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new version of secs1d
author cdf
date Sun, 25 Mar 2012 22:53:03 +0000
parents e567b7ac3d1f
children 67cd7d263dd4
files extra/secs1d/doc/manual.pdf extra/secs1d/doc/manual.tex extra/secs1d/doc/secs1d_manual.pdf extra/secs1d/doc/secs1d_manual.tex
diffstat 4 files changed, 267 insertions(+), 266 deletions(-) [+]
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Binary file extra/secs1d/doc/manual.pdf has changed
--- a/extra/secs1d/doc/manual.tex	Sun Mar 25 22:44:30 2012 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,266 +0,0 @@
-\documentclass[10pt]{article} 
-\usepackage{geometry} 
-\geometry{a4paper}
-\hoffset=-1cm 
-\usepackage{graphicx} 
-\usepackage{amssymb} 
-\usepackage{epstopdf} 
-\usepackage{cprotect} 
-\usepackage{float} 
-\floatstyle{plain} 
-\newfloat{demo}{thp}{dem} 
-\floatname{demo}{Demo} 
-\newfloat{demoout}{thp}{deo} 
-\floatname{demoout}{Demo Output} 
-\newcommand{\unit}[1]{\mathrm{#1}}
-\newcommand{\electronvolt}{\unit{eV}}
-\newcommand{\kelvin}{\unit{K}}
-\newcommand{\nano}{\unit{n}}
-\newcommand{\meter}{\unit{m}}
-\newcommand{\second}{\unit{s}}
-\newcommand{\volt}{\unit{V}}
-\newcommand{\Ampere}{\unit{A}}
-
-
-\title{secs1d}
-\author{Carlo de Falco \and Riccardo Sacco}
-\begin{document}
-\maketitle
-\tableofcontents
-
-\begin{table}
-\caption{secs1d Package Description}
-\centering
-\begin{tabular}{|l|l|}
-\hline
-{\bf Name: } & secs1d\\  \hline
-{\bf Description: } &
-A Drift-Diffusion simulator for 1d semiconductor devices\\  \hline
-{\bf Version: } & 0.0.9\\  \hline
-{\bf Release Date: } & 2012-03-25\\  \hline
-{\bf Author: } & Carlo de Falco\\   \hline
-{\bf Maintainer: } & Carlo de Falco\\  \hline
-{\bf License: } & GPL version 2 or later\\  \hline
-{\bf Depends on: } &
-octave ($>=$ 3.0.0), bim ($>=$ 0.0.0), \\  \hline
-{\bf Autoload: } &No\\  \hline
-\end{tabular}
-\end{table}
-
-\part{Mathematical models}
-
-\section{Full model}
-\subsection{Conservation laws}
-
-\begin{equation}\label{eq:conservation}
-\left\{
-\begin{array}{ll}
--\lambda^{2}\mathrm{div}\ \left(\varepsilon_{r} \mathrm{grad}\ 
-\varphi \right) = p - n + N_{D} - N_{A} \\[5mm]
--\mathrm{div}\ \left(J_{n} \right) + R_{n} \, n = G_{n} \\[5mm]
-\phantom{-}\mathrm{div}\ \left(J_{p} \right) + R_{p} \, p = G_{p}
-\end{array}
-\right.
-\end{equation}
-
-\section{Constitutive relations}
-
-\subsection{Currents}
-
-\begin{equation}\label{eq:currents}
-\left\{
-\begin{array}{ll}
-J_{n} = \phantom{-}\mu_{n} \left( \mathrm{grad}\ n - n\ \mathrm{grad}\ \varphi\right) 
-\\[5mm]
-J_{p} = -\mu_{p} \left( \mathrm{grad}\ p + p\ \mathrm{grad}\ \varphi\right)  
-\end{array}
-\right.
-\end{equation}
-
-\subsection{Mobilities}
-
-\begin{equation}\label{eq:mobilities}
-\left\{
-\begin{array}{ll}
-\mu_{n} = \displaystyle \frac{2\bar{\mu}_{n}}
-{1 + \sqrt{1 + 4 \left( \displaystyle \frac{\bar{\mu}_{n}|E|}{v_{sat,n}}\right)^{2}}}
-; \qquad
-\bar{\mu}_{n} = \mu_{min, n} + 
-\displaystyle \frac{\mu_{0,n} - \mu_{min,n}}
-{1 +\displaystyle \left(\frac{N_{D}+N_{A}}{N_{ref,n}}\right)^{\beta_{n}}}
-\\[10mm]
-\mu_{p} = \displaystyle \frac{2\bar{\mu}_{p}}
-{1 + \sqrt{1 + 4 \left( \displaystyle \frac{\bar{\mu}_{p}|E|}{v_{sat,p}}\right)^{2}}}
-; \qquad
-\bar{\mu}_{p} = \mu_{min, p} + 
-\displaystyle \frac{\mu_{0,p} - \mu_{min,p}}
-{1 +\displaystyle \left(\frac{N_{D}+N_{A}}{N_{ref,p}}\right)^{\beta_{p}}}
-\end{array}
-\right.
-\end{equation}
-
-\subsection{Production terms}
-
-\begin{equation}\label{eq:recombination}
-\left\{
-\begin{array}{ll}
-R_{n} = \displaystyle 
-\frac{p}{\tau_{n} (p + \theta) + \tau_{p} (n + \theta)}
-+ p \left(C_{n} n + C_{p} p \right)
-\\[5mm]
-R_{p} = \displaystyle 
-\frac{n}{\tau_{n} (p + \theta) + \tau_{p} (n + \theta)}
-+ n \left (C_{n} n + C_{p} p \right)
-\end{array}
-\right.
-\end{equation}
-
-\begin{equation}\label{eq:generation}
-G_{n} = G_{p} = 
-\displaystyle 
-\frac{\theta^{2}}{\tau_{n} (p + \theta) + \tau_{p} (n + \theta)}
-+ \theta^{2} \left(C_{n} n + C_{p} p \right)
-+ \left(\alpha_{n} |J_{n}|+ \alpha_{p} |J_{p}| \right)
-\end{equation}
-
-%\subsection{Ionization coefficients}
-
-\begin{equation}\label{eq:ioniz_coeff}
-\left\{
-\begin{array}{ll}
-\alpha_{n} = \displaystyle 
-\alpha_{n}^{\infty} \exp \left( -\frac{E_{crit,n}}{|E|} \right)
-\\[5mm]
-\alpha_{p} = \displaystyle 
-\alpha_{p}^{\infty} \exp \left( -\frac{E_{crit,p}}{|E|} \right)
-\end{array}
-\right.
-\end{equation}
-
-\newpage
-
-\section{Simplified model used for Newton's method}
-\subsection{Conservation laws}
-
-\begin{equation}\label{eq:conservationN}
-\left\{
-\begin{array}{ll}
--\lambda^{2}\mathrm{div}\ \left(\varepsilon_{r} 
-\mathrm{grad}\ \varphi \right) = p - n + N_{D} - N_{A} \\[5mm]
--\mathrm{div}\ \left(J_{n} \right) + R_{n} \, n = G_{n} \\[5mm]
-\phantom{-}\mathrm{div}\ \left(J_{p} \right) + R_{p} \, p = G_{p}
-\end{array}
-\right.
-\end{equation}
-
-\section{Constitutive relations}
-
-\subsection{Currents}
-
-\begin{equation}\label{eq:currentsN}
-\left\{
-\begin{array}{ll}
-J_{n} = \phantom{-}\mu_{n} \left( \mathrm{grad}\ n - n\ \mathrm{grad}\ \varphi\right) 
-\\[5mm]
-J_{p} = -\mu_{p} \left( \mathrm{grad}\ p + p\ \mathrm{grad}\ \varphi\right)  
-\end{array}
-\right.
-\end{equation}
-
-\subsection{Production terms}
-
-\begin{equation}\label{eq:recombinationN}
-\left\{
-\begin{array}{ll}
-R_{n} = \displaystyle \frac{p}{\tau_{n} (p + \theta) + \tau_{p} (n + \theta)}
-+ p \left(C_{n} n + C_{p} p \right)
-\\[5mm]
-R_{p} = \displaystyle \frac{n}{\tau_{n} (p + \theta) + \tau_{p} (n + \theta)}
-+ n \left (C_{n} n + C_{p} p \right)
-\end{array}
-\right.
-\end{equation}
-
-\begin{equation}\label{eq:generationN}
-G_{n} = G_{p} = 
-\displaystyle \frac{\theta^{2}}{\tau_{n} (p + \theta) + \tau_{p} (n + \theta)}
-+ \theta^{2} \left(C_{n} n + C_{p} p \right)
-\end{equation}
-
-\newpage
-
-\section{Scaling factors/adimensional parameters}
-
-Given any generic quantity $u$ having units $U$, we
-define the {\em scaled} quantity $\widehat{u}$ as
-$$
-\widehat{u} : = \displaystyle \frac{u}{\overline{u}}
-$$
-where $\overline{u}$ is the scaling factor associated with $u$
-and having the same units as $u$. 
-
-\begin{table}[h!]
-\begin{center}
-\begin{tabular}{lll}\hline
-\textbf{Scaling factor}	& \textbf{Value} & \textbf{Units}\\ \hline
-$\overline{x}$            & $L$            & $\meter$ \\[1mm]
-$\overline{n}$            & $\| N_D^+ - N_A^-\|_{L^{\infty}(0,L)}$  
-& $\meter^{-3}$ \\[1mm]
-$\overline{\varphi}$      & $K_B T / q \simeq 26 \cdot 10^{-3}$ 
-& $\volt$ \\[1mm]
-$\overline{\mu}$          & $\max\left\{ \mu_{0,n}, \, \mu_{0,p}\right\}$ 
-&  $\meter^2\,\volt^{-1}\,\second^{-1}$ \\[1mm]
-$\overline{t}$          & $\overline{x}^2/(\overline{\mu} \, \overline{\varphi})$
-&  $\second$ \\[1mm]
-$\overline{R}$          & $\overline{n}/\overline{t}$
-&  $\meter^{-3} \second^{-1}$ \\[1mm]
-$\overline{E}$          & $\overline{\varphi}/\overline{x}$
-&  $\volt \meter^{-1}$  \\[1mm]
-$\overline{J}$          & $q \, \overline{\mu} \, \overline{n} \, 
-\overline{E}$ &  $\Ampere \meter^{-2}$  \\[1mm]
-$\overline{\alpha}$ & $\overline{x}^{-1}$ & $\meter^{-1}$ \\[1mm]
-$\overline{C}_{Au}$ & $\overline{R}/\overline{n}^3$ & 
-$\meter^{6} \second^{-1}$ \\[1mm]
-\hline
-\end{tabular}
-\caption{Scaling factors for the Drift-Diffusion model equations.}
-\label{tab:model_param_1d}
-\end{center}
-\end{table}
-
-We also introduce the following adimensional numbers
-$$
-\lambda^2:= \displaystyle \frac{\varepsilon_0 \overline{\varphi}}
-{q \, \overline{n} \, \overline{x}^2}, \qquad
-\theta:= \displaystyle \frac{n_i}{\overline{n}}
-$$
-having the meaning of squared normalized Debye length and
-normalized intrinsic concentration, respectively.
-
-\part{Function reference}
-
-\section{Drift-Diffusion solvers}
-
-\subsection{secs1d\_dd\_gummel\_map}
-\input{function/secs1d_dd_gummel_map.tex}
-
-\subsection{secs1d\_dd\_newton}
-\input{function/secs1d_dd_newton.tex}
-
-\section{Non-linear Poisson solver}
-\subsection{secs1d\_nlpoisson\_newton}
-\input{function/secs1d_nlpoisson_newton.tex}
-
-\section{Physical constants and material properties}
-\subsection{secs1d\_physical\_constants.m}
-\input{function/secs1d_physical_constants.m.tex}
-
-\subsection{secs1d\_silicon\_material\_properties.m}
-\input{function/secs1d_silicon_material_properties.m.tex}
-
-\appendix
-\section{Licence}
-\input{COPYING.tex}
-
- 
-\end{document}
\ No newline at end of file
Binary file extra/secs1d/doc/secs1d_manual.pdf has changed
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/extra/secs1d/doc/secs1d_manual.tex	Sun Mar 25 22:53:03 2012 +0000
@@ -0,0 +1,267 @@
+\documentclass[9pt]{amsart} 
+\usepackage{geometry} 
+\geometry{a4paper}
+\usepackage{graphicx} 
+\usepackage{amssymb} 
+\usepackage{epstopdf} 
+\usepackage{cprotect} 
+\usepackage{float} 
+\floatstyle{plain} 
+\newfloat{demo}{thp}{dem} 
+\floatname{demo}{Demo} 
+\newfloat{demoout}{thp}{deo} 
+\floatname{demoout}{Demo Output} 
+\newcommand{\unit}[1]{\mathrm{#1}}
+\newcommand{\electronvolt}{\unit{eV}}
+\newcommand{\kelvin}{\unit{K}}
+\newcommand{\nano}{\unit{n}}
+\newcommand{\meter}{\unit{m}}
+\newcommand{\second}{\unit{s}}
+\newcommand{\volt}{\unit{V}}
+\newcommand{\Ampere}{\unit{A}}
+
+
+\title{secs1d}
+\author{Carlo de Falco \and Riccardo Sacco}
+\begin{document}
+\maketitle
+\titlepage
+\tableofcontents
+
+\begin{table}
+\caption{secs1d Package Description}
+\centering
+\begin{tabular}{|l|l|}
+\hline
+{\bf Name: } & secs1d\\  \hline
+{\bf Description: } &
+A Drift-Diffusion simulator for 1d semiconductor devices\\  \hline
+{\bf Version: } & 0.0.9\\  \hline
+{\bf Release Date: } & 2012-03-25\\  \hline
+{\bf Author: } & Carlo de Falco\\   \hline
+{\bf Maintainer: } & Carlo de Falco\\  \hline
+{\bf License: } & GPL version 2 or later\\  \hline
+{\bf Depends on: } &
+octave ($>=$ 3.0.0), bim ($>=$ 0.0.0), \\  \hline
+{\bf Autoload: } &No\\  \hline
+\end{tabular}
+\end{table}
+\clearpage
+
+\part{Mathematical models}
+
+\section{Full model}
+\subsection{Conservation laws}
+
+\begin{equation}\label{eq:conservation}
+\left\{
+\begin{array}{ll}
+-\lambda^{2}\mathrm{div}\ \left(\varepsilon_{r} \mathrm{grad}\ 
+\varphi \right) = p - n + N_{D} - N_{A} \\[5mm]
+-\mathrm{div}\ \left(J_{n} \right) + R_{n} \, n = G_{n} \\[5mm]
+\phantom{-}\mathrm{div}\ \left(J_{p} \right) + R_{p} \, p = G_{p}
+\end{array}
+\right.
+\end{equation}
+
+\section{Constitutive relations}
+
+\subsection{Currents}
+
+\begin{equation}\label{eq:currents}
+\left\{
+\begin{array}{ll}
+J_{n} = \phantom{-}\mu_{n} \left( \mathrm{grad}\ n - n\ \mathrm{grad}\ \varphi\right) 
+\\[5mm]
+J_{p} = -\mu_{p} \left( \mathrm{grad}\ p + p\ \mathrm{grad}\ \varphi\right)  
+\end{array}
+\right.
+\end{equation}
+
+\subsection{Mobilities}
+
+\begin{equation}\label{eq:mobilities}
+\left\{
+\begin{array}{ll}
+\mu_{n} = \displaystyle \frac{2\bar{\mu}_{n}}
+{1 + \sqrt{1 + 4 \left( \displaystyle \frac{\bar{\mu}_{n}|E|}{v_{sat,n}}\right)^{2}}}
+; \qquad
+\bar{\mu}_{n} = \mu_{min, n} + 
+\displaystyle \frac{\mu_{0,n} - \mu_{min,n}}
+{1 +\displaystyle \left(\frac{N_{D}+N_{A}}{N_{ref,n}}\right)^{\beta_{n}}}
+\\[10mm]
+\mu_{p} = \displaystyle \frac{2\bar{\mu}_{p}}
+{1 + \sqrt{1 + 4 \left( \displaystyle \frac{\bar{\mu}_{p}|E|}{v_{sat,p}}\right)^{2}}}
+; \qquad
+\bar{\mu}_{p} = \mu_{min, p} + 
+\displaystyle \frac{\mu_{0,p} - \mu_{min,p}}
+{1 +\displaystyle \left(\frac{N_{D}+N_{A}}{N_{ref,p}}\right)^{\beta_{p}}}
+\end{array}
+\right.
+\end{equation}
+
+\subsection{Production terms}
+
+\begin{equation}\label{eq:recombination}
+\left\{
+\begin{array}{ll}
+R_{n} = \displaystyle 
+\frac{p}{\tau_{n} (p + \theta) + \tau_{p} (n + \theta)}
++ p \left(C_{n} n + C_{p} p \right)
+\\[5mm]
+R_{p} = \displaystyle 
+\frac{n}{\tau_{n} (p + \theta) + \tau_{p} (n + \theta)}
++ n \left (C_{n} n + C_{p} p \right)
+\end{array}
+\right.
+\end{equation}
+
+\begin{equation}\label{eq:generation}
+G_{n} = G_{p} = 
+\displaystyle 
+\frac{\theta^{2}}{\tau_{n} (p + \theta) + \tau_{p} (n + \theta)}
++ \theta^{2} \left(C_{n} n + C_{p} p \right)
++ \left(\alpha_{n} |J_{n}|+ \alpha_{p} |J_{p}| \right)
+\end{equation}
+
+%\subsection{Ionization coefficients}
+
+\begin{equation}\label{eq:ioniz_coeff}
+\left\{
+\begin{array}{ll}
+\alpha_{n} = \displaystyle 
+\alpha_{n}^{\infty} \exp \left( -\frac{E_{crit,n}}{|E|} \right)
+\\[5mm]
+\alpha_{p} = \displaystyle 
+\alpha_{p}^{\infty} \exp \left( -\frac{E_{crit,p}}{|E|} \right)
+\end{array}
+\right.
+\end{equation}
+
+\newpage
+
+\section{Simplified model used for Newton's method}
+\subsection{Conservation laws}
+
+\begin{equation}\label{eq:conservationN}
+\left\{
+\begin{array}{ll}
+-\lambda^{2}\mathrm{div}\ \left(\varepsilon_{r} 
+\mathrm{grad}\ \varphi \right) = p - n + N_{D} - N_{A} \\[5mm]
+-\mathrm{div}\ \left(J_{n} \right) + R_{n} \, n = G_{n} \\[5mm]
+\phantom{-}\mathrm{div}\ \left(J_{p} \right) + R_{p} \, p = G_{p}
+\end{array}
+\right.
+\end{equation}
+
+\section{Constitutive relations}
+
+\subsection{Currents}
+
+\begin{equation}\label{eq:currentsN}
+\left\{
+\begin{array}{ll}
+J_{n} = \phantom{-}\mu_{n} \left( \mathrm{grad}\ n - n\ \mathrm{grad}\ \varphi\right) 
+\\[5mm]
+J_{p} = -\mu_{p} \left( \mathrm{grad}\ p + p\ \mathrm{grad}\ \varphi\right)  
+\end{array}
+\right.
+\end{equation}
+
+\subsection{Production terms}
+
+\begin{equation}\label{eq:recombinationN}
+\left\{
+\begin{array}{ll}
+R_{n} = \displaystyle \frac{p}{\tau_{n} (p + \theta) + \tau_{p} (n + \theta)}
++ p \left(C_{n} n + C_{p} p \right)
+\\[5mm]
+R_{p} = \displaystyle \frac{n}{\tau_{n} (p + \theta) + \tau_{p} (n + \theta)}
++ n \left (C_{n} n + C_{p} p \right)
+\end{array}
+\right.
+\end{equation}
+
+\begin{equation}\label{eq:generationN}
+G_{n} = G_{p} = 
+\displaystyle \frac{\theta^{2}}{\tau_{n} (p + \theta) + \tau_{p} (n + \theta)}
++ \theta^{2} \left(C_{n} n + C_{p} p \right)
+\end{equation}
+
+\newpage
+
+\section{Scaling factors/adimensional parameters}
+
+Given any generic quantity $u$ having units $U$, we
+define the {\em scaled} quantity $\widehat{u}$ as
+$$
+\widehat{u} : = \displaystyle \frac{u}{\overline{u}}
+$$
+where $\overline{u}$ is the scaling factor associated with $u$
+and having the same units as $u$. 
+
+\begin{table}[h!]
+\begin{center}
+\begin{tabular}{lll}\hline
+\textbf{Scaling factor}	& \textbf{Value} & \textbf{Units}\\ \hline
+$\overline{x}$            & $L$            & $\meter$ \\[1mm]
+$\overline{n}$            & $\| N_D^+ - N_A^-\|_{L^{\infty}(0,L)}$  
+& $\meter^{-3}$ \\[1mm]
+$\overline{\varphi}$      & $K_B T / q \simeq 26 \cdot 10^{-3}$ 
+& $\volt$ \\[1mm]
+$\overline{\mu}$          & $\max\left\{ \mu_{0,n}, \, \mu_{0,p}\right\}$ 
+&  $\meter^2\,\volt^{-1}\,\second^{-1}$ \\[1mm]
+$\overline{t}$          & $\overline{x}^2/(\overline{\mu} \, \overline{\varphi})$
+&  $\second$ \\[1mm]
+$\overline{R}$          & $\overline{n}/\overline{t}$
+&  $\meter^{-3} \second^{-1}$ \\[1mm]
+$\overline{E}$          & $\overline{\varphi}/\overline{x}$
+&  $\volt \meter^{-1}$  \\[1mm]
+$\overline{J}$          & $q \, \overline{\mu} \, \overline{n} \, 
+\overline{E}$ &  $\Ampere \meter^{-2}$  \\[1mm]
+$\overline{\alpha}$ & $\overline{x}^{-1}$ & $\meter^{-1}$ \\[1mm]
+$\overline{C}_{Au}$ & $\overline{R}/\overline{n}^3$ & 
+$\meter^{6} \second^{-1}$ \\[1mm]
+\hline
+\end{tabular}
+\caption{Scaling factors for the Drift-Diffusion model equations.}
+\label{tab:model_param_1d}
+\end{center}
+\end{table}
+
+We also introduce the following adimensional numbers
+$$
+\lambda^2:= \displaystyle \frac{\varepsilon_0 \overline{\varphi}}
+{q \, \overline{n} \, \overline{x}^2}, \qquad
+\theta:= \displaystyle \frac{n_i}{\overline{n}}
+$$
+having the meaning of squared normalized Debye length and
+normalized intrinsic concentration, respectively.
+
+\part{Function reference}
+
+\section{Drift-Diffusion solvers}
+
+\subsection{secs1d\_dd\_gummel\_map}
+\input{function/secs1d_dd_gummel_map.tex}
+
+\subsection{secs1d\_dd\_newton}
+\input{function/secs1d_dd_newton.tex}
+
+\section{Non-linear Poisson solver}
+\subsection{secs1d\_nlpoisson\_newton}
+\input{function/secs1d_nlpoisson_newton.tex}
+
+\section{Physical constants and material properties}
+\subsection{secs1d\_physical\_constants.m}
+\input{function/secs1d_physical_constants.m.tex}
+
+\subsection{secs1d\_silicon\_material\_properties.m}
+\input{function/secs1d_silicon_material_properties.m.tex}
+
+\appendix
+\section{Licence}
+\input{COPYING.tex}
+
+ 
+\end{document}
\ No newline at end of file