Transcript Scanning Tunneling Microscope (STM)

Scanning Tunneling Microscope (STM)
xyz-Piezo-Scanner
z
high voltage
amplifier
y
x
probing tip
I
feedback
regulator
sample
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.
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)
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 ! )
Piezoelectric effect
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.
Piezoelectric scanners work with the transverse piezoelectric effect.
The crystal is elongated perpendicular to the applied electric field.

L  d31  L  E

E electric field, L length, L
elongation, d31 transverse
piezoelectric coefficient
L
L

E
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: d31 = -2.62Å/V
i.e.
L=1 cm, L = 1 m, E=380 V/mm
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:
z  d31 V 
L
H
V: applied voltage, L length, H thickness, d31 transverse piezoelectric coefficient.
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 millimeter 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 kilometers 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.
Feedback regulator
P * ( I  I0 )
STM
I  e  z
I0
+
I *

0
z
( I  I 0 )dt
How does one keep the tunneling current I constant in STM ? The current is
compared to a reference current I0 (typically 0.1 nanoampere). The difference
(I-I0) 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-I0) one can use the time
integral over (I-I0), 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-I0) 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.
Vibration damping
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.
STM (0’ , Q’)
xs ( t )  xs 0 sin( t   ' )
x ( t )  x0 sin( t   )
TS 
  



'
 0
2
xs 0

2
x0
   2    2
1  
   


   '0    Q'  '0 


Transfer function of the STM
Damped table (0 , Q)
2
x~ ( t )  x~0 sin( t )
Total transfer function: TT = T ·TS
  

1  
x0
 Q0 
T ~ 
2
x0
   2    2
1      

  0    Q0 


Transfer function of the table
Atomic Force Microscope (AFM)
deflection
sensor
cantilever
probing tip
feedback
regulator
sample
xy-piezo (lateral position)
high voltage
amplifier
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.
Deflection sensors
Photodiode with
four quadrants
Laser
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.
AFM Cantilever and Tip
To obtain an extra sharp AFM tip one can attach a carbon nanotube
to a regular, micromachined silicon tip.
40 m
Principle of AFM
V(r)
UF
Contact mode
Non-contact
mode
rz
repulsive attractive
Figure 3.16. Potent ial energy between t ip and
sample as a funct ion of the distance between them.
potent ialtip
is atand
tractive
when they
far apart of their distance z.
Energy U and force F The
between
sample
as are
a function
(non-con
t act), butof
it will
strongly
The force is the derivative
(= slope)
thebecome
energy.
It is attractive at large distances
repulsive when t hey are close together (contact ).
(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.
Dynamic Force Detection
f
(b)
(I)
(II)
amplitude
(a)
frequency
A
f0
frequency
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
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.
(S)TEM
(Scanning) Transmission Electron Microscopy
Atomic resolution image
of atom columns in Si
(aberration corrected)
Diffraction pattern:
Higher order spots
improve the resolution.
Conventional
Z contrast at an interface
Aberration corrected
Batson, Dellby, Krivanek, Nature 418, 617 (2002).
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.
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 EG :
h / EG  keV / eV  103
 Pulse height proportional h