A technique has been developed for tunneling from thin Pb films into Pb single crystals formed by a high-vacuum melting process. A preliminary investigation of the energy-gap anisotropy has been carried out. Data are presented from ten separate junctions, including ones on the (001) and (111) crystal facets. In all cases, two energy gaps, ${\Delta }_1$ and ${\Delta }_2$ (${\Delta }_1<{\Delta }_2$), were apparent in the characteristics and differed from each other by 10-15%. The maximum variation of ${\Delta }_1$ was 5% over the tunneling directions studied, while ${\Delta }_2$ varied by considerably less than this. The maximum observed value of $2{\Delta }_2\mathrm{}\left(0\right)\mathrm{}$ was 2.78±0.01 meV and the minimum value of $2{\Delta }_1\mathrm{}\left(0\right)\mathrm{}$ was 2.36±0.01 meV. A comparison was made with a published theory of the energy-gap anisotropy. In some respects the agreement is fairly good, while in other respects it is poor. No evidence was found for the predicted structure due to critical points of the energy-gap surface in k space. Second-derivative measurements ($\frac{d^{2}V}{d{I}^2}$ versus $V$) showed an extra (compared to results from thin-film Pb junctions) peak in the group of structures associated with the transverse phonon modes.

• Received 21 April 1969

DOI:https://doi.org/10.1103/PhysRev.186.397