扫描隧道显微镜ppt

x ( t ) = x0 sin(ω t + ϕ )
Damped table (ω0 , Q) ω
Transfer function of the STM
~ ~ x ( t ) = x0 sin(ω t )
ω 1+ Qω x0 0 T= ~ = 2 x0 ω 2 ω 2 1 − + ω 0 Qω 0
Transfer function of the table
2
Total transfer function: TT = T ·TS
Atomic Force Microscope (AFM)
deflection sensor
cantilever probing tip sample high voltage amplifier feedback regulator
∆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.
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 µm, E=380 V/mm
Feedback regulator
STM I ∝ e −κ z
P * ( I − I0 )
I0
I*∫
−τ 0
+
( I − I 0 ) dt
∆z
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.
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.
ω ω' 0
2
STM (ω0’ , Q’) ω
x s ( t ) = xs 0 sin(ω t + ϕ ' )
TS =
xs 0 = 2 x0 ω 2 ω 2 1 − ω ' + Q' ω ' 0 0
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)
xy-piezo (lateral position) 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.
Scanning Tunneling Microscope (STM)
xyz-Piezo-Scanner
z
y x
high voltage amplifier
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.
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 sensitivite 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 ! )