Scanning tunneling spectroscopy (STS), an extension of scanning tunneling microscopy (STM), is used to provide information about the density of electrons in a sample as a function of their energy.
In scanning tunneling microscopy, a metal tip is moved over a conducting sample without making physical contact. A bias voltage applied between the sample and tip allows a current to flow between the two. This is a result of quantum tunneling across a barrier; in this instance, the physical distance between the tip and the sample
The scanning tunneling microscope is used to obtain "topographs" - topographic maps - of surfaces. The tip is rastered across a surface and (in constant current mode), a constant current is maintained between the tip and the sample by adjusting the height of the tip. A plot of the tip height at all measurement positions provides the topograph. These topographic images can obtain atomically resolved information on metallic and semi-conducting surfaces
However, the scanning tunneling microscope does not measure the physical height of surface features. One such example of this limitation is an atom adsorbed onto a surface. The image will result in some perturbation of the height at this point. A detailed analysis of the way in which an image is formed shows that the transmission of the electric current between the tip and the sample depends on two factors: (1) the geometry of the sample and (2) the arrangement of the electrons in the sample. The latter is described quantum mechanically by an "electron density". The electron density is a function of both position and energy, and is formally described as the local density of electron states, abbreviated as local density of states (LDOS), which is a function of energy.
Spectroscopy, in its most general sense, refers to a measurement of the number of something as a function of energy. For scanning tunneling spectroscopy the scanning tunneling microscope is used to measure the number of electrons (the LDOS) as a function of the electron energy. The electron energy is set by the electrical potential difference (voltage) between the sample and the tip. The location is set by the position of the tip.
At its simplest, a "scanning tunneling spectrum" is obtained by placing a scanning tunneling microscope tip above a particular place on the sample. With the height of the tip fixed, the electron tunneling current is then measured as a function of electron energy by varying the voltage between the tip and the sample (the tip to sample voltage sets the electron energy). The change of the current with the energy of the electrons is the simplest spectrum that can be obtained, it is often referred to as an I-V curve. As is shown below, it is the slope of the I-V curve at each voltage (often called the dI/dV-curve) which is more fundamental because dI/dV corresponds to the electron density of states at the local position of the tip, the LDOS.
Introduction
right|thumb|250 px|Mechanism of how density of states influence V-A spectra of tunnel junction
Scanning tunneling spectroscopy is an experimental technique which uses a scanning tunneling microscope (STM) to probe the local density of electronic states (LDOS) and the band gap of surfaces and materials on surfaces at the atomic scale. Generally, STS involves observation of changes in constant-current topographs with tip-sample bias, local measurement of the tunneling current versus tip-sample bias (I-V) curve, measurement of the tunneling conductance, <math>dI/dV</math>, or more than one of these. Since the tunneling current in a scanning tunneling microscope only flows in a region with diameter ~5 Å, STS is unusual in comparison with other surface spectroscopy techniques, which average over a larger surface region. The origins of STS are found in some of the earliest STM work of Gerd Binnig and Heinrich Rohrer, in which they observed changes in the appearance of some atoms in the (7 x 7) unit cell of the Si(111) – (7 x 7) surface with tip-sample bias. STS provides the possibility for probing the local electronic structure of metals, semiconductors, and thin insulators on a scale unobtainable with other spectroscopic methods. Additionally, topographic and spectroscopic data can be recorded simultaneously.
Tunneling current
Since STS relies on tunneling phenomena and measurement of the tunneling current or its derivative, understanding the expressions for the tunneling current is very important. Using the modified Bardeen transfer Hamiltonian method, which treats tunneling as a perturbation, the tunneling current (<math>I</math>) is found to be
where <math>f\left(E\right)</math> is the Fermi distribution function, <math>\rho_s</math> and <math>\rho_T</math> are the density of states (DOS) in the sample and tip, respectively, and <math>M_{\mu\nu}</math> is the tunneling matrix element between the modified wavefunctions of the tip and the sample surface. The tunneling matrix element,
\ ,</math>|
describes the energy lowering due to the interaction between the two states. Here <math>\psi</math> and <math>\chi</math> are the sample wavefunction modified by the tip potential, and the tip wavefunction modified by sample potential, respectively.
For low temperatures and a constant tunneling matrix element, the tunneling current reduces to
which is a convolution of the DOS of the tip and the sample.
By using modulation techniques, a constant current topograph and the spatially resolved <math>dI/dV</math> can be acquired simultaneously. A small, high frequency sinusoidal modulation voltage is superimposed on the D.C. tip-sample bias. The A.C. component of the tunneling current is recorded using a lock-in amplifier, and the component in-phase with the tip-sample bias modulation gives <math>dI/dV</math> directly. The amplitude of the modulation V<sub>m</sub> has to be kept smaller than the spacing of the characteristic spectral features. The broadening caused by the modulation amplitude is 2 eVm and it has to be added to the thermal broadening of 3.2 k<sub>B</sub>T. In practice, the modulation frequency is chosen slightly higher than the bandwidth of the STM feedback system. The tip-sample bias is swept between the specified values, and the tunneling current is recorded. After the spectra acquisition, the tip-sample bias is returned to the scanning value, and the scan resumes. Using this method, the local electronic structure of semiconductors in the band gap can be probed. Generally, a minimum tip-sample spacing is specified to prevent the tip from crashing into the sample surface at the 0 V tip-sample bias. Lock-in detection and modulation techniques are used to find the conductivity, because the tunneling current is a function also of the varying tip-sample spacing. Numerical differentiation of I(V) with respect to V would include the contributions from the varying tip-sample spacing. Introduced by Mårtensson and Feenstra to allow conductivity measurements over several orders of magnitude, VS-STS is useful for conductivity measurements on systems with large band gaps. Such measurements are necessary to properly define the band edges and examine the gap for states. Because the topographic image and the tunneling spectroscopy data are obtained nearly simultaneously, there is nearly perfect registry of topographic and spectroscopic data. As a practical concern, the number of pixels in the scan or the scan area may be reduced to prevent piezo creep or thermal drift from moving the feature of study or the scan area during the duration of the scan. While most CITS data obtained on the times scale of several minutes, some experiments may require stability over longer periods of time. One approach to improving the experimental design is by applying feature-oriented scanning (FOS) methodology.
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.
Feenstra et al. argued that the dependencies of <math>T\left(E, eV, r\right)</math> and <math>T\left(eV, eV, r\right)</math> 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 <math>B\left(V\right)</math> normalizes T to the DOS and <math>A\left(V\right)</math> describes the influence of the electric field in the tunneling gap on the decay length. Under the assumption that <math>A\left(V\right)</math> and <math>B\left(V\right)</math> vary slowly with tip-sample bias, the features in <math>\left(dI/dV\right)/\left(I/V\right)</math> reflect the sample DOS,