CONTEMPORARY PHYSICS - EXPERIMENT 4
The STM
The Scanning Tunneling Microscope (STM)
Equipment used:
1) Burleigh Instructional STM
Objectives:
A) Demonstration of wave-like nature of electrons by observing a tunnel current
B) Use an STM to image the surface of a (001) plane of graphite and relate the image features to
the crystal structure
C) Compare STM results with results of electron diffraction and X-ray diffraction of graphite.
References:
P. A. Tipler, Elementary Modern Physics, Worth Publisher, New York (1992); Section 3-9
(p. 100) and essay on pp. 111-114.
R. A. Serway, C. J. Moses, and C. A. Moyer, Modern Physics, 2nd Edition, Saunders College
Publishing, New York (1997); Chapter 6 (p. 228) and essay on pp. 256-262.
K. S. Krane, Modern Physics, Wiley, New York (1996); Section 5.7, pp. 159-168.
Tunneling Electrons
One of the premises of quantum mechanics is that particles have a wave-like nature. A wave
equation – the Schrödinger equation – describes the behavior of these matter waves. The solution
of the Schrödinger equation for a given situation is a wave function that is related to the
probability of finding the particle in a particular region of space. The most basic situation is an
electron confined in space by infinitely high potential “walls” (electron in a box). For this case
the wave functions vanish at the walls and beyond, which means that the probability of finding
the electron outside the confined space is zero; the electron is always somewhere inside the box.
If we change the potential to a finite height, the situation changes. Now the wave functions
penetrate somewhat into the potential walls; however, its amplitudes decrease exponentially and
quickly become so small that for all practical purposes we can call them zero. While the wave
function between the walls (i.e. inside the box) is oscillatory (“wavy”), the wave function in the
walls are non-oscillatory of the form e–x.
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The STM
V(x)
0
L1 L2
x
wave function "tunnels"
through narrow barrier
wave function
-Vo
Fig. 1: Electron in a “leaky” box.
Now consider the potential shown in Fig. 1. This represents the one-dimensional case of an
electron in a box with a thin, “leaky” wall at x = L1. Initially the electron is confined inside the
box (0 < x < L1). There the wave function is “wavy”. Note, however, that the wave function does
not vanish within the confining wall at L1< x < L2, but that it decreases exponentially. Since the
wall is very thin there is some amplitude left in the region x > L2, the wave function of the
electron “leaks” outside and hence there is a small but non-zero probability of finding the
electron outside the box. Classically this could not happen since the total energy of the electron is
lower than the potential barrier. Thus this phenomenon is referred to as the Tunnel Effect.
a)
V(x)
V=0

x
unoccupied state s
la st filled state
(most wea kly bound elec trons)
oc cupied states
-Vo
b)
c)
Tunneling
Curre nt
Bias Volta ge
Fig. 2:
a) Electrons in a conductor are confined by a potential well. b) Two potential wells at
close proximity allow a tunnel current when a bias voltage is applied (c).
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The STM
Electrons in a Conductor
A conductor, such as a metal, or graphite, is an example of electrons in a potential well. A metal
crystal consists of atoms regularly arranged in a lattice. Most of the electrons of the atoms are
bound, but the outermost electrons are free to move inside the crystal. The minimum energy
required to remove the most weakly bound electrons is called the work function – you already
know about this form Experiment #1 (Fig. 2a). Bringing two pieces of metal in close proximity
without actually allowing them to touch creates a situation similar to the “leaky” box (Fig. 2b). If
the distance between the two conductors is small we can have electrons from one metal tunnel to
the other. However, there is one problem: once the electron tunnel to the other side, where do
they go? Electrons follow the Pauli exclusion principle which forbids them to share the same
quantum state, i.e. there can be no two electrons with the same quantum numbers. Thus an
electron form the top-most level on the left would not find a free state after it tunnels to the right,
and so tunneling does not occur. Applying a small bias between the two conductors raises the
potential energy of the electrons in one conductor with respect to the electrons in the other
conductor (Fig. 2c). Now the tunneling electrons end up in unoccupied states, and a tunneling
current can be observed as the electrons from one side tunnel across to the other side.
STM Tip
Tunneling Current
Sample Surface
Fig. 3:
A good STM tip has only one atom at the tip. This restricts the tunneling current
between the tip and the sample surface to just a few atoms.
From Tunnel Effect to a Microscope
Once established the tunneling current remains constant if the distance between the two
conductors stays the same. But because the wave function in the tunneling region between the
two conductors has the form e–x, the tunneling current is extremely sensitive to changes in
distance. Therefore, if we move one of the conductors across the other, the tunneling current will
vary with the distance between the two conductors due to bumps and dips at the conductor
surface. To achieve a good spatial resolution the probe-conductor is shaped as a very pointy tip
which ideally is only one atom wide (Fig. 5). Scanning the tip across a (conducting) sample
surface and recording the tunneling current as a function of the tip position results in a “map” of
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The STM
the sample surface as “seen” by the tip. The tip always stays at the same overall height with
respect to the sample surface, hence this mode is referred to as the constant height mode. Another
way to collect STM image data is the constant current mode. For this mode the distance of the
tip to the sample surface is changed such that the resulting tunneling current remains constant.
Plotting the distance of the tip to the sample surface vs. the tip position also results in an image
of the sample surface.
An STM can thus be realized – in principle – by using a very sharp tip and moving it a few
nanometers above a conducting surface in a controlled fashion. While this may sound simple, a
few experimental details remain. In a building, such as Culler Hall, small vibrations are always
present from passing vehicles in the street, running motors in the building, people walking in the
hall or in the lab. Even minor vibrations have amplitudes of 0.1 to 1 m, 100 to 1000 times larger
than the sample-tip separation. It is obvious that the STM must be isolated from the floor and
building vibrations. This may be done by springs or a cushion of compressed air upon which a
massive table rests. In our simple experiment vibration isolation is achieved by a granite slab
resting on a pressurized inner tube. While the experiment is being performed you should refrain
from walking in the lab; even loud conversation will have detrimental effects on the image
quality.
In order to obtain atomic resolution the tip must be extremely pointed. Cutting a small wire with
regular wire cutters does not make a very fine tip – at least not on a microscopic scale. Chemical
etching can sharpen the tip radius to about 1000 nm, still much too coarse for a resolution of
order 1 nm. Here the experimenter needs, in addition to skill, luck: the etched tip may exhibit
roughness of a few atomic dimensions (Fig. 3). The tunneling current from such a tip originates
practically from just a few individual atoms; such a tip yields a topographic map with atomic
resolution.
The last ingredient for a practical STM is the precise position control of the tip with respect to
the sample surface. The tip must be capable to move and position itself within a fraction of a
nanometer in x, y, and z directions. This can be accomplished using piezoelectric ceramics, often
referred to as PZT. Piezoelectric ceramics are materials that expand or contract upon application
of a voltage across its ends.† With a tip mounted at the end of a PZT ceramic it is possible to
control the tip’s movement to 0.1 nm. At the same time the PZT control voltage can be used to
keep track of the tip position. In our experiment a computer is interfaced with the STM control
electronics and draws a topographic map of the surface that is being scanned. Once an image is
stored in the computer’s memory in can be manipulated to improve image quality. However,
keep in mind that even the most sophisticated image enhancement software is worthless if
applied to a poor raw image.
You may know this effect from its reverse application in cigarette lighters. They contain a small piezoelectric
crystal which gets mechanically hit by when you push the “on” button. This abruptly changes the shape of the crystal
and a high voltage spike results causing a spark which then lights the gas.
†
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CONTEMPORARY PHYSICS - EXPERIMENT 4
The STM
For Your Report
1. Peel off the top layer(s) of the graphite sample to obtain a fresh surface. This can be done
simply by pressing a piece of tape onto it, then peeling off the tape; some of the sample will
come away with the tape. Now obtain an STM scan of the exposed (001) plane.
2. Note that only alternate atoms in each hexagon are imaged, because the electron wave
function projects alternately above or below the plane of hexagons to form the bonds between
planes. On your hard copy of the STM image, draw in at least three adjacent hexagons of
carbon atoms. To do this you'll have to show the three atoms per hexagon which are not
imaged! Don't be fooled by the initial impression that you are seeing the hexagons with an
extra atom mysteriously in the center.
3. Now measure directly from your STM image of graphite to obtain the values of the dspacing respectively between (100) planes, and between (110) planes. Compare with the
values for these d-spacings obtained respectively by electron diffraction and by X-ray
diffraction.
4. In the X-ray powder diffraction image of graphite, there is no peak corresponding to (001)
planes. (True, we did not scan down to the angle 2 where it would be – what angle is that? –
but if we had, we wouldn’t have seen the peak!) In fact the overwhelmingly most intense
peak corresponds to reflections from the (002) planes. Clearly explain the difference
between the (001) planes and the (002) planes. Carefully explain why X-ray diffraction
shows reflections from the (002) planes but not the (001) planes. Clearly explain why we
can image the (001) planes with the STM.
5. If the (002) reflections are so strong in the X-ray diffraction image, why didn't you see them
in your electron diffraction image of graphite? At what angle 2 would reflections from the
(002) planes occur if you used an electron accelerating voltage of 4 kV?
6. The electron wavelengths differed from the 1.54 Å wavelength of the copper KX-rays we
used in the X-ray diffraction experiment. Would you therefore expect the diffraction peak for
a given plane in the electron diffraction experiment to fall at a larger or a smaller value of
2than does the diffraction peak for the same plane in the X-ray diffraction experiment?
Explain. What would the value of the electron accelerating voltage have to be to make the
electrons’ deBroglie wavelength equal to 1.54 Å?
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CONTEMPORARY PHYSICS - EXPERIMENT 4
The STM
Procedure: Scanning Tunneling Microscope
I. Startup
A. Turn on Monitor, Computer, and STM Control Electronics.
B. Turn on Printer (Security Block must be installed and printer unplugged from it until
True Image software is loaded)
II. True Image Software for WINDOWS
Commands you enter or pull down (Click on the last of the sequence) are in boldface.
A. Double-click on BURLEIGH icon.
B. File | Load | Open File
C. C:\burleigh\PHY293
Scroll down the list of image file names and double-click on PHY293, or type PHY293
and Click on OK.
D. Collect | Configure
E. “Configure” selects parameters for image.
Set Scan Delay to zero for scanning graphite in constant height mode. Set Zoom
Multiplier to match Magnification (Scan Range) on Control Electronics Console.
It is suggested that for your first scan, you select image size as a square with equal
Scan Range for x and y; each side of the square equals Scan Range/Zoom
Multiplier = 7500 Å/250 = 30 Å.
Note: If you choose (nA) for current mode, the tip will stay a set distance above the macroscopic
surface and the scanner records the current as it goes up and down with distance to the
microscopic surface. If on the other hand you choose (Å) for topographic mode, the tip is set to
keep the current flow constant and so it moves up and down in order to do so. Here the scanner
records the height above the surface at which the tip is kept.
Click on OK.
III. STM Tip and Sample
The STM Head is a vibration-isolated rectangular box; through its window you can access the tip
and sample, each of which is mounted on a removable carriage. Control Electronics power
must be off before changing tip or sample. Before changing either, you must make sure there
is plenty of clearance so the tip does not hit the sample while you make adjustments.
A. Remove bell jar.
B. Turn Sample Position Dial down about 1 1/2 turns. (It turns stiffly!)
C. Use tweezers to remove tip carriage.
D. Cut a tip from Pt-Ir wire, and use tweezers to insert tip carriage.
E. Prepare sample, and use tweezers to insert sample carriage.
F. Turn Sample Position Dial up so that sample is about 1 mm from the tip.
G. Replace bell jar.
IV. Control Electronics
A. Monitor Bias Voltage. Set to 0.02 – 0.10 V for scanning (PZT should read -150 V if not
scanning).
B. Set Reference Current. Set to 0.1 – 10 nA for graphite.
C. Set Filter Control to MAX (cuts out high frequencies to smooth the image) .
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CONTEMPORARY PHYSICS - EXPERIMENT 4
The STM
D. For approach set Time Constant to MIN and Gain to MAX.
E. Set X and Y sliders to zero position (locates tip relative to sample).
V. Scanning
A. In software Collect | Scan Unidirectional
B. On Central Electronics Console momentarily press Coarse Retract, and then hold down
Auto Approach to bring tip and sample slowly together. DO NOT use Coarse Approach,
or
you will probably crash the tip.
C. Monitor Tunneling Current. With the Sample far away, this current will read zero. As
tunneling begins, this will start to read the same as the preset Reference Current.
D. To scan in constant height mode, set Time Constant to MAX and Gain to MIN.
E. Keep vibration to a minimum by being quiet and still.
F. Watch the image being collected. You may need to make small adjustments to Reference
Current and Bias Voltage. When you are satisfied with the image type H to Halt data
collection. If you choose to abort a scan, type A; this will clear the screen. You can
resume
scanning with Collect | Scan Unidirectional.
VI. Saving and Printing the Image
A. If you have not already done so, plug printer cable into Security Block.
B. Press Print Screen key on keyboard.
C. File | Exit
D. You are prompted to save your image file. Click on OK and Yes to overwrite the existing
PHY293.IMG file.
E. Double-click on Paint Shop Pro icon in WINDOWS Program Manager and also when
Paint
Shop Pro software loads. Click on OK on information screen.
F. Edit | Paste and your image will appear on the screen.
G. Click on Hand icon and, holding down the mouse button, drag the hand onto your image;
then release the mouse button.
H. File | Print Click on OK to accept default printer. Printing the image will take about
4–5 minutes.
I. As you gain experience you may learn about processing your image to make it clearer.
You
can make measurements of the lattice spacings directly from your image hardcopy; a scale
is included in the image.
VII. Shutdown
A. On the Electronics Control Module, press Coarse Retract until the Tip is well clear of the
Sample.
B. In software, close Paint Shop Pro. Close Burleigh, close Program Manager and exit
WINDOWS.
C. Turn off power to all the electronics.
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