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removed the surface roughness but the waviness of the surface was still present (compare figures 9-1 and 9~5) • This technique greatly reduced the surface resistance by removing the surface roughness and some of the work—hardened layers.

C e C L C u r r e n t A -m p s 119

C«.a VoLta<)<. VoLti

F IG l/A E q-4- : C U R R E Nt/v o uT A O E C H A A A C T E R l S r / C OF E L E C T R O PO LIS H /N O CEl-t.

tfacjni-ficakion XlOO

Ho-ri^ontoi l'laj ni^cca t io n X lO O \/i rtlcaC M a g n i f i c a t i o n y

2

FIGURE q-5 : PHOTOGRAPH AND TAL y Süß F TRACE OF ELECTRO POUSHE D COPPER

fiacjni-f ¿cat ion X l O O Ho-rijonf'aí l'laj-ni^lcaí’tO'*' X 3 .0 0 Vtfticat Ma^ni^icattoiv VC 2.0,000 F IG U R E « Í - 5 : PHOTOGRAPH A N D T A L y S U R F T R A C E O F EC ECtRO POLISHED C O P P E R

m

9-2— 3 Annealing

No annealing facilities were available for this work. I ara therefore grateful to Shell Thornton Research Centre for

annealing the samples. The removal of the cold-worked conditions occurs by three successive processes, (^9,70)naraely recovery, recrystallization and grain growth. Recovery is the re-arrange- ment of the dislocations introduced b y cold-working of the metal to reduce the lattice strain energy. Recrystallization is a nucleation and growth process whereby stress-free grains grow from nucleii in the deformed matrix. Structure-sensitive properties of the material change significantly during this stage. The final stage, grain growth, occurs with extensive annealing when larger grains grow at the expense of small grains.

Annealing was performed at pressures below 10 ^ Torr. The rf conductivity of the eloctropolished sample, annealed at 850°C for one hour increased to a value approaching that of the dc standard. The rf conductivity of the machined samples, annealed at 650°C for

2h

Bussey (57) ^ using a similar cavity, measured the conductivity of copper at 10 GHz to be 55.6 x IO6

(SI

amount of work-hardoning would therefore bo present. There would, howover, seem to be some agreement between this result and those

shown in Table 9-1 for tho annoalod samples.

9-3 Measurements on Thin Film Samnles

The actual surface resistance, R, of a conductor of finite thickness is complicated by tho presence of reflections from the

(52)

back surface of the sample. It can be shown ' that the surface

resistance of such a conductor is givon by

sinh (2t

/<f'

cosh (2t/<f> 1 O O w /■—s ro _$

where R is the surface resistance of an infinitely thick s

sample

t is the thickness

S is the skin depth

A full derivation of equation 9-1 may be found in Appendix 5. A plot of R/Rs versus is given in figure 9-6. It can be seen

that for thicknesses greater than three skin depths the surface resistance approaches that for the infinite case. However, it can also be seen that a minimum occurs when t/<f - Tf/2 (~1.57). This can bo explained by considering the relationship between the current, I_, on the front surface and tho back surface current I£ If the intrinsic impedance of the film is much loss than that of the propagating media on either side, then those quantities are related by (see Appendix 5)

123

¿■6

Thickness to S/ci-n Depth Ratio t / S

F IG U R E q - 6 ¡ G R A P H SHOW/Wfr V R R iA T / O N O F S U R F A C E R E S I S T A N C E