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1、1,Scanning Probe Microscope,Scanning Tunneling Microscope Atomic Force Microscope,2,Scanning Tunneling Microscope,Basic concepts Tunneling current Local barrier height More physics Applications,Iron atoms adsorbed on a copper (111) surface forming a “quantum corral” in a very low temperature (4K).,3
2、,Basic Concepts,The basic principle of scanning tunneling microscopy (STM) is based on the tunneling current between a metallic tip, which is sharpened to a single atom point and is made of a conducting material. A small bias voltage (mV to 3 V) is applied between an atomically sharp tip and the sam
3、ple. If the distance between the tip and the sample is large no current flows. However, when the tip is brought very close (10 ) without physical contact, a current (pA to nA) flows across the gap between the tip and the sample.,4,Basic Concepts,Such current is called tunneling current which is the
4、result of the overlapping wavefunctions between the tip atom and surface atom, electrons can tunnel across the vacuum barrier separating the tip and sample in the presence of small bias voltage. The magnitude of tunneling current is extremely sensitive to the gap distance between the tip and sample,
5、 the local density of electronic states of the sample and the local barrier height. The density of electronic states is the amount of electrons exist at specific energy. As we measure the current with the tip moving across the surface, atomic information of the surface can be mapped out.,5,How STM w
6、orks?,Although the STM itself does not need vacuum to operate (it works in air as well as under liquids), ultrahigh vacuum is required to avoid contamination of the samples from the surrounding medium.,6,Tunneling Current,To understand the theory of how STM works, it is vital to know what is tunneli
7、ng current, and how it relates to all the experimental observations. Tunneling current is originated from the wavelike properties of particles (electrons, in the case) in quantum mechanics. When an electron is incident upon a vacuum barrier with potential energy larger than the kinetic energy of the
8、 electron, there is still a non-zero probability that it may traverse the forbidden region and reappear on the other side of the barrier.,7,Tunneling Current,It is shown by the leak out electron wave function in the picture below.,8,Tunneling Current,If two conductors are so close that their leak ou
9、t electron wave functions overlap. The electron wave functions at the Feimi level have a characteristic exponential inverse decay length K given by m is the mass of electron, is the local tunneling barrier height or the average work function of the tip and sample.,9,Simple Calculations,E2,E1,x,0,x0,
10、x0,10,Simple Calculations,Solution of these equations comes out as:,x0,x0,where,and,After rearrangement, one obtains,x0,x0,;,A, B, C and D are constants.,11,Simple Calculations,Since both,and,should continue at x=0,C and D can be expressed using B by:,At the positive infinity, thus A=0.,The last con
11、stant B can be determined by,.,12,Wave Function Leak out,Actually, the constants are not important. What really matters is that the wave function decays exponentially when x0. When x0 is the vacuum and x0 is a metal, the kinetic energy of electrons is the Feimi energy of this metal and E1 is the ene
12、rgy of vacuum, then where is the work function of the metal.,13,Tunneling Current,The overlapped electron wave function in the vacuum from both the sample and the tip permits quantum mechanical tunneling and a current, I will flow across the vacuum gap.,14,More Physics,Based on the Bardeens tunnelin
13、g current formalism where,V is the applied voltage, MTS the tunneling matrix element between the tip wave function T and the sample surface wave function s, ET and Es the energy of a state in the absence of tunneling.,is the Feimi function,15,More Physics,The matrix element MTS is obtained from For
14、small tunneling voltages and low temperature, f(E) can be expanded to obtain,the integral is taken over a surface lying entirely within the vacuum barrier region between the tip and the sample.,16,More Physics,In particular, if the tip and sample are identical materials, the wave functions in the va
15、cuum gap can be written as,is the inverse decay length, is the local barrier height.,Therefore, the tunneling current exhibits an exponential dependence on the separation d given by,17,More Physics,With the spherical tip configuration shown in the picture, the surface wave functions can be expanded
16、in plane waves parallel to the surface with decaying amplitude into the vacuum,where s is the sample volume, K is inverse decay length, k is the surface wavevector and G is a two-dimensional reciprocal lattice vector of the surface. The first few factors aG are typically of the order unity.,18,More
17、Physics,The spherical tip (R k -1 ) wave function are expanded in similar form where T is the probe volume and R is the radius of curvature of the tip. The resulting matrix elements where r0 is center of the curvature of the tip.,19,More Physics,Therefore, the tunneling current is where DT(EF) is th
18、e tip density of states per unit volume. Divide the current by bias voltage, conductance is obtained as,20,Tunneling Current,At low voltage and temperature d is the distance between tip and sample. If the distance increased by 1 Angstrom, the current flow decreased by an order of magnitude, so the s
19、ensitivity to vertical distance is terribly high. As the tip scans across the surface, it gives atomic resolution image.,21,Remember!,STM does NOT probe the nuclear position directly, but rather it is a probe of the electron density. So STM images do not always show the position of the atoms, and it
20、 depends on the nature of the surface and the magnitude and sign of the tunneling current.,22,Local Barrier Height,It is obvious that the current is exponentially depends on both gap distance and the local barrier height, change of current might be due to corrugation of the surface or to the locally
21、 varying local barrier height. The two effects can be separated by the relationship.,23,Local Barrier Height,The tip is vibrating vertically and the current is measured, in theory, the local barrier height can be calculated. Again, if the tip rasters the surface, map of local barrier height can be o
22、btained. However, the local barrier image also contain topographic features, some questions related to the local barrier have so far remained unexplained. So, extra care needs to be taken in performing such experiments.,24,Local Density of States (LDOS),Density of States (DOS) represents the amount
23、of electrons exist at specific values of energy. The tunneling conductance (or I/V ), is proportional to the LDOS. where (r0, E) is the local density of states of the sample.,25,Local Density of States (LDOS),Keeping the gap distance constant, measure the current change with respect to the bias volt
24、age can probe the LDOS of the sample. Moreover, changing the polarity of bias voltage can get local occupied and unoccupied states.,26,Local Density of States (LDOS),When the tip is negatively biased, electrons tunnel from the occupied states of the tip to the unoccupied states of the sample.,27,Loc
25、al Density of States (LDOS),If the tip is positively biased, electrons tunnel from the occupied states of sample to the unoccupied states of the tip.,28,An example,Here are the spectra for Si(111)-7 x 7 surface. The bottom spectrum is the area averaged tunneling conductance measured by STM, and the
26、top spectrum is the surface states spectrum measures photoemission and inverse photoemission. both spectra show similar features.,29,STM Application Example I,Since the bonding geometry of atoms at the surface differs from that in the bulk, on some surfaces the atoms rearrange and form a structure e
27、nergetically more favorable than the truncated bulk. In surface physics, such a rearrangement is called reconstruction.,surface reconstructions: the rearrangement of surface atoms,30,STM Application Example I,Among the metals, the 5d-elements iridium, platinum and gold show a strong tendency towards
28、 reconstruction, i.e., most or all of their low-index faces are reconstructed. The surfaces of the 3d and 4d elements remain unreconstructed. So we can gradually increase the tendency towards reconstruction by alloying the 3d-element Ni and the 5d-element Pt and look what the surface looks like with
29、 increasing Pt concentration.,31,STM Application Example I,Whereas the (100)-oriented surface of Ni is a simple square lattice of atoms, Pt(100) reconstructs, having one close-packed (pseudohexagonal, hex) layer of atoms on top of the square lattice of the unreconstructed second layer. And this is w
30、hat the (100) surface of a PtNi alloy looks like at approx. 68% Pt concentration in the first monolayer:,32,STM Application Example I,What you see in most of the image are single bright rows of atoms shifted by half an interatomic distance in the direction of the rows (red arrow). You will also noti
31、ce that these atoms have a hexagonal environment (6 nearest neighbors) in the first monolayer, which is already the same local structure as in the hex reconstruction of pure Pt. Since the shifted row atoms do not sit in the hollow sites between four atoms of the second layer, but rather in bridge si
32、tes between two second-layer atoms, they are higher and thus brighter in the STM image. The black patches in the image are due to an impurity.,33,STM Application Example II,In the upper right corner you can also see two stripes of the hex reconstruction. There, the close-packed surface layer has a h
33、igher atom density than the square lattice below, i.e., 8 surface atoms per 7 substrate atoms. Some surface atoms sit on top of substrate atoms, some in bridge sites and some in the the hollow sites between four atoms of the second layer, and thus lower.,You can see these height differences as diffe
34、rent brightness of the atoms in the STM image.,34,STM Application Example I,With higher platinum concentration the whole surface layer becomes pseudohexagonal:,35,STM Application Example I,Whereas the above image shows only the geometrical structure, we can also obtain an image showing a superpositi
35、on of geometry and chemical contrast.,In this image the Ni atoms appear as bright blobs, whereas Pt atoms in the same row (same geometric height) are darker.,36,STM Application Example I,It is obvious that more Ni atoms (bright blobs) are found in the higher positions, especially in the sites on top
36、 of second-layer atoms, where the coordination is lowest.,Platinum prefers sites with higher coordination, as there are only a few bright Ni atoms in the lower rows.,37,STM Application Example I,An important point is the driving force of the reconstruction, i.e., the question “why does Pt reconstruc
37、t?“. A detailed analysis of the reconstructed alloy surfaces shows that the reconstruction cannot be due to tensile stress in the surface, which was often believed to be the driving force of the hex reconstruction. Since the hex reconstruction reduces the number of surface atoms with the lowest coor
38、dination number, it rather seems plausible that the tendency of Pt to avoid low-coordinated sites, as seen in the image above, plays an important role.,38,STM Application Example II,Dislocations are linear defects inside a crystal lattice and govern the plastic behavior of a material. Since dislocat
39、ions cannot end somewhere inside a crystal, they must either form dislocation loops or reach the surface. That is where we can see them by STM.,dislocations: defects of the Crystal Lattice,39,STM Application Example II,A dislocation is characterized by its Burgers vector: If you imagine going around
40、 the dislocation line, and exactly going back as many atoms in each direction as you have gone forward,you will not come back to the same atom where you have started. The Burgers vector points from start atom to the end atom of your journey :,40,STM Application Example II,Of course, one cannot see t
41、he dislocation line on an STM image, since it leads into the bulk, but only its end. Dislocations like this one, where the Burgers vector is perpendicular to the dislocation line, are called edge dislocations.,41,STM Application Example II,A dislocation may split into two partial dislocations, where
42、 the Burgers vector of each partial is less than one interatomic distance. Such partial dislocations span a stacking fault between them. At the surface, the stacking fault is often seen as a small step with a height of less than one atom layer. The lower side of this “1/3 step“ looks dark in the fol
43、lowing STM image.,42,STM Application Example II,A dislocation with its Burgers vector parallel to the dislocation line is called screw dislocation.,And that is what it looks like in an STM image: A step begins at the dislocation core.,43,STM Application Example III,In contrast to most metals, which
44、come in only one crystallographic form, iron (Fe) can have two crystallographic modifications:,crystallography of Fe films - fcc, bcc and the transition,body centered cubic (bcc) iron, also called alpha iron or the ferritic phase, and face centered cubic (fcc) iron, also called gamma iron or the aus
45、tenitic phase.,44,STM Application Example III,At ambient conditions, pure iron is bcc and ferromagnetic. Above approximately 920 0C, it becomes fcc. Whereas the bcc phase gains its stability from magnetism, the high-temperature fcc phase is paramagnetic. In order to study the magnetic properties of
46、the fcc phase of pure Fe at lower temperatures, researchers have been experimenting for many decades with metastable fcc Fe precipitates (i.e., inclusions) in copper (Cu) as well as with thin films on an fcc substrate like copper.,45,STM Application Example III,In the late 1980s, it was discovered t
47、hat ultrathin Fe films (less than 5 atomic layers thick) grown on the (100) oriented face of copper single crystals are ferromagnetic, although fcc iron precipitates in Cu are not. Ever since, this observation has been interpreted as direct evidence for the presence of ferromagnetic fcc iron in thes
48、e films, a hypothetical phase proposed almost 40 years ago.,46,STM Application Example III,The (100) face of an fcc material is a perfect square lattice, as that one in the upper right part of the image, where the film is five layers thick. What we see in most parts of the image is a zigzag pattern,
49、 however.,There, the atoms do not form a square lattice (with an angle of 90 between the two directions of atoms), but rather a lattice with approx. 76angle.,47,STM Application Example III,By comparing this lattice with that of different crystallographic structures of Fe, it is easy to see that it comes very close to the (110)-surface of bcc iron, much closer than to (100)-oriented fcc iron. The right figure shows schematic views of these two surface structures and also how they relate to the cubes of the bcc and fcc structure shown abov