Cantilever

The sensor used in our SPM is a microfabricated tip attached to a cantilever. These cantilevers are supplied by Budgetsensors and Nanosensors. They are composed of Si with a 10 to 20 nm Al coating. The sensitivity of the static cantilever in three dimensions (3D) to an applied force is given by its longitudinal spring constant kL

as Hooke’s law applies for the deflections small compared to the cantilever’s length

Fn= kL∆xn where Fn = ˆn· F and ∆xn = ˆn· (x − x0) (4.1) where x = (x, y, z) is the 3D position vector of the cantilever, ˆn is a unit vector along the easy deflection direction, ∆xnis the position of the tip apex relative to the equilibrium position in the absence of interactions, x₀. The smaller the longitudinal spring constant, the larger the cantilever deflection for a given force. The longitudinal force constant of the cantilever can be calculated from its dimensions (width wc, thickness τcand length ℓc) and from Young’s modulus E

kL= Ew_c· d³c

4 · ℓ³c

(4.2) Therefore the cantilever dimensions can be designed to provide a certain force constant. The fundamental resonance frequency of the cantilever is given by [65].

f0= 1.875²d_c 4√

3π · ℓ²c

s E

̺mass

(4.3) Here, ̺mass denotes the density of the cantilever material^∗. In table 4.1 the used cantilevers are summa-rized. The cantilevers Multi75–Gfrom Budgetsensors are both delivered for AFM (non–magnetic) and MFM

∗̺mass,Si= 2.33 g/cm³ from http://www.icknowledge.com/misc_technology/Silicon\%20properties.pdf.

Table 4.1: Table of used cantilevers

kAll MFM cantilevers are made of n⁺Si with a deflection coating on the detector side of (non-magnetic) Aluminum. Tip side coated with magnetic Al. Multi75–G coated with an unknown Al alloy.

†Mean width value.

‡R = tip radius.

§HC= magnetic coercitivity.

¶MR= magnetic remanence

♥Hard magnetic coating

♣Soft magnetic coating

⋆⋆http://www.budgetsensors.com/magnetic-afm-probes.html.

⋆http://www.nanosensors.com/prod_cat_mfm.html.

(magnetic) applications. They offer the lowest specifications or Q factor, since they have the largest tip ra-dius R and an unspecified coercitivity of an undefined Al alloy. These cantilevers are useful for testing and calibration of the setup. The cantilevers from Nanosensors can be divided into three different categories.

There are two differentPPP–MFMtips and two comparableSSS–MFMtips. ThePPP–LM–MFMR^† is an AFM probe designed for magnetic force microscopy with reduced disturbance of the magnetic sample by the tip and enhanced spatial resolution. The force constant of this probe type is specially tailored for magnetic force microscopy yielding high force sensitivity while simultaneously enabling tapping mode and lift mode operation.

The PPP–LM–MFMRhas a hard magnetic coating, which means that it has a relative high coercitivity and remanence magnetization. Therefore, these cantilevers should be used for the study of samples with small ferromagnetic domains. The SSS–MFMR^‡ also has a hard magnetic coating, but its tip radius is even smaller and therefore higher resolution values are expected. These tips are by far the most expensive and should only be used if stable operation is expected. ThePPP–LC–MFMR^§on the other hand, has a soft magnetic coating, corresponding to low coercitivity and low remanence magnetization. These cantilevers are useful for the study of magnetic domains in soft magnetic samples. Due to the low coercitivity of the tip coating the magnetization of the tip will easily get reorientated by hard magnetic samples.

Before conducting MFM measurements, the choice of cantilever with respect to sample characteristics and/or environmental conditions, is a critical one. The wrong choice of cantilever can easily lead to increased noise levels, unwanted tip crashes and low resolution and/or sensitivity measurements. A lot of research has been performed on the subject of cantilever performances and dynamics, for instance by John Sader et al. [66, 67] and by Georg Hermann Simon [68]. Also a lot of research has been performed on the subject of magnetic cantilevers, for instance by Giorgio et al., who investigated the dissipative losses of cantilevers due to exposure to magnetic fields [69]. Although for now these results are beyond the scope of this thesis, they should be taken into account for further optimization of the system. Magnetic properties of the probe can be characterized using the technique of cantilever magnetometry [70]. In this technique, the sample is mounted directly on a cantilever and the assembly is placed in a magnetic field. For thermally limited FM measurements Straver [56] calculated, in accordance with the minimum detectable compliance (Eq. 2.22), the minimum measurable magnetic moment for a cantilever vibrating in a static magnetic field. Subsequently using equations 4.2 and 4.3 yields

m_min= 2 with ℓef f = ℓc/1.38 the effective cantilever’s length. The ideal cantilevers for sensitive magnetic moment

†Point probe plus–low momentum–magnetic force microscopy reflex coating.

‡Super sharp silicon–magnetic force microscopy reflex coating.

§Point probe plus–low momentum–magnetic force microscopy reflex coating.

measurements are thin, narrow and short cantilevers, with high Q factors. We have used the scanning electron microscope (SEM) of the Photonics and Semiconductor Nanophysics (PSN) group to characterize the tip dimension of the Budgetsensors cantilevers. The pictures are shown in Fig. 4.1. As one can see from the pictures, the tip dimensions match the specifications as given by table 4.1. For further optimization of resolution and sensitivity, these tips are expected not to offer the best specifications.

(a) × 1, 900 − 10 µm (b) × 10, 000 − 1 µm (c) × 100, 000 − 100 nm

Figure 4.1: SEM pictures of the Budgetsensors MFM Multi75–G chip holder at different magnification. The caption shows the magnification and the value of the scale bar. The last picture shows the tip at a magnification of × 100, 000. As one can see is the tip radius R comparable to the specified < 60 nm (table 4.1).

In order to acquire magnetic or topographic contrast information, a F(z)-z spectroscopy must be set up. This is done in static mode operation with the feedback modulation switched off. In this case, the force F(z) exerted on the cantilever is displayed as function of the distance z to the sample surface. In accordance with the Lennard–

Jones potential (Fig. 1.3a), Fig. 4.2 shows an idealized F(z)-z curve [71]. This curve can be understood as fol-lows.

Figure 4.2: Theoretical F(z)-z curve. For a detailed description, see the text.

The tip is initially at a large distance z from the sam-ple surface with no tip–samsam-ple interactions present A.

As z decreases, the tip suddenly is pulled towards the surface and makes contact with the sample (i.e. the cantilever ‘snaps into’ contact) B. As a result, the deflection of the cantilever is down from its equilib-rium position. As z continues to decrease, the can-tilever starts to deflect upwards C and the relation-ship between z motion and the detector voltage is recorded. As z then reaches its minimum value and starts to increase, the deflection starts to decrease D, but the tip maintains contact with the surface for a larger z because of capillary forces between tip and sample. The tip eventually breaks contact E and snaps back to its equilibrium position. As the z in-creases to a large value, the tip and sample are again separated by such a large amount that the cantilever remains at its equilibrium position F . Note the slope at large tip–sample separation is shown flat in this idealized picture. However in reality, there may be

either an upward or downward trend as z decreases due to long–range forces acting between tip and sample along with oscillations due to laser interference with light scattered from the sample. In practice, the deflec-tion of the cantilever, rather than the actual force is measured and for small tip–sample separadeflec-tions (curve C or D), the slope of the F(z)-z curve can be used to convert the photoreceiver voltage into a z height. In accordance with Eq. 2.1, this slope will be equal to the force constant k of the cantilever. Once this slope is determined, it can be used to determine the force setpoint of the cantilever for dynamic mode operation. This is shown in Fig. 4.3a. This curve can be understood in the following manner. Initially, the cantilever is freely oscillating around its equilibrium position in the absence of tip–sample interaction A. The feedback loop is opened and the cantilever is kept oscillating while the distance to the sample surface decreases as a result of

–381.0 –381.2

–380.8

–380.6

A B

C E

F D

(a) Dynamic mode operation

– 27 – 28 – 29 – 30

(b) Amplitude and phase response Figure 4.3: (a) Determination of the force setpoint in dynamic mode operation. In this case, the relative position of the cantilever to the sample surface is measured as a function of time. E determines the preferred setpoint for noncontact mode operation, F shows the actual force setpoint. (b) Amplitude (top) and phase (bottom) response of the cantilever. The inset of the pictures show the modulation of the feedback signal, taken after a sufficient amount of time for the cantilever to relax around the setpoint position. The images were obtained while working in CE lock–in mode. The cantilever was the magnetic Multi75–G cantilever from Budgetsensors (table 4.1), operating at a drive frequency of 84.2 kHz with an excitation amplitude Vpof 90 mVp. The Q factor of the cantilever was 164 under ambient conditions. The sample under investigation was the new hard disk drive sample (chapter 5.1.3).

the pre–set force setpoint B. In this case, the cantilever is retracted before it reaches the sample’s surface and the cantilever is kept oscillating around the force setpoint F , instead of the preferred setpoint E indicated by the dashed line D. Fig. 4.3b show the corresponding amplitude and phase response signal of the cantilever. If the force setpoint is set incorrectly, additional noise may be introduced to the feedback channels. Moreover, if the tip crashes onto the sample during the initial approach, this can result in a change of the resonance frequency, unrepairable damage of the tip or modification of the tip magnetization.