Mechanical scanning probe nanolithography: modeling and application
The paper presents a study on modeling the mechanical interaction between the tip of a scanning atomic force microscope (AFM) and surfaces of various types, which makes it possible to optimize parameters and modes for mechanical AFM nanolithography. The practical assessment of mechanical nanoprob...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2012
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| Cite this: | Mechanical scanning probe nanolithography: modeling and application / P.M. Lytvyn, O.S. Lytvyn, O.M. Dyachyns’ka, K.P. Grytsenko, S. Schrader, I.V. Prokopenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2012. — Т. 15, № 4. — С. 321-327. — Бібліогр.: 23 назв. — англ. |
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| author | Lytvyn, P.M. Lytvyn, O.S. Dyachyns’ka, O.M. Grytsenko, K.P. Schrader, S. Prokopenko, I.V. |
| author_facet | Lytvyn, P.M. Lytvyn, O.S. Dyachyns’ka, O.M. Grytsenko, K.P. Schrader, S. Prokopenko, I.V. |
| citation_txt | Mechanical scanning probe nanolithography: modeling and application / P.M. Lytvyn, O.S. Lytvyn, O.M. Dyachyns’ka, K.P. Grytsenko, S. Schrader, I.V. Prokopenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2012. — Т. 15, № 4. — С. 321-327. — Бібліогр.: 23 назв. — англ. |
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| container_title | Semiconductor Physics Quantum Electronics & Optoelectronics |
| description | The paper presents a study on modeling the mechanical interaction between the tip of a
scanning atomic force microscope (AFM) and surfaces of various types, which makes it
possible to optimize parameters and modes for mechanical AFM nanolithography. The
practical assessment of mechanical nanoprobe lithography based on the method of a
direct surface patterning was carried out during fabrication of functional elements for
molecular electronics. Polymethine dye nanowires of a specified configuration and the
cross-section 3×20 nm have been successfully formed in a multilayer
polytetrafluoroethylene/gold/silicon nanostructure.
|
| first_indexed | 2025-12-07T15:33:57Z |
| format | Article |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 4. P. 321-327.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
321
PACS 81.16.Nd
Mechanical scanning probe nanolithography:
modeling and application
P.M. Lytvyn
1
, O.S. Lytvyn
1
, O.M. Dyachyns’ka
1
, K.P. Grytsenko
1
, S. Schrader
2
, I.V. Prokopenko
1
1
V. Lashkaryov Institute of Semiconductor Physics NAS of Ukraine, 41, prospekt Nauky, 03028 Kyiv, Ukraine
2
Institute of Photonics, Laser and Plasma Technology, University of Applied Sciences Wildau, F.-Engels-Str. 63,
15745, Wildau, Germany
The paper presents a study on modeling the mechanical interaction between the tip of a
scanning atomic force microscope (AFM) and surfaces of various types, which makes it
possible to optimize parameters and modes for mechanical AFM nanolithography. The
practical assessment of mechanical nanoprobe lithography based on the method of a
direct surface patterning was carried out during fabrication of functional elements for
molecular electronics. Polymethine dye nanowires of a specified configuration and the
cross-section 3×20 nm have been successfully formed in a multilayer
polytetrafluoroethylene/gold/silicon nanostructure.
Keywords: scanning probe microscope, nanolithography, nanostructures.
Manuscript received 18.07.12; revised version received 03.09.12; accepted for
publication 17.10.12; published online 12.12.12.
1. Introduction
The dimensions of components for integrated circuits are
mainly determined by lithographic processes, which are,
in their turn, constantly developing in accordance with
the increasing requirements of micro- and nano-
electronics. The minimum size currently achieved is in
the order of several tens of nanometers. Over the period
of 50 years, industrial lithography has reduced the size
of the functional elements of structures from 1 cm (first
transistors in 1958) to ~22 nm (the elements of
processors, 2012) [1]. According to forecasts, the
traditional methods of production will reach the
maximum of their capabilities at around 22 nm, while
technology in 2016 will be based on the functional
elements having a size of about 11 nm. There are two
main approaches in the nanometer size range. The first
one began with the microelectronic technology and was
based on principles of optical, electron-beam, ion-beam,
X-ray, extreme ultraviolet lithography [2-5]. Reducing
the wavelength of light used for exposure of photoresist
as well as usage of X-rays and electron beams provide
the possibility to create patterns with feature sizes less
than 100 nm.
The second approach, nanotechnological, is based
on using a controlled solid state nanoprobe and is known
as scanning probe lithography (SPL) [6, 7]. SPL can be
successfully applied as a separate operation in a
technological cycle and, also, can directly create
functional elements of structures in the prototypes of
leading-edge devices (such as dielectric layers,
nanocontacts, active junctions, etc.).
The most low-cost and relatively easy to implement
methods are those of mechanical scanning probe
lithography. The probe of an atomic force microscope
operating in contact or tapping modes can be used for
both mechanical modifications of a resist film with its
subsequent transferring and etching through a formed
mask, as well as for direct removal of material by
scratching or coining. In this case, the probe is used as a
high precision point contact tool to form trenches in a
resist or metal film covering the substrate surface. Direct
mechanical manipulation can be done with great
accuracy, but it is not always possible to obtain trenches
with edges of acceptable quality because of their
roughness. To achieve required characteristics of a
pattern, it is necessary to optimize a number of
parameters of surfaces as well as probes, and especially,
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 4. P. 321-327.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
322
the dynamic parameters of tip-surface interaction. When
standard silicon or nitride probes are used, mechanical
lithography can be applied on relatively soft substrates,
and there occurs only local modification of the substrate
surface topography without its qualitative transfor-
mation. Electrophysical properties under this technique
do not change. This particular method of SPL is the
focus of this paper.
2. Theory and modeling of the tip – surface
interaction
Hertzian analytical solution of the problem for
elastically deformed state of material that occurs when a
ball is pressed into a plane [8, 9] is the foundation for the
basic models of a contact interaction between the probe
tip of a scanning probe microscope (SPM) and a surface.
In a general case, the relationship between the
interaction force and penetration depth of an n-sided
regular pyramid with the angle of inclination and the
apex in the form of a hemisphere with a radius Rc, which
is not deformed by a contact with the surface, is defined
as [10]:
A
*
),(
),(*=)( ddrr
rf
rpF
where is the penetration depth of an ideal tip; ),( rf
is a function of the tip penetration; ),(* rp is an
analytical function of the tip shape.
Let а be the radius of the contact area, b is radial
distance to the transition point from the spherical tip to
the edge of the pyramid (Fig. 1a). Assuming that a < b,
f(r) is a function of the shape of a spherical tip with
radius Rc, and the Hertzian model for this case can be
expressed as:
2/32/1
2)1(3
4
=
cR
E
F
where E and are Young’s modulus and Poisson’s ratio
for the tip, respectively.
If a > b, for a typical SPM probe in the form of a
quadrangular pyramid, we have:
,
3tan
2
)(
3
arcsin
2tan
2
1
2
=
222/1
2/122
322/1
2
c
c
R
bab
ba
R
a
a
ba
a
E
F
aba
R
a
a
ba
c
2/122
2/3
)(arcsin
2
2
tan
.
If b 0, then we have a regular quadrangular
pyramid, and the expression is presented as:
2
22/1 1
tan
2
1
E
F .
Meanwhile, the effective radius of the contact is
defined as
2/12/tana .
In SPM, load force is determined by the value of
elastic deformation of the cantilever tip:
F = - kx,
2
3
4l
wEt
k .
Here, E is Young’s modulus for the cantilever; t, w,
l are thickness, width and length of the cantilever,
respectively. At the same time, deformation is gauged by
the SPM laser-optical measuring system and calculated
using the calibration data of vertical displacement (Z)
and sensitivity of the measuring system. The example of
SPM “load force - penetration depth” curves is presented
in Fig. 1b.
Depending on the selected cantilever stiffness, it is
possible to get the same displacement when applying
different load forces F (Fig. 2) and thus to have control
over resolution through force:
cR
a
k
F
Z
2
;
3/1
)2
4
1(3
E
FR
a c .
Fig. 1. Model of the hard tip penetration in a soft elastic
surface (a); the experimental load - penetration curves of the
quadrangular pyramidal silicon tip in a gold film (b) measured
at different maximal loading forces [11].
7.35 µN 12.22 µN
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 4. P. 321-327.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
323
Fig. 2. The load force versus the vertical displacements of
SPM probes with different stiffness. Stiffness increases in the
direction of the arrow from 0.01 to 40 N/m (increment of
0.5 N/m).
When a line (trench) is created by means of
scratching the surface of material with a given force, its
geometrical parameters can be described by a simple
phenomenological relation:
,ln)(
,ln)(
22
11
tnn
tnn
FFFm
FFFp
where p is the depth and m is the width of a line; 1 and
2 are coefficients that characterize the wedging and width
of penetration, respectively; 2,1tF are corresponding
threshold forces, after exceeding which the line is formed.
The value of the threshold force can be estimated
from the following ratio:
*
388.1 32
E
HR
F c
t
where Н, Е* are hardness and reduced Young’s modulus
of the sample.
Application of thin and soft layers provides several
advantages: in addition to increasing resolution, it also
prolongs the probe lifetime by preventing premature
wear or an uncontrolled modification of the form of the
tip apex, which happens in the case of engraving on hard
surfaces. On the other hand, under these conditions
(small load forces, soft plastic surface) the contribution
of surface forces to the probe – surface interaction
increases, and for a successful pattering process they
must be taken into consideration.
The most widely used models describing this type
of probe – surface interactions are those of Johnson-
Kendall-Roberts (JKR [12]) and Deryagin-Muller-Topov
(DMT [13, 14]). The phenomenon of a surface capturing
a probe when it is approaching the critical distance is
most often caused by long range attractive forces such as
van der Waals forces. Whereas, when a probe is brought
into a contact with a surface, there occur short-range
force interactions, the most significant of which when
operating in air are capillary forces arising due to the
condensation of moisture on the surface of the probe and
the sample [15].
The applicability of JKR, DMT or transitional
Maugis model [16], for which the first two
approximations are extreme cases, can be easily verified
with the criterion μ proposed by Muller [17]:
,
)1(8
3
32
3/1
3
0
2
22
ZE
R
where Z0 is a typical interatomic distance, is the surface
energy. Under the condition that 1, the
approximation of DMT theory is valid, meanwhile for
µ 1, JKR model becomes applicable. Fig. 3 illustrates
the dependence of the parameter µ on the probe radius for
different values of the surface energy. It is evident that
only at low values of the surface energy and small tip
radii µ can approach 1 (approximation of DMT theory).
Using the Lenard-Jones potential, characteristic
magnitude of van der Waals interaction can be estimated
from the following relation [18]:
,
30
1
6 8
8
0
2
0
2
0
H
ZZ
Z
RA
F
Where AH is the Hamaker constant. Fig. 4 illustrates the
van der Waals interaction force for SPM probes with
different radius and for different values of the surface
energy (the Hamaker constant [19]).
The derivative of force with respect to distance
F/ as a function of distance (Fig. 5a) allows us to
evaluate whether there will occur sticking to the surface
of the probe with a given console stiffness. At the same
time, modeling of JKR interaction for a probe with a
radius of 30 nm at different values of the surface energy
is shown in Fig. 5b.
Fig. 3. Muller’s parameter versus the tip radius of a SPM
probe at the surface energy per unit area from 0.01 to 1 N/m
(increment of 0.02 N/m) as indicated by the arrow.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 4. P. 321-327.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
324
Fig. 4. The van der Waals interaction force versus the probe –
surface distance: (a) – for different values of the SPM probe
radius (5, 10, ... 30 nm); (b) – for different values of the
Hamaker constant (0.1, 0.15, ..., 0.5 aJ). 2
0Z = 0.35 nm.
Arrows indicate increasing of above mentioned parameters.
As it has been already noted, moisture
condensation as well as the formation of water menisci
and capillary bridges between the tip and surface leads
to a significant increase in adhesive interactions
observed in SPM. Within the simplest analytical models,
it has been demonstrated that the maximum force of the
capillary bridge rupture in the first approximation is
calculated as [20, 21]:
ςπγ4)0(
effL RF ,
where L is surface tension for water (72.8 mN/m);
1
1
RR
RR
R c
eff
is the effective curvature radius in the
contact area between the sample and probe, here 1R
corresponds to the local curvature of the convex part of
the sample surface, and Rс is the curvature of the tip of
the probe. For the area of the surface with negative
curvature (depression, pit)
effR is replaced by
effR :
c
eff
RR
RR
R
1
1 .
Fig. 5. Derivation F/ versus probe – surface distance for the
tip radii of 5, 10, …, 30 nm (a). JKR interaction forces for the
tip radius of 30 nm at surface energies of 0.05, 0.06, ...
0.10 N/m (b). Arrows indicate increasing of above mentioned
parameters.
Angles and are local wetting angles of the
sample in the considered nanoarea and of the probe,
respectively; and = (cos + cos)/2 is the average
cosine of the wetting angle for two solid surfaces in
contact.
According to the Young’s formula [22], the
macroscopic wetting angle is determined only by the
surface energy of areas between which a capillary bridge
is formed:
LSSL γγcosγ ,
where S is the surface energy of solids, LS is the solid –
liquid interface energy.
It follows that capillary forces depending on the
radius of the probe (from 30 to 50 nm) can reach values
of 20 up to 50 nN for flat surface areas. For concave
sections, however, the forces may exceed this value by
1.5 – 2 times or more. This is one of the important
factors that affect the quality and controllability of
nanolithographical processes. In particular, the pressing
force of the probe to the surface changes, which in its
turn influences the friction forces that must be overcome
for a horizontal contact motion. On a rough surface, the
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 4. P. 321-327.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
325
value of this additional force can vary considerably,
which is especially relevant for softer materials like
resists. Besides, this also affects the smoothness of
manipulation with the probe on the stages of its
penetration and withdrawing from the material, crossing
existing grooves, etc. Furthermore, in the presence of
surface phase inhomogeneity that is manifested in an
inhomogeneous wetting angle, there arise some
additional (determined by the gradient of the surface
energy) forces acting along the surface, hindering or
helping the horizontal movement of the probe.
3. Results and discussion
The practical implementation of mechanical lithography
was carried out by means of NanoScope IIIa Dimension
3000 (Digital Instruments/Bruker AXS) SPM using
specialized hardware oriented to the macros language
NanoScript
TM
and commercial software code compiler
C
++
. Test patterns were written on nanometer (100 nm)
layers of gold, polytetrafluoroethylene (PTFE) and
multilayer structures based on them (such as PTFE
(10 nm) / Au (30 nm)) formed on silicon substrates.
Silicon, silicon nitride and diamond probes with tips of
different configurations were used to perform the
pattering. The shape of the probe tip was examined
before and after manipulations applying the method
described by us in [23]. As for the structures, they were
manufactured by the technique of thermal deposition in
vacuum. The accuracy with which layers of given
thickness were formed was achieved through precise
calibration of a quartz-crystal resonator in the deposition
chamber via ex situ AFM measurements of the test
layers thickness.
Fig. 6 and 7 demonstrate the selection result for the
value of the load force necessary to form lines (trenches)
with a specified depth in a film of gold on silicon. A series
of lines were created with increasing loads and the
obtained values of depth were compared with the
calculated ones. It can be seen (Fig. 7) that the data
correlate well with the only exception of the cases of
significant depths where an effect the substrate produced
on mechanical properties of the film becomes noticeable.
As for uniformity of depth along the lines, the obtained
values of deviations are approximately equal to the relief
amplitude of a gold film. This indicates the stability of
probe-surface force interaction, despite protrusions of
accumulated material (pile-up) along the edges of the lines.
The problem of the pile-ups can be solved in two
ways: first, by selection of the tip shape and choosing
the optimal scanning direction (Fig. 8), and, second, by
using thin resist layers. As can be seen, the patterning
using a diamond tip in the shape of cube corner with the
apex radius of about 30 nm in the direction along the
probe cantilever creates symmetrical pile-ups (Fig. 8a).
However, the patterning in the direction perpendicular to
the cantilever produces pile-ups only on one side of the
lines (Fig. 8b). Meanwhile the use of a silicon nitride
probe with the same tip radius, but with the angle at the
apex of 30 ensures the formation of a clear line with
minimal pile-ups (Fig. 8c).
Fig. 9 shows an example of test structures patterned
on a PTFE (30 nm) /Au (80 nm) film on silicon by
means of a probe with the tip radius 10 nm and the angle
at the apex close to 17. It can be seen that at the
intersection points the trajectory of the probe movement
remains stable and a straight line is created. Such
approach enables one to manufacture nanostructures by
means of a technique known as “bottom-up”. In this
case, the shallow trenches are formed in the thickness of
the insulator, a layer of PTFE, while the deep trench cut
through to open the gold layer. Filling trenches with
polymethine dye allowed us to obtain predefined
nanowires of dye with the width of 20-100 nm and
height ranged within 1 to 10 nm. The shapes of wires
could be controlled by the cross-section shape of
nanopattern and dye deposition parameters (Fig. 10).
Fig. 6. A series of trenches in a gold film with a thickness of
80 nm created by means of mechanical lithography using a
silicon probe at an increasing load force from 2.3 to 23 µN in
increment of 2.3 µN. AFM images of the surface (a); surface
profile taken perpendicular to the lines (b).
Fig. 7. Experimental (triangles) and calculated (dashed line)
dependences of the trench depth on the loading force.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 4. P. 321-327.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
326
Fig. 8. Formation of pile-ups of different types on the edges of
trenches depending on the motion direction of AFM tip as well
as on its shape and size: diamond tip on a metal cantilever (the
motion is perpendicular to (a) and along (b) the rear edge of the
triangular pyramid of the probe); silicon probe with the tip in
the shape of a regular quadrangular pyramid (c). The surface is
a gold film on silicon.
Fig. 9. 3D AFM image of series of perpendicular lines created
on the PTFE/Au/Si structure by mechanical SPL technique.
Fig. 10. Nanowire of polymethine dye localized in the trench
of the PTFE layer cut through the underlying gold surface
(a). Cross-sections taken in four various points along the
nanowire (b).
4. Conclusions
In our study, we carried out a multilevel theoretical
modeling of the interaction between the tip of an atomic
force microscope and surfaces of different nature, which
allowed us to find the optimal parameters for pattern
application depending on the mechanical properties of
material. Implemented was a prototype of practical
nanoprobe lithography by the technique of a direct
surface patterning through its mechanical modification.
The method was tested in the course of fabrication of
functional elements for molecular electronics. In
particular, in the multilayer polytetraftorethylen/gold/
silicon nanostructure we successfully formed nanowires
of polymethine dye of the 1.520 nm cross-section size
in predefined positions. The created prototype provides
the possibility of a cheap and express technique for
manufacturing a wide range of elements for test
nanostructures of various purposes.
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| id | nasplib_isofts_kiev_ua-123456789-118721 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2025-12-07T15:33:57Z |
| publishDate | 2012 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Lytvyn, P.M. Lytvyn, O.S. Dyachyns’ka, O.M. Grytsenko, K.P. Schrader, S. Prokopenko, I.V. 2017-05-31T05:16:38Z 2017-05-31T05:16:38Z 2012 Mechanical scanning probe nanolithography: modeling and application / P.M. Lytvyn, O.S. Lytvyn, O.M. Dyachyns’ka, K.P. Grytsenko, S. Schrader, I.V. Prokopenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2012. — Т. 15, № 4. — С. 321-327. — Бібліогр.: 23 назв. — англ. 1560-8034 PACS 81.16.Nd https://nasplib.isofts.kiev.ua/handle/123456789/118721 The paper presents a study on modeling the mechanical interaction between the tip of a scanning atomic force microscope (AFM) and surfaces of various types, which makes it possible to optimize parameters and modes for mechanical AFM nanolithography. The practical assessment of mechanical nanoprobe lithography based on the method of a direct surface patterning was carried out during fabrication of functional elements for molecular electronics. Polymethine dye nanowires of a specified configuration and the cross-section 3×20 nm have been successfully formed in a multilayer polytetrafluoroethylene/gold/silicon nanostructure. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Mechanical scanning probe nanolithography: modeling and application Article published earlier |
| spellingShingle | Mechanical scanning probe nanolithography: modeling and application Lytvyn, P.M. Lytvyn, O.S. Dyachyns’ka, O.M. Grytsenko, K.P. Schrader, S. Prokopenko, I.V. |
| title | Mechanical scanning probe nanolithography: modeling and application |
| title_full | Mechanical scanning probe nanolithography: modeling and application |
| title_fullStr | Mechanical scanning probe nanolithography: modeling and application |
| title_full_unstemmed | Mechanical scanning probe nanolithography: modeling and application |
| title_short | Mechanical scanning probe nanolithography: modeling and application |
| title_sort | mechanical scanning probe nanolithography: modeling and application |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/118721 |
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