Thermal strain in thin lead films III: Dependences of the strain on film thickness and on grain size

Abstract

The effects of film thickness h or of average grain size g on strains ε 33 ' due to the mismatch of the thermal expansion coefficients were studied by an X-ray diffraction technique for thin lead films 0.03–1.0 μm thick evaporated onto silicon substrates. Films with the same average grain size and with different film thicknesses were prepared by a sputter-etch-thinning technique after the film depositions had been completed. Films with small grain sizes were prepared by deposition at liquid nitrogen temperature or by seeding a very thin layer of gold or palladium before the lead deposition. These films were cooled from 300 ro 4.2 K using a cold stage attached to an X-ray diffractometer. For films with h < g/5, the ε 33 ' levels were found to be determined by h. The critical film thickness h c was 0.15 μm. h c was defined so that for h < h c no strain relaxation was observed, independent of grain sizes. For h < h c the ε 33 ' values were found ro be proportional to 1/ h. The h dependence on the ε 33 ' values was analyzed based on an assumption that dislocate glide was the dominant strain relaxation mechanism. It was found that the dislocation pinning distance was about four times smaller than the film thickness, which agrees with the previous result obtained by a cantilever beam technique. For films with h > g/5 the critical grain size g c was determined to be about 1 μm. When g > g c the ε 33 ' levels decreased with increasing g. When g < g c the ε 33 ' values were found to be independent of g and also of h. However, ε 33 ' did not reach the calculated maximum strain value. We propose that the difference between the calculated strain and the measured strain was due to an absorption of the strain at grain boundaries. The fact that g c was about six times larger than h c means that g exerted a stronger effect than h did on the inhibition of strain relaxation during cooling to 4.2 K. It was found that the intermetallic compounds Pb 3Au or Pb 2Pd which were formed in the binary films did not greatly affect the inhibition of strain relaxation. The ε 33 ' levels in these binary films were also determined by the grain sizes.