A theory of vacuum tunneling microscopy

Electron tunneling across the surface potential barrier has been applied for many years to probe surface atomic and electronic structure. This had led, for example, to the development of the field emission microscope, and more recently, of electron tunneling spectroscopy of insulating barriers in MIM structures. Some four years ago, Binning, Rohrer and coworkers developed the first vacuum tunneling microscope with atomic resolution. In this device, electrons tunnel across a vacuum gap between a sample surface and a scanning tip. Since then, a growing number of research groups have constructed such devices. The STM has provided detailed insight into the atomic structure of surfaces. The feasibility of scanning tunnel spectroscopy (STS) has been demonstrated, though fewer results have been reported. However, before the full potential of the twin techniques of STM and STS can be realized, two problems have to be resolved: (1) A more quantitative, but tractable theory, has to be developed to permit an unambiguous interpretation of the data. (2) A more reliable procedure for the preparation of the tip has to be developed to assure the quantitative reproducibility of the data. A critical review of tunneling theory and the transfer Hamiltonian formalism is presented. Inelastic and elastic resonant tunneling are discussed. The construction and operation of the STM are briefly described. The transfer Hamiltonian theory of the device is reviewed. The concept of surface corrugation is also discussed. Recent results by Kuk on the dependence of the observed corrugation amplitude on the atomic structure of the scanning tip are analyzed. Lastly, image potential states and their significance in the STS study of the electronic structure of the surface barrier are considered.

https://iopscience.iop.org/article/10.1088/0031-8949/35/2/007/pdf

Tunneling and Scanning Tunnel Microscopy: a Critical Review

The transfer Hamiltonian approach to the scanning tunneling spectroscopy (STS) is extended in a twofold direction. First, a theory representing an extension to the case of arbitrary temperature and applied voltage of the work of Chen [Phys. Rev. B 42, 8841 (1990)] is developed. Within this framework analytical expressions of the tunneling current and its derivative can be obtained under rather general assumptions for the tip density of states. In particular, the situation of a general electronic structure of the tip states is considered. The calculation of theoretical $dI∕dV$ curves and conductivity maps, to be compared with experiments and numerical simulations, becomes possible and these results lead also to the best normalization procedure of the current derivative to obtain the desired physical information, namely, the sample local density of states, provided the electronic tip properties are known. Second, a general theoretical description in terms of the system spectral densities is derived, providing a generalization of the approach developed by Feuchtwang and Cutler [Phys. Scr. 38, 252 (1988)]. We believe that with these achievements the forecast of STS theory gets significantly closer to the experimental results.

Transfer Hamiltonian analytical theory of scanning tunneling spectroscopy

Inelastic Electron Tunneling Spectroscopy (IETS) is used for the investigation of vibronic and electronic excitations of molecules deposited as interlayers in aluminum/ alumina/lead tunneling junctions. In this review the method itself is briefly discussed. As examples, investigations by IETS on sublimated merocyanine and phthalocyanine dye molecules are reviewed. Then further doping techniques developed by Jaklevic and Gaerttner and applications of IETS to problems in the physics of interfaces are discussed.

Excitation of molecules in inelastic electron tunneling spectroscopy

A model independent, transfer Hamiltonian theory of the scanning tunneling microscope (STM) is presented. The theory is used to determine which surface characteristics are probed by the STM. It is demonstrated that the most useful presentation of the data is the two-dimensional Fourier transform of the tunneling current I(z; k) or, for an ordered sample surface, the coefficients of the two-dimensional Fourier series expansion of the periodic current, I(z; G). In this case, the inversion of the STM data yields the corresponding two-dimensional Fourier transform (or expansion coefficients) of the spectral density. From these, less microscopic or detailed quantities such as the LDOS or its Fourier transform can be determined. It is also demonstrated that approximation schemes to simplify the inversion of the STM data yield less detailed or fundamental characteristics than the exact inversion. The representation of the tip's effect on the tunneling current as an instrument function is explored and used to obtain a semi-empirical procedure for the determination of this function. This obviates the need for a precise model of the tip which is generally required to determine the instrument function. The conditions under which the tunneling current is proportional to the LDOS are found to be restrictive. An extension of the theory to the case when the transfer Hamiltonian is inapplicable is suggested. The application of the theory to elastic or resonant scanning tunneling spectroscopy is also indicated.

http://iopscience.iop.org/article/10.1088/0031-8949/38/2/028/pdf

T. E. Feuchtwang

Papers

Tunneling theory without the transfer Hamiltonian formalism. V. A theory of inelastic-electron-tunneling spectroscopy