3-1 Atomic Force Microscope
In this study, our AFM equipment is Park System XE-100, and cantilever used in Table 5. The force constant, resonance frequency and tip radius are noted in different mode when measuring samples. Atomic Force Microscope is composed of piezoelectric scanner that has three axes perpendicularly to each other, position sensitive photodector, feedback system and external probe.
Fig. 16 Entity diagramof AFM [12]
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3-1-1 Principle of AFM
[12][13]Atomic force microscope is composed of piezoelectric scanner that has three axes perpendicularly to each other, position sensitive photodector, feedback system and external probe. As shown in Fig. 17.
The basic principle of AFM is using laser to irradiate on cantilever, and when probe moved on a sample, cantilever would bend along with height of sample surface.
And bending variation of cantilever would let laser shift on position sensitive photodector, as shown in Fig. 18. The position sensitive photodector generated signals by shifting, and then transferred to feedback system generating feedback signals.
Finally, using feedback signals to control movement of piezoelectric scanner and image with controlling distance of probe and sample.
Fig. 17 AFM systems [14]
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Fig. 18 Diagram of probe height to PSPD [14].
We could know relationship of force and distance of probe and sample surface in Fig. 19. According to distance of probe and sample surface and using force between atom and atom, there are three kinds of operating modes. There are contact mode, non-contact mode and tapping mode, respectively. When using contact mode to scan samples, it is several Å in length of probe and sample surface. The force of probe and sample is repulsive force between atoms. Because van der Waals force is short-range force, it can touch sample surface effectively. The probe touched sample surface closely so contact mode would obtain atomic-level resolution easily.
Fig. 19 distance and force of probe and sample surface [14].
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3-2 Piezoresponse Force Microscopy
In 1991, H. Birk,J. Glatz-Reichenbach et al. used this technique to measure ferroelectric polymers firstly. [16] At the time they used scanning tunneling microscopy with lock-in amplifier to measure it then using Au film and Al film as electrodes.
They applied AC voltage signal of 20Hz and 10V on electrodes. It made sample strain and shock, and measured deformation of surface by probe, and obtained piezoresponse hysteresis loop by lock-in amplifier.
The principle of piezoresponse force microscopy built on inverse piezoelectric effect. It is composed of atomic force microscope and lock-in amplifier. While measuring samples, probe is as upper electrode and detecting deformation of the sample surface to obtain piezoresponse signal by lock-in amplifier.
According to different polarization directions of samples, it can be differentiate as vertical and lateral signal of piezoresponse force microscopy. In this study, we only used vertical piezoresponse force microscopy.
Fig. 20 Left is XE-100AFM and Bottom right is SR830 lock-in amplifier.
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3-2-1 Vertical piezoresponse force microscopy
When we didn’t apply DC voltage, it had two ferroelectric domains of opposite polarization in ferroelectric materials. At that time, two ferroelectric domains didn’t deform, as shown in Fig. 21(a) [17]. We assumed that two ferroelectric domains of -ferroelectric domain would shrink, as shown in Fig. 21 (c)[17] .
Fig. 21 Strain behavior of ferroelectric materials (a) no voltage is applied (b) applying a positive
voltage (c) applying a negative voltage.[17]
From the foregoing, we applied electric field to make ferroelectric materials strain and we could calculate its deformation. Deformation of sample showed following equation.
ΔZ= -d＊
V ．．．．．．．．．．．．．．．．．．．．．．．．．．．．(3-1)
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Eq.: Z is deformation of surface in vertical.
d＊ is piezoelectric coefficient of ferroelectric materials.
V is DC voltage.
In equation (3-1) negative could show that deformation of c in vertical is for what strain contributing. For example, when we applied positive voltage on ferroelectric materials, direction of electric field is opposite of polarization of c+ ferroelectric domain. We could obtain ΔZ is negative from equation and it could show that deformation in vertical is contributed by shrinking.
Assuming a d33 of ferroelectric materials is 50pm/V. If we applied a 2V of DC voltage, we could measure deformation of 0.1nm in vertical. The roughness is approximately 10~102nm so small deformation would be covered by topography signal. Therefore using DC voltage is not suitable to measure samples of the ferroelectric materials with rough surfaces. So we need to use AC voltage with lock-in amplifier to obtain oscillation signal of sample surface. The equation of AC modulation signal isＶ＝Ｖ０cos(ωt + ϕ ) and deformation of sample surface showed following equation. [18]
ΔZ=ΔZ0cos(ωt + ϕ )．．．．．．．．．．．．．．．．．．．．．．．．(3-2)
Eq.: ΔZ0=d33
V
0d33 is piezoelectric coefficient along electric field in vertical.
V0 is amplitude signal of AC voltage.
ϕ is phase of AC voltage signal and ferroelectric domain polarization.
When phase ϕ = 0, directions of ferroelectric domain polarization and electric field were forward so deformation of samples was expansive. But phase ϕ = π, directions of ferroelectric domain polarization and electric field were reverse so deformation of samples was shrinking.
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Generally atomic force microscope is using laser to irradiate on cantilever , and when probe moved on a sample, cantilever would bend along with height of sample surface. And bending variation of cantilever would let laser shift on position sensitive photodector. We analyzed this displacement to obtain height of surface. But position sensitive photodector of piezoresponse force microscopy would receive topography signals and oscillation signals by AC voltage. In order to distinguish two signals, we used lock-in amplifier to filter topography signals and receive oscillation signals. We received first harmonic is piezoelectric constant. We obtained piezoresponse signal that was related to oscillation amplitude and phase.
We measured piezoresponse signal that using probe on one point optionally and showed following equation [19].
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3-2-2 Hysteresis loop
[20]The circuits of piezoresponse force microscopy were refit. Besides we could measure ferroelectricity domain, we could fix point to measure electricity. The way of measuring hysteresis loop is series connection with DC voltage and AC voltage. We otputted a DC voltage by using high voltage amplifier and computer system, and computer system changed DC voltage signals with pulse wave and residence time step by step. Then measuring piezoresponse signal at voltage was zero, as shown in Fig.
22. And we recorded piezoresponse signal in every residence time. Finally we obtained piezoresponse amplitude and phase images with different voltage, as shown in Fig. 23 (b) and (c). Then we could use equation (3-3) to obtain piezoresponse signal with piezoresponse amplitude and phase images.
In order to obtain good hysteresis loop, we could judge correct domain by using piezoresponse force microscopy to obtain amplitude and phase images. From Fig.
23(b) and (c) we could know that amplitude would have twice low point and it was overturn position of phase. We obtained amplitude and phase images by piezoresponse force microscopy, it had a shadoweave in middle of two bright areas.
At the same position, it had two area of bright and dark in phase images. We could use this way to obtain ferroelectric domain location.
Fig. 22 Form of outputting pulse DC voltage by measuring hysteresis loop [20].
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Fig. 23 (a) piezoresponse signal image (b) amplitude image (c) phase image [21]
3-2-3 Piezoelectric coefficient
We measured piezoresponse signals instead of exact displacements by PFM. If we wanted to know about relationship of applying voltage and ferroelectric materials deformation, we must detect piezoelectric coefficient.
In equation (3-3), the piezoresponse signal is related with sensitivity, piezoelectric coefficient d33 and applying voltage Vaccos(ϕ). If we wanted to obtain piezoelectric coefficient, we needed a standard sample to calibrate d33.
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Firstly, we used a standard sample of known piezoelectric coefficients, we choose x-cut quartz (d11 = 2.3pm/V) as standard sample. We coated Ag on x-cut quartz as upper electrode and stainless steel sheet as bottom electrode. Then we applied a continuous AC voltage on electrodes, we could obtain a piezoresponse signal. The equation showed in (3-4-1)：
vω(ϕ) = Rcos(ϕ) = aVac cos(ϕ) + b (理論上，b = 0) ．．．．．．．．．．．．(3-4-1) Where a is transformation factor of piezoresponse signal and applying AC voltage ( a is transformation factor of x-cut quartz ) , therefore be regarded as：
vω(ϕ) = Rcos(ϕ) = aVac cos(ϕ) ．．．．．．．．．．．．．．．．．．．(3-4-2) We compare eq. (3-4-2) and eq. (3-3), we could obtain eq. (3-5)：
δd11 Vac cos(ϕ) = a Vac cos(ϕ) ．．．．．．．．．．．．．．．．．．．．．(3-5) We knew d11 = 2.3pm/V and we could obtain that：
δ = a/d11 ．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．(3-6)
We changed from standard sample to the sample. Then we applied a continuous AC voltage on electrodes and changed amplitude, we could obtain a piezoresponse signal. The equation showed in eq. (3-4-2) and eq. (3-5-1)
δd33Vac cos(ϕ) = a’Vac cos(ϕ) ．．．．．．．．．．．．．．．．．．．．．．(3-5-1) Where a’ is transformation factor of piezoresponse signal and applying AC voltage. Because parameters were not changed and sensitivity was same, we could obtain piezoelectric coefficient d33 by taking eq. (3-6) into eq. (3-5-1) ：
d33 = d11 × (a’/ a) ．．．．．．．．．．．．．．．．．．．．．．．．．(3-7)
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3-3 X-ray diffraction system
We analyze crystal structure of film by using X-ray diffraction system and we emitted X-ray by using electron to hit metal target (Cu, Fe et al.). Because wavelength of X-ray is smaller than distance among crystal planes, it is suitable for light source of structural analysis. According to Bragg’s law (Fig. 24) , when the atomic planes of a crystal caused an incident beam of X-rays to interfere with one another as they leave the crystal. It made wave path difference of reflection beam 2dsinθ be equal to wavelength or integral multiple and formed different intensity constructive interference with diffraction beam. The detectors received on specific angle and obtained intensity signal in different crystal plane.
2dsinθ= nλ
d： Distance of two adjacent planes
θ： The angle between incident beam and plane
n： Arbitrary integer when wave path is integer multiple of wavelength λ： Wavelength of X-ray
Fig. 24 Diagram of Bragg’s law [15]
In this study, we measured structure and composition of samples using X-ray diffraction system (Rigaku Ultima IV) in NUK Professor Chiou Lab. (Fig. 25)
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The power is 40KV, 40mA. The target is Cu and Kα wavelengthλ is 1.5418 Å . We selected step was 0.02°, scan speed was 2.4°/min, scan range was 30°~80° and power is 1.6KW. In measuring process, it had declination with pressing sample, so we would do θ scan to fix the declination.
Fig. 25 X-ray diffraction system [15]
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3-4 Mangeto Optical Kerr Effect
Principle of mangeto-optical effect was when a incident light penetrate or reflect a ferromagnetic material, electric field and magnetic field of light and magnetization of spontaneity of ferromagnetic materials had a interaction affect. It made polarization state of light change.
In nineteenth century, Kerr found that a linearly polarized light reflected with magnetic materials, then reflected light became elliptically polarized light and long axis deviate polarization plane of original incident light, we called it Kerr rotation angle ϕk, as shown in Fig. 26(a). This is due to the angle between direction of the light and direction of magnetization in materials would affect refractive index of materials.
We called mangeto-optical Kerr effect, MOKE [1]
.
According to the different experiment system, there are three kinds of mangeto-optical Kerr effect：
(1) Polar-MOKE, P-MOKE：The direction of magnetization is perpendicular with sample surface and it is parallel with plane of incident light. Fig. 26 (b)
(2) Longitudinal-MOKE, L-MOKE：The direction of magnetization is parallel with sample surface and it is parallel with plane of incident light. Fig. 26 (c)
(3) Transverse-MOKE, T-MOKE：The direction of magnetization is parallel with sample surface and it is perpendicular with plane of incident light. Fig. 26 (d)[22]
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(a) (b)
(c) (d)
Fig. 26 (a) change of reflected light in polarization direction (b) P-MOKE (c) L-MOKE (d) T-MOKE
L-MOKE system is showed in Fig. 27. We used He-Ne laser in our lab and its wavelength is 633nm. This wavelength is equivalent to infrared light and the power is 10mW. The laser was changed to linearly polarized light by polarizer, then it reflected by sample and elliptically polarized light went through the analyzer to let photo detector received signal. Finally, we used digital multimeter and computer to analyze data.
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Fig. 27 L-MOKE system
Fig. 28 MOKE signal ∝ Ex2
As Fig. 27, when the laser went through the polarizer, just electric field of y component (linearly polarized light) went through. The reflected light became elliptically polarized light via magnetic sample and long axis deviate polarization plane of original incident light. We called it Kerr rotation angle. When the elliptically polarized light went through the analyzer, just electric field of x component went
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through. Finally, photo detector received signals and transformed signals into MOKE signals, as shown in Fig. 28.
Because Kerr rotation angle signal was similar to magnetization, we could obtain hysteresis curve. The Kerr effect was sensitive to deflection of magnetic moment so we often measured hysteresis properties with magnetic ultrathin film and laser penetration depth is approximately 30nm. Besides we could use Helmholtz coils for our magnetic field source, we also could use horseshoe electromagnet. The following is MOKE systems in our lab, as shown in Fig. 29.
Fig. 29 Left is L-MOKE system and right is P-MOKE system.
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3-5 RF magnetron sputtering system
The radio frequency magnetron sputtering system is composed of high vacuum chamber system, pressure sensors, gas controller, specimen holder, AC voltage power and sputtering guns.
We prepared samples using the radio frequency magnetron sputtering system in our lab. Its principle is the following. We passed into working gas such as argon or oxygen in low vacuum pressure. When chamber pressure was stable, we applied AC voltage to sputtering gun. We made target and sample distinguish to cathode and anode respectively. Then part of working gas would be dissociated to plasma. The positive ion of plasma would hit cathode target. The kinetic energy of positive ion could be transform into target so the molecule of target would get out from target surface and attached on the substrates.
In order to let it sputter efficiently, we configured magnet in sputtering guns.
Besides it could fix target, the magnetic field would make electrons hit working gas and ions to strike target efficiently. it could increase plasma density and coating rate.
Fig. 31 is Diagram of radio frequency magnetron sputtering system in our lab.
Our permalloy samples were prepared in this system, and we introduce process in 4-1.
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Fig. 30 Diagram of radio frequency magnetron sputtering system.
Fig. 31 Picture of radio frequency magnetron sputtering system.
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