Dynamical screening in the scanning tunneling microscope and metal-insulator-metal junctions

We investigate electron tunneling in a system consisting of two curved metal surfaces separated by insulator or vacuum. In particular, we calculate the modifications of the tunneling barrier due to dynamical screening, i.e., interaction with charge fluctuations. We apply our general results to the planar metal-insulator-metal (MIM) junction, and to the scanning tunneling microscope (STM), describing the tip and the sample surface in STM by two rotational hyperboloids. We analyze the influence of the shape, dielectric properties, and work functions of both metals on the tunneling characteristics in the MIM and STM systems. For metals with different plasma frequencies, charge-fluctuation modes are effectively decoupled, and the electron interaction with these modes is significantly different than in the case of like metals, causing asymmetry in the barrier and also in the tunneling currents and conductivities. We also show that, for geometrical reasons, the tunneling barrier in the STM is lowered near the tip apex, which leads to focusing of the tunneling current and increased lateral resolution of STM.