Comparison of characterization techniques

Similarly, Nishio et al.(11) also investigated the resonant frequency detection of nanomechanical resonators by focusing a single stationary electron beam in the vibration centre of the resonator with SEM/FIB to record the secondary voltage changes. Their detailed method can be seen in ref. (11). However, his theory and experiment only works, when the vibration amplitude of the resonantor is much larger than the diameter of the resonator.

Ivo Utke’s group (87) also explored the resonant frequency and Q-factor of nanomechanical resonators by using a single stationary electron beam focused on the edge of the vibrating resonator in an SEM as shown in section 4.5. A group of tungsten nanomechanical resonators were tested with his setup as shown in section 5.6. However, the limitation of his research setup is that the absolute vibration amplitude is impossible to obtain. Nonaka et al.

(174) used thermal noise to excite the resonator to oscillation and used linescan was analysed to obtain the vibration amplitude by fitting a model. With their model vibration amplitude smaller than the radius of the resonators can be detected. Their model took consideration of the cross-sectional geometry by assuming a cylindrical resonator with uniform material properties. This limited the application of their technique. The technique I have developed in this thesis enables me to overcome this issue and detect the vibration amplitude with model-independent.

5.5.9 Comparison of static and dynamic measurement of C-W nanorods

Figure 5.45 shows the relationship between the Young’s modulus and the diameter of tungsten nanowires fabricated by FIB-induced deposition. The blue data are obtained by static measurements, i.e. AFM force-displacement curves. The experimental details can be seen in section 4.4. The green data are obtained by dynamic measurements, i.e. resonant frequency detection in an SEM. Since the resonant frequency is detected, the young’s modulus can be calculated from the measured resonant frequency according to equation (5.21). The experimental details of dynamic measurement are described in section 5.5. We can see that the Young’s modulus exhibits a size effect, although both measurement techniques overlap within the accuracy of the measurement. The Young’s modulus decreases from ~110 GPa to ~20 GPa with an increasing diameter of tungsten nanowire from 110 nm to 330 nm.

Figure 5. 45: Young’s modulus as a function of the diameter of nanowires fabricated with FIB induced tungsten deposition (a) Young’s modulus as a function of the diameter of nanowires, where the red dots represent the Young’s modulus obtained from dynamic (Data of figure 5.20 replotted) (b) Same data as (a) replotted with Young’s modulus obtained from

dynamic measurement and an additional data point: the green dot here is the Young’s modulus from dynamic measurement of a nanowire thinned by the FIB milling technique

This result suggests that nanowires fabricated with FIB induced deposition have radially non-uniform mechanical properties. EDS analysis of FIB-deposited carbon pillars (179) shows that the core of the nanowire is a gallium-rich region and that the carbon percentage decreases from the core to the edge of the nanowire. The edge of the pillar is a carbon rich

(a)

(b)

region and the size of the gallium rich region is limited to around 40 nm (179). Similar results also have been found in the work of Kometani et al. (176). In the context of our nanowires, it is reasonable to assume that when the nanowire is very thin, it contains less carbon and tungsten; hence the stiffness of the nanowire is dominated by the gallium rich region leading to a comparatively high value of the Young’s modulus. Conversely when the nanowire is thicker, the carbon and tungsten in the nanowire shell result in a comparatively low value of Young’s modulus.

To confirm this conjecture, we have used FIB milling to remove the outer (possibly carbon-rich) shell of the nanowire along its entire length. The detailed procedure can be seen in section 4.4. Figure 5.46 shows the SEM images of the nanowire shows before and after the thinning process. Then the dynamic measurement was conducted on this nanowire, giving a Young’s modulus of 213 GPa.

The original diameter of the nanowire in figure 5.46 (a) is 180 nm and the diameter is reduced to 110 nm after being thinned by FIB milling as shown in figure 5.46 (b). The length of the nanowire is not changed. From figure 5.46 (b), we can see a layer of thickness 35 nm was removed from the surface of the nanowire. Therefore, one of the important reason for the large Young’s modulus is that the thinning process removed the shell of the nanowire (probably the carbon rich region), which has a lower Young’s modulus. The second possible reason is that the FIB milling caused gallium-ion implantation into the nanowire. Hence, the thinning process by FIB milling confirms the core-shell structure of the nanowire fabricated with FIB induced tungsten deposition.

In this section, dynamic measurement of tungsten nanomechanical resonator fabricated with FIB-induced deposition was carried out. The results show that the variation of resonant frequency with the dimension of nanorod is consistent with the theory. The Q-factor of the resonators ranges from 300 to 600. The mass sensitivity can reach to the level of 10^-16 g. In

Figure 5. 46: SEM images of vertical nanowire fabricated by FIB induced tungsten deposition (a) is the original nanowire fabricated by FIB induced tungsten deposition (the length is 18 µm and the diameter is 180 nm) (b) is the same nanowire thinned from its sides

wall by FIB milling (length is 18 µm and diameter is 110 nm)

addition, the measurement technique developed in this work took the advantages of SEM, which enable the noise floor of amplitude detection as low as 5 nm.