A group of physicists from Germany, Spain and the UK have solved a long-standing problem in surface science - namely the discrepancy between experimental and theoretical values for the lifetimes of "holes" in metal surfaces. The holes are left when electrons are excited to higher energy bands in the surface. Until now the experimental data and theoretical predictions differed by as much as a factor of seven.
In fact, the researchers have improved both the experiment and the theory. Previous data from photoelectron spectroscopy could not take account of defects in the metal surface, which are known to reduce lifetimes by coupling the surface state electrons to bulk states in the metal.
The group's new set-up uses a scanning tunnelling microscope (STM) operating at 4.6 K, which first identifies a defect-free area of the metal surface (silver, gold or copper). Then the tungsten tip of the STM measures the differential conductance (dI/dV) within that region, effectively measuring the density of electronic states at the surface. A steep rise in dI/dV indicates the presence of surface states and the hole lifetime for the metal can be directly calculated from the width of this onset.
Meanwhile the researchers also set about refining the theoretical description. Two processes limit the lifetime of holes: coupling between electrons and phonons (quantized vibrations of the metal lattice), and inelastic electron-electron scattering. Previous estimates of the latter assumed that the holes would be filled by interband transitions involving bulk electrons near the surface - a "three-dimensional" decay channel. However, the new treatment takes account of surface effects as well as band structure - the competing "two-dimensional" intraband transition significantly increases the contribution from electron-electron scattering.
The new calculations are in good agreement with the STM data. "For the first time," said the researchers, "a consistent account is found for hole lifetimes." They expect to extend their approach to studying adsorbed atoms, alloys and thin films, thereby promising new insight into surface and interface electronic structure.