3. Experimental Techniques
3.3. Atomic Force Microscopy (AFM)
3.3.1.
Principles of AFM
The Veeco Multimode AFM with the Nanonis SPM controller in both contact and tapping modes were used. Figure 3.16 (a) is an image of the instrument, figure (b) is an example SEM image of the SiN cantilever tip used.
The principle behind atomic force microscopy is to measure the force exerted on a sample surface by a cantilever tip as a function of distance as the tip is tracked along the sample surface resulting in a topographical representation of the surface. The cantilever is made from silicon nitride and the tip has a width of 8 to 10nm. This means that the tip is unable to resolve features that are less than 10nm apart. In this study a minimum scan size of 50nm x 50nm scans were obtained in tapping mode by adjusting the gains.
Figure 3.16: (a) Veeco Multimode AFM, (b) SiN AFM cantilever and tip [127] and (c) AFM head with labelled parts [128]. Piezoelectric scanner Photodetector digital display (a) (b) (c) AFM head
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Figure 3.17 shows the tip-sample interaction forces using the tip-sample Lennard- Jones potential, Uts(z) (equation 3.12). This equation describes the interaction
between two neutral atoms (one on the cantilever tip and another on the sample surface) and consists of two parts: 1) a term describing the van der Waals attractive forces and 2) the repulsive forces [129]:
Uts(z) = 4U0 [ (Za z) 12 ⏟ repulsion (short range) − (Za z) 6 ⏟ attraction (long range)] (Equation 3.12)
Where: Za is the tip-sample distance at which Uts(z) = 0, U0 is the depth of the potential well and, z, is the radius between atoms. Differentiating the Lennard Jones potential with respect to, z, gives the corresponding force between tip and sample, Fts.
Figure 3.16 shows a plot of Fts vs z
Za (in red). The vertical black dashed line represents
the boundary where the forces transition from repulsive forces between atoms to Van der Waals attractive forces.
Figure 3.17: Lennard-Jones force between sample and tip, Fts (red), plotted with cantilever spring constant
forces (in blue) the gradient of which is k. Taken from Voigtlander [129].
Van der Waals attractive interaction Repulsive interaction
Increasing cantilever spring constant
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The cantilever can be treated like a spring and so obeys Hooke’s law for different vertical deflections along, z, where z0 is the zero-point deflection and k is the spring
constant:
Fcant(z, z0) = k(z − z0) (𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 3.13)
Equation 3.13 can be integrated with respect to z to give the cantilever spring potential, Ucant. If the cantilever is far from the sample surface, i.e.: a large z0, a stable spring
potential minimum is obtained at 𝑧 ≈ 𝑧0. As the tip is brought closer to the sample surface, the potential minimum close to z0 vanishes due to stronger attractive forces
and a new stable potential minimum will found that is closer to the sample surface. This is explained in figure 3.17. Points ‘a’ to ‘c’ show the cantilever approaching the sample surface, where δFts
δz < k holds. Points ‘b’ and ‘e’ correspond to two minimum
potentials and point ‘g’ corresponds to a potential maximum in between. When the tip reaches 𝑍0𝐶, δFts
δz > k and the tip jumps from an unstable point ‘c’ to the stable
potential minimum point ‘d’. This is known as snapping to contact. At point ‘f’ snap out of contact takes place because δFts
δz again becomes larger than the spring constant,
k as 𝑧/Za increases (i.e.: when the tip retracts from the surface).
3.3.2.
Scanning modes:
3.3.2.1.
Contact mode
In contact mode the tip makes full contact with the sample surface. The sample is first mounted on a stage. A laser is beam is fired at the cantilever top surface, and the reflected beam is adjusted to strike at the centre of a photodetector as shown in figure 3.15 (c). A triple axis piezoelectric scanner is positioned underneath the sample, where the z direction is perpendicular to the sample surface (001).
As the sample is moved under a stationary tip over a cross sectional area, feedback is provided from the photodiode to maintain a constant laser deflection by adjusting the sample in the z direction using the piezoelectric scanner. The Nanonis software records
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the z position at each x and y position of the scan and hence a topographical image of the sample can be gathered.
3.3.2.2.
Tapping mode
In tapping mode, the cantilever is oscillating. Snap to contact would stop the oscillation due to the very narrow potential minimum close to the surface and so it must be prevented. This is achieved by using cantilevers with a larger spring constant, k. If the gradient of Fcant line is greater than the Fts curve, then snap to contact never occurs as
shown by the orange dashed line figure 3.16.
Another method to prevent snap to contact is by using large oscillation amplitudes which results in Fcant > Fts. This can be achieved by ‘tuning’ the cantilever to its
resonant frequency thus achieving maximum amplitude.
The benefit of carrying out contact mode AFM is that large scan sizes can be obtained. In this investigation up to 100µm x 100µm scans were carried out. If the sample is relatively sturdy, then contact mode should be the preferred choice to scanning a sample as it gives a complete topographical representation of the surface without missing any features. However, if the sample is relatively fragile such as suspended membranes then tapping mode serves as the better scanning method since snap to contact could destroy the membrane [130].
Additionally, tapping mode allows for higher resolution scans since constant contact isn’t made to the sample surface the sample z height is constantly adjusted to maintain a fixed oscillation amplitude which allows for higher resolution of the scan in the z direction. The scan resolution is limited by the width of the tip and so in this investigation the highest resolution scan that was able to gather any data was at 100nm x 100nm.
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3.3.3.
Image analysis
In both contact and tapping mode, the proportionality and time constants can be adjusted in the software as can the scanning speed. Generally, a scanning speed of 0.5sec/line was used for most samples, however for dense features, such as the facets in low temperture Ge buffer layers (chapter 4) a much slower scan speed of 4 sec/line was used to resolve the shape of the features. Image analysis of the scans was carried out using Gwyddion SPM software. In unprocessed AFM images surface artefacts caused by tip shape, scanner hysteresis and dirt on the sample have to be removed before extracting data such as rms roughness (Rrms) and z-height.
The first step of image processing involves calculating and subtracting a plane from all the image data points. The second is to remove noise using an nth order polynomial function from the data in both the x and y directions. Selecting a value of value of n where no further increase in n causes considerable to change to Rrms. The third step is
to use a height median tool to remove any horizontal lines (artefacts caused by rastering the tip across the sample) that were created when scanning the sample. If additional scarring is seen on the scan in limited region due to dirt, a mask can be applied and subtracted from the main scan.
Whether doing contact or tapping mode, to ascertain the true roughness of the surface of the sample the sample should be scanned across a range of scan sizes. With contact mode the scan size ranges from 1µm x 1µm to 100µm x 100µm. Whilst with tapping mode the scan sizes range from 100nm x 100nm to 50µm x 50µm. If yi is the
horizontal deflection from that of the ideal surface, then the rms roughness (Rrms) is given as: Rrms = √1 n∑ yi 2 n i=1 (Equation 3.14)
The Rrms is determined when the scan size is large enough to maximise the mean
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