Scanning tunneling microscopy (STM) is a remarkable, revolutionary technique that enables one to obtain images with atomic resolution of the surfaces of metal and semiconductor crystals. The idea of tunneling spectroscopy was conceived in the early 1960's but technical difficulties prevented the idea from being put to practical use until twenty years later. In 1978, Gerd Binnig and Heinrich Rohrer began to work on the development of an STM, and by 1981 they were in a position to document their first success. Finally in 1982, they reported their results on the structure of the Si(111) surface [See Note #1], at the time a particularly intriguing topic in surface science. In 1986, Binnig and Rohrer received the Nobel Prize in physics for the invention of the STM and its inital use in elucidating surface structures.

Tunneling Through a Potential Barrier

STM is based on the well-known quantum mechanical principle of particle tunneling through a barrier. According to quantum mechanics, there is a finite probability of a particle moving from one location to another even when it does not have enough energy to surmount a potential barrier that is in the way.

If the particle is an electron being removed from a surface and accelerated toward a cathode, the potential barrier is approximately equal in value to the ionization energy, or work function, of the sample. Penetration through this barrier results in a tunneling current where no current would have been observed if classical mechanics were obeyed. We will see that the tunneling current is extremely sensitive to the distance between the surface and the cathode.

Suppose that you have a simple electrical circuit, shown in the figure below, in which a wire touching a surface completes the circuit.

The electrons travel around the circuit in the direction shown. If the wire is separated from the plate, a potential barrier is produced because energy is now required to remove the electrons from the surface. This energy is equal to the work function of the metal, j, which can be thought of as the ionization potential of the metal. When no voltage is applied, the barrier can be approximated by a one-dimensional potential barrier of width d and height j.

When a voltage is applied, this potential barrier becomes slanted and is thus reduced. This is shown in the figure below. Its shape changes even further due to the Schottky effect. (See Solymar and Walsh, Sec. 6.6) but this effect is not shown in the figure. Although the Schottky effect is not small, we will ignore it in the following discussion since the general ideas of tunneling can be presented without including it.

The voltage applied between the surface and the wire results in a potential energy of V(x)=eEx across the gap. In this equation, e is the electron charge, E is the electric field and x is the distance from the surface. The total potential barrier is determined by adding this to the barrier which exists when no potential is applied. The result is given below.

From quantum mechanics we know that an electron on the surface with energy less than j_eff still has some probability of reaching the wire. The smaller the distance between the surface and the wire, the higher the probability for penetration through the barrier caused by the gap. The tunnelling current can be calculated by solving the Schrodinger equation for the potential shown in Figure B. The result is approximated by the expression,

  [1]

K is a constant with a value of about 1.025 A^-1eV^-½ for a vacuum gap. Notice that the current changes exponentially with the size, d, of the vacuum gap. For a work function of 4.0 eV and an applied voltage of 1 V, the current change as a function of d is as shown in the figure below.

Note that changing the vacuum gap by 1.0A changes the tunneling current by more than an order of magnitude.

The Scanning Tunneling Microscope

The above discussion demonstrates that small changes in the size of the vacuum gap produce significant and measurable changes in the tunneling current. One can take advantage of this fact to construct a microscope with atomic resolution. For example, imagine scanning a sharp needle tip across, and slightly above, a row of atoms:

The tunneling current between the tip and surface will depend on whether the tip is positioned directly above an atom or in between two atoms. Thus, by measuring the current as the tip is moved across the row of atoms, an electronic image of the surface can be obtained. The difficulty in implementing this idea lies in constructing a device which can scan a sharp probe over a surface within a few Angstroms of that surface and steadily enough to avoid the blurring which would be associated with mechanical vibrations. In 1982, Binnig and Rohrer accomplished this feat and went on to solve an important problem in the field of surface science concerning the surface structure of Si(111). Since then, construction of very small, compact devices have led to fewer difficulties in vibration isolation.

The basic design of the STM has a probe positioned on a mount which can be moved in the x, y, and z directions by means of the piezoelectric effect. Certain crystals, such as quartz, exhibit the piezoelectric effect, meaning that they change shape when a voltage is applied on opposite sides of the crystal. Piezoelectric crystals thus provide a precise means of moving devices in minute amounts. Originally, orthogonal piezoelectric positioners were used, and the entire microscope was vibrationally isolated by an elaborate system involving magnetic levitation, a heavy stone slab, and inflated rubber tires. More recent designs are much smaller and more rigid so that the vibrational isolation requirements are not as severe. In addition, in some designs, piezoelectric positioners that move in an angular fashion have replaced the set of three orthogonal positioners. An example of this kind of design, the Carl Zeiss Beetle-STM, is shown schematically in a later section.

The STM tip is scanned by applying voltages across the X and Y axis crystals. The separation of the tip and the surface is changed by applying a voltage across the Z axis crystal. The current that flows between the tip and the surface is due to tunneling and is measured by a sensitive ammeter. Two imaging modes are commonly used, the constant current mode and the constant height mode. In the constant current mode, the position (height) of the tip is changed during the scan in order to keep the current constant. This is shown in the figure below. In the simplest situation in which the work function remains the same along the surface, keeping the current constant requires keeping the tip-surface separation constant. This in turn requires the height of the tip to be changed. The voltage applied to the Z positioner (which is proportional to the relative height) is recorded as a function of the voltages applied to the X and Y positioners. One way of illustrating the measured data is by means of a three-dimensional plot of height (in volts) vs x and y position (also in volts). Another visually attractive way of presenting the data is to show the height as a varying brightness, proportional to the voltage applied.

The constant height mode is illustrated in the figure below. In this mode, the current is measured as a function of x, y position. This allows for faster scanning than in the constant current mode, but a smoother surface is required in order to avoid having the tip bump into irregularities on the surface. From Equation [1] we see that a change in the surface work function, j, can also change the measured tunneling current. This complication can be addressed by also measuring the first derivative of the current as a function of the tip-surface separation. This is done through suitable electronics in which the tip bias voltage is changed slightly and the resultant change in tunneling current is measured (thus giving DI_t/DV_t).

Theory

The STM electronics monitors both the surface-tip current and the voltage applied to the z-direction piezo, which affects the surface-tip separation. Another voltage involved, that applied to the tip itself, is set and is not part of the imaging process. When the current is held constant, the STM signal (image) is the z-direction piezo voltage as a function of x and y position. The surface-tip current depends on the overlap of electronic states on both the surface and the tip; the greater the overlap, the greater the current. This overlap changes as the separation between the surface and the tip changes but is also changes when the number and/or shape of the electronic states change.

The reason that overlap of quantum mechanical states is required is that there must be a finite probability for an electron to reside in the gap between the surface and tip and this can only happen if the electronic state has a reasonable probability of existing in this region.

Another requirement for tunneling is that the energies of the surface and tip states must be close together. If the energy difference is too large, movement between states requires a change in energy which lowers the probability for that event to happen. This is analogous to resonance states which occur in molecules; individual states form resonances when they are close in energy.

There are a large number os states found near the surface and the tip, not just one as shown above. The more states available to the electrons, the higher the probability that tunneling will occur and the higher the current that is measured. The number os states in a given energy interval and in a particular region of the surface is referred to as the local density of states. In order to understand this more fully it is useful to qualitatively discuss quantum mechanical states on the surface of and within a solid.

We can imagine that electrons in a bulk, conducting solid (e.g., a metal) could be described quantum mechanically as particles in a box. In the crudest approximation, the energy states of a single electron in such a box could be calculated using an infinite-well potential, shown below in one dimension.

The Schrodinger equation fro both the one-dimensional and three-dimensional potentials are easy to solve and are discussed in any introductory quantum mechanics text.

A better approximation for describing an electron moving in a conducting solid would be to use a finite-well potential since, in reality, there is a finite probability that the electron could leave the bulk solid.

In the above figure, the ground state wave function is drawn on top of the potential function. The energy states in this case show some "leakage" outside the box. This potential can be made even more realistic by considering the presence of individual atoms in the lattice of the solid. A simple way of incorporating these would be to include a periodic square-well potential inside the box as shown below in one dimension.

Of course, more than one electron exists in a solid. When a system of many electrons is considered, the calculations are further complicated by electron-electron interactions. Since the complete problem is formidable, different levels of approximations (with different levels of sucess!) are used. An important branch of the field called solid state physics focusses on calculating the energy states of electrons in a solid.

Without discussing further any of the complex methods of calculations used in this problem, we can agree that the end result of solving the Schrodinger equation is a set of energy levels corresponding to the allowed electronic energy states of the system. At T=0K, the electrons will fill the lowest energy states. We can define a density of states as the number of states within a particular energy range. As an illustrative example, consider the quantum mechanical states of an electron in a three-dimensional infinite square-well potential. The energies of the states are given by,

If we evaluate this equation, we can determine the number of states in any energy region. For example, let us determine the distribution of states up to an energy of 110 h²/8mL². The distribution of states, placed in groups of 10 h²/8mL², is shown in the figure below. For example, in the region between 0 and 10 h²/mL² there are seven states with n_x, n_y, and n_z values of 111, 112, 121, 211, 122, 122, 212, and 221. We can readily see from this figure that the density of states increases as the energy increases.

Now let's step back to the periodic square-well potential and describe how the energy levels in that system differ from those in an isolated square-well potential. Suppose that the solution to the Schrodinger equation with a particular isolated square potential shows that the well contains two bound states. If we now construct a potential composed of N such wells, there will be N states contained within the wells. If N is large, the collection of states (there will be N states) will be so close together that they can be considered as energy bands. The following figure shows this idea.

In a real solid, the bands at the bottom of the potential well will be valence bands while those further away would be conduction bands. When an electron is in a conduction band, it is free to move through the solid.

The following figure shows a simplified band structure in which there is one valence band and one conduction band. The electrons fill the energy levels up to a certain level. At T=0 K, the electrons will fill the valence band and no electrons are excited into the conduction band. At higher temperatures, some electrons are excited into the conduction band.

The highest filled energy level at T=0 is called the Fermi level. It is analogous to the HOMO in a molecule but with one important difference. In a conductor the electrons are easily excited to higher states within the conduction band even at room temperature while much higher energies (corresponding to visible and UV radiation) are usually required to excite an electron inot the LUMO of a molecule.

The above threeo-dimensional potentials apply only to the bulk solid. AT the surface, the electronic states change because the molecular bonding must change. Currently, there is no simple way to calculate the properties of the bulk and surface together as one entity so these two regions are generally treated separately. The bulk is a three-dimensional object with useful periodic characteristics while a surface is closer to two-dimensional and has its own periodic character which may be different from the bulk. Therefore, we talk separately about bulk states and surface states. The ideas about quantum mechanical states presented above are still useful but the theoretical methods used in calculating these states are different.

We are now in a position to analyze the most accepted theoretical description of the origin of the STM image, which states that the image produced at constant current corresponds to a map of constant local state density at the Fermi level [Tersoff and Hammann (1983)]. The Fermi level is the highest filled level at T=0 K and consists of a densely packed (in energy) set of overlapping energy levels (states). The actual density of those states at this level is hypothesized as the critical parameter for explaining the STM image. For real surfaces, one can imagine that the atom potentials can be divided into different sets. Rather than having all the atoms described by the same potential, different types of atoms have different potentials. This idea is shown below in one dimension.

In such a case the density of states may change for different positions on the surface and it is then useful to refer to the local density of states.

At this point, it would be helpful to look at an actual STM image. The image can be displayed in a number of ways. A common display is to show the image three dimensionally with the x and y axes corresponding to the surface plane and the z axis corresponding to the surface-tip separation. Another common display is shown below for a graphite surface.

The x and y axes of the surface are within the plane of the page and the z position, i.e., the surface-tip separation, is given by the brightness of the image. Thus, the bright spots on the figure correspond to large surface-tip separations while the dark regions correspond to smaller separations.

The hexagonal structure of the graphite surface is shown above with every other atom displayed as a large grey dot. Careful inspection reveals that ony alternate atoms show up a bright spots on the STM image. There has not been any definitive explanation given for this yet. One possibility relates to the fact that the local density of states is higher for the atoms at site "A" because these atoms are directly connected to atoms in the layer below. Since the "B" and "C" sites have lower local dinsity of states, they show up less brightly in the STM image. [See Park and Quate, 1986].

So far we have only concerned ourselves with the importance of the sample surface states in understanding the origin of the STM image, but the surface states on the STM tip are also involved. The best image is one with the maximum visual contrast between peaks and valley, i.e., the maximum "corrugation" amplitude. It has been found theoretically (see Chen, Ch. 5) that the corrugation amplitude increases for tip states in the order,

Qualitatively this can be explained by the fact that the state projects deeper and more sharply into the vacuum gap. Thus, most STM tips are constructed from d-band metals such as tungsten and iridium.

The STM tip is fragile in that the predominant surface state is easily changed by the forces on the tip. These forces could, for example, move some tip atoms about, thus changing the structure of the tip. A change in the surface state, for example from to , can substantially change the appearance of the STM image. Not only can the contrast change but it can even become inverted so that bright regions are converted to dark regions and vice versa. This complicates one's understanding of a particular STM image. The image of the graphite surface is particularly affected by the tip electronic states. In practice, this means that tunneling conditions, e.g., surface-tip distance and bias voltage, and physical changes in the tip structure dramatically affect the image.

Imaging of molecules adsorbed on surfaces

It is perhaps surprising that the STM is also able to image adsorbed, nonconducting molecular layers on conducting surfaces, but when we think about the density of states at the surface, the situation becomes more clear. An adsorbed atom or molecule can perturb the local state density thereby changing the surface-tip distance (image) required to keep the current constant. Thus the atom or molecule can be "seen". The perturbation of the local density of states is similar to the situation when two atoms come together to form a bond. The atomic states clearly change when the bond is formed and new molecular states are formed. Even when the two atoms do not react to form a molecule, the atomic states can be shifted by the field, however weak, imposed by the presence of another atom. The same thing happens when an atom or molecule is adsorbed to a surface; its presence shifts the surface states.

Tersoff and Hamann introduced a theory describing the STM image of an adsorbate through changes in the local density of states. This suggests that more strongly adsorbed species which affect the local density of states more significantly would produce a more highly contrasted imaged. Contrary to this expectation, an experiment by Eigler, Weiss, Schweizer and Lang showed that xenon, which only weakly interacts with metal surfaces, could be imaged on a nickel surface. This surprising result did not actually contradict the original theory of Tersoff and Hamann but its explanation required an extension of the thoery which showed that the size of the adsorbate was also an important contributing factor. Although xenon does not perturb the locals density of states very much, it is a very large atom and its outer 6s orbital, which is the one involved in the tunelling, extens far out into the vacuum. This extension enhances the tunneling probability in the vacinity of the Xe atom. The following figure shows somewhat more quantitatively the results of the xenon/nickel experiment.

At constant current, the STM tip moves up 1.52 A due to the presence of the xenon atom. Although this allows the xenon to be imaged, note that the change in the tip-surface distance does not correspond to the actual size of the xenon.

A large number and variety of adsorbed species have been observed using the STM. In this lab, we will focus on substituted long chain alkanes which are relatively easy to observe in air at room temperature. These molecules have the interesting property of forming very ordered monolayers on surfaces. They lie flat on the surface with the alkyl chains parallel to each other. Unsubstituted alkanes line up as shown in Figure A. Alkanols show similar ordering, but a herring bone structure, as shown in Figure B, is evident. In the latter structure, the -OH groups are believed to line up with each other to take advantage of hydrogen bonding.

Cyr et al have done a systematic study of primary substituted alkanes on graphite. The alkyl chains are alway parallel to each other but the functional groups exhibit varying degrees of "brightness" with the following ordering:

 -SH ³ -I > -Br > -NH₂ > -Cl ~ -OH ~ -CH₃

 The -SH group is the brightest substituent and the last three were not distinguishable from the brightness of the remainder of the alkyl chain. Despite the existence of molecular energy levels which are far from the Fermi level of the surface, alkanes can still be imaged because they affect the surface density of states. What is being observed in an STM scan is an enhanced image of the graphite, i.e., the locations of the molecules on the surface are observed because the contrast of the graphite in those regions is higher.

STM studies of monolayers on surfaces provide information which help us better understand the forces involved in monolayer formation The following papers are recommended for their explanations of the STM images of substituted alkanes on graphite surfaces. The second paper by McGonigal was copied for you and directly relates to the experiment you will be doing but the other two should also be useful.

REFERENCES AND NOTES

Notes:

1. Crystals can be cut, or cleave, along different planes. The arrangement of atoms on the newly exposed surfaces depends on the particular plane chosen for cleaving. To designate which surface is exposed, Miller indices are used as labels. In the example of Si(111), the (111) are the Miller indices. One reason chemists are interested in knowing the Miller indices of a surface is that the reactivity of the surface toward incident atoms and molecules depends on the arrangement of surface atoms. For more information on Miller indices, see any Physical Chemistry text.

General

A. L. de Lozanne, "Scanning Tunneling Microscopy", Phys. Meth. of Chem., Vol. IXA, p. 141, (1993). This article is a good recent review with useful references.

L. Solymar and D. Walsh, "Lectures on the Electrical Properties of Materials", 4th Ed., pg. 112 (Oxford Univ. Press, Oxford, 1988). This book has some relevant information about tunneling.

C. J. Chen, "Introduction to Scanning Tunneling Microscopy", Oxford Series in Optical and Imaging Sciences, (Oxford Univ. Press, Oxford, 1993). This is an excellent advanced text which has nice sections covering the theoretical aspects of the STM.

G. Binnig and H. Rohrer, "Scanning Tunneling Microscopy - From Birth to Adolescence", Rev. Mod. Phys. 59, 615 (1987). Some historical perspective given. Pictures of graphite and silicon.

C. F. Quate, "Vacuum Tunneling: A New Technique for Microscopy", Physics Today, (August 1986), pg. 26.

Graphite

S-I. Park and C. F. Quate, "Tunneling Microscopy of Graphite in Air", Appl. Phys. Lett. 48, 112 (1986). The surface structure of graphite is given.

G. Binnig, H. Fuchs, Ch. Gerber, H. Rohrer, E. Stoll, and E. Tosatti, "Energy-Dependent State-Density Corrugation of a Graphite Surface as Seen by Scanning Tunneling Microscopy", Europhys. Lett. 1, 31 (1986).

Theory

J. Tersoff and D. R. Hamann, Phys. Rev. Lett. 50, 1998 (1983); Phys. Rev. B 31, 805 (1985).

P. Saute, "Images of Adsorbates with the Scanning Tunneling Microscope: Theoretical Approaches to the Contrast Mechanism", Chem. Rev. 97, 1097 (1997).

D. M. Eigler, P. S. Weiss, E. K. Schweizer, and N. D. Lang, "Imaging Xe with a Low-Temperature Scanning Tunneling Microscope", Phys. Rev. Lett. 66, 1189 (1991).

Molecules Adsorbed on Graphite - Ordered Layers

K. Spong, H. A. Mizes, L. J. LaComb Jr., M. Dovek, J. E. Frommer, and J. S. Foster, "Contrast Mechanism for Resolving Organic Molecules with Tunnelling Microscopy", Nature 338, 137 (1989).

G. C. McGonigal, R. H. Bernhardt and D. J. Thomson, "Imaging Alkane Layers at the Liquid/Graphite Interface with the Scanning Tunneling Microscope", Appl Phys. Lett. 57, 28 (1990).

G. C. McGonigal, R. H. Bernhardt, Y. H. Yeo, and D. J. Thomson, "Observation of Highly Ordered, Two-dimensional n-alkane and n-alkanol Structures on Graphite", J. Vac. Sci. Technol. B. 9, 1107 (1991).

B. Venkataraman, G. W. Flynn, J. L. Wilbur, J. P. Folkers, and G. M. Whitesides, "Differentiating Functional Groups with the Scanning Tunneling Microscope", J. Phys. Chem. 99, 8684 (1995).

D. M. Cyr, B. Venkataraman, G. W. Flynn, A. Black and G. M. Whitesides, "Functional Group Identification in Scanning Tunneling Microscopy of Molecular Adsorbates", J. Phys. Chem. 100, 13747 (1996).

A. Stabel, R. Heinz, J. P. Rabe, G. Wegner, F. C. De Schryver, D. Corens, W. Dehaen, and C. Süling, "STM Investigation of 2D Crystals of Anthrone Derivatives on Graphite: Analysis of Molecular Structure and Dynamics", J. Phys. Chem. 99, 8690 (1995).