microscopy iwdjoiqwjdjsdlkajsldj;lkasjdaljdlkjoiwjjd/smc.s/mn/ml km'k mlm 'lmdmm m

7/23/2019 Microscopy iwdjoiqwjdjsdlkajsldj;lkasjdaljdlkjoiwjjd/smc.s/mn/ml km'k mlm 'lmdmm m

1/18

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

xy-!ieo-"canner


2/18

Technology Required for a STM

Sharp, clean tip (Etching, ion bombardment, field desorption by pulsing)

Piezo-electric scanner (Tube scanner, xyz scanner)

Coarse approach (icrometer scre!s, stic"-slip motors)

#ibrational damping(Spring suspension !ith eddy current damping, $iton stac")

%eed-bac" electronics (&mplify the current difference, negati$e feedbac" to the z-piezo)


3/18

'sually, only oneatom at the end ofthe tip carries most

of the current Thisis the atom thatstic"s out the most(emember thefactor *++ decreasein the tunneling

current per atomdiameter)

The atom at the endof the tip comparesto a ping-pong ballat the top of theatterhorn (TheST !as in$entedin S!itzerland)


4/18

L

Piezoelectric effect

Piezoelectric scanners !or" !ith the trans$erse piezoelectric effectThe crystal is elongated perpendicular to the applied electric field

ELdL #$ L

E electric field,

L

length, L

elongation, d*trans$erse

piezoelectric coefficient

& typical material is P.T (lead zirconium titanate) The ratio bet!een lead andzirconium determines the Curie-temperature and the piezoelectric coefficientExample/ P.T-01/ d

31

2 -34356# ie 72* cm, 7 2 * m, E28+ #6mm

E

& piezoelectric material changes its length!hen an electric fieldis applied#ice $ersa, it generates an electric field !hen s9ueezed or expanded

The analog to piezoelectricity in magnetism is called magnetostriction

:t is produces un!anted magnetic fields in strained nanomagnets


5/18

Piezoelectric scanners

%or three-dimensional positioning one uses xyz-leg scanners or tube scanners

The tube scanner is more compact ($ibrates less, more sturdy) :ts sensiti$ity is/

H

LVdz =

31

V/ applied $oltage, Llength, Hthic"ness, d*trans$erse piezoelectric coefficient.


6/18

Coarse approach

Surprisingly, this has been one of the most difficult obstacles in getting ST goingThin" of the problem the follo!ing !ay/ ;ne starts out !ith the tip about a milli-

meter a!ay from the sample and has to get !ithin about a nanometer to get the

tunneling current started That is a factor of a million :t is li"e dri$ing *+++ "ilo-

meters and stopping from full speed to zero !ithin a meter That might be possible

going $ery slo!ly in a car !ith good bra"es, but it !ould ta"e days (!ee"s


7/18

Feedback regulator

% % )(& dtIII

)(& %IIP

zeI

STM

' -

%I

1o! does one "eep the tunneling current : constant in ST< The current is

compared to a reference current :+(typically +* nanoampere) The difference

(:-:+) is amplified by a factor P and con$erted into a $oltage for the z-piezo

(typically *++#) The sign is important to ma"e sure that the tip mo$es a!ay

if the current too high, thereby reducing it (negati$e feedbac"):n addition to this linear feedbac"(proportional to :-:+)one can use the time

integral o$er (:-:+), as sho!n in the lo!er branch of the diagram This produces

long-term stability and pre$ents feedbac" oscillations

;ne can also use the time deri$ati$e of (:-:+) as feedbac" in order to increase the

scanning speed =y itself the deri$ati$e is prone to oscillations, but it can bestabilized by combining it !ith an integral feedbac"


8/18

ibration da!ping

>amped table (+ , ?)

ST (+@ , ?@)

2

0

22

0

2

0

0

0

1

1

~

+

+

==

Q

Q

x

xT

2

0

22

0

2

0

0

0

'''1

'

+

==

Q

x

xT

s

S

Total transfer function/ TT =T TS

)sin()( % txtx

)sin()( % txtx

)sin()(%

txtxss

Transfer function of the table

Transfer function of the ST

The "ey to $ibration damping is to "eep the resonance fre9uency +of the ST as lo!

as possible (typically * 1z) This !ay most other $ibrations are so far abo$e resonancethat they couple $ery little The main problem is lo!-fre9uency noise (for example fromair conditioning fans) ;ne can try to calculate all of this (see belo!), but it is faster tohoo" up a spectrum analyzer to the tip height signal to find the sources of $ibrations


9/18

"to!ic Force Microscope ("FM)

sample

feedbac"regulator

high $oltageamplifierxy-piezo (lateral position)

deflection

sensor

probing tip

cantile$er

z-piezo(tip-sample distance)

Negative feedback keeps the force constant by ad*usting the -pieo such

that the up-down bending angle of the thin cantilever remains constant.


10/18

#eflection sensors

Laser

Photodiode with

four quadrants


11/18

$ea!%deflection !ethod

& light beam is reflected from the cantile$eronto a photodiode di$ided into A segments

The $ertical difference signal pro$ides theperpendicular deflection

The horizontal difference signal pro$ides thetorsional bending of the cantile$er

The t!o deflections determine perpendicularand lateral forces simultaneously


12/18

A+ m

"FM Cantile&er and Tip

To obtain an extra sharp AFM tip one can attach a carbon nanotubeto a regular, micromachined silicon tip.


13/18

Energy ' and force % bet!een tip and sample as a function of their distance z

The force is the deri$ati$e (2 slope) of the energy :t is attracti$e at large distances($an der Baals force, non-contact mode), but it becomes highly repulsi$e !hen theelectron clouds of tip and sample o$erlap (Pauli repulsion, contact mode)

:n &% the force is "ept constant, !hile in ST the current is "ept constant

Principle of "FM

r

V(r)

Non-contact

modeContact mode

F)

repulsi$e attra!ti$e

z


14/18

#yna!ic Force #etection

f r e 9 u e n c y

am

p

litu

d

e

f r e 9 u e n c y

f

f+

A

( a ) ( b )

( I )

( I I )

The cantile$er oscillates li"e a tuning for" at resonance %re9uency shift and amplitude

change are measured for detecting the force

(a) 1igh ?-factor 2 lo! damping (in $acuum)/

Sharp resonance, detect fre9uency change, non-contact mode

(b) 7o! ?-factor 2 high damping (in air, li9uid)/

&mplitude response, detect amplitude change, tapping mode


15/18

STM &ersus "FM

STM is particularly useful for probingelectrons at surfaces, for example theelectron waves in quantum corrals or theenergy levels of the electrons in danglingbonds and surface molecules.

"FMis needed for insulating samples.Since most polymers and biomoleculesare insulating, the probe of choice for

soft matter is often AFM. This imageshows !A on mica, an insulator.


16/18

(S)T'M (Scanning) Trans!ission 'lectron Microscopy

"onventional Aberration corrected

Batson, Dellby, Krivane, !ature A*8, "#$ (%&&%).

Atomic resolution imageof atom columns in Si#aberration corrected$

% contrast at an interface

iffraction pattern&'igher order spotsimprove the resolution.


17/18

dentify 'le!ents by ''S ('lectron 'nergy oss Spectroscopy)

An element can be identified byits characteristic energy lossesvia excitation of core levels.

The same transitions as seen by()ray absorption

spectroscopy.


18/18

dentify 'le!ents by '#* ('nergy%#ispersi&e *%ray "nalysis)

*dentify an element by its corelevel fluorescence energy.

Semiconductor Si#+i$ etector

An ()ray photon creates manyelectron)hole pairs in silicon,whose number is proportionalto the ratio between photonenergy hand band gap - &

h- /e0 e0 123

4ulse height proportional h

microscopy iwdjoiqwjdjsdlkajsldj;lkasjdaljdlkjoiwjjd/smc.s/mn/ml km'k mlm 'lmdmm m

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