUATION OF THE DENSITIES OF

THE FOUR NBS SILICON CRYSTAL

STANDARDS

H. A. Bowman

R. M. Schoonover

C. L Carroll

Institute for Basic Standards

National Bureau of Standards

Washington, D. C. 20234

August 1975

Final

Prepared for Mechanics Division

Institute for Basic Standards

Washington, D. C. 20234

U.S. DEPARTMENT OF COMMERCE, Rogers C.B. Morton, Secretary

James A. Baker, III, Under Secretary

Dr. Betsy Ancker*Johnson. Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Acting Director

Reevaluation of the Densities of the

Four NBS Silicon Crystal Standards

by

H.A. Bowman, R.M. Schoonover, and C.L. Carroll

ABSTRACT

There were a few features of our recently completed

density standard experiment which were based upon ideas

which, we believe, should be changed. This report

lists these changes and their justification. The

result is to increase the assumed values of the

densities of the crystals by about 1.88 ppm. The new assumed values are

X2 = 2.329 1289 g/cm3

X3 = 2.329 1253 g/cm3

X4 = 2.329 1228 g/cm3

X5 = 2.329 1226 g/cm3

Additionally, we now believe that the densities of the

crystals are stable, and not appreciably changing due

to oxidation -- a point left unresolved in our published report.

Key Words: Density standard; phase shift; silicon
-Si
Reevaluation of the Densities of the Four NBS Silicon Crystal Standards

by

H.A. Bowman, R.M. Schoonover, and C.L. Carroll

1. Introduction

From 1969 to 1974 the NBS Mass and Volume Section developed the

apparatus and procedures necessary to the accomplishment of the

following rather difficult tasks:

a. Measurement of the geometry of six steel balls in

terms of the universally accepted wavelength displacement scale. This instrument was described by

Saunders, NBS [1].*

b. Calculation of ball volumes from these geometric

measurements based upon the theory of Johnson, NBS [2].

c. Derivation of the volumes of four silicon crystals

from the previously determined ball volumes. This

required the development of a hydrostatic volume

comparator which would provide the unknown volume of

an object as a fraction of the known volume of a standard. This work, in which the balls were

standards and the crystals were unknowns is described

in [3].

d. Calculation of the crystal densities from a mass measurement and the previously derived crystal volumes. At this point in time (late 1973) NBS abandoned

the use of pure water as a density standard and

commenced referring all density measurements to the

silicon crystals. While the balls could have served

equally well as density standards in future work, for

practical reasons silicon crystals were chosen for

this task. The apparatus and procedures for this and

future routine density work, and reasons for discarding water as a standard, are discussed in [4].

This article results from a very critical examination of all of

the above four tasks in which apparatus, procedures, data

reduction techniques all came under very close scrutiny. As is

always the case, there are several features which we would

improve if the project were just beginning.

Numbers in brackets refer to similarly numbered references

at the end of this paper.
a. With more forethought in the design of the thermal

system controlling the ball interferometer, we would

^:\/)f:,bnhS-: have obtained very much better temperature measurements.

b. We wish we had employed five rather than four 200 gram

silicon crystals (summation mass = 1 kilogram) which

would have reduced the uncertainties in the crystal masses. This was our original intent, but, as explained in the caption to figure 6 of our final

report [3], one of them was accidentally destroyed.

c. We wish we had employed balls of 2.465 inches in

diameter (mass = 1 kilogram) but we were dazzled by

the low cost of the off-the-shelf 2h inch size.

Our re-examination has disclosed four numerical errors -- either

blunders or misprints -- of no overall significance. Other

features of the experiment which have received additional

attention include the algorithm used in the reduction of the

photographically obtained interferograms during the etalon length

studies, the cleaning procedure applied to the balls prior to the

interferometric diameter determinations, and the growth of oxide

films on the surfaces of the silicon crystals.

Additionally we discuss some features of the experiment which

should have been included in our final report such as the initial

four-color interferometry on the etalon length and the basis of

our phase shift assumptions upon which our data reduction

formulas were based.

2. Phase Shift Correction 9,15

No other topic created as much discussion during the experiment

as our assumption regarding the algebraic sign of the phase shift

correction. In our report we stated that the phase of light re- flected from a metal surface is retarded with respect to that

which is reflected from an equidistant quartz surface. Our

formulas for the reduction of interferometric data on ball

diameters were based upon this assumption. Our assumption was formed after a careful reading of the very concise statement of

Englehardt [5] who said that ". . . . gage blocks measured by

light waves seem to be too short .... when wrung on an insulating plate . . . . " At a meeting of our senior division

staff members in the division conference room, this statement was suspected of being in disagreement with the (then) newly

published report of Bennett [6]. Although this is outside of

our expertise, we can find no disagreement. She states that the

- 2

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optical path is s horter t han the geometric path which is

equivalent to having the reflection occur at a fictional surface

in front of the real surface. Her measured phase change from a metallic surface (aluminum film) is 157°. In other words, light

appears to be reflected from a surface 180°/2 in front of a quartz surface but only 157V2 in front of a metallic surface.

Candler [7] discussing this particular point says ". . . . When

light is reflected at a glass surface, the phase changes by -n which means that the light apoears to be reflected from the

geometric surface. When light is reflected in air at a metallic

surface, an additional change of phase occurs; in effect the

light then appears to oenetrate the metal, and the reflecting

surface is displaced from the geometric surface." Candler is

obviously discussing destructive interference when he states that

light is reflected from the glass surface (zero order indicates

zero distance). Bennett is interested in absolute phase shift

under which circumstances the position of the apparent reflecting

surface has great significance. On the other hand, since

Englehardt and Candler refer to comparative experiments, it makes

no difference where the apparent reflecting planes are located

(in front of or behind) the real surface.

The significant point is that all three authors agree that the

reflection from a ouartz surface appears to come from a plane

CLOSER TO the source than the reflection from an equidistant

metal surface. This is the sense of our stated assumption and

the resulting formulas. It has been suggested that a proper

solution of the Fresnel equations would eliminate any doubt on this point. If such a solution is presented to us, we will

quickly make an appropriate adjustment to our data.

Metrologists sometimes define the phase shift correction as the

difference between optical and mechanical measurements, in which

case they assume a mul ti -component phenomena. One of these com- ponents, described by Strang [8] results from hills and valleys

on the reflecting surface, the effect of which is a fringe broadening and a shift of the reflecting surface away from the source. Although we did have measurements on our ball surfaces, appendix

1, we did not apply such a correction because we assumed that the

hydrostatic liquid used in the volumetric transfer tests would

fill these hills and valleys, in which case the hydrostatic sur- face was equal to the reflection surface and (hence) no correction is called for.

3. Average Etalon Length from 4-Color Interferometry

The first interferometri c measurements of the length of the

etalon employed the four bright mercury lines. Wavelengths in

air were calculated by Edlen's formulas [9] from tabulated values

of vacuum wavelength and observed values of air temperature,

barometric pressure and relative humidity. Some selected data

are given below.

- 3

-
Line

Blue

Green

Yellow - 1 Yellow - 2

Wavelength

in Air

,435 837 223 m

,546 079 632

.576 965 376

.579 070 915

Test

Temp

19.91°C

19.92

19.90

19.99

Observed

Fraction

.683

.057

.792

.362

The computer was set up to assume a value of etalon length and

coefficient of expansion at 20 °C and to calculate the fringe

fraction which would have been observed had the assumed etalon

length been correct. The calculated fraction was subtracted from

the fraction actually observed. If the difference between the

observed and calculated fraction was less than 0.05 for aVl_ four

colors, the computer printed out the assumed etalon length and

all four differences.

We had a preliminary measurement of the etalon length based upon

gage blocks and a mechanical comparator of 67471.4 ym. The

computer was called on to scan possible etalon lengths at every

0.005 ym increment between 67000 and 68000 ym and to calculate

fractions appropriate to the assumed lengths. The criterion for

recognizing a correct solution was that the difference between

observed and calculated fractions would not only pass through

zero for all colors but all four algebraic signs would swing from

(-) to (+). Over this entire 1000 ym range, there was only one solution meeting the above criterion. The values are as follows:

Assumed Etalon

Length at 20%

67471.565 ym

67471.570

Calculated Minus Observed Fractions

Blue Green Yellow-1 Yenow-2

(-)7. 96X10-5

(+)2. 92X10-2

(-)9.44X10"3

(+)8. 87X10-3

(-)l. 64X10-2

( + )9. 71X10-'^

(-)4. 59X10-3

(+)1. 27X10-2

From the above data and several other sets of less internal

consistency, we concluded that the etalon length lay between

67471.565 and 67471.570 ym. As explained in Saunders' report,

this four color work was performed only to provide us with a reliable estimate of the integral order of interference for later

etalon length measurements using a single laser line. The later

laser work was necessary because the four color work provided us with the length averaged over the entire aperture of the etalon.

In use, the working aperture was only a few square millimeters

and we had no justification for assuming these two lengths would

be equal. Additionally, the temperature measurements were unreliable during the four color work because the configuration

of the optical system employed during this work required that the

etalon be removed from its thermostat housing during

measurements

.

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4. Fringe Pattern Analysis

k'hen r^easuring the etalon length, either by four color or single

color i nterferometry , the etalon functions as a Fabry-Perot

interferometer. When the calibrated etalon is used to measure

ball diameters, it acts as a Newton's Rings generator. Although

the pattern o-^ interference is superficially the same in each case (concentric rings about a bull's-eye) there is a significant

difference. In the Fabry-Perot situation, the order of interference increases with rings of decreasing diameters while in the case of Newton's Rings, the order decreases with decreasing

diameters l.7j.

Our interference patterns were photographed on 35 mm film, and

measurements were made directly upon the negatives. Under these

circumstances, black (or opacue) rings were areas of constructive

interference while transparent rings were of destructive

interference. Measurements were made using a traveling

microscope, with the film positioned so that the cross hairs in

the evepiece passed through the center of the bull's-eye.

Position data i.ndicated on the dials of the microscope were

recorded whenever the cross hairs lay on a boundary between a black and a transparent ring.

This setup provided us with the inside and outside diameters, d^' and dQ, of the first few rings surrounding the bull's-eye. From

these measurements, we were able to calculate a number

proportional to the area enclosed by a circle at some average

position within the ring

df + d2

The rings were numbered N=l, N=2, etc. and the data points (A^^,

N^), (A^.N^), (Aj.Ng) were fitted to

N = X + YA + ZA2

which provided us with a value of N when the area. A, was zero. Ke assum^ed that the fractional portion of X was the desired

fringe fraction. In this work we used the first five rings and

the reduced data is given in table 3 of our final report.

The geometry of our system was such that we should have obtained

the same fractional order of interference regardless of the

direction of the light through the etalon — that is, left-toright or right-to-left. In most of the etalon measurements

presented in table 3 of the final report [311, four fractions are

- 5

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shown, two in each direction. The final calculation of the

etalon length is based upon the average value of these four

fractions. The range over which these four fractions varied

(within a single test) averaged 0.024.

A slightly different technique was employed during reduction of

the ball interferograms

.

The fringe reduction formula, developed below, was worked out for

us by D.P. Johnson, NBS. In this procedure, in which all fringes

are assujned to have equal area, we confine our attention to the

three opaque rings surrounding a transparent bull's-eye as shown

in figure 1 or the three transparent rings surrounding an opaque

bull's-eye. Twelve observations, 0^ to 0^2 ai^e made on the

indicating dials of the traveling microscope when the reticle is

positioned as indicated in the figure. From these twelve

observations we can calculate numerical values of Y which are proportional to the areas of the six circles which form the

(O7 -

(Og - \

- (Oio-

(0,,-

\

- (O12- 0,)2

A is defined as a number proportional to the area of a complete

fringe, that is, a transparent ring plus an adjacent opaque ring.

We have two estimates of the value of A, that is

- - 2A = Yg - Y2

V 2A = Y5 - Y,

4A = Yg + Y5 - Y2 - Y^ (1)

Let F be the number of fringes between the optical center of the

intermediate second ring under observation, that is, the circle

of complete constructive or destructive interference, and the

center of the bull's-eye. Then FA is proportional to the area of

the circle defining the optical center of the intermediate ring.

This circle divides this intermediate ring into two nearly equal

areas, WA. FA and WA are shown in the sketch.

- 6

-
We may write and add

follows

together six observation equations as

- WA - A + FA = Y + WA - A + FA = Y^

- WA + FA = Y3 + WA + FA - Y^

- WA + A + FA = Y5

+ WA + A + FA = Y^

b

6FA =[Yi + Y2 + Y3 + Yi, + Y5 + Ye] (2)

From equations (1) and (2)

+ Y^ + Y3 -H Y, + Y3 +

(3)

The fractional component of F is the desired fringe fraction or

its complement depending upon whether constructive or destructive

interference is of interest.

It was suggested that we would have been better advised to employ

this same procedure in reducing etalon data. We were delighted

to find that this suggestion resulted in a reduction in range of

data by almost one-half. Use of the newly calculated fractions

resulted in a measured value of etalon length shorter than the

published value by about 0.0048 ym. This was probably due to

systematic reading errors made during estimating diameters of the

very thin outer rings which are not involved in Johnson's

technique.

The recalculated etalon data is presented in table 1 which may

be compared with table 3 in the published report.

5. Ball Cleaning

We had three sources of information on the approximate diameters

of our balls a necessary prerequisite to monochromatic

interferometry . These sources were:

a. Measurements made by the manufacturer by comparing the

balls to standard balls of "known" diameter.

b. Measurements by the NBS Dimensional Metrology Laboratory by comparison with stacks of gage blocks between

flat-faced probes.

- 7-
c. Measurements by our Gage Block Laboratory against

different gage blocks, but in a mechanical comparator

employing spherical probes. In this case, since

lateral displacement of the ball from the measuring

axis would result in a decrease in the indicated

diameter, this measurement must be considered a "minimum" value that is, the ball may be larger than

indicated but relatively less probably, smaller.

These three values, see figure 2, were in agreement to the extent

that we had no worries about our ability to assume a proper value

for the integral order of interference in later tests by the

etalon interferometer.

Very early in the program, we realized that the ball diameters

calculated from interferometric data varied systematically with

the cleaning procedure applied to the balls prior to insertion in

the interferometer. We made extensive tests on this phenomenon

employing Balls A and B. Two methods of cleaning were examined:

A. CHEMICAL CLEANING. This procedure involved the following steps washing with a detergent followed by

washing in acetone followed by rinsing in benzene

followed by rinsing in methyl alcohol followed by

wiping with a laboratory cleaning paper (Kimwipes). An

alternative cleaning procedure involved all of the

above steps except that a commercial gage block cleaner

(Doall degreaser) was used instead of the acetone,

benzene and methyl alcohol.

B. VAPOR DECREASING. This process involved chemical

cleaning by either of the above two procedures except

that wiping was eliminated and instead the ball was immersed in a stainless steel vapor degreaser in which

we boiled a commercial solvent (Dow Chemical Co. No.

WR-5) which was especially developed to have only a few

ppm of nonvolatile components. After about an hour's

exposure to the hot vapor, the ball was removed from

the apparatus. Due to its high temperature when first

removed (about 130°C) any residual liquid evaporated so that wiping the ball was unnecessary.

After cleaning (by either method) the worker always wore clean

polyethylene gloves whenever the ball was handled. When

inserting the ball in the interferometer, vacuum tweezers

machined out of teflon were used. The diameters calculated from

interferometric data were always slightly larger when vapor degreasing preceded the tests than when chemical cleaning was used.

This was true regardless of which method of chemical cleaning was employed.
These interferometrically measured diameters are shown in table

2. It is clear that there is a systematic difference depending

upon how the ball was cleaned prior to test. Inasmuch as the

difference is so clearly systematic, we felt that we should not

average all measurements together but should select one type of

cleaning or the other. Inasmuch as the range of the diametric

measurements is smaller when vapor degreasing is used, all future

work on the balls followed vapor degreasing.

Since the publication of our report, we have had serious second

thoughts regarding the wisdom of that decision. To investigate

this phenomenon more completely, we obtained a group of 52100

steel gage blocks (the same alloy from which the balls were

made). Two of the blocks were cleaned chemical "ly and two by

vapor degreasing.

These four blocks were turned over to Dr. John Yates and

associates, NBS Surface Chemistry Section, who examined them by

Auger Spectroscopy [12] to explore any surface film which might

be associated with the cleaning procedure. He found no differences between the films on the two pairs of blocks except

for weak zinc lines and some extraneous secondary electron

emission from the chemically cleaned blocks. The zinc lines were

believed to come from contamination due to the tissue paper used

to wipe the balls following chemical cleaning. His conclusion

was that no surface film was present which would account for the

large measured diametric difference unless the film was volatized

in the Auger spectrometer vacuum.

Our next thought was that the cleaning procedure altered the

optical properties of the 52100 surfaces in a manner systematic

with the procedure. To check this, we turned the 52100 blocks over to Dr. Allan Melmed and Mr. James Carroll, NBS Corrosion and

Electrodeposi tion Section, for a measurement of the optical phase

shift on reflection from the surfaces. Although these tests

indicated (in green light) that there was a 1° difference in

phase shift systematic with the cleaning procedure, the magnitude

of the difference would not account for the measured diametric

differences. (See section 8a).

Inasmuch as neither of the above two tests provided any indication why, on the average, vapor degreased balls appeared about

0.037 ym larger than the same balls after chemical cleaning, we consulted a metrologist whose judgment we trust, Mr. Arthur

Strang, NBS. He told us that when there are unexplained

statistically significant differences between two groups of

exterior measurements on the same object, the rul e-of-thumb is to

accept the smaller value. This is based upon the assumption that

- 9

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the larger value includes some foreign surface layer or film. We

shall accept this philosophy, pending future work, and subtract

0.0347 ym from the reported value of each of the six balls. This

amounts to a volumetric decrease of about 0.00022 cm^ or 1.6 ppm.

(See table 2.)

6. Oxide Growth

We have been experimenting with silicon crystals since the early

1950' s at which time we were using the Cartesian Diver [10]] to

measure the density differences between small (2 or 3 gram)

specimens. We were aware of the possibility of a growth of oxide

altering the densities of the samples so we subjected them to a treatment which was believed to accelerate the oxide growth prior

to our density tests. This treatment, suggested by R.D.

Deslattes, NBS Quantum Metrology Section, consisted of boiling

the crystals in water for several hours. ^ Although we did not know the thickness of the oxide growth

obtained during the treatment, we felt that it amounted to

several years' normal growth which put us far out on the

exponential curve of Archgr [11] which estimates an increase in

thickness of about 6.8 A per decade. The crystals used in this

experiment were given this treatment but, in addition, they were

steamed in our vapor degreaser for about a day.

We were fortunate in that one of the technical referees to whom

the NBS Editorial Board submitted our manuscript, Mr. Clayton

Teague, NBS Optics and Micrometrology Section, had some familiarity with the growth of oxide on silicon surfaces. His

comments to us, appendix 3, indicated that under the worst

circumstances and with no pretreatment of the surfaces, the

crystal could change in density by about 1/10 ppm during the

first year. In the absence of definitive data on the form or character of the oxide, it was impossible to state with assurance

whether the density change would be positive or negative.

Without information on the adequacy of our pretreatment, we included Teague 's remarks without comment in our manuscript.

We have recently looked into this matter in some detail. We

described the pretreatment process to George Liberman, NBS

Semiconductor Characterization Section, who estimated that our process "probably" added an oxide film between 50 and 100 A

thick. By Archer's equation, it would appear that 20 years would

be required to grow such a film, with an additional 6.8 A forming

in the next decade (200 years). We performed the following

tests:

- 10 -
1. We made six determinations on the density of our crystal, X5, two based upon each of our other three

crystals. These six measurements gave us

2.329 1198 g/cm3

87 "

92 "

86 "

80 "

76 "

AVERAGE 2.329 1186 g/cm^

2. We etched X5 in HF which presumably removed the

existing oxide growth. This resulted in reducing the mass of X5 from 199.932 644 grams to 199.426 601

grams.

3. We again made six determinations on X5 using X2, X3

and X4 as standards which gave us density values of

2.329 1175 grams/cm3

87

71

91 "

86

82

AVERAGE 2.329 1182 grams/cm^

These twelve measurements on the density of X5 are plotted in

figure 3, and it is obvious that if there was a change in X5's

density, it was at a level far below our ability to observe it

with any degree of reliability.

In light of the above comments, we believe that the pretreatment

applied to our four silicon crystals is quite adequate. Dr.

Liberman has suggested that future crystals be treated in

superheated steam which permits an accurate prediction of the

thickness of the oxide layer to be grown. We are presently

preparing a pair of these crystals for BIPM, and this treatment

will be given to them.

- 11 -
7. Recalculation of Crystal Densities

A. Numerical Errors

We made four numerical mistakes in the fringe

fractions associated with the interferometric

, measurements of the diameter of Ball A:

Date Test Sense

Value

Reported

Correct

Value

2-17-72 6 Right 0.668 0.678

2-17-72 9 Left 0.395 0.335

3-6-72 3 Right 0.194 0.320

3-6-72 8 Left 0.036 0.090

The correction of these errors changes the average

diameter of Ball A, in the caption to table 4a in the

final report, from 6.350 Oil 16 cm to 6.350 Oil 03 cm and the average volume from 134.067 062 cm^ to

134.067 052 cm^. This changes our assumption of the sum of the volumes of balls A and B (used in the

least squares solution shown in table 6 of the final

report) from 268.133 950 cm'' to 268.133 940 cm^.

This represents a change of (-) 0.000 010 cm^ or (-)

0.037 ppm in the assumed volume of the standards in

Determination A-B. We must make proportional

reduction in the least squares estimate of tHe

volumes of the four crystals obtained in this

determination. Since the final overall estimate of

the crystal volumes was the average of three determinations and no errors were found in determinations

C-D and E-F, the required reduction of our final

overall estimate of the volumes of the four crystals

need be reduced by only 1/3 of the - 0.037 ppm men- tioned above or (-) 0.012 ppm.

B. Recalculation of Etalon Length.

As pointed out in section 4 on Fringe Pattern

Analysis, the preferred method of fringe pattern data

reduction results in reducing the data spread by

about 1/2 but it also results in a reduction of (-)

0.0048 ym in our average etalon length. This results

in a reduction of all measured values of all ball

diameters by an equal amount. For an average ball

diameter of 63500 ym, this is (-) 0.076 ppm in

diameter or (-) 0.227 ppm in the volumes of the balls

AND ALSO of all four crystals.

- 12 -
C. Change in data associated vn"th ball cleaning.

In table 2 it is seen that the measured diameter of

balls A and B were smaller by an average of 0.0347 um when cleaned chemically than when by vapor

degreasing. The values given in our final report

were based upon vapor degreased surfaces. For the reason given in section 5 we now believe that we should have chemically cleaned the ball surfaces.

Accordingly, we shall apply a correction of (-)

0.C347 um to all measured diameters. This amounts to

a diametric reduction of the balls of 0.546 ppm, or a volumetric reduction of the balls AND THE CRYSTALS of

1.639 ppm.

D. The total correction to crystal densities.

The total correction to crystal volumes is the sum of

numerical correct^'on -0.012 ppm

etalon length change -0.227 opm

cleaning correction -1.639 ppm

total -1.878 ppm

We assume that a reduction of 1.878 ppm in the

volumes of the four crystals results in an equal

increase in their densities. The recalculated values

of the crystal densities are given below..

Crystal

X2

X3

X4

X5

Previously Reported

Value

2.329 1245 g/cm3

2.329 1209

2.329 1184

2.329 1182 "

New Accepted

Val ue

2.329 1289 g/cm^

2.329 1253 "

2.329 1228 "

2.329 1226 "

8. Future Work

We are now in the realm of speculation. There are at least two

laboratory arts which, when improved, will permit us to improve

the values of crystal densities by mere recalculation (i.e.

without additional measurement effort on our part):

- 13 -
The phase shift occurring in the interferometer

illumination when it is reflected from the surfaces

of the 52100 steel balls. We assumed this to be

about 202° (180°+22°) in our published report. To

the best of our knowledge, this has not been measured

directly in light of 6328 A. R.D. Deslattes feels

that this is a major source of error. We have

requested the appropriate group at NBS to make such a measurement under conditions of both vapor degreased

and chemically cleaned 52100 steel surfaces. This

will be done in the foreseable future.

An improved value of air density based upon an improved algorithm involving temperature, barometric

pressure and relative humidity, all of which were

measured in the course of crystal weighings. This

work is being actively pursued in the Mass and Volume

Section.

- 14 -
REFERENCES

[1] Saunders, J.B. Sr., Ball and Cylinder Interferometer, J.

Res. Nat. Bur. Stand. (U.S.), 76C (Eng. and Instr.), Nos. 1 and 2, (Jan. -June 1972),

[2] Johnson, D.P., Geometrical Considerations in the Measurement

of the Volume of an Approximate Sphere, J. Res. Nat. Bur.

Stand. (U.S.), 78A, No. 1, (Jan. -Feb. 1974).

[3] Bowman, H.A., Schoonover, R.M., and Carroll, C.L., A Density

Scale Based on Solid Objects, J. Res. Nat. Bur. Stand.

(U.S.), 78A, No. 1, (Jan. -Feb. 1974).

[411 Bowman, H.A., Schoonover, R.M., and Carroll, C.L., The

Utilization of Solid Objects as Reference Standards in

Density Measurements, Metrologia 10, 117-121 (1974)

(Springer-Verlag , 1974).

CSn Englehard, E., Precise Interferometric Measurement of Gage

Blocks, Nat. Bur. Stand. (U.S.), Circ. 581, p. 13, (1957).

[6] Bennett, J.M., Precise Method for Measuring the Absolute

Phase Change on Reflection, Jour. Opt. Soc. Amer. 54, No. 5,

p. 612 (May 1961).

[7D Candler, C, Modern Interferometers, Hilger and Watts, Ltd.,

(1951).

C8II Strang, A.G., Surface Characteristics of Gage Blocks, Nat.

Bur. Stand. (U.S.), Circ. 581, p. 87, (1957).

C9II Edlen, B., The Refractive Index of Air, Metrologia, Vol. 2,

No. 2 (1966).

[ion Bowman, H.A. and Schoonover, R.M., Cartesian Diver as a Density Comparator, J. Res. Nat. Bur. Stand. (U.S.), 69C,

No. 3, (July-Sept. 1965).

[11] Archer, R.J., Optical Measurements of Film Growth on Silicon

and Germanium Surfaces in Room Air, Jour, of the Electrochemical Society, (Oct. 1957).

[12] Palmberg, P.W., Auger Electron Spectroscopy, Proc. Int'l.

Conf. on Electron Spectroscooy , Edited by D. A. Shirley,

North Holand, (1972).

- 15 -
FIGURE / . THIS SIKFTCH OF /)N iNTER FERCriETRIC RIN6 SYSTLH INDlCf^TEb JHE

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- 16 -
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- 17 -
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- 18 -
U.S. DEPAHTIVIEWT OF COIViryiERCE

rJational Bureau of Sltandards

Washington, D.C. 20234

232.12

Date. Jane 14, 1972

To: Horace Eo^jmaa

Ma^s, Lengch and Volune Section (232,09)

From: Dennis A. Svr/t

oir.ensional Technologv Section (2 32,12)

Subject: ?-fsasurenent or five spheres

The arithmetic averarje surface rouglinsss (AA) has been r.oasured, for five

spheres, using a Talysurf stylus instniTnent './ith a curved surface datum

attachment, Sone relevant parameters arc: sphere diameters of approximately 2,5 inches; a stylus diameter of 200 microinches; a stylus pressure

of 50 milligrams; a meter wavelength cutoff of ,010 inch; a meter gain of

20,000; a full scale reading of 10 microinches; a reading precision of

-r ,1 m.icroinch; and an inherent noise level prohably of less than ,5 microinches.

Six pairs of readings were taken at roughly equally spaced points on the

surface oZ the spheres. The averages of the pairs of readings appear in

Table I; the mean value and TMS deviations from the mean \l\ V3.1ue for

each -sphere are given in Table II.

t\ sample profile trace is appended. It should ^e noted th.at the cur^/aturn

of the trace corresponds to the difference between (1) the surface of the

sphere and (2) the curve generated by the datum attachment of the device;

therefore, the trace curvature may not be interpreted in terms of the

sphere surface alone.

Table I, Arith_metic average surface roughness readings.

(microinches)

SI S2 53 S5 01

1.55 1.35 1.70 1.25 2.25

1.70 1.3'^ 1.75 1.20 l."5

1.70 1.^5 1.55 1.25 2.35

1.50 1 . 30 1.70 1.50

1.^)0 1.25 1.A5 1.65 2.05

1.35 1 .25 1 . 7

-^ 1.^5

^ne rleciinal -place is significant.
Table II » Mean AA readings for each sphere

(microinchss)

SI 1.32 + .08

S2 1.57 + .13

S3 1.64 + .11

S5 1.38 + .18

Ql 2.13 + .19

* Only one decimal place is significant.

I

i


U.S. DEPARTMENT OF COMMERCE

National Bureau of Stantlards

WMh+Bgton. D.C. 20234

March 2h, 1975

MEM0RAIJDUI4 FOR Horace Bowman

Mass and Volume Section

Optical Physics Division

From: Johji T. Yates, Jr. J- /< Acting Chief, Surface Processes

and Catalysis Section, 11-3

Subject: Auger Analysis of Gauge Blocks

In consideration of your request, a report on the Auger analysis

of gauge "blocks by "att Ono and Ralph Gorden, Jr. of the Surface

Processes and Catalysis Section is attached.

Attachment
AUGER ANALYSIS OF GAUGE BLOCKS

Matt Ono

Ralph Gorden, Jr.

S\irface Processes and Catalysis Section

Institute for Materials Research

National Bureau of Standards

Washington, D.C. 2023^

Two gauge blocks received from Dr. H, Bovman, IBS, vere analyzed in an attempt to determine whether some surface deposit may he responsible for

dimensional differences observed by optical measurements. One block was chemically cleaned and the other vapor cleaned. The samples were inscribed

J661A (0.1001 in.) and J199A (O.IOOU in.), respectively.

An Auger spectrometer was used to analyze the surface of the samples.

A sputter ion gun was then used for layer by layer removal of the surface

using 1 kV argon ions produced in U x 10 ^ Torr pressure of argon gas. An

Auger analysis was performed intermittently during sputtering. The time

of bombardment (therefore the thickness of layer removed in each interval)

did not coincide in every analysis for both gauge blocks, but the ciunulative

sputtering loss should be nearly the same in both analyses.

SURFACE ANALYSIS BEFORE ION BOMBARDMENT

The following chart tabulates results from the initial surface examination:

ELEMENT

ELECTRON

ENERGY

SAMPLE

J199A(v.cl.

)

SAMPLE

J661A(c.c1. )

eV

C

0

Zn

S

B/Cl

Na

Fe

273

510

99h

152

179/181

990

598

651

703

Auger peak height

(arbitrary units)

U.02

6.35

.03

.19

.51

? 1.70

Auger peak height

(arbitrary units)

1.80

5.25

.07

.16

.28

V

l.i+2

- 1 -
At the very surface, carbon is much more abundant on the vapor

cleaned (v.cl.)j Sample J199A. For zinc, the signal approaches noise

level especially in sample J199A and may not be distinguished from

sodium which appears in the same vicinity of the spectrum. From other

experiments, zinc is more positively identified on sample J66IA, although

it may contain a trace of sodiiam. All other elements are of similar

concentration on both blocks.

The secondary electron spectrum below 60 eV is normal in sample J199A,

but significantly different in J66IA. This may signify some abnormal

surface phenomenon (see Spectra 10 and 11).

DEPTH PROFILING

The results are illustrated in Figures 1, 2, and 3 for carbon,

oxygen, and iron. In Figure 3, the Auger yields of carbon and oxygen

are normalized to that of iron. There is little difference in the depth

profiles of the two gauge blocks. Oxygen increases to a maximum at about

five minutes of ion bombardment, while carbon goes through a miniraiim

at that time then increases to an apparently constant value after fifteen

minutes

.

Iron increases steadily showing an inflection, when oxygen is near

its maximum, then continues to a fairly constant value after about fifteen

minutes sputtering.

' Zinc and/or sodium is removed by sputtering for about 30 seconds in

sample J199A and for less by sputtering than 2 minutes on sajnple J66IA.

A trace of sulfur is present on both blocks. Trace amounts of Mo,

CI, and/or B may be present but could not be unambiguously identified,

since the argon lines appear in this same energy range.

INTERPRETATION OF RESULTS

The rate of (Ar"*") ion sputtering for pure al\imin\im layers has been

o estimated experimentally to be 8 A/minute at the ion current densities

employed in this work. This sputter rate may be used as a crude approximation in interpretation of our sputtering profile data.

The sputter profiles obtained in this study (Figs. 1 and 2) indicate

that in both cases there is a thin carbon impurity layer (removed in about

- 2 -
five minutes) overlaying a layer of iron and oxygen. These may be in the

form of iron oxide since their Auger intensities increase simultaneously

for about five minutes where oxygen begins to rapidly decrease and iron

levels off. As this layer is removed, the clean surface of the block is

exposed. This results in an increase in iron and carbon intensities until

they level off (at about fifteen minutes bombardment) no doubt reflecting

the composition of the bulk iron of the blocks.

The small differences in the curves of Fig. 3 may be due to interruption

or differences in sputtering time between the two samples.

There is practically no difference in the surface composition of the

two blocks. However, one cannot discount the possibility of some surface

impurity pumping away in the ultrahigh vacuum system (at pressures of the

order of lO""^*^ Torr arid at temperature of 300 K).

The differences observed between the two samples by optical measurements

may be related to the different secondary electron behavior observed here,

or possibly to non-uniform distribution of surface contaminants. Further

.examination by replica electron microscope, IMA, or XPS may be desirable.

- 3 -




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UNITED STATES DEPARTMENT OF COMMERCE

National Bureau of Standards

Washington. D.C. 20234

May 30, 1973

MEMORANDUM FOR Horace A. Bowman

Mass and Volume Section

From: E. Clayton league

Optics and Micrometrology -^ec

Subject: Some consideration of the effects of oxide growth on

the density of silicon specimens.

The bases for these considerations is the following.

p(silicon) = Pg^ ~ 2.33 g/cm^

p(silicon oxide) = Pgio ~ ^° 2.66 g/cm^

The specific value depends on the oxide growth conditions

and the resultant crystallographic form of the oxide, see Silicon Semiconductor Data Edited by Wolf.

At room temperature, the change in oxide thickness after an initial oxidation

of several hours is approximately 5 nm for a 2 year oxidation. This value is an estimate obtained from A. T. Fromhold, Jr. , at Auburn University in private

communication

.

Assuming no silicon is lost during the oxidation process, the silicon specimen's change in mass with oxidation, dm, may be expressed as:

^"^^ ^ PsiO

where dv^ is the change in the oxide's volume and a is a constant determined

by the oxide's molecular form. If the molecular form is Si02 then a is

approximately 0.5. If the net specimen density and volume is p and v repectively then the fractional change in density is:

a p „ . , dv dv

J SiO o s dp = - , p bi

where dv^ is the specimen's change in volume.

A PPewDi^ 3 - PA 6^ /

m'-'6 19'^'
With the data from Wolf Pc.p./Pc^ approximately 1. Therefore:

J dv dv

dp _ o s p V V

In the two extreme cases:

dv = dv ; The specimen surface is displaced by the

oxide growth's thickness.

and

dv < < dv

s o

one obtains the result: inrA'i

;rr>i:Ui>/i I £2. I _ I i ^ I 2. P 1-a

as an upper bound on the magnitude of the density change. For your cylindrical

density specimens, approximately 1 inch by 2 inches in diameter, this value is:

^1= 2|l-a| (i.i) AC,

where h = cylinder height, r=^ cylinder radius, and At = oxide thickness change.

The use of Fromhold's 5 nm value for At and an a of 0.5 (for Si02) gives: — 4 X 10

' P

'

over a tv/o year period. • *

A lower bound for the density change, other than zero, appears very difficult to

estimate without going into greater detail on the molecular forms, accurate values

of the oxide density, etc.

USCOMM-NBS-Dt
NBS-114A IREV. 7-73)

U .S. DEPT. OF COMM.

RIRI lOf^RAPHir DATA

SHEET

1. lU IM IC A I'U'tN OK HI- I'OH V NO.

NBSIR 75-768

No.

3. Ki-c ipicnt '.s At i c-s.sion No.

4. riTI.K .\Nn SUBTITLl-:

Keevaiuation ot tne uensines ot tne

Four NBS Silicon Crystal Standards

5. Publ!> .itK.n n.irc August 1975

6. Pcrformia^ ()r>^an i /.ai ion f i)dt

^' '"f?'jA\^ Bowman, R.M. Schoonover, and C.L. Carroll8« l^^crformin^ Or^iin. K.cp<-)rt Nu. NBSIR 75-768

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Proiccr Task ^ork Unit No.

11. Contract Grant No.

12. Sponsoring Organization Name and Complete Addres.s (Street, City, State. ZIP

j

SAME

13. Type of Report &: Period Covered

Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRAC!T (A 200-word or less factual summary of most si^iiicant information. If document irtcludes a si/inificant bibliography or literature survey, mention it here.)

There were a few features of our recently completed

density standard experiment which were based upon ideas

which, we believe, should be changed. This report

lists these changes and their justification. The

result is to increase the assumed values of the

densities of the crystals by about 1.7 ppm. The new assumed values are

X2 = 2.329 1289 g/cm^

X3 = 2.329 1253 g/cm^

X4 = 2.329 1228 g/cm^

X5 = 2.329 1226 g/cm^

Additionally, we now believe that the densities of the

crystals are stable, and not appreciably changing due

to oxidation -- a point left unresolved in our published report.

17. KEY ^'ORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons

)

Density standard; phase shift; silicon

18. AVAILABILITY ^Unlimited 19. SECURITY CLASS

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