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 ε33' 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 ε33' levels were found to be determined by h. The critical film thickness hc was 0.15 μm. hc was defined so that for h < hc no strain relaxation was observed, independent of grain sizes. For h < hc the ε33' values were found ro be proportional to 1/h. The h dependence on the ε33' 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 gc was determined to be about 1 μm. When g > gc the ε33' levels decreased with increasing g. When g < gc the ε33' values were found to be independent of g and also of h. However, ε33' 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 gc was about six times larger than hc 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 Pb3Au or Pb2Pd which were formed in the binary films did not greatly affect the inhibition of strain relaxation. The ε33' levels in these binary films were also determined by the grain sizes. © 1979.