Moiré pattern in scanning tunneling microscopy: Mechanism in observation of subsurface nanostructures

The origin of moir\'e patterns in scanning tunneling microscopy (STM) is clarified. It is found that two factors are important in observing the moir\'e patterns in STM. One is interface scattering in lattice-mismatched systems, which produces nanoscale lateral waves. The other is a qualitative difference of decay behavior in the vacuum region between the nanoscale and atomic-scale lateral waves, because of the typical value of work functions. Different from those in transmission electron microscopy (TEM), the moir\'e patterns in STM are not the beat of waves but are essentially due to three-dimensional tunneling. Furthermore, it is found that the nanoscale waves propagate through many layers without decay due to the typical value of Fermi energies. This means that nanoscale structures can be observed in STM even if they are buried deep in surfaces. These findings are evidently demonstrated by numerical calculations. The mechanism of this paper clarifies conditions for obtaining subsurface information by STM. \textcopyright{} 1996 The American Physical Society.