  The tunnel junction between tip and sample in a scanning tunneling microscope
is an ideal platform to access the local density of states in the sample
through the differential conductance. We show that the energy resolution that
can be obtained is principally limited by the electromagnetic interaction of
the tunneling electrons with the surrounding environmental impedance as well as
the capacitative noise of the junction. The parameter tuning the sensitivity to
the environmental impedance is the capacitance of the tunnel junction. The
higher the junction capacitance, the less sensitive the tunnel junction to the
environment resulting in better energy resolution. Modeling this effect within
P(E)-theory, the P(E)-function describes the probability for a tunneling
electron to exchange energy with the environment and can be regarded as the
resolution function of the tunnel junction. We experimentally demonstrate this
effect in a scanning tunneling microscope with a superconducting aluminum tip
and a superconducting aluminum sample at a base temperature of 15mK, where it
is most pronounced.
