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5. Scanning Tunneling Microscopy Lab
Suzanne Amador Kane 3/13/06 (parts of this manual were adapted from the
Burleigh Instruments ISTM manual, and the Physics 407 Lab manual from
University of Wisconsin)
1) Introduction
In this lab, you will learn about the principles behind the operation of the scanning
tunneling microscope, the first of many modern “scanning probe microscopies” that have
opened up the wonders of surface nanoscale imaging for scientists. You will see how the
basic quantum mechanical principles of tunneling are utilized in the operation of this
instrument, how tunneling is used to create a surface “topogram” which allows the height
of the surfaces of conductors to be imaged at the atomic-scale, and how one can use this
information to take quantitative measurements on surfaces. You will learn how to
operate our Nanosurf EasyScan STM (an instructional STM capable of atomic resolution)
and take images of a gold-coated nanoscale grid, the surface of graphite and other
samples with nanometer-scale features. You will use surface analysis tools to measure
the dimensions of the nanogrid (and calibrate your STM) and the bond angles and lengths
for graphite. If you have time, you can also use mathematical image processing methods
to process the images to reduce noise and to extract useful information.
We will review six important topics in this lab to understand how STM works. While we
are studying these topics in the context of STM, they all are of great general utility and
interest for experimental science:
1) How quantum mechanical tunneling works in STM
2) How to control very small displacements using piezoelectric transducers
3) How to use feedback to control tunneling currents
4) How to vibrationally isolate sensitive systems
5) How to collect data electronically
6) How to image process STM data to extract useful information
2) Background on Tunneling and the STM
The quantum mechanical phenomenon of tunneling is described in texts such as Griffiths,
Introduction to Quantum Mechanics (section 8-2, pp. 320-325), Eisberg and Resnick
Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles (pp. 199-209) and
Modern Physics by Bernstein, Fishbane and Gasiorowicz (pp. 203-218). You should
reread the relevant sections of your textbook if you are not familiar with them at this
point.
We first consider the case of a massive particle such as an electron which travels along a
one-dimensional path from a region with potential energy V=0 to one with potential
energy V = Vo = constant (this is known as a step potential). (Fig. 1(a)) The electron
wave is totally reflected from the interface, yet unlike a classical particle, the electron has
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a finite probability of being found in the classically forbidden region where E < Vo. This
is because its wavefunction decays to zero exponentially over a distance determined by
Vo and E. (Fig. 1(b))
(a)
(b)
Figure 1. (a) Potential energy function for a step potential and corresponding
wavefunction (b). Reproduced from Eisberg and Resnick.
Now, consider the case where the potential energy only equals Vo over a distance a, after
which it drops back down to V=0. This case, known as a barrier potential, is illustrated
in Fig. 2(a). Now, the wavefunction will not in general have decayed to zero when it
reaches the other side of the potential energy barrier. :
(a)
(b)
Figure 2. (a) Potential energy function for a barrier potential and corresponding
wavefunction (b). Reproduced from Eisberg and Resnick.
The net result is that the electron wavefunction has nonzero amplitude with probability
amplitude T (for transmission) on the other side of the barrier, with approximate
dependence:
T  exp( - 2 k a)
Eq.1
where 1/k is a measure of the distance over which the exponentially varying
wavefunction decays within the barrier. (Here we have kept only the dominant
exponential variation of T; see the recommended texts for a full equation for T.) It is
determined by the values of the particles total energy, E, and the potential energy, V(x),
within the barrier by:
2m
Eq.2
Vo  E 
k
2
This means that if the electron wavefunction describes a situation in which an electron is
incident from the left, it has a probability of either being reflected from the barrier or
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being transmitted, even though it must pass through a classically forbidden region to do
so. It is as though a tennis ball thrown against your dorm room wall suddenly disappears
from your room and reappears on the other side!
The electrons within an electrical conductor (such as a metal or suitably prepared
semiconductor) are in states well described by a free particle wavefunction. As a result,
when two conductors are brought very close together yet still separated by an insulating
barrier (such as an air gap or layer of insulating oxide), electrons can still flow between
them by tunneling. If an electrical circuit is completed between the two conductors, this
flow of electrons can be sustained and measured as an electrical current. Just as the
transmission coefficient, T, has an exponential dependence on distance, so does the
tunneling current depend exponentially upon separation between the two conductors.
This is the situation in many common lab settings. If you join two pieces of wires by
twisting them together or by sticking them into a breadboard, you often are relying on
efficient tunneling across the small gap between them to complete your circuit. This is
because you often have thin layers of insulating metal oxides coating the surfaces of
copper wires.
This is also what happens in STM. There, one conductor is the very sharp tip of a metal
such as tungsten or platinum (with a small 10% admixture of iridium to improve its
stiffness). These materials are chosen because you can use them to produce STM tips
that have very sharp protrusions ending in only one or a few atoms (if you are lucky!)
Imagine that you get a tip in which one atoms protrudes beyond the others by a few
Angstroms, as shown in Fig. 3
Figure 3. The STM tip (at top) narrows down to a very sharp point at which one (or
a very few) atoms protrude by atomic dimensions. The sample to be imaged is
shown at the bottom. From Wisconsin ISTM manual.
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The sample to be imaged is shown at the bottom of Fig. 3. The sample must be
approximately flat and itself electrically conducting (or at least a semiconductor). Now
the distance, a, between conductors is the tip-sample separation between the bottom-most
tip atom and the atoms most close to it on the sample. Now, assume there is some way to
bring the tip and sample to a separation of several Angstroms. The tunneling current
between them varies exponentially with tip-sample separation, a. This allows us to see
why we can get away with assuming that just the one protruding atom contributes to the
tunneling current. The tiny extra distance between the sample and the other tip atoms
leads to an enormous reduction in their tunneling currents, due to this strong exponential
drop-off. As a result, in the discussion to follow, we will assume that the tunneling
current arises only from the one protruding atom.
There are two ways in which STM tunneling is more complicated than the barrier
potential discussed above. First, the potential energies of the electrons in the tip and
samples may differ. This corresponds in the simplest case to different workfunctions
(like the workfunctions discussed in the photoelectric effect) for the different conductors.
Second, in order to keep the tunneling current flowing, one must apply an electrical
“bias” voltage between the tip and sample. This results in a bias electric field being
applied across the gap between the tip and sample, and this modifies the potential energy
function the electron experiences. (Fig. 4)
Figure 4
From Wisconsin ISTM manual
Instead of a constant, flat-topped barrier, a sloping potential energy barrier results, with:
V(x) = W – e x,
Eq.3
where e = electronic charge, W = work function for one of the metals, x = distance across
the gap, and

= electric field from the applied bias voltage. To compute the new
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transmission coefficient, T, which is proportional to the tunneling current, one would
compute instead:


2m
V x   E  
T  exp   2 dx
Eq.4
2



using the equation above for V(x). This detailed relation still yields a tip-sample
tunneling current vs. distance that varies approximately exponentially. (Fig. 5)
Figure 5. From Wisconsin ISTM manual
SUMMARY: We expect our tunneling current from the STM: to be virtually zero for
large tip-sample separations; to be dominated by tunneling currents from only the
bottom-most atom for nanometer scale separations; to vary exponentially with tipsample separation; and to depend upon tip-sample bias voltage.
3) STM Operation
The EasyScan STM works in one of two modes for imaging the surfaces of samples.
You can see how these work in a good video at the website:
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http://www.iap.tuwien.ac.at/www/surface/STM_Gallery/stm_schematic.html The easiest
to understand is Constant Height mode. (Also, see the EasyScan Manual page 30. Note
that your laboratory notebook contains two EasyScan manuals: one for the instrument
and one for the software. Unless we specify the software manual, you should assume that
references to the manual refer to the main instrument manual.) In this mode, one simply
scans the tip in the plane of the sample, left and right, while holding the height of the tip
constant. The tip’s motions are controlled by a cylinder of piezoelectric material. Such
materials have the properties that they respond to an applied voltage by changing their
dimensions. One polarity of voltage results in a shortening of the piezoelectric, while the
opposite polarity induces an expansion. By varying the voltage on a piezoelectric,
displacements at the sub-Angstrom range can be achieved reproducibly. The position of
the STM tip can thus be finely controlled both in the plane of the sample (the x-y plane)
and in the z-direction.
The tip-sample spacing varies as the tip is scanned horizontally over the sample, because
the surface has atomic-level peaks and valleys due to its atomic structure, and so the
tunneling current also varies. So, if one measures the tunneling current It as a function of
in-plane location (x,y), one can “map out” the topography with atomic precision; high
current corresponds to a raised area of the sample. The act of repeatedly scanning x and
y back-and-forth to yield an image is also called rastering. (Fig. 6(c)). This yields a map
of (x,y,It) from which an image of the sample’s surface can be made. Since one cannot
plot in three dimensions, two methods are used to create such surface plots. Either colors
(or shades of gray) are used to indicate current (a scale bar is conventionally printed by
the side of the image to indicate correspondences between currents and shadings) or a
computer reconstruction of the surface is generated and the image is viewed from an
angle to indicate its 3D structure. (Fig. 6)
(a)
(b)
(c)
Figure 6
Different methods of represent STM measurements. (a) Burleigh
instruments image of the surface of graphite, in which gray-scale (shades of gray)
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are used to indicate height within the plane; (b) IBM image of a “quantum corral”
(ring of atoms binding a surface electron) in which computer 3D reconstructions are
used to indicate surface structure. (c) Cartoon of how rastering works to
accumulate images, and how the information collected is used to make up images of
the
sort
shown
in
(a)
and
(b).
(IBM
STM
Gallery
http://www.almaden.ibm.com/vis/stm/gallery.html)
Current mode/constant height mode is a good method for imaging atomic scale structure
and you will use it to image the surface of graphite at atomic resolution. However, if you
try to use constant height mode to image structures with bumps large compared to the tipsample spacing, you will hit your tip on the sample and damage it! You can avoid this
problem by imaging instead in Constant Current mode. (See the EasyScan Manual
page 30.) In this mode, feedback is used to fix the current at a constant target value
(called the Reference Current) as the piezoelectric is used to scan the tip back-and-forth
in-plane. If the sample surface is higher at one point than another, the tunneling current
goes up. The feedback circuit responds by retracting the tip so the tunneling current is
restored to the reference value. If the sample surface is lower at one point, the tunneling
current decreases, and the feedback circuit and uses the piezos to lower the tip until the
tunneling current returns to the reference value. In this mode, the position of the tip
(rather than tunneling current) is recorded to yield the map of the surfaces’ topography as
(x,y, tip z). This interplay between measurement (of tunneling current) and regulated
control (of tip height, which regulates the tunneling current) is an instance of negative
feedback. It’s negative feedback because a greater tunneling current results in a tip
displacement that reduces the tunneling current. In other words, the motion of the tip
always opposes the change measured in the tunneling current.
As a practical matter, you will begin imaging by using Constant Current mode, then—if
you wish to see atomic scale details—switch over to Constant Height mode after you
have found a flat region to safely scan this way.
Understanding the Easy Scan STM Controller Electronics
The EasyScan STM is controlled by a computer attached to a controller box that allows
you to set and monitor the tunneling current, bias voltage, scan range and feedback
controls. While these controls are described in the manual, which follows this
introduction, it will help if you have an overview first. All of this is controlled in
software only (no external knobs to turn!) within the Easy Scan program. You should
have an icon for this program on your lab setup. First, be sure you have the EasyScan
power supply turned OFF. This is so you can use the software in simulation mode to
understand how it works. When you double-click on the EasyScan icon on your desktop
to start the program, it will say that it cannot find the controller box, and ask if you wish
to run in simulation mode. Answer “Yes”, and proceed.
The X-Range setting determines how wide a range you scan over (how large the sample
area scanned is). You will use a point and click technique to determine where on the
sample you scan. To start your scans, it is helpful to click “Full” on the top menu. This
starts the scans at the largest scan range, 560 nm. You can then zoom in using
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instructions in the manual in section pp. 27-28. The Z-Range setting determines over
how wide a range of z-values are recorded. This is necessary because the height values
are stored as an 8-bit number. An 8-bit number can only represent at most 28 values =
256 separate distinct z-values. When you use a large Z-Range, you can measure a wider
range of z-values, but your smallest distinguishable step in z is large. A small Z-Range
allows finer measurements of z, but your tip can go off-scale more easily by measuring zvalues too high or too low to “fit” into the measurement range.
You can also set a few options relating to the samples overall tilt. It may not look tilted,
but at the submicron scale, it’s impossible to avoid a little bit of a tilt. This may be so
large as to make it hard to see your actual sample’s features. A section in the manual (pp.
25-27) tells you how to correct for sample tilt by subtracting out an average slope in the
data.
Nanosurf suggests standard working values for the reference tunneling current, called the
SetPoint of 1.00 nA. This is the average value the system tries to maintain in constant
current mode. You will see a working display of the actual measured current as you
scan. Since the STM must scan in order to image, this current will vary in time in either
mode. A feedback circuit is used to regulate the current at a constant value (in constant
current mode).
Their suggestion for GapVoltage (the tip-sample voltage, also called the Bias Voltage) is
0.05 Volts. This voltage corresponds to the tip-to-sample voltage in our earlier
discussion.
Your STM’s feedback circuit uses a common design known as PID (for proportional/
integral/differential.) You will find such feedback circuits commonly used in
applications such as temperature control where a physical quantity (temperature,
humidity, current, etc.) needs to be regulated by using a physical device (heater,
dehumidifier, piezotube, etc.) to adjust its value to a set, desired level. Your STM has
several ways of achieving this feedback. You will be using recommended values of these
parameters determined by trial-and-error, but here is a short justification of what these
different settings do. The proportional setting (P-Gain, default value 13) is useful if you
are trying to correct for currents far from the set current value. The correction voltage
applied to the piezos to correct the current is equal to a gain factor (set by the P-Gain in
software) multiplied by I = (actual current) – (reference current). If I is large, the
correction voltage is large, and the sign of the correction voltage varies with the sign of
I, as it should. However, just proportional gain by itself becomes less effective as the
current approaches that of its set point, since then I ~ 0 and no information is available
to adjust the piezo for good control. In this case, it’s useful to move the piezos based on
an electronically filtered version of the I signal. (If you remember how low and high
pass filters work from electronics, that will form a good model for what happens next.)
The Integral setting basically has the piezo voltage respond to an integrated version of the
, while the Differential setting (not used here in the EasyScan STM) changes the piezo
voltage based on a differentiated version of In filter, terms, the integral mode
responds to low frequencies, while the high pass responds to high frequencies in the
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current signal.) The time constant over which the current difference signal is integrated
is set by the Integrator I-Gain (default value 13) software control. The net effect is to
give information about the time behavior of the way the current difference changes, to
enable the circuit to more effectively maintain the current at its set value. Since a
differentiated signal responds strongly to high frequency fluctuations the most, and noise
introduces unimportant high frequency fluctuations, the Nanosurf EasyScan STM uses
only integration. The integrator can give a time-integrated feedback to the piezo which
helps it track larger-scale outlines of the surface, which helps in tracing out longer range
scans with more surface topography.
We have found that the default settings of the proportional and integral gain do well for
the gold nanogrid imaging in constant current mode. However, for moving to atomicscale imaging, you may wish to start with these values, then reduce the I-Gain to around
2 (to preserve some tracking to avoid crashing the tip) and the P-gain to 0 (to avoid
having the tip simply move to track the atomic scale features.) However you may find
other values work better for your samples at the atomic-scale; for instance, sometimes it
works well to start with the defaults and gradually lower the gains to see what gives the
best atomic-scale image quality.
4
The STM Experiments
4.1 Experiment A: Running the STM in Simulation Mode
You will first get acquainted with your software by leaving the STM controller power
supply turned off, and starting the software in Simulation Mode. This is done
automatically if you startup without power to the STM. Double-click on the EasyScan
E-line icon to start the software, and indicate you wish to run it in Simulation Mode when
a window appears saying “No connection to microscope!” by clicking on “Start
Simulation”. Follow the instruction in the manual starting on page 21. (ignore the
instructions about mounting tips and samples for now!) Do all of the exercises up to page
30. AT NO TIME WILL YOU BE TOUCHING THE STM DURING THESE
EXERCISES! USE THEM TO FAMILIARIZE YOURSELF WITH THE SOFTWARE!
ONCE YOU HAVE FINISHED, WITH YOUR
INSTRUCTOR’S PERMISSION, PROCEED TO THE NEXT
STEP.
4.2 Experiment B: The Gold-coated Nanogrid
Nanogrid: STM Magnification Experiment
To attain atomic resolution for gold, the STM signal has to be particularly low in noise.
The very nature of the metal means that the electrons will be strongly delocalized
between the atoms and there will only be small variations in the electron density with
atomic position. The periodic modulations are typically on the order of 0.1 Å, so one
should not expect to image gold atoms in normal room conditions. In addition, gold
surfaces are ordinarily fairly rough on atomic dimensions, unless they have been freshly
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annealed—a process whereby one heats the gold surface close to its melting point, then
allows it to cool so as to leave atomically-flat regions. The purpose of this experiment is
instead to introduce the concepts of tunneling and the extremely delocalized nature of
electrons defined by the metallic state.
The first sample to examine is the gold-coated nanogrid. This sample is described by its
manufacturer as a grid made by injection-molded plastic with a spacing of 160 nm. This
sample illustrates imaging in Constant Current mode and allows you to study the level of
magnification possible with the STM and imaging of (relatively) larger samples. We have
previously collected some good images of the grating for you to use and analyze later if
for some reason you cannot get good STM images of your gratings; for now, procede to
the next step, setting up your STM for imaging.
Getting set up to image & imaging the Gold Nanogrid
Get your instructor to give you a tour of the actual STM before you begin. You will be
following instructions in the EasyScan Manual (attached). The apparatus consists of four
pieces of equipment:
1) The STM itself
2) An electronics controller box that measures and sets tunneling current, sets the
bias voltage, sets the piezo voltages and provides the feedback.
3) A computer that communicates with the electronic control box to run
experiments, assemble STM images, and allow analysis and storage of the
images.
4) A vibration isolation chamber--in this case, a granite block with shock-absorbing
feet.
IMPORTANT NOTE: Many components inside the STM are very static
sensitive. Put on the grounding wrist strap before you handle the STM!!!
Remember—the piezo voltages are in the hundreds of volts—treat these
electronics with care and respect!
A few comments on vibration isolation: The very best modern vibration isolation
technologies employ special tables that sense any acceleration and counteract it. This is
called active (feedback-based) noise reduction. These devices can do an excellent job at
suppressing vibrational noise from the tens of Hertz (Hz) range to very high frequencies,
and we use them in our atomic force microscopy (AFM) facility. Non-active noise
suppression methods are cheaper and simpler. They always entail two components:
moving resonant frequencies toward very low frequencies far away from the scanning
frequencies of the device, and using an energy absorbing mechanism to damp vibrational
energies at higher frequencies. Your EasyScan STM uses such a simple but effective
method for suppressing vibrational noise: 1) The entire device is mounted on a block of
granite. This material is chosen both for its rigidity (so it does not flex and itself vibrate
during scans) and because of its density. Its large mass means that the resonant
frequencies of the device will be moved toward lower frequencies, which are less likely
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to affect the device’s operation. To see why this is so, recall the relationship between
resonant frequency and mass for a simple harmonic oscillator:  = (k/m). 2) The
granite block rests on feet made of a black plastic gel which absorbs energy from the
environment. The gel is designed to absorb high frequencies efficiently. Even so,
remember you are trying to image objects at atomic resolution. This means that
you must not lean on or shake the table during imaging or whenever the tip is in
contact with the surface. Be aware of this once you bring the tip into tunneling
mode! Even when you use the computer, be very careful.
Read in the EasyScan STM manual pp. 5-7 and 15-19. Now you are ready to mount a tip
(if you need a new one—ask your instructor if you can keep using the tip provided) and a
sample.
Either use the tip provided (if your instructors say it’s a good one) or make a fresh tip and
WITH YOUR INSTRUCTOR’S ASSISTANCE, mount your tip. Instructions are on
pages 15-16 of the manual.
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Now, find the nanogrid sample and the sample holder. Be very careful not to touch either
you’re your fingers at any time. Samples for this instrument are pre-mounted on
magnetic disks (Fig. 7). The gold nanogrid is in a clearly marked plastic box that says
“Nanogrid” on the lid. You must at no time touch the sample or trip, or sample holder
with your hands! If you do, ask your instructor to clean the contaminated surfaces (with
the instrument disconnected from the power supply!) with a clean cotton swab and
rubbing alcohol. Take a careful look at your sample before you place it inside your STM.
The sample side has a shiny gold region. The sample does not cover the entire magnetic
mount; instead a dot of silver paint is placed on the side of the sample to provide
electrical contact with the magnetic mount. This is because the nanogrid itself (beneath
the gold) is not conducting. Without the gold coating and the silver paint, you would get
no tunneling current. Now you are ready to place the sample carefully back into the
STM. Follow the manual’s instructions on pages 17-19 for mounting samples. Be
especially sure not to damage the tip! Be sure to position it so the very center of the gold
surface (not the edges) is centered under the tip.
Figure 7 : Side view of the STM magnetic sample holders. The sample is glued to a
magnetic disk and a conductive paste or paint is used to establish a conductive
pathway between the sample surface and the sample holder.
Your tip and sample are now a considerable distance apart. Use the magnifying loupe to
watch the tip and sample carefully under magnification while you gently use the black
knob on the sample holder to move the sample closer to the tip. Decrease this distance to
about 1mm. (You will get a chance to bring them closer together later under electronic
control, so don’t risk crashing the tip!) After you are done, gently place the clear plastic
cover back on. You can use its built-in magnifier to check your tip-sample distance
again.
Now, follow the manual’s instructions on pages 20 and following pages to establish a
tunneling current. First use the Approach Panel manual approach to close up the distance
between the tip and the sample to around 0.5mm or less if you feel comfortable. (This
entails holding down the left mouse button while clicking on the down arrow, WHILE
CLOSELY WATCHING THE TIP APPROACH THE SAMPLE UNDER THE
MICROSCOPE! BE CAREFUL NOT TO CRASH THE TIP) Then, use the automatic
approach, as explained in the EasyScan manual.
If you cannot get the STM to tunnel and the red LED stays lit, ask your instructor for
help! Some ideas: you may wish to move the sample and try another region of the
sample to image. You also may wish to try a few approaches with the same tip since the
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tip may improve on repeated attempts. You may also wish to use a faster approach
speed. If your tip is too long, it may vibrate too much for good tunneling. If nothing else
works, you may wish to replace the tip. (Check out the Troubleshooting section in the
STM manual before doing so.)
Once you have a tunneling current, follow the manual’s instructions for imaging the
sample.
Record the following for your lab report. Indicate what current, voltage and gain
settings you used to perform your scans. 1) Use the “Full” setting in the Scan Panel
to image at the largest x and y-range. Correct for sample tilt if you need to. Print
out your image. 2) Then, reduce the Scan Range to zoom in at different
magnifications. Do the features on your nanogrid change size the way they should?
If so, this gives you a check on the reality of your images. 3) Using the largest
range, use the Tools menu to measure the spacing of the grid. See the Software
manual pp. 40-47. Try out at least two different ways to measure the spacing, using
the Measure Distance command and the Create a Cross Section command. How
does your measured spacing compare with the manufacturer’s value? Note that we
have been told that that the EasyScan’s calibration was done at atomic resolution,
and the device’s piezos are not linear from atomic to micron scales. Given this
information, how would you calibrate your device for imaging at the scale of 100’s
of nanometers? 4) Use the instructions on “Achieving Atomic Resolution” on
manual pages 27-28 to see if you can image gold atoms on the flat tops of the grid.
Print out your highest magnification image. Write comments directly on each of
your images, explaining what you did and learned in each case, to use in writing up
your lab report.
4.3 Experiment C: Imaging Graphite at Atomic Resolution
This lab should provide direct observation of atomic features of graphite surfaces.
Graphite is one form of carbon in which the carbons atoms form planar layers, called
graphene, in which each carbon atom is covalently bound to its nearest neighbors in a
honeycomb arrangement. See Fig. 8 below. The adjacent planes are only weakly
associated via noncovalent van der Waals interactions, so they can easily be pulled apart.
(This explains why graphite powders are used as dry lubricants.) Your goal is to obtain a
good image of graphite at atomic resolution and to check its interatomic spacing and
bond angles.
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Figure 8 Atomic ordering of carbon atoms in the planes of graphite and the actual
restructured surface layer.
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Preparing a freshly cleaved graphite surface
Take out the HOPG (highly oriented pyrolytic graphite) sample. Your graphite sample is
in a clear plastic holder, along with several other samples. It is mounted on another
magnetic holder and you should be able to see the thin layer of shiny, slightly darker gray
that indicates where the graphite is. While the sample may work OK out of the box, you
will probably need to remove a top layer of graphite to expose a fresh layer for imaging.
ASK YOUR INSTRUCTOR IF YOU NEED TO CLEAVE THE GRAPHITE. The
layers of the pyrolytic graphite lie, to high accuracy, in the plane of the sample surface.
As explained above, the forces holding layers of graphite together are weaker than the
forces between graphite atoms within layers, so you will be able to lift off intact layers to
expose a fresh layer below. To do this, take a piece of clear packing tape. Press a corner
of the tape onto the graphite sample (sticky side down) so as to cover it entirely, but not
to entirely cover the sample holder. Next, using your fingernail, gently smooth the tape
against the graphite so it the tape presses uniformly against its surface. There should be
no bubbles where the tape does not stick to the sample. Then, smoothly and gently lift up
on the tape so as to peel off an intact layer of graphite on the tape, exposing the graphite
surface beneath. You should be able to see the layer peeled off and sticking to the tape,
as well as a fresh, dark graphite layer on your sample holder. Look from the side to make
sure no edges of the graphite protrude upward; if any do, gently remove them or tap them
down using a pair of tweezers. Mount the sample as before.
Use the manual’s instructions on imaging graphite and imaging at atomic resolution,
along with the comments on the scanning parameters above. You may wish to inspect
the application notes on Graphite at the end of the ring binder in the lab for exact
feedback, setpoint current and gap voltages values to use. We have found that you can
start with the values for the gold nanogrid, but that you will wish to reduce the
proportional gain quite a lot for optimal imaging, retaining some integral gain to follow
larger contours on the surface. This enables the STM to function in constant height mode
rather than constant current mode, but you may need to experiment to find the best
imaging conditions. You also wish to first look at the graphite at a very large scale to
correct for sample tilt and to find locally flat regions. (The graphite is flat only over
sections, and will have steps between plateaus of atomically-flat regions.) Make sure you
are zooming in on a locally-flat region and gradually go down by steps until you imaging
at an x and y range corresponding to one of your smallest values (around 5.6 to 2.8 nm
wide typically.)
If you cannot get good atomic resolution images, withdraw the tip and change tips. You
should also cleave the surface again if repeated attempts don't bring out atomic details.
Sample graphite images are shown in the manual, and in the application notes at the end
of the STM notebook. The images reproduced in the manual are to be considered a “best
ever” type of image, so yours will likely not be as clean. If you get very stable graphite
images, you should collect a number of scans, as a function of magnification and bias.
For most images it should be possible to determine the hexagonal surface structure bond
angles and approximate bond lengths of graphite. Multiple tip effects may also be
observable—this would show up if every carbon atom appears to be a double-pair of
atoms because the tip itself has two atoms projecting.
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Useful information on comparing your data to those for graphite
(images from the Burleigh Surface Topography Applications, No. 7
IMPORTANT NOTE: You will be surprised to see that STM images of graphite
actually only display peaks for every other carbon atom. As a result, consult the
EasyScan manual and the application notes on imaging graphite to see how to interpret
your images! There is also a section in the ring binder provided with the instrument that
describes in detail how to interpret graphite images. Consult this to be sure.
(a)
(b)
(c)
Figure 9 a) Illustration of a method for determining the average distance between
surface graphite atoms along a single atomic line. Using the Tools in the Easyscan
software, measure the total length of the line, then divide by the number of atomic
spacings to get the average. b) measure the angle between different lines of atoms
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using the angle feature. c) Accepted values for the lattice spacings for the graphite
hexagonal “honeycomb” lattice. Actual STM images actually only detect every
other atom, resulting in an apparent triangular lattice with lattice spacings as
shown. (Reproduced from the Burleigh Instruments Surface Topography Exercises
Vol. 7, Supplementary Lab Exercises for the ISTM: Calibration using the atomic
lattice of graphite)
You can compare the measured distances between the atoms on the graphite surface
(shown as open circles on the schematic diagram below) and those in graphite (shown
schematically as vertices on the honeycomb lattice in the sketch, along with accepted
spacings), by computing your measured atomic spacings along more than one direction,
then the angles between adjacent lines of atoms. Any discrepancies would be resolved in
practice by correcting your STM’s calibration by a factor to bring your values into
agreement with the accepted values. Explain what calibration correction factors you
would recommend using for your STM, and how you arrived at these values.
For this part, be sure to include in your writeup:
 Your best quality atomic resolution images (use past images provided by the
instructor if you were unable to get any).
 Your analysis of the lattice spacings, with explanations of how you compared
your images with those in the samples and the values included in the lab
manual. Include any relevant sketches to show how you compared your
data to the figure above.
 Explain how you would change the calibration of your STM to reproduce the
correct lattice spacings for graphite, prior to investigating an unknown
sample’s atomic-level structure.
Other questions to answer in your writeup:
1. Sometime during the use of the STM, the tip may have “crashed.” This is observable
has a sudden large change in the current. This occurs when there is a change in the
surface topography to which the feedback loop does not respond quickly enough and the
tip touches the surface. Calculate the effective resistance of the tunneling gap for
the conditions used in your experiment (see Fig. 3 ) and compare that to the expected
resistance if the tip was in direct Ohmic contact with the surface. The resistivity of gold is
2.44  10-8 -m and that of platinum-iridium is .000025 ohm-cm. (Question—what
material would form the effective “wire” at this junction? This turns out to be a tricky
question, but do your best to guess!). This comparison should illustrate the difference
between tunneling and regular conduction.
2. As the temperature of metals is raised, the resistance to current flow increases. Discuss
the mechanism of resistance in metals and compare this mechanism to electron tunneling.
How would the temperature dependence of the two mechanisms differ? Would you
expect the STM temperature dependence be a strong or a weak one, and why? Comment
on the relevance of the comparison between thermal energy at room temperature (find
this in eV if you don’t know it already, then memorize it!) and the work functions of gold
(about 5.1 eV) and graphite (around 4.5 eV).
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3. Because these experiments were conducted in air, air, adsorbed water, solvents, and
gases are undoubtedly on the surface. How do these molecules affect the tunneling
process and how might the tip perturb their distribution? (Compare this case to one
where the tip is separated from the sample by either air or vacuum.) Contaminants on the
tip are also likely problems. Explain how this would affect the noise on your STM
experiment.
4. Consider the problem of the electron source in these experiments. If the tip is not
scanned but left stationary over the surface, at a fixed distance that corresponds to a
tunneling current of 1 nA, calculate the number of electrons/second, N, that flow through
the atoms that participate in the tunneling process between the gold and tip surfaces. The
noise in such a current flow is partly due to shot noise—Poisson statistical fluctuations
due to the granularity of the charge carriers. The signal to noise ratio is limited to N/N
as a result. Compute this for your sample and comment on its value. Of course, this
assumes we count for one second to measure current and often one wishes to make a
faster measurement. What would the sampling frequency have to be in order to limit
your measurement to about 10:1 signal to noise ratio?
5. What would the order of magnitude of the electron’s energy in eV have to be for your
electrons to have a wavelength comparable to the size of the atomic spacing in graphite?
(If you are clever, you can avoid doing a calculation by using your lab manual and results
from your or another group’s work this semester.) Do your tunneling electrons have this
much energy? (This is an instance of how the diffraction limit does not apply in the nearfield limit. You are not limited to resolving only objects larger than the wavelength of
the probe if you are in “near-field” mode—so close you are within a few wavelengths of
the sample being images. It’s like using a stethoscope to locate someone’s heart—the
wavelength of the beating heart’s sound is awfully long—like meters—but you can locate
the heart to around 5cm or better this way!)