Introduction to nano-scale materials imaging techniques:
Physical principle and operation. 1 Lec. (6)
Slide 2
1981 Invention of Scanning Tunneling Microscopy 2
Slide 3
Scanning Tunneling Microscope (STM) x feedback regulator high
voltage amplifier z y I Negative feedback keeps the current
constant (pA-nA) by moving the tip up and down. Contours of
constant current are recorded which correspond to constant charge
density. probing tip sample xyz-Piezo-Scanner 3
Slide 4
Technology Required for a STM Sharp, clean tip (Etching, ion
bombardment, field desorption by pulsing) Piezo-electric scanner
(Tube scanner, xyz scanner) Coarse approach (Micrometer screws,
stick-slip motors) Vibrational damping (Spring suspension with eddy
current damping, viton stack) Feed-back electronics (Amplify the
current difference, negative feedback to the z-piezo) 4
Slide 5
Usually, only one atom at the end of the tip carries most of
the current. This is the atom that sticks out the most. (Remember
the factor 100 decrease in the tunneling current per atom
diameter.) The atom at the end of the tip compares to a ping-pong
ball at the top of the Matterhorn. (The STM was invented in
Switzerland ! ) 5
Slide 6
LL Piezoelectric effect Piezoelectric scanners work with the
transverse piezoelectric effect. The crystal is elongated
perpendicular to the applied electric field. L E electric field, L
length, L elongation, d 31 transverse piezoelectric coefficient A
typical material is PZT (lead zirconium titanate). The ratio
between lead and zirconium determines the Curie-temperature and the
piezoelectric coefficient. Example: PZT-5H: d 31 = -2.62/V i.e. L=1
cm, L = 1 m, E=380 V/mm E E A piezoelectric material changes its
length when an electric field is applied. Vice versa, it generates
an electric field when squeezed or expanded. The analog to
piezoelectricity in magnetism is called magnetostriction. It is
produces unwanted magnetic fields in strained nanomagnets. 6
Slide 7
Piezoelectric scanners For three-dimensional positioning one
uses xyz-leg scanners or tube scanners. The tube scanner is more
compact (vibrates less, more sturdy). Its sensitivity is: V:
applied voltage, L length, H thickness, d 31 transverse
piezoelectric coefficient. 7
Slide 8
Coarse approach Surprisingly, this has been one of the most
difficult obstacles in getting STM going. Think of the problem the
following way: One starts out with the tip about a milli-meter away
from the sample and has to get within about a nanometer to get the
tunneling current started. That is a factor of a million. It is
like driving 1000 kilo-meters and stopping from full speed to zero
within a meter. That might be possible going very slowly in a car
with good brakes, but it would take days (weeks?). These days the
tip approach is automated and run by a computer program. One uses
two z-motions, a stick-slip motor with coarse motion and a z-piezo
for the fine approach. The following two steps are repeated over
and over again: 1)Expand the z-piezo fully while checking for
tunneling current. 2)If no current is detected, retract the z-piezo
all the way and move the coarse motor. Eventually, a tunneling
current will be detected and the loop stops. 8
Slide 9
Feedback regulator + zz - How does one keep the tunneling
current I constant in STM ? 1.The current is compared to a
reference current I 0 (typically 0.1 nanoampere). 2.The difference
(I-I 0 ) is amplified by a factor P and converted into a voltage
for the z-piezo (typically 100V). The sign is important to make
sure that the tip moves away, if the current too high, thereby
reducing it (negative feedback). 3.In addition to this linear
feedback (proportional to I-I 0 ) one can use the time integral
over (I-I 0 ), as shown in the lower branch of the diagram. This
produces long-term stability and prevents feedback oscillations.
One can also use the time derivative of (I-I 0 ) as feedback in
order to increase the scanning speed. By itself the derivative is
prone to oscillations, but it can be stabilized by combining it
with an integral feedback. 9
Slide 10
Vibration damping Damped table ( 0, Q) STM ( 0 , Q) Total
transfer function: T T = T T S Transfer function of the table
Transfer function of the STM The key to vibration damping is to
keep the resonance frequency 0 of the STM as low as possible
(typically 1 Hz). This way most other vibrations are so far above
resonance that they couple very little. The main problem is
low-frequency noise (for example from air conditioning fans). One
can try to calculate all of this (see below), but it is faster to
hook up a spectrum analyzer to the tip height signal to find the
sources of vibrations. 10
Slide 11
Atomic Force Microscope (AFM) sample feedback regulator high
voltage amplifier xy-piezo (lateral position) deflection sensor
probing tip cantilever z-piezo (tip-sample distance) Negative
feedback keeps the force constant by adjusting the z-piezo such
that the up-down bending angle of the thin cantilever remains
constant. 11
Slide 12
G. Binning, C.F. Quate and C. Berger Atomic Force Microscopy,
Phys. Rev. Lett. 56, 930-933 (1986) 1986 Invention of Atomic Force
Microscopy1986 Invention of Atomic Force Microscopy 12
Slide 13
Deflection sensors Laser Photodiode with four quadrants 13
Slide 14
A light beam is reflected from the cantilever onto a photodiode
divided into 4 segments. The vertical difference signal provides
the perpendicular deflection. The horizontal difference signal
provides the torsional bending of the cantilever. The two
deflections determine perpendicular and lateral forces
simultaneously. Beam-deflection method 14
Slide 15
40 m AFM Cantilever and Tip To obtain an extra sharp AFM tip
one can attach a carbon nanotube to a regular, micromachined
silicon tip. 15
Slide 16
Energy U and force F between tip and sample as a function of
their distance z. The force is the derivative (= slope) of the
energy. It is attractive at large distances (van der Waals force,
non-contact mode), but it becomes highly repulsive when the
electron clouds of tip and sample overlap (Pauli repulsion, contact
mode). In AFM the force is kept constant, while in STM the current
is kept constant. F U repulsive attractive z 16 Principle of
AFM
Slide 17
Dynamic Force Detection The cantilever oscillates like a tuning
fork at resonance. Frequency shift and amplitude change are
measured for detecting the force. (a) High Q-factor = low damping
(in vacuum): Sharp resonance, detect frequency change, non-contact
mode (b) Low Q-factor = high damping (in air, liquid): Amplitude
response, detect amplitude change, tapping mode 17
Slide 18
STM is particularly useful for probing electrons at surfaces,
for example the electron waves in quantum corrals or the energy
levels of the electrons in dangling bonds and surface molecules.
AFM is needed for insulating samples. Since most polymers and
biomolecules are insulating, the probe of choice for soft matter is
often AFM. This image shows DNA on mica, an insulator. 18
Slide 19
(S)TEM (Scanning) Transmission Electron Microscopy Conventional
Aberration corrected Batson, Dellby, Krivanek, Nature 418, 617
(2002). Atomic resolution image of atom columns in Si (aberration
corrected) Z contrast at an interface Diffraction pattern: Higher
order spots improve the resolution. 19
Slide 20
Identify Elements by EELS (Electron Energy Loss Spectroscopy)
20 An element can be identified by its characteristic energy losses
via excitation of core levels. The same transitions as seen by
X-ray absorption spectroscopy.
Slide 21
What is a Plasmon ? A plasmon is a density wave in an electron
gas. It is analogous to a sound wave, which is a density wave in a
gas consisting of molecules. Plasmons exist mainly in metals, where
electrons are weakly bound to the atoms and free to roam. In
contrast to the single electron wave function that we encountered
already, a plasmon is a collective wave where billions of electrons
oscil-late in sync.
Slide 22
Identify Elements by EDX (Energy-Dispersive X-ray Analysis)
Identify an element by its core level fluorescence energy.
Semiconductor Si(Li) Detector An X-ray photon creates many
electron-hole pairs in silicon, whose number is proportional to the
ratio between photon energy h and band gap E G : h / E G keV / eV
10 3 Pulse height proportional h 22