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Inelastic Electron Tunnelling Spectroscopy is a powerful and versatile technique for obtaining vibrational densities of states of amorphous materials and adsorbed molecules. The experimental device, or tunnel junction, consists of two metal electrodes separated by a thin (2nm) layer of the material under study. This thesis looks at features in the tunnelling spectrum due to electrode phonons, and also at the effects of substrate roughness on the spectrum. Two coupled linear chains are used to model the vibrational behaviour of joined lattices in order to consider the penetration of phonons of one material into the other; penetration does not occur unless the two chains have very similar properties. Work with Al-I-Al-Pb tunnel junctions confirms the model results, as no sign is seen of lead phonon peaks in the tunnelling spectrum. However, other workers have seen lead peaks in Al-I-Ag-Pb junctions, and invoked phonon penetration in explanation. Microscopic examination of similarly prepared silver films reveals that they are pinholed; and this, it is argued, gives rise to the lead peaks. Results are presented on the magnitudes of electrode phonon structure in tunnelling spectra, and models for the occurrence of these features are reviewed. It is argued, from comparison of the experimental data with bulk self energies from superconducting tunnelling, that the electron-phonon coupling responsible is characteristic of the bulk metal; interaction does not take place in the barrier. This is consistent with the linear chain model. The effects of roughening tunnel junctions with calcium fluoride substrates are studied. Little change is noted with undoped junctions, but investigation of formate-doped junctions confirms the loss in dopant peak intensity seen by other workers and some variation is noticed in the rate of loss of intensity between C-H and CO<SUB>2</SUB> modes. The mechanism which best explains these observations is that roughening encourages penetration of the organic layer by atoms of the top electrode metal.