433 lines
18 KiB
TeX
433 lines
18 KiB
TeX
\Part[
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\eng{Condensed matter physics}
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\ger{Festkörperphysik}
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]{cm}
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\TODO{Bonds, hybridized orbitals, tight binding}
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\Section[
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\eng{Bravais lattice}
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\ger{Bravais-Gitter}
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]{bravais}
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% \begin{ttext}
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% \eng{
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% }
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% \ger{
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% }
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% \end{ttext}
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\eng[bravais_table2]{In 2D, there are 5 different Bravais lattices}
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\ger[bravais_table2]{In 2D gibt es 5 verschiedene Bravais-Gitter}
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\eng[bravais_table3]{In 3D, there are 14 different Bravais lattices}
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\ger[bravais_table3]{In 3D gibt es 14 verschiedene Bravais-Gitter}
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\Eng[lattice_system]{Lattice system}
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\Ger[lattice_system]{Gittersystem}
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\Eng[crystal_family]{Crystal system}
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\Ger[crystal_family]{Kristall-system}
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\Eng[point_group]{Point group}
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\Ger[point_group]{Punktgruppe}
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\eng[bravais_lattices]{Bravais lattices}
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\ger[bravais_lattices]{Bravais Gitter}
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\newcommand\bvimg[1]{\begin{center}\includegraphics[width=0.1\textwidth]{img/bravais/#1.pdf}\end{center}}
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\renewcommand\tabularxcolumn[1]{m{#1}}
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\newcolumntype{Z}{>{\centering\let\newline\\\arraybackslash\hspace{0pt}}X}
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\begin{table}[H]
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\centering
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\caption{\gt{bravais_table2}}
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\label{tab:bravais2}
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\begin{adjustbox}{width=\textwidth}
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\begin{tabularx}{\textwidth}{||Z|c|Z|Z||}
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\hline
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\multirow{2}{*}{\GT{lattice_system}} & \multirow{2}{*}{\GT{point_group}} & \multicolumn{2}{c||}{5 \gt{bravais_lattices}} \\ \cline{3-4}
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& & \GT{primitive} (p) & \GT{centered} (c) \\ \hline
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\GT{monoclinic} (m) & $\text{C}_\text{2}$ & \bvimg{mp} & \\ \hline
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\GT{orthorhombic} (o) & $\text{D}_\text{2}$ & \bvimg{op} & \bvimg{oc} \\ \hline
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\GT{tetragonal} (t) & $\text{D}_\text{4}$ & \bvimg{tp} & \\ \hline
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\GT{hexagonal} (h) & $\text{D}_\text{6}$ & \bvimg{hp} & \\ \hline
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\end{tabularx}
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\end{adjustbox}
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\end{table}
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\begin{table}[H]
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\centering
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\caption{\gt{bravais_table3}}
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\label{tab:bravais3}
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% \newcolumntype{g}{>{\columncolor[]{0.8}}}
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\begin{adjustbox}{width=\textwidth}
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% \begin{tabularx}{\textwidth}{|c|}
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% asdfasdfadslfasdfaasdofiuapsdoifuapodisufpaoidsufpaoidsufpaoisdfaoisdfpaosidfupaoidsufpaoidsufpaoidsufpaoisdufpaoidsufpoaiudsfpioaspdoifuaposidufpaoisudpfoiaupsdoifupasodf \\
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% asdfasdfadslfasdfaasdofiuapsdoifuapodisufpaoidsufpaoidsufpaoisdfaoisdfpaosidfupaoidsufpaoidsufpaoidsufpaoisdufpaoidsufpoaiudsfpioaspdoifuaposidufpaoisudpfoiaupsdoifupasodf \\
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% \end{tabularx}
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% \begin{tabular}{|c|}
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% asdfasdfadslfasdfaasdofiuapsdoifuapodisufpaoidsufpaoidsufpaoisdfaoisdfpaosidfupaoidsufpaoidsufpaoidsufpaoisdufpaoidsufpoaiudsfpioaspdoifuaposidufpaoisudpfoiaupsdoifupasodf \\
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% asdfasdfadslfasdfaasdofiuapsdoifuapodisufpaoidsufpaoidsufpaoisdfaoisdfpaosidfupaoidsufpaoidsufpaoidsufpaoisdufpaoidsufpoaiudsfpioaspdoifuaposidufpaoisudpfoiaupsdoifupasodf \\
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% \end{tabular}
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% \\
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\begin{tabularx}{\textwidth}{||Z|Z|c|Z|Z|Z|Z||}
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\hline
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\multirow{2}{*}{\GT{crystal_family}} & \multirow{2}{*}{\GT{lattice_system}} & \multirow{2}{*}{\GT{point_group}} & \multicolumn{4}{c||}{14 \gt{bravais_lattices}} \\ \cline{4-7}
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& & & \GT{primitive} (P) & \GT{base_centered} (S) & \GT{body_centered} (I) & \GT{face_centered} (F) \\ \hline
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\multicolumn{2}{||c|}{\GT{triclinic} (a)} & $\text{C}_\text{i}$ & \bvimg{tP} & & & \\ \hline
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\multicolumn{2}{||c|}{\GT{monoclinic} (m)} & $\text{C}_\text{2h}$ & \bvimg{mP} & \bvimg{mS} & & \\ \hline
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\multicolumn{2}{||c|}{\GT{orthorhombic} (o)} & $\text{D}_\text{2h}$ & \bvimg{oP} & \bvimg{oS} & \bvimg{oI} & \bvimg{oF} \\ \hline
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\multicolumn{2}{||c|}{\GT{tetragonal} (t)} & $\text{D}_\text{4h}$ & \bvimg{tP} & & \bvimg{tI} & \\ \hline
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\multirow{2}{*}{\GT{hexagonal} (h)} & \GT{rhombohedral} & $\text{D}_\text{3d}$ & \bvimg{hR} & & & \\ \cline{2-7}
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& \GT{hexagonal} & $\text{D}_\text{6h}$ & \bvimg{hP} & & & \\ \hline
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\multicolumn{2}{||c|}{\GT{cubic} (c)} & $\text{O}_\text{h}$ & \bvimg{cP} & & \bvimg{cI} & \bvimg{cF} \\ \hline
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\end{tabularx}
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\end{adjustbox}
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\end{table}
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\TODO{FCC, BCC, diamond/Zincblende wurtzize cell/lattice vectors}
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\TODO{primitive unit cell: contains one lattice point}\\
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family of plane that are equivalent due to crystal symmetry
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\begin{formula}{miller}
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\desc{Miller index}{}{}
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\desc[german]{Millersche Indizes}{}{}
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\eq{
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(hkl) & \text{\GT{plane}}\\
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[hkl] & \text{\GT{direction}}\\
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\{hkl\} & \text{\GT{millerFamily}}
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}
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\end{formula}
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\Section[
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\eng{Reciprocal lattice}
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\ger{Reziprokes Gitter}
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]{reci}
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\begin{ttext}
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\eng{The reciprokal lattice is made up of all the wave vectors $\vec{k}$ that ressemble standing waves with the periodicity of the Bravais lattice.}
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\ger{Das rezioproke Gitter besteht aus dem dem Satz aller Wellenvektoren $\vec{k}$, die ebene Wellen mit der Periodizität des Bravais-Gitters ergeben.}
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\end{ttext}
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\begin{formula}{vectors}
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\desc{Reciprocal lattice vectors}{}{$a_i$ real-space lattice vectors, $V_c$ volume of the primitive lattice cell}
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\desc[german]{Reziproke Gittervektoren}{}{$a_i$ Bravais-Gitter Vektoren, $V_c$ Volumen der primitiven Gitterzelle}
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\eq{
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\vec{b_1} &= \frac{2\pi}{V_c} \vec{a_2} \times \vec{a_3} \\
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\vec{b_2} &= \frac{2\pi}{V_c} \vec{a_3} \times \vec{a_1} \\
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\vec{b_3} &= \frac{2\pi}{V_c} \vec{a_1} \times \vec{a_2}
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}
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\end{formula}
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\Subsection[
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\eng{Scattering processes}
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\ger{Streuprozesse}
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]{scatter}
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\begin{formula}{matthiessen}
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\desc{Matthiessen's rule}{Approximation, only holds if the processes are independent of each other}{$\mu$ mobility, $\tau$ scattering time}
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\desc[german]{Matthiessensche Regel}{Näherung, nur gültig wenn die einzelnen Streuprozesse von einander unabhängig sind}{$\mu$ Moblitiät, $\tau$ Streuzeit}
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\eq{
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\frac{1}{\mu} &= \sum_{i = \textrm{\GT{\fqname}}} \frac{1}{\mu_i} \\
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\frac{1}{\tau} &= \sum_{i = \textrm{\GT{\fqname}}} \frac{1}{\tau_i}
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}
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\end{formula}
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\Section[
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\eng{Free electron gas}
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\ger{Freies Elektronengase}
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]{free_e_gas}
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\begin{ttext}
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\eng{Assumptions: electrons can move freely and independent of each other.}
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\ger{Annahmen: Elektronen bewegen sich frei und unabhänig voneinander.}
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\end{ttext}
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\begin{formula}{drift_velocity}
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\desc{Drift velocity}{Velocity component induced by an external force (eg. electric field)}{$v_\text{th}$ thermal velocity}
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\desc[german]{Driftgeschwindgkeit}{Geschwindigkeitskomponente durch eine externe Kraft (z.B. ein elektrisches Feld)}{$v_\text{th}$ thermische Geschwindigkeit}
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\eq{\vec{v}_\text{D} = \vec{v} - \vec{v}_\text{th}}
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\end{formula}
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\begin{formula}{mean_free_time}
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\desc{Mean free time}{}{}
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\desc[german]{Streuzeit}{}{}
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\eq{\tau}
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\end{formula}
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\begin{formula}{mean_free_path}
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\desc{Mean free path}{}{}
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\desc[german]{Mittlere freie Weglänge}{}{}
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\eq{\ell = \braket{v} \tau}
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\end{formula}
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\begin{formula}{mobility}
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\desc{Electrical mobility}{}{$q$ charge, $m$ mass}
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\desc[german]{Beweglichkeit}{}{$q$ Ladung, $m$ Masse}
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\eq{\mu = \frac{q \tau}{m}}
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\end{formula}
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\Subsection[
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\eng{Drude model}
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\ger{Drude-Modell}
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]{drude}
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\begin{ttext}
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\eng{Classical model describing the transport properties of electrons in materials (metals):
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The material is assumed to be an ion lattice and with freely moving electrons (electron gas). The electrons are
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accelerated by an electric field and decelerated through collisions with the lattice ions.
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The model disregards the Fermi-Dirac partition of the conducting electrons.
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}
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\ger{Ein klassisches Model zur Beschreibung der Transporteigenschaften von Elektronen in (v.a.) Metallen:
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Der Festkörper wird als Ionenkristall mit frei beweglichen Elektronen (Elektronengas).
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Die Elektronen werden durch ein Elektrisches Feld $E$ beschleunigt und durch Stöße mit den Gitterionen gebremst.
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Das Modell vernachlässigt die Fermi-Dirac Verteilung der Leitungselektronen.
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}
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\end{ttext}
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\begin{formula}{motion}
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\desc{Equation of motion}{}{$v$ electron speed, $\vec{v}_\text{D}$ drift velocity, $\tau$ mean free time between collisions}
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\desc[german]{Bewegungsgleichung}{}{$v$ Elektronengeschwindigkeit, $\vec{v}_\text{D}$ Driftgeschwindigkeit, $\tau$ Stoßzeit}
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\eq{\masse \odv{\vec{v}}{t} + \frac{\masse}{\tau} \vec{v}_\text{D} = -e \vec{E}}
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\end{formula}
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\begin{formula}{current_density}
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\desc{Current density}{Ohm's law}{$n$ charge particle density}
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\desc[german]{Stromdichte}{Ohmsches Gesetz}{$n$ Ladungsträgerdichte}
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\eq{\vec{j} = -ne\vec{v}_\text{D} = ne\mu \vec{E}}
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\end{formula}
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\begin{formula}{conductivity}
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\desc{Drude-conductivity}{}{}
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\desc[german]{Drude-Leitfähigkeit}{}{}
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\eq{\sigma = \frac{\vec{j}}{\vec{E}} = \frac{e^2 \tau n}{\masse} = n e \mu}
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\end{formula}
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\Subsection[
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\eng{Sommerfeld model}
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\ger{Sommerfeld-Modell}
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]{sommerfeld}
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\begin{ttext}
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\eng{Assumes a gas of free fermions underlying the pauli-exclusion principle. Only electrons in an energy range of $\kB T$ around the Fermi energy $\EFermi$ participate in scattering processes.}
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\ger{Annahme eines freien Fermionengases, welches dem Pauli-Prinzip unterliegt. Nur Elektronen in einem Energiebereich von $\kB T$ um die Fermi Energe $\EFermi$ nehmen an Streuprozessen teil.}
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\end{ttext}
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\begin{formula}{current_density}
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\desc{Current density}{}{}
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\desc[german]{Stromdichte}{}{}
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\eq{\vec{j} = -en\braket{v} = -e n \frac{\hbar}{\masse}\braket{\vec{k}} = -e \frac{1}{V} \sum_{\vec{k},\sigma} \frac{\hbar \vec{k}}{\masse}}
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\end{formula}
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\TODO{The formula for the conductivity is the same as in the drude model?}
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\Subsection[
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\eng{2D electron gas}
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\ger{2D Elektronengas}
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]{2deg}
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\begin{ttext}
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\eng{Lower dimension gases can be obtained by restricting a 3D gas with infinetly high potential walls on a narrow area with the width $L$.}
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\ger{
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Niederdimensionale Elektronengase erhält man, wenn ein 3D Gas durch unendlich hohe Potentialwände auf einem schmalen Bereich mit Breite $L$ eingeschränkt wird.
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}
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\end{ttext}
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\begin{formula}{confinement_energy}
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\desc{Confinement energy}{Raises ground state energy}{}
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\desc[german]{Confinement Energie}{Erhöht die Grundzustandsenergie}{}
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\eq{\Delta E = \frac{\hbar^2 \pi^2}{2\masse L^2}}
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\end{formula}
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\Eng[plain_wave]{plain wave}
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\Ger[plain_wave]{ebene Welle}
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\begin{formula}{energy}
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\desc{Energy}{}{}
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\desc[german]{Energie}{}{}
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\eq{E_n = \underbrace{\frac{\hbar^2 k_\parallel^2}{2\masse}}_\text{$x$-$y$: \GT{plain_wave}} + \underbrace{\frac{\hbar^2 \pi^2}{2\masse L^2} n^2}_\text{$z$}}
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\end{formula}
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\Subsection[
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\eng{1D electron gas / quantum wire}
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\ger{1D Eleltronengas / Quantendraht}
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]{1deg}
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\begin{formula}{energy}
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\desc{Energy}{}{}
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\desc[german]{Energie}{}{}
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\eq{E_n = \frac{\hbar^2 k_x^2}{2\masse} + \frac{\hbar^2 \pi^2}{2\masse L_z^2} n_1^2 + \frac{\hbar^2 \pi^2}{2\masse L_y^2} n_2^2}
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\end{formula}
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\Subsection[
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\eng{0D electron gas / quantum dot}
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\ger{0D Elektronengase / Quantenpunkt}
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]{0deg}
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\TODO{TODO}
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\Section[
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\eng{Semiconductors}
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\ger{Halbleiter}
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]{semic}
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\begin{formula}{charge_density_eq}
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\desc{Equilibrium charge densitites}{}{}
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\desc[german]{Ladungsträgerdichte im Equilibrium}{}{}
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\eq{
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n_0 &\approx N_\text{c}(T) e^{-\frac{E_\text{c} - \EFermi}{\kB T}} \\
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p_0 &\approx N_\text{v}(T) e^{-\frac{\EFermi - E_\text{v}}{\kB T}}
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}
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\end{formula}
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\begin{formula}{charge_density_intrinsic}
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\desc{Intrinsic charge density}{}{}
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\desc[german]{Intrinsische Ladungsträgerdichte}{}{}
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\eq{
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n_\text{i} \approx \sqrt{n_0 p_0} = \sqrt{N_\text{c}(T) N_\text{v}(T)} e^{-\frac{E_\text{gap}}{2\kB T}}
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}
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\end{formula}
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\Section[
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\eng{Measurement techniques}
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\ger{Messtechniken}
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]{meas}
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\Subsection[
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\eng{ARPES}
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\ger{ARPES}
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]{arpes}
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what?
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in?
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how?
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plot
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\Subsection[
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\eng{Scanning probe microscopy SPM}
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\ger{Rastersondenmikroskopie (SPM)}
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]{spm}
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\begin{ttext}
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\eng{Images of surfaces are taken by scanning the specimen with a physical probe.}
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\ger{Bilder der Oberfläche einer Probe werden erstellt, indem die Probe mit einer Sonde abgetastet wird.}
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\end{ttext}
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\Eng[name]{Name}
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\Ger[name]{Name}
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\Eng[application]{Application}
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\Ger[application]{Anwendung}
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\begin{minipagetable}{amf}
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\entry{name}{
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\eng{Atomic force microscopy (AMF)}
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\ger{Atomare Rasterkraftmikroskopie (AMF)}
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}
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\entry{application}{
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\eng{Surface stuff}
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\ger{Oberflächenzeug}
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}
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\entry{how}{
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\eng{With needle}
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\ger{Mit Nadel}
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}
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\end{minipagetable}
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\begin{minipage}{0.5\textwidth}
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\begin{figure}[H]
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\centering
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\includegraphics[width=0.8\textwidth]{img/cm_amf.pdf}
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\caption{\cite{Bian2021}}
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\end{figure}
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\end{minipage}
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\begin{minipagetable}{stm}
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\entry{name}{
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\eng{Scanning tunneling microscopy (STM)}
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\ger{Rastertunnelmikroskop (STM)}
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}
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\entry{application}{
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\eng{Surface stuff}
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\ger{Oberflächenzeug}
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}
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\entry{how}{
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\eng{With TUnnel}
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\ger{Mit TUnnel}
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}
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\end{minipagetable}
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\begin{minipage}{0.5\textwidth}
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\begin{figure}[H]
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\centering
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\includegraphics[width=0.8\textwidth]{img/cm_stm.pdf}
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\caption{\cite{Bian2021}}
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\end{figure}
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\end{minipage}
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\Section[
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\eng{Fabrication techniques}
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\ger{Herstellungsmethoden}
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]{fab}
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\begin{minipagetable}{cvd}
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\entry{name}{
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\eng{Chemical vapor deposition (CVD)}
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\ger{Chemische Gasphasenabscheidung (CVD)}
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}
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\entry{how}{
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\eng{
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A substrate is exposed to volatile precursors, which react and/or decompose on the heated substrate surface to produce the desired deposit.
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By-products are removed by gas flow through the chamber.
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}
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\ger{
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An der erhitzten Oberfläche eines Substrates wird aufgrund einer chemischen Reaktion mit einem Gas eine Feststoffkomponente abgeschieden.
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Nebenprodukte werden durch den Gasfluss durch die Kammer entfernt.
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}
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}
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\entry{application}{
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\eng{
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\begin{itemize}
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\item Polysilicon \ce{Si}
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\item Silicon dioxide \ce{SiO_2}
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\item Graphene
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\item Diamond
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\end{itemize}
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}
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\ger{
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\begin{itemize}
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\item Poly-silicon \ce{Si}
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\item Siliziumdioxid \ce{SiO_2}
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\item Graphen
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\item Diamant
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\end{itemize}
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}
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}
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\end{minipagetable}
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\begin{minipage}{0.5\textwidth}
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\centering
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\includegraphics[width=\textwidth]{img/cm_cvd_english.pdf}
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\end{minipage}
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\Subsection[
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\eng{Epitaxy}
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\ger{Epitaxie}
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]{epitaxy}
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\begin{ttext}
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\eng{A type of crystal groth in which new layers are formed with well-defined orientations with respect to the crystalline seed layer.}
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\ger{Eine Art des Kristallwachstums, bei der mindestens eine kristallographische Ordnung der wachsenden Schicht der des Substrates entspricht.}
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\end{ttext}
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\begin{minipagetable}{mbe}
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\entry{name}{
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\eng{Molecular Beam Epitaxy (MBE)}
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\ger{Molekularstrahlepitaxie (MBE)}
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}
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\entry{how}{
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\eng{In a ultra-high vacuum, the elements are heated until they slowly sublime. The gases then condensate on the substrate surface}
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\ger{Die Elemente werden in einem Ultrahochvakuum erhitzt, bis sie langsam sublimieren. Die entstandenen Gase kondensieren dann auf der Oberfläche des Substrats}
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}
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\entry{application}{
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\eng{
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\begin{itemize}
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\item Gallium arsenide \ce{GaAs}
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\end{itemize}
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\TODO{Link to GaAs}
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}
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\ger{
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\begin{itemize}
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\item Galliumarsenid \ce{GaAs}
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|
\end{itemize}
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|
}
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|
}
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|
\end{minipagetable}
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|
\begin{minipage}{0.5\textwidth}
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\centering
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\includegraphics[width=\textwidth]{img/cm_mbe_english.pdf}
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\end{minipage}
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|