Influence of scanning probe geometry on the imaging
of diffusional processes at the nanoscale
Ulrich Janus, Supervisors: David P. Burt, Dr. Julie V. Macpherson (Department of Chemistry).
Summary
(2) Typical Probe Geometries
Imaging diffusional profiles is important in many different areas ranging from life sciences to materials.
Combined scanning electrochemical - atomic force
microscopy (SECM-AFM) probes allow simultaneous
investigation of surface topography and reactivity at
higher resolution and improved precision than with
SECM alone. For this technique, it is crucial that the
disturbance of the diffusion profile by the tip is minimal. Simulations were carried out to test the effect of
different AFM probe designs on diffusion to support
experimental results.
2.1 Electron microscopy images
This indicates the position of
the electrode in a combined
SECM-AFM tip.
SECM tip
2.2 Probe representation for the simulation
2.3 Probe Dimensions
4.3 Fitting the
simulation results
to experiment
Figure 3.1: (a) Substrate current image (white = no
hindering, black = strong hindering) resulting from
scanning an AFM probe (Si3N4) across an insulating
surface with an electrode embedded in its center. The
triangular shape of the cantilever is reflected in the
current profile (cmp. Figure 2.1). The normalised
current profile along the horizontal line is shown in (b).
Fitting experimental data to the simulation results for LO−FESP − scaled 1.0001.
Fitting experimental data to the simulation results for SiN probe − scaled with 1.012.
1.1
1.1
(a)
The tip is
far away
from the
substrate.
Current is
maximal.
experimental data
simulation data
(b)
1.08
1.05
1.06
1.04
1
Normalized current
Figure 2.3: Electron microscopy images of
the MM-FESP type AFM probe (single
beam cantilever).
Normalized current
Figure 2.2: Electron microscopy images of
the LoT-FESP type AFM probe (single
beam cantilever).
(b)
(a)
The influence of an approaching probe on the concentration
profile evolving around an active site (modelled as a disc
electrode) embedded in an insulating substrate can be investigated by measuring the current at the electrode as the
probe tip is brought close and into contact with the substrate (at the center point of the embedded electrode).
The current at the disc electrode is the result of a diffusionlimited reduction of Ru (NH3)63+. An AFM probe approaching the disc electrode from the top (z direction) or from the
side (x,y direction) hinders the diffusion of the reacting
species to the electrode and reduces the resulting current.
Figure 2.1: Electron microscopy images of
the Si 3N4 type AFM probe (triangular
cantilever).
evolving
diffusion
field
(3) Background
0.95
experimental data
simulation data
0.9
1.02
1
0.98
0.96
height
Figure 1.1: The impact of a conventional
SECM tip on a diffusion field from an active
site.
(1) Introduction
base radius
18 µ m
40°
24°
24°
Base radius
2.7 µ m
6.7 µ m
6.5 µ m
Cant. radius
6 µm
25 µ m
10 µ m
Figure 4.4: The figures show the
simulation approach curves in
comparison with experimental
results. The currents are normalised
with respect to the theoretical
current for a disk-shaped electrode
in bulk solution. (a) Si 3N4 probe,
(b) LoT-FESP, (c) MM-FESP
(oxidised), (d) MM-FESP (metal
coated)
active site
0.94
0.85
0.92
0.8
0
0.2
0.4
0.6
0.8
1
Distance cm
1.2
1.4
1.6
1.8
0.9
2
0
1.08
0.2
0.4
0.6
0.8
−3
x 10
Fitting experimental data to the simulation results for oxi MM−FESP − scaled with 1.004 .
1
Distance cm
1.2
1.4
1.6
1.8
2
−3
x 10
Fitting experimental data to the simulation results for coated MM−FESP − scaleld 1.02 .
1.1
1.8
experimental data
simulation data
(c)
experimental data
simulation data
(d)
1.7
1.06
1.6
1.04
1.5
1.02
1
0.98
1.4
As the tip approaches the surface
it hinders the diffusion to the
electrode and thereby reduces the
current.
1.3
1.2
0.96
1.1
0.94
1
0.92
0.9
0
0.2
0.4
0.6
0.8
1
Distance cm
1.2
1.4
1.6
1.8
0.9
2
0
0.2
0.4
0.6
−3
x 10
0.8
1
Distance cm
1.2
1.4
1.6
1.8
2
−3
x 10
The simulations were carried out using the software package FEMLab,
which implements the Finite Element
Method to solve systems of partial
differential equations (PDE), which
describe the diffusion process. For a
given geometry the concentration
profile of the species diffusing away
from the active site was computed.
10 µ m
7 µm
5 µm
4 µm
3 µm
2 µm
1 µm
0.8
0.7
0.6
0.5
0.4
0.01
0.1
1
Normalised Current
The model consisted of a 2D box
with a disk electrode (an ideal active site) embedded in the bottom
boundary, from where the reduced
species diffuse (Figure 4.1). The
probe was treated as a cone and the
cantilever as a disk “floating” in the
solution.
10
0.95
0.90
1 µm
2 µm
3 µm
4 µm
0.85
0.80
0.75
0.01
Figure 4.7: Influence of the
cantilever (modelled as a
floating disc) radius.
Boundary conditions: At the electrode the species concentration was
maximal, the embedding surface
0.1
1
10
Z Displacement (µm)
Z Displacement (µm)
Figure 4.6: Influence of the
probe base radius.
Figure 4.5: Influence of probe
height on the diffusion to the
electrode.
Mesh: The geometry was meshed
using a quadratic mesh growing
exponentially away from critical
edges (Figure 4.3).
1.0
0.9
5 µm
10µm
15 µm
20 µm
30 µm
50 µm
100 µm
0.8
0.7
0.6
0.01
0.1
1
10
Z Displacement (µm)
[1] Gardner, C. E., Macpherson, J. V., Anal. Chem. 2002, 74,576A.
[2] Dobson,P.S., Weaver, J.M.R., Holder, M.N., Unwin, P.R., Macpherson, J.V.,
Anal. Chem. 2005, 77, 424-434.
Tip base radius µm
C=0
probe
C=0
glass
active site
Acknowledgement
Figure 4.1: Concentration profile for the
Si3N4 tip close to the active site.
insulation
Figure 4.3: Geometry of the “floating probe”
model.
Figure 4.2: The system was solved on a
quadratic mesh growing exponentially away
from critical edges.
100
Height of the probe: Increasing the height
of the approaching tip while keeping its
base radius constant decreases the hindering of the diffusion and in turn results in a
higher current (Figure 4.5).
Base radius of the probe: Increasing the
base radius (or equivalently the angle) of
the tip cone decreases the diffusion to the
electrode and therefore reduces the current
(Figure 4.6.).
Radius of the cantilever: A large cantilever leads to a reduction of the current by
blocking the diffusion. This effect is more
pronounced for probes with a small tip
height such as the Si3N4 probe (Figure
4.7).
(5) Conclusions
n
Tip Height µm
electrode
4.4 Influence of different
probe geometries on the diffusion to the disk electrode.
1.00
0.9
Normalised Current
4.1 Software
and the probe were usually insulating. At the extreme boundaries of
the domain the species concentration was assumed to be zero, while
the left boundary was set to satisfy
a symmetry condition (Figure 4.2).
Normalised Current
(4) Simulations:
References
Thanks go to David Burt, Julie Macpherson and Pat Unwin for assisting me in this
project. I also thank Nikki Rudd, Peter Cock and Martin Edwards for bringing me up
to speed with FemLab.
MM-FESP
15 µ m
1.0
probe
[3] Kwak, J., Bard, A.J., Anal. Chem. 1989, 61, 1221-1227.
LoT-FESP
3.3 µ m
Cone angle
4.2 The Model
axis of symmetry
Finding reliable estimates on the disturbance of the probe
on the diffusion process and using probes that minimise
this disturbance are crucial for these imaging techniques.
While it is generally known that a smaller electrode size
improves the image resolution and minimises disturbance,
the influence of the probe design is less well studied.
Si 3N 4
cantilever radius
Imaging diffusional transport at interfaces is important in
the study of biological processes such as ion transport
across membranes or the release of neurotransmitters at
the synapse.
Scanning electrochemical microscopy (SECM) is a powerful technique used to image interfacial kinetics and concentration profiles over active diffusional sites, though its
resolution is usually limited to the micron scale. Atomic
force microscopy (AFM) is capable of measuring topographical information of the substrate at the nanometer
scale. Recently combined SECM-AFM tips have been
developed to simultaneously gain information on the topography and concentration profiles at high resolutions
and with much more precision at active sites than with
SECM alone[1].
Height
Normalized current
cone
angle
Normalized current
active site
Figure 4.8: The current at the electrode
(colour coded) when the probe is very
close to the electrode (maximal hindering
of the diffusion) as a function of the probe
height and its base radius.
Hindering of the diffusion to the electrode is minimal for high and
narrow probe tips. From Figure 4.8 it can be concluded that the height
of the tip is the determining factor.
n
The design of the cantilever affects diffusion more significantly
when the probe has a small cone height, for example the Si3N4 probe
(see Figure 4.7).