X-Git-Url: https://git.ucc.asn.au/?a=blobdiff_plain;f=thesis%2Fthesis.tex;h=01c0a7662677a3dce0714aca782a4e7ff427ee2f;hb=cab343146875585d84d3c23ed82e8de401d3ad97;hp=1d352b7eab6b3d4907fc876c2410b8f8ce354a0f;hpb=3e0bbeaa77f2305ae77c99654c3e46474fe0a0e2;p=matches%2Fhonours.git diff --git a/thesis/thesis.tex b/thesis/thesis.tex index 1d352b7e..01c0a766 100644 --- a/thesis/thesis.tex +++ b/thesis/thesis.tex @@ -93,11 +93,10 @@ \item Number of applications where high absorbance into IR is required \item These have all been studied before though. \end{itemize} - \item They are the way of the future. Embrace the future. \item The electron spectra of metal-blacks have not yet been examined. \item Remarkable difference between Metal-Black films (bad vacuum) and normal metal films (UHV) \begin{itemize} - \item No (detailed/satisfactory) explanation (that I can find :P) for difference + \item No (detailed/satisfactory) explanation (that I can find...) for difference \end{itemize} \item Talk about plasmonic based computing? Moore's law? Applications to thin film solar cells? @@ -120,30 +119,70 @@ \section{Overview of Theory} Summarise the literature, refer to past research etc -\subsection{Electron structure of surface} +\subsection{Electron Spectra of a Surface} \begin{itemize} - \item Overview of electron spectrum properties + \item Description of the near surface region \begin{itemize} - \item Density of states $n(E)$ - \item Energy band structure $E(\vect{k})$ - \end{itemize} - \item Properties of surface region - \begin{itemize} - \item Difference between potential of surface and bulk + \item All real solids occupy finite volumes in space. + \item The surface of a solid is important because interactions between the solid and its surroundings occur in the near surface region. + \item Characterised physically by: \begin{itemize} - \item Change between the two limits in the ``near-surface'' region + \item Termination of periodic crystal lattice + \item Violation of geometric order + \item Distortion of interatomic distances and hence interaction forces + \item There is a transition ``near surface'' region between bulk and surface properties, roughly 5 atomic distances. \end{itemize} - \item Theoretical models for the potential, 1D vs 3D + \item Potential seen by an electron at a surface can differ greatly from the bulk + \item $\implies$ the electron spectra of the near surface region differs from the bulk spectra + \item Simplest case: Step potential at surface \begin{itemize} - \item Simplest case is a step potential. - \item Various improvements on this model, discussed in Komolov's book. - \item It would be interesting to adapt my CQM project to numerically solve for an electron entering the various potentials + \item Metal & Semiconductor + \end{itemize} + \item In reality, + + \end{itemize} + + \item The Electron Spectra + \begin{itemize} + \item Electron Spectra describes the energy eigenstates for an electron in a Bulk or Surface potential + \item Characterised by + \begin{enumerate} + \item Energy dispersion $E(\vect{k})$ \begin{itemize} - \item Only do this when EVERYTHING ELSE is done! Otherwise I will get too involved with it! + \item Dependence of Energy on electron wave vector + \item Obtained theoretically by solving Scrhrodinger's Equation + \item For a free electron gas, $E = \frac{\hbar^2 k^2}{2m} + \item Periodic potential in bulk solid leads to band gap structure of $E(\vect{k})$ + \item Periodic potential $\implies$ E is periodic. Only needs to be defined in first Brillouin zone. \end{itemize} - \end{itemize} - \item Limitations of theoretical models + \item Density of States $N(E)$ + \begin{itemize} + \item $N(E) = \frac{\Delta N}{\Delta E} = \frac{1}{4\pi^3}\int_S\left(\der{E}{k}\right)^{-1} dS$ + \item Integral is in momentum space over the isoenergetic surface of energy $E$ + \item For a free electron gas, $N(E) = $ + \end{itemize} + \end{enumerate} \end{itemize} + + \item Surface states + \begin{itemize} + \begin{enumerate} + \item Tamm States: Periodic potential in solid, free space outside, jump at surface + \begin{itemize} + \item Energy eigenvalues lie in the forbidden band of the bulk spectra + \item Attenuation of eigenvalues from surface to vacuum, oscillation of state within surface + \item Max electron density occurs on the crystal surface + \end{itemize} + \item Shockley states: Potential of surface and bulk cells equal + \begin{itemize} + \item Corresond to free valences (dangling bonds) at the surface + \end{itemize} + \end{enumerate} + \item Tamm and Shockley states arise from two extreme models (large change and small change respectively between bulk and surface). In reality, a combination of Tamm and Shockley states appear. + \item These states arise from termination of the lattice; but the surface cells are assumed undistorted + \item In reality surface cells are distorted by relaxation and reconstruction of the surface + \end{itemize} + \item Main reference: Komolov "Total Current Spectroscopy" \item "Solid State Physics" textbooks and "Electron Spectroscopy" textbooks \end{itemize} @@ -211,7 +250,10 @@ I really think I should actually find plasmonic effects before writing too much \subsection{Total Current Spectroscopy} \begin{itemize} - \item Overview of technique + \item + \item Total Current Spectroscopy methods measure the total current of secondary electrons as a function of primary electron energy. + \item These methods are distinguished from ``differential'' methods (such as Auger electron spectroscopy and energy loss spectroscopy) which measure the secondary electron spectrum at a fixed primary electron energy. + \item \begin{itemize} \item Low energy beam of electrons incident on sample \item Measure slope of resulting I-V curve @@ -276,7 +318,7 @@ I really think I should actually find plasmonic effects before writing too much \item Wrote software for data aquisition and data processing \end{itemize} -\section{Experimental Difficulties / Detailed stuff / Appendix} +\section{General notes} \subsection{TCS} \begin{itemize} \item Optimise setup of gun