STMP
                     Lecture 6  Scanning Tunneling Microscopy (STM)
• General components of STM;
• Tunneling current;
• Feedback system;
• Tip --- the probe.
Brief Overview of STM
Basic components of STM:
The scanner 
can be Five basic components:
mounted with 
the tip or the 
sample stage. 1. Metal tip, 
2. Piezoelectric scanner, 
3. Current amplifier (nA),
4. Bipotentiostat (bias),
5. Feedback loop (current).
• Tunneling current from tip to sample or vice-versa depending on bias;
• Current is exponentially dependent on distance;
• Raster scanning gives 2D image;
• Feedback is normally based on constant current, thus measuring the height on surface.
Inventors of STM 
The Nobel Prize in Physics 1986
Nobel Laureates Heinrich Rohrer and Gerd Binnig 
Brief History of STM
l The first member of SPM family, scanning tunneling microscopy (STM), 
was developed In 1982, by Gerd Binnig and Heinrich Rohrer at IBM in 
Zurich created the ideas of STM (Phys. Rev. Lett., 1982, vol 49, p57). Both 
of the two people won 1986 Nobel prize in physics for their brilliant 
invention. 
STM is really 
small in size.
Nobel Laureates Heinrich Rohrer and Gerd Binnig (B. 1947) 
STM Tips
• STM tip should be conducting (metals, like Pt);
• STM plays with the very top (outermost) atom at the tip and the 
nearest atom on sample; so the whole tip is not necessarily very sharp 
in shape, different from the case of AFM, where spatial “contact” is 
necessary and crucial for feedback.
• How do we obtain these wonderful tunneling tips where only one 
atom is at the top?
Answer: really easy to obtain such tips, simply by cutting a thin metal 
wire using a wire cutter --- there is always a single atom left over at the 
very top.
Tunneling Current
a result of the overlap of tip and sample electron wavefunctions
Two requirements: 1. small distance --- electron wavefunction overlap
2. bias --- for net current flow.
In a metal, the energy When the specimen and the If the distance d between 
levels of the electrons are tip are brought close to each specimen and tip is small 
filled up to a particular other, there is only a narrow enough, electrons can ‘tunnel’
energy, known as the region of empty space left through the vacuum barrier. 
‘Fermi energy’ EF. In between them. On either When a voltage V is applied 
order for an electron to side, the electrons are between specimen and tip, the 
leave the metal, it needs present up to the Fermi tunneling effect results in a net 
an additional amount of energy. They need to electron current. In this example 
energy F, the so-called overcome a barrier F to from specimen to tip. This is the 
‘work function’. travel from tip to specimen or tunneling current.
vice versa.
Electron density of states: Fermi level 
Electron density of states: Fermi level 
• The electrons fill up the energy valley in the sample until there are no 
more electrons. 
• The top energy level at which electrons sit is called the Fermi level, eF.
• For every energy e, the density of states is the number of electrons 
sitting within De of e, divided by De. So, for the energy shown above as 
a blue strip, DOS(e) is approximately 7 / De. 
Tip and Sample: lined up exactly under zero bias 
The electrons in the tip and the sample are sitting in two separate 
valleys, separated by a hill which is the vacuum barrier. 
Electron density of states: Fermi level 
• Electrons are happy sitting in either the tip or the sample, i.e. they're sitting in nice 
energy valleys. 
• It takes energy to remove an electron into free space. We can think of the vacuum 
around the tip as an energy hill that the electron would need to climb in order to 
escape. The height of this energy hill is called the work function, f.
• In order to bring an electron up and over the vacuum energy barrier from the tip into 
the sample (or vice versa), we would need to supply a very large amount of energy.
• Climbing hills is hard work! 
• Luckily for us, quantum mechanics tells us that the electron can tunnel right through
the barrier. Note: this only works for particles (with both wave and particle 
characteristics, i.e., wave-particle duality), not for macroscopic objects. Don't you try 
walking through any closed doors! J
• As long as both the tip and the sample are held at the same electrical potential, their 
Fermi levels line up exactly. There are no empty states on either side available for 
tunneling into! This is why we apply a bias voltage between the tip and the sample.
Tunneling current at bias 
By applying a bias voltage to the sample with respect to the tip, we effectively raise the Fermi 
level of the sample with respect to the tip. Now we have empty states available for tunneling into. 
Tunneling Current 
• A thin metal tip is brought in close proximity of the sample 
surface. At a distance of only a few Å, the overlap of tip 
and sample electron wavefunctions is large enough for an 
electron  tunneling to occur. 
• When an electrical voltage V is applied between sample 
and tip, this tunneling phenomenon results in a net 
electrical current, the ‘tunneling current’. This current 
depends on the tip-surface distance d, on the voltage V, 
and on the height of the barrier F:
• This (approximate) equation shows that the tunneling 
current obeys Ohm’s law, i.e. the current I is proportional 
to the voltage V. 
• The current depends exponentially on the distance d. 
• For a typical value of the work function F of 4 eV for a 
metal, the tunneling current reduces by a factor ~10 for 
every 0.1 nm increase in d. This means that over a typical 
F: the work function (energy barrier), atomic diameter of e.g. 0.3 nm, the tunneling current 
e: the electron charge, changes by a factor ~1000! This is what makes the STM 
m: the electron mass, so sensitive.
h: the Planck’s constant,
V: applied voltage, • The tunneling current depends so strongly on the distance 
d: tip-sample distance. that it is dominated by the contribution flowing between the 
last atom of the tip and the nearest atom in the specimen  
Next page: F of common metals.
--- single-atom imaging!
Work Function of Common Metals
Metal F(eV) 
(Work Function)
Ag (silver) 4.26
Al (aluminum) 4.28
Au (gold) 5.1
Cs (cesium) 2.14
Cu (copper) 4.65
Li (lithium) 2.9
Pb (lead) 4.25
Sn (tin) 4.42
Chromium 4.6
Molybdenum 4.37
Stainless Steel 4.4
Gold 4.8
Tungsten 4.5
Copper 4.5
Nickel 4.6
Basic components of STM:
The scanner 
can be Five basic components:
mounted with 
the tip or the 
sample stage. 1. Metal tip, 
2. Piezoelectric scanner, 
3. Current amplifier (nA),
4. Bipotentiostat (bias),
5. Feedback loop (current).
• Tunneling current from tip to sample or vice-versa depending on bias;
• Current is exponentially dependent on distance;
• Raster scanning gives 2D image;
• Feedback is normally based on constant current, thus measuring the height on surface.
Feedback based on Tunneling Current
• The principle of the STM is based on the strong distance dependence of the quantum 
mechanical tunneling effect.
• Maintaining a constant tunneling current by adjusting the height with a piezo-electric crystal, 
and monitoring the piezo voltage while scanning, allows one to image a surface, under ideal 
conditions, to atomic resolution. (If the tip is scanned over the sample surface while an electronic 
feedback loop keeps the tunneling current constant ( constant current mode), the tip height follows a 
contour of constant local density of electronic states and provides information on the topography of 
the sample surface if the surface is composed of the same atoms.)
• Most of the tunneling current flows through a single protruding atom on the tip and thus sub-
angstrom resolution in z can be achieved on a clean surface with a sharp tip. 
• The x-y resolution is somewhat larger. 
STM: constant current mode 
Raster Scanning of STM: 2D imaging 
Constant height Constant current 
mode mode
Tell if same atoms Tell heights for the same atoms
Imaging the different surface Imaging the surface topography at atomic 
atoms (due to their different work resolution if the surface is composed of 
functions), revealing the surface the same atoms, i.e., the only factor 
composition or defects. affecting the tunneling current is the 
distance.
Scanning resolution of STM 
STM does NOT 
probe the nuclear 
position directly, 
but rather it is a 
probe of the local 
density of 
electronic states,
i.e., the size of the 
whole atom 
dominated by the 
electron cloud.
Principle of scanning tunneling microscopy: Applying a negative sample voltage yields electron 
tunneling from occupied states at the surface into unoccupied states of the tip. Keeping the 
tunneling current constant while scanning the tip over the surface, the tip height follows a 
contour of constant local density of states.
Factors affecting the resolution
• One of the factors affecting resolution is corrugation, i.e. how much the electron 
density of surface atoms varies in height above the surface.
• Graphite has a large corrugation, and is very planar, and thus is one of the easiest 
materials to image with atomic resolution. (see next slide for example)
• STM does NOT probe the nuclear position directly, but rather it is a probe of the 
local density of electronic states , so STM images do not always show the 
position of the atoms. STM imaging depends on the nature of the surface and the 
magnitude and sign of the tunneling current. For example, if you have Cu and Si on the 
same surface, under the same condition, the current with Cu is much higher . 
• Since STM images the outermost atom on sample surface, UHV is normally 
required to assure no surface contamination (e.g., coverage of air molecules or 
water) so as to image single atoms or at atomic resolution.
Copied from: http://nanoprobes.aist-nt.com/apps/HOPG%20info.htm
6 carbons in a ring can be classified into 3 A (α) and a B (β) atoms according to their positions relative the 
lower layer of graphene. B (β) atoms , not sitting atop an atom underneath, gives high tunneling current（
“visible”） when imaged under constant height mode, as seen from above result. 
constant current mode
(a) (Color online) Experimental STM image of HOPG at constant-current mode, Vb=−50 mV. (b) Calculated 
STM image at constant-height mode, Vb=−50 mV, and tip-surface distance of 1.2 Å. The triangular structure is 
visualized in both images. (c) And (d) line profiles along the lines indicated in Figs. 1(a) and 1(b), respectively. 
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.79.205431#fulltext
Constant height mode
The 3 β atoms show brighter (higher 
current) than the 3 α atoms, when 
imaged under the same height.
(a) (Color online) Experimental STM image of HOPG at constant-height mode, Vb=−300 mV. (b) Calculated 
STM image at constant-height mode, Vb=−300 mV, and tip surface distance of 1.2 Å. Both images reveal 
the hexagonal atomic structure which is compound by α and β atoms. (c) And (d) are line profiles along the 
lines indicated in (a) and (b), respectively.
STM image of highly oriented pyrolytic graphite (HOPG)
(0001) 5x5 nm, in constant current mode
Among the 6 carbons in a ring, only the 
3 β atoms can be imaged under 
constant current mode, since these 
3 carbons give much higher 
tunneling current, which in turn is 
due to their much higher higher 
local density of states, resulting in 
so called “giant corrugations” 
(enormous apparent heights of 
atoms).
Compared to TEM imaging
Graphite surface: temperature dependence (thermal agitation of electrons)
77 K 29 Å x 29 Å 295 K 37 Å x 37 Å 
Imaged in Constant height mode
Brief Overview of STM
• In the scanning tunneling microscope the sample is scanned by a very fine metallic tip; the scanning can 
be controlled in 3D by a piezo-scanner either bound to the tip or attached under the sample stage. 
• The sample is positively or negatively biased so that a small current, the "tunneling current" flows if the 
tip is in close proximity to the sample. This feeble tunneling current is amplified and measured. 
• With the help of the tunneling current the feedback electronic keeps the current between tip and sample 
constant. If the tunneling current exceeds its preset value, the distance between tip and sample is 
increased, if it falls below this value, the feedback decreases the distance. This is the constant current 
mode for STM, and similarly one can have the constant height mode using the same feedback system. 
• The tip is scanned line by line above the sample surface following the topography of the sample. 
Brief Overview of Tunneling Current
• The tunneling current flows across the small gap that separates the tip from the sample, a case that 
is forbidden in classical physics but that can be explained by the better approach of quantum 
mechanics.
• The tunneling current I has a very important characteristic: it exhibits an exponentially decay with an 
increase of the gap d: I= c*V*e -(k*d); k and c are constants, V is the bias. 
• Very small changes in the tip-sample separation induce large changes in the tunneling 
current!
• This has the consequence that: The tip-sample separation can be controlled very exactly.
• The tunneling current is only carried by the outermost tip atom; the atoms that are second nearest 
carry only an negligible amount of the current: The sample surface is scanned by a single atom!
Brief Overview of STM
https://www.youtube.com/watch?v=HE2yE
8SvHmA
More about STM imaging of HOPG (0111) surface
Basically, the highly oriented pyrolytic graphite (HOPG) crystal is formed by layers of 
honeycomb atomic array of carbon atoms with interatomic distance of 1.42 Å (a single layer 
is called graphene). The layers are held together by van der Waals forces and they present 
an ABAB stacking sequence. This stacking sequence gives rise to a 4-carbon atom unit cell 
with two nonequivalent atomic sites: the α-type-sites, atoms with neighbors directly above 
and below in adjacent layers, and the β-type-sites, atoms without such neighbors 15 (in 
what follows α and β atoms, respectively).
The widely accepted theory for STM image formation of Tománek et al. 12 predicts, for low-
bias voltages, that only β atoms are visible as a consequence of the asymmetry in the 
interlayer interaction in the bulk graphite. Such asymmetry occurs due to the higher local 
density of states (LDOS) of the β atoms compared with α atoms near the Fermi level. This 
(often called triangular) electronic surface structure has a unit cell length of about 2.46
Å corresponding to the periodicity of the lattice, and it is usually reported in the STM 
experiments.1,2 I
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.79.205431#fulltext