Kinetic and Strain-Induced Self-Organization of SiGe ...
Kinetic and Strain-Induced Self-Organization of SiGe ...
Kinetic and Strain-Induced Self-Organization of SiGe ...
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30 CHAPTER 3. METHODS OF INVESTIGATION<br />
3.1 Transmission Electron Microscopy (TEM)<br />
Optical microscopes are limited in image resolution due to the long wavelength <strong>of</strong> visible<br />
light. Historically, this has been the reason for the introduction <strong>of</strong> electrons into microscopy.<br />
After de Broglie’s famous equation (Eq. 3.1), in which particle momentum p <strong>and</strong> its wave-<br />
length λ are related via Planks’s constant h,<br />
λ = h<br />
p<br />
(de Broglie) → λ[nm] ∼ 1.22<br />
� E[eV ]<br />
(3.1)<br />
<strong>and</strong> from a simple transformation, high energy 200 keV-electrons (accelerated by a corre-<br />
sponding voltage <strong>of</strong> 200 kV) have a wavelength λ <strong>of</strong> about 2.5 pm (0.0025 nm), which is sub-<br />
stantially smaller than atomic diameters. This diffraction limit <strong>of</strong> resolution is out <strong>of</strong> reach,<br />
mainly due to electron lenses. These are the crucial <strong>and</strong> limiting point in electron microscopy<br />
since electromagnetic lenses are by far not perfect. Compared to glass lenses that can be pro-<br />
duced with perfect quality the best electromagnetic lenses would correspond to ”the bottom<br />
<strong>of</strong> a Coke bottle as magnifying glass” (cite Williams <strong>and</strong> Carter [73]). Typical values for the<br />
practical resolution <strong>of</strong> a TEM are 0.15–0.3 nm <strong>and</strong> therefore the maximum useful magnifica-<br />
tion in the best high-resolution TEM is about 10 6 (resolution <strong>of</strong> eye approximately 0.1 mm).<br />
For thick samples these limit <strong>of</strong> resolution cannot be obtained due to the increased energy<br />
spread ∆E resulting in chromatic aberration. The mean free path for inelastic scattering<br />
depends on the electron energy, <strong>and</strong> therefore with higher acceleration voltages good high<br />
resolution can even be achieved with relative thick samples (50 nm) [73, 75, 76].<br />
Sample preparation has to be performed carefully <strong>and</strong> is probably the most important step in<br />
order to obtain good high-resolution images. It dem<strong>and</strong>s great skill to prepare thin electron-<br />
transparent (→ 50–100 nm!) specimen over a wide area. Ideally, the volume considered for<br />
TEM-analysis should be free <strong>of</strong> defects <strong>and</strong> artifacts originated by the time consuming prepa-<br />
ration.<br />
In order to image the corrugation <strong>of</strong> buried interfaces (see Ch. 6), or the wire pr<strong>of</strong>ile <strong>of</strong> the pro-<br />
cessed Si-samples (see Ch. 7), cross-sectional specimen have to be prepared. The preparation<br />
cycle for cross-sectional (Si-)samples is outlined in Ref. [1].<br />
The specimen in this work were investigated with a JEOL-2011 FasTEM (HR type) trans-<br />
mission electron microscope [77] with an acceleration voltage <strong>of</strong> 200 kV using a LaB6-cathode.<br />
For this TEM facility a point image resolution <strong>of</strong> 0.23 nm is specified; the magnification can be<br />
chosen from 2000 to 1.5 million. Images are either recorded with a conventional photo-plate<br />
camera, or, nowadays, mainly with a Gatan CCD-camera (1 megapixel).