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Study of the surface electron states in semiconductors based on the processes of cold emission in scanning tunneling microscopy

Keywords:

А.М. Mandel – Ph.D. (Eng.), Professor, Physics Department, Moscow State University of Technology STANKIN. E-mail: arkadimandel@mail.ru
А.I. Loskutov – Ph.D. (Chem.), Associated Professor, Physics Department, Moscow State University of Technology STANKIN. E-mail: ailoskutov@yandex.ru
V.B. Oshurko – Dr.Sci. (Eng.), Head of Physics Department, Moscow State University of Technology STANKIN. E-mail: vbo08@yandex.ru
G.I. Solomakho – Ph.D. (Eng.), Professor, Physics Department, Moscow State University of Technology STANKIN. E-mail: solgeo@yandex.ru
Ya.А. Fedotova – Student, Moscow State Technical University of Civil Aviation. E-mail: juli_fedotova@mail.ru


It is well known that important information about surface electron states in scanning tunneling microscopy (STM) can be obtained by measurement of so-called current-voltage curves or I–V characteristics. There are some works where sufficient difference between direct and inversed branches of I–V characteristics was observed in case of different adsorbed organic molecules. (“Direct branch” means that positive potential is applied to surface + adsorbate and negative one is applied to tip). It was found that direct curves sufficiently depend on the type of adsorbed molecules while inversed branches were coincident. In traditional STM description transition probability depends on both initial quantum state (surface) and accepting one (tip) in almost similar way. If we take into account that in the case of direct branch electron current from surface to tip is much greater than e-current from tip to surface than idea of possibility cold emission mechanism looks promising. Cold emission means that the electron can have increased probability to leave surface in presence of electric field even if energy of electron in this field is less than work function value. In this case transition probability can be calculated as follows. It is known that probability of emission of surface electron strongly depends on the surface state localizing. Different types of electrons localizing are possible on the real surface: 1-dimensional (1D) localizing is usual for Tamm’s and Shokley’s surface states (it means that electron wave function amplitude exponentially decreases toward to bulk of material); 2D localizing may take place in staircase defects; point defects or impurities can produce 3D localizing. Intermediate case of non-integer n can also have physical meaning: it means that there are several states of different localizing which give contribution (quantum mechanical linear combination) in real state. To calculate the probability of emission we can use method of zero-range potential. According to this method, we present potential in Schrodinger equation as periodic one depending on “non-localizing” coordinates and potential, which is proportional to Dirac’s delta-function depending on “localizing” coordinates. As a result, solutions of Schrodinger equation are proportional to correspondent Green’s functions. Using traditional approximations analytical solution and emission probability were obtained. It was found that the emission probability depends not only on electric field but also on initial electron “localizing dimension” n. In case of very weak electric field and 1D localizing (n = 1) this formula coincides to traditional expression from theory of STM. On the other hand, it predicts possibility of almost direct calculation of “localizing dimension” n from shape of experimental I-V curves. In order to test this theory series of experiments were carried out. In experiments highly-oriented pyrolytic graphite surface was used. Graphite surface was degased by exposure in vacuum (10–5 Pa) during six hours. Scanning tunneling microscope “Solver HM-MFM” with vacuum cell was used for surface analysis. In experiments I-V curves were recorded on the flat surface and near to different topological inhomogeneities (staircases, points etc.). It was found that values n calculated from experimental I–V curves are non-integer and deal with “localizing inhomogeneity dimension” (e.g. stair or pin). These experimental results gave not exact evidence for proposed mechanism. However, they support that proposed mechanism should be taken into account in interpretation of STM results. This mechanism also provides useful information about electron state localization which is very important for micro- and nanoelectronics.
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