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[Octave-cvsupdate] SF.net SVN: octave:[10058] trunk/octave-forge/extra/secs1d
|
From: <cd...@us...> - 2012-03-25 22:44:39
|
Revision: 10058
http://octave.svn.sourceforge.net/octave/?rev=10058&view=rev
Author: cdf
Date: 2012-03-25 22:44:30 +0000 (Sun, 25 Mar 2012)
Log Message:
-----------
new version of secs1d
Modified Paths:
--------------
trunk/octave-forge/extra/secs1d/DESCRIPTION
trunk/octave-forge/extra/secs1d/INDEX
Added Paths:
-----------
trunk/octave-forge/extra/secs1d/bak/
trunk/octave-forge/extra/secs1d/bak/DDG/
trunk/octave-forge/extra/secs1d/bak/DDN/
trunk/octave-forge/extra/secs1d/bak/PKG_ADD
trunk/octave-forge/extra/secs1d/bak/Utilities/
trunk/octave-forge/extra/secs1d/bak/secs1d_demo_pndiode.m
trunk/octave-forge/extra/secs1d/bak/src/
trunk/octave-forge/extra/secs1d/doc/
trunk/octave-forge/extra/secs1d/doc/COPYING.tex
trunk/octave-forge/extra/secs1d/doc/function/
trunk/octave-forge/extra/secs1d/doc/function/images/
trunk/octave-forge/extra/secs1d/doc/function/images/secs1d_dd_gummel_map_205.png
trunk/octave-forge/extra/secs1d/doc/function/images/secs1d_dd_newton_819.png
trunk/octave-forge/extra/secs1d/doc/function/images/secs1d_nlpoisson_newton_85.png
trunk/octave-forge/extra/secs1d/doc/function/secs1d_dd_gummel_map.tex
trunk/octave-forge/extra/secs1d/doc/function/secs1d_dd_newton.tex
trunk/octave-forge/extra/secs1d/doc/function/secs1d_nlpoisson_newton.tex
trunk/octave-forge/extra/secs1d/doc/function/secs1d_physical_constants.m.tex
trunk/octave-forge/extra/secs1d/doc/function/secs1d_silicon_material_properties.m.tex
trunk/octave-forge/extra/secs1d/doc/manual.pdf
trunk/octave-forge/extra/secs1d/doc/manual.tex
trunk/octave-forge/extra/secs1d/inst/secs1d_dd_gummel_map.m
trunk/octave-forge/extra/secs1d/inst/secs1d_dd_newton.m
trunk/octave-forge/extra/secs1d/inst/secs1d_nlpoisson_newton.m
trunk/octave-forge/extra/secs1d/inst/secs1d_physical_constants.m
trunk/octave-forge/extra/secs1d/inst/secs1d_silicon_material_properties.m
Removed Paths:
-------------
trunk/octave-forge/extra/secs1d/README
trunk/octave-forge/extra/secs1d/inst/DDG/
trunk/octave-forge/extra/secs1d/inst/DDN/
trunk/octave-forge/extra/secs1d/inst/Utilities/
trunk/octave-forge/extra/secs1d/inst/secs1d.m
trunk/octave-forge/extra/secs1d/inst/secs1d_demo_pndiode.m
trunk/octave-forge/extra/secs1d/src/
Modified: trunk/octave-forge/extra/secs1d/DESCRIPTION
===================================================================
--- trunk/octave-forge/extra/secs1d/DESCRIPTION 2012-03-25 22:35:18 UTC (rev 10057)
+++ trunk/octave-forge/extra/secs1d/DESCRIPTION 2012-03-25 22:44:30 UTC (rev 10058)
@@ -1,12 +1,12 @@
Name: SECS1D
-Version: 0.0.8
-Date: 2008-08-23
+Version: 0.0.9
+Date: 2012-03-25
Author: Carlo de Falco
Maintainer: Carlo de Falco
Title: SEmi Conductor Simulator in 1D
Description: A Drift-Diffusion simulator for 1d semiconductor devices
Categories: Electrical Engineering
-Depends: octave (>= 2.9.17)
+Depends: octave (>= 3.0), bim
Autoload: no
License: GPL version 2 or later
Modified: trunk/octave-forge/extra/secs1d/INDEX
===================================================================
--- trunk/octave-forge/extra/secs1d/INDEX 2012-03-25 22:35:18 UTC (rev 10057)
+++ trunk/octave-forge/extra/secs1d/INDEX 2012-03-25 22:44:30 UTC (rev 10058)
@@ -1,23 +1,9 @@
secs1D >> SEmiConductor Simulator in 1D
-DDG
- DDGelectron_driftdiffusion
- DDGgummelmap
- DDGhole_driftdiffusion
- DDGn2phin
- DDGnlpoisson
- DDGp2phip
- DDGphin2n
- DDGphip2p
- DDGplotresults
-DDN
- DDNnewtonmap
-Utilities
- constants
- Ubern
- Ubernoulli
- Ucompconst
- Ucomplap
- Ucompmass
- Udriftdiffusion
- Umediaarmonica
- Uscharfettergummel
+Drift-Diffusion solvers
+ secs1d_dd_gummel_map
+ secs1d_dd_newton
+non-linear Poisson solver
+ secs1d_nlpoisson_newton
+Physical constants and material data
+ secs1d_physical_constants.m
+ secs1d_silicon_material_properties.m
\ No newline at end of file
Deleted: trunk/octave-forge/extra/secs1d/README
===================================================================
--- trunk/octave-forge/extra/secs1d/README 2012-03-25 22:35:18 UTC (rev 10057)
+++ trunk/octave-forge/extra/secs1d/README 2012-03-25 22:44:30 UTC (rev 10058)
@@ -1,22 +0,0 @@
-
- SECS1D - A 1-D Drift--Diffusion Semiconductor Device Simulator
- -------------------------------------------------------------------
- Copyright (C) 2004-2007 Carlo de Falco
-
-This program is free software; you can redistribute it and/or modify
-it under the terms of the GNU General Public License as published by
-the Free Software Foundation.
-
-This program is distributed in the hope that it will be useful,
-but WITHOUT ANY WARRANTY; without even the implied warranty of
-MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-GNU General Public License for more details.
-
-You should have received a copy of the GNU General Public License
-along with this program (see the file COPYING); if not, see
-<http://www.gnu.org/licenses/>.
-
-For more information, you may also contact me by email at
-
- de...@ma...
-
Added: trunk/octave-forge/extra/secs1d/bak/PKG_ADD
===================================================================
--- trunk/octave-forge/extra/secs1d/bak/PKG_ADD (rev 0)
+++ trunk/octave-forge/extra/secs1d/bak/PKG_ADD 2012-03-25 22:44:30 UTC (rev 10058)
@@ -0,0 +1,19 @@
+dirlist = {"Utilities","DDG","DDN"};
+
+dir = fileparts (mfilename ("fullpath"));
+
+if (! exist (fullfile (dir, "inst"), "dir"))
+ ## Run this if the package is installed
+ for ii=1:length(dirlist)
+ addpath ( [ canonicalize_file_name([dir "/.."]) "/" dirlist{ii}])
+ endfor
+else
+ ## Run this if we are testing the package without installation
+ for ii=1:length(dirlist)
+ addpath ([ canonicalize_file_name(dir) "/inst/" dirlist{ii}])
+ endfor
+endif
+
+warning ("off", "Octave:fopen-file-in-path");
+warning ("off", "Octave:load-file-in-path");
+clear dirlist dir
Copied: trunk/octave-forge/extra/secs1d/bak/secs1d_demo_pndiode.m (from rev 10018, trunk/octave-forge/extra/secs1d/inst/secs1d_demo_pndiode.m)
===================================================================
--- trunk/octave-forge/extra/secs1d/bak/secs1d_demo_pndiode.m (rev 0)
+++ trunk/octave-forge/extra/secs1d/bak/secs1d_demo_pndiode.m 2012-03-25 22:44:30 UTC (rev 10058)
@@ -0,0 +1,138 @@
+## Copyright (C) 2009 Carlo de Falco
+##
+## SECS1D - A 1-D Drift--Diffusion Semiconductor Device Simulator
+##
+## SECS1D is free software; you can redistribute it and/or modify
+## it under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 2 of the License, or
+## (at your option) any later version.
+##
+## SECS1D is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with SECS1D; If not, see <http://www.gnu.org/licenses/>.
+##
+## author: Carlo de Falco <cdf _AT_ users.sourceforge.net>
+
+function secs1d_demo_pndiode ()
+
+ constants
+
+ len = 1e-6;
+ Nnodes = 1000;
+
+ vmin = -2;
+ vmax = 2;
+
+ vstep=.4;
+
+ istep = 1;
+ va = vmin
+
+ x = linspace(0,len,Nnodes)';
+ xm = mean(x);
+
+ Nd=1e25;
+ Na=1e25;
+
+ D = Nd * (x>xm) - Na * (x<=xm);
+
+ nn = (Nd + sqrt(Nd^2+4*ni^2))/2;
+ pp = (Na + sqrt(Na^2+4*ni^2))/2;
+
+ xn = xm+1e-7;
+ xp = xm-1e-7;
+
+ %% Scaling coefficients
+ xs = len;
+ ns = norm(D,inf);
+ idata.D = D/ns;
+ Vs = Vth;
+ us = un;
+ Js = xs / (us * Vs * q * ns);
+
+
+ while va <= vmax
+
+ vvect(istep) = va;
+
+ n(:,istep) = nn * (x>=xn) + (ni^2)/pp * (x<xn);
+ p(:,istep) = (ni^2)/nn * (x>xp) + pp * (x<=xp);
+
+ Fn = va*(x<=xm);
+ Fp = Fn;
+
+ V(:,istep) = (Fn - Vth * log(p(:,istep)/ni));
+
+ %% Scaling
+ xin = x/xs;
+ idata.n = n(:,istep)/ns;
+ idata.p = p(:,istep)/ns;
+ idata.V = V(:,istep)/Vs;
+ idata.Fn = (Fn - Vs * log(ni/ns))/Vs;
+ idata.Fp = (Fp + Vs * log(ni/ns))/Vs;
+
+ lambda2(istep) = idata.l2 = (Vs*esi)/(q*ns*xs^2);
+ idata.nis = ni/ns;
+ idata.un = un/us;
+ idata.up = up/us;
+
+ %% Solution of DD system
+
+ %% Algorithm parameters
+ toll = 1e-3;
+ maxit = 20;
+ ptoll = 1e-10;
+ pmaxit = 100;
+ verbose = 0;
+ sinodes = [1:length(x)];
+ idata.tn = inf;
+ idata.tp = inf;
+
+ [odata,it,res] = DDGgummelmap (xin,idata,toll,maxit,ptoll,pmaxit,verbose);
+ [odata,it,res] = DDNnewtonmap (xin,odata,toll, maxit,verbose);
+
+ n(:,istep) = odata.n;
+ p(:,istep) = odata.p;
+ V(:,istep) = odata.V;
+
+ DV(istep) = odata.V(end) - odata.V(1);
+ Emax(istep) = max(abs(diff(odata.V)./diff(xin)))
+
+ Bp = Ubernoulli(diff (V(:, istep)),1);
+ Bm = Ubernoulli(diff (V(:, istep)),0);
+ Jn(:,istep) = -odata.un * (n(2:end, istep).*Bp-n(1:end-1, istep).*Bm)./diff (xin);
+ Jp(:,istep) = odata.up * (p(2:end, istep).*Bm-p(1:end-1, istep).*Bp)./diff (xin);
+
+ va = va+vstep
+ istep = istep+1;
+
+ endwhile
+
+ %% Descaling
+ n = n*ns;
+ p = p*ns;
+ V = V*Vs;
+ J = abs (Jp+Jn)*Js;
+
+ close all
+
+ figure();
+ plot(x, n.')
+ xlabel("x")
+ ylabel("n")
+
+ figure();
+ plot(vvect, J)
+ xlabel("V")
+ ylabel("J")
+
+ figure();
+ plot(vvect, Emax)
+ xlabel("V")
+ ylabel("max(abs(\\phi^\'))")
+
+endfunction
\ No newline at end of file
Added: trunk/octave-forge/extra/secs1d/doc/COPYING.tex
===================================================================
--- trunk/octave-forge/extra/secs1d/doc/COPYING.tex (rev 0)
+++ trunk/octave-forge/extra/secs1d/doc/COPYING.tex 2012-03-25 22:44:30 UTC (rev 10058)
@@ -0,0 +1,345 @@
+
+\begin{verbatim}
+ GNU GENERAL PUBLIC LICENSE
+ Version 2, June 1991
+
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+ Everyone is permitted to copy and distribute verbatim copies
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+ If you develop a new program, and you want it to be of the greatest
+possible use to the public, the best way to achieve this is to make it
+free software which everyone can redistribute and change under these terms.
+
+ To do so, attach the following notices to the program. It is safest
+to attach them to the start of each source file to most effectively
+convey the exclusion of warranty; and each file should have at least
+the "copyright" line and a pointer to where the full notice is found.
+
+ <one line to give the program's name and a brief idea of what it does.>
+ Copyright (C) <year> <name of author>
+
+ This program is free software; you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation; either version 2 of the License, or
+ (at your option) any later version.
+
+ This program is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ GNU General Public License for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with this program; if not, see <http://www.gnu.org/licenses/>.
+
+Also add information on how to contact you by electronic and paper mail.
+
+If the program is interactive, make it output a short notice like this
+when it starts in an interactive mode:
+
+ Gnomovision version 69, Copyright (C) year name of author
+ Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+ This is free software, and you are welcome to redistribute it
+ under certain conditions; type `show c' for details.
+
+The hypothetical commands `show w' and `show c' should show the appropriate
+parts of the General Public License. Of course, the commands you use may
+be called something other than `show w' and `show c'; they could even be
+mouse-clicks or menu items--whatever suits your program.
+
+You should also get your employer (if you work as a programmer) or your
+school, if any, to sign a "copyright disclaimer" for the program, if
+necessary. Here is a sample; alter the names:
+
+ Yoyodyne, Inc., hereby disclaims all copyright interest in the program
+ `Gnomovision' (which makes passes at compilers) written by James Hacker.
+
+ <signature of Ty Coon>, 1 April 1989
+ Ty Coon, President of Vice
+
+This General Public License does not permit incorporating your program into
+proprietary programs. If your program is a subroutine library, you may
+consider it more useful to permit linking proprietary applications with the
+library. If this is what you want to do, use the GNU Library General
+Public License instead of this License.
+
+
+
+\end{verbatim}
+\null
+
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Added: trunk/octave-forge/extra/secs1d/doc/function/secs1d_dd_gummel_map.tex
===================================================================
--- trunk/octave-forge/extra/secs1d/doc/function/secs1d_dd_gummel_map.tex (rev 0)
+++ trunk/octave-forge/extra/secs1d/doc/function/secs1d_dd_gummel_map.tex 2012-03-25 22:44:30 UTC (rev 10058)
@@ -0,0 +1,183 @@
+\begin{verbatim}
+
+
+ [n, p, V, Fn, Fp, Jn, Jp, it, res] = secs1d_dd_gummel_map (x, D, Na, Nd,
+ pin, nin, Vin, Fnin,
+ Fpin, l2, er, u0n,
+ uminn, vsatn, betan,
+ Nrefn, u0p, uminp, vsatp,
+ betap, Nrefp, theta, tn, tp,
+ Cn, Cp, an, ap, Ecritnin, Ecritpin,
+ toll, maxit, ptoll, pmaxit)
+
+ This function solves the scaled stationary bipolar DD
+ equation system using Gummel algorithm
+
+ input:
+ x spatial grid
+ D, Na, Nd doping profile
+ pin initial guess for hole concentration
+ nin initial guess for electron concentration
+ Vin initial guess for electrostatic potential
+ Fnin initial guess for electron Fermi potential
+ Fpin initial guess for hole Fermi potential
+ l2 scaled Debye length squared
+ er relative electric permittivity
+ u0n, uminn, vsatn, Nrefn electron mobility model coefficients
+ u0p, uminp, vsatp, Nrefp hole mobility model coefficients
+ theta intrinsic carrier density
+ tn, tp, Cn, Cp,
+ an, ap,
+ Ecritnin, Ecritpin generation recombination model parameters
+ toll tolerance for Gummel iterarion convergence test
+ maxit maximum number of Gummel iterarions
+ ptoll convergence test tolerance for the non linear
+ Poisson solver
+ pmaxit maximum number of Newton iterarions
+
+ output:
+ n electron concentration
+ p hole concentration
+ V electrostatic potential
+ Fn electron Fermi potential
+ Fp hole Fermi potential
+ Jn electron current density
+ Jp hole current density
+ it number of Gummel iterations performed
+ res total potential increment at each step
+
+
+\end{verbatim}
+
+
+
+
+\subsection{Demo 1 for unction secs1d\_dd\_gummel\_map}
+\begin{verbatim}
+
+ % physical constants and parameters
+ secs1d_physical_constants;
+ secs1d_silicon_material_properties;
+
+ % geometry
+ L = 10e-6; % [m]
+ xm = L/2;
+
+ Nelements = 1000;
+ x = linspace (0, L, Nelements+1)';
+ sinodes = [1:length(x)];
+
+ % dielectric constant (silicon)
+ er = esir * ones (Nelements, 1);
+
+ % doping profile [m^{-3}]
+ Na = 1e23 * (x <= xm);
+ Nd = 1e23 * (x > xm);
+
+ % avoid zero doping
+ D = Nd - Na;
+
+ % initial guess for n, p, V, phin, phip
+ V_p = -1;
+ V_n = 0;
+
+ Fp = V_p * (x <= xm);
+ Fn = Fp;
+
+ p = abs (D) / 2 .* (1 + sqrt (1 + 4 * (ni./abs(D)) .^2)) .* (x <= xm) + ...
+ ni^2 ./ (abs (D) / 2 .* (1 + sqrt (1 + 4 * (ni ./ abs (D)) .^2))) .* (x > xm);
+
+ n = abs (D) / 2 .* (1 + sqrt (1 + 4 * (ni ./ abs (D)) .^ 2)) .* (x > xm) + ...
+ ni ^ 2 ./ (abs (D) / 2 .* (1 + sqrt (1 + 4 * (ni ./ abs (D)) .^2))) .* (x <= xm);
+
+ V = Fn + Vth * log (n / ni);
+
+ % scaling factors
+ xbar = L; % [m]
+ nbar = norm(D, 'inf'); % [m^{-3}]
+ Vbar = Vth; % [V]
+ mubar = max (u0n, u0p); % [m^2 V^{-1} s^{-1}]
+ tbar = xbar^2 / (mubar * Vbar); % [s]
+ Rbar = nbar / tbar; % [m^{-3} s^{-1}]
+ Ebar = Vbar / xbar; % [V m^{-1}]
+ Jbar = q * mubar * nbar * Ebar; % [A m^{-2}]
+ CAubar = Rbar / nbar^3; % [m^6 s^{-1}]
+ abar = 1/xbar; % [m^{-1}]
+
+ % scaling procedure
+ l2 = e0 * Vbar / (q * nbar * xbar^2);
+ theta = ni / nbar;
+
+ xin = x / xbar;
+ Din = D / nbar;
+ Nain = Na / nbar;
+ Ndin = Nd / nbar;
+ pin = p / nbar;
+ nin = n / nbar;
+ Vin = V / Vbar;
+ Fnin = Vin - log (nin);
+ Fpin = Vin + log (pin);
+
+ tnin = tn / tbar;
+ tpin = tp / tbar;
+
+ u0nin = u0n / mubar;
+ uminnin = uminn / mubar;
+ vsatnin = vsatn / (mubar * Ebar);
+
+ u0pin = u0p / mubar;
+ uminpin = uminp / mubar;
+ vsatpin = vsatp / (mubar * Ebar);
+
+ Nrefnin = Nrefn / nbar;
+ Nrefpin = Nrefp / nbar;
+
+ Cnin = Cn / CAubar;
+ Cpin = Cp / CAubar;
+
+ anin = an / abar;
+ apin = ap / abar;
+ Ecritnin = Ecritn / Ebar;
+ Ecritpin = Ecritp / Ebar;
+
+ % tolerances for convergence checks
+ toll = 1e-3;
+ maxit = 1000;
+ ptoll = 1e-12;
+ pmaxit = 1000;
+
+ % solve the problem using the full DD model
+ [nout, pout, Vout, Fnout, Fpout, Jnout, Jpout, it, res] = ...
+ secs1d_dd_gummel_map (xin, Din, Nain, Ndin, pin, nin, Vin, Fnin, Fpin, ...
+ l2, er, u0nin, uminnin, vsatnin, betan, Nrefnin, ...
+ u0pin, uminpin, vsatpin, betap, Nrefpin, theta, ...
+ tnin, tpin, Cnin, Cpin, anin, apin, ...
+ Ecritnin, Ecritpin, toll, maxit, ptoll, pmaxit);
+
+ % Descaling procedure
+ n = nout*nbar;
+ p = pout*nbar;
+ V = Vout*Vbar;
+ Fn = V - Vth*log(n/ni);
+ Fp = V + Vth*log(p/ni);
+ dV = diff(V);
+ dx = diff(x);
+ E = -dV./dx;
+
+ % band structure
+ Efn = -Fn;
+ Efp = -Fp;
+ Ec = Vth*log(Nc./n)+Efn;
+ Ev = -Vth*log(Nv./p)+Efp;
+
+ plot (x, Efn, x, Efp, x, Ec, x, Ev)
+ legend ('Efn', 'Efp', 'Ec', 'Ev')
+ axis tight
+\end{verbatim}
+
+\begin{figure}\centering
+\includegraphics[width=.7\linewidth]{function/images/secs1d_dd_gummel_map_205.png}
+\caption{Figure produced by demo number 1 for function secs1d\_dd\_gummel\_map}
+\label{fig:secs1d_dd_gummel_map_figure_1}
+\end{figure}
+\clearpage
Added: trunk/octave-forge/extra/secs1d/doc/function/secs1d_dd_newton.tex
===================================================================
--- trunk/octave-forge/extra/secs1d/doc/function/secs1d_dd_newton.tex (rev 0)
+++ trunk/octave-forge/extra/secs1d/doc/function/secs1d_dd_newton.tex 2012-03-25 22:44:30 UTC (rev 10058)
@@ -0,0 +1,169 @@
+\begin{verbatim}
+
+
+ [n, p, V, Fn, Fp, Jn, Jp, it, res] = secs1d_dd_newton (x, D, Vin, nin,
+ pin, l2, er, un,
+ up, theta, tn, tp,
+ Cn, Cp, toll, maxit)
+
+ Solve the scaled stationary bipolar DD equation system using Newton's method
+
+ input:
+ x spatial grid
+ D doping profile
+ pin initial guess for hole concentration
+ nin initial guess for electron concentration
+ Vin initial guess for electrostatic potential
+ l2 scaled Debye length squared
+ er relative electric permittivity
+ un electron mobility model coefficients
+ up electron mobility model coefficients
+ theta intrinsic carrier density
+ tn, tp, Cn, Cp generation recombination model parameters
+ toll tolerance for Gummel iterarion convergence test
+ maxit maximum number of Gummel iterarions
+
+ output:
+ n electron concentration
+ p hole concentration
+ V electrostatic potential
+ Fn electron Fermi potential
+ Fp hole Fermi potential
+ Jn electron current density
+ Jp hole current density
+ it number of Gummel iterations performed
+ res total potential increment at each step
+
+
+\end{verbatim}
+
+
+
+
+\subsection{Demo 1 for function secs1d\_dd\_newton}
+\begin{verbatim}
+
+ % physical constants and parameters
+ secs1d_physical_constants;
+ secs1d_silicon_material_properties;
+
+ % geometry
+ L = 1e-6; % [m]
+ x = linspace (0, L, 10)';
+ sinodes = [1:length(x)];
+
+ % dielectric constant (silicon)
+ er = esir * ones (numel (x) - 1, 1);
+
+ % doping profile [m^{-3}]
+ Na = 1e20 * ones(size(x));
+ Nd = 1e24 * ones(size(x));
+ D = Nd-Na;
+
+ % externally applied voltages
+ V_p = 10;
+ V_n = 0;
+
+ % initial guess for phin, phip, n, p, V
+ Fp = V_p * (x <= L/2);
+ Fn = Fp;
+
+ p = abs(D)/2.*(1+sqrt(1+4*(ni./abs(D)).^2)).*(D<0)+...
+ ni^2./(abs(D)/2.*(1+sqrt(1+4*(ni./abs(D)).^2))).*(D>0);
+
+ n = abs(D)/2.*(1+sqrt(1+4*(ni./abs(D)).^2)).*(D>0)+...
+ ni^2./(abs(D)/2.*(1+sqrt(1+4*(ni./abs(D)).^2))).*(D<0);
+
+ V = Fn + Vth*log(n/ni);
+
+ % scaling factors
+ xbar = L; % [m]
+ nbar = norm(D, 'inf'); % [m^{-3}]
+ Vbar = Vth; % [V]
+ mubar = max(u0n, u0p); % [m^2 V^{-1} s^{-1}]
+ tbar = xbar^2/(mubar*Vbar); % [s]
+ Rbar = nbar/tbar; % [m^{-3} s^{-1}]
+ Ebar = Vbar/xbar; % [V m^{-1}]
+ Jbar = q*mubar*nbar*Ebar; % [A m^{-2}]
+ CAubar = Rbar/nbar^3; % [m^6 s^{-1}]
+ abar = xbar^(-1); % [m^{-1}]
+
+ % scaling procedure
+ l2 = e0*Vbar/(q*nbar*xbar^2);
+ theta = ni/nbar;
+
+ xin = x/xbar;
+ Din = D/nbar;
+ Nain = Na/nbar;
+ Ndin = Nd/nbar;
+ pin = p/nbar;
+ nin = n/nbar;
+ Vin = V/Vbar;
+ Fnin = Vin - log(nin);
+ Fpin = Vin + log(pin);
+
+ tnin = tn/tbar;
+ tpin = tp/tbar;
+
+ % mobility model accounting scattering from ionized impurities
+ u0nin = u0n/mubar;
+ uminnin = uminn/mubar;
+ vsatnin = vsatn/(mubar*Ebar);
+
+ u0pin = u0p/mubar;
+ uminpin = uminp/mubar;
+ vsatpin = vsatp/(mubar*Ebar);
+
+ Nrefnin = Nrefn/nbar;
+ Nrefpin = Nrefp/nbar;
+
+ Cnin = Cn/CAubar;
+ Cpin = Cp/CAubar;
+
+ anin = an/abar;
+ apin = ap/abar;
+ Ecritnin = Ecritn/Ebar;
+ Ecritpin = Ecritp/Ebar;
+
+ % tolerances for convergence checks
+ ptoll = 1e-12;
+ pmaxit = 1000;
+
+ % solve the problem using the Newton fully coupled iterative algorithm
+ [nout, pout, Vout, Fnout, Fpout, Jnout, Jpout, it, res] = secs1d_dd_newton (xin, Din,
+ Vin, nin, pin, l2, er,
+ u0nin, u0pin, theta, tnin,
+ tpin, Cnin, Cpin, ptoll, pmaxit);
+ % Descaling procedure
+ n = nout*nbar;
+ p = pout*nbar;
+ V = Vout*Vbar;
+ Fn = V - Vth*log(n/ni);
+ Fp = V + Vth*log(p/ni);
+ dV = diff(V);
+ dx = diff(x);
+ E = -dV./dx;
+
+ % compute current densities
+ [Bp, Bm] = bimu_bernoulli (dV/Vth);
+ Jn = q*u0n*Vth .* (n(2:end) .* Bp - n(1:end-1) .* Bm) ./ dx;
+ Jp = -q*u0p*Vth .* (p(2:end) .* Bm - p(1:end-1) .* Bp) ./ dx;
+ Jtot = Jn+Jp;
+
+ % band structure
+ Efn = -Fn;
+ Efp = -Fp;
+ Ec = Vth*log(Nc./n)+Efn;
+ Ev = -Vth*log(Nv./p)+Efp;
+
+ plot (x, Efn, x, Efp, x, Ec, x, Ev)
+ legend ('Efn', 'Efp', 'Ec', 'Ev')
+ axis tight
+\end{verbatim}
+
+\begin{figure}\centering
+\includegraphics[width=.7\linewidth]{function/images/secs1d_dd_newton_819.png}
+\caption{Figure produced by demo number 1 for function secs1d\_dd\_newton}
+\label{fig:secs1d_dd_newton_figure_1}
+\end{figure}
+\clearpage
Added: trunk/octave-forge/extra/secs1d/doc/function/secs1d_nlpoisson_newton.tex
===================================================================
--- trunk/octave-forge/extra/secs1d/doc/function/secs1d_nlpoisson_newton.tex (rev 0)
+++ trunk/octave-forge/extra/secs1d/doc/function/secs1d_nlpoisson_newton.tex 2012-03-25 22:44:30 UTC (rev 10058)
@@ -0,0 +1,121 @@
+\begin{verbatim}
+
+
+ [V, n, p, res, niter] = secs1d_nlpoisson_newton (x, sinodes, Vin, nin, pin,
+ Fnin, Fpin, D, l2, er, toll, maxit)
+
+ input:
+ x spatial grid
+ sinodes index of the nodes of the grid which are in the semiconductor subdomain
+ (remaining nodes are assumed to be in the oxide subdomain)
+ Vin initial guess for the electrostatic potential
+ nin initial guess for electron concentration
+ pin initial guess for hole concentration
+ Fnin initial guess for electron Fermi potential
+ Fpin initial guess for hole Fermi potential
+ D doping profile
+ l2 scaled Debye length squared
+ er relative electric permittivity
+ toll tolerance for convergence test
+ maxit maximum number of Newton iterations
+
+ output:
+ V electrostatic potential
+ n electron concentration
+ p hole concentration
+ res residual norm at each step
+ niter number of Newton iterations
+
+
+\end{verbatim}
+
+
+
+
+\subsection{Demo 1 for function secs1d\_nlpoisson\_newton}
+\begin{verbatim}
+
+ secs1d_physical_constants
+ secs1d_silicon_material_properties
+
+ tbulk= 1.5e-6;
+ tox = 90e-9;
+ L = tbulk + tox;
+ cox = esio2/tox;
+
+ Nx = 50;
+ Nel = Nx - 1;
+
+ x = linspace (0, L, Nx)';
+ sinodes = find (x <= tbulk);
+ xsi = x(sinodes);
+
+ Nsi = length (sinodes);
+ Nox = Nx - Nsi;
+
+ NelSi = Nsi - 1;
+ NelSiO2 = Nox - 1;
+
+ Na = 1e22;
+ D = - Na * ones (size (xsi));
+ p = Na * ones (size (xsi));
+ n = (ni^2) ./ p;
+ Fn = Fp = zeros (size (xsi));
+ Vg = -10;
+ Nv = 80;
+ for ii = 1:Nv
+ Vg = Vg + 0.2;
+ vvect(ii) = Vg;
+
+ V = - Phims + Vg * ones (size (x));
+ V(sinodes) = Fn + Vth * log (n/ni);
+
+ % Scaling
+ xs = L;
+ ns = norm (D, inf);
+ Din = D / ns;
+ Vs = Vth;
+ xin = x / xs;
+ nin = n / ns;
+ pin = p / ns;
+ Vin = V / Vs;
+ Fnin = (Fn - Vs * log (ni / ns)) / Vs;
+ Fpin = (Fp + Vs * log (ni / ns)) / Vs;
+
+ er = esio2r * ones(Nel, 1);
+ l2(1:NelSi) = esi;
+ l2 = (Vs*e0)/(q*ns*xs^2);
+
+ % Solution of Nonlinear Poisson equation
+
+ % Algorithm parameters
+ toll = 1e-10;
+ maxit = 1000;
+
+ [V, nout, pout, res, niter] = secs1d_nlpoisson_newton (xin, sinodes,
+ Vin, nin, pin,
+ Fnin, Fpin, Din, l2,
+ er, toll, maxit);
+
+ % Descaling
+ n = nout*ns;
+ p = pout*ns;
+ V = V*Vs;
+
+ qtot(ii) = q * trapz (xsi, p + D - n);
+ end
+
+ vvectm = (vvect(2:end)+vvect(1:end-1))/2;
+ C = - diff (qtot) ./ diff (vvect);
+ plot(vvectm, C)
+ xlabel('Vg [V]')
+ ylabel('C [Farad]')
+ title('C-V curve')
+\end{verbatim}
+
+\begin{figure}\centering
+\includegraphics[width=.7\linewidth]{function/images/secs1d_nlpoisson_newton_85.png}
+\caption{Figure produced by demo number 1 for function secs1d\_nlpoisson\_newton}
+\label{fig:secs1d_nlpoisson_newton_figure_1}
+\end{figure}
+\clearpage
Added: trunk/octave-forge/extra/secs1d/doc/function/secs1d_physical_constants.m.tex
===================================================================
--- trunk/octave-forge/extra/secs1d/doc/function/secs1d_physical_constants.m.tex (rev 0)
+++ trunk/octave-forge/extra/secs1d/doc/function/secs1d_physical_constants.m.tex 2012-03-25 22:44:30 UTC (rev 10058)
@@ -0,0 +1,18 @@
+\begin{verbatim}
+
+
+ some useful physical constants
+
+ Kb = Boltzman constant
+ q = quantum of charge
+ e0 = permittivity of free space
+ hplanck = Plank constant
+ hbar = Plank constant by 2 pi
+ mn0 = free electron mass
+ T0 = temperature
+ Vth = thermal voltage
+
+
+\end{verbatim}
+
+\clearpage
Added: trunk/octave-forge/extra/secs1d/doc/function/secs1d_silicon_material_properties.m.tex
===================================================================
--- trunk/octave-forge/extra/secs1d/doc/function/secs1d_silicon_material_properties.m.tex (rev 0)
+++ trunk/octave-forge/extra/secs1d/doc/function/secs1d_silicon_material_properties.m.tex 2012-03-25 22:44:30 UTC (rev 10058)
@@ -0,0 +1,42 @@
+\begin{verbatim}
+
+
+ material properties for silicon and silicon dioxide
+
+ esir = relative electric permittivity of silicon
+ esio2r = relative electric permittivity of silicon dioxide
+ esi = electric permittivity of silicon
+ esio2 = electric permittivity of silicon dioxide
+ mn = effective mass of electrons in silicon
+ mh = effective mass of holes in silicon
+
+ u0n = low field electron mobility
+ u0p = low field hole mobility
+ uminn = parameter for doping-dependent electron mobility
+ betan = idem
+ Nrefn = idem
+ uminp = parameter for doping-dependent hole mobility
+ betap = idem
+ Nrefp = idem
+ vsatn = electron saturation velocity
+ vsatp = hole saturation velocity
+ tp = electron lifetime
+ tn = hole lifetime
+ Cn = electron Auger coefficient
+ Cp = hole Auger coefficient
+ an = impact ionization rate for electrons
+ ap = impact ionization rate for holes
+ Ecritn = critical field for impact ionization of electrons
+ Ecritp = critical field for impact ionization of holes
+ Nc = effective density of states in the conduction band
+ Nv = effective density of states in the valence band
+ Egap = bandgap in silicon
+ EgapSio2 = bandgap in silicon dioxide
+
+ ni = intrinsic carrier density
+ Phims = metal to semiconductor potential barrier
+
+
+\end{verbatim}
+
+\clearpage
Added: trunk/octave-forge/extra/secs1d/doc/manual.pdf
===================================================================
(Binary files differ)
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Added: svn:mime-type
+ application/octet-stream
Added: trunk/octave-forge/extra/secs1d/doc/manual.tex
===================================================================
--- trunk/octave-forge/extra/secs1d/doc/manual.tex (rev 0)
+++ trunk/octave-forge/extra/secs1d/doc/manual.tex 2012-03-25 22:44:30 UTC (rev 10058)
@@ -0,0 +1,266 @@
+\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
Deleted: trunk/octave-forge/extra/secs1d/inst/secs1d.m
===================================================================
--- trunk/octave-forge/extra/secs1d/inst/secs1d.m 2012-03-25 22:35:18 UTC (rev 10057)
+++ trunk/octave-forge/extra/secs1d/inst/secs1d.m 2012-03-25 22:44:30 UTC (rev 10058)
@@ -1,15 +0,0 @@
-# Run this only if the package is installed
-## PKG_ADD: if (! exist (fullfile (fileparts (mfilename ("fullpath")), "inst"), "dir"))
-## PKG_ADD: dirlist= {"Utilities","DDG","DDN"};
-## PKG_ADD: for ii=1:length(dirlist)
-## PKG_ADD: addpath ( [ fileparts( mfilename("fullpath")) "/" dirlist{ii}])
-## PKG_ADD: end
-## PKG_ADD: end
-
-# Run this only if the package is installed
-## PKG_DEL: if (! exist (fullfile (fileparts (mfilename ("fullpath")), "inst"), "dir"))
-## PKG_DEL: dirlist= {"Utilities","DDG","DDN"};
-## PKG_DEL: for ii=1:length(dirlist)
-## PKG_DEL: rmpath ( [ fileparts( mfilename("fullpath")) "/" dirlist{ii}])
-## PKG_DEL: end
-## PKG_DEL: end
Added: trunk/octave-forge/extra/secs1d/inst/secs1d_dd_gummel_map.m
===================================================================
--- trunk/octave-forge/extra/secs1d/inst/secs1d_dd_gummel_map.m (rev 0)
+++ trunk/octave-forge/extra/secs1d/inst/secs1d_dd_gummel_map.m 2012-03-25 22:44:30 UTC (rev 10058)
@@ -0,0 +1,302 @@
+%% Copyright (C) 2004-2012 Carlo de Falco
+%%
+%% This file is part of
+%% SECS1D - A 1-D Drift--Diffusion Semiconductor Device Simulator
+%%
+%% SECS1D is free software; you can redistribute it and/or modify
+%% it under the terms of the GNU General Public License as published by
+%% the Free Software Foundation; either version 3 of the License, or
+%% (at your option) any later version.
+%%
+%% SECS1D is distributed in the hope that it will be useful,
+%% but WITHOUT ANY WARRANTY; without even the implied warranty of
+%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+%% GNU General Public License for more details.
+%%
+%% You should have received a copy of the GNU General Public License
+%% along with SECS1D; If not, see <http://www.gnu.org/licenses/>.
+
+%% [n, p, V, Fn, Fp, Jn, Jp, it, res] = secs1d_dd_gummel_map (x, D, Na, Nd,
+%% pin, nin, Vin, Fnin,
+%% Fpin, l2, er, u0n,
+%% uminn, vsatn, betan,
+%% Nrefn, u0p, uminp, vsatp,
+%% betap, Nrefp, theta, tn, tp,
+%% Cn, Cp, an, ap, Ecritnin, Ecritpin,
+%% toll, maxit, ptoll, pmaxit)
+%%
+%% This function solves the scaled stationary bipolar DD
+%% equation system using Gummel algorithm
+%%
+%% input:
+%% x spatial grid
+%% D, Na, Nd doping profile
+%% pin initial guess for hole concentration
+%% nin initial guess for electron concentration
+%% Vin initial guess for electrostatic potential
+%% Fnin initial guess for electron Fermi potential
+%% Fpin initial guess for hole Fermi potential
+%% l2 scaled Debye length squared
+%% er relative electric permittivity
+%% u0n, uminn, vsatn, Nrefn electron mobility model coefficients
+%% u0p, uminp, vsatp, Nrefp hole mobility model coefficients
+%% theta intrinsic carrier density
+%% tn, tp, Cn, Cp,
+%% an, ap,
+%% Ecritnin, Ecritpin generation recombination model parameters
+%% toll tolerance for Gummel iterarion convergence test
+%% maxit maximum number of Gummel iterarions
+%% ptoll convergence test tolerance for the non linear
+%% Poisson solver
+%% pmaxit maximum number o...
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