Scanning Tunneling Microscope (STM) x feedba ck regula tor 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
Transcript
Slide 1
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
Slide 2
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)
Slide 3
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 ! )
Slide 4
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.
Slide 5
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.
Slide 6
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.
Slide 7
Feedback regulator + zz - How does one keep the tunneling
current I constant in STM ? The current is compared to a reference
current I 0 (typically 0.1 nanoampere). 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). 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.
Slide 8
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.
Slide 9
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.
Slide 10
Deflection sensors Laser Photodiode with four quadrants
Slide 11
Beam-deflection method 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.
Slide 12
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.
Slide 13
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. Principle of AFM F U repulsive attractive z
Slide 14
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
Slide 15
STM versus AFM 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.
Slide 16
(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.
Slide 17
Identify Elements by EELS (Electron Energy Loss Spectroscopy)
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 18
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