STM is known to be used for the investigation of surface topography. However, we are more interested in the electronic properties of our samples which can be analyzed by Scanning Tunneling Spectroscopy (STS). By measuring I-V characteristics, insight in the local density of states (DOS) at the sample surface position at which the tip is located can be gained.

The tunneling current I is, in a simple approximation, proportional to the DOS of the sample surface at the tip position and to the tip's DOS, ρ_s and ρ_t, respectively. Also, the tunneling matrix element T enters:

Here, d denotes the distance between tip and sample, V the applied voltage and E the energy with respect to the Fermi energy E_F. The Fermi functions f involved can most easily be treated if the measurements are conducted at the lowest possible temperature: at low temperatures they can be considered as step functions. Following the theory by Tersoff and Hamann, the sample's local DOS at E_F is measured at tip center. However, a number of assumption concerning the tip has been made.

One of the major problems in STM/STS is its surface sensitivity. Physical (adsorbants) or chemical (oxides) modifications can easily disturb any tunneling measurement. The best what can be done about this is in situ cleaning and keep the sample in UHV.

In order to achieve optimal resolution (spatially as well as energetically) isolation against mechanical vibrations and electrical noise is important.

A sharp-pointed tip (2) is physically attached to a piezo (1). A coarse drive (not shown) allows for coarse positioning of the tip with respect to the sample. It usually enables movements in the μm- to mm-range. By using the piezo the tip is positioned in close proximity (sub- or lower nm-range in z-direction) to the sample (3) to enable tunneling. For this, a bias voltage is applied between tip and sample. The tip is scanned over the sample's surface (in x- and y-direction) by applying the appropriate voltages to the piezo. Here, either the current is kept constant (by keeping a constant local sample-tip distance) and the tip's absolute height is changed accordingly (constant current mode) or vice versa (constant height mode). This, of course, happens computer controlled (5). The resulting image (4) is constructed from the known displacement of the tip. In constant current mode, the images correspond to planes of constant DOS at EF (for low bias).

This scheme was taken from the web but I forgot the source's location. Nonetheless, I thank the author.

• For spectroscopy, the tip is kept at a predefined position (constant x and y) and the feedback loop of the STM controller is opened (constant z).
• Then, the bias voltage V is ramped to obtain the I-V characteristics. To improve the energy resolution a lock-in can be used to modulate V and to measure dI/dV directly.
• From the I-V-curves, information about the local DOS can be inferred (see above). The advantage of measuring I/dV lies in the fact that it is, for smooth T, directly proportional to ρ_S.

thermal equilibrium, zero bias

positive bias: tunneling into empty sample states

negative bias: tunneling from occupied sample states