An atomic force microscope measures the forces between a sample material surface and a micron-millimeter-scale mechanical cantilever with a sharp nano-sized tip attached,
using precise piezoelectric scanners, where the sample surface is roughly in the x, y plane and the z piezo allows careful approach of the tip to the surface. For standard topographic
imaging, as the distance zc between the tip and the surface is varied, the cantilever
experiences a spatially varying force F (z) = −∂V /∂z due to a combination of attractive and repulsive tip-sample interactions, summing to a potential energy V . The traditional detection method uses an optical lever as depicted in Fig. 2.9(a): a laser is focused onto the end of a piezoelectrically driven cantilever, and the reflected light is incident on a split photodiode. The signal on the photodiode can be used to readout a cantilever deflection in contact AFM modes or a change in cantilever vibration amplitude in dynamic modes. For contact mode, as the tip is pressed into the sample, the cantilever bends and reflects the light towards the top or bottom half of the photodiode, and the difference of the intensity gives a static deflection signal. Because the distance between the cantilever apex and the detector is orders of magnitude larger than the deflection amplitude, this optical lever can sensitively detect small changes in force. When the cantilever is then translated in the x, y plane along the sample surface, the deflection signal can be read out to image the topography in two dimensions.
We have described a non-feedback deflection type of contact mode imaging. However, normal AFM operation uses a continuous proportional-integral feedback loop to move the tip closer or farther from the surface. Many AFM modes exist for tracking the height of a surface. Broadly, these are divided into contact and dynamic modes. In contact AFM, the compliant cantilever, usually silicon-nitride, has a low < 1 N/m spring constant allowing it to deflect a large amount under short-range repulsive forces, thus enabling a large optical lever signal. Here, the deflection setpoint is the error signal in a feedback loop to adjust the tip-sample separation. The advantage of this AFM mode is simplicity for imaging relatively flat, hard surfaces. In this thesis work, contact mode AFM is used to measure diamond surface morphology and roughness after various processing steps.
IR laser z (a) (b) sample Si AFM probe split PD
Figure 2.9: Illustration of atomic force microscopy (AFM) based on an optical lever. A laser is reflected from a silicon cantilever into a split photodiode (PD) detector. Deflection of the cantilever due to forces between its sharp tip and a sample surface causes the reflected laser to primarily hit the top or bottom of the PD. This signal gives a measure of static deflection in contact mode (a), and in a resonantly driven cantilever (b) lock-in detection gives a change in amplitude, frequency, or phase. The error between a setpoint deflection or amplitude and the measured signal, for example, can be used as input for a feedback loop that controls the z position of the cantilever with nanometric resolution to keep the tip-sample force constant. Drawing not to scale: cantilever lengths are ∼ 200 µm while the optical path length is several cm.
However, we do not use contact mode for magnetometry primarily because contact-mode scanning is more damaging than non-contact scanning. In addition, undesirable snap-to- contact (or snap-in) due to strong attractive forces can easily occur in floppy cantilevers, which makes maintaining a tip-sample separation on the order of nanometers impossible. Using high-stiffness probes in dynamic mode can mitigate the snap-in issue.
Dynamic AFM (Fig. 2.9(b)) comes in many varieties that rely upon resonant excita- tion and response of the probe cantilever. The oscillation amplitude, frequency, or phase
can be used as error signals in a feedback loop to adjust the tip-sample separation zc,
and different types of forces can be measured including magnetic forces. We focus on amplitude modulation AFM (AM-AFM) for scanning magnetometry, which is suitable for simple operation in ambient conditions at slow scan rates since the Q is lower than in vacuum, thus allowing a faster response time. In this mode, the cantilever is driven on or near its resonance frequency, and the amplitude is used as the sole feedback parameter. As the tip approaches below 100 nm of the surface, short-range Van der Waals attractive forces cause a change in the shape of the resonance curve. Consequently, the amplitude changes, usually becoming lower than the free driven amplitude [176]. The analysis of the tip motion in AM-AFM is complicated and non-linear due to the non-constant force
gradient as a function of zc. Theoretical analysis of the problem shows that there are
generally two solutions for the amplitude, and either or both may be most stable for small changes in driving amplitude and tip-sample separation. Generally, solution A is non-contact where the tip never feels appreciable contact forces and solution B is inter- mittent contact, or tapping mode, where the fraction of time per period in contact with
the surface increases as zc is reduced, thus reducing the amplitude. We use the tapping
mode, B.
Other detection methods exist for dynamic-mode imaging beyond the optical lever and micro-cantilever. Another approach is to use a macroscopic quartz tuning fork os-
(a) (b)
z
drive
detect
sample
Figure 2.10: Illustration of AFM using a self-sensing quartz tuning fork in (a) intermit- tent tapping mode with oscillation normal to the sample surface and (b) shear-force mode with oscillation parallel to the surface. In both cases, the tuning fork is elec- trically driven (red lead) at the mechanical resonance frequency (f ≈ 32 kHz) and an independent lead (blue) is used for current readout; one tip-attached tine is me- chanically free in both, while the other tine is fixed to a piezo x, y, z scanner. Either detection of amplitude or frequency modulation can be used for feedback to control the z height of the tip above the sample.
cillator [177], which is advantageous for scanning-NV magnetometry because no extra optics are necessary. Such probes are called “self-sensing” because they are electrically driven at a resonance that corresponds to the mechanical shape of the device, and they can then be electrically read out via current from an independent metal lead on the de- vice. Beyond elimination of an optical system, the quartz tuning fork detection has the
benefit of an extremely high spring constant of order 104 N/m, which more effectively
prevents undesirable snap-in of the tip to the sample. By comparison, typical tapping mode Si cantilevers have spring constants of 0.1-100 N/m. The macroscopic tuning fork is also a versatile platform because any number of different commercial tips or diamond scanning probes can be glued on while keeping the spring constant and resonance fre- quency relatively unchanged. However, while mass production of silicon cantilever probes is achieved routinely with wafer-scale lithographic fabrication methods, the assembly of a tip on a tuning fork cannot yet be mass-produced in the same way.
2.10(a)) or in shear-force mode (Fig. 2.10(b)) [61]. Shear-force mode is often used in high vacuum for non-contact imaging at atomic-scale resolution. In shear-force mode, it has been reported that one must be more careful to mount and operate the tip with parameters that ensure it comes within nanometers of the sample surface [178, 66]. One advantage of the alternative of tapping mode is that it is easier to determine that the amplitude is changing due to actual intermittent tip contact with the sample, and this is the primary method we employ for our scanning probe Magnetometer B in ambient conditions.