The energy resolution function of a tunnel junction

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.