Scanning Tunneling Spectroscopy - Data Interpretation

Data Interpretation

From the obtained I-V curves, the band gap of the sample at the location of the I-V measurement can be determined. By plotting the magnitude of I on a log scale versus the tip-sample bias, the band gap can clearly be determined. Although determination of the band gap is possible from a linear plot of the I-V curve, the log scale increases the sensitivity. Alternatively, a plot of the conductance, versus the tip-sample bias, V, allows one to locate the band edges that determine the band gap.

The structure in the, as a function of the tip-sample bias, is associated with the density of states of the surface when the tip-sample bias is less than the work functions of the tip and the sample. Usually, the WKB approximation for the tunneling current is used to interpret these measurements at low tip-sample bias relative to the tip and sample work functions. The derivative of equation (5), I in the WKB approximation, is

where is the sample density of states, is the tip density of states, and T is the tunneling transmission probability. Although the tunneling transmission probability T is generally unknown, at a fixed location T increases smoothly and monotonically with the tip-sample bias in the WKB approximation. Hence, structure in the is usually assigned to features in the density of states in the first term of equation (7).

Interpretation of as a function of position is more complicated. Spatial variations in T show up in measurements of as an inverted topographic background. When obtained in constant current mode, images of the spatial variation of contain a convolution of topographic and electronic structure. An additional complication arises since in the low-bias limit. Thus, diverges as V approaches 0, preventing investigation of the local electronic structure near the Fermi level.

Since both the tunneling current, equation (5), and the conductance, equation (7), depend on the tip DOS and the tunneling transition probability, T, quantitative information about the sample DOS is very difficult to obtain. Additionally, the voltage dependence of T, which is usually unknown, can vary with position due to local fluctuations in the electronic structure of the surface. For some cases, normalizing by dividing by can minimize the effect of the voltage dependence of T and the influence of the tip-sample spacing. Using the WKB approximation, equations (5) and (7), we obtain:

Feenstra et al. argued that the dependencies of and on tip-sample spacing and tip-sample bias tend to cancel, since they appear as ratios. This cancellation reduces the normalized conductance to the following form:

where normalizes T to the DOS and describes the influence of the electric field in the tunneling gap on the decay length. Under the assumption that and vary slowly with tip-sample bias, the features in reflect the sample DOS, .