Scanning Force Microscopy

An alternative method for imaging domain structures is the use of scanning force microscopy (SFM), a modification of atomic force microscopy (AFM) [Binnig86]. This non-destructive scanned imaging technique provides a high lateral resolution that is confined to a near-surface volume. Under controlled conditions, SFM is becoming an es- tablished technique for both visualizing and inverting ferroelectric domains [Kolosov95; Eng98; Hu02; Kalinin02; Xue03].

The SFM technique was first applied to visualize ferroelectric domains by oscillating the tip on a piezoelectric sample and detecting the resulting electrostatic forces via a lock-in amplifier [Saurenbach90]. By instead applying an oscillating voltage to a metalized AFM tip in contact mode, the small piezoelectric deflections of the crystal were detected by a lock-in amplifier [Kolosov95]. In this technique later referred to as piezoelectric force microscopy (PFM), the voltage applied to the piezoelectric material changed its thickness via the converse piezoelectric effect.

The change in the thickness of a piezoelectric material under an applied electric field follows [Jungk07],

∆t

t =Edp (3.1)

∆t=Etdp =V dp (3.2)

where ∆t is the change in the thickness t, E = V /t is the applied electric field, V is the applied voltage, anddp is the relevant piezoelectric coefficient. From this first order

approximation, the change in the thickness of the sample is dependent upon the voltage and not the electric field at the tip. This is true even for an inhomogeneous E-field because V =R₀tE(s)ds.

Quantitative data can be obtained by measuring the deflection of the tip when scanning over a large-area electrode on the crystal. Electrical contact between the SFM tip and the electrode presents a uniform voltage across a large area of the crystal. Without this electrode, the tip affects a small volume of the crystal only and results in a clamped mechanical deflection, diminishing the apparent piezoelectric response [Jungk07]. This clamped response is one reason the reported piezoelectric deflections vary considerably as compared to those measured by other techniques.

A PFM can generate many types of measurement signals. Regular AFM signals include the internal signal (change in cantilever vertical position, related to the derivative of topography), topography (calculated from the internal signal), and lateral force (mea- suring in-plane forces, such as friction). The primary PFM signals, due to the applied oscillating voltage and detected by a lock-in amplifier, are the amplitude,A(magnitude of cantilever deflection), and phase, φ(phase of cantilever deflection) responses. These PFM signals are commonly combined to form the X-signal, X = A cos(φ), and the

Y-signal, Y = A sin(φ).

Due to the inversion of the piezoelectric response in domains of opposite orientation, the piezoelectric deflection of opposite domains should have identical amplitudes (A) but 180◦ relative phase shift (φ) between them. However until recently PFM measurements have been fraught with an unexplained frequency dependence, different amplitudes and a non-180◦ phase shift between anti-parallel domains, resulting in inconsistent data in the literature. Typical frequencies used are in the range 1–100 kHz, well below mechanical resonances of LN [Ogi02] or the cantilever. Nonetheless, a frequency-dependent back- ground response of the system has been observed and strongly influences measurements.

The reason this background is so important is that it contains both an amplitude, A, and phase, φ, thus typically reducing both the amplitude and phase contrast of an unprocessed signal. From the measured signals of the +z (P) and −z (N) faces, the background system response, B, at each angular frequency ω, is determined according to the relation,

B= 1

-D

D

-D

D

P

P

N

N

f

B

B

f

Y = A sin(f)

X = A cos(f)

P

= B

-

D

N = B + D

B = ½ (P + N)

Figure 3.3: Background-correction technique for quantitative PFM scans. Two dif- ferent background signals, B1 and B2, are shown for two angular frequencies,ω1 and

ω2, respectively, after [Jungk06].

as graphically depicted in Figure 3.3. To determine the corrected domain response, D, this background must be subtracted (for example, D = N−B) [Jungk06]. With the background-corrected signal, the amplitude and phase can be completely recovered, and can reliably determine not only which regions are anti-parallel, but also their absolute orientation. This same background signal was observed on glass and metal samples, and therefore is independent of the sample type and must be a property of the PFM setup.

An alternative mode of operation is referred to as dynamic-contact electrostatic force microscopy (DC-EFM) in which an AC or DC voltage is applied to a tip in contact or non-contact with the surface [Hong98]. The tip is deflected by surface charge and therefore has been proposed to image ferroelectric domains via the surface compensation charges which are of opposite polarity on the−z and +z faces. However, this mode of operation is very similar to PFM and there is considerable disagreement in the literature whether electro-static or piezoelectric forces are measured. Many recent publications, however, have attributed the images to the piezoelectric response. In this thesis, the term DC-EFM has been used only when DC voltages have been applied to the sample under test.