Page 48 - Principles and Applications of NanoMEMS Physics

34 Chapter 1

z~0.5nm from a flat surface, will experience a force ~-5.5nN.
Based on the method employed to extract F , and hence the surface
TS
image, AFM operation is classified following three modes:

1) Contact Mode-Static AFM: In this mode the tip is in repulsion regime
and exerts a large normal and lateral force on the sample. The force applied
to the cantilever is kept constant during the scan by applying feedback, while
the z-displacement is measured yielding the surface topography. The main
drawback of this technique is that it can only be applied in certain cases,
namely, at low temperatures, due to the need to circumvent its low-
frequency noise and thermal expansion effects on resonance frequency [42].

2) Non-Contact Mode-Dynamic AFM: In this mode the cantilever is
mounted on an actuator which vibrates and, thus, excites it with amplitude
A and frequency f to oscillate above the sample. The tip-sample
drive drive
distance is such that operation is in the attractive regime. This may avoid
the force and noise problems of contact mode, but is subject to jump-to-
contact if the spring constant corresponding to the tip-sample potential
overcomes that of the cantilever, i.e., if k < k . The imaging signal is
max TS
derived from the change in cantilever amplitude and phase that result when
the tip approaches the sample. Since the excitation signal may consist of,
either fixed amplitude and fixed frequency, or fixed amplitude and varying
frequency, these two modes of operation are distinguished. The former is
called AM-AFM and, while this method does provide atomic resolution, the
fact that the time required to capture the tip-surface interaction
τ ≈ 2Q f is proportional to the quality factor (Q) of the cantilever,
AM 0
which may be tens of thousand, makes it relatively slow.
The latter mode, in which the amplitude is fixed, but the frequency is
varied, is called FM-AFM mode of operation. This mode also provides
atomic resolution, but it is much faster than AM-AFM because the tip-
surface interaction time is only τ ≈ 1 f .
FM 0

3) Intermittent Contact Mode-Dynamic AFM : In this mode the tip is
excited to oscillate above sample, also in the attractive regime, but it is made
to contact (“tap”) the sample for a short time during every cycle.

One of the key aspects of AFM is the design of the cantilever,
particularly, its spring constant and resonance frequency. These are given by
Eqs. (7) and (8), respectively, for a beam of thickness t, width w, length L,
Young’s modulus E, and mass density ρ .