scat.h

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/*
   This file belongs to Aeneas. Aeneas is a GNU package released under GPL 3 license.
   This code is a simulator for Submicron 3D Semiconductor Devices. 
   It implements the Monte Carlo transport in 3D tetrahedra meshes
   for the simulation of the semiclassical Boltzmann equation for both electrons.
   It also includes all the relevant quantum effects for nanodevices.

   Copyright (C) 2007 Jean Michel Sellier <sellier@dmi.unict.it>
 
   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 3, 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/>.
*/


// Created on : 11 june 2007, Siracusa, Jean Michel Sellier
// Last modified : 02 august 2007, Siracusa, Jean Michel Sellier

// scattering step of the EMC algorithm

void scat(int Material)
{
 int j=0;
 register int i,ie=0;
 double ksquared,thesquareroot,superparticle_energy;
 double r1,finalenergy=0.,finalk,cosinus,sinus,fai;
 double f,cb,cf,sf,skk,a11,a12,a13,a21,a22,a23,a32,a33,x1,x2,x3,sb,r2;
 double ki,kf,cs,sn;
 double aaa=1.999,bbb=0.333;
 double ra1,ra2;

  if(IV==9) return;
  if(Material==SIO2) return;

// One-valley Materials Scattering Selection
// #########################################
 if(Material!=SIO2 && NOVALLEY[Material]==1){
  ksquared=KX*KX+KY*KY+KZ*KZ;
  thesquareroot=sqrt(1.+4.*alphaK[Material][1]*HHM[Material][1]*ksquared);
  superparticle_energy=(thesquareroot-1.)/(2.*alphaK[Material][1]);
  if(superparticle_energy<=0.) return;
  ie=((int)(superparticle_energy/DE))+1;
  if(ie>DIME) ie=DIME;

// Selection of scattering process
  r1 = rnd();
// Non-Polar optical phonons
  for(i=1;i<=6;i++){
// Emission of an optical phonon
    if(r1<=SWK[Material][0][i*2-1][ie] && j==0){
       finalenergy=superparticle_energy-HWO[Material][i-1];
       j=1;
    }
// Absorbation of an optical phonon
    if((r1<=SWK[Material][0][i*2][ie]) && j==0){
       finalenergy=superparticle_energy+HWO[Material][i-1];
       j=1;
    }
  }
// Acoustic phonon
  if((r1<=SWK[Material][0][13][ie]) && j==0){
     finalenergy=superparticle_energy;
     j=1;
  }
// Impact ionization
  if((r1<=SWK[Material][0][14][ie]) && j==0){
     ra1=0.5-rnd();
     ra2=pow(rnd(),2.);
     finalenergy=bbb*superparticle_energy*(1.0+aaa*ra1*ra2);
     finalenergy=superparticle_energy-finalenergy;
     j=1;
  }
  if((finalenergy<=0.) || j==0) return;

// determination of the final states
  finalk = SMH[Material][1]*sqrt(finalenergy*(1.+alphaK[Material][1]*finalenergy));
  cosinus = 1.-2.*rnd();
  sinus = sqrt(1.-cosinus*cosinus);
  fai = 2.*PI*rnd();
  KX = finalk*cosinus;
  KY = finalk*sinus*cos(fai);
  KZ = finalk*sinus*sin(fai);
  return;
 }

// 2-valleys materials Scattering Selection
// ########################################
 if(Material!=SIO2 && NOVALLEY[Material]==2){
   ksquared=KX*KX+KY*KY+KZ*KZ;
   ki=sqrt(ksquared);
   thesquareroot=sqrt(1.+4.*alphaK[Material][IV]*HHM[Material][IV]*ksquared);
   superparticle_energy=(thesquareroot-1.)/(2.*alphaK[Material][IV]);
  if(superparticle_energy<=0.) return;
  ie=((int)(superparticle_energy/DE))+1;
  if(ie>DIME) ie=DIME;

// Selection of scattering process in the first-Valley
// ===================================================
  if(IV==1){
    r1 = rnd();
// Non-Polar optical phonons
// Emission of an optical phonon
      if(r1<=SWK[Material][1][1][ie] && j==0){
         finalenergy=superparticle_energy-HWO[Material][0];
         if(finalenergy<0.) return;
         j=1;
// linea 20
       kf=SMH[Material][IV]*sqrt(finalenergy*(1.+alphaK[Material][IV]*finalenergy));
       f=2.*ki*kf/(ki-kf)/(ki-kf);
       if(f<=0.) return;
       cb=(1.+f-pow(1.+2.*f,rnd()))/f;
// linea 30 -- determination of the final states
       sb=sqrt(1.-cb*cb);
       fai=2.*PI*rnd();
       cf=cos(fai);
       sf=sin(fai);
       skk=sqrt(KX*KX+KY*KY);
       a11=KY/skk;
       a12=KX*KZ/skk/ki;
       a13=KX/ki;
       a21=-KX/skk;
       a22=KY*KZ/skk/ki;
       a23=KY/ki;
       a32=-skk/ki;
       a33=KZ/ki;
       x1=kf*sb*cf;
       x2=kf*sb*sf;
       x3=kf*cb;
       KX=a11*x1+a12*x2+a13*x3;
       KY=a21*x1+a22*x2+a23*x3;
       KZ=a32*x2+a33*x3;
       return;
      }

// Absorption of an optical phonon
      if((r1<=SWK[Material][1][2][ie]) && j==0){
         finalenergy=superparticle_energy+HWO[Material][0];
         if(finalenergy<0.) return;
         j=1;
// linea 20
       kf=SMH[Material][IV]*sqrt(finalenergy*(1.+alphaK[Material][IV]*finalenergy));
       f=2.*ki*kf/(ki-kf)/(ki-kf);
       if(f<=0.) return;
       cb=(1.+f-pow((1.+2.*f),rnd()))/f;
// linea 30 -- determination of the final states
       sb=sqrt(1.-cb*cb);
       fai=2.*PI*rnd();
       cf=cos(fai);
       sf=sin(fai);
       skk=sqrt(KX*KX+KY*KY);
       a11=KY/skk;
       a12=KX*KZ/skk/ki;
       a13=KX/ki;
       a21=-KX/skk;
       a22=KY*KZ/skk/ki;
       a23=KY/ki;
       a32=-skk/ki;
       a33=KZ/ki;
       x1=kf*sb*cf;
       x2=kf*sb*sf;
       x3=kf*cb;
       KX=a11*x1+a12*x2+a13*x3;
       KY=a21*x1+a22*x2+a23*x3;
       KZ=a32*x2+a33*x3;
       return;
      }
// Emission
      if((r1<=SWK[Material][1][3][ie]) && j==0){
         finalenergy=superparticle_energy-HWO[Material][0]+EC[Material][1]-EC[Material][2];
         if(finalenergy<0.) return;
         IV=2;
         j=1;
// determination of the final states
       kf = SMH[Material][IV]*sqrt(finalenergy*(1.+alphaK[Material][IV]*finalenergy));
       cs = 1.-2.*rnd();
       sn = sqrt(1.-cs*cs);
       fai = 2.*PI*rnd();
       KX = kf*cs;
       KY = kf*sn*cos(fai);
       KZ = kf*sn*sin(fai);
       return;
      }
// Absorption
      if((r1<=SWK[Material][1][4][ie]) && j==0){
         finalenergy=superparticle_energy+HWO[Material][0]+EC[Material][1]-EC[Material][2];
         if(finalenergy<0.) return;
         IV=2;
         j=1;
// determination of the final states
       kf = SMH[Material][IV]*sqrt(finalenergy*(1.+alphaK[Material][IV]*finalenergy));
       cs = 1.-2.*rnd();
       sn = sqrt(1.-cs*cs);
       fai = 2.*PI*rnd();
       KX = kf*cs;
       KY = kf*sn*cos(fai);
       KZ = kf*sn*sin(fai);
       return;
      }
// Acoustic phonon
    if((r1<=SWK[Material][1][5][ie]) && j==0){
       finalenergy=superparticle_energy;
       if(finalenergy<0.) return;
       finalk=sqrt(ksquared);
       j=1;
// determination of the final states
       kf = SMH[Material][IV]*sqrt(finalenergy*(1.+alphaK[Material][IV]*finalenergy));
       cs = 1.-2.*rnd();
       sn = sqrt(1.-cs*cs);
       fai = 2.*PI*rnd();
       KX = kf*cs;
       KY = kf*sn*cos(fai);
       KZ = kf*sn*sin(fai);
       return;
    }
// Impurity scattering
    if((r1<=SWK[Material][1][6][ie]) && j==0){
     finalenergy=superparticle_energy;
     if(finalenergy<0.) return;
     r2=rnd();
     cb=1.-r2/(0.5+(1.-r2)*ksquared/QD2);
     kf=ki;
// linea 30 -- determination of the final states
     sb=sqrt(1.-cb*cb);
     fai=2.*PI*rnd();
     cf=cos(fai);
     sf=sin(fai);
     skk=sqrt(KX*KX+KY*KY);
     a11=KY/skk;
     a12=KX*KZ/skk/ki;
     a13=KX/ki;
     a21=-KX/skk;
     a22=KY*KZ/skk/ki;
     a23=KY/ki;
     a32=-skk/ki;
     a33=KZ/ki;
     x1=kf*sb*cf;
     x2=kf*sb*sf;
     x3=kf*cb;
     KX=a11*x1+a12*x2+a13*x3;
     KY=a21*x1+a22*x2+a23*x3;
     KZ=a32*x2+a33*x3;
     return;
    }
// Impact ionization
    if((r1<=SWK[Material][1][7][ie]) && j==0){
       ra1=0.5-rnd();
       ra2=pow(rnd(),2.);
       finalenergy=bbb*superparticle_energy*(1.0+aaa*ra1*ra2);
       finalenergy=superparticle_energy-finalenergy;
       j=1;
    }
    if((finalenergy<=0.) || j==0) return;

// determination of the final states
    finalk = SMH[Material][1]*sqrt(finalenergy*(1.+alphaK[Material][1]*finalenergy));
    cosinus = 1.-2.*rnd();
    sinus = sqrt(1.-cosinus*cosinus);
    fai = 2.*PI*rnd();
    KX = finalk*cosinus;
    KY = finalk*sinus*cos(fai);
    KZ = finalk*sinus*sin(fai);
    return;
   }
// Selection of scattering process in the second-Valley
// ====================================================
  if(IV==2){
    r1 = rnd();
// Non-Polar optical phonons
// Emission of an optical phonon
      if(r1<=SWK[Material][2][1][ie] && j==0){
         finalenergy=superparticle_energy-HWO[Material][0];
         if(finalenergy<0.) return;
         j=1;
// linea 20
       kf=SMH[Material][IV]*sqrt(finalenergy*(1.+alphaK[Material][IV]*finalenergy));
       f=2.*ki*kf/(ki-kf)/(ki-kf);
       if(f<=0.) return;
       cb=(1.+f-pow((1.+2.*f),rnd()))/f;
// linea 30 -- determination of the final states
       sb=sqrt(1.-cb*cb);
       fai=2.*PI*rnd();
       cf=cos(fai);
       sf=sin(fai);
       skk=sqrt(KX*KX+KY*KY);
       a11=KY/skk;
       a12=KX*KZ/skk/ki;
       a13=KX/ki;
       a21=-KX/skk;
       a22=KY*KZ/skk/ki;
       a23=KY/ki;
       a32=-skk/ki;
       a33=KZ/ki;
       x1=kf*sb*cf;
       x2=kf*sb*sf;
       x3=kf*cb;
       KX=a11*x1+a12*x2+a13*x3;
       KY=a21*x1+a22*x2+a23*x3;
       KZ=a32*x2+a33*x3;
       return;
      }
// Absorbation of an optical phonon
      if((r1<=SWK[Material][2][2][ie]) && j==0){
         finalenergy=superparticle_energy+HWO[Material][0];
         if(finalenergy<0.) return;
         j=1;
// linea 20
       kf=SMH[Material][IV]*sqrt(finalenergy*(1.+alphaK[Material][IV]*finalenergy));
       f=2.*ki*kf/(ki-kf)/(ki-kf);
       if(f<=0.) return;
       cb=(1.+f-pow((1.+2.*f),rnd()))/f;
// linea 30 -- determination of the final states
       sb=sqrt(1.-cb*cb);
       fai=2.*PI*rnd();
       cf=cos(fai);
       sf=sin(fai);
       skk=sqrt(KX*KX+KY*KY);
       a11=KY/skk;
       a12=KX*KZ/skk/ki;
       a13=KX/ki;
       a21=-KX/skk;
       a22=KY*KZ/skk/ki;
       a23=KY/ki;
       a32=-skk/ki;
       a33=KZ/ki;
       x1=kf*sb*cf;
       x2=kf*sb*sf;
       x3=kf*cb;
       KX=a11*x1+a12*x2+a13*x3;
       KY=a21*x1+a22*x2+a23*x3;
       KZ=a32*x2+a33*x3;
       return;
      }
// Emission
    if((r1<=SWK[Material][2][3][ie]) && j==0){
       finalenergy=superparticle_energy-HWO[Material][0];
       if(finalenergy<0.) return;
       j=1;
// determination of the final states
       kf = SMH[Material][IV]*sqrt(finalenergy*(1.+alphaK[Material][IV]*finalenergy));
       cs = 1.-2.*rnd();
       sn = sqrt(1.-cs*cs);
       fai = 2.*PI*rnd();
       KX = kf*cs;
       KY = kf*sn*cos(fai);
       KZ = kf*sn*sin(fai);
       return;
    }
// Absorbation
    if((r1<=SWK[Material][2][4][ie]) && j==0){
       finalenergy=superparticle_energy+HWO[Material][0];
       if(finalenergy<0.) return;
       j=1;
// determination of the final states
       kf = SMH[Material][IV]*sqrt(finalenergy*(1.+alphaK[Material][IV]*finalenergy));
       cs = 1.-2.*rnd();
       sn = sqrt(1.-cs*cs);
       fai = 2.*PI*rnd();
       KX = kf*cs;
       KY = kf*sn*cos(fai);
       KZ = kf*sn*sin(fai);
       return;
    }
// Emission
    if((r1<=SWK[Material][2][5][ie]) && j==0){
       finalenergy=superparticle_energy-HWO[Material][0]+EC[Material][2]-EC[Material][1];
       if(finalenergy<0.) return;
       IV=1;
       j=1;
// determination of the final states
       kf = SMH[Material][IV]*sqrt(finalenergy*(1.+alphaK[Material][IV]*finalenergy));
       cs = 1.-2.*rnd();
       sn = sqrt(1.-cs*cs);
       fai = 2.*PI*rnd();
       KX = kf*cs;
       KY = kf*sn*cos(fai);
       KZ = kf*sn*sin(fai);
       return;
    }
// Absorbation
    if((r1<=SWK[Material][2][6][ie]) && j==0){
       finalenergy=superparticle_energy+HWO[Material][0]+EC[Material][2]-EC[Material][1];
       if(finalenergy<0.) return;
       IV=1;
       j=1;
// determination of the final states
       kf = SMH[Material][IV]*sqrt(finalenergy*(1.+alphaK[Material][IV]*finalenergy));
       cs = 1.-2.*rnd();
       sn = sqrt(1.-cs*cs);
       fai = 2.*PI*rnd();
       KX = kf*cs;
       KY = kf*sn*cos(fai);
       KZ = kf*sn*sin(fai);
       return;
    }
// Acoustic phonon emission
    if((r1<=SWK[Material][2][7][ie]) && j==0){
       finalenergy=superparticle_energy;
       if(finalenergy<0.) return;
       finalk=sqrt(ksquared);
       j=1;
// determination of the final states
       kf = SMH[Material][IV]*sqrt(finalenergy*(1.+alphaK[Material][IV]*finalenergy));
       cs = 1.-2.*rnd();
       sn = sqrt(1.-cs*cs);
       fai = 2.*PI*rnd();
       KX = kf*cs;
       KY = kf*sn*cos(fai);
       KZ = kf*sn*sin(fai);
       return;
    }
// Impurity scattering
    if((r1<=SWK[Material][2][8][ie]) && j==0){
     finalenergy=superparticle_energy;
     if(finalenergy<0.) return;
     r2=rnd();
     cb=1.-r2/(0.5+(1.-r2)*ksquared/QD2);
     kf=ki;
// linea 30 -- determination of the final states
     sb=sqrt(1.-cb*cb);
     fai=2.*PI*rnd();
     cf=cos(fai);
     sf=sin(fai);
     skk=sqrt(KX*KX+KY*KY);
     a11=KY/skk;
     a12=KX*KZ/skk/ki;
     a13=KX/ki;
     a21=-KX/skk;
     a22=KY*KZ/skk/ki;
     a23=KY/ki;
     a32=-skk/ki;
     a33=KZ/ki;
     x1=kf*sb*cf;
     x2=kf*sb*sf;
     x3=kf*cb;
     KX=a11*x1+a12*x2+a13*x3;
     KY=a21*x1+a22*x2+a23*x3;
     KZ=a32*x2+a33*x3;
     return;     
    }

// Impact ionization
    if((r1<=SWK[Material][2][9][ie]) && j==0){
       ra1=0.5-rnd();
       ra2=pow(rnd(),2.);
       finalenergy=bbb*superparticle_energy*(1.0+aaa*ra1*ra2);
       finalenergy=superparticle_energy-finalenergy;
       j=1;
    }
    if((finalenergy<=0.) || j==0) return;

// determination of the final states
    finalk = SMH[Material][2]*sqrt(finalenergy*(1.+alphaK[Material][2]*finalenergy));
    cosinus = 1.-2.*rnd();
    sinus = sqrt(1.-cosinus*cosinus);
    fai = 2.*PI*rnd();
    KX = finalk*cosinus;
    KY = finalk*sinus*cos(fai);
    KZ = finalk*sinus*sin(fai);
    return;
   }
  }
}

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