j ： numbers assigned to other copper atoms inside the cut-off radius other than a certain copper atom affected by the Morse force of cutter
RESULTS AND DISCUSSION
The AFM probe used by the paper to perform simulation and experimental operation is MikroMasch’s AFM rectangular cantilever probe in NSC15/50 model made of silicon, with density ρ=2330kg/m3 and elastic modulus being 179Gpa. The NSC15/50 rectangular cantilever probe photographed in SEM experiment is shown in Fig.6. After measurement and rearrangement, the dimensions of the cantilever probe are:
length L=100μm, width W=41.3μm and thickness H=4.0μm.
The measured half-side bevel angle of probe tip is , radius R of probe tip radius is 9.4nm, and the height of probe tip is 21μm.
50
. 16
On the AFM machine in D3100 model, the study uses the rectangular cantilever probe in NSC15/50 model to conduct TM-AFM experimental measurement of TGZ01. During experimental measurement, the resonance frequency of probe is 317.4kHz, and the resonance amplitude is 12.56nm. The scanning speed of 0.1Hz is used to conduct TM-AFM experimental measurement of the sample. The acquired 3D surface profile diagram is the same as the section profile diagram drawn from the experiment, as shown in Fig.7.
fr
Ar
In addition, the study carries out TM-AFM simulated measurement and experimental measurement of TGZ01 ladder standard sample under the vibrations in different external environments. The acquired surface profile results are compared, as shown in Fig.8. After comparison, it is found that is vibration in external environment, the acquired surface profile error will be increased, thus producing greater edge effect. Figure 9 shows the surface profiles of the top of TGZ01 ladder standard sample acquired from TM-AFM experimental measurement and simulated measurement. It can be seen that the trends of error change between two surface profiles are very identical. It refers that the surface profile acquired from the experimental measurement without isolation from vibration is very similar to the surface profile acquired from TM-AFM simulated measurement under a sinusoidal
t F t
Fexternal()= 0cosωf action of vibration in external
environment. As seen from Fig.10, the surface profile bevel angle of the vertical edge acquired from simulated measurement and experimental measurement is around , which is almost equivalent to the bevel angle of the probe tip.
The produced horizontal deviation of its vertical edge is mainly caused by scanning speed during experimental measurement.
However, scanning speed is not considered by the study during simulated measurement.
50
. 16
CONCLUSIONS
The study supposes a sinusoidalFexternal(t)=F0cosωft vibration wave in external environment, and investigates the influence of vibration in external environment on the simulated measurement of standard sample. As a result, a TM-AFM fixed-amplitude simulated measuring model is constructed, and the construction of a TM-AFM fixed-amplitude simulated measuring model with vibration in external environment is completed. According to the established TM-AFM fixed-amplitude simulated measurement, different dimension parameters of probe are used to carry out simulated measurement. The study compares the acquired surface profile results between the simulated measurement with sinusoidal Fexternal(t)=F0cosωft vibration and the experimental measurement without real vibration-isolated facility. After comparison, it is found on its plane that there exist waves in similar shape, revealing that the simulated measuring model with sinusoidal Fexternal(t)=F0cosωft vibration established by the study is reasonable in qualitative analysis. As found in the results of simulated measurement and experimental measurement, the bevel edge angle of the vertical edge of the surface profile acquired from simulated measurement and experimental measurement is almost equivalent to the bevel angle of the probe. On the other hand, the bevel edge angle of its probe tip is a factor of the produced error of edge effect. As the bevel edge angle is smaller, the bevel edge angle error of its surface profile will be smaller.
Comparing the acquired surface profiles between TM-AFM simulated measurement and experimental measurement, it is found that there are similar edge effects, and the error in between is not great and is within an acceptable area.
Therefore, it can be proved that the TM-AFM simulated measuring model constructed by the study under the vibration in external environment is reasonable and acceptable, and can be referential in the qualitative analysis of the influence of selected probe dimensions and vibration in external environment on TM-AFM measurement.
Table 1. Parameter value of Morse potential energy of TM-AFM simulated measuring model [11].
DSi(J) αSi(1010m-1) r0Si(10-10m)
4.8573×110-19 0.7891 4.208
Parameter
Si-Si
Figure 1. TGZ01 ladder standard sample [8].
Figure 2. Rectangular cantilever probe NSC15/50 of TM-AFM [9].
Figure 3. Schematic diagram of TM-AFM simulated measuring atomic model.
x z n
t
Fi
r
iforce
φ
ψ
Fxi
Fyi
FvSiix
FvSiiz
FvSii
Figure 4. Force FvSii
borne by a certain atom on the probe tip.
dstart
Z(t)
Z0 Sample
Figure 5. Schematic diagram of the vibrating cantilever probe of TM-AFM scanning measurement.
Figure 6. Results of NSC15/50 rectangular cantilever probe photographed in SEM experiment.
Figure 7. Surface profile of TGZ01 ladder standard sample from TM-AFM measurement.
3000 4000 5000 Ideal Simulation Cose Vibration Isolation Lab.
Noisolation Lab.
Figure 8. Comparison of surface profiles of TGZ01 ladder standard sample acquired from TM-AFM simulated measurement and experimental measurement.
3000 4000 Ideal Simulation Cose Vibration Isolation Lab.
Noisolation Lab.
(a) Comparison of surface profile results between experimental measurement and simulated measurement under the vibrations in different external environments.
3200 3400 3600 3800
10.5 Ideal Simulation Isolation Lab.
(b) Comparison of surface profile results between simulated measurement without consideration of the vibration in external environment and experimental measurement with isolation from vibration.
Figure 9. Surface profiles of the top of TGZ01 ladder standard sample acquired from TM-AFM experimental measurement and simulated measurement.
4200 4300 4400 4500
-12 Ideal Simulation Cose Vibration Isolation Lab.
Noisolation Lab.
16.47o
16.49o 16.51o
16.54o
Figure 10. Gradient of the vertical edge of TGZ01 ladder standard sample acquired from TM-AFM experimental measurement and simulated measurement.
NOMENCLATURES
H = Thickness of rectangular cantilever, μm.
K =Spring constant, kgm-1.
L = Length of rectangular cantilever, μm.
Meff=Effective mass, kg.
W = Width of rectangular cantilever, μm.
start
d =Distance between the TM-AFM cantilever and the sample surface at the beginning of scanning, μm.
fa =Driving frequency, Hz.
α =Si-Si Morse material parameter value, 10Si 10m-1 ζ =Damping ratio.
ω =Driving angular frequency, radsa -1. ωd
=Damped angular frequency, rads-1. ωf
=Vibration angular frequency, rads-1. ωn
=Natural angular frequency, rads-1. ACKNOWLEDGMENTS
The authors would like to thank the National Science Council for financial support of this research under contract No. NSC 95-2221-E-011-014-MY3 and No. NSC 96-2221-E-011-106-MY3.
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