4.9
Scanning Probe Microscopies: Scanning Tunneling
Microscopy (STM)
4.9.1
Basic Electronic Structure of Solids
Before we can understand tunneling phenomena, we need to briefly look at the
electronic structure of solids (e.g. see P.A. Cox, "The Electronic Structure and
Chemistry of Solids" Oxford University Press, 1987 for details)
As we move from
single atom → multiple atoms → solid
electronic properties change from
atomic orbitals → molecular orbitals → band
1 atom
2 atoms
10 atoms
N atoms
E
σ*
σ
N(E)
Density of states (DOS), N(E), is number of energy levels between E and E +
dE (states·eV-1)
- States may have s, p, d, f… or mixed (hybrid) character depending on
origin
Band is effectively (i) continuous and (ii) delocalized over solid
- Bands may be separated by band-gaps of energy Eg
CEM 924
8.1
Spring 2001
- Width of band determined by magnitude of overlap between
individual orbitals
- Depending upon number of electrons and DOS, band may be filled,
partially filled or empty
- Top (partially-)filled band called valence band
- Bottom empty band called conduction band
Empty Band
Fermi
level E F
Band-gap E g
Filled Band
Insulator
Semiconductor
Metal
Energy level dividing filled-empty bands called Fermi level, EF
4.9.2
Surface Electronic Structure
0
free
electron
_
Vacuum Level E V
Workfunction φ
Fermi Level E F
+
hole
Energy level of (just) free electron called Vacuum level, EV
Energy require to move electron from EF to EV at the surface called
workfunction,
CEM 924
8.2
Spring 2001
-
Envisaged as attraction between departing electron and positive image
state (hole)
-
< 2eV (alkali metals) to > 5 eV (transition metal)
Workfunction varies between (i) materials (ii) crystal faces
Polycrystal
φ (eV)
Single crystal
φ (eV)
Na
2.4
W(111)
4.39
Cu
4.4
W(100)
4.56
Ag
4.3
W(110)
4.68
Au
4.3
W(112)
4.69
Pt
5.3
W(poly)
4.5
Workfunction also sensitive to
- adsorbates
- external electric fields
- reconstruction
Workfunction presents a barrier to electron emission - near surface, electron
behaves like a particle in a box
4.9.3
The Tunneling Effect
Solution of the Schrödinger equation inside and outside a solid with noninfinite walls
HΨ = EΨ
 h  d2Ψ
−  
= EΨ
2
2m
  dx
 h  d 2Ψ
−  
+ VΨ = EΨ
 2m dx2
CEM 924
8.3
inside solid
outside solid (V = φ)
Spring 2001
This has solutions
Ψin = Ae i⋅k⋅x + A'e −i⋅k⋅x
1 / 2

2
k =  2 ⋅ m ⋅ E /h 


Ψout = Be i⋅k⋅ x + B' e−i⋅k⋅ x
1 / 2

2
k =  2 ⋅ m ⋅ (V − E ) /h 


The wavefunction outside the solid consists of two parts: the Be-i·k·x part which
is imaginary when E < V and the B'ei·k·x part which is an exponentially
decaying wave
E
V
Electron Ψ in solid
Exponential decay
φ
V
EF
x
Barrier
- Electron density decays exponentially away from surface
- Inverse decay length K (reciprocal of distance for density to fall to
1/e)
-
K=
2⋅ π
2 ⋅ me ⋅ φ
h
= 0.51 φ
for K in Å -1 and φ in eV
- K ≈ 1-2 Å-1 for a typical metal
CEM 924
8.4
Spring 2001
Tunneling occurs if two metals are brought in close proximity (φ1 = φ2)
Metal
E
Vacuum
Metal
V
φ1
φ2
EF
d
BUT current flow equal in both directions?
Apply potential V(ext) to one metal to drive electrons one way (metal 1
negative)
Metal 1
E
Vacuum
Metal 2
V
φ1
long K
short K
EF
φ2
V(ext)
With metal 1 negative with respect to metal 2 (as above)
- tunneling from filled states within V(ext) of EF in metal 1 → empty
states at EF in metal 2
With metal 1 positive with respect to metal 2
- tunneling from filled states within V(ext) of EF in metal 2 → empty
states at EF in metal 1
CEM 924
8.5
Spring 2001
Tunneling is sensitive to electronic structure - convolution of filled
DOS of metal A (-) and empty DOS of metal B (+)
In addition to DOS, Itunnel depends of (i) height of barrier (φ) and (ii) thickness
of barrier (d):
(
I tunnel = A ⋅ exp −2 ⋅ K ⋅ d
)
For a typical metal (K = 1 Å), current falls about an order of magnitude for an
increase of 1.0 Å in d
Consequences?
(1)
very sensitive dependence of tunnel current on d - good "vertical"
resolution
(2)
if one metal is sharp tip, most of Itunnel will travel through pinnacle
atom - good "lateral" resolution
Atomically
sharp tip
99 % of
current
90 % of
current
CEM 924
d
8.6
Spring 2001
4.9.4
Instrumentation for Scanning Tunneling Microscopy (STM)
z
xyz
control
y
x
V
tip
bias
I
Electronics
&
computer
sample
Monoatomically sharp tip (W, Pt/Ir) mounted on 3-D positioner in air, liquid or
vacuum
- tip diameter has pronounced effect on image
- sharp tips produced by mechanical cutting, ion beam milling or
electrochemical etching
Electronics control V (0-3 V) and measure I (1 pA-10 nA)
- "resistance" of gap 107-1010 Ω
- sample-tip separation typically 2-5 Å
Step-size
Start
Computer controls
movement of tip (x, y, z)
in raster fashion on
surface
1 pixel
y (slow)
x (fast)
CEM 924
8.7
Spring 2001
Computer converts each Itunnel measurement to pixel (color α Itunnel) plotted
versus x, y position to generate image
100 Å x 100 Å unfiltered Au(111) STM image
3-D scanner based on piezoelectric materials:
Natural
-x
_
+
+
V
-y
_
+x
_
V
+y
+
4 sector
tube scanner
Piezoelectric material has permanent dipole moment across unit cell PbZrTiO3 (PZT)
If dipoles are oriented, material changes length in applied electric field
- 10-4 to 10-7 % length change per V allows < 1 Å positioning
CEM 924
8.8
Spring 2001
4.9.5
STM Operating Modes
Two ways to operate:
(1)
Constant Height Mode
d
Tip-sample distance fixed - variation in Itunnel forms image
Fast but only works for flat samples
(2)
Constant Current Mode
z
Keep Itunnel constant by moving tip up and down (feedback circuitry) - z
movement becomes image
Slower but works for rough surfaces
Most common
CEM 924
8.9
Spring 2001
4.9.6
Applications of STM - Clean Surfaces
Pt(111) surface (1 x 1
µm) after heating in O2 (1
atm) at 600 °C for 10
minutes
Dissociation of O2 on the
hot Pt surface probably
causes the etching seen
here
Note the atomically flat
terraces and monoatomic
height steps
See work of Gabor
Somorjai (Berkeley)
Atomic resolution (20 x
30 Å) Au(111) surface
Remember that STM
probes the local density of
states (LDOS) of the
surface (and tip). In this
case, the sample is biased
negative 0.3 V and so we
are (mostly) imaging the
filled Au 4f states near
the Fermi level.
CEM 924
8.10
Spring 2001
The so-called Pt(100)
"hex" reconstruction
Pt is a FCC metal so the
(100) surface should
show 4-fold symmetry.
The reconstruction ranges
over many Å but is
largely based on the
movement of different
rows of atoms
See Surf. Sci. 400 (1998)
290
Si(111) surface (200 x
200 Å) showing the (7x7)
reconstruction
This structure puzzled
scientists for many years
before STM
See early work of Robert
Hamers (Wisconsin)
CEM 924
8.11
Spring 2001
4.9.7
Applications of STM - Adsorbate Covered Surfaces
CH3(CH2)20CHOH on
graphite - molecule "lays
down" in all-trans
configuration and headto-tail alignment
Each H atom (only one
per C atom, other points
towards surface) appears
as site of high Itunnel
Dark trough is though to
be position of -OH group
See work of George
Flynn (Columbia)
Mixed monolayer of Cophthalocyanine and Cuphthalocyanine
Co(II) is d7 with halffilled dz2 band (band at
EF) - appears bright in
center of molecule
Cu(II) is d9 with filled dz2
band - appears dark in
center of molecule
See work of Kerry Hipps
(Washington State)
CEM 924
8.12
Spring 2001
C2H2 (acetylene) imaging
and rotation on Cu(100)
surface at different
temperatures
Rotation is activated at
about 68 K
See recent work of
Wilson Ho (Cornell)
CEM 924
8.13
Spring 2001
4.9.8
Applications of STM - Manipulation and Chemistry
Several researchers have successfully moved atoms and molecules on surfaces
using one of several methods
- field effect - under influence of high electric field, polarizable
molecule or atom can be made to jump from surface to tip or vice
versa
- dragging - vdW forces between close tip and adsorbate can be used to
drag species
Xe on Ni(110) at 4 K
The first atom-by-atom
manipulation
See Nature 344 (1990)
524-526
Fe on Cu(111)
Construction of a
"quantum corral" and the
visualization of electron
standing waves near EF
inside the corral
See work by Don Eigler
(IBM, Almaden)
CEM 924
8.14
Spring 2001
Recently, several groups have used electrons from tip to break intramolecular
bonds
Dissociation of two O2
molecules on Pt(111) at
50 K by increasing tunnel
current
Note that each molecule
can be dissociated
individually by
positioning the STM tip
above the molecule of
interest
See W. Ho et al Phys.
Rev. Lett. 78, (1997)
4410-4413
4.9.9
Scanning Tunneling Spectroscopy (STS)
Many surface sensitive techniques give information about average atom of
molecule
Chemistry may be very position sensitive
In principle, STM can map out electronic structure of surface with atomic
precision
- when tip is biased negative - get information about empty electronic
states on surface
- when tip is biased positive - get information about filled electronic
states on surface
CEM 924
8.15
Spring 2001
- by changing bias can resolve "location" of individual electronic states
- between -0.15 and -0.6 V current due to dangling bond states in
faulted half of unit cell
- between -0.6 and -1.0 V current due to dangling bonds in second layer
of atoms
- between -1.6 and 2.0 V current due to Si-Si bonds
CEM 924
8.16
Spring 2001
Plot of Itunnel versus V (bias) provides information about local electronic (and
even vibrational) structure
- often plotted as I/V, dI/dV or d2I/dV2 curves
CEM 924
8.17
Spring 2001
4.10 Summary
"Real space" images
Excellent lateral (<1 Å) and vertical (<0.1 Å) resolution
Obtain information about surface unit cell size and symmetry or electronic
structure
- can directly image molecular orbitals
Some spectroscopic information (STS) may allow identification
Fast enough to allow some dynamic information
Can both initiate and probe electron-induced chemistry
BUT
Complex and expensive instrumentation - especially UHV version
Subject to noise (electrical, vibration)
Image is convolution between tip and surface electronic structure - not truly a
topographic measurement
Must fabricate tips - dull tips or multiple tips create serious artifacts
Only works for conductive samples - metals, semiconductors - though can
tunnel through thin insulators (<20-30 Å)
CEM 924
8.18
Spring 2001
4.11 Scanning Probe Microscopies: Atomic Force and Related
Microscopy (AFM)
Developed by Binnig, Quate and Gerber in 1986 from scanning tunneling
microscope (STM)
Relies on measuring forces between a sharp tip (< 100 Å diamater) and surface
at very short distances (2-100 Å tip-surface separation)
- tip supported on flexible cantilever
4.11.1
Surface Forces
V
Intermitant
contact
mode
d
Contact
mode
Non-contact
mode
(1)
Non-contact AFM vdW attraction 10-100 Å tip-surface separation
(2)
Contact AFM e--e- repulsion <5 Å tip-surface separation
(3)
Intermittent contact AFM (tapping mode AFM) 5-20 Å tip-surface
separation
(1)
In contact mode:
F(x) = −k ⋅ x
Hooke's Law
Spring constant of cantilever is less than surface, cantilever bends
CEM 924
8.19
Spring 2001
Cantilever
F=-k·x
Pyramidal
tip
x
Typical atom-atom k ~ 10 N·m-1, typical cantilever k 0.1-1 N·m-1
Total force on sample 10-6 to 10-8 N
If spring constant of cantilever is greater than surface, surface deformed
- nano-machining?
Deflection of tip measured by "beam bounce" method:
Semiconductor
diode laser
Position
sensitive
detector
(PSD)
Piezoelectric positioners
or use of piezoelectric cantilever (resistance change with deformation)
CEM 924
8.20
Spring 2001
Can operate in two modes:
(A) Constant force - z piezo moves sample to keep constant tip
deflection
accurate topography, but slow (limited by time constant of
cantilever)
(B) Constant height - keep z piezo fixed and measured deflection
directly
fast, but flat samples only
(2)
In non-contact mode:
Very small force on surface (~ 10-12 N)
- tip-surface distance 10-100 Å
- best for soft or elastic surfaces
- least contamination
- least destructive
- long tip life
Such small forces are difficult to measure using direct beam-bounce method use AC driven oscillating cantilever (100-1000 Hz frequency, 10-100 Å
amplitude)
- resonant frequency ν =
1
k
2⋅ π m
- k varies with external force gradient (dF(x)/dx) so frequency changes
with external force
- electronics adjust tip-surface distance to keep resonant frequency
constant - constant tip force
CEM 924
8.21
Spring 2001
Contact and non-contact show similar topography except for soft/deformable
materials
(3)
In intermittent contact (tapping) mode:
Similar to non-contact AFM using vibrating cantilever except at one extent tip
"taps" into contact mode
Useful for soft surfaces - less prone to external vibration/noise than noncontact - but will not image water layers (pierce)
Less destructive than contact AFM and can image rougher samples
4.12 AFM and Other Scanning Probe Microscopies
4.12.1
Magnetic Force Microscopy (MFM)
Coat AFM tip with magnetic material - probe magnetic structure of surface
Must collect data at different tip-surface separations
- in non-contact mode (< 100 Å) topography
- in far non-contact mode (>100 Å) magnetic field
(left) Contact AFM image of magnetic hard drive surface (right) same area but
in MFM mode. Approximately 25 x 25 µm
CEM 924
8.22
Spring 2001
4.12.2
Lateral Force Microscopy (LFM)
Measure both vertical and lateral (twisting) deflection of tip in contact mode
AFM
A
PSD
B
Vertical
deflection
Lateral
deflection
A
C
B
D
Vertical
deflection
- gives information about friction (tribology)
- but must acquire simultaneous AFM and LFM images to deconvolute
twisting due to surface roughness
Direction of
tip travel
Material A
Material B
LFM Image
Direction of
tip travel
Material A
LFM Image
CEM 924
8.23
Spring 2001
4.12.3
Instrumentation for AFM and Related Techniques
Cantilevers and tips are typically of Si3N4 or BN (hard)
100-200 µm long, 0.1-2 µm thick and 10-40 µm wide
k = 0.1-10 N·m-1, νresonant = 1-100 kHz
Fabricated by thin film growth on Si wafer
Silicon nitride
Si etch pit
(pyramidal)
~20 µm
Finished
cantilever
~200 µm
Shape of etch pit determines shape of tip - can be ~ 50 Å in diameter
Shape of tip (aspect ratio) affects resolution - closest that two objects can be
separated (50 % baseline)
High aspect
(conical)
tip
Low aspect
(pyramidal)
tip
Tip path
Surface
Sharper tip can be made by ion beam milling at grazing incidence or electron
beam deposition and lateral resolution of AFM now approaching STM
CEM 924
8.24
Spring 2001
Scanning electron micrographs of a pyramidal and conical AFM tip.
An example of a double-tip artifact image
4.12.4
Applications of AFM
Ambient tapping mode
AFM of DNA strand on
mica (1 x 1 µm)
Each DNA strand is 20 Å
high and would be easily
compressed using contact
AFM
See Digital Instruments
(www.di.com)
CEM 924
8.25
Spring 2001
50 x 50 µm tapping mode
AFM of dried protozoan,
Tetrahymena, showing
cilia-covered body and
mouth structures. The
sample was dried onto a
glass slide.
See C. Mosher and E.
Henderson, Iowa State
University
Atomic resolution on
NaCl(100) surface using a
variant of contact mode
UHV AFM - bright (high)
spots correspond to Clions?
Arrows mark positions of
surface defects
See work of H.-J.
Güntherodt (University of
Basel, CH)
CEM 924
8.26
Spring 2001
A 14 x 14 µm non-contact
AFM image of a screw
dislocation in a single
crystal of a long chain
alkane (C36H74)
See University of Bristol
(UK) SPM group.
CEM 924
8.27
Spring 2001
4.13 Summary
Not limited to conducting samples - especially powerful for biological, organic
and polymer samples
Simpler instrumentation than STM
Commercial tips and cantilevers
Provides true topographic imaging
Related AFM techniques can measure other physical properties hydrophobicity, magnetism, electrostatic charge, friction, elastic modulus
Non-contact or tapping mode causes minimum damage to soft/fragile samples
Recent results demonstrate atomic resolution using special tips (<2 Å lateral)
BUT
Noise, vibration sensitive
Presence of water (capillary action) may distort image
Contact mode can damage surface
"Chemically blind"
As with STM, tip shape convolutes into image
Typical lateral resolution ~50 Å
CEM 924
8.28
Spring 2001