From 73e377ff3309cb0bcd67295f906c0f1290cda5bd Mon Sep 17 00:00:00 2001 From: aj Date: Mon, 11 Nov 2019 15:33:04 +0000 Subject: [PATCH] added lattice matching --- coursework.lyx | 48 ++++++++++++++++++++++++++++++++++++++++++++---- coursework.pdf | Bin 222750 -> 301349 bytes references.bib | 7 ++++++- 3 files changed, 50 insertions(+), 5 deletions(-) diff --git a/coursework.lyx b/coursework.lyx index c46710a..4a6fd4a 100644 --- a/coursework.lyx +++ b/coursework.lyx @@ -374,7 +374,7 @@ Material \begin_inset Text \begin_layout Plain Layout -Lattice Constant (Å) +Lattice Constant, α (Å) \end_layout \end_inset @@ -414,7 +414,7 @@ GaAs \begin_inset Text \begin_layout Plain Layout -5.653 +5.6532 \end_layout \end_inset @@ -434,7 +434,7 @@ InP \begin_inset Text \begin_layout Plain Layout -5.869 +5.8687 \end_layout \end_inset @@ -452,6 +452,14 @@ InP \begin_layout Plain Layout Lattice constants for prospective well and barrier materials +\begin_inset CommandInset citation +LatexCommand cite +key "new_semiconductor_materials_archive" +literal "false" + +\end_inset + + \begin_inset CommandInset label LatexCommand label name "tab:Lattice-constants" @@ -479,7 +487,39 @@ name "tab:Lattice-constants" In order to compute a compound lattice constant for InGaAs, Vegard's law can be applied. Vegard's law provides an approximation for the lattice constant of a solid - solution by + solution by finding the weighted average the individual lattice constants + by composition ratio and is given by: +\end_layout + +\begin_layout Standard +\begin_inset Formula +\[ +\alpha_{A_{(1-x)}B_{x}}=(1-x)\alpha_{A}+x\alpha_{B} +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +Applying this to the prospective well material gives the following, +\end_layout + +\begin_layout Standard +\begin_inset Formula +\[ +\alpha_{In_{0.53}Ga_{0.47}As}=0.53\cdotp6.0583+0.47\cdotp5.6532=5.8679 +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +This shows that to 4 significant figures the composition of InGaAs is lattice + matched to InP to within 0.001Å which is sufficient for this application. \end_layout \begin_layout Subsubsection diff --git a/coursework.pdf b/coursework.pdf index 27dc7bfc4c5966e309945bacb04007303dee82c5..7f54d0444ac82ddfcf037be8b77333023abbae90 100644 GIT binary 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