Final report - Leibniz Gemeinschaft

Final report
Space-resolved nanomechanical
properties of functional surfaces experimenent and simulation
Leibniz-Institute: Leibniz-Institut für Oberflächenmodifizierung
Reference number: SAW-2011-IOM-2
Project period: 01.05.2011-30.11.2014
Contact partner: Prof. Dr. Stefan G. Mayr
1
Space-resolved nanomechanical properties of functional surfaces -experimenent
and simulation
Executive Summary
The aim of the project was the space-resolved investigation of mechanical properties of surfaces, thin films
and nanostructures. The work was split into three parts according to the three participating work groups.
Within the group of Prof Grundmann core shell ZnO-BiFeO 3 heterostructures were deposited using pulsedlaser-deposition (PLD) to demonstrate the realizability of ferroelectric heterostructures. The mechanical
characterization was done by measuring the magnetoelectric coupling of BaTiO 3 -BiFeO 3 multilayer
structures. The magnetoelectric coefficient was thereby measured as function of PLD oxygen pressure
during growth and temperature. Within the group of Prof Rauschenbach hexagonal GaN films were grown
on 6H-SiC(0001) substrates by nitrogen ion beam assisted molecular beam epitaxy (IBA-MBE). Using
contact-resonance atomic force microscopy (CR-AFM) the indentation modulus was measured using CRAFM for three different layer thicknesses at three different temperatures. Thereby it was shown that the
indentation modulus is significantly higher for material samples with a thickness of only a few contact radii.
This effect is attributed to the stiffer SiC substrate. Additionally it was shown that the sample is significantly
softer at a temperature of 600 °C compared to the substrate temperatures of 700 °C and 730 °C. This effect
can be traced back to the number of defects in the sample. Furthermore the indentation modulus of Substoichiometric nitrogen ion implanted silicon was measured. While after implantation the indentation
modulus decreases, implantation with fluences > 1 × 1016 N ions cm--2 and subsequent annealing led to an
increase of the indentation modulus above values of crystalline silicon. X-ray photoelectron spectroscopy
showed the presence of Si-N bonds that can explain the stiffening effect of the procedure.
Within the work group of Prof. Mayr, a combined approach of systematic CR-AFM measurements and finite
element analysis was performed to study the behavior of the tip modulus as fit parameter within a multireference sample analysis. The strong deviation found between tip modulus and indentation modulus of
the tip's material is essentially explained by its shape. Finite element analysis unraveled the relationship
between opening angle of the tip apex and the effective tip modulus.
Using DFT simulations the elastic constants of silicon and strontium titanate thin films was studied and used
to design a FEM layer model to study the influence of surface elasticity on the indentation modulus.
Additionally an analytical model is proposed describing the reduction of the indentation modulus with
contact radius agreeing well with the simulation results. Finally, mechanical properties around GaN crystal
steps were studied using molecular dynamics simulations. A reduction of the microscopic elastic constants
was measured within a lateral distance of 1 nm to the step edge. The effects of surface presence and breakdown of half-space symmetry were discussed separately by employing additional finite element
simulations.
2
Final report for SAW project
Space-resolved nanomechanical properties of functional surfaces -experimenent and
simulation
1. Questions at the beginning and aim of project (see project application)
Surfaces, nanoscaled objects as well as nanostructured solids show up different mechanical
properties compared to their bulk counterparts. Although the main origin lies in the existence of
interfaces or boundary surfaces, i.e. a reduced dimensionality, the actual underlying physical
principles are not well understood up to now. The objective of this research project is the
investigation of local mechanical properties during nanoscaled deforming of surfaces, thin films and
freestanding nanostructures. Using representative examples of a few uniquely defined metals and
semiconductors, we want to enlighten the underlying materialphysical scenarios. Therefore we want
to deploy systematic experiments and computer simulations (ab initio, classical molecular dynamics
and finite elements). The gained knowledge should be used for the development of new concepts
optimizing mechanical properties of functional surfaces and nanostructures.
2. Development of realized work including deviations from initial concept
project partner Universität Leipzig, Institut für Experimentelle Physik II, Abt. Halbleiterphysik:
Preparation of surfaces, thin films and nanostructures
coworkers in the project:
Prof. Dr. M. Grundmann, Dr. Helena Franke, M.Sc. Peter Schwinkendorf, Prof. Dr. M. Lorenz
Semiconductor Physics Group at University Leipzig has experience for decades in growth of thin oxide
films, multilayers with single layer thickness in nm-range [UL1 to UL11], and nanostructures [UL12 to
UL16] by pulsed laser deposition (PLD). With that, the initial conditions for the envisaged preparation
work can be considered as excellent. However, we realized during the first attempts to grow BaTiO3based nanowire arrays that the established ZnO growth processes cannot be adopted to BaTiO3, see
results below. ZnO exhibits a strongly anisotropic hexagonal wurtzite structure while BaTiO3 is
tetragonal (nearly cubic) and almost isotropic.
Therefore, we have grown core-shell nano heterostructures consisting of a ZnO core and a BaTiO 3
shell. Because of the dimensions in the nm-range, the corresponding nanomechanical
characterization of the core-shell structures is not trivial. Therefore we worked in parallel on planar
multilayer structures of BaTiO 3 and BiFeO 3 . In such structures, information about the
nanomechanical networking of both crystalline phases can be gained by measurement of the
magnetoelectric coupling, i.e. the strain-coupled interaction of the magnetic (BiFeO 3 ) and
ferroelectric component (BaTiO 3 ). This strain-coupling on a microscopic length scale is a current hot
research topic because of the application relevance of multiferroic and magnetoelectric composites
for future memory concepts.
3
project partner Leibniz-Institut für Oberflächenmodifizierung – work group Prof. Rauschenbach
Characterization of surfaces, thin films and nanostructures
Beteiligte Mitarbeiter:
Prof. Dr. B. Rauschenbach, M. Sarmanova
Contact resonance AFM
For the mechanical characterization we used a self-implemented CR-AFM based upon a commercial
programmable AFM (MFP-3D, Asylum Research), which allowed us to perform a quantitative analysis
of the samples based upon a multi-reference samples approach [IOM-1, IOM-2]. The AFM probes
used for CR-AFM imaging were PPP-NCLR (NanoSensors, Switzerland) with spring constants in the
range between 19 and 33 N/m. Accurate values of the spring constants were determined by an
integrated thermal-noise calibration method of the employed AFM. The applied tip loads varied
between 225 and 900 nN, depending on individual probe stiffness and setup configuration.
Representative 2nd contact resonance frequency values for investigated samples were acquired over
the squared area on each sample. The Quantitative measurements were conducted by point
mapping over 1×1 μm2. 20 uniformly distributed points were taken for each square area. The multireference samples approach was employed for the quantitative stiffness analysis. The Qualitative
results were obtained by continuous scanning over 100×100 nm². Three types of reference samples
were used: amorphous fused silica (FS, indentation modulus M s = 75 GPa), (100) oriented silicon (Si,
M s = 165 GPa) and sapphire (M s = 433 GPa).
After the CR-AFM measurements, every individual probe was visualized from the top and side by
means of scanning electron microscopy (SEM). The obtained images were subsequently digitized for
finite element analysis of the cantilever dynamics, yielding relationship between contact resonance
frequencies and contact stiffness of the tip-sample system k. The latter describes the interactions
between the tip and the sample. Indentation moduli of the implanted samples were determined by
fitting the equation
k m
∗
E ∗ = Eref
(
)
k ref
using experimental data points for both reference samples. Here, the index ref relates to fused silica
and Si reference samples, respectively. E* is the reduced elastic modulus of the tip-sample system
defined from the indentation moduli of the tip M tip and the indentation modulus of the sample
M sample :
1
1
1
=
+
∗
Mtip M𝑠𝑎𝑚𝑝𝑙𝑒
E
Materials
GaN films
The investigated samples were epitaxial c-plane (0001) gallium nitride (GaN) films. They were grown
on 6H-SiC(0001) substrates by nitrogen ion beam assisted molecular beam epitaxy (IBA-MBE). In situ
analysis by reflection high energy electron diffraction (RHEED) was performed for controlling the
4
deposition process. The alterable processing parameters in this study were the SiC substrate
temperature during deposition and the deposition time. Three sets of films were produced. Every set
corresponds to certain substrate temperature during deposition: 630°C, 700°C or 730°C. Ga remains
on the surface were transformed to homoepitaxial GaN by a post-ion nitridation process step at
substrate temperature of 700°C. Films with three characteristic thicknesses were grown for every
substrate temperature: “thin” films with the thickness of several tens of nm, “middle-thickness” films
with the thickness of around 100 nm and “thick” films with the thickness higher than 200 nm. The
crystalline structure of the GaN films was studied ex situ by x-ray diffraction (XRD).
Sub-stoichiometric nitrogen ion implanted silicon
Commercial (100)-oriented silicon samples with a thickness of 410 µm were used as substrate
material. The samples were implanted at room temperature with 100 keV N+ ions at fluences
between 1 × 1015 and 1 × 1017 cm-2. Afterwards, the implanted samples were annealed at 800°C in
three half-hour steps in Ar gas flow between 0.1 and 0.2 l/min, employing a heating rate of
100°C/min.
The depth distribution of nitrogen was determined by time-of-flight secondary ion mass
spectrometry (ToF-SIMS) with 2 keV O+ ions for sputtering and 15 keV Ga+ ions for creating the
secondary ions for analysis. For the nitrogen content, monitoring the secondary ion intensity of Si 2 N+
was found to be the most effective. Depth profiles were recorded after the first (0.5 h) and the third
annealing step (1.5 h). The structure of a Si sample implanted with the highest fluence of 1 × 1017 cm2
and annealed for 1.5 h was investigated by glancing angle X-ray diffraction measurements (XRD).
Chemical bonds states were studied by means of x-ray photoelectron spectroscopy (XPS). Depth
profiles for the signals of O 1s, N 1s and Si 2p were measured. Quantitative analysis of the spectra
and simulation of the chemical states of the elements in the case of insufficient energetic resolution
was performed using commercial XPS data analysis software. Particularly, summing of functions
representing individual peaks corresponding to SiN x , SiO 2 and Si (including a second shifted peak due
to band bending) gives a curve that represents the measured Si 2p peak. Here, a depth step was
corresponding to approximately 20 nm. The depth calibration was in all cases realized by optical
confocal microscopy with 10 nm resolution for determining the final crater depth.
The measurement of complex contact stiffnesses and Q-factors of real surfaces, amorphous thin
films/glasses was too much of challenge, but first measurements of glassy metals were already done
and suggest that surface changes slightly during the measurement.
Project partner Leibniz-Institut für Oberflächenmodifizierung – work group Prof. Mayr
Modelling of surfaces, thin films and nanostructures
coworkers in the project:
Prof. Dr. S. G. Mayr, M. Jakob, J. Buchwald
CR-AFM
With the help of the performed quantitative studies [IOM-1, IOM-2], we were able to make an
essential contribution to the enhancement and better understanding of the method using finite
element analysis of the tip-sample contact [IOM-3], which explains the occurrance of the low tip
modulus compared to the indentation modulus of the material.
5
Thin films
To investigate the mechanical behavior of surfaces, we first applied density functional theory (DFT)
calculations to ultrathin films, i.e. films up to 5 lattice constants thickness. Utilizing the multiscale
approach, the results were compared to atomistic simulations and interpreted employing a
continuum model that contains surface elasticity from the beforehand calculated surface elastic
constants. These constants were implemented building up a layer model that reflects the surface
elasticity. Given that local and surface sensitive properties are nearly exclusively accessible by
scanning probe techniques we used FEM simulations to study the effect of surface elasticity on
indentation response. From the results, especially, the contact radius and force (of a spherical tip)
dependence of the indentation modulus, we found an analytical model that describes the reduction
of the indentation modulus at a surface.
Nanostructures
Besides smooth surfaces we also looked at the mechanical behavior of a step of a few lattice
parameters in height. This was done by evaluating a microscopic expression of the elastic constants,
derived from the fluctuation-dissipation theorem and also by the indentation modulus derived down
to the atomic scale. But also for such a local expression surroundings like the break-down of half
space symmetry plays a non-negligible role. Therefore additional finite element simulations, in which
surface stresses and elasticity are omitted, were done and compared to atomistic simulations.
3. Presentation of achieved results and discussion, future applications
UNI – work group Prof. Grundmann
(a) Growth of ferroelectric BaTiO 3 nanostructures
BaTiO 3 nanostructures were grown in the PLD Q-chamber (Fig. 1) at temperatures in between 500°C
and 950°C, Ar-pressures in between 1 mbar and 200 mbar, and a flow rate of 10 sccm, and target-tosubstrate distance from 3 to 4 cm. Pressures around 1 mbar correspond to the PLD film mode (used
for ZnO films), while higher pressures around 100 mbar induce a vapour-liquid-solid (VLS) growth
process (reported for GaAs nanowires),
Fig. 1. Scheme of PLD Q-chamber for growth of nanostructures: Focused laser pulses (a) provided by the excimer laser hit
the target (b) and excite the plasma (c). The plasma expands in off-axis direction and is scattered at the background gas
to condensate at the substrate (d).
The following growth processes were testes in detail:
• at as-received substrates: fused silica (SiO 2 ), SrTiO 3 (100)
• at substrates with Ti and TiO x nucleation layer
6
•
•
•
at Si substrates with Ti nucleation layer plus Au nanoparticles as additional catalyst (Fig. 2)
at preprepared BaTiO 3 film with Au nucleation nanoparticles (from gold colloide solution)
at different prepared layer stacks: BaTiO 3 , ZnO template from W-chamber, ZnO-wire
template, GaN-wire template
• at substrate with Au catalyst from colloide solution.
There were a lot of experimental efforts to extend the well developed state of knowledge on growth
of ZnO-based nanostructures in the Grundmann group at University Leipzig, see for example [UL1,
UL8, UL12-16], to ferroelectric materials such as for example the cubic BaTiO 3 . For that, the well
established high-pressure pulsed laser deposition [UL13, UL15] was adapted to BaTiO 3 . Figures 2 to 4
show results of these first attempts to grow BaTiO 3 nanostructures.
Fig. 2. Scanning electron microscopy (SEM) images of typical BaTiO 3 nanostructures (sample Q1417) on SiO 2 (fused silica)
with gold nucleation seeds. The scale bars bottom right correspond to 300 µm (left, 60 x) and 30 µm (right, 600 x).
Au (200)
Au (111)
64
BTO (002), (200)
100
BTO (111)
144
BTO (101), (110)
BTO (001), (100)
Intensity (counts)
Fig. 3. Spectrum of EDX element analysis (left) and SEM image (right) of a BaTiO 3 nanostructure (Q1417), see Fig. 2. The
EDX analysis evidenced the relevant elements Ba und Ti (of BaTiO 3 ), Au of the nucleation layer, and Si of SiO 2 substrate.
The scale bar in the SEM image corresponds to 3 µm.
36
16
4
0
15
20
25
30
35
40
45
50
55
60
65
2Theta-Omega (°)
Fig. 4. X-ray diffraction pattern (2 θ-ω scan with Cu K α ) of the BaTiO 3 nanostructures of Fig. 2 and 3 (same sample).
Beside the reflections of gold the BaTiO 3 -peaks are visible, which are broadened due to the reduced coherence length in
the nanostructures. Indexing of peaks was done according to JCPDS 2.0, Au 04-0784 and BaTiO 3 83-1880.
Figures 1 and 2 show that the shape of the BaTiO 3 nanostructures is up to now not regular, although
the transfer of chemical elements in the high-pressure PLD process appears stoichiometric. Most
7
probably, the almost isotropic tetragonal/cubic crystalline structure of BaTiO 3 with isotropic growth
velocities in all three crystallographic directions is the reason for its different growth behavior in
relation to the wurtzite ZnO. The hexagonal ZnO structure with highly anisotropic growth velocities in
a- and c-direction induces the preferential c-axis oriented growth of ZnO-based nanostructures with
high aspect ratio [UL13, UL15]. Because of the missing anisotropy in BaTiO 3 , we have investigated
ZnO nanowires as core which are covered with nm-thin BaTiO 3 films, see following section.
(b) Core-shell ZnO-BaTiO 3 nano heterostructures
Another possibility to grow BaTiO 3 nanostructures are core-shell structures made of ZnO nanowires
(core) deposited with a thin BaTiO 3 film (shell). Such structures with hexagonal core (ZnO) and cubic
wrapping (YSZ/Al 2 O 3 Braggspiegel) have been successfully demonstrated in the work group.
Therefore, we consider this route as practicable for the realization of ferroelectric nanostructures.
(a)
(b)
Fig. 5. (a) Deposited GaN nanowire. The unregular surface structures are BaTiO 3 . (b) Horizontal cross section of a covered
ZnO nanowire. In the center is the ZnO core, which is covered by BaTiO 3 , and subsequently by gold and platinum.
(a)
(b)
Fig. 6. (a) Cross section of a BaTiO 3 -covered ZnO wire (diameter ca. 200 nm), with designation of the materials. From
center to outer edge of the structure we see the almost hexagonal ZnO wire, a BaTiO 3 layer, and gold plus platinum. (b)
ZnO-BaTiO 3 core-shell structure with designation of individual diameter and thickness of ZnO wire and BaTiO 3 film,
respectively.
8
(a)
(b)
Fig. 7. (a) Vertical cross section through a core-shell structure. (b) Obviously, at the top side of the ZnO wire remains a
hollow space by covering with the BaTiO 3 shell. The dimensions of the hollow space are given in (b).
Furthermore, we have deposited in the PLD G-chamber existing nanowire samples of ZnO and GaN.
Homogeneously covered core-shell structures were the result (Fig. 5-7). Vertical growth of BaTiO 3
could be conditionally observed.
Figures 5 to 7 show as final result the successful growth and microscopic demonstration of ZnOBaTiO 3 core-shell nano heterostructures by means of a combination of high- and low-pressure PLD
techniques (unpublished).
(c) BaTiO 3 -BiFeO 3 multilayers with magnetoelectric coupling
The above in section (b) demonstrated ZnO-BaTiO 3 core-shell structures could not be further
characterized by nanomechanical and ferroelectric investigations in the course of the project
because of limited experimental possibilities for nano-sized samples. Therefore, the activities were
further developed towards multiferroic 2-2 nanocomposite thin films.
(a)
(b)
Fig. 8. (a) Transmission electron microscopy image (dark field STEM, (110) cross section) of a multilayer with 15 layer
pairs BaTiO 3 /BiFeO 3 at MgO(100), grown with 0.01 mbar oxygen pressure (G4178). (b) XRD reciprocal space map around
the SrTiO 3 (001) reflection. The multilayer shows clearly resolved fringe satelite peaks because of the layer stack. The
satellite peaks are broadened horizontally due to the tilt mosaizity of the films. The images were taken from [UL17].
2-2 nanocomposites are multilayer structures consisting of two different crystalline phases (here in
our case BaTiO 3 and BiFeO 3 ), that are both arranged two-dimensionally (called 2-2 composite) on top
of each other. Fig. 8 shows a typical cross section taken by transmission electron microscopy (TEM,
9
kindly measured by G. Wagner and O. Oeckler from Faculty of Chemistry of Universität Leipzig) of
such a heterostructure with nano dimensions. The single layer thickness amounts here only 14 to 23
nm, and at higher PLD growth pressure only about 6.1 nm (BTO) and 7.7 nm (BFO), for more details
see [UL2 and UL17].
1x10-3
50 BaTiO3/BiFeO3 Multilayer p(O2) = 0.01 mbar
0
0
-25
Polarization (10-2 C/m2)
25
Current (µA)
5x10-4
20
-20
-50
(a)
-26
-13
0
13
Electric field (106 V/m)
26
µ0M(T)
T = 300 K
10-4
0
-10-4
0
-0.3
BTO
BFO
BTO67/BFO33
BTO33/BFO67
15xBTO/BFO
-5x10-4
-1x10-3
(b)
-4
T = 300 K
0.0
0.3
-3
-2 -1 0 1 2
Magnetic field µ0H (T)
3
4
Fig. 9. Multiferroic properties of BaTiO 3 /BiFeO 3 multilayers: (a) Typical dynamic current-voltage loop (green) mit
indications of broad ferroelectric switching peaks, and ferroelectric hysteresis loop P(E) (blue), measured at 2 kHz. (b)
Magnetic hysteresis loop of a 15 x BTO/BFO multilayer (red), in comparison with the indicated composite and single layer
samples. The multilayer (red curve) shows highest saturation magnetization. Figures taken from [UL2].
Fig. 9 demonstrates the multiferroic functionality of the BaTiO 3 -BiFeO 3 multilayers at room
temperature (300 K), i.e. the samples are simultaneously ferroelectric (Fig. 9 a) and weakly
ferromagnetic (Fig. 9 b). Of particular interest for future application in memory devices is however
the magnetoelectric coupling in the samples, i.e. if the ferroelectric polarization can be influenced by
means of a magnetic field. Experimentally available is the dynamically measured magnetoelectric
coefficient αME = δE/δH demonstrated in Fig. 10, see [UL2] and references therein for details of
measurement. The generally accepted model of magnetoelectric coupling is based on the
magnetostrictive and piezoelectric effect. A magnetic field induces strain of the magntostrictive
phase of the composite, which is transferred mechanically via strain coupling to the piezoelectric
phase and results in changed ferroelectric polarization. The demonstrated ME coefficient of the
multilayer samples at room temperature can be controlled via the PLD growth pressure, as shown in
Fig. 10 (a). The detailed temperature dependence of ME coefficient as given exemplary for two
different multilayer samples in Fig. 10 (b) is up to now not understood completely. The structural
phase transitions of BaTiO 3 may play a role here. This is subject of current and future investigations
to design multiferroic composites with even higher magnetoelectric coupling suitable for applications
[UL17].
10
20
15
10
5
(a)
20
ME coefficient (V/cmOe)
ME coefficient (V/cmOe)
25
0.01
p(O2)(mbar)
0.1
18
16
14
12
10
(b)
8
0
24
22
20
18
0.1 mbar
16
0.25 mbar 14
12
10
50 100 150 200 250 300
Temperature (K)
Fig. 10. Magnetoelectric coefficient of BaTiO 3 /BiFeO 3 ×15 multilayers in dependence on (a) the PLD oxygen partial
pressure during growth, and (b) on the temperature for two selected growth pressures as indicated. The figures are
adapted from [UL17].
IOM – work group Prof. Rauschenbach
GaN films
The AFM images in Fig. 1 represent typical surfaces of epitaxial GaN films. Surfaces of all specimens
mostly consist of the terrace-step structure which is characteristic for the preferred two-dimensional
growth. From RHEED and XRD measurements it is known that the produced GaN films consist mainly
of the thermodynamically stable hexagonal GaN polytype. There is no big qualitative difference
between the topography of films prepared with different substrate temperature conditions.
Nevertheless, the surface of GaN films prepared on the SiC substrate at the temperature of 630°C
exhibits more pores and consists of smaller crystallites. This is induced by a lower adatom mobility
during growth at the lower substrate temperature.
Fig. 11. Topography of the “middle-thick” GaN films (~100 nm). Substrate temperature: a) 630°C, b) 700°C and c) 730°C.
AFM images.
Dealing with the low-thickness films demands accurate determination of the contact area, because
the problem of the substrate influence on the measured elasticity value is of great interest in this
case. Stable measurements were performed with the same probe at all 11 samples, including GaN
films and reference Si and FS specimens. The probe was visualized directly after CR-AFM
measurements by SEM (Fig. 12). The tip apex contour can be regarded as flat punch with a diameter
of 25±5 nm. The corresponding contact radius ac between the tip and the surface is 13±3 nm.
11
Accurate measured material volume can be determined from the distribution of the stress induced in
the film by the tip. For utilized experimental conditions stress decays at the depth over 400 nm.
Fig. 12. SEM image of the probe after CR-AFM measurements.
Elasticity values calculated from the measured contact resonance are plotted in Fig. 13. In the whole,
indentation moduli are quite low and correspond to the values typical for bulk GaN (E=181 GPa). The
typical measurement inaccuracy is in the range of 5-10%. According to the stress distribution the
account of the substrate contribution into the measured indentation moduli is important. But for the
thick films measured elasticity values are free of the substrate influence within the inaccuracy. There
is no qualitative difference between films prepared with the substrate temperatures 700°C and
730°C. At the same time, the elasticity of the films which were produced with the substrate heated to
630°C is significantly lower. This could be explained by the presence of high amount of defects inside
the films and smaller crystallites.
Fig. 13. Indentation moduli of GaN films measured at an applied load of 300 nN.
A thickness dependence of the measured indentation moduli could be attributed to the influence of
the stiff SiC substrate. The percentage contributions into the indentation moduli of the GaN films
with different thicknesses are summarized in Table 1. The elasticity of thick films could be measured
directly, while for the thinner ones it is necessary to take into account the influence of the substrate.
Young’s modulus for the SiC substrate was measured also by CR-AFM to be 430±40 GPa. This means
that the measured values of indentation moduli are high due to the influence of the stiff material
beneath the GaN film.
12
Table 1. Portion of the response from the GaN films with different thicknesses when measuring indentation moduli. A tip
with the shape of a flat punch and a diameter of 25 nm is assumed.
Thickness, nm
31
43
51
95
100
230
238
250
Portion, %
65.4
74.9
79.0
89.9
90.6
97.7
97.9
98.1
Sub-stoichiometric nitrogen ion implanted silicon
In general, keV ion implantation is accompanied by sputter erosion that leads to surface roughening
due to its stochastic nature. In the present experiments, the surface topography of 100 keV N-ion
implanted Si surfaces was studied by using AFM before and after thermal annealing (Fig. 14). From
the lack of roughening we surmise that the surface damage/erosion due to nitrogen ion implantation
and subsequent annealing was negligible.
Fig. 14. AFM surface topographs of the Si samples after the last annealing step; the calculated root mean square
roughnesses (RMS) are also given.
According to the SRIM simulation and calibrated SIMS measurements the implanted layer extends up
to a depth of about 400 nm with an N concentration maximum at 270 nm. The achieved nitrogen
concentrations were significantly below a level of 5.8 × 1022 cm-3 (or 53.7 at.% N) that is necessary for
stoichiometric Si 3 N 4 . Since the annealing temperature was chosen relatively low, no diffusion of
atoms inside the silicon nitride layer is expected. The total nitrogen content did not change, but
some surface oxide layer was formed during the last annealing procedures. XRD measurement
indicates existence of crystallites with different crystal orientations.
13
st
Fig. 15. Secondary ion mass spectrometer (SIMS) depth profiles for the Si samples after the 1 annealing step (solid lines)
and ion depth profiles obtained by the SRIM modeling (dashed lines).
To estimate the material volume measured by CR-AFM, the nanometer–resolved SEM was
performed for visualization of the tip apex of the every individual probe. Significant blunting was
observed for all used probes. The contours of the tip apexes can be regarded as flat punches with a
diameter of several tens of nm.
Indentation moduli as a function of the annealing duration are plotted in Fig. 16. The level of the
indentation moduli for crystalline Si is shown for comparison. As-implanted samples are softer
(stiffness between 110 and 120 GPa) than the original crystalline silicon material because of the
implantation induced amorphization. It is also shown, that the stiffness decreases with increasing ion
fluence. An annealing procedure for 0.5 h at 800°C partially recovers defects in the damaged material
layer. Consequently, the indentation modulus increases in all implanted samples, where the samples
with low-fluence implantation increased up to the value, close to the initial level of stiffness (165 GPa
for crystalline silicon). In contrast, the high-fluence implanted samples required 1 h of annealing to
obtain this recovering level. Moreover, the high-fluence implanted and annealed samples exhibit
higher stiffness than crystalline silicon and the indentation moduli reached values up to 180 GPa. This
result indicates that some nitrogen-silicon bonds can be formed after implantation with fluences >
1 × 1016 N ions cm--2 and annealing.
Fig. 16. Calculated indentation moduli as a function of annealing time. Also shown is an exemplary SEM micrograph of a
blunted tip apex.
14
XPS measurements allowed the detection of Si-N bonds inside the implanted layers. Detailed analysis
was performed for the sample with the highest nitrogen ion fluence. The nitrogen peak N 1s at 397.2
eV indicates the presence of Si-N chemical bonds in the material. The total atomic content of the N
atoms bonded to Si atoms at the distribution maximum was found to be 10% which is almost equal
to the total atomic content of nitrogen in the maximum (see Fig. 15). Si 2p doublets with different
energy as result of the curve fitting procedure are indicative for Si atoms connected to N atoms. The
binding energy of 102.4 eV is attributed to bonding of Si with four N atoms (as in stoichiometric
silicon nitride) and the doublet peak at an energy of 100.7 eV characterizes Si atoms connected to
less than four N atoms (Fig. 17). At the same time, the concentration of the Si atoms with four Si-N
bonds was less than 1% that does not exceed the noise error of the measurements. Therefore, all N
atoms were connected to Si atoms, but they did not form stoichiometric silicon nitride.
Returning to the long term annealing, the observed subsequent abrupt decrease of the indentation
moduli down to values between 100 and 130 GPa can be caused by strong oxidation during the 3rd
annealing step. The thickness of the oxide layer for implanted and annealed sample was measured
with high resolution by XPS. Thick oxide layer was detected at the sample surfaces with a thickness
between 30 and 60 nm. This indicates that oxidation has a strong influence on the stiffness values
obtained by CR-AFM, because near-surface oxide layers give a substantial contribution to the
measured values.
Fig. 17. XPS spectra of the Si sample with the highest nitrogen ion fluence after the last annealing step (signal acquired at
the distribution maximum).
IOM – work group Prof. Mayr
CR-AFM
For the quantitative determination of the elastic properties, we did some multireference sample
studies [IOM-1, IOM-3] including finite element analysis of the contact model adjusting shape-index n
and tip modulus Mtip. The FEM simulations led to good predictions of the dispersion relations of the
first two eigenmodes. From this we could conclude that the small tip modulus, which was already
determined similar by others, can be ascribed essentially to physical processes and the applied
contact model and has hardly something to do with the beam bending model [IOM-3]. Further FEM
simulations utilizing a conical indenter with experimentally measured values of the contact radius
and opening angle and literature values of the elasticity tensor led to a good prediction of the tip
15
modulus. It has been shown that the tip modulus is not just a function of the elastic constants, but
also of the opening angle and converges to the indentation modulus for big opening angles (Fig. 18).
Fig. 18. a) Sideview of two DLC coated cantilever tips b) radialsymetric FEM-model of the simulated tip and related
pressure distribution c) Relative behavior of the tip modulus related to the indentation modulus of Si for different
opening angles an tips (from [IOM-3]).
Thin films
Besides the question of the low tip modulus it was not clear up to now how surface elasticity caused
by surface stresses affects the contact stiffness as well as the indentation modulus especially for such
a surface sensitive techniques like CR-AFM. Therefore, we simulated ultra-thin films of different film
thicknesses, of just a few lattice constants for two materials (silicon and strontiumtitanate). Within
the approach of continuum theory, the reduction of the elastic constants of a thin film caused by
implemented surface stresses as a function of its film thickness L can be described by
𝐶𝑖𝑗𝑘𝑙 (L) = C𝑏𝑢𝑙𝑘
𝑖𝑗𝑘𝑙 + 2
𝑑𝑖𝑗𝑘𝑙
L
because the force which is acting on a volume element is shrinking with increasing film thickness.
a)
b)
Fig. 19. Elastic constants a) C xxxx and C zzzz and b) C xxyy and C xxzz, for Si.
16
a)
b)
Fig. 20. Elastic Constants a) C yzyz and C xyxy for Si and b) C xxxx and C zzzz for SrTiO 3 .
Within the DFT simulations we were able to reproduce this qualitative behavior especially in the
diagonal elements of the elasticity tensor (Fig.: 19 a), 20 a), 20 b) and 21 a)) while the non-diagonal
elements vary widely (Fig. 19 b) and 21 a)). Greater deviations from that law are only observed for
the smallest thicknesses, i.e. for silicon, one lattice constant and three lattice constants for
strontiumtitanate. These deviations are no properties of the single surface, but are explained by the
interactions of both surfaces.
From the DFT calculated surface elastic constants d ijkl , we were able to build up a continuum model,
where the surface elasticity is implemented by layers of the same film thickness differing (reduced)
elastic constants. Further FEM simulations using different tip radii/forces which led to different
contact radii gave us an estimation from which contact radii, surface elasticity becomes important
and has to be taken into account. In Fig. 21 b) we see that a significant change for both materials is
observed already at a contact radius rc of 5 nm. From the simulation results we were able to devise
an analytical model that describes the indentation modulus as a function of its contact radius
assuming each layer can be described by an effective indentation modulus Mi=M inf -c/ai, where c
denotes the reduction, i the number of layers and a the thickness of each layer. Assuming further
that the stress field increases along each direction linearly with the contact radius and each layer
contributes equally, we get the following expression for the indentation modulus as function of the
number of contributing layers (which is proportional to the contact radius r c ):
𝑛
1
1
𝑐�
𝑛
𝑖=1 𝑀𝑖𝑛𝑓 − 𝑎𝑖
𝑀(𝑛) = ��
−1
=�
−1
𝑛
1
𝑐
1
+ 2
�
𝑐 �
𝑀𝑖𝑛𝑓 𝑀𝑖𝑛𝑓 𝑎𝑛
𝑖=1 𝑖 − 𝑎𝑀𝑖𝑛𝑓
at which the last term in the denominator can be approximated by a harmonic series which we
represent by is asymptotic expansion:
−1
𝑐
1
1
+ 2
�𝑙𝑛(𝑛) + 𝛾 +
+. . . ��
𝑀(𝑛) ≈ �
2𝑛
𝑀𝑖𝑛𝑓 𝑀𝑖𝑛𝑓 𝑎𝑛
where γ is the Euler-Mascheroni number. In Fig. 21 b), we fitted the simulation data by the
expansion up to the third term of the expansion taking c as a free fitting parameter.
17
a)
b)
Fig. 21. a) Elastic Constants C xxyy C xxzz, C yzyz and C xyxy for SrTiO 3 b) FEM-Simulation of rel. Indentationsmoduls as a
function of Contact radius r c .
Nano structures
Another interesting point is the dissolvability of smallest nanostructures at surfaces using CR-AFM.
There we can find similar effects as with thin films, where additional stresses change the elastic
behavior. For the investigation of the local elastic properties, we analyzed the stress fluctuations of
the surface around a step of a few lattice constants height (Fig. 22).
Fig. 22. yy- component of Stress fluctuation (multiplied by the quadratic Wigner-Seitz volume) of the upper
Ga atoms along y-axis.
The stress fluctuations can be connected to elastic constants using the fluctuation dissipation
theorem:
𝐵𝑜𝑟𝑛
�−
𝐶 𝑙𝑜𝑐 = �𝐶𝑖𝑗𝑘𝑙
2𝑁𝑘𝑏 𝑇
𝑉
��𝜎𝑖𝑗 𝜎𝑘𝑙 � − �𝜎𝑖𝑗 �⟨𝜎𝑘𝑙 ⟩� +
�𝛿𝑖𝑘 𝛿𝑗𝑙 − 𝛿𝑖𝑙 𝛿𝑗𝑘 �
𝑘𝑏 𝑇
𝑉
At which the first term (Bornterm) only differs for atoms with different coordination numbers and
the last term (kinetic term) can be neglected for small temperatures. The stress fluctuations were
compared to a local defined indentation modulus (Fig. 23 a)) which is extracted from the forces
acting on a specific atom and the two-dimensional Wigner-Seitz volume, which one get from the
projection of the voronoi cells of the surface atoms to the surface plane. The same simulation was
18
also done for a bigger contact radius, realized force acting on all surface atoms within a certain radius
(Fig. 23 b)). Here we see an effective softening, when the indenter is approaching the step edge
(y=9). To measure this effect one would need a lateral resolution of < 1 nm. At the bottom of the
step edge, we don't see this effect, although one would expect that surface stresses also affect the
mechanical properties at the bottom. This can be understood by comparing at the local modulus
which is more sensitive to surface effects (Fig. 23 a)) and FEM-simulations (Fig. 24), where surface
stresses are neglected.
a)
b)
2
Fig. 23. MD-Simulation of the local indentation modulus with contact area a) A C =0.09 nm and b) A C =1.23 nm² on top
and below the GaN step edge.
The local indentation modulus is notably sensitive to local stresses, as the effective contact area is
minimal. Therefore it agrees pretty good with the stress fluctuation, so it decreases both at the
bottom and on top of the step edge, while the FEM simulations show a clear dependence of the step
height, and even an increase of the elastic constants at the bottom of the step (Fig. 24).
From these results one can conclude that both effects cancel in the MD simulation of the flat punch
indentation with the bigger radius at the bottom of the step. Also on top we have an overlap of both
effects, where the geometrical effect dominates the stress effect, which is seen by the range, but
also by the difference between different step heights.
19
2
Fig. 24. FEM simulation of the indentation modulus (A C =1.23 nm ) on top and below the GaN step edge (without
consideration of surface stresses.)
4. Statement about commercialization
Application demonstrators for future magnetoelectric memory and sensor devices are possible in
case of further successful work on the multilayers according to section (c) above.
5. Cooperation partners
Katholieke Universiteit (KU) Leuven, Belgien, Instituut voor Kern- en Stralingsfysica, Celestijnenlaan
200D, B-3001 Leuven, Dr. Vera Lazenka, Prof. André Vantomme, Prof. Kristiaan Temst (measurement
of ME coefficients); Prof. Dr. H. Karl, Institute of Physics, University of Augsburg (nitrogen
implantation).
6. Graduation thesis
PhD thesis Peter Schwinkendorf, submission expected for 2015
PhD thesis Alexander Melvin Jakob (2014)
PhD thesis Jörg Buchwald, submission expected for 2015
PhD thesis Marina Sarmanova, submission expected for 2014
7. List of publications (bold with direct relation to the SAW project)
[UL1] M. Lorenz, M S Ramachandra Rao (guest eds.), Special issue "25 years of pulsed laser
deposition" J. Phys. D: Appl. Phys. 47, 030301 (2014)
[UL2] M. Lorenz, V. Lazenka, P. Schwinkendorf, F. Bern, M. Ziese, H. Modarresi, A. Volodin, M. J
Van Bael, K. Temst, A. Vantomme and M. Grundmann, Multiferroic BaTiO3–BiFeO3 composite thin
films and multilayers: strain engineering and magnetoelectric coupling, J. Phys. D: Appl. Phys. 47,
135303 (2014)
[UL3] M. Lorenz, A. de Pablos-Martin, C. Patzig, M. Stölzel, K. Brachwitz, H. Hochmuth, M.
Grundmann and T. Höche, Highly textured fresnoite thin films synthesized in situ by pulsed laser
deposition with CO2 laser direct heating, J. Phys. D: Appl. Phys. 47, 034013 (2014)
[UL4] M. Jenderka, J. Barzola-Quiquia, Z. Zhang, H. Frenzel, M. Grundmann, and M. Lorenz, Mott
variable-range hopping and weak antilocalization effect in heteroepitaxial Na2IrO3 thin films, Phys.
Rev. B 88, 045111 (2013)
[UL5] K. Brachwitz, T. Böntgen, M. Lorenz, and M. Grundmann, On the transition point of thermally
activated conduction of spinel-type MFe2O4 ferrite thin films (M=Zn, Co, Ni), Appl. Phys. Lett. 102,
172104 (2013)
[UL6] M. Stölzel, A. Müller, G. Benndorf, M. Brandt, M. Lorenz, and M. Grundmann, Determination of
unscreened exciton states in polar ZnO/(Mg,Zn)O quantum wells with strong quantum-confined Stark
effect, Phys. Rev. B 88, 045315 (2013)
[UL7] M. Grundmann, T. Böntgen, M. Lorenz, Occurrence of Rotation Domains in Heteroepitaxy,
Phys. Rev. Lett. 105, 146102 (2010).
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[UL8] M. Lorenz, Pulsed Laser Deposition of ZnO-based Thin Films, chapter 7 in: K. Ellmer, A. Klein, B.
Rech (eds.), "Transparent Conductive Zinc Oxide. Basics and Applications in Thin Film Solar Cells"
(Springer Series in Materials Science Vol. 104, Berlin, 2008) p. 303-358.
[UL9] E. M. Kaidashev, M. Lorenz, H. von Wenckstern, A. Rahm, H.-C. Semmelhack, K.-H. Han,
G. Benndorf, C. Bundesmann, H. Hochmuth, M. Grundmann, High electron mobility of epitaxial ZnO
thin films on c-plane sapphire grown by multistep pulsed-laser deposition, Appl. Phys. Lett. 82, 3901
(2003).
[UL10] M. Lorenz, H. Hochmuth, D. Natusch, H. Börner, K. Kreher, W. Schmitz, Large-area
double-side pulsed laser deposition of YBCO thin films on 3-inch sapphire wafers,
Appl. Phys. Lett. 68, 3332 – 34 (1996).
[UL11] http://www.uni-leipzig.de/~grundm/publ.php
[UL12] Thomas Nobis, Evgeni M. Kaidashev, Andreas Rahm, Michael Lorenz, Marius Grundmann
Whispering gallery modes in nano-sized dielectric resonators with hexagonal cross section Phys. Rev.
Lett. 93, 103903 (4 pages) (2004)
[UL13] M. Lorenz, E.M. Kaidashev, A. Rahm, Th. Nobis, J. Lenzner, G. Wagner, D. Spemann, H.
Hochmuth, M. Grundmann, MgxZn1-xO (0≤x<0.2) nanowire arrays on sapphire grown by highpressure pulsed-laser deposition, Appl. Phys. Lett. 86, 143113 (3 pages) (2005)
[UL14] M. Grundmann, Architecture of nano- and microdimensional building blocks, phys. stat. sol.
(b) 247, 1257-1264 (2010)
[UL15] M. Lorenz, A. Rahm, B. Cao, J. Zúñiga-Pérez, E.M. Kaidashev, N. Zhakarov, G. Wagner, T. Nobis,
C. Czekalla, G. Zimmermann, M. Grundmann, Self-organized growth of ZnO-based nano- and
microstructures, phys. stat. sol. (b) 247, 1265-1281 (2010)
[UL16] C. Czekalla, T. Nobis, A. Rahm, B. Cao, J. Zúñiga-Pérez, C. Sturm, R. Schmidt-Grund, M. Lorenz,
M. Grundmann, Whispering gallery modes in ZnO nano- and microwires phys. stat. sol. (b) 247, 12821293 (2010).
[UL17] M. Lorenz, G. Wagner, V. Lazenka, P. Schwinkendorf, H. Modarresi, M. J. Van Bael, A.
Vantomme, K. Temst, O. Oeckler, M. Grundmann, Correlation of magnetoelectric coupling in
multiferroic BaTiO3-BiFeO3 superlattices with oxygen vacancies and antiphase octahedral
rotations, revision submitted to Appl. Phys. Lett (2014).
[IOM-1] A. M. Jakob, M. Müller, B. Rauschenbach and S. G. Mayr, Nanoscale mechanical surface
properties of single crystalline martensitic Ni–Mn–Ga ferromagnetic shape memory alloys, New J.
Phys. 14 (2012) 033029.
[IOM-2] A. M. Jakob, M. Hennes, M. Müller, D. Spemann, S. G. Mayr, Coupling of Micromagnetic
and Structural Properties Across the Martensite and Curie Temperatures in Miniaturized Ni-Mn-Ga
Ferromagnetic Shape Memory Alloys , Adv. Func. Mat. 23 (2013) 4694–4702
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[IOM-3] A.M. Jakob, J. Buchwald, B. Rauschenbach and S. G. Mayr, Nanoscale-resolved elasticity:
contact mechanics for quantitative contact resonance atomic force microscopy, Nanoscale, 6
(2014) 6898-6910
[IOM-5] J. Buchwald and S.G. Mayr, Influence of surface stresses on indentation response,
submitted
[IOM-6] M. Sarmanova, H. Karl, S. Mändl, D. Hirsch, S.G. Mayr and B. Rauschenbach, Elastic
properties of sub-stoiciometric nitrogen ion implanted silicon, submitted
22