Benutzer:Bronger/paper
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\journal{J. Non-Cryst. Solid}
\begin{document}
\begin{frontmatter}
%% Title, authors and addresses
%% use the tnoteref command within \title for footnotes; %% use the tnotetext command for the associated footnote; %% use the fnref command within \author or \address for footnotes; %% use the fntext command for the associated footnote; %% use the corref command within \author for corresponding author footnotes; %% use the cortext command for the associated footnote; %% use the ead command for the email address, %% and the form \ead[url] for the home page: %% %% \title{Title\tnoteref{label1}} %% \tnotetext[label1]{} %% \author{Name\corref{cor1}\fnref{label2}} %% \ead{email address} %% \ead[url]{home page} %% \fntext[label2]{} %% \cortext[cor1]{} %% \address{Address\fnref{label3}} %% \fntext[label3]{}
\title{Anomalous Hall effect in microcrystalline Si:H films} %\title{Anomalous Hall effect in ??\textmu{c-Si:H}}
%% use optional labels to link authors explicitly to addresses: %% \author[label1,label2]{<author name>} %% \address[label1]{<address>} %% \address[label2]{<address>}
\author[fzj]{C.~Sellmer\corref{cor1}}
\author[fzj]{T.~Bronger}
\author[fzj,malibu]{W.~Beyer}
\author[fzj]{R.~Carius}
\cortext[cor1]{Corresponding author. Tel.: +49\,2461\,618726; fax: +49\,2461\,613735; Email address: c.sellmer@fz-juelich.de}
\address[fzj]{IEK-5: Photovoltaik, Forschungszentrum J\"{u}lich GmbH, 52425 J\"{u}lich, Germany}
\address[malibu]{Malibu GmbH \& Co.KG, B\"{o}ttcherstrasse 7, 33609 Bielefeld, Germany}
\address{}
\begin{abstract}
The anomalous sign of the Hall coefficient in amorphous semiconductors is still poorly understood. It seems accepted, however, that an anomalous sign of the Hall coefficient indicates a different charge transport mechanism compared to free carrier motion on which the Lorentz force is acting. We find anomalous Hall coefficient signs in phosphorus doped microcrystalline silicon films after irradiation with high energy electrons and subsequent annealing. These films are mixtures of amorphous and crystalline phases. We analyze measurements of Hall effect, electrical conductivity and thermopower on such samples prior to and after electron irradiation and annealing and use the anomalous Hall effect sign as a phenomenological indication of electronic transport in the amorphous phase. We deduce that the material consists of crystalline particles embedded in an amorphous matrix.
\end{abstract}
\begin{keyword}
Anomalous Hall effect \sep microcrystalline silicon
%% keywords here, in the form: keyword \sep keyword
%% MSC codes here, in the form: \MSC code \sep code %% or \MSC[2008] code \sep code (2000 is the default)
\end{keyword}
\end{frontmatter}
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%% main text \section{Introduction}
One of the poorly understood properties of amorphous silicon is the anomalous sign of the Hall effect. Compared to the sign expected from the type of doping and from the type of majority charge carriers determined by methods like the thermoelectric power or I--V characteristics, the sign of the Hall coefficient is generally found to be opposite~\cite{comber1977,beyer-mell-77,BeyMelOve77}.
While it seems accepted that an anomalous sign of the Hall coefficient indicates a different charge transport mechanism compared to free carrier motion on which the Lorentz force is acting~\cite{emin77}, its understanding is still quite limited. Phenomenologically, however, amorphous silicon exhibits the anomalous sign, while microcrystalline silicon exhibits the normal sign in the Hall effect~\cite{carius97}.
Here, we report on the measurement of the Hall coefficient in doped microcrystalline silicon. By electron irradiation and subsequent annealing, the Fermi level in the material was changed and the Hall coefficients signs are found to vary. By analysis of the experimental data, information about the material microstructure is obtained.
\section{Experimental Procedures}
The samples were deposited by plasma chemical vapour deposition (PECVD) at a temperature of \unit{200}{\celsius} under conditions to get a rather compact material \cite{Vetterl200097}. Gas mixtures of hydrogen, silane and phosphine were used and the silane concentration ($SC$) was set at $6\%$~\cite{astakhov:104205,BaiaNeto2002274}. The sample investigated in detail here was grown with $5\,\mathrm{ppm}$ phosphine doping and had a crystallinity of 28\%, determined by Raman spectroscopy~\cite{houben98}. This sample was about \unit{4}{\micro\metre} thick and was deposited on a $0.4\,\mathrm{mm}$ thick quartz glass substrate.
To shift the Fermi energy in the microcrystalline material, irradiation with high energy electrons was used. The electron beam with an energy of \unit{2}{\mega\electronvolt} and a dose of \unit{1.1\cdot 10^{18}}{\per\centi\metre\squared}, applied at a temperature of \unit{80}{\kelvin}, leads to generation of defects in the material so that the Fermi level is shifted closer to midgap~\cite{astakhov2007}.
The thermoelectric power (thermopower) measurements were done as reported previously \cite{BeyOve84}. The thermovoltage was measured across a gap of about $6\,\mathrm{mm}$ defined by the evaporated chromium contacts to which thin (\unit{50}{\micro\metre}) thermocouples were attached.
For the Hall measurements, a magnetic field of \unit{1.88}{\tesla} was applied and a Hall bar geometry with chromium as contact material was used \cite{bronger07}.
Conductivity was measured along with the measurements of the Hall coefficient and thermoelectric power in a two-contact arrangement.
\section{Results}
\begin{figure}[<+htpb+>]
\includegraphics[scale=0.57]{05B280_A_Hall}
\caption{Hall coefficient $R_\mathrm{H}$ as a function of inverse temperature for phosphorus-doped microcrystalline silicon with Raman crystallinity of $28\%$. As deposited material (a) and (b)-(d) electron irradiated material for various annealing steps from $345$ to \unit{430}{\kelvin}.}
\label{fig:05B280_A_Hall}
\end{figure}
For the non-irradiated material, a normal Hall effect sign was observed for material with a Raman crystallinity $> 25\%$ and an anomalous Hall effect sign for material with a Raman crystallinity $< 25\%$ in the whole temperature range investigated ($130-\unit{430}{\kelvin}$).
In the following, we focus on material with a Raman crystallinity of $28\%$. While this material shows in the non-irradiated state a normal Hall effect, in the irradiated state an anomalous effect is observed as shown in Fig.~\ref{fig:05B280_A_Hall}. The Hall coefficient $R_\mathrm{H}$ plotted in Fig.~\ref{fig:05B280_A_Hall} was determined by $R_\mathrm{H} = U_\mathrm{H}/(U_1 \sigma B)\frac{l}{w}$ with $U_\mathrm{H}$ the Hall voltage, $U_1$ the applied voltage, $B$ the magnetic field, $\sigma$ the conductivity and $l$ and $w$ the length and width of the specimen parallel to the applied voltage. For a better visibility we used a logarithmic scale.
While in the as-deposited state (Fig.~\ref{fig:05B280_A_Hall}a) the Hall coefficient shows a negative sign in agreement with the n-type doping, after electron irradiation and moderate annealing at \unit{345}{\kelvin}, a positive sign (i.e.\ an anomalous Hall effect) prevails (Fig.~\ref{fig:05B280_A_Hall}b). Further annealing (Fig.~\ref{fig:05B280_A_Hall}b~and~c) gives almost symmetric positive and negative Hall effect signals, i.e.\ measurements at the same temperature resulted in both positive and negative Hall voltages $U_\mathrm{H}$. Reason for this ambiguity is the very small Hall voltage signal which was probably dominated by noise. After annealing at \unit{430}{\kelvin}, however, a clear separation between anomalous Hall effect at low temperature and normal Hall effect at higher temperature is observed (Fig.~\ref{fig:05B280_A_Hall}d).
The corresponding results of conductivity and thermoelectric power measurements are shown in Figs~\ref{fig:05B280_l} and~\ref{fig:05B280_S}. No thermopower was measured for the as-deposited state. Note that according to the thermopower measurements, the dominant charge carriers are always electrons, in agreement with the n-type doping of the sample.
\begin{figure}[<+htpb+>]
\includegraphics[scale=0.57]{05B280_l}
\caption{Conductivity as a function of inverse temperature of sample of Fig.~\ref{fig:05B280_A_Hall}.}
\label{fig:05B280_l}
\end{figure}
The conductivity measurements show a strong shift of the Fermi level towards midgap by electron irradiation, caused by the irradiation-generated defects. Near room temperature, indicated by the dashed line, the conductivity drops by more than three orders of magnitude.
By annealing, the concentration of these defects is apparently reduced again, as the conductivity increases and the thermopower drops. Apparently, the Fermi level tends to move back to its original state. According to electron irradiation experiments~\cite{corbett1966,takeda1999}, the used dose is not sufficient to effect the structure of the sample, and in particular, the amorphous/microcrystalline fraction is unlikely changed by electron irradiation. Thus, the change of the Hall coefficient in Fig.~\ref{fig:05B280_A_Hall} upon irradiation/annealing must be due to the shift of the Fermi level. We suggest that this is because in an inhomogeneous material consisting of amorphous and crystalline fractions, a change of the Fermi level can result in a change of the dominating transport path.
\begin{figure}[<+htpb+>]
\includegraphics[scale=0.56]{05B280_S}
\caption{Thermoelectric power versus inverse temperature of sample of Fig.~\ref{fig:05B280_A_Hall}}
\label{fig:05B280_S}
\end{figure}
\section{Discussion}
In the discussion we will focus on two models for the transport in microcrystalline silicon -- (i) parallel transport paths of amorphous and crystalline material and (ii) a material where (spherical) crystalline inclusions are embedded in an amorphous matrix.
The parallel transport paths model is sketched in Fig.~\ref{fig:parallel_paths_both}. Such parallel paths of amorphous and microcrystalline Si areas are often assumed for a partially microcrystalline material. The irradiation and subsequent annealing process could lead not only to a shift of the Fermi level but also to the change of the main transport path. Note that in crystalline silicon, charge transport takes place at the crystalline silicon band edge, whereas in amorphous silicon, it takes place at the mobility edge~\cite{mott_electronic_1979}, which is the counterpart of the band edge in disordered material, and which is higher in energy. Therefore, for similar Fermi levels, the conductivity in the crystalline material will always have a lower activation energy. Thus, at low temperature, the charge transport in crystalline material will dominate conductivity while at higher temperatures due to its high volume fraction the amorphous material fraction may contribute to the total charge transport (see Fig.~\ref{fig:combined_conductivity}). If we relate the charge transport in the amorphous material with the cross-sectional area $A_1$ and the Hall mobility $\mu_{1}^\mathrm{A}$ (of anomalous Hall effect sign) and the charge transport in the crystalline material with the cross-sectional area $A_2$ and the Hall mobility $\mu_{2}^\mathrm{N}$ (of normal Hall effect sign), according to~\cite{mott_electronic_1979} the total mobility $\mu$ of equation~\ref{eq:Hall_R_F} should be:
\begin{figure}[<+htpb+>]
\centering
\subfloat[]{
\label{fig:parallel_paths}
\includegraphics[scale=0.7]{parallel_paths}}
\subfloat[]{
\label{fig:parallel_paths_Schaltung}
\includegraphics[scale=0.7]{parallel_paths_Schaltung}}
\caption{\subref{fig:parallel_paths} Hall measurement setup for parallel transporth paths, \subref{fig:parallel_paths_Schaltung} corresponding simplified resistor network.}
\label{fig:parallel_paths_both}
\end{figure}
\begin{figure}[<+htpb+>]
\includegraphics[scale=0.75]{combined_conductivity}
\caption{Activation of the conductivities of amorphous and crystalline path.}
\label{fig:combined_conductivity}
\end{figure}
\begin{equation}
\mu_\mathrm{H} = \frac{A_1 \sigma_1}{A \sigma} \cdot \mu_{1}^\mathrm{A} + \frac{A_2 \sigma_2}{A \sigma} \cdot \mu_{2}^\mathrm{N}.
\label{eq:Hall_R_F}
\end{equation}
Here, $\sigma_1$ is the conductivity in the amorphous material, $\sigma_2$ in the crystalline material and $\sigma = \sigma_1 + \sigma_2$ and we define a mobility of negative sign by the mobility associated with the anomalous Hall effect. Annealing may lead to a change of the dominating transport path and could explain a sign change of $\mu_\mathrm{H}$ as a function of the annealing temperature. However, because of dominance of crystalline Si charge transport at low temperature, the Hall effect should have a normal sign, and an anomalous sign at high temperature opposite to what is observed in Fig.~\ref{fig:05B280_A_Hall}d. Thus, a charge transport by parallel paths cannot explain the present results.
In the second model, we consider microcrystalline silicon as a material consisting of an amorphous matrix with crystalline inclusions assumed to be spherical for simplicity. Hall mobility $\mu_{1}^\mathrm{A}$ and conductivity $\sigma_1$ of the amorphous matrix is assumed to differ from that of the crystalline grains $\mu_{2}^\mathrm{N}$. This model, which was described in detail for Hall measurements of Li-doped NiO~\cite{deWit1972,vandaal1967}, can explain the observed sign change of the Hall mobility as a function of temperature for the given sample. However, one needs to keep in mind that combining paths with different mobilities which was also done by~\cite{lipskis1971,heleskivi1972,volger1950} assumes charge transport with different Hall mobilities through crystalline materials whereas the here investigated material consists partly of an amorphous phase where the Hall effect has an anomalous sign.
\begin{figure}[<+htpb+>]
\centering
\subfloat[]{
\label{fig:spherical_crystals}
\includegraphics[scale=0.7]{spherical_crystals}}
\subfloat[]{
\label{fig:spherical_crystals_Schaltung}
\includegraphics[scale=0.7]{spherical_crystals_Schaltung}}
\caption{\subref{fig:spherical_crystals} Hall measurement for spherical inclusions, \subref{fig:spherical_crystals_Schaltung} corresponding simplified resistor network.}
\label{fig:spherical_crystals_both}
\end{figure}
For the simplified resistor network in Fig.~\ref{fig:spherical_crystals_Schaltung}, one can distinguish three different cases: %Following Ref.~ , one can distinguish three different cases for the simplified resistor network in Fig.~\ref{fig:spherical_crystals_Schaltung}: \begin{enumerate}
\item For very low temperatures ($R_\mathrm{a}\gg R_\mathrm{c}$) and $\sigma_\mathrm{a} \ll \sigma_\mathrm{c}$, the currents through both paths shown in Fig.~\ref{fig:spherical_crystals_Schaltung} are almost equal. Only the transport through the bottom path in Fig.~\ref{fig:spherical_crystals_Schaltung} will be considered because only this path may lead to a normal Hall effect. Then the Hall voltage can be calculated by adding up the Hall voltages of both phases:
\begin{align}
U_H &= R_\mathrm{H_a} \cdot I \cdot B/d_1 + R_\mathrm{H_c} \cdot I \cdot B/d_2 \nonumber \\
&= \big(\mu_\mathrm{a}/(\sigma_\mathrm{a} \cdot d_1) + \mu_\mathrm{c}/(\sigma_\mathrm{c} \cdot d_2)\big) \cdot I \cdot B,
%&= (\mu_\mathrm{H_a}/(\sigma_\mathrm{a} \cdot d_1) + \mu_\mathrm{H_c}/(\sigma_\mathrm{c} \cdot d_2)) \cdot I \cdot B,
\label{eq:voltage_lowT}
\end{align}
where $d_1$ and $d_2$ equals the thickness (parallel to the magnetic field) of the amorphous and crystalline paths. Assuming that the current through both phases is limited by the amorphous phase and the charge carrier mobilities of both phases have the same order of magnitude (but different signs), the Hall voltage is dominated by the amorphous phase.
\item For very high temperatures ($R_c\gg R_a$) the transport path through the amorphous phase (top transport path in Fig.~\ref{fig:spherical_crystals_Schaltung}) is dominating, see Fig.~\ref{fig:combined_conductivity}. The Hall voltage is therefore also dominated by the amorphous phase.
\item If the conductances have the same order of magnitude and the absolute value of the mobility of the crystalline phase is higher than that of the amorphous phase ($|\mu_\mathrm{H_a}|<|\mu_\mathrm{H_c}|$) a normal Hall effect is found for equation~\ref{eq:voltage_lowT}.
Small variations of the relative conductivity contributions can lead to positive and negative Hall voltages at the same temperature which can be seen in Fig.~\ref{fig:05B280_A_Hall} after the first annealing steps. \end{enumerate}
\begin{figure}[<+htpb+>]
\includegraphics[scale=0.65]{05B280_mu_vs_rezT_sph_Betrag}
%\includegraphics[scale=0.67]{05B280_mu_vs_rezT_sph_Betrag}
\caption{Hall mobility as a function of inverse temperature. The three lines mark calculation for three different crystalline fractions. Hall mobility measurements after the last annealing step are marked as filled and open squares corresponding to normal (positive Hall mobility) and anomalous (negative Hall mobility) Hall effect measurements.}
\label{fig:deWit_mu_vs_T}
\end{figure}
Figure~\ref{fig:deWit_mu_vs_T} shows the Hall mobility as a function of the inverse temperature for mobilities $\mu_\mathrm{c} = \unit{1}{\centi\metre\squared\per\volt\second}$ and $\mu_\mathrm{a} = -1/3$ and a crystalline fraction of $25$, $28$, $31\%$. The conductivities of the matrix and the inclusions were adjusted to the measured conductivity of Fig.~\ref{fig:05B280_l}. The filled and open square symbols mark the Hall mobility for measurements where the normal and the anomalous Hall effect was detected after annealing at \unit{430}{\kelvin}. The black pentagons again mark the measurements after deposition.
As shown in Fig.~\ref{fig:deWit_mu_vs_T}, an increase of the crystalline fraction leads to a stronger influence of the crystalline inclusions to the effective Hall mobility. However, the Hall mobility saturation value for dominating amorphous electronic properties and a crystalline fraction of $25\%$, which fits best the experimental data, lies roughly a factor of two higher than the measured values for low temperatures. The saturation value for low temperatures depends in particular on the Hall mobility of the amorphous phase and the crystalline fraction in microcrystalline silicon.
\begin{figure}[<+htpb+>]
\includegraphics[scale=0.65]{05B280_mu_ratio_vs_sigma_ratio}
\caption{Ratio of Hall mobility and mobility of the amorphous matrix as a function of the ratio of conductivities of crystalline inclusions and amorphous matrix for three different crystallinities (see legend). Note that positive values of $\mu_\mathrm{H} / \mu_\mathrm{a}$ mean that the anomalous Hall effect dominates.}
\label{fig:deWit_mu_vs_sigma}
\end{figure}
Further, this model can also explain the change of the sign after annealing the irradiated sample. Figure~\ref{fig:deWit_mu_vs_sigma} shows the ratio of the Hall mobility and the mobility of the matrix as a function of the ratio of the conductivity of the inclusion and the matrix. The change of the sign of the mobility happens if the ratio of the conductivities is close to unity. This is the case if using the assigned conductivities for the inclusion and the matrix already used for the modeling in Figure~\ref{fig:deWit_mu_vs_T}. The lower the crystalline fraction the smaller the normal Hall effect. Interestingly, for high $\sigma_\mathrm{c}/\sigma_\mathrm{a}$ ratios and the mobilities $\mu_\mathrm{c}$, $\mu_\mathrm{a}$ used above an anomalous Hall effect in this model is not detectable if the crystalline fraction is higher $33\%$. Vice versa, to measure a normal Hall effect in microcrystalline silicon a crystalline fraction higher than $21\%$ needs to be present.
\section{Conclusion}
The results show that in microcrystalline silicon with low crystalline fraction the Hall mobility is strongly affected when the Fermi level is changed by, e.g., electron irradiation. Two models are discussed aiming to explain the observed Hall voltage sign change. A model with two parallel transport paths could explain a sign reversal, but not the observed one with an anomalous sign at low temperatures and a normal sign at high temperatures. The other model, however, where the crystalline parts are incorporated as inclusions in an amorphous matrix can qualitatively describe the observed effects.
\section*{Acknowledgments}
The authors wish to thank U.~Rau for his contribution to this work.
%% The Appendices part is started with the command \appendix; %% appendix sections are then done as normal sections %% \appendix
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%% References %% %% Following citation commands can be used in the body text: %% Usage of \cite is as follows: %% \cite{key} ==>> [#] %% \cite[chap. 2]{key} ==>> [#, chap. 2] %% \citet{key} ==>> Author [#]
%% References with bibTeX database:
\bibliographystyle{model1a-num-names}
%% Authors are advised to submit their bibtex database files. They are %% requested to list a bibtex style file in the manuscript if they do %% not want to use model1a-num-names.bst.
%% References without bibTeX database: \begin{thebibliography}{18} \expandafter\ifx\csname natexlab\endcsname\relax\def\natexlab#1{#1}\fi \providecommand{\bibinfo}[2]{#2} \ifx\xfnm\relax \def\xfnm[#1]{\unskip,\space#1}\fi %Type = Article \bibitem[{LeComber et~al.(1977)LeComber, Jones, and Spear}]{comber1977} \bibinfo{author}{P.~G. LeComber}, \bibinfo{author}{D.~I. Jones},
\bibinfo{author}{W.~E. Spear}, \bibinfo{journal}{Philosophical Magazine}
\bibinfo{volume}{35} (\bibinfo{year}{1977}) \bibinfo{pages}{1173}.
%Type = Inproceedings \bibitem[{Beyer and Mell(1977)}]{beyer-mell-77} \bibinfo{author}{W.~Beyer}, \bibinfo{author}{H.~Mell}, in:
\bibinfo{editor}{W.~E. Spear} (Ed.), \bibinfo{booktitle}{Proceedings of the
7th International Conference on Amorphous and Liquid Semiconductors},
\bibinfo{address}{Edinburgh}, p. \bibinfo{pages}{333}.
%Type = Inproceedings \bibitem[{Beyer et~al.(1977)Beyer, Mell, and Overhof}]{BeyMelOve77} \bibinfo{author}{W.~Beyer}, \bibinfo{author}{H.~Mell},
\bibinfo{author}{H.~Overhof}, in: \bibinfo{editor}{W.~E. Spear} (Ed.),
\bibinfo{booktitle}{Proceedings of the 7th International Conference on
Amorphous and Liquid Semiconductors}, \bibinfo{address}{Edinburgh}, pp.
\bibinfo{pages}{328--332}.
%Type = Article \bibitem[{Emin(1977)}]{emin77} \bibinfo{author}{D.~Emin}, \bibinfo{journal}{Philosophical Magazine}
\bibinfo{volume}{35} (\bibinfo{year}{1977}) \bibinfo{pages}{1189--1198}.
%Type = Article \bibitem[{Vetterl et~al.(2000)Vetterl, Finger, Carius, Hapke, Houben, Kluth,
Lambertz, M{\"u}ck, Rech, and Wagner}]{Vetterl200097}
\bibinfo{author}{O.~Vetterl}, \bibinfo{author}{F.~Finger},
\bibinfo{author}{R.~Carius}, \bibinfo{author}{P.~Hapke},
\bibinfo{author}{L.~Houben}, \bibinfo{author}{O.~Kluth},
\bibinfo{author}{A.~Lambertz}, \bibinfo{author}{A.~M{\"u}ck},
\bibinfo{author}{B.~Rech}, \bibinfo{author}{H.~Wagner},
\bibinfo{journal}{Solar Energy Materials and Solar Cells}
\bibinfo{volume}{62} (\bibinfo{year}{2000}) \bibinfo{pages}{97--108}.
%Type = Article \bibitem[{Astakhov et~al.(2009)Astakhov, Carius, Finger, Petrusenko, Borysenko,
and Barankov}]{astakhov:104205}
\bibinfo{author}{O.~Astakhov}, \bibinfo{author}{R.~Carius},
\bibinfo{author}{F.~Finger}, \bibinfo{author}{Y.~Petrusenko},
\bibinfo{author}{V.~Borysenko}, \bibinfo{author}{D.~Barankov},
\bibinfo{journal}{Physical Review B} \bibinfo{volume}{79}
(\bibinfo{year}{2009}) \bibinfo{pages}{104205}.
%Type = Article \bibitem[{Neto et~al.(2002)Neto, Lambertz, Carius, and
Finger}]{BaiaNeto2002274}
\bibinfo{author}{A.~L.~B. Neto}, \bibinfo{author}{A.~Lambertz},
\bibinfo{author}{R.~Carius}, \bibinfo{author}{F.~Finger},
\bibinfo{journal}{Journal of Non-Crystalline Solids}
\bibinfo{volume}{299-302} (\bibinfo{year}{2002}) \bibinfo{pages}{274--279}.
%Type = Article \bibitem[{Astakhov et~al.(2007)Astakhov, Finger, Carius, Lambertz, Petrusenko,
Borysenko, and Barankov}]{astakhov2007}
\bibinfo{author}{O.~Astakhov}, \bibinfo{author}{F.~Finger},
\bibinfo{author}{R.~Carius}, \bibinfo{author}{A.~Lambertz},
\bibinfo{author}{Y.~Petrusenko}, \bibinfo{author}{V.~Borysenko},
\bibinfo{author}{D.~Barankov}, \bibinfo{journal}{Thin Solid Films}
\bibinfo{volume}{515} (\bibinfo{year}{2007}) \bibinfo{pages}{7513--7516}.
%Type = Article \bibitem[{Beyer and Overhof(1984)}]{BeyOve84} \bibinfo{author}{W.~Beyer}, \bibinfo{author}{H.~Overhof},
\bibinfo{journal}{Semiconductors and Semimetals} \bibinfo{volume}{21}
(\bibinfo{year}{1984}) \bibinfo{pages}{257--307}.
%Type = Article \bibitem[{Bronger and Carius(2007)}]{bronger07} \bibinfo{author}{T.~Bronger}, \bibinfo{author}{R.~Carius},
\bibinfo{journal}{Thin Solid Films} \bibinfo{volume}{515}
(\bibinfo{year}{2007}) \bibinfo{pages}{7486--7489}.
%Type = Book \bibitem[{Corbett(1966)}]{corbett1966} \bibinfo{author}{J.~W. Corbett}, \bibinfo{title}{Electron radiation damage in
semiconductors and metals}, \bibinfo{publisher}{Academic Press New York and
London}, \bibinfo{year}{1966}.
%Type = Article \bibitem[{Takeda and Yamasaki(1999)}]{takeda1999} \bibinfo{author}{S.~Takeda}, \bibinfo{author}{J.~Yamasaki},
\bibinfo{journal}{Phys. Rev. Lett.} \bibinfo{volume}{83}
(\bibinfo{year}{1999}) \bibinfo{pages}{320--323}.
%Type = Book \bibitem[{Mott and Davis(1979)}]{mott_electronic_1979} \bibinfo{author}{N.~Mott}, \bibinfo{author}{E.~A. Davis},
\bibinfo{title}{Electronic Processes in {Non-Crystalline} Materials},
\bibinfo{publisher}{Oxford University Press, {USA}}, \bibinfo{edition}{2}
edition, \bibinfo{year}{1979}.
%Type = Article \bibitem[{de~Wit(1972)}]{deWit1972} \bibinfo{author}{H.~de~Wit}, \bibinfo{journal}{Journal of Applied Physics}
\bibinfo{volume}{43} (\bibinfo{year}{1972}) \bibinfo{pages}{908--913}.
%Type = Article \bibitem[{{Van Daal} and Bosman(1967)}]{vandaal1967} \bibinfo{author}{H.~J. {Van Daal}}, \bibinfo{author}{A.~J. Bosman},
\bibinfo{journal}{Phys. Rev.} \bibinfo{volume}{158} (\bibinfo{year}{1967})
\bibinfo{pages}{736--747}.
%Type = Article \bibitem[{Lipskis et~al.(1971)Lipskis, Sakalas, and
Vi\v{s}\v{c}akas}]{lipskis1971}
\bibinfo{author}{K.~Lipskis}, \bibinfo{author}{A.~Sakalas},
\bibinfo{author}{J.~Vi\v{s}\v{c}akas}, \bibinfo{journal}{physica status
solidi (a)} \bibinfo{volume}{4} (\bibinfo{year}{1971})
\bibinfo{pages}{K217--K220}.
%Type = Article \bibitem[{Heleskivi and Salo(1972)}]{heleskivi1972} \bibinfo{author}{J.~Heleskivi}, \bibinfo{author}{T.~Salo},
\bibinfo{journal}{Journal of Applied Physics} \bibinfo{volume}{43}
(\bibinfo{year}{1972}) \bibinfo{pages}{740--742}.
%Type = Article \bibitem[{Volger(1950)}]{volger1950} \bibinfo{author}{J.~Volger}, \bibinfo{journal}{Phys. Rev.} \bibinfo{volume}{79}
(\bibinfo{year}{1950}) \bibinfo{pages}{1023--1024}.
%Type = Article \bibitem[{Carius et~al.(1997)}]{carius97} \bibinfo{author}{R.~Carius}, \bibinfo{author}{F.~Finger}, \bibinfo{author}{U.~Backhausen}, \bibinfo{author}{M.~Luysberg}, \bibinfo{author}{P.~Hapke}, \bibinfo{author}{L.~Houben}, \bibinfo{author}{M.~Otte}, \bibinfo{author}{H.~Overhof},
\bibinfo{journal}{MRS Proceedings} \bibinfo{volume}{467}
(\bibinfo{year}{1997}) \bibinfo{pages}{283--294}.
%Type = Article \bibitem[{Houben et~al.(1997)}]{houben98} \bibinfo{author}{L.~Houben}, \bibinfo{author}{M.~Luysberg}, \bibinfo{author}{P.~Hapke}, \bibinfo{author}{R.~Carius}, \bibinfo{author}{F.~Finger}, \bibinfo{author}{H.~Wagner},
\bibinfo{journal}{Philosophical Magazine A} \bibinfo{volume}{77}
(\bibinfo{year}{1998}) \bibinfo{pages}{1447--1460}.
\end{thebibliography}
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\end{document}
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