Scanning tunneling spectroscopy (STS)

A conducting tip probes the energy-dependent local density of states by recording tunnel current versus applied bias, often measuring $dI/dV$ with a small bias modulation and lock-in detection. At low temperature and for slowly varying tip density and matrix element, $dI/dV$ is proportional to sample local density of states at the corresponding bias energy. Thermal broadening, surface structure and energy-dependent tunnelling selectivity limit a direct interpretation as bulk band structure.

Interference between incident and elastically reflected surface-state waves gives density oscillations proportional to $\cos (2kx+\varphi )$. Their real-space period is $\pi /k$, half the travelling-wave wavelength.

Vibrational excitation opens additional tunnelling channels at biases satisfying $|eV|=\hslash \omega$. A step in differential conductance gives paired opposite-sign features in its voltage derivative.