Scanning tunneling spectroscopy
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Scanning tunneling spectroscopy (STS) performed with a scanning tunneling microscope (STM) is a technique which gives information about the local density of electronic states on surfaces at atomic or molecular scale. The tunneling current (I) is measured from the variation in the bias voltage (V) between the probe (tip) and the sample surface at the measurement point. As a result, the current-voltage (I-V) curve or the normalized differential conductance-voltage (dI/dV)/(I/V)-V curve is obtained. As the relation between the tunneling current spectrum and the surface electronic state is sensitive to the sample and the configuration of the tip, a strict calculation is needed in each case. The local electronic state, however, is given by the following approximation:
where E is the electron energy based on the Fermi state of the sample, ρs is the density of the electronic state of the sample surface, and ρt is the density of the electronic state of the tip. The tunneling of electrons between the two conductors continues until the Fermi levels are equal. In this case, the tunneling current shows electron transfer from the filled state of the tip to the empty state of the sample. Therefore, dI/dV is expressed as follows under the assumption that the density of the electronic state of the tip has no variation within the range of measurement:
Consequently, the first derivative dI/dV is proportional to the density of the electronic state of the sample.
Actual spectroscopic images corresponding to the spatial variation of dI/dV contain topographic and electronic structure information. The first derivative dI/dV can be obtained from the measured I-V curves by calculated differentiation. In order to minimize the influence of the separation between the tip and sample, the differential conductance dI/dV should be normalized to the total conductance I/V. The normalized value (dI/dV)/(I/V)= (d ln I/d ln V) appropriately represents the density of the electronic states.
