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THE

E L E C T R I C A L P R O P E R T I E S

OF

G O L D A N D T A N T A L U M

T H I N F I L M S

AFTER

A R G O N I O N I M P L A N T A T I O N

R. G. R. ROBINSON, B .S c . DUNELM 1943

oc\ o

Foreword by I.H. Wilson (Supervisor)

This thesis has been assembled by myself from papers found

at his home after the tragic death of Graham Robinson3 known to

us all as Gray. His experimental work was nearly complete and he had

finished the chapters on experimental procedure and the results

for his thesis. The other main document available to us was

his transfer report and parts of this are reproduced in the

appropriate chapters. The work falls into two parts - argon

bombardment of gold filmss and drgon bombardment of tantalum

films. The transfer report refers only to the former and so

comments by myself (in italics) will be included where necessary.

Extracts from other material will be included where appropriate.

The main results of the work on gold films has already been 1

published.

(iii)

Abstract 11 Introduction 42 Theory 7

2.1 Introduction 72.2 The effect of sputtering on the conductivity 8

of thin films2.2.1 Ion bombardment 82.2.2 Electrical resistance 92.2.3 Tantalum films (unknown density) 10

2.3 Strain sensitivity 112.3.1 Longitudinal gauge factor 132.3.2 Transverse gauge factor 14

2.4 The temperature coefficient of strain gauge 14factor 8

2.5 Theoretical value of the temperature 15coefficient of resistance a

2.6 Statistical methods 173 Experimental Techniques 18

3.1 Thin films 183.1.1 Substrate Preparation 183.1.2 Gold Films 183.1.3 Tantalum Films 183.1.4 Electrode Pads 193.1.5 Ion Bombardment 19

3.2 Measurements 20

ContentsPage

( i v )

3.2.1 Resistance Measurement 203.2.2 Temperature Control and Measurement 233.2.3 Temperature Coefficient of Resistance 253.2.4 Strain-Gauge Factor ' 27

3.3 Anodising 313.4 Vacuum Annealing 34

4 Results 374.1 Gold Films 38

4.1.1 Sheet Resistance 384.1.2 Resistivity 404.1.3 Annealing 404.1.4 Temperature Coefficient of Resistance 464.1.5 Strain-Gauge Coefficient of Resistance 464.1.6 Temperature Coefficient of Strain-Gauge 52

Factor4.1.7 S.E.M. Microscope Examination 524.1.8 Microprobe Analysis 55

4.2 Tantalum Films Before Bombardment 554.2.1 Sheet Resistance 574.2.2 Temperature Coefficient of Resistance 574.2.3 Strain-Gauge Coefficient of Resistance 62

4.3 Bombarded Tantalum Films 674.3.1 Resistance 674.3.2 Temperature Coefficient of Resistance 714.3.3 Strain-Gauge Factor 754.3.4 Annealing 754.3.5 Depth profiling by anodization 80

Contents (continued)

(v)

5 Discussion of results 87

5.1 Gold films 87

5 .1 .1 Strain gauge coefficient (y) 87

5 .1 .2 Tunnelling 88

5 .1 .3 Metallic conduction 89

5 .1 .4 The temperature coefficient of . . 90resistance (a)

5 .1 .5 The temperature coefficient of strain : 91gauge factor ( 8)

5 .1 .6 The structure of the bombarded films 92

5 .1 .7 The resistance ageing effect 93

5 .1 .8 The drop in resistance for doses below • 952 x 1015 ions cm 2

5.2 Tantalum films 95

5 .2 .1 The as-deposited films 95

5 .2 .2 The effect of argon bombardment on 95re sistiv ity

5 .2 .3 Changes in T.C.R. as a result of argon 97bombardment

5 .2 .4 Changes in strain gauge factor as . 98a result of argon bombardment.

5 .2 .5 Resistance ageing 93

6 Conclusions iqo

6.1 Argon bombardment of gold films 100

6.2 Argon bombardment of tantalum films 102

7 References 104

8 Appendices 10$

Contents (continued)

ABSTRACT

Evaporated gold and tantalum films have been bombarded with argon ions. In the case of gold films this resulted in an increase of the sheet-resistance by sputter etching to a maximum of 40 kft/a .The strain-gauge coefficient of resistance (y) (i.e. the fractional change in resistance per unit strain) was measured for films with a wide range of sheet-resistance, and was found to be almost invariant with an average of 2.6. This contrasts, greatly with the published values of y of up to 100 for thin island-structure evaporated films of similar sheet-resistance.

The temperature coefficient of strain-gauge factor (8) was found to be similar in magnitude but opposite in sign to the temper­ature coefficient of resistivity (a), which was measured as +12 x 10V°C.

The measured values of y, 8 and a agree well with values calculated assuming metallic conduction modified by reduction of the electron mean- free-path. We, therefore, conclude that a connected metallic layer still exists at very high values of sheet-resistance.

In the case of tantalum films (that contain 30 atomic

per cent oxygen) conduction was found to be by a combination

of metallic and activated tunnelling. In the latter case

there is some evidence for an increase in importance of this

mechanism with oxygen concentration and for the existence of

at least two activation energies.

After bombardment with low doses of argon the resistivity

(p/ and also a shifted markedly towards values expected of very

pure tantalum films3 probably as a result of radiation enhanced

diffusion and preferential sputtering of oxygen combined with

re-arrangement of the film to form large precipitates of b.c.c.

tantalum.

There was aso a significant increase in y (from cm

average of 3 up to 5 .2) at similar doses3 possibly as a result

of changes in the microstructure increasing the importance of

strain induced changes in the metallic conduction paths in the

film..

The metallic phase appears to be metastable as p increases

with time (up to two years) at room temperature3 probably due to

reaction with oxygen near the film/substrate interface.

For higher doses p drops (but not in a way explainable by

sputter etching) a changes from a large positive value to a small

negative oney and y drops towards a value of 2 which is the pre­

dicted value for Ta. on glass.

ABSTRACT (continued)

These results indicate that a single phase3 stable3 low

sputtering rate compound is formed, probably by reaction with

the glass substrate. This compound has a mixture of activated

tunnelling and metallic conduction with the strain gauge factor

apparently determined by the metallic component of conduction.

Some preliminary attempts at electrical depth profiling

of the bombarded tantalum films by anodization are reported

and the results support the models proposed above.

ABSTRACT (continued)

1. Introduction

This work is part of a programme aimed at understanding the effects of ion bombardment on the electrical properties of thin metal films.

Measurement of strain-gauge coefficient of resistance, henceforth called strain-gauge factor, was undertaken because it provides information on conduction mechanisms that are dom­inant in the implanted thin films, and because work on active ion implantation of active metal films has indicated that this— . 2i3~technique might be used to produce useful devices;

Argon bombardment of gold films was chosen for the first study because of the inert nature of ion and target, and because the sputtering characteristics are reasonably well understood.In addition evaporated gold films have shown a very large dif­ference in strain-gauge factor (y) (two orders of magnitude) between structures of the connected type (metallic conduction) and discontinuous island structures (tunnelling conduction).

The strain gauge factor is defined by; y E (<$R/R) / (5£/il) where R is the resistance and i is the length of the conductor.

Continuous 200 & evaporated gold films on glass substrates have been bombarded with 40 keV argon ions to increase the sheet- resistance by several orders of magnitude, into the region where

. _

thin evaporated films would be discontinuous. The values of y and a(the temperature coefficient of resistance or T.C.R.) and also the temperature coefficient of the strain-gauge factor (8), were measured.

6

In the second study the same (inert) ion was used

but a chemically reactive film3 tantalum3 was used in order

to determine the effects on strain-gauge factor of structural6 , 7 , 8

changes observed by other workers at Surrey on similar films.

A large amount of data was accumulated on the properties of

the1 as deposited’films (resistivity3 T.C.R.3 activation energy

for conduction3 strain-gauge factor and stability)3 as well as

determination of the effects of argon bombardment on these

properties.

A first attempt was made at determining electrical

properties as a function of depth by anodic oxide profiling.

ATthough the latter was not completely successful it provided the

groundwork,that lead to a very successful, technique being developed

by other workers at Surrey. 8

2.I Introduction

This section is a compilation of the relationships

devised by Gray. These are used in the results section for

comparison with experimental results.

2. Theory

8

2.2 The effect of sputtering ori the conductivity of thiri filmsConsider 1 cm3 of pure gold. Its mass is 19.3 g,

and its relative mass is 19.3 mole.197

The number of atoms contained in 1 cm3, is, byAvogadro’s Number,

19.3 x 6.025 x 1023, = 59 x 1021 atoms.197

Thus the number of gold atoms per unit atomic area in a 1 cm length is, on average,

^ 5 9 x 1021' = 3.893 x 107 ;per unit atomic area

and the average numbei^in the thickness of a 240 film is240 x 10 x 3.893 x 107 =* 93.5 atoms.

The mean linear distance between atoms is 2.57 & ,

2.2.1 Ion BombardmentA monatomic layer of gold 1 cm2 in area would contain,

(3.893 x 107)2 = 15.15 x 10lk atoms.Let the number of conducting atoms affected by the

ion bombardment be S atoms/ion. ^Note: this is'-similar to thesputter rate which, for gold, is 10 atoms/ion with argon ions at 40 lcevj]

The number of ions required to remove, by sputtering, the numberof atoms equivalent to;a monatomic layer of gold is, therefore,

“215.15 x 101** ions.cm ;S

and this would involve an electric charge of-1 915.15 x 1011* x 1.60 x 10 coulomb/cm2

S” 242 pC.cm • — — — — — — — — 2.1

S

9

u The charge to remove atoms equivalent to a film of mean

thickness 240-X would be„ 2

22620 yC.cm.S

2 .2 .2 E lectrical Resistance

The re sistiv ity of gold in bulk is-6

= 2.285 x 10 ft cm, (at 30 C),

and the resistance of a slab, of thickness t , length £ and

breadth b is

R * p £_ ft bt

When the slab is of square format £ = b, and the

resistance

R = £ ft/D .t

The Conductance of such a slab, of thickness 240 & ,

is

G = 1 “ 240 x 10

R 2.285 x 10*“= 1.05 siemen/square (at 30°C).

Under argon-ion bombardment the film thickness (and

hence the film conductance) w ill be reduced.

Consider such a film after ion bombardment with

charge C coulomb. The mean film thickness remaining w ill be '22620

t (22620 - SC) cm.22620 22620

10

The conductance would be G = t (22620 - SC)

22620O,S/D 2.2

which is shown in figure 4-.3 for. three-.values of .S.

The resistance of the film would be R = 22620 pp

t (22620 - SC)ft/Q -2 .3

2 .2 .3 Tantalum films (unknown density)

3 _DAtoms/cm = x No

(Wt)Atoms/cm = 3*

Wt cmlinear spacing =

3\f D x No

' DNo (Wt)

%Atoms/cm monolayer = D No

(Wt)

Ions needed to remove a monolayer = —\ ONo'

wry

Ions needed to remove thickness t

I•&, % D NoWET wt

D Noy3

D No (Wt) x t Ions/cm"

NoT— ---^AtWt

x t

11

N = D 6.025 x 1023 ^ _ ~ 8 v , '■g x l 8~o" 95----- x 750 x 10 Ions/cm

= £ x 0,250 x 1017 Ions/cm2S

By experiment this = 3 x 1017 i Ons/cm2determined by extrapolation of the resistance versus dose curve

° ‘25 § . = 3 D = 12S

N = D x 0.25 x 1017 = 3 x 1017 Ions/cm

Film sheet resistance during bombardment

N(N - » )

RS . = £ x N - - - - 2 . 4

2,3 Strain Sensitivity y.-Under tensile e lastic deformation the change in resistance

of a thin film is given by

dR = d£ = db - dt_ + dpR £ b t p

Poisson’ s ratio for unconstrained dimensions would give

db = dt = - a , and£

Parker and Krinsky1* have shown that this leads to a Strain-

Gauge Coefficient of Resistance of

v = dR/R = i + 2a + dp/pY a , i 2-5

12

The dimensions (apart from the thickness) of thin films, however, may be assumed to be the same as those of the substrate, so that the width b is constrained by the contraction experienced by the substrate; that is

db = -a d&— s — 9b £ a circumstance which gives rise to a differential lateral tensilestrength of amount

which, in turn, causes a further lateral strain in the direction of the film thickness' and a stress reaction in the direction of jfche applied strain.

Consider the three principal strains in an isotropic medium (the film);

V = |< - ° f ( P; * p ,) =EE s

V = P2 - Of { P1 + P3) _0E~ -----5 =

h Es

e. = - qf (pi + p2) ■T E

where = strain in the direction of the length & andthe applied stress p s

£ = strain in the direction of the width b and2the differential lateral stress p ,

2

13

e3 = strain in the direction of the thickness tand the lateral stress p , (=0),

3

E = Young’s modulus for the film material,Es = Young's modulus for the substrate,

Rs = the stress applied to the substrate by thebending rig.

By combining the above three equations and applying theknown end-conditions, e • may be obtained in terms of e .• and

3 i

Poisson's ratios for film and substrate, e = a (1 - a ) .B f S' G 5

(1 - Of ) 1ii . - ofa - o ) d4or t -----------

( 1 - af) i

This leads to values for the strain-gauge coefficients of resistance.

V = « £ = 1 + a t o - ( 1 - Vd i / i s f ________ + dp/p

( 1 - af) d i / i

2 . 6

l oThis is similar to the result of Verma

2.3.1 Longitudinal Gauge Factor YhChange of resistance is measured in the direction (± i ) of

the applied strain.iThe resistance R0 = p __ >

* btso that 3R = 3p - 3t t 3JI - 8b

Ri p t i b *

Using the relationship derived above, the longitudinal ,'strain-gauge coefficient of resistance is;

Y& " 9R/R£ = + (1 + aQ) + crf (1 - os) + 8p/p

B£/£ £ 7 3£/£(1 - a jf-

2.7

2.3.2 Transverse Gauge Factor y^

In this case change of resistance is measured in the direction(±b) at right-angles to the direction (±£) of the applied strain.

The resistance R, = p k ,b £ t

so that aR = 3 £ - l t - 3 £ + 8bR. p t £ bD

again, using the same relationships, the transverse strain- gauge coefficient of resistance is formulated as,

yb - 9R7Rb = - ( 1 + a ) + af ( l - a ) + 3p/p

W * -

2 . 8

It is assumed that the films are isotropic, and that, Pb = = P .

2.4 The temperature coefficient of strain-gauge factor 8The temperature coefficient of resistance (T.C.R.) is defined

15

as1 3y

Writing the temperature coefficient of strain-gauge factor

we have

and

y,9T 9

1 38 - 3R/R 3T

3 SL/Z

3 R

3R/R

& = 3R/3& 3&3T1 U & 3T

1 3R R 3T

The first term is a temperature coefficient of the rate of change of resistance with length - which should be invariant: the second term is the coefficient of linear expansion, which may be neglected as being two orders of magnitude below the third term: the third term is the T.C.R. This result has been obtained by Witt and Coutts11,

8 = - a 2.9

2.5 Theoretical value of the temperature coefficient of resistance aWe will derive a value of q assuming metallic conduction in

the film that is limited by the reduction in electron mean freepath caused by the proximity of the film surfaces.

1 2It has been suggested that the average free path length is

given byT - 3t t £nA - -jj. + j

XB

where t is the film thickness and Xg is the bulk mean free path. The relative conductivity is then given by

o , A _

BSt , t

1 6

where is the bulk conductivity. This expression has to be13 9m

modified to account for diffuse scattering at boundaries , giving

the relation

3t4A, (1 + 2 ) (&n + 0.4228}

2.10

where p is the fraction of incident electrons specularly reflected 2

and p <:<i. Using an extension of Matthiessen1s rule, the re s is t­

iv ity of the film is the sum of components due to la ttice

scattering scattering by defects and impurities (pR) and

su rface scattering (p ) . The bulk resistiv ity p is just composedS D

of the f ir s t two components since p is assumed to be negligible.sThe T.C.R. is defined as

_ _1 dR _ _1 dp• R dT " p dT

As a f ir s t approximation one can say that pn and p do notu sdepend strongly on temperature so that for a continuous, homogeneous film

a, ' i f fdT

1 ’dp] Pf dT

and

a. _ 1 - dP«-B '• PB- dT

dpjdT~

Then

a,a

1 2B

Using Heavens’ approximate solution for eqn.2.10 for t « A ,

‘f ~ % iiri + 0,4228}-l

Now the sheet re s istiv ity Rg p _/t so that f

f+ 0.4228}

2.11This model includes a large number of assumptions, and i t may

be more re a listic to take into account scattering at grain boundaries.

2 .6 S tatistica l Methods

The measurements made in the course o f this strain-gauge

evaluation include unpredictable errors s an(} although an attempt

was made to minimise their occurrence the graphs show their

preswence only too clearly.

It is assumed that these errors are randan in occurrence

and magnitude, and that they have a Normal probability,distribution.

It follows, therefore, that Standard Deviations may be calculated

for suitable quantities such that the probability o f the quantity

lyirg within the range

It is usually satisfactory to take the range ± 1.96 S.D. as

defining the 95% confidence lim its.

mean value ± 1 S.D. is 0.68

or mean value ±1.96 S.D. is 0.95

or mean value ± 2.58 S.D. is 0.99

3.1 Thin Films

Films were vacuum evaporated onto soda-glass substrates

approximately I ram thick. High temperature annealing was not employed.

It was therefore hoped that no problems would be encountered from out-other metal ions from the substrate,

diffusion of sodium an d / For gold films 3” x 1" glass was used

whilst for tantalum both l n x I 1’ squares and 3" x 0 .2 ” strips

were used. A few tantalum films were laid onto mica and some

onto alumina substrate: these were used for sheet resistance and

TCR measurements but no significant difference was noted as'a result

of their use.

3 .1 .1 Substrate Preparation

The substrate was cleaned by gentle abrasion in hot detergent

"'solution . By rinsing in hot water and hot d istille d water, and

with a fin al rinse in de-ionised water. Drying was carried out on a

lamina-flow bench, and only those substrates that dried without

cloudiness to give clear specula reflections were used for film

deposition.

3 .1 .2 Gold Films

Gold was evaporated from a tungsten wire spiral e lectrica lly_ 6 _ G

heated in a vacuum of between 1 x 10 and 2 x 10 torr. The sub­

strate temperature was that o f the equipment ambient.

Films were laid down having a thickness within the range 200 8

to 300 &. This was measured after evaporation by Talystep Indicator.

But thickness was monitored during some evaporation runs using a

quartz crystal thickness monitor oscillating at about 250 Khz, whilst

for other runs the resistance o f a test film was monitored, and evap­

oration was stopped when this had reached a resistance o f 10 ft.

3 .1 .3 Tantalum Films

Tantalum was evaporated by electron-bean heating in an ultra-

high vacuum system pumped by an o i l diffusion pump and fitted with a

18

3.______Experimental Techniques

19

liquid nitrogen cold trap. A titanium sublimation pump was

available, enabling a pressure of 5 x 1CT9 torr to be reached at

the start of each evaporation run. During evaporation the pressure

(and temperature) rose and after about five minutes had reached an-6

indicated level of about 10 , at which point the run was usually

interrupted for cooling.

Film thickness measurements made after unloading the evap­

orator indicated consistently a rate of deposition of tantalum of

50 X per minute, and this rate was used to estimate film thickness

during the subsequent evaporation runs.

3 .1 .4 Electrode Pads

Each film had gold electrodes formed at either end to define

the film length and to enable electrical connections to be made. The

gold pads were evaporated in vacuo through masks, after a preliminary

flash evaporation of a titianium "glue" layer. The resulting elect­

rodes were robust enough to allow connecting leads to be soft-soldered

into place.

The. masks used for the gold and tantalum films are shown in

Figures 3.1 and 3.2 respectively,

3 .1 .5 Ion Bombardment

The ion bombardment was carried out in a 500 keV heavy ion

accelerator with sector-magnet mass-analysis and closed loop voltage

control using the mass defining s l i t s . Uniformity of dose was achieved

by electrostatic scanning of the beam on a raster equivalent to double

the area of the beam defining aperture. Uniformity is estimated at

better than 1%, beam convergence is estimated to be less than 0. 2° .

The ion dose was monitored by measuring the charge collected by the

target. An electrostatic fie ld was used to suppress secondary electrons.

The target chamber was pumped by liquid nitrogen trapped diffusion

pump with a cold finger (liquid nitrogen) mounted close to the target.

Typical operating pressure was 5 X 10 7 torr.

20

All electrical measurements were conducted with the specimens

at atmospheric pressure.

The effect of the unimplanted ends on the r e sistiv ity , TCR

and strain gauge factor of implanted gauges was corrected for by

using formulae derived by M. R. Moulding (transfer report 1977) and

reproduced here as appendix 3.

3 .2 .1 Resistance Measurement

An equal-arm Wheatstone Bridge circuit was used for measuring

film resistance, the DC supply being 2 V for most films so as to lim it

the power dissipation to 2 mW/cm2 and so avoid thermal errors. For

high resistance films the bridge ratio arms were unequal and the

supply could be increased to 10 V.

3.2 ’ ■ Measurements

21

Mask for electrode areas.

i

Smm.

n

■*-—----—---(> teJl-— Howe,.

Mask for strain-gauge film.f7 ntm. it

$ Tnm »

Ion bombardment mask.>& *mtjv

- g -J10 »vtft

■»— — 33'hwi-- ►*-f urn**

Specimen strqin-gauge.

FIG. 3.1 MASKS FOR GOLD FILMS.

22

10 mm

1 <

10mm

Tantalum films Gold electrodes Bombardment window

1" x 1” Composite film

2 5 mm

Bombardment area

Tantalum film

Electrode mask

3” x 0.2” Composite film

FIG. 3.2 MASKS FOR TANTALUM FILMS

23

For the measurement o f the gold films a centre-zero micro-

ammeter was used as balance detector (+-100 pA range), and a series

of spot measurements was made for each run. In the case o f the

tantalum films an x-y plotter was available and this allowed a

continuous record to be made o f the measurements.

Before use the films were annealed at rocm temperature for a

minimum time o f one week, and also at 120° C for two hours.

3 .2 .2 Tenperature Control and Measurement

In order to avoid errors due to tenperature variation during

the measurement o f strain-gauge factor the temperature must be held

constant. The use of glass as the substrate lim its the maximum safe

strain to about 250 PPM and the change o f resistance this gives is ,in

the case o f gold film s, the equivalent of a temperature change o f less

than one h alf degree celsius. Thus, for there to be no more than a

5% error in strain-gauge factor from this cause the temperature must

not vary by more than 0 .02° C during straining. This is d iffic u lt to

achieve over protracted periods but seems possible for the duration o f

one strain run.

The four-point straining rig was positioned inside a fan-blown

environmental chamber in such a way that strain could be applied, and

measured, from the outside. The schematic arrangenent o f this equip­

ment is shown in Figure 3 .3 . Temperature could be tightly controlled

by a closed-loop servo over the range 20° C to 120° C using a filamentary

air-heating element and a filamentary tungsten resistor as the sensor.

The temperature was measured with an iron-constantan thermocouple

soldered to a copper vane o f 2 sq.cm. placed in the air stream of the

chamber, and with the cold junction kept in melting ice . The thermal

24

PhMS3OW

FHo

o

a*oC/3. I

CO

c o

OI—!FH

25

EMF was read on a moving co il indicator. Temperature control was

possible, but to a reduced accuracy, over the extended range - 20° C

to + 150° C with the aid of auxiliary cooling or heating.

The environmental chamber was also used for making TCR

measurements.

3 .2 .3 Temperature Coefficient of Resistance

In the case of the gold films precise measurements o f r e s is t ­

ance were made at about twelve spot temperatures between room tempera­

ture and 120° C both for rising and for falling temperature. The

results were corrected for end effects in the case o f bombarded films

by a simple computer routine, and were displayed as a graph plot for a

visual check on high temperature sta b ility : a simple line fittin g pro­

cedure was used to obtain the TCR and the sheet resistance at 30° C.

Host o f the tantalum films were measured with the aid o f an x-y

p lotter, vertical deflection being the out-of~balance output of the

Wheatstone Bridge and horizontal deflection the thermocouple EMF. The

procedure adopted here was to heat the chamber to about 120° C, to

start the x-y p lo t, and to allow the chamber to cool slowly over a

period o f about an hour. Half way through the period water cooling

was started so as to maintain a more or less constant cooling rate down

to room temperature. The resistance scale was calibrated each time by

altering the bridge balance point and marking the change on the p lo t,

and the temperature scale was calibrated once and for a l l with the thermo

junction in steam. A b e s t -f it straight line was drawn through the p lo t,

and this was subsequently corrected for end effects to give the TCR and

sheet resistance at 30° C. Figure 3.4 shows a typical TCR run for a

tantalun film .

A few tantalum films were measured over the extended temperature

range -190° C to + 110° C.*'' 'These films were mounted within an aluminium

27

block narrow enough to pass through the neck o f an ordinary picnic

dewar flask and also through an aperture into the environmental

chamber; see Figure 3 .5 . The flask was half f i l le d with liquid

nitrogen and the block was carefully lowered into i t so as to cool

the films to -195° C. The block was then raised so that the temper­

ature would rise slowly, to reach 0° C after about four hours.

Temperature was again measured by thermocouple and moving co il

indicator, and resistance by Wheatstone Bridge., Spot measurements

were made at approximately 10° C intervals, and when the temperature

had reached about + 5° C the block was transferred to the environ­

mental chamber, and heating was applied in steps to + 110° C. The

results were corrected for end effect and were plotted (R V.T)and

(log R v .l /T ) . Typical outputs o f data for these plots are shown

in Table 3.1 and plotted in Figure 3. 6.

3 ,2 .4 Strain/-Gauge Factor

The substrates were loaded into the four-point bending rig

positioned inside the environmental chamber, see Figure 3 .7 . Strain

was calculated fran a measurement o f substrate deflection, made mid-way

between the two fixed posts o f the bender. Using a d ifferen tial trans­

former transducer. With the maximum safe strain for 1 mm thick glass

substrate applied by the rig (+-250 x 10 6) the deflection obtained was

0.1 irm and the transducer output was +- 118 m illiv o lt .

For gold films the transducer output was measured on a centre-

zero millivoltmeter having a backing-off fa c ility . A number o f spot

readings o f resistance and deflection were taken as the strain was

applied; then the results were corrected for end e ffe c ts , were displayed

in graphical form, and a straight line established through than to give

the strainvgavge factor. , A ll these calculations and the plots were

28

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29

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31

carried out using a d igital computer. Each strain run was completed

within a time span of about two minutes so as to minimise temperature

errors (see Section 3 .2 .2 ) , and the results from four runs in tension

and four in compression were averaged to obtain the final strain-gauge

factor. A typical computer plot for a gold strain-gauge is shown in

Figure 3 .8 .

For the tantalum films the x-y plotter was available, and this

was used to display Wheatstone Bridge out-of-balance vertically and

transducer output horizontally. A typical strain run for a tantalum

film is shown in Figure 3 .9 . , where the film was strained from tension

to compression and back again as a check on temperature d r ift . The

resistance scale was established by altering the bridge balance point,

the slope of the best straight line drawn through the plot being used

to calculate the strain-gauge factor after end corrections had been

applied. The correction for the unbombarded section of bombarded

gauges necessary in order to determine the true value of K was done

using formulae similar to those derived by M. R. Moulding' (transfer

report 1977) Appendix

3.3 Anodising

Some of the tantalum films were examined in layers by progressive

anodic oxidation. A strong solution of acetic acid was used as: the

electrolyte (50% glacial acetic acid in water), and a platinum fo il of

2.5 sq. cm. was the counter electrode. A d ifficu lty encountered in this

work is that of insulating the submerged electrode and defining the anodised

portion of the film . This was overcome here by the use of a generous

layer of apiezon wax applied over the electrode and its lead so as partially

to cover the tantalum film and to leave the required window exposed.

The anodic potential was increased in steps of approximately 2 V

from a source current limited to 25 yA. At each step the film was withdrawn

from the electrolyte, washed in several changes of d istille d water, dried,

and placed in the environmental chamber for the resistance and TCR

3 2 NO 026 * 60 DEG 16 1000 iXVSQCM,5 0 5 * 0 0 0

5 0 5 * 7 5 0

TENSION4 3 2 1

43 m*»\

5 0 5 - 7 0 0 4 2 1

5 0 5 - 6 5 0 4 2 3 1

5 0 5 - 6 0 0 4 3 2 1

5 0 5 - 5 5 0 4 3 2

5 0 5 - 5 0 0 +-0.05 0-00 — f- 0 n 0 5

5 0 5 - 4 5 0

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4 B

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j o5 0 5 - 4 0 0

5 0 5 - 3 3 0 431

5 0 5 - 3 5 0

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5 0 5 » 3 0 0

5 0 5 - 2 B0 4 2 1

FIG . 3 . 8

Strain measurement of an Argon- bombarded Gold Film.(E lectrical Resistance/

Substrate D eflection)

33

34

to be measured. Anodising was continued at increasing potential

until the film became open circu it. The results of a typical run

are listed in Table 3 .2 .

3 .4 . Vacuum Annealing

A number of tantalum films were annealed isothermally in

vacuo at temperarures up to 300°C.

The films were loaded .onto a sliding platform. This was

positioned at the cool end of a metals research vacuum furnace and

kept there until the pressure was reduced below lO” 1* Torr. The

platform was then pushed into the hot region of the furnace for one

hour, by which time the pressure was usually better than 5 x 10*"5

Torr. The platform was then withdrawn to cool for haly* an hour, and

then unloaded.

At each step in the annealing^the sheet resistance of the films

was measured. This was done using a four-point probe because of the

impracticability of using soft-soldered jo in ts . The probe spacing was

1.0 mm and a current of 1 mA was used for measuring the low resistance

films and 0.1 mA for those with high resistance.

The temperature was increased in steps of 50° C from 150° C to

300° C.

TABLE

3.2

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TABLE

3.2

Anod

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of 850

-1 Ta

ntal

um

Film

36

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37

*4-.~ Results

The electrical properties of the metal films made as described above in section 3, have been measured for different levels of bombard­ment with argon ions. In this work all ion bombardment was carried out using argon.

The electrical properties investigated are:

Sheet Resistance,Temperature Coefficient of Resistance, Strain-Gauge Coefficient of Resistance.

38

A ll the gold films were made by evaporation *in vacuo1 onto

glass substrate; the film thickness being controlled (see 3 .1 .2 )

so as to produce films o f approximately 12 ohms resistance.

4 .1 .1 Sheet Resistance

The sheet resistance o f the gold film at evaporation was, on

average, 4 .8 ohm/sq + - 0 ,6 ohn/sq, measured at 30° C. Multiplication

by the film thickness shows an apparent resistiv ity o f 11.5 microhm-cm.

(The re sistiv ity o f bulk gold is 2.25 microhm-an.)

The effect o f ion bombardment on the sheet resistance of a

single 240 - 2 gold film is shown in Figure 4 ,1 . Here the resistance

of a particular film is plotted against bombardment dose at different

stages duriqg the ion bombardment. The main feature is the dramatic

increase in sheet resistance that occurs at a bombardment dose o f 6.5 x 10

ions/cm2 (corresponding to 1050 pC/cm2), It is at this level o f bombard­

ment that the film goes open c ircu it, so that only a small increase in

bombardment effects a large chaqge.

In itia lly on bombardment the sheet resistance drops sligh tly with

increasing ion dose, reaching -40% at 1.5 x 1015 ions/cm2. Beyonjd

this dose the resistance rises steadily through two orders of magnitude.

For argon-ion bombardment above 6.5 x 1015 ions/cm2 the resistance rises

rapidly to an open-circuit condition.

The continuous curve shown in Figure 4 .1 is anbest f i t " line

calculated using equn.2.3 for assumed values o f sputter rate and in it ia l

r e s is tiv ity , and is based on the promise that the film is uniformly

thinned as the bombardment proceeds. The curve which most closely f i t s

the observed points is that for a sputter rate o f 20 atoms/ion and an

in it ia l re sistiv ity o f 22.5 microhm-cm.

4.1 Gold Films

Film

Sh

eet

Re

sist

an

ce

►

Oh

ms/

squ

are

39

Electrical Resistance Changes of a Gold Film during Argon— ion bombardment.(Sheet Resistance/lon Dose)

Ion Bombardment Dose Ions / cm

40

4 .1 .2 R esistivity

The effective resistiv ity o f the film during ar gon bombardment

may be calculated frcm the sheet resistance/bombardment dose relation­

ship plotted in Figure 4 .1 by assuming the film thickness to vary

inversely as the dose. This calculated result is plotted in Figure 4.2

against bombardment dose.

The in it ia l re sistiv ity o f this film was 24 yQ.cm., but dropped

gradually to 12 yft.cm. at a bombardment dose o f 1.9 x 1015ions/cm2. On

further bombardment the re sistiv ity progressively increased {intil the film became effectively open-circuit.In Figure 4 .3 is shown the variation o f conductivity with ion dose with

theoretical curves for three values o f sputtering rate. The relationshipXT' V

between volune re sistiv ity and sheet resistance is shown in Figure 4 .4 .

4 .1 .3 Annealing

The isothermal annealing o f gold films at rocm temperature is

shown in Figures 4 .5 , and 4 .6 . Figure 4.5 shows the resistance change

for a film bombarded to a resistance o f 100 ohms. No significant change

occurred over a period of about 200 hours (-1 week), but after this the

resistance increased steadily and reached 2000 ohms after 1000 hours.

Beyond this period the resistance remained practically constant. During

the rapid resistance change the slope o f the line (on the log /log scale)

is 2 , indicating a second-order dependance with time.

Annealing curves for several more films are given in Figure 4 .6 .

The resistances have been normalised to the values obtaining at the end o f

the ion banbardment. It is characteristic o f a l l films that the re s is t­

ance remained constant for about 200 hours, increased during the next 200

or 300 hours, and thereafter remained relatively unchanged for several

thousand hours.

The extent o f the resistance change has been observed to be as much

41

2 3 AA r g o n Ion B o m b a r d m e n t

5 x i o sIons / cm*

42

\43

OMO - U

n/a

44

45

® h <o m co oj

*'VI<iTi J> pKrqtru.J yp ^

as x40 and as l i t t le as x l . l , but the high resistance films become

open-circuit eventually, after about 5000 hours.

The resistance changes for 12 films are given in Table 4 .1 .

4 .1 .4 Temperature Coefficient o f Resistance

The tonperature coefficient of resistance (TCR) of the

sputtered films was measured after annealing for two weeks at room

temperature and two hours at 120° C, and is plotted against their

sheet resistance in Figure 4.7£a; lijln the main the TCR’ s a l l lie

between 1000 parts per million per degree C and 1500 PPM/°C, though

there is some indication o f an increase in TCR at low sheet resistance

(above 10 ohms/square). The average TCR df ion-bombarded gold films

Slaving sheet resistances between 3 ohms/square and 4 x 1011 ohms/square

is +1175 PPM/°C + - 95 PPM/°C.

The theoretical curve is based on equn.2.11 for the TCR of thin

film s, using MPF = 800 resistiv ity = 50 yQ.cm and TCR of bulk gold

= 4000 PPM/°C.

Values of TCR for 15 specimens are given in Table 4 .2 . It from this and Fig. 4.7 (#=),

can be seen/that for the 35M.fi/square specimen we have a negative value.

4 .1 .5 Strain-Gauge Coefficient of Resistance

The strain-gauge coefficients o f the sputter-etched gold film s,

measured after annealing, are shown in Figure 4.8 plotted against their

sheet resistance. Those having low sheet resistance (< 6 ohm/sq) are

for films measured before bombardment, although the sheet resistances

extend from less than 3 ohms/square to more than 4 x 10H ohms/square the

resulting strain-gauge coefficients show no corresponding variation. The

average value o f strain-gauge coefficient for a l l gauges is y = 2.58+-0.07.

The straight horizontal line drawn at y = 2,43 is developed frcm

the theoretical relationship given in equn. 2 .6 .

( a /u /u ) J*

CO

/a)

50

52

The curved line is taken from the work o f Parker and Krinsky,

and shows the variation in y with sheet resistance found by them for

evaporated thin gold films (without ion bombardment). They found

that the strain-gauge factor o f this type o f film has a minimum value

of y = 1.2 at R - 150 ohms/square, that i t rises to the bulk value

(y = 4.48) for low sheet resistances (thicker film s), and that i t

rises steeply towards y = 100 for films having Rg greater than about

2 x 105 ohms/square.

4 .1 .6 . Temperature Coefficient o f Strain-Gauge Factor

Measurements were made by strain-gauge factor at different

temperatures, with the result shown in Figure 4 .9 . Because no sig ­

nificant variation o f y was found with change in Rg due to ion bombard­

ment, measurements are included of films having had different ion bomb­

ardment doses. The very large scatter in the strain-gauge measurements

arises from d iffic u ltie s in controlling the bending o f the specimens in

the environmental chamber.

A simple lin e -fitt in g routine was used to obtain the temperature

coefficient of strain-gauge factor o f p = - 1590 PPM/°C + - 1100 PPM/°C,

and an average value for y of 2.58 at 30° C. This result is s ta tis tic a lly

sign ifican t.

4 .1 .7 S.E.M. Microscopic Examination

The structure o f the bombarded gold films has been examined under

the scanning electron microscope at a magnification o f X14000.

UrXbombarded films show a smooth featureless surface; but after bombardment

this is found covered with irregularly shaped dark areas (substrate).

Figure 4.10 shows micrographs of four films at different bombardment levels.

At a dose o f 4 x 1015ions/cm2(Film No. 25) the micrographs shows

thin fissures in the film surface: the resistance o f this film had been

4

53

54

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i oroi5

3 1

oo

oHH2awOT

55

increased by ion bombardment to 30 ohm/sq. A second film (No.47)

bombarded to 4.7 x 1015 ions/cm2 , had a sheet resistance of 980 ohm/sq.

The fissures in this had thickened about five times without a significant

increase in their length, though the mean spacing o f the damage sites was

the same as in the f ir s t case.

Film No.26 had been bombarded to 6.2 x 1015ions/cm2 . Here the

areas of damage (dark areas) covered more than half the film surface and

the remaining metal had taken on a spongifom appearance. The resistance

o f this film seens unually low (being 290 ohm/sq) since film No. 21, bomb­

arded to 6.5 x 1015 ions/cm2 had a sheet resistance o f 99 kilohm/sq. In

this film also the appearance was spongiform, though having a finer texture

than that o f No. 26.

4 .1 .8 Microprobe Analysis

An examination was made o f the light and dark areas shown in the

micrographs, using x-ray analysis in a C .S .I. microprobe analiser. Film

No. 26 was used for this(bombardment was 4.7 x 1015 ions/cm2): the

spectrograms are shown in Figure 4 .11. The trace on the le ft was made

with the probe on a light area, and it shows a well defined gold response

o f about one-half that obtained for silicon . On the right is the trace

for a dark area, which has no gold peak but shows correspondingly similar

values for sodium, silicon and calcium.

This result demonstrates that the light areas of the micrographs

are gold film and that the dark areas are holes in the film through which

the soda glass substrate is observed.

With the probe directed to an unbombarded part o f the film the

response peaks for gold and for silicon were o f equal amplitude.

4.2 Tantalun Films before Bombardment

The tantalum films used for strain measurement were a l l deposited

<ncoa ?

y o x23 2 r-o —~ ^ r* Pm O ^o PH'“'’■* CLu ^O 55 □H-1 c{

o0003

_

57

onto glass substrates, but a few others - used for sheet resistance

and TCR measurement - were deposited onto alumina and a few onto mica

substrates, no noticeable difference was observed in their use.

4 .2 .1 Sheet Resistance

The variation o f sheet resistance with film thickness was

explored within the thickness range 50 8 to 2600 X, and was found to

extend from R = 80 KQ/sq to R = 14Q/sq respectively. A plot of s sthis result is given in Figure 4 .12 . The sheet resistance varies

inversely with film thickness, being asymptotic to a line p = 360 pfi.cm

for the thicker films and rising steeply above this line at film thick­

nesses below 100 S.

The corresponding variation o f re sistiv ity with film thickness

has been calculated for the mean sheet resistance line (shown dotted in

Figure 4.12) and is given in Figure 4 .13. This shows that for film

thickness above 400 X the resistiv ity is sensibly constant, being

380 pfi.cm for T = 2500 X and 400 pQ.cm for T = 400 8. Below this

thickness the resistiv ity rises rapidly, and reaches 2500 pfi.cm at

T = 50 8.

4 .2 .2 . Temperature Coefficient of Resistance

The TCR of evaporated tantalum film measured between rocm

tanperature and about 120° C is very small, and is practically constant

for films of greater thickness than 200 8. The average TCR of these

films is -150 PPM/° C. Films o f lesser thickness show a progressively

greater negative TCR, 50-X films having a TCR of -1800 PPM/ °C'. This

is shown in Figure 4 .14 . The transition (around T = 150 8) between

large negative TCR and a constant, small TCR is quite abrupt.

TCR plotted against sheet resistance is given in Figure 4 .15 .

The region of constant TCR extends from R = 14 Q/sq to R = 9KQ/sq.

58

Relation between Sheet Resistance and Film Thickness of Tantalum Films.(Sheet Resistance/

Film Thickness)

360 pQ. cm

59

ot *

60

a o uejs isa y jo j u a p i j j a o o ajnjBJadoiaj[

1000

1500

2000

25

00Fi

lm

Thic

knes

s

k

I

/u'd-'d. ^ jd ' ^nyx^kvcjwTr I

62

At greater sheet resistance the TCR becomes larger and more negative,

but the transition is not abrupt.

A few films with sheet resistance below 1000 ft/sq have TCR

greater than usual, but this seems to be abnormal.

The resistance o f one film (No.3706, T = 730 X) has been

observed over the temperature range -195° C to + 110° C, see Figure

4.16 . By treating this result as a second order relationship the

following expression is obtained:

R = 40.9(1 - 144 x 10~6 T + 0.28 x 10~6 T2) ft /sq .s

Extrapolation indicates a minimum sheet resistance of 40.1 ft/sq.

occurring at a temperature of 257° C.

An Arrhenius plot from these resistance/temperature measurements

is given in Figure 4 .17 . Three activation levels are evidence in th is ;

at tenperatures below -130° C an activation energy o f 0 .23 x 10 3 eV;-

between -130° C and -35 ° C a level o f 0.51 x 10 3 eV; and for temperatures

above -35° C a level o f 1.04 x 10 3 eV . These activation energies stand

approximately in the ratios 1 :2 :4 .

The activation energies o f a l l films are shown plotted against

sheet resistance in Figure 4 .18 . The energies were measured over the

temperature range room temperature to about 120° C. Although there is a

general trend towards higher activation energy at greater sheet resistance,

there is a considerable spread in the energy values, extending over about

one order o f magnitude.

4 .2 .3 Strain-Gauge Coefficient o f Resistance

Strain-gauge measurements were made on tantalum films evaporated

to a nominal thickness o f 750 X : those used had sheet resistances between

30 ft/D and 50 ft /p . Under simple four-point bendirg up to a value of

about 250 m icro-strain, the strain-gauge effect was linear, with an average*

coefficient o f y = 3.04 and, standard error 0.15 (5%). No significant change

in y was observed with sheet resistance, see Figure 4 .19 .

Log.

64

0. 23 mV

1.04 mV

Arrhenius Plot Tantalum Film without Ion Bombardment. t ■ 730 X.

Log(resistivity)/_______ Reciprocal Temperature

- 8-14

- 8 M 3

65

a

it- F

Tm-u-;

::::

OS’

67

Strain-gauge factor was used as a measure o f the repeatability

of the evaporated tantalum film s. Figure 4.20 shows histograms o f y

for three different evaporation runs and also for the combined result.

The mean y obtained in each evaporation run is within 3% of the average

value for y quoted above for a l l runs combined, and generally is very

much closer than th is .

A cumulative frequency diagram for the same films is shown in

Figure 4 .21 .

4 .3 Bombarded Tantalum Films

The films previously used for strain-gauge measurements were

then subjected to argon-ion bombardment at 50 KeV. The projected

Q16range of such ions in - tantalum is 210 A , so that nearly a ll the

beam energy was absorbed within the film thickness, nominally o f 750 $ .

The maximum dose used was 2.8 x 1017 ions/cm2 .

4 .3 .1 Resistance

The effect o f ion bombardment on the resistance o f tantalum films

was similar to its effect on gold film s. In itia lly bombardment reduced

the resistance but as i t proceeded the resistance was increased until

eventually the film became open circuit. At a dose of 0 .6 x 1017ions/cifi

the sheet resistance was reduced to 50% of its original value (40 £2/D ) ,

and this was followed by a steady rise in resistance that reached 6000 S7/CI

at 2.6 x 1017 ions/cm2 (see Figure 4 .2 2 ). A ll the films bombarded with

doses greater than 2.8 x 1017 ions/cm2 were found to be open circuit upon

measurement.

Shown as a continuous line is the result o f simple sputtering

theory (equn.2.4).

The minimum ion dose needed to remove a given film completely is

related to this value, but a contributary cause of increased resistance

must be the oxidation that follows breaking the vacuum. Thus i t may be

68

Of O Of'&7ru*-r/lr»4,

70

Ion Bombarded Tantalum Films(Sheet Resistance/

Bombardment Dose)

I art lem<5 j {

X / o 17

assumed that a dose o f 3.0 x 1017 ions/cm2 is required to sputter

such films right throqgh. Assuming this and also that sputtering

uniformly reduces the film thickness, values for film re sistiv ity

were calculated and plotted against ion dose; Figure 4 .23 . The

in it ia l resistivityuwas 360 pft.cm before bombardment, which was

reduced to 160 yft.cm at 0.6 x 1017 ions/cm2 and thereafter increased

steadily towards in fin ity at a dose o f 3 x 1017 ions/cm2 .

The re sistiv ity o f bulk tantalum is 13.9 pft.cm at 30° C.

4 .3 .2 Temperature Coefficient of Resistance

Figure 4.24 shows the TCR of tantalum films plotted against ion

bombardment dose: TCR was measured between roan temperature and + 120°C.

Films bombarded with a dose greater than 1 .3 x 1017 ions/cm2

showed constancy in TCR; the value being close to -100 PPM/°C. This

was sligh tly less than the TCR of unbombarded films o f -150 PPM/°C.

Between 0.2 x 1017 and 1 .2 x 1017 ions/cm2 bombardment raises

the TCR considerably. In this region the curve forms a cusp, centred

at 0 .6 x 1017 ions/cm2 , which extends into positive TCR values. The

largest TCR value encountered so far is + 420 PPM/° C.

The resistance o f four films having representative values of

bombardment within the dose range established above was measured over

the temperature range boiling point o f nitrogen to the boiling., point of water.

.The graphs of the non-bombarded. film- have already, beqn reported, see .Figures

4.16 and 4 .17 , but a l l the results accord well with measurements made only

above room temperature. Table 4 .3 shows the principal results for these

film s. Negative TCR is shown both by the non-bombarded and by the heavily

bombarded film (with dose = 2.6 x 1017 ions/cm2 ) ; the TCR of the bombarded

film being sligh tly the lesser (-127PPM/°C as against -160PPM/°C before

bombardment.) The two films with bombardment doses within the transition

72

73

region both show positive TCR with values similar to those given above

in Figure 4 .2 4 ., and they show considerably linearity in their

resistance-temperature p lots ; the standard error being only about one

part in 10 ** in each case. Arrhenius plots were made for these films

and were found to have a linear region at each end of the temperature scale

FILM NUMBER 3706 3610 3714 3703

BOMBARDMENT DOSE

' (X 1017IONS/CM2)

NIL 0.6 0.8 2.6

SHEET RESISTANCE

( ft /P 30° C)

00orf- 28.6 36.8 7 330

TCR (PPM/°C) -160 +177 +175 -127

ACTIVATION ENERGY

T < -130°C (me\0

T > -35°C {m&V)

0.25

X. 02

-0 .24

-1 .41

- 0.22

-1 .51

0.20

0.90

Table 4 .3 Tantalum Film Resistance Measurements over the Temperature Range -195*C to + HO* C.

connected by a curved transition. In the case o f the non-bombarded film

three linear regions were evident (see section 4 .2 .2 . and Figure 4 .1 7 ) .The

ratio o f the activation energy at high temperature to that at low temper­

ature is about 4 :1 for the negative TCR films.

75

The Strain-Gauge factors found for non-bombarded tantalum films

averaged y = 3.04. A plot of strain-gauge factor of films bombarded

with different ion dose levels is given in Figure 4 .25 . It shows a

transition region between doses of 0 .3 x 1017 ions/cm2 and 1 .3 x 1017

ions/cm2 in which y increased to a maximum value o f about 5.2 and then

returned to about 3 .0 . This is followed by a linear region in which y

was reduced as bombardment proceeded, being 2.2 at a dose o f 2.8 x 1017

ions/cm2.

4 .3 .4 Annealing

After manufacture a l l the films were kept for about one week (at

room temperature) before any measurements could be made. Additionally

this isothermal annealing period was followed by heating to about 130° C

for two or three hours so as to stab ilise the resistance and prevent d rift

during the TCR runs. The bombarded films were also heat stabilised at

130°C before use.

The long-term history o f four bombarded films has been followed

over a period of two years. This annealing was carried out at room

temperature without the heat ageing, except that two o f the films were

annealed at 130°C after 2000 hours. These results are shown in Figures

4.26 and 4.27.

Figure 4.26 shows changes in the resistance o f two films bombarded

with doses in the transitional region, i .e . 0.6 x 1017ions/cm2 and 0.8 x 1017

ions/cm2 respectively. The resistance continued to rise with time lapse,

and after 2000 hours had increased by two orders o f magnitude. This was

the case for both film s.

The change in resistance of the films reported in Figure 4.27 on the

other hand, amounted only to a rise of 10% in 2000 hours. These films had

been bombarded with 0.98 x 101.7ions/cm2 & 1 .1 x 10l 7ions/cm respectively.

4.3.3. Strain-Gaqge Factor

76

7 7

78

4

o/u

79

After the.heat aging one film had not changed at a l l and the resistance

of the other had increased by a further 7%. At the end o f 18000 hours

(two years) an additional 4% increase was observed in the resistance of

both film s.

8 0

Shown in Figure 4.28 a3b and o are the results of

incremental anodic profiling of an unbombarded tantalum film

and one bombarded to a dose of 0.35 x 1017 ions/crrT2 . This

was an early attempt to use this technique and there is a large

scatter of values3 probably resulting from drifts of resistance

between measurements (time between measurement steps could vary

from a few minutes to a weekend). One can tell from these

measurements (assuming that the ,anodization- rate stayed constant)

that the bombarded film was thinner3 both films appear to have a

region of uniform conductivity near the surface with lower conduc-

tivity near the substrate. From the TCR plot it appears that the

unbombarded film is fairly uniform3 whilst the bombarded film has

a region of very positive TCR (remember the curve is an integral

one)j falling to the original value as the substrate is approached).

Similar results for a dose of 2 x 1017 ions/crrTz are shown

in Figure 4.29. The bombarded film is much thinner and of lower

conductivity and lower (negative) TCR3 but the electrical properties appear to vary little with depth.

4.3.5. ' Depth Pro filing by. Anodization

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»lS

/mO

N

DfP

TH

»- Vo

L.T3

86

87

5.1 Gold Films

The films examined in this section are gold film s, and range

in sheet resistance from 3 fi/d to above 4 x IQ1* Q/Q . Those of

low resistance are films used "as deposited" and without ion bombard­

ment, and were nominally o f 200 8 thickness. The high-resistance

films were evaporated as 200 $ low-resistance films and were then

bombarded with argon ions until the resistance was increased to the

desired value.

This inert ion bombardment o f low-resistance films is the most

significant difference between the films described here and those of

other workers. Parker and Kirnsky1*; and Nishiura, Yoshida and Kinbara5

stopped short the nucleation upon reaching the particular resistance

values required, and Stroud2 bombarded already high-resistance titanium

films (~400fi) with oxygen ions - a reactive combination. Parker and

Krinsky covered their films in vacuo with a thick layer o f .Si02 to pre­

vent oxidation: a l l other films discussed have been le ft exposed to

the atmosphere.

These differences make it important to exanine the conduction

mechanism taking place in the film s, and this w ill be done fir s t in the

context o f the strain-gauge coefficient of resistance (S.G .C.R.)

5 .1 .1 Strain-Gauge Coefficient (y)

It has been shown (equn.2 . 6) that the strain-gauge factor of a

thin film carried on a substrate should be

y = 1 + a + a (1 - a ) + d p/ ps t s '(1 -aJ" dZ/Z f

where Gg and = Poisson's ratio for substrate and film , respectively,

5._____Discussion of the Results

88

£ = the longitudinal dimension o f the film ,

and e = d£/£ = the applied strain.

Large values o f gauge-factor (y) may only be expected for

correspondingly large rates o f change o f resistiv ity (p) with strain

(e ) . Two possible conduction mechanisns may be postulated for such

films - an activated tunnelling mechanism whereby charge carriers

cross the d ielectric regions in an island structure of metal, or

m etallic conduction with restriction (due to edge effects) o f the

electron mean-free-path.

5 .1 .2 Tunnelling4*-----------------------------------------------———— — —— ---—

An implication o f this type of e lectrical conduction is the

relation between y and sheet resistance. Parker and Krinsky1* show

(by measurement) that for gold y rises from a minimum value around

1 . 1 , to 100 as the resistance changes between 102 ft/ui and 105 ft/u ,

and this is attributed to an increase in the separation o f metallic

islands in the film . Such dependence of y on Rg is not found to be

the case here, however, since y remained constant for a l l resistance

values measured, i .e . up to 4 x 10** ft/a . Parker and Krinsky derive

the following relation between S.G.C.R. (y ) and particle separation (s)

y = 1.03 e st owhere £. is an effective electron barrier potential lying between 0 and

0 (the metal work function).

Working backwards, to estimate the particle separation implied

by the measured values o f y (average = 2.58 at 30°C), and assuming 8 = 0o

Island separation = E - = 1.138 .1.03£ 2 o

p = the film resistivity,

= 4.9 eV for gold (P and K’s choice),

89

This separation is less than the mean atomic spacing for bulk

gold (= 2.57 8, see section 2. 2) , and lends support for the view

against tunnelling as the conduction mechanism of the films reported

here.

5 .1 .3 Metallic Conduction

This model is based on the assumption that conduction within

the film substantially follows the value o f re sistiv ity found in bulk

material, but that the proximity of the film surfaces severly lim its

the mean-free-path (m .f.p .) of the conduction electrons. Parker and

Krinsky give the m .f.p . in most metals as lying between 200 - 800 $.

We have already derived an expression for the conductivity (equn,

2 . 10) , in terms of resistiv ity we have;

3t (1 + 2p)

P "XB

To a f ir s t approximation the conductance may be taken to be

proportional to film thickness, so that resistance

p _ const dR = _ dtt 9 R t

and

• _dp = - dtp t

d t - - 0 ( 1 - a ) d2t (See section 2.3)

(1 - o ) £

-

M*

in + 0.4228L* t

This leads to

1 dp = G (1 - G )p «3e -----—

(1 " crf )

90

Y = 1 + a + c r /1 ° s 1 + ^2.(T~-' a~)- p eso that S.G.C.R. becomes

y - 1 + 0 +20 (1 ' as}s f-------(1 - a J -----------------------------5.1r

Kaye and Laby9 give values for Poisson's ratio ,

for Gold, o^ = 0 .44 ,

and for Glass,Og = 0.25 (average),

so that the predicted value o f S.G.C.R. for gold film on glass is

X ~ 2.43

This is in very good agreement with the observed values, the

average o f which is 2.58 ± 0.07 at the 95% confidence lim its.

5 .1 .4 The Temperature Coefficient o f Resistance (a)

The positive TCR of the bombarded films also indicates that

m etallic conduction is the predominant mechanism.

An approximate relationship between sh eet-resistivity (Rg) and

the TCR of the film (a ) is derived in section 2.5 (equn.2.11);

Also, from equn.2.6, we have

aF ~ aB/F

fx n+ 0.4228Ln R 1 B s

PF _

where is the TCR of the bulk material, is the resistiv ity of the

film and A the electron mean-free-path in the bulk. This assumes

metallic conduction modified by the reduction of electron mean-free-path

caused by the proximity of surfaces. It also assumes that the surface

and defect scattering is temperature independent and that the film thick­

ness is much less than X .D

This function is plotted in Figure 4.7 as the continuous curve_4

for A = 800 p = 50 pficm and a_ = 40 x 10 °C 1 .o r B

91

The agreement is reasonable considering the approximations

that have been made. Certainly the reduction o f TCR with increasing

sheet resistance is observed.

Over the range o f sheet resistance from 30 ft/O to lO^ft/rj

measurement shows the TCR to be almost invariant, the average value

at the 95% confidence level being,

a = 11.75 x 10~" ± 0.95 x lO"**

5 .1 .5 The Temperature Coefficient of Strain-Gauge Factor ( 8)

It has been shown (section 2 .4 ) from the definitions of y , a and

8 that the relationship 8 = - a should hold true.<#■

The results for the gold films appear to confirm this prediction

experimentally for the f ir s t time.

In the present work the variability of S.G.C.R. measurement

makes i t impracticable to arrive at reliable values of 8 for individual

film s, but, on the grounds that the S.G.C.R. is independent of sheet

resistance, a simultaneous reduction o f a ll data has been carried out.

Table 4.2 and Figure 4.9 show the related S.G.C.R. and temperature values

and the result o f the computations. The points on the graph of Figure

4.9 are very scattered, and the correlation coefficient is only 0 .26 . How

ever, an application o f Fisher's z -te s t15 indicates that this is a s ig ­

nificant correlation at well above the 95% confidence level. On the

assumption, therefore, that a linear relationship holds, i t is possible

to calculate the mean intercept and slope, and this yields values, within

the 95% probability lim its ,o f

Intercept = mean S.G.C.R. at 0°C = 2.71 ± 0 .0 7 , and

Slope /Intercept = mean temperature coefficient of S.G .C.R .,

8 = -16 x 10_l* ± 11 x 10“ **.

92

The lim its o f the temperature coefficient are seen to be

extremely wide, showing the uncertainty associated with its true

value. However, by using this value o f temperature coefficient,

the mean S.G.C.R. may be adjusted to 30°C, giving

mean y = 2 .5 8 ± 0 .0 7 at 30°C.

The mean value for 6 o f -16 x 10 compares favourably with

the mean T .C .R ., a , for these same film s, o f 11.75 x 10 T

5 .1 .6 The Structure o f the Bombarded Films

The lack o f change in y with sheet-resistance and the positive

value o f a indicate that m etallic conduction remains the predominant ■#

mechanism.

This result is remarkable when one considers that i f one assumes

the very high re sistiv ity of say 1000 yftcm for the 40 kft/p films this

would infer, assuming a uniform film , that the film thickness is o f the

order of one monolayer. This would only be the case i f the thickness

change due to sputtering is extremely uniform.1 8

It has been shown that the sputtering rate o f gold varies with

orientation such that the surface of a polycrystalline specimen soon

becomes very irregular, with low sputtering rate grains standing proud

of the r e s t . This would lead to a network type o f structure where the

gold in a thin film is removed in the areas o f high sputtering rate to

expose the substrate. The stereoscan micrographs (Figure 4.10) reveal

that a network structure is indeed formed. It appears therefore that

the resistance increases with dose due to a reduction in the number o f

interconnecting necks, rather than an overall decrease in film thickness.

This would explain the apparently very high sputtering rate. Most

material w ill be removed around the edge o f the holes due to the oblique

electrodes, and i t appears that with our films the gaps between the

islands of gold remaining on the film are too large for tunnelling

type conduction.

The mean thickness o f the 'necks' must stay o f the order o f

the film thickness until the width decreases rapidly to zero, as y

does not fa l l to the minimum value o f about 1.0 reported for many

thin evaporated films where the network structure is f ir s t established.

Another explanation o f the results could be that gold is

implanted into the surface of the glass to form a gold-glass cermet

of a similar type to that produced by sputter deposition o f a mixture 1 9

of gold and glass.

The mechanism whereby this is done is the sc change o f momentum

between an argon ion and a gold atom in the film . This leads to the

familiar recoil sputtering with gold ejected from the surface, and also

to transmission sputtering where the gold is implanted into the glass.2 0 2 1

It has been predicted theoretically and demonstrated experimentally

that the transmission sputtering yield can be considerably greater than

the recoil sputtering yield .

5 .1 .7 The Resistance Ageing Effect

Inspection o f the h istorical record of gold film number 038

(see Figure 4 .5) shows that the resistance increased from about 100 0

to 2000 fi! in the f ir s t 1000 hours after ion bombardment. Thereafter

the resistance, thoigh having s t i l l increased, did so at a reduced rate.

A similar effect is apparent with a ll films (Figure 4 .6 ) , though

the resistance change was not always so severe.

Two mechanisms could be proposed to explain the increase and

saturation of resistance with time and also the increase in resistance

incidence of the bean until there is no connecting pathway between

94

on annealing. Either oxidation o f the gold surface or diffusion

o f gold atoms to form clusters. Clustering would decrease the

nunber o f conducting pathways and therefore increase the resistance

o f the film . In the case o f the films that go open circuit i .e .

those with a resistance immediately after ion bombardment of greater

than 10,000 fi, a discontinuous island structure may be formed where

the island separation is usually too large for a significant amount

of conduction by tunnelling. The one film with a large negative

TCR (see Table 4 .2 ) may be o f this type, with an island separation

that is smaller than usual.

The in it ia l incubation period o f about one week, when l i t t le

change occurs, is indicative o f another mechanism that prevents

diffusion, or oxidation, for this time, but we have no explanation

for this behaviour at present.

As a chemical element gold is in Group 1 o f the Periodic Table,

Sub-group (b ), which comprises Cu, Ag, and Au. Gold may be either

uni- or trivalent and, although trivalency characterises most of its1 ?

compounds, forms auric oxide - unstable and sligh tly acidic.

The films reported here were a ll kept in closed (but not airtight)

boxes, but were exposed to the atmosphere during measurement. When

heated above 90°C an irreversible increase in resistance always occurred

(see, for example, film 044 in Figure 4 .6 ) . Neither this nor the ageing

of films at room temperature materially effected the value o f S.G.C.R.

95

5.1.8 The Initial Drop in Resistance fgr doses below

2 x 10 ions/cm 2

There is a dramatic reduction in the resistivity of the gold

films from 24 yft cm to 12 yft cm (bulk value 2.25 ]ift cm) for a dose1 5

of 1.8 x 10 ions cm 2 (Figure 4.2). This effect has been observed2 2 j 2 3

by other workers for other films and has been attributed to6

desorption of gases in the surface of the film. More recent results

indieate that it is more probable that the reduction in resistivity

arises from re-arrangement of 'the film structure; a form of radiation

enhanced annealing, plus possible reduction of oxides by preferential sputtering of oxygen.

5. 2 Tantalum Films

5.2.1 The as-deposited Films

Films above 200 2 in thickness appear to have fairly uniform

properties with a resistivity of 370 lift cm and TCR of -150 PPM/°C

(one batch has larger negative values of TCR, possibly due to a poor

vacuum during deposition). These values are similar to those6.» 1» 8

measured by other workers using the same deposition system . From

their results it seems probable that the films are b.c.c. tantalum,

semi amorphous (grain size <50 2 ), with 40 2 of surface oxide and

an average of 30 atomic per cent of oxygen dissolved in the rest of the film.

The large negative values of TCR (and high resistivity) for

t £ 200 2 indicate that the first 200 2 to be deposited contain larger

amounts of oxygen (due to gettering)3 there is therefore no continuous

metallic conduction path and activated tunnelling dominates the con­

duction process.

The measured activiation energies for thicker films (Figure 4.17)

are low because one is seeing the combined effects of metallic and

activated tunnelling mechanisms. There appears to be evidence for at

96

least two thermally activated mechanisms one becoming evident above

-130° C and the other above -35°C. The actual value of activation

energy measured will depend sensitively on the balance between

metallic and activated conduction and this will be greatly affected

by the microstructure of the films. This would explain the large

scatter in measured values of activiation energies (Figure 4.18)

which can be taken as evidence for differences in micro structure (or

oxygen concentration) and the trend to higher values at higher resist­

ivity indicates the reduced contribution from metallic conduction as the oxygen concentration increases as it will do for the thinner films.

Although strain-gauge factor has been measured over a much

narrower range of sheet resistance it seems clear that there is very

little scatter in the Value (3.02 ± 0.15). This indicates that the

strain-gauge factor is less sensitive than net activation energy (and

TCR) to the micro structure of the films and is probably (like the gold

films) determined by relative changes in the metallic component of

conduction but not by the absolute magnitude of resistance. The value

of strain-gauge factor using equn.5.l and the value of Poisson’s ratio9

given for bulk tantalum (0.342) is; y = 2.03. Some factor is acting

to increase the strain sensitivity of our tantalum films. A possible

mechanism to explain the higher value of y is proposed in section 5.2.4.

5.2.2 The Effect of Argon Bombardment .on Resistivity

The initial drop in resistivity towards values expected of bulk

tantalum could be explained by preferential sputtering of oxygen

(particularly in view of the vast difference in mass between oxygen and

tantalum) and radiation enhanced diffusion of oxygen to the surface and

re-arrangement of the film resulting in a more metallic phase being

formed. This is supported by the microscope observations of others* 7

workers , by the anodic stripping results reported here (Figure 4.28),2 *+

and by theoretical predictions on preferential sputtering.

97

1 7 “ 2After passing through a minimum at 0.6 x 10 ions/cm the

resistivity rises with increasing dose3 but the linear rate of

increase cannot be fitted to a simple sputtering theory3 and there

is a large scatter in values. The latter could arise from differences

in micro structure that affect the balance between conduction mechanisms.

The slow rise could be explained if a phase of low sputtering rate is

formed by reaction with the substrate3 the oxygen content increasing with increasing ion dose.

5.2.3 Changes in TCR as a result of Argon Bombardment

The TCR reaches a peak positive value at the same dose as the

minimum in resistivity and the peak value measured (+ 400 PPM per °C)* 25approaches the value one would expect from a very pure tantalum film .

This fully supports the ideas of purification and re-arrangement of the film at low doses as detailed in the last section.

It is curious that although a similar swing to a large positive

TCR has been seen for in-situ measurements on oxygen bombarded tantalum5

films j no such effect has been seen for in-situ measurements for argon e

bombardment or for later measurements (taken after removal from the8

target chamber) on oxygen bombarded films .

It must however be pointed out that the latter measurements were

made on annealed (5 hr. at 250°C) films whereas the results presented

here are for films which are only heated to 120°C at the start of the

TCR run. Thus the apparent discrepancy could arise if the metallic

phase leading to low values of resistivity and high positive TCR is a

metastable phase3 which changes to a more stable (oxide?) phase on

annealing at higher temperatures. The wide scatter of values in the

region of the TCR peak would be explained if some annealing takes place

at room temperature (see section 5.2.5 below) as the time before deter­

mination of the TCR varies from sample to sample.

98

At high, doses there is little scatter in TCR values indicating

that a stable phase has been formed3 and the value of TCR is similar6

to that measured by other workers.

5.2.4 Changes in Strain-Gauge Factor as a Result of Argon Bombardment

The strain-gauge factor peaks at a similar dose to the peak in

TCR and values of y as high as 5.2 have been observed. Once more a

wide scatter in the values is observed. It is not clear why this

structure has a strain sensitivity greater than that of 2.03 predicted

using the bulk value of Poisson's ratio. The highly metallic proper­

ties indicate that a cermet film is not formed in this case. One

could postulate that when the film is strained the phase structure is

such that the number of metallic conducting pathways is reduced so

increasing resistance whilst retaining the dominance of metallic con­

duction. If this is so then bombardment induced changes in micro­

structure seems to enhanoe the effect. This process would have to be

reversible as no hysteresis is observed.

At high doses where TCR measurements indicate that a stable phase

is formed the gauge factor approaches the predicted value of 2.

5.2.5 Resistance Ageing

The results of ageing tests (Figures 4.26 and 4.27) support fully

the models for film structure proposed above. At doses where a suppos­

edly metastable metallic structure is formed the resistance increases by

up to two orders in magnitude after two years at room temperature. The

most probable mechanism for the disappearance of the metallic phase is

by reaction with the oxygen that remains below the metal phase near the

film/substrate interface. This model is supported by the results of26

other workers.

At higher doses where it is proposed that a stable structure is

99

formed by reaction with the substrate, an extremely stable structure

is indeed formed which is little affected by annealing at 130°C. These

models are also supported by the results of anodic profiling.

It seems clear that while the effects of argon bombardment of

gold films can be explained in terms of sputter etching, the mechanisms

that determined the observed changes in electrical properties °ftantalum films are changes in phase structure and chemical effects - • and reaction

such as preferential sputtering of oxygen /with the glass substrate.

100

6.1 Argon Bombardment o f Gold Films2,1* j 5 > 2 2 , 2 3

Many workers have examined the strain-gauge properties of

gold film prepared by thermal avaporation to have sheet resistances

of up to a few thousand ft/Q . Gauge factors rising to ~100 have

been measured, coupled with a negative temperature coefficient o f

resistance(TCR). These factors have been satisfactorily explained

on the basis of electrica l conduction by tunnelling across the

boundaries o f islands o f metal.

The films examined in this thesis do not, however, exhibit

the same behaviour even though the sheet resistances cover much the

£ame range (3 ft/D to 4 x 10 ft/Cf ) . The strain-gauge factor (S.G.C.R.)

has been found to be invariant, and to have an average value o f 2.58.

The TCR has been found to be positive, and with a constant value o f about

11.75 x 10 \ The temperature coefficient o f S.G.C.R. has been measured

as -16 x 10 T A ll these values are inconsistent with electron tunnel­

ling but they are consistent with m etallic electrical conduction, the

resistiv ity being presumed to have the bulk value modified by a reduction

of the electron mean-free-path.

This fundamental divergence in results can only be attributed to

the method o f film preparation. Althoigh the films of the other workers

were also prepared by condensation at room temperature from thermally

evaporated gold (the same method as was used in the present work), evap­

oration of the films reported here was not stopped on reaching the desired

resistance, but was continued down to resistances o f ~ 5ft/Q . The films

were then bombarded.with argon until the resistance had been increased to

the desired value. By this means the structure o f the film had been made

similar in effect to that o f bulk metal, a feature which is evidently

retained after ion bombardment.

6. Conclusions

101

The effect o f apgon bombardment of thin gold films appears

to be the formation o f a 'network1 structure where m etallic conduction

is retained.

When the film eventually becomes discontinuous either by further

bombardment, or by processes taking place during ageing, the island

separation appears to be too great for conduction by tunnelling.

The increasing resistance during bombardment is attributed to a

reduction in the number o f connecting pathways rather than a reduction

in their size .

Exposure to the atmosphere results in an irreversible increase

in resistance. The in it ia l 'incubation' during ageing and the ageing

mechanism have yet to be fu lly explained.

The film quality as determined by re sistiv ity is improved for

low doses (below one quarter o f the dose required to make the film go

open-circuit).

102

The as deposited films have electrical properties consistent

with conduction by a combination of metallic and activated tunnelling

mechanisms. The latter component appears to increase in importance

as the oxygen content of the film increases, and there is evidence for

at least two activation processes.

The strain-gauge factor appears to be determined by changes in

the metallic component but is higher than predicted from bulk metal

values, possibly as a result of strain altering (reversibly) the number

of conducting pathways in the film, thereby changing the resistance, but

not the conduction mechanism. Bombardment with argon results first in *

a change in electrical properties towards those expected of very pure

tantalum films. This is thought to be the result of preferential sput­

tering of oxygen, radiation enhanced diffusion of oxygen to the surface

and re-arrangement of the film to form large islands of b.c.c. tantalum.

The strain-gauge factor is increased to up to 5.2 at this point, possibly

because the change in phase structure has increased the effect of the conducting path way mechanism proposed above.

The tantalum phase appears to be metastable and the resistance

increases markedly with time at room temperature, probably as a result

of reaction with oxygen that exists near the film/substrate interface.

For higher doses of argon it appears that-.a single phase, stable,

low sputtering rate compound is formed, probably by reaction with the

glass substrate. This compound has a mixture of activated and metallic

conduction with a strain-gauge factor (probably determined by the metallic

component) close to that predicted for a tantalum film on a glass substrate.

To summarise the overall result of this work it appears that the

phenomenon that dominates the electrical properties of argon ion bombarded

6.2 Argon Bombardment of Tantalum Films

103

gold films is that of sputter etching3 whilst for tantalum (plus

oxygen) films changes in phase structure and chemical effects dominate.

104

1.

2 .

3.

4.

5.

6.

7.

1k

9.

10.

11.

12.13.

14.

15.

16.

17.

18.

19.

20.

7. Re f erences

R.G.R. Robinson, K.G. Stephens and I.H. Wilson;Thin Solid Films; 27(1975) 251.

P.T. Stroud; AWRE Nucl.Research Note No. 29/71.

I.H. Wilson, K.H. Goh and K.G. Stephens; Int.Conf. on Application of Ion Beams to Metals. Albuquerque (1973) paper V8.

R.L. Parker and A. Krinsky; J .o f Appl.Phys. 34 (1963) 2700.

M. Nishiura, S. Yoshida and A. Kinbara; Thin Solid Films 15 (1973) 133.

I.H. Wilson, K.H. Goh and K.G. Stephens; Thin Solid Films; 33 (1976) 205.

K.H. Goh; Ph.D. Thesis, University of Surrey,(1976 .)

K.G. Stephens and I.H. Wilson; Thin Solid Films;50 (1978)

G.W.C. Kaye and T.H . Laby; Tables o f Physical and Chemical Constants; Longmans.

(a)B .S . Verma; Measurement o f Strain Coefficient of Resistance in Silver Films; Thin Solid Films, 7 ,(1971) 259-264.

(b) B.S. Verma and H.J. Juretschke; J.Applied Phys. 41, (1970) 109. G.R. Witt and T.J. Coutts; Thin Solid Films 7,(1971), Rl.

0 .5 . Heavens; Thin Film Physics, Methuen.

R. Fuchs; Proc.Cambridge P hil.Soc., 34 (1938) 100.

E.H. Sondheimer; Advan.Phys., 1 (1952) 1.

J.C. Turner, Modern Applied Mathematics, E.U.P.

W.S. Johnson and J.F. Gibbons; Projected range s ta tistic s in semiconductors (1970).

G.R. Davies; Chemistry, article in Chambers Encyc.Vol. I I I .

1.H. Wilson and M.W. Kidd; J. o f Materials Science,6, (1971) 1362.

T.J. Coutts; Thin Solid Films 4 (1969) 429.

P. Sigmund; Phys.Rev. 184 (1969) 383.

105

21. J.G. Perkins and P.T. Stroud; Nucl.Instrunents and Methods 102 (1972) 109.

22. B. Navinsek and G. Carter; Can.J. Phys., 46 (1968) 719

23. M. Deery, K.H. Goh, K.G. Stephens and I.H . Wilson,Thin Solid Films, 17 (1973) 59.

24. H.M. Naguib and R.Kelly; Radiat.Effects, 25 (1975) 1.

25. L.G. Feinstein and R.D. Huttemann, Thin Solid Films,20 (1974)

26. M.R.M. Moulding, Ph.D Thesis, University o f Surrey 1979.

106

Appendices

1 COMPUTER PROGRAMMES

1.1 Computation of slope of line through strain gauge data

1.2 "Free" formal input of decimal data from paper tape

1.3 Subroutine to calculate to "best f i t " straight line

1.4 Graph plotting

2 EXTRA RESULTS AND CORRELATIONS (OF USE TO OTHER WORKERS)

2 .1 Bending ring for 1" strain gauges2.2 Rg vs. thickness (Ta) showing different evaporation

runs2.3 TCR vs. Rs (Ta) showing different evaporation runs2.4 TCR vs. thickness (Ta) showing different evaporation

runs2.5 TCR vs. thickness (Ta ) showing different evaporation

runs2.6 TCR vs. activation energy (Ta)

2.7 Activation energy vs. thickness (T )

2 .8 Activation energy vs. thickness (Ta) showing different runs

2.9 Activation energy vs. Rs (Ta ) showing different runs

i2.10 Rs vs. (tim e)2 (Ta )12.11 Rs vs. (tim e)2 (Ta)2.12 SGF vs. Ro ( T )

S a.

2.13 SGF vs. TCR (Ta)a.

'2 .14 Relative resistance vs. R (after 1000 hrs. ) , Au film s.

3 END CORRECTIONS FOR IMPLANTED STRAIN GAUGES

J

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F O R M A T ( » 0 * T 2 ' S P E C I M E N * T i l . I 3 . T 1 4 ’ » T E M P = ' T 2 4 . I 2 T 2 7 ' D E G

1 0 P E = ‘ T 4 3 . E 1 0 . 3 * T 5 3 * ♦ C O R R C O E F F = « T 6 9 , E 1 0 . 3 )

F O R M A T ( * 0 ' T 6 . 3 6 A 2 / )

F O R M A T { ' 1 * )

F O R M A T ( 3 6 A 2 )

I L P - 3

I T R = 4

R E A D ( I T R . 4 0 0 0 ) N O T E

W R I T E ! I L D » 3 0 0 2 ) N O T E .

. N U M = 2 0

C A L L G R E A D ( N U M ♦ X )

1 F ( X < 1 ) ) 2 i 1 . 3

W R I T E ( I L - . 3 0 0 3 )

C A L L E X I T

W R I T E H L P . 3 0 0 0 ) { X m . I = l , 1 9 , 2 ) . { X ( I ) . I = 2 » 2 0 . 2 )

I N 0 = I F I X ( X ( 1 ) )

1 T E M P = I F I X ( X ( 2 ) )

K = 0D O 6 1 = 4 , 2 0 . 2

I F < X ( I ~ 1 ) ) 5 » 4 » 5

I F C X ( I ) > 5 , 6 * 5

K = K + 1

X ( K ) = X ( I ~ 1 )

Y ( . < ) - X ( I )

C O N T I N U E

C A L L G R Y L L ( K . X . Y . A . 8 » C )

W R I T E { I L P . 3 0 0 1 ) I N O * I T E M P . A , C

G O , T O 1

E N D

A T U R E S S U P P O R T E D

M E W O R D I N T E G E R S

OCS

vS

R E R E Q U I R E M E N T S F O R G R A A L

O M M O N 0 V A R I A B L E S 112 P R O G RA M 308

G R A A L 1

G R A A L 2

G R A A L 3

G R A A L A 3

G R A A L 4

G R A A L 5

G R A A L ’ 6

G R A A L 7

G R A A L 8

G R A A L 9

G R A A L 1 0

G R A A L 1 1

G R A A L 1 2 1

G R A A L 1 3

G R A A L 1 4

G R A A L 1 5

G R A A L 1 6

G R A A L1 7

G R A A L 1 8

G R A A L 1 9

G R A A L 2 0

G R A A L 2 1

G R A A L 2 2

G R A A L 2 3

G R A A L 2 4

G R A A L 2 5 ;

G R A A L 2 6

G R A A L 2 7 ;

G R A A L 2 S

G R A A L 2 9

G R A A L 3 3

i

I , ■Ml

A 1.2

*GE 1 * 4 J OB

ENG0I72C

1001 2001 2 CCI * E N G 0 1720

3G CRIVE 0000 0001

CART SPEC10012001

CART AVAIL PHY DRIVE1001 COCO2001 0 0 0 21002 0001

> M i l CONFIG 8K3AT VERSION D.M. SYSTEM VI M02

FREE FORMAT INPUT' FCR vAME GREAC .1ST SOURCE PROGRAM 3NE WORD INTEGERS

SU BRO UTI NE GR E A C( IPR , N , OUT )DIMENSION 0UT(1 ) , INPUT ( 72 ) ,'K INC < 15 )

GREACG R E A C 2

/ 0DATA KIND/*L. 1 , * , ’ /) F O R M A T (72A 1 )READ INPUT RECCRC.

R E A C ( IPR,AO ) ( INPUT! I ) , TEST ARRAY SUBSCRIPT RANGE

IS* 1I F (N )1 9,1 9,II F (N - 3 6 )3 » 3 , 2 NN = 3 6 GC TC 4 NN = N

INITIAL I Z EDO 5 1=1,NN O U T ( I ) = 0 .

SEPARATE THE DATA WORDS DO 18 1=1,NN

P LEADING BLANKS DO 51 K = I S ,72 DO 51 L = 2 » 15

1 GREACGREAD 4 GREAD 5 GREAC 6

1=1,72) GREACGREACGREACGREAC- 10GREAC 11

GREAC 13 GREAD 14GREAC 15 GREAD 16 GREAC 17

S KI

L

GREAC 19 GREAD 20 GREAD 21 GREAD 22

IF( INPUT(K)-KIND(L) )51,52,51 CCNT INUE GC TC 19

START NEW CATA WORD

GREACGREAC

2324

I S = K IF = IS + 7I F( IF-72)7,7, 6 I F = 72 SIGN= 1 •1 DP = C MM = 0

SEPARATE AND IDENTIFY DATA CHA RACTERS CC 16 J= IS, IF DO 8 K=l, 15IF( I N P U T ! J )- K I N D (K ) ) 8 , 9 , 8 CONTINUE GC TC 16 I F ( K - 2 )16,17,10 IF (K -1 3) 13,14, 11 IF CK -1 5) 12,17,17

GREACGREAD

2526

G R E A C " 27 GREAC 28 GREAD 29 GREAD 30 GREAD 31GREAD 32 GREAD 33 GREAC 34GREAT 35 GREAC 36GREACGREAD

3730

GREAC 31 GREAD 32 GREAD 33

10=34 j

_________ _______

5 AGE EN G01720

12 5 IGN= S I G N * (- 1 GC TC 16

: BUILD DATA VALUEL 3

14 LAI14215 L 6

O U T ( I )= O U T ( I)*10.+FL0AT(K-3) I F ( MM) 16♦ 16, 15 I F ( I C P ) 142, 142 , 141 I DP = MM I DP = I CP + 1 MM*MM+_1

GREAD=3^ GPEAC 3^ GREAD 31 GREAC 3£ GREAD 35 CP.EAC 4<| GREAD 41 GREAC 4J

17

CONTINUE J = J-l IS=J +1

G R EAC M

: INSERT DECIMAL POINT AND SIGN

+KgREA0K4! GREAC 4 GREAC 4i

ONE WORD INTEGERS

:ORE REQUIREMENTS FOR GREAC COMMON 0 VARIABLES 106 PROGRAM 37 C

RELATIVE ENTRY >OINT ADDRESS IS CC7C (HEX)

;NC OF COMPILATION

'/ CUP

*CELET E :ART ID 2001

GREAC CB ACDR 1220

2CC 1 DB CNT 001 8

*STORE WS UA GREAD 2001 2001:ART ID 2001 DB ACDR 1850 DB CNT 001B

Y (I )=Y ( I )-YMEAN COMPUTE TOTALS

X T O T = X T O T + X ( I ) Y T O T * Y T O T + Y ( 1 )

GRYLL 26G R Y L L 27GRYLI^28 G R Y L L , 29

X Y T O T = X Y T O T + X ( I ) * YJ I ) X 2 T O T = X 2 T O T + X ! I ) * X ( I ) Y 2 T OT = Y 2 T O T + Y ( I ) *Y ( I ) CONTINUI

GRYLL 30GRYLL 31 GRYLL 32

r.GRY.t't=33COMPUTE SAMPLE MEAN

^ X B A R = X T O T / A G G RVALUES GRYLL 34

GRYLL^35YBAR=YTOT /A GGR X Y B A R = X Y T O T / AGGR

GRYLL 36 G R YL U= 3?

X2B AR =X2T0T/AGGRY2B AR =Y2T0T/AGGR

GRYLL 38GRYLL 39

■ 4 - ifnr* - -i’T.ft

A 1.3 (conti.)

AGE E0 000295

S.E

DO 4 I = 1» K COVARIANCE

COV AR= COV AR + (X ( I )-XBAR )*(Y( I J-YBAR)VARIANCES

V A R X = V A R X + (X (I)-XBAR)*(X( I )-XBAR)VARY=VARY + ( Y ( I J-YBAR)*(Y( I )~YBAR)

CORRELATION COEFFICIENTC = C O V A R / S Q R T ( V A R X * V A R Y )I F (N - 2 )5,6 » 6

SOLUTION BY X-REGRESSION SLOPE OF LINE

A=VARY/C OVA R VARIANCE OF DEVIATIONS

S = (V A R X - C O V A R * C O V A R / V A R Y )/ F L O A T ( K-2 )S.E. OF SLOPE

D= S Q R T (S /V A R Y )D=D*A*A OF INTERCEPT

E = S Q R T ( S * ( l . / A G G R + Y B A R * Y B A R / V A R Y ) )E=-E*A GO TO 7

SOLUTION BY Y-R EGRESS ION SLOPE OF LINE

A=COV AR/V ARX VARIANCE OF DEVIATIONS

S = ( V A R Y - C O V A R * C O V A R / V A R X )/ F L O A T (K-2)S.E. OF SLOPE AND INTERCEPT

S Q R T (S /V A R X )E = S Q R T ( S * ( l . / A G G R + X B A R * X B A R / V A R X ))

INTERCEPTB = Y BAR-A*X BAR IF (N -2 )14,14,8

SOLUTION BY DOUBLE REGRESSION SUM OF SQUARES OF PER PEN DICULAR DISTANCES

P D 2 = 0 .DO 9 1=1,KPD2 = PD2+(A*X( I )-Y( I ) + B )*<A*X(I)-Y{I)+B)

(. , P D 2 = P D 2 / ( A*A+1. )OPTIMISATION OF MEAN SQUARE DISTANCE PERPENDICULAR DISTANCE OF CENTROID

0 P D C E N = ( A * X B A R - Y B A R + B )/(l.+A*A)INTERIM VALUES

F=F+1.S T O R l = 2 . * A G G R / ( 1 . + A * A )STOR 2=B *X8 AR -XY BARSTOR3 = Y2BAR - X2BAR + B * (B - 2.*YBAR)

FIRST DIFFERENTIAL COE FFICIENTSGRDA=STORl*( STOR2- ( A / ( 1 ,+A*A ) )* ( STOR3 + 2 . *A*STOR2 ) ) GR DB= 2.* AG GR* PDC EN

SECOND DIFFERENTIAL COEFFICIENTSG R D A 2 = S T O R l * { S T 0 R 3 - 2 . * A * ( 3 . + A * A )* S T O R 2 - 3 .* A * A * X 2 B A R )/(( l.+A*AJ*

1 ( 1 . + A * A ))GRDB2=ST0R1G R D A B = S T O R l * ( X B A R - 2 . * A * P D C E N )

INVERSION OF THE HESSIAN MATRIX DETERMINANT

DE T= GR DA 2* GR DB 2 -G RD AB *G RD AB

GRYLL 40 GRYLL 41 GRYLL 42 GRYLL 43 GRYLL 44 GRYLL 45 GRYLL 46 GRYLL 47 GRYLL 48 GRYLL 49 GRYLL 50 GRYLL 51 G R Y L L A 5 1 G R Y L L B 5 1 GRYLLC51 GRYLL D 5 1 G R Y L L E 5 1 G R Y L L F 5 1 G R Y L L G 5 1 G R Y L L H 5 1 GRYLL 52 GRYLL 53 GRYLL 54 GRYLL 55 GRYLLA55 GRYLL B55 GRYLLC55 GRYLLD55 GRYLLE55 GRYLL 56 GRYLL 57 GRYLL 58 GRYLL 59 GRYLL 60 GRYLL 61 GRYLL 62 GRYLL 63 GRYLL 64 GRYLL 65 GRYLL 66 GRYLL 67 GRYLL 68 GRYLLA68 GRYLL 69 GRYLL 70 GRYLL 71 GRYLL 72 GRYLL 73 GRYLL 74 GRYLL 75 GRYLL 76 GRYLL 77 GRYLL 78 GRYLL 79 GRYLL 80 GRYLL 81 GRYLL 82

A 1.3 (cont.)

'AGE 3 EOOOO 29 5

NEW

NEW

3

DET = DET *1 -1.)I F ( D ET )11, 14, 11

INVERTED MATRIX H 1 = G R D B 2 /DE T H2=-GRDAB/DET H3 = H2H4=GRDA2/DETVALUES OF SLOPE AND INTERCEPT AA=A +H1 *GR DA +H2 *G RDB BB=B+H3* GRD A+H 4*G RD BVALUE OF SUM OF SQUARES OF PER PEN DICULAR DISTANCES SUM= 0•DO 12 1=1,KS U M = S U M + ( A A * X ( I )—Y CI )+BB)*(AA*X(I)-Y(I)+BB)SUM= S U M / (A A * A A + 1•)

TEST FOR VALIDITY OF CORRECTION OP T= (PD 2-S UM )/P D2 I F ( O P T ) 131,131,13

Br*PLY CORRECTIONS A= A A B = BB PD2 = SUMI F ( 1•-(O P T * 1.E 0 4 ))10,14, 14 F = -F

REPLACE AXESDO 15 1=1 ,'K X( I ) = X ( I )+XMEAN Y ( I ) = Y ( I ) + YMEAN B=B+ YME AN- A* XME AN RETURN END

GRYLLGRYLLGRYLLGRYLLGRYLLGRYLLGRYLLGRYLLGRYLLGRYLLGRYLLGRYLLGRYLLGRYLLGRYLL

8364858687888990919293949596 9 7

GRYLL 98 GRYLL 99GRYLL100G R Y L L 101G R Y L L 102 GRYLL103GRYLL104 GRYLL 105GRYLLA05

G R Y L L 107 G R Y L L 108 G R Y L L 109 G R Y L L 110 GRYLL111 G R Y L L 112

EATURES SUPPORTED ONE WORD INTEGERS

ORE REQUIREMENTS FOR GRYLL COMMON 0 VARIABLES

ELATIVE ENTRY POINT ADDRESS IS 0062 (HEX)

86 PROGRAM 1058

ND OF COMPILATION

A 1.4

// JOB 1001 1002

LOG DRIVE CART SPEC CART AVAIL 0000 1001 10010001 1002 1002

VI MOO CONFIG 8K

CCAT VERS ION D.M. SYSTEM VI MOOi t M f j H P L O T D N q

/ / F O R* I O CS (C A R D . 1132 PR INTER *PLOT T E R )*IOCS( CARD.TYPEWRI TER * KEYBOARD, 11.3 2 PR I NTER pPAPER TAPE .DISK) ONE WORD INTEGERS

« LIST SOURCE PROG RAMDIMENS ION RES IS C 16 > RUN I16.4) »TITLE(6)DATA B/« •/

C READ TITLEIF BLANK FINISH7 R E A D (2 t100) TITLE

IF ( T I T L E { 1 ) - B ) 20,21.20

C MOVE PEN TO L*HoSt AND PA PE R FORWARD

20 CALb S C A L F ( l o O . l c O . O * )CALL F P L O T (1♦ 7c6*13oO)CALL S C A L P ( l * 0 . 1 * 0 » 0 o « 0 o )

C DRAW 3 LINES TO DIVIDE GRAPHS AND GO BACK TO L.H.S*CALL F P L O T ( l » 0 * 0 » - 0 * 8 5 )CALL F P L O T ( 2 . 8 « 2 » “ Oo85)CALL FP L0T (1. 0*0*-6.2>CALL F P L O T ( 2 , 8 . 2 > - 6 « 2 >CALL F P L O T (1.0.0 ,-11,6)CALL FPLOT(2, 8. 2.-11. 61- CALL F P L O T ( 1 .OoO.OcO)

C WRITE TITLECALL F C H A R ( 1 • 0 8 . 0 ♦ 2 f0«2,0•0)W R I T E ( 7 * 1 0 0 ) TITLE

100 FORMAT(6A4)CALL F P L O T (1 ,1. ,0* >DO 16 L = 1 »2CALL S C A L F (1 . 0 . 1 o O . O . , 0 o )

PAGE 1 C C S T F 6 7 5

DO 2 1=1.16R E A D (2.102) RES I S (I )*(R U N ( I »K ).K = 1,4)

C IF FIRST RES I ST AN CE IS ZERO NO CO MPRESSION DATA I F ( R E S I S ( 1 ) )6 » 7.6

C IF RE SI ST AN CE IS ZERO STOP READ ING AND CALCULATE RANGE 6 I F ( R E S I S ( I ))2.3.22 CONTINUEC FIND RANGE OF RE SI STA NCE S102 F O R M A T ( F 9 * 3 » 4 ( 1 X # F 6 & 4 ) )3 11=1-1

PHY DRIVE 0000 0001

1002 * C C S T F 6 7 5

RANGE = RES IS( I I ) - RES I 5(1 ) IF(L~1)14»13»14

C TOP IS TOP OF GRAPH AREA 13 TOP =-1,

GO TO 1514 TOP =-6 o 3515 CALL FCHAR(1.0t-«5+TOPtO.2*0.2i0o0)

I F (L - l )19 * 17 * 19

C WRITE GRAPH DESCRIPTION17 W R I T E (7 * 101) ‘101 FORMAT( 1 TENSION ')

GO TO 18 19 WRITE(7,107)107 FORMAT('COMPRESSION* )18 CALL SCALF(1.0,1*0,3.0,0.)

CALL FPLOT(1,1. ,8,0)BACK -RANGE-(TOP*RANGE/5,)

\C CHANGE SCALE AND ORIGIN FOR PLOTTING

CALL SCALF(1/0.02»5•/RANGE *-•052 * BACK)

A 1.4PAGE 2 C C S T F 6 7 5

C NOW FOR* THE ACTUAL PL OTT ING DO 4 J - 1 , 1 I Y = R E S I S ( J ) - R E S I S ( 1)CALL FCHAR (- 0*08,Y,«l m 1»0)

I F {R E S I S (J ) ~ 9 9 9 9 o )10,10,1110 W R I T E (7,201) RESIS(J)2 01 F O R M A T (F 9•3)

GO TO 1211 W R I T E (7 * 203) RESIS(J)203 F O R M A T (F 9 . 2 )12 DO 4 K-1,4

C IF X VALUE IS lo DON'T PLOT I F (R U N ( J >K ) -* 1 ,>5*4*5

5 CALL F C H A R (R U N (J »K ) ,Y , 0 « 1 , 0 o1 » 0 00 )W R I T E ( 7 ,200) K

200 FORMAT(II)4 CONTINUE

C DRAW X “AXISCALL FG RI D( 0» -# 05 0 * 0 * 0 . 0 5 * 2 >X = ~ • 1DO 9 1=1,3 X = X + 0 •05CALL F C H A R ( 0 0 5 , - . 1 7 * R A N G E / 5 ,**08 *.08 *0)

9 W R I T E (7 * 202) X202 F O R M A T ( F 5 . 2 )

C LINE UP FOR NEXT GRAPHCALL F P L O T (1 *~ •076 * BACK)

16 CONTINUEGO TO 7

A 1.4

2 1 CALL E-XIT END

FEATURES SUPPORTED ONE WORD INTEGERS IOCS

CORE RE QU IR EM EN TS FOR COMMON 0 VARIA BLE S 198 PROGRAM

END OF CO MPI LA TIO N

// DUP

# DELETE IMGRFCART ID 1002 DB ADDR 440F DB CNT 002C

PAG E 3 C C S T F 6 7 5

630

*STORE UA IHGRF 1002 1002CART ID 1 0 02 ’ DB ADDR ‘440F DB CNT 002C

A 2.1

BENDING RIG FOR 1» STRAIN-GAUGE SUBSTRATES

Material;- Mild Steel, Duralumin, Brass, or Stainless Steel, except where stated.All fixing screws may be 4B.A. or 6B.A.

— - 6 3 -----------

PLAN VIEW

. . . . ... .rA

|lll

)3i_bi-L-__'l ■ ■

d e t a :L A

. 1In

10-jvjr• l I

fo-Z6-

Bearing Block. Reamed as a bearing for part C.

O* 2!i «, U -Jt

r\?i*Ty SS yi =0

H oJLS_

SIDE ELEVATION Shown with one guido- plate removed.

10

TU)3-

ij r I h <7« 5 2 "_ A-.lu.__i___ vS ju_‘ t i 1

< >nc.-=.-W- J'. 'C-t.-.

Hill

d e t a i l b

End Block. Tapped 4B.A. to fit part C.

DETAIL CLead Screw. Material;- Silver Steel 4 m m dia„, threaded 4B*A. at one end. The sleeve, GmrnO.D., is hard-soldered in position and threaded OB.A.

-*— z s -— r-H» 1

0 ©u7 1r

-*4 & !-*- -*43 U-I th-

Slide Block. Tapped.OB.A. to fit part C.

DETAIL E Work Holder. 2 off,

‘Wd/dL Jo 'd^rrp^cjwsTr f

RfAc

XnM

sp

->- x

l! a

PF.M.

A 2.4

jx> -7w x>4 rc u » j

A 2.6

A 2.7

V

Grap

h Da

ta

5032

Lo

g 3

A 2.8

~1 ?. 3 . ' . 5 6 7 8 9 1 2 3 4 5 C 7 8 9 J

■

A 2.9

THC

1;‘f

4.u\' X-si_J

r

'~usnypO>NYyV\j

A 2.10

?A

I\-

o(l5\A

SL \K

£

A 2.11

§X— O CO f'' i£>

otu»|_| OOOI -^ 7 » ^ w v y T r T y ^ -r * CL .*t 1/ CJ-

APPENDIX 3

STRAIN GAUGE FACTOR CORRECTION CALCULATIONS

(i) Virgin Gauge

X YAPP SHORT x yREAL SHORTREAL LONG APP LONG yApp LQ^G YApp SH0RT

where: Y ^ at = Real strain gauge factor of virgin filmKbnLi i-jUJNo

Y.^. = Strain gauge factor of virgin film assuming‘APP LONGfour point bending

Y ™ ..tATim - Result of strain measurements on virgin film which 'APP SHORTY»tati had gold electrodes extended to bombardment area.'APP LONG

Four point bending assumed.

= Result of the calibration of the short geometry 'REAL SHORT JY . ^ with micro-measurements strain gauge.'APP ShORl

Evaluating we have:-

OR

YREAL LONG YAPP LONG X 1,06 X °*766

Y = Y x 0.814’REAL LONG TAPP LONG

(ii) Implanted Film

S i . 4,^ y < >

\ % *' «'V J « ■v» V '\ *fc \ :^.J—M “1* M A - -VI

- cs.~— v \ A / V

fto- W V w •o

Now,

*T = Ru + RIMP (i)

where R, = total resistance of compound film = resistance of unimplanted film

^IMP^ resds4:ance implanted film

OR

Let the specimen be strained in the bending rig then:-

ARt = ARU + ARIHp

ART ~ RuYue2 + RIMPYIMPE1 (ii)

where R = resistance uYu - strain gauge factor j- of the unimplanted film e2 = strain

R„,.„ = resistance IMPYIMP = straan 6auSe factor

= strain■ of the implanted film

Now if we assume a relationship between the two strain levels:-

£2 = KE1 (iii)

substituting (iii) into (ii):-

ART = RuYuKGl + RIMPYIMPE1

thus:-

(ii'O

ART/RT _ RuYuK * RIMPYIMP G1 RU + RIMP

(iv)

Now:-

a r t /r t

YT(app) e~app

where YfCapp) = strain gauSe factor of the combined gaugeassuming 4 point bending

e = apparent strain in specimen assuming 4 point bending,®PP .

(v)

But:-

AR_/R_ £ , , xT T real short (vi)YT(app) " £ X £1 app short

where £ = result from central region strain calibrationreal short ^Eapp short 0.766^

thus substituting (iv) into (vi) we have:-

_ RuY uK + RIMPY IMP 1 , .MYTAPP R + R 0.766 (vu. IMP

Determination of K

Now,

= ^1 + 2 (v iii)

where ^ = total gauge length

Z^ = length of implanted gauge

Z = length of unimplanted gauge

mm

i ' )

Hence

AJZ.t = A£^ + A&2

OR

eT^T ~ Zl £l + Z2 C2 (ix)

where = integrated strain over &T= integrated strain over

e2 = integrated strain over &2

From equation (ix):-

thus:-

e2 (eT/ei^T “ *1

evaluating

= 1.3 cm5, = 0.67 cm

2 0.63 cm

fl = £long - 1 (from part (i))

therefore

and

Note

where

<ylSubstituting this value of K into equation (vii)

R Y 0.879 + RTMnY_.m .u ‘u IMP IMP „ 1’T APP (R t RTM_) 0.766u IMP

Y k APPRT °’766 - V u °'879IMP - RIHp

R^ can be determined from:-

^2*u *= *B1

Rri = resistance of gauge before implantation