Сканирующая зондовая микроскопия поверхности графита и углеродосодержащих покрытий тема автореферата и диссертации по физике, 01.04.04 ВАК РФ

б/--**- //мг

Физико-технический институт им. А.Ф.Иоффе, Российская Академия Наук

На правах рукописи

Вакар Зафар

СКАНИРУЮЩАЯ ЗОНДОВАЯ МИКРОСКОПИЯ ПОВЕРХНОСТИ ГРАФИТА И УГЛЕРОДОСОДЕРЖАЩИХ ПОКРЫТИЙ

Специальность: 01.04.04. - физическая электроника

диссертация на соискание ученой степени кандидата физико-математических наук

Научный руководитель доктор физико-математических наук главный научный сотрудник Титков А.Н.

Санкт-Петербург- 2001

Contents

Introduction 4 Chapter 1. Scanning Tunneling and Atomic Force Microscopy

Scanning Tunneling Microscopy

1.1. Introduction 12

1.2. Principle of Operation 16

1.2.1. Metal- Metal Tunnel Contact 17

1.2.2. Metal- Semiconductor Tunnel Contact 18

1.2.3. Tunneling Current 18

1.3. Morphology and Atomic Structure Studies 19

1.4. The Current-Voltage (I-V) Characteristics 23

1.5. Local Density of States (LDOS) Studies 25 Atomic Force Microscopy

1.6 Introduction 29

1.7. Principle of Operation 30 1.7.1 Force/Distance Relationship 30

1.7.2. Measuring Forces 31

1.7.3. Non-Modulated Methods 31

1.7.4. Modulation Techniques 31

1.7.5. Feedback Controls 32

1.8. Nature of Sample and Sample Surface Contamination 32

1.9. Cantilever and Tip 33

1.10. AFM Imaging Modes: (a).Contact Mode, (b) Non-Contact Mode.

(c) Tapping Mode. 35

Conclusions 39

Chapter 2. Atomic Hydrogen Interaction with Highly Oriented Pyrolitical Graphite

2.1. Background of Hydrogen-Graphite Interaction Studies and Motivation of our Work 41

2.2. Samples Preparation 44

2.3. STM and AFM Morphological Studies of Atomic Hydrogen Interacted-HOPG Surface 48

2.4. STS Studies of Atomic Hydrogen-Interacted HOPG Surface 63 Conclusions 69

Chapter 3. Graphite layers on Ir and Re Surfaces

3.1. Graphite layers on Metals: Background and Motivation of our Work 70

3.2. Samples Preparation 72

3.2.1. Preparation of Graphite Layers on Ir(l 11) and Re(1010) 73

3.2.2. Intercalation ofCs Between Graphite Layer and Ir Substrate 73

3.3. Surface Morphology of Graphite Layer on Ir(l 11) and Re(1010) 74

3.4. Electronic Surface Superstructure on Graphite Layer on Ir(l 11) 80 Conclusions 82

Chapter 4. Thin Carbon Films

4.1. Carbon Films: Background and Motivation for our Work 83

4.2. Samples Preparation 84

4.3. Surface Morphology and Emission Properties of the Carbon Films 87

4.4. Effect of Treatments of Substrates on Characteristics of Grown Carbon Films 91 Conclusions 96

3

Brief Summary of the Presented Work (Conclusions) 98

References 101

Acknowledgements 107

Itttr

oduc*on

Introduction

Importance of this Research Topic

Scanning probe microscope (SPM) studies of atomic hydrogen-interacted highly oriented pyrolitical graphite (HOPG) and carbon-based thin films is a very interesting research topic because of enormous applications for conventional, new energy sources, and electronics device technology. The SPM is a versatile technique, which in microscopy mode reveals the morphology of surfaces with resolutions up to atomic levels and in spectroscopy mode gives the occupation of electron density of states of the surfaces. Such key information is the base for further research and practical applications. Carbon-based materials play an important role in our everyday life. From burning of raw coal in power plants up to the core of tiny electronic devices, all make use of carbon-contained substances. The interaction of HOPG with atomic-hydrogen is important because of the graphite use as 1st shielding sheet in nuclear reactors and fusion devices. This interaction helps to understand changes taking place on plasma (hydrogen-contained) facing graphite plane The hydrogen storage in graphite materials has recently emerged a new burning issue and is being searched as a safe and compatible energy source for electronic devices and small power plant applications. Thin solid films on metals is a very hot research issue and it has attracted attention of a large number of investigators because of technological importance of these films in applied fields like modern communication and semiconductor electronic device manufacturing technology. Some of these forms have such unusual physical and chemical properties that can drastically change adsorption, catalytic and emission properties of the substrate materials. During some past years, carbon films having different phases like amorphous carbon, diamond-like carbon and chemical vapor deposition diamond have emerged as promising materials for cold cathodes. The electron field emission from such films has been widely studied and such films are being considered future candidates for microelectronic field emission devices. Their unique properties such as high hardness, chemical inertness and optical transparency are very attractive. These properties make these films preferable over other types of materials used for optical and electrical applications.

Goal of these Investigations

For hydrogen-graphite system, taking into account the fact that atomic hydrogen-graphite surface interaction earlier received very small attention and hydrogen storage in graphite materials has recently emerged as a new research activity, we decided to perform detailed studies on atomic hydrogen-HOPG system. The main target was to study atomic hydrogen-HOPG interaction specially concentrating on the surface morphological changes taking place on the exposed HOPG surface. The study of the modified surface local density of states of atomic hydrogen interacted-HOPG surface was also aimed. The surface morphology study of the graphite monolayer on Ir and Re sufaces was the 2 part of this work. The surface morphology study of graphite monolayer on Ir and Re revealing atomic resolution provided direct information on structural and intercalation properties of monolayer graphite coverage on metals. In the 3rd part, we performed surface morphology studies of thin carbon films grown on Si and ceramic substrates. We studied effect of change of the films deposition parameters and effect of performing different pre-growth treatments of substrates on characteristics of the grown carbon films.

Novelty of the Work

Regarding atomic hydrogen-HOPG interaction studies, we observed a new phenomenon of hydrogen accumulation between graphene layers. The hydrogen accumulation was found stable over periods of several months. By performing thermal desorption of hydrogen, the HOPG surface was found atomically flat and covered with 12 layers deep, nearly circular etch-pits. At edges of the etch-pits we revealed localized electronic surface states by performing scanning tunneling spectroscopy.

The surface morphology studies of graphite monolayer on Ir and Re permitted to characterize the morphology of polycrystalline Ir and Re metal ribbons and directly revealed on their surfaces graphite monolayer grown in the procedure of benzene decomposition over heated metal surface.

The surface morphology and electron emission characteristics of thin carbon films

deposited on Si and ceramic substrates were studied in detail and effect of deposition parameters and pre-growth treatments of substrates on characteristics of grown carbon films was observed.

The Main Findings of this Work

1. It is shown that hydrogen atoms may penetrate in perfect graphite layers and accumulate in graphite in the spaces between graphite layers transforming them in the net of densely spaced blisters. This was established in ambient AFM and UHV STM studies of graphite surface morphology before and after exposure of the graphite surface to hydrogen atoms. After exposure to hydrogen atoms, initially atomically flat graphite surface demonstrated appearance of bumps with the heights upto 5 nm.

Hydrogen thermodesorbtion from graphite makes the graphite surface again atomically flat but covered with many nearly circular etch-pits with depth 1-2 graphite monolayers. On repetition of hydrogen sorbtion-desorbtion cycles the already created etch-pits grow in sizes and new etch-pits are created in the next graphite planes. Thus gradual erosion of graphite surface takes place on repeating the hydrogen sorption-desorption cycles, resulting in layer-by-layer removal of the graphite sheet.

The scanning tunneling spectroscopy investigations manifested presence of localized electronic surface states at the edges of the circular pits. The localized edge surface state revealed by tunneling spectroscopy appears as maximum of the local density of states in the energy range of 90 - 250 meV above the Fermi level.

2. The graphite monolayers coverage grown in the procedure of benzene decomposition over heated metal surfaces was observed with atomic resolution on Ir(l 11) and Re(1010) metal surfaces. On the flat terraces of Ir(lll) surface graphite monolayer was continues, growing in crystalline-geometrical correlation with Ir(lll) metal lattice. There were also found few local defects (dislocations in plane) in graphite monolayerlayer. In general, high crystalline perfection of the graphite monolayer on the Ir(lll) surface was demonstrated.

Cs+ ions intercalation beneath the graphite monolayer on Ir(lll) surface changes initially flat morphology of graphite layer to a bump like structure which presents new

possibilities for the intercalation phenomena studies with nanometer lateral resolution and it causes a better atomic resolution of the graphite monolayer due to possible electron exchange from the Cs.

Surface morphology and electron surface emission of carbon films on Si and ceramic substrates prepared by low temperature high frequency (VHF) plasma deposition were studied. Some correlation between morphology and emission characteristics have been found: in general, films providing superior emissivity were characterized by lower roughness and grain size. We have also found influence of pre-growth treatments of substrates on surface morphology and emission characteristics of the deposited carbon films.

The results of this work were presented at the following international conferences:

1. International Conference Probe Microscopy-98,2-5 March (1998), Nizhny Novogord, Russia.

2. Materials Research Society (MRS) Spring Meeting, (1998), San Francisco, USA.

3. The 14th International Vacuum Congress (IVC-14) and 10th International Conference of Solid Surfaces (ICSS-10), 31 Aug.-4 Sep. (1998), Birmingham, UK.

4. 10th International Conference on Radiation Effects in Insulators, 18-23 July, (1999), Jena, Germany.

5. International Conference Probe Microscopy-99, 10-13 March (1999), Nizhny Novogord, Russia.

6. International Conference on Vacuum Microelectronics (IVMC-99) 6-9 July (1999), Darmstadt, Germany.

7. 10th European Conference on Diamond, Diamond like Materials, Nitrides and Silicon Carbide, 12-17 September (1999), Prague, Czech Republic.

8. 4th International Symposium on Diamond Films and Related Materials (ISDF-4), 20.22. Sep. (1999), Krakow, Poland.

9. 18th European Conference on Surface Science (ECOSS-18), 21-24 September (1999), Vienna, Austria.

10. The Electrochemical Society 197th Annual Meeting, 14-18 May, (2000),

Toronto, Canada.

11.5th International Workshop on Hydrogen Isotopes in Solids, May 17-19, (2000), Stockholm, Sweden.

12. 2nd International Conference on Scanning Probe Spectroscopy (SPS-2000) 19-22 July, (2000), Hamburg, Germany.

The dissertation contains introduction, four chapters, and brief summary of the presented work. There are 109 pages, 42 Figs., 2 tables and 115 references in the dissertation.

The 1st chapter deals with basic principles of operation of used main characterization techniques: STM and AFM. This chapter has two main sections. The 1st one deals with STM, while 2nd is on AFM. Then use of STM and AFM to reveal surface morphological features of samples in present studies is illustrated. There are 12 Figs, and 24 references in this chapter.

In the 2nd chapter, a glimpse of background of hydrogen-graphite system existing studies, followed by motivation of our atomic hydrogen-HOPG studies is presented. After having presented sample preparation details, detailed studies of surface morphology of atomic hydrogen interacted-HOPG surface using STM and AFM are presented. Then follow the results on scanning tunneling spectroscopy experiments on atomic hydrogen interacted-HOPG surface. At the end, the conclusions on results of performed AFM and STM/S experiments are given. In this chapter there are 17 Figs, and 45 references.

The 3rd chapter is devoted to the surface morphology studies of graphite monolayers on Ir(lll) and Re(10l0) surfaces. In the beginning, background and motivation of our studies have been presented. Then sample preparation details are given. Next follows the surface morphology study of graphite monolayer on Ir and Re together with the Cs intercalation between graphite monolayer and the Ir substrate. At the end of the chapter, conclusions have been presented. There are 6 Figs and 23 references in this chapter.

In the 4th chapter surface morphology and electron emission investigations of thin carbon films prepared by low temperature high frequency plasma deposition on Si and ceramic substrates are presented. The chapter starts with background of thin carbon films and motivation of our studies in this connection. Mainly there are two sections in this

chapter. In the 1st section, studies of carbon films prepared by setting a variety of deposition parameters are presented. In the 2nd part, influence of pre-growth treatments of substrates on characteristics of grown carbon films has been described. There are 7 Figs., 2 tables and 23 references in this chapter.

After the 4th chapter there has been given a brief summary of all presented work, highlighting main physical statements. Then at the end there are given acknowledgements thanking all those who guided, cooperated or appreciated in any way during all span of these studies.

This work was published in proceedings of conferences and in journals as below:

1. AFM study of morphology of low temperature carbon films prepared by VHF CVD: correlation with field emission.

A. N. Titkov, A. I. Kosarev, A. J. Vinogradov, Z. Waqar, I. V. Makarenko and T. Felter.

MRS Spring Meeting San Francisco, USA, Symposium Proceedings, Vol. 509, (1998) P. 149.

2. Topography of two dimensional graphite film on (1010) Re.

Z. Waqar, N. R. Gall, I. V. Makarenko, A. N. Titkov, A. Ya. Tantegode, M. M. Usufov and E. V. Rutkov.

The 14th International Vacuum Congress (IVC-14) and 10th International Conference of Solid Surfaces (ICSS-10), Birmingham, UK, 31 Aug. - 4 Sep. (1998), Conference Proceedings P.76.

3. Topographic study by scanning tunneling microscopy of a two dimensional graphite film on (1010) Re.

L. N. Bolotov, Z. Waqar, N. R. Gall, I. V. Makarenko, E. V. Rutkov, A. N. Titkov, A. Ya. Tantegode and M. M. Usufov.

Physics of the Solid State (Fizika Tveordovo Tela), Vol. 40, No. 8, August (1998), P. 1423-1426.

Maik Nauka/Interperiodica @1998 American Institute of Physics.

4. AFM and STM investigations of textured monolayer graphite films on (111) Ir and (lOfO) Re.

Z. Waqar, N. R. Gall, I. V. Makarenko, E. V. Rutkov, A. N. Titkov, A. Ya.

Tantegode and M. M. Usufov.

International Conference Probe Microscopy-98, Nizhny Novogord, Russia, 2-5 March (1998), Conference Proceedings, P. 164 and published in Surface Investigation: X-Ray, Synchrotron & Neutron Techniques (Poverkhnost Rentgenovskie, Senkhrotronie, e Nietronie Issoledovania), No. 7, July (1999) P.39-42.

5. Hydrogen-graphite interaction: hydrogen adsorption, desorption and etch-pits formation on graphite surface.

M. Z. Waqar, E. A. Denisov, T. N. Kompaniets, I. Y. Makarenko and A. N. Titkov. 18th European Conference on Surface Science (ECOSS-18), Vienna, Austria, 21-24 September (1999), Europhysics Conference Abstracts, Vol. 23 G, Th-P-022.

6. Substrate pre-growth treatments effects on characteristics of low temperature carbon films prepared by VHF CVD.

M. Z. Waqar, A. N. Titkov, A. N. Andronov and A. I. Kosarev.

18th European Conference on Surface Science (ECOSS-18), Vienna, Austria, 21-24

September (1999), Europhysics Conference Abstracts, Vol. 23G, Wed-P-048.

7. Emission properties of carbon films deposited in discharge with flat inductive coil. M. V. Shutov, A. J. Vinogradov, A. I. Kosarev, A. S. Smirnov, A. N. Titkov, I. V. Makarenko and Z. Waqar.

International Conference on Vacuum Microelectronics (IVMC-99), Darmstadt, Germany, 6-9 July (1999), Technical Digest, 264-265.

8. Adsorption of hydrogen and erosion of the top layers of pyrolitical graphite surface.

Z. Waqar, E. A. Denisov, T. N. Kompaniets , I. V. Makarenko and A. N. Titkov. International Conference Probe Microscopy-99, Nizhny Novogord, Russia, 1013 March (1999), Conference Proceedings P. 202.

9. Carbon and related films, prepared by VHF CVD: characterization and field emission. A. I. Kosarev, A. S. Abramov, A. N. Andronov, A. J. Vinogradov, M. V. Shutov, M. Z. Waqar, A. N. Titkov and I.V. Makarenko.

Proceedings of 4th International Symposium on Diamond Films and Related Materials

(ISDF-4), Krakow, 20.- 22. Sep. (1999) P. 209-213.

10. Observations of local electron states on the edges of the circular pits on hydrogen-etched graphite surface by scanning tunneling spectroscopy.

Z. Klusek, Z. Waqar, E. A. Denisov, T. N. Kompaniets, I. V. Makarenko, A. N. Titkov and A. S. Bhatti.

Applied Surface Science, 161, (2000) P. 508-514.

11. Effect of atomic hydrogen sorption and desorption on topography and electronic properties of pyrolytical graphite.

Z. Waqar, Z. Klusek, E. Denisov, T. Kompaniets, I. Makarenko, A. Titkov and A. Saleem.

The Electrochemical Society 197th Annual Meeting, Toronto, Canada, 14-18 May, (2000), Conference Abstracts, Abstract No. 1118 and Published In Proceedings Volume "Hydrogen at Surfaces and Interfaces", Editors, G. Jerkiewicz, J. M. Feliu, and B.N. Popov, .ECS, Pennington, NJ, (2000) P. 254-264.

12. Modification of graphite surface in the course of atomic hydrogen sorption: STM and AFM study.

Z. Waqar, E. A. Denisov, T. N. Kompaniets, I. V. Makarenko and A. N. Titkov. 5th International Workshop on Hydrogen Isotopes in Solids, May 17-19, (2000), Stockholm, Sweden, Conference Abstracts P. 45.

13. Effect of back contact on field emission from carbon films deposited by VHF CVD.

A. I. Kosarev, A. N. Andronov, A. J. Vinogradov, Т. E. Felter, A. N. Titkov, I. V. Makarenko Z. Waqar, S. V. Robozerov and M. V. Shutov. International Conference on Vacuum Microelectronics (IVMC-99) Darmstadt, Germany, 6-9 July (1999), Technical Digest P. 418-419, and Published In JVST В January 2001, Vol.19, Issue 1 (2001), P. 39-41.

14. Pyrolytical graphite surface morphology after interaction with atomic hydrogen.

Z. Waqar, E. A. Denisov, T. N. Kompaniets, I. V. Makarenko, V. A. Maryshak and A. N. Titkov

Technical Physical (Zhurnal Tekhnicheskoi Fiziki), Vol. 71, Issue 6 (2001) P. 133-138 Maik Nauka/Interperiodica @ 2001 American Institute of Physics.

CHAPTER ONE

Chapter I

Scanning Tunneling and Atomic Force Microscopy

Scanning Tunneling Microscopy (STM) 1.1. Introduction

The scanning tunneling microscope (STM) is the ancestor of all scanning probe microscopes. It was invented in 1981 by Gerd Binning and Heinrich Rhorer at IBM Zurich. Five years later they were awarded the Nobel Prize in physics for its invention. The STM was the first instrument to generate real-space images of surfaces with atomic resolution and it proved as the catalyst of a great technological revolution era in surface observation instrumentation [1]. Imaging with STM has brought us up close and personal to single atoms, molecules and molecular assemblies, and techniques are advancing to include more interactive experiments by using these instruments as nanoscopic tools rather than microscopes. The strong interaction between the probe tip and the sample has also been used to move atoms around on the surface, allowing the construction of nanostructures [2-4]. In following sections a brief description of STM is presented.

STM is composed of the tunneling and scanning assembly with a sample-tip approach mechanism, sometimes referred to as head, a vibration isolation system, electronics that include computer controller circuits (voltage & current amplifiers, digital-to-analog & analog-to-digital converters, etc). Computer with high-resolution monitor is used for data storage and image display.

The STM scanners are made in one of the following two geometries: the tripod or the tube configuration. The tripped scanner consists of three orthogonal bars made of piezoelectric material, usually a lead zircon titanate (PZT). In Fig.l showing typical STM controlling circuits, we have tripod scanner.

Fig.2. The tube scanners operation presentation by showing voltage signals applied to segments of the tube to induce various motions.

The high-voltage power supplies connected to the x and у piezoelectric elements usually have variable gains and are programmed with co-ordinated ramp functions to cause scanning. The low-voltage power supply provides the sample-tip bias and is programmable for spectroscopy measurements. As the magnitudes of tunneling currents are in the range of nanoamps, it is necessary to amplify this signal to 7-10 orders of magnitude. This should be done as close as possible to the tunnel junction, because any noise incorporated into the signal before this amplifier will be amplified. The output of the current amplifier enters the feedback controller, which compares the value to a reference and outputs a signal to the z voltage supply that will alter the tip position appropriately.

Resolution is achieved by means of attaching a sharp conducting tip (ideally terminating in a single atom) to a piezoelectric material, which expands or contracts when voltage is applied to it, enabling the STM to resolve detailed micro-morphological features on the sample surface. To achieve high-resolution images 0.1 A vertically and 1.0 A laterally imposes the requirements that noise from any source be less than 0.01 A along z and 0.1 A along x and у directions.

There are different sources of vibrations that can reach the sample-tip junction. Mechanical vibrations are a large component of the noise, originating from the building and surroundings.

There may be different designs to reduce the vibrations reaching the STM, the strategy for vibration isolation is the same in all cases and can be divided into three frequency regimes. The low-frequency regime is below 20 Hz, the medium-frequency range is 20-200 Hz and the high-frequency range is 200 Hz-1 kHz.

The low-frequency regime contains the vibrations from the building and the resonances of certain system components. An effective way to damp these vibrations is to suspend the microscope on long tension wires. This can be done suspending a massive table from the ceiling by rubber cords, where the length of the cord, the mass of the table, and the spring constant of the cords can be varied to achieve maximum attenuation at the frequencies of concern. If Li is initial legth of cord before suspension of STM unit and L2 cord length after suspension of STM unit, then AL=L2-Li, and frequency of vibrations is given by f = 27r[g/.AL]1/2 where g is acceleration due to gravity. The microscope is placed on this table and further itself could be suspended with tension springs, where again the length and spring constant could be chosen in the most effective range. The relative contribution of this noise to the image can be reduced, by increasing the scan rate. It is often possible to scan fast enough that the low-frequency noise that does get into the image is in the form of a curved background that can be easily eliminated in image analysis. The scan rate is limited by the resonant frequency of the scanner, which should be as high as possible.

The vibrations in medium-frequency range result from mechanical vibrations from motors, resonance of the table and chamber that are acoustically excited, and unattenuated acoustic noise. The techniques that are used to damp vibrations in this

frequency range are to mount the scanner assembly on a stack of materials of different elastic modulii or to suspend the scanner on tension springs with a magnet at bottom of the microscope stand, as illustrated in Fig.3.

<ь> steel posts

Fig.3. Two approaches to attenuate mechanical vibrations in the medium-frequency range, (a) Alternating layers of steel plates and viton polymeric balls, (b) Long tension springs with magnets at the bottom for damping oscillations.

The high-frequency vibrations originating as resonances of the piezoelectric elements, can be eliminated from the signal with electrical filters without altering the part of the signal that represents the structural information; however, the design strategy is to have the scanner resonance so high that it is not excited during operation.

1.2. Principle of Operation

In the STM, a conducting probe is brought to ~ 5-50 A from a conducting sample, and a bias voltage (V) is applied between them. This causes a tunnel current (several pA to few nA) to flow between the sample and the probe, due to the tunneling effect. The basic principle of STM is the quantum tunneling of electrons, through a barrier, from the tip to the surface (or vice versa, depending on applied bias). This barrier may be air (AIR-

STM) or vacuum (UHV-STM). Electron tunneling occurs between two conductors separated by a sufficiently thin insulting layer or, in physical terms, potential barrier.

1.2.1. Metal- Metal Tunnel Contact

When two metals are brought near each other at a distance (barrier) of 'd' and a bias 'V' is applied, a shift in their Fermi levels takes place. This situation is shown in Fig.4.

Fig.4. Schematic of potential barrier between metal electrodes for vacuum tunneling, (a) Two nointeracting metal electrodes, seperated by vacuum. The Fermi levels EF differ by an amount equal to the workfunction difference, (b) A voltage is applied between electrodes, there is a voltage drop across the gap, the potential in the barrier is no longer constant. The arrows indicate the range Vb of energy over which tunneling can occur. At higher energies, there are no electrons on either side to tunnel, while at lower energies there are no ampty states to tunnel into.

For tunneling between sample and tip at a bias voltage 'V', only states within 'V' of the Fermi level can tunnel. At positive sample bias, the net tunneling current arises from electrons that tunnel from the occupied states of the tip into the unoccupied states of

the sample. At negative sample bias the situation is reversed. The exponential decay of

the wave functions into vacuum is often written interms of inverse decay length k, as К = [2m(V-E)]1/2/h of electron.

Where E is energy of electron measured with respect to the Fermi level, m is electron mass and h is planks constant.

1.2.2. Metal- Semiconductor Tunnel Contact

In the case a metal tip and a semiconductor sample are brought near each other, at a tunneling distance d, and a bias voltage 'V' is applied between them, a shift in Fermi levels takes place. In this case the Fermi level EF of sample (semiconductor) is ~ middle of the energy gap (i.e. between the valence band and the conduction band). Under tunneling situations, the unoccupied surface states ( above the Fermi level) and occupied surface states (below the Fermi level contribute to tunnel current to reveal the surface relief. For any given lateral position of the tip, above the sample (r), the tunneling current (I) is determined by the sample-tip separation (z), the applied voltage (V) and the electronic structure of the sample and tip, which is quantitatively described by their respective density of states [ps(E)]. Let us describe the problem of electrons tunneling between STM tip and the sample to be studied.

1.2.3. Tunneling Current

In vacuum tunneling, the vacuum plays the role of a potential barrier between the two conducting electrodes, in this case the surface and the tip. In Fig.4 this barrier width width'd' is shown.

The transmission probability for a wave incident on a simple barrier in one dimension can be easily calculated. For a simple rectangular barrier in one dimension (with width d), the solutions of Schroedinger's equation have the form;

4> = e"kd (1)

Where к = [2m(VB-E)] I/2/h, E is the energy of the state, and Vb is the potential in the barrier. In general, Vb may not be constant across the gap as shown in Fig.4, but for

present discussion, it is adequate to replace the potential in the barrier with its average value, so that we need only to consider a rectangular barrier. In the simplest case Vb is simply the vacuum level; so for states at the Fermi level, Vb - E is just the work function and denoted as Ф =( <Dtip + <J>sampie)/2.

The transmission probability, or the tunneling current, thus decays exponentially with barrier width and height as;

I oc e"2kd (2)

The exponential dependence of tunneling current upon 'd' gives a linear relationship between the relative current difference and the separation change as:

Д1/1 = - 2kAd

Now the generalization to a real three-dimensional surface could be taken as: For tunneling between two metals at a voltage V, only states within Vb of the Fermi level can tunnel while other states can't contribute in tunneling, as shown in Fig.4. For energies above the Fermi level of the negative electrode (on the left in Fig.4b), there are no electrons to tunnel. For energies below the Fermi level of the positive electrode (on the right in Fig.