Chapter 4 Excitation Source and Transmission
4.1 Cantilever Holder Design
4.1.4 Chip-clamped modification
The adjustable preload holder not only changes the preload on the cantilever chip, but also the preload on the piezoelectric actuators. Therefore, the cantilever clamp design could constrain the movement of the piezoelectric actuators. Besides, the steel T-shape clip connects the cantilever chip and the holder base, and the vibration can also transmit through it. Therefore, a clamp-modification holder is developed for decreasing the affection from the holder base. As shown in Figure 4.13, the steel spring chip is isolated to the holder base, and is screwed on the chip support directly.
(a) Holder structure
(b) Holder pictures
Figure 4.13 Clamp-modification holder
The driving amplitude is 1V, and Figure 4.14(a) shows the result of the flexural signal spectrum of the PPP-NCHAuD cantilever. Only the PPP-NCHAuD No.2 is shown, because the PPP-NCHAuD No.01 is broken accidentally during handling the cantilever. The result shows the first flexural resonant peak can be excited, but few peaks appear around 300 kHz. Figure 4.14(b) shows the lateral signal spectrum, and two peaks appear around 830 kHz and 1015 kHz.
(a) Flexural signal
Amplitude (mV) Flexural excitation spectrum Frequency (kHz)
PPP-NCHAuD No.02
(b) Lateral signal
Figure 4.14 Spectrums of cantilever PPP-NCHAuD
The flexural signal spectrums of the CSC38B cantilevers with two different frequency ranges are shown in Figure 4.15(a). Unlike the experimental results of the previous holder, the first flexural resonant peak around 3~4 kHz can be excited clearly.
However, the second flexural resonant peak can’t be observed, and spurious peaks appear between 200 kHz and 400 kHz. Besides, the resonant peak in the excitation spectrum is sharper than that in the thermal fluctuation spectrum. The Q-factors of CSC38B No.01 and No.02 in the thermal fluctuation spectrums are 1.8 and 1.7. On the other hand, the Q-factors of the two cantilevers are 14.7 and 23.9 in the excitation spectrums. From the lateral signal spectrums shown in Figure 4.15(b), the torsional resonant peak can also be excited. No spurious peak is observed on the spectrum of the cantilever CSC38B No.01. However, the torsional resonant peak of the cantilever CSC38B No.02 is smaller, and a spurious peak appears around 230 kHz.
0 200 400 600 800 1000 1200 1400 1600 1800 2000 0
0 200 400 600 800 1000 1200 1400 1600 1800 2000 0
200 400 600
Frequency (kHz) Amplitude (mV) Torsional excitation spectrum
PPP-NCHAuD No.02
(a) Flexural signal
Power (μV2 /Hz) Thermal fluctuation spectrum
0 1 2 3 4 5 6 7 8 9 10
Amplitude (mV) Flexural excitation spectrum
0 50 100 150 200 250 300 350 400 450 500
0 200 400
Power (μV2 /Hz) Thermal fluctuation spectrum
0 50 100 150 200 250 300 350 400 450 500
0 500 1000
Amplitude (mV) Flexural excitation spectrum Frequency (kHz)
CSC38B No.01 CSC38B No.02
(b) Lateral signal
Figure 4.15 Spectrums of cantilever CSC38B
4.2 Conclusion
In this chapter, the material modification shows a suppressed effect for spurious peaks. Next, the adjustable preload holder is developed, and shows that the excitation spectrum can be optimized through adjusting the preload. However, it also changes the preload on the piezoelectric actuators, and the affection needs to be further identified.
Finally, the clamp-modification holder is developed. This design isolates the spring clip and the holder base, and avoids the constriction on the piezoelectric actuators. On this holder with simple mechanical structure, both the flexural and torsional peaks can be excited on two different kinds of cantilevers.
0 50 100 150 200 250 300 350 400 450 500 Amplitude (mV) Torsional excitation spectrum
CSC38B No.01 CSC38B No.02
Chapter 5
Cantilever Detection System
The cantilever detection system is used for measuring the cantilever deformation, and its sensitivity directly affects the force resolution. The astigmatic detection system (ADS) is adopted because of advantages of the small spot size (~ 1 μm), the high bandwidth (80 MHz), and the compact dimensions (48.7 × 36.7 × 7.5 mm) [54]. For realizing effective operation in water, the optimal water thickness is evaluated and examined to minimize the influence of water, and the optical scanning mode in water is also successfully demonstrated. Besides, a time-saving and non-damaging spring constant calibration process is proposed and verified based on the ADS, and this method can be extended to calibrate the other tipless cantilever used in biotechnology.
5.1 Astigmatic Detection Method
The astigmatic detection method is widely used in the digital versatile disk (DVD) pickup head, and its optical configuration is illustrated in Figure 5.1(a). A laser beam is focused onto the cantilever through a collimator and an objective lens. After passing through a cylindrical lens, the reflective laser beam is detected by the photodetector integrated chip (PDIC). As shown in Figure 5.1(b), the four quadrant photosensors (A~D) on the PDIC generate voltage signal UA, UB, UC, and UD, respectively. When the laser is exactly focused on the cantilever, the laser spot on the PDIC is circular as illustrated at the point (II). But, any defocused displacement ± z will cause the laser spot to change into elliptical shape as displayed at points (I) and (III). The cantilever displacement is measured by the focus error signal UFES = (UA + UC) - (UB + UD), and
the UFES versus cantilever displacement curve (S-curve) characterizes their linear relationship with a range of ± 3 µm roughly. The focus error signal UFES can thus be directly related to the cantilever displacement in the linear region.
(a)
(b)
Figure 5.1 (a) Configuration of ADS and (b) focus error signal UFES versus cantilever displacement
For further experiments, an astigmatic pickup head (TOP1100Sc, TopRay Technologies) is chosen, and its structure and specification are shown in Figure 5.2 and Table 5.1, respectively. The DVD-wavelength of 655 nm is adopted in the experiments,
Figure 5.2 Astigmatic pickup head
Table 5.1 Specification of TopRay pickup head
Item DVD CD Laser diode
wavelength 655 nm 790 nm
Objective lens Aspheric plastic lens Aspheric plastic lens
Focal length (FL) 2.33 mm 2.35 mm
NA 0.6 0.47
Working distance 1.28 mm 0.91 mm
Detection method Astigmatism Astigmatism Photo detector PDIC with I/V amplifier PDIC with I/V amplifier PDIC response
5.2 Detective Sensitivity in Water
For reading the data on the DVD optical disc as shown in Figure 5.3(a), the astigmatic pickup head is designed with an objective lens, which has the focal length (FL) of 2.33 mm and the numerical aperture of 0.6. The numerical aperture (NA) and the refractive index nair of air determine the focused angle θair of laser in air as following Equation (5.1). The laser angle θair in air is 36.87o.
air
nair
NA= sinθ , (5.1)
A 0.6-mm thick polycarbonates layer refracts the laser beam to focus on the recording layer. Equation (5.2) describes its refractive relation. Through the refractive index npc of 1.58, it derives a focusing angle θpc of 22.32o. For measuring in water environment, the optical path is modifed as Figure 5.3(b).
A cover glass is placed above the water layer to avoid a cambered water surface. The thickness hglass of the cover glass (Hecht Assistent) is 0.15 mm, and its refractive index nglass is 1.52. The laser angles θglass of 23.24o and θwater of 26.82o can be derived from where the refractive index nwater of water is 1.33.
For compensating the change of mediums, the optimal water thickness hwater needs to be evaluated. Supposing that the laser path before into the glass is unvaried, the water thickness hwater should satisfy
water where the calculated optimal water thickness hwater is 0.36 mm.
(b)
Figure 5.3 Optical paths of (a) DVD optical disc, and (b) water environment
For examining the sensitivity of the ADS, an experimental setup is established as shown in Figure 5.4. Glass slices are stacked on a mirror for adjusting the water thickness hwater, and water is contained between the mirror and the cover glass. The mirror is brought into the working distance of the pickup head through a Z stepper motor, and a closed-loop XYZ scanner (P611.3S NanoCube, Physik Instrumente) is utilized to obtain the S-curve. Besides the original objective lens with FL = 2.33 mm, a plastic aspheric lens with FL = 3.30 mm (CAY033, ThorLab) and a glass aspheric lens with FL = 3.10 mm (352330-B, ThorLab) are also tested for comparison.
Figure 5.4 ADS sensitivity measurement setup
Figures 5.5(a) shows the S-curves equipped with the original objective lens with FL = 2.33 mm, and Figures 5.5(b) and 5.5(c) represent the results of the lenses with FL
= 3.30 mm and FL = 3.10 mm, respectively. The overload occurs when UFES is over ± 10.7 V due to the output limitation of the pickup head pre-amplifier. The S-curves of the lenses with FL = 3.30 mm and 3.10 mm are more symmetric than that of the original lens with FL = 2.33 mm, and their peak to peak values are inverse proportioned to the water thickness hwater. Under the same water thickness hwater, the S-curve of lens with FL
= 3.10 mm has larger peak to peak value than that with FL = 3.30 mm. On the other hand, the curve of the original lens with FL = 2.33 mm has larger peak to peak value at hwater = 0.19 and 0.48 mm.
(a) Original lens with FL = 2.33 mm
(b) Lens with FL = 3.30 mm
(c) Lens with FL = 3.10 mm
Figure 5.5 UFES versus displacement curves (S-curves)
The slope of the linear region of the S-curve is calculated through the first degree polynomial curving fitting, and represents the sensitivity SADS defined by the UFES
variation per unit displacement. The results are listed in Table 5.2, and the sensitivity variations with the water thickness hwater are shown in Figure 5.6. The lenses with FL = 3.30 mm and FL = 3.10 mm have highest sensitivities in air, and their sensitivities are inverse proportioned to the water thickness hwater. On the other hand, the original objective lens with FL = 2.33 mm has highest sensitivity of 4.040 mV/nm at hwater = 0.48 mm. In this condition, the sensitivity approximates to the result obtained by passing through the polycarbonates layer in air. According to the experimental results,
the shorter working distance will raise the difficulty on the cantilever holder design.
Therefore, the original objective lens is still adopted, and the optimal combination of the cover glass (hglass = 0.15 mm) and the water thickness (hwater = 0.48 mm) is obtained.
Table 5.2 Sensitivity SADS of objective lenses under different water thicknesses Water
0.19 1.869 1.188 2.736 0.48 4.040 0.994 2.119 0.57 3.429 0.979 1.795 0.80 2.074 0.952 1.567 0.91 1.708 0.849 1.344 1.11 0.810 0.760 0.711
In air 1.210 1.569 3.382
Through polycarbonates
layer in air
4.209
Figure 5.6 Sensitivity SADS versus water thickness hwater
5.3 Optical Scanning Images in Water
For investigating the affections of the water thickness on the laser spatial resolution, the ADS setup in Figure 5.4 is utilized to scan a bio-sample in water [61]. The breast cancer cells Michigan cancer foundation – 7 (MCF-7) are prepared on a silica wafer, and water is dropped between the cover glass and the wafer. The sample is brought into the working distance of the pickup head by the Z stepper motor, and Figure 5.7 shows the S-curves obtained through the XYZ scanner. The blue and green lines represent the results at hwater = 1.56 mm and hwater = 0.55 mm, respectively. The peak to peak value at hwater = 1.56 mm is smaller than that at hwater = 0.55 mm, and their sensitivities SADS are 0.140 mV/nm and 0.474 mV/nm, respectively. Comparing with the results on the mirror, the sensitivity on the wafer is smaller, because the reflectivity of the wafer is lower than the mirror.
Figure 5.7 UFES versus displacement curves (S-curves)
For searching the target cell on the wafer, an additional optical microscope is equipped to observe the sample surface. When the target cell is positioned in the scan range of the XYZ scanner, the sample is scanned in the XY plane, and UFES is recorded for imaging simultaneously. The Z position is kept constant during the scanning. Figure 5.8(a) and 5.8(b) show the optical scanning images of the cells at hwater = 1.56 mm and hwater = 0.55 mm, respectively. At hwater = 1.56 mm, diffraction patterns appear around these two cells and particles, and obscure the image. On the other hand, no obvious diffraction can be observed at hwater = 0.55 mm. The higher spatial resolution is achieved through applying an appropriate hwater. This result implies that the optimal water thickness hwater not only affects the detection sensitivity, but also changes the measurable minimum dimensions of the cantilever in water.
(a) hwater = 1.56 mm
(b) hwater = 0.55 mm
Figure 5.8 Optical scanning images of MCF-7 breast cancer cell
5.4 Spring Constant Calibration
The spring constant of the cantilever is an essential parameter for quantitative measurements. For calibrating the spring constant, the thermal fluctuation method is widely practiced in the commercial AFM, because no extra additive such as the attached mass or information about the cantilever’s dimensions is needed. In this method, the Equipartition theorem is used for the spring constant calculation through measuring the cantilever thermal fluctuation. However, for deriving the spring constant with the optical beam deflection technique, it requires to know the sensitivity of the position sensitive detector (PSD) to the cantilever deflection. During a routine calibration procedure, a cantilever probe is brought into contact with a stiff substrate to measure a
used in various mass sensing applications. Additionally, the calibration accuracy can also be affected by the potential scattered interference from the substrate in this approach. Furthermore, the tilt angle between the cantilever and the substrate also affects the sensitivity calibration of the PSD slightly.
To establish an efficient procedure, the ADS with the thermal fluctuation method is developed to calibrate the spring constant of cantilevers. In comparison with the technique of optical beam deflection, the ADS is more sensitive to the vertical and less sensitive to the angular displacement of a cantilever. The acquisition of deflection sensitivity of the optoelectronic sensor can be achieved by simply moving the cantilever vertically with a known distance, and no substrate is involved. Therefore, the whole process can be time saving and also avoid damaging the cantilever tip. Furthermore, this new approach can be extended to obtain the spring constant of a tipless cantilever.
5.4.1 Thermal fluctuation method
Without any external excitation, the cantilever is subject to the thermal stimulation at room temperature. According to the well-known Equipartition theorem Equation (5.6):
where kB is Boltzmann’s constant, T is the cantilever temperature in Kelvin, the spring constant k of an ideal spring can be calculated through measuring its mean square amplitude <x2>. Burnham et al. derived the thermal distribution function of a simple harmonic oscillator (SHO) [62], and its raw thermal power spectrum can be fitted by the following equation
where <x2(f)> is the mean square amplitude at frequency f, and the first and second terms represent 1/f noise and white noise, respectively. The parameters A, B, mean square amplitude <x2(fr)>, quality factor Q, and resonant frequency fr are obtained from the fitting curve. The spring constant k can thus be derived by
r where Δf is the frequency resolution of the thermal power spectrum.
5.4.2 ADS setup for spring constant calibration
Figure 5.9 shows the calibration setup. The astigmatic pickup head (TOP1100Sc, TopRay Technologies) is used to detect the cantilever displacement. The X- and Y- coarse stages are responsible for the alignment of the laser spot on the free end of the cantilever, and the Z-coarse stage for focusing the laser spot on the cantilever. The aligning and focusing processes can be simultaneously monitored by a microscope and a CCD-camera. For deflection sensitivity calibration, a real-time controller (sbRIO-9632, National Instruments) generates the triangular voltage waveform to vertically drive the piezoelectric positioning system, which includes the closed-loop XYZ scanner (P611.3S NanoCube, Physik Instrumente) and the piezo-controller (E644, Physik Instrumente). Its acquired UFES is processed by the pre-amplifier first and further by the digitizer (PCI-9820, ADLINK) with a sampling rate of 5 MHz. The digitized signal is then delivered to the computer to implement the “Fast Fourier Transform (FFT)” to derive
(a)
(b)
Figure 5.9 (a) Configuration and (b) construction of calibration setup
5.4.3Calibration on AFM and ADS
For comparison, the spring constants of several cantilevers are separately calibrated by the optical beam deflection technique and our developed ADS. The three-lever chip (CSC38, AlBS, MikroMasch) with three rectangular cantilevers is utilized as the testing sample. The three cantilevers, Lever A, Lever B, and Lever C have same width b of 35 μm and thickness h of 1 μm, but different lengths L of 250 μm, 350 μm, and 300 μm, respectively. In addition, the ADS is also applied to measure the spring constant of a tipless cantilever (Arrow TL1Au, NanoWorld). The scanning
electron microscope (SEM) images of all the cantilevers are displayed in Figure 5.10.
(a) Lever A, B, and C (b) Tipless cantilever Figure 5.10 SEM images of cantilevers
For demonstrating the optical beam deflection technique, cantilever spring constants are calibrated in a commercial AFM (MultiMode, Bruker). To obtain the flexural deflection sensitivity, the force curves are measured by approaching a sapphire substrate to the cantilevers. The substrate is driven to load and unload the cantilever tip with a defined displacement. Figure 5.11(a) shows the measured cantilever deflection signal UDEF. From the slopes on the ramp regions, the deflection sensitivities SOBD on the Levers A, B, and C are 18.6 mV/nm, 12.3 mV/nm, and 14.6 mV/nm, respectively.
For the same linear displacement, the shorter cantilever produces a larger angular deflection than the longer ones and, consequently, a larger voltage variation on UDEF. The longer cantilever also requires a larger movement to detach from the substrate after the contact has been made. Figure 5.11(b) shows the thermal fluctuation spectrums of the three cantilevers. The resonant frequencies fr of the Levers A, B, and C are 14.2 kHz,
(a) Force curves on sapphire substrate
(b) Thermal fluctuation spectrums Figure 5.11 Experimental results on AFM
On the ADS, through the linear actuation by using the closed-loop controlled piezo stage, the S-curves of the Levers A, B, C, and the tipless cantilever are acquired and shown in Figure 5.12(a). The slopes in the middle linear regions of the S-curves are
used for calibration of the deflection sensitivities. The deflection sensitivities SADS of the Levers A, B, C, and the tipless cantilever are 2.5 mV/nm, 2.6 mV/nm, 2.5 mV/nm, and 2.8 mV/nm, respectively. Their thermal fluctuation spectrums are shown in Figure 5.12(b). The resonant frequencies fr of the Levers A, B, and C are 14.2 kHz, 7.7 kHz, and 10.4 kHz, and the corresponding spring constants kADS are 0.090 N/m, 0.029 N/m, and 0.056 N/m. The resonant frequency fr and spring constant kADS of the tipless cantilever are 5.5 kHz and 0.041 N/m. Table 5.3 provides an overview of all experimental results.
(a) S-curves
(b) Thermal fluctuation spectrums Figure 5.12 Experimental results on ADS
Table 5.3 Experimental results on AFM and ADS
AFM ADS
The deflection sensitivities SOBD of the Levers A, B, and C derived on the AFM are significantly related to the cantilever length. On the contrary, their measured deflection sensitivities SADS on the ADS are very close, but SADS of the tipless cantilever is higher than the others slightly. The difference comes from the reflectivity difference between the gold coating on the tipless cantilever and the aluminum coating on the Levers A, B, and C. On the spring constant, a similar result has been obtained with both the AFM and ADS methods for the longest Lever B. Yet, the apparent disagreements were also found for the Levers A and C. As for which method generates more accurate outcome, it remains to be examined. Nevertheless, our current proposed calibration method with the ADS is experimentally verified as an efficient procedure without application of a substrate. It also provides a natural extension to calibrate the tipless cantilever, which acts as a key component in cantilever-based mass sensors.
5.5 Conclusion
For applying the ADS to water environment, its measurement sensitivity is investigated. Through calculating the equivalent water thickness to the polycarbonates layer in DVD optical disc, the optimal water thickness hwater of 0.36 mm is derived. In the experiments, the highest sensitivity SADS of 4.040 mV/nm is obtained at hwater = 0.48 mm, which approximates to the sensitivity through a polycarbonates layer in air.
Besides, the water thickness hwater also affects the spatial resolution on the optical scanning mode. A sample of the breast cancer cell MCF-7 is scanned, and the unwanted diffraction patterns can be eliminated by applying an appropriate hwater.
By using this ADS, a novel calibration method for the spring-constants of micro
deflection used in the AFM, no substrate is needed in the ADS-calibration. Therefore, it avoids all effects induced by the substrate such as the laser interference, capillary force, cantilever tilt, and tip blunting. Besides, this method can be applied to tipless cantilevers, which are widely applied in many cantilever-based mass sensors. Furthermore, this developed ADS-calibraiton is also time efficient by omitting tip-substrate approaching procedure.
Chapter 6
Liquid Environment AFM
Based on the experiences of cantilever design, excitation method, and detection method, a liquid-AFM system is designed and developed for adapting to the detection in liquid environment. In order to widen its application field, torsional cantilever excitation
Based on the experiences of cantilever design, excitation method, and detection method, a liquid-AFM system is designed and developed for adapting to the detection in liquid environment. In order to widen its application field, torsional cantilever excitation