  Quantum-confined electronic states such as quantum-well states (QWS) inside
thin Pb(111) films and modified image-potential states (IPS) above the Pb(111)
films grown on Si(111)7$\times$7 substrate were studied by means of
low-temperature scanning tunnelling microscopy (STM) and spectroscopy (STS) in
the regime of constant current $I$. By plotting the position of the $n-$th
emission resonances $U^{\,}_n$ versus $n^{2/3}$ and extrapolating the linear
fit for the dependence $U^{\,}_n(n^{2/3})$ in the high-$n$ limit towards $n=0$,
we estimate the local work function for the Pb(111) film: $W\simeq 3.8\pm
0.1\,$eV. We experimentally demonstrate that modifications of the shape of the
STM tip can change the number of the emission peaks associated with the
resonant tunnelling via quantized IPS levels for the same Pb terrace; however
it does not affect the estimate of the local work function for the flat Pb
terraces. We observe that the maxima in the spectra of the differential
tunnelling conductance $dI/dU$ related to both the QWS and the modified IPS
resonances are less pronounced if the STM tip becomes more blunt.
