src/material/Si/Si_mob_Philips.cc

   1 /*****************************************************************************/
   2 /*                                                                           */
   3 /*              8888888         88888888         88888888                    */
   4 /*            8                8                8                            */
   5 /*           8                 8                8                            */
   6 /*           8                  88888888         88888888                    */
   7 /*           8      8888                8                8                   */
   8 /*            8       8                 8                8                   */
   9 /*              888888         888888888        888888888                    */
  10 /*                                                                           */
  11 /*       A Two-Dimensional General Purpose Semiconductor Simulator.          */
  12 /*                                                                           */
  13 /*  GSS material database Version 0.4                                        */
  14 /*  Last update: Feb 17, 2006                                                */
  15 /*                                                                           */
  16 /*  Gong Ding                                                                */
  17 /*  gdiso@ustc.edu                                                           */
  18 /*  NINT, No.69 P.O.Box, Xi'an City, China                                   */
  19 /*                                                                           */
  20 /*****************************************************************************/
  21 //
  22 // Material Type: Silicon
  23
  24
  25 #include "PMI.h"
  26
  27 class GSS_Mob_Philips : public PMIS_Mobility
  28 {
  29 private:
  30   // parameters for Philips mobility
  31   PetscScalar MMNN_UM;
  32   PetscScalar MMXN_UM;
  33   PetscScalar NRFN_UM;
  34   PetscScalar ALPN_UM;
  35   PetscScalar TETN_UM;
  36   PetscScalar NRFD_UM;
  37   PetscScalar CRFD_UM;
  38
  39   PetscScalar MMNP_UM;
  40   PetscScalar MMXP_UM;
  41   PetscScalar NRFP_UM;
  42   PetscScalar ALPP_UM;
  43   PetscScalar TETP_UM;
  44   PetscScalar NRFA_UM;
  45   PetscScalar CRFA_UM;
  46   PetscScalar NSC_REF;
  47   PetscScalar CAR_REF;
  48   PetscScalar me_over_m0;
  49   PetscScalar mh_over_m0;
  50   PetscScalar me_over_mh;
  51   // temperature
  52   PetscScalar T300;
  53   // parameters for high field modification
  54   PetscScalar BETAN;
  55   PetscScalar BETAP;
  56   void Mob_Philips_Init()
  57   {
  58     MMNN_UM = 5.220000E+01*cm*cm/V/s;
  59     MMXN_UM = 1.417000E+03*cm*cm/V/s;
  60     NRFN_UM = 9.680000E+16*pow(cm,-3);
  61     ALPN_UM = 6.800000E-01;
  62     TETN_UM = 2.285000E+00;
  63     NRFD_UM = 4.000000E+20*pow(cm,-3);
  64     CRFD_UM = 2.100000E-01;
  65
  66     MMNP_UM = 4.490000E+01*cm*cm/V/s;
  67     MMXP_UM = 4.705000E+02*cm*cm/V/s;
  68     NRFP_UM = 2.230000E+17*pow(cm,-3);
  69     ALPP_UM = 7.190000E-01;
  70     TETP_UM = 2.247000E+00;
  71     NRFA_UM = 7.200000E+20*pow(cm,-3);
  72     CRFA_UM = 5.000000E-01;
  73
  74     NSC_REF = 3.97e13*pow(cm,-2);
  75     CAR_REF = 1.36e20*pow(cm,-3);
  76     me_over_m0 = 1.0;
  77     mh_over_m0 = 1.258;
  78     me_over_mh = 1.0/1.258;
  79     T300    = 300.0*K;
  80
  81     BETAN   = 2.000000E+00;
  82     BETAP   = 1.000000E+00;
  83   }
  84
  85   //---------------------------------------------------------------------------
  86   // Electron low field mobility
  87   PetscScalar ElecMobPhilips(const PetscScalar &p,const PetscScalar &n,const PetscScalar &Tl) const
  88   {
  89     PetscScalar mu_lattice = MMXN_UM*pow(Tl/T300,-TETN_UM);
  90     PetscScalar mu1 = MMXN_UM*MMXN_UM/(MMXN_UM-MMNN_UM)*pow(Tl/T300,3*ALPN_UM-1.5);
  91     PetscScalar mu2 = MMXN_UM*MMNN_UM/(MMXN_UM-MMNN_UM)*sqrt(T300/Tl);
  92     PetscScalar Na  = ReadDopingNa()+1e0*pow(cm,-3);
  93     PetscScalar Nd  = ReadDopingNd()+1e0*pow(cm,-3);
  94     PetscScalar Nds = Nd*(1.0+1.0/(CRFD_UM+(NRFD_UM/Nd)*(NRFD_UM/Nd)));
  95     PetscScalar Nas = Na*(1.0+1.0/(CRFA_UM+(NRFA_UM/Na)*(NRFA_UM/Na)));
  96     PetscScalar Nsc = Nds+Nas+fabs(p);
  97
  98     PetscScalar P   = 1.0/(2.459/(NSC_REF/pow(Nsc,PetscScalar(2.0/3.0)))+3.828/(CAR_REF/fabs(n+p)*me_over_m0))*(Tl/T300)*(Tl/T300);
  99     PetscScalar pp1 = pow(P,PetscScalar(0.6478));
 100     PetscScalar F   = (0.7643*pp1+2.2999+6.5502*me_over_mh)/(pp1+2.3670-0.8552*me_over_mh);
 101     //PetscScalar G   = 1-0.89233/pow(0.41372+P*pow(Tl/T300/me_over_m0,0.28227),0.19778)+0.005978/pow(P*pow(Tl/T300/me_over_m0,0.72169),1.80618);
 102     PetscScalar G   = 1-4.41804/pow(39.9014+P*pow(Tl/T300/me_over_m0,PetscScalar(0.0001)),PetscScalar(0.38297))+0.52896/pow(P*pow(T300/Tl*me_over_m0,PetscScalar(1.595787)),PetscScalar(0.25948));
 103     PetscScalar Nsce = Nds+Nas*G+fabs(p)/F;
 104     PetscScalar mu_scatt = mu1*(Nsc/Nsce)*pow(NRFN_UM/Nsc,ALPN_UM)+mu2*(fabs(n+p)/Nsce);
 105     return 1.0/(1.0/mu_lattice+1.0/mu_scatt);
 106   }
 107   AutoDScalar ElecMobPhilips(const AutoDScalar &p,const AutoDScalar &n,const AutoDScalar &Tl) const
 108   {
 109     AutoDScalar mu_lattice = MMXN_UM*pow(Tl/T300,-TETN_UM);
 110     AutoDScalar mu1 = MMXN_UM*MMXN_UM/(MMXN_UM-MMNN_UM)*pow(Tl/T300,3*ALPN_UM-1.5);
 111     AutoDScalar mu2 = MMXN_UM*MMNN_UM/(MMXN_UM-MMNN_UM)*sqrt(T300/Tl);
 112     PetscScalar Na  = ReadDopingNa()+1e0*pow(cm,-3);
 113     PetscScalar Nd  = ReadDopingNd()+1e0*pow(cm,-3);
 114     PetscScalar Nds = Nd*(1.0+1.0/(CRFD_UM+(NRFD_UM/Nd)*(NRFD_UM/Nd)));
 115     PetscScalar Nas = Na*(1.0+1.0/(CRFA_UM+(NRFA_UM/Na)*(NRFA_UM/Na)));
 116     AutoDScalar Nsc = Nds+Nas+fabs(p);
 117
 118     AutoDScalar P   = 1.0/(2.459/(NSC_REF/pow(Nsc,PetscScalar(2.0/3.0)))+3.828/(CAR_REF/fabs(n+p)*me_over_m0))*(Tl/T300)*(Tl/T300);
 119     AutoDScalar pp1 = pow(P,PetscScalar(0.6478));
 120     AutoDScalar F   = (0.7643*pp1+2.2999+6.5502*me_over_mh)/(pp1+2.3670-0.8552*me_over_mh);
 121     //PetscScalar G   = 1-0.89233/pow(0.41372+P*pow(Tl/T300/me_over_m0,0.28227),0.19778)+0.005978/pow(P*pow(Tl/T300/me_over_m0,0.72169),1.80618);
 122     AutoDScalar G   = 1-4.41804/pow(39.9014+P*pow(Tl/T300/me_over_m0,PetscScalar(0.0001)),PetscScalar(0.38297))+0.52896/pow(P*pow(T300/Tl*me_over_m0,PetscScalar(1.595787)),PetscScalar(0.25948));
 123     AutoDScalar Nsce = Nds+Nas*G+fabs(p)/F;
 124     AutoDScalar mu_scatt = mu1*(Nsc/Nsce)*pow(NRFN_UM/Nsc,ALPN_UM)+mu2*(fabs(n+p)/Nsce);
 125     return 1.0/(1.0/mu_lattice+1.0/mu_scatt);
 126   }
 127
 128   //---------------------------------------------------------------------------
 129   // Hole low field mobility
 130   PetscScalar HoleMobPhilips(const PetscScalar &p,const PetscScalar &n,const PetscScalar &Tl) const
 131   {
 132     PetscScalar mu_lattice = MMXP_UM*pow(Tl/T300,-TETP_UM);
 133     PetscScalar mu1 = MMXP_UM*MMXP_UM/(MMXP_UM-MMNP_UM)*pow(Tl/T300,3*ALPP_UM-1.5);
 134     PetscScalar mu2 = MMXP_UM*MMNP_UM/(MMXP_UM-MMNP_UM)*sqrt(T300/Tl);
 135     PetscScalar Na  = ReadDopingNa()+1e0*pow(cm,-3);
 136     PetscScalar Nd  = ReadDopingNd()+1e0*pow(cm,-3);
 137     PetscScalar Nds = Nd*(1.0+1.0/(CRFD_UM+(NRFD_UM/Nd)*(NRFD_UM/Nd)));
 138     PetscScalar Nas = Na*(1.0+1.0/(CRFA_UM+(NRFA_UM/Na)*(NRFA_UM/Na)));
 139     PetscScalar Nsc = Nds+Nas+fabs(n);
 140
 141     PetscScalar P   = 1.0/(2.459/(NSC_REF/pow(Nsc,PetscScalar(2.0/3.0)))+3.828/(CAR_REF/fabs(n+p)*mh_over_m0))*(Tl/T300)*(Tl/T300);
 142     PetscScalar pp1 = pow(P,PetscScalar(0.6478));
 143     PetscScalar F   = (0.7643*pp1+2.2999+6.5502/me_over_mh)/(pp1+2.3670-0.8552/me_over_mh);
 144     //PetscScalar G = 1-0.89233/pow(0.41372+P*pow(Tl/T300/mh_over_m0,0.28227),0.19778)+0.005978/pow(P*pow(Tl/T300/mh_over_m0,0.72169),1.80618);
 145     PetscScalar G   = 1-4.41804/pow(39.9014+P*pow(Tl/T300/mh_over_m0,PetscScalar(0.0001)),PetscScalar(0.38297))+0.52896/pow(P*pow(T300/Tl*mh_over_m0,PetscScalar(1.595787)),PetscScalar(0.25948));
 146     PetscScalar Nsce = Nas+Nds*G+fabs(n)/F;
 147     PetscScalar mu_scatt = mu1*(Nsc/Nsce)*pow(NRFP_UM/Nsc,ALPP_UM)+mu2*(fabs(n+p)/Nsce);
 148     return 1.0/(1.0/mu_lattice+1.0/mu_scatt);
 149   }
 150   AutoDScalar HoleMobPhilips(const AutoDScalar &p,const AutoDScalar &n,const AutoDScalar &Tl) const
 151   {
 152     AutoDScalar mu_lattice = MMXP_UM*pow(Tl/T300,-TETP_UM);
 153     AutoDScalar mu1 = MMXP_UM*MMXP_UM/(MMXP_UM-MMNP_UM)*pow(Tl/T300,3*ALPP_UM-1.5);
 154     AutoDScalar mu2 = MMXP_UM*MMNP_UM/(MMXP_UM-MMNP_UM)*sqrt(T300/Tl);
 155     PetscScalar Na  = ReadDopingNa()+1e0*pow(cm,-3);
 156     PetscScalar Nd  = ReadDopingNd()+1e0*pow(cm,-3);
 157     PetscScalar Nds = Nd*(1.0+1.0/(CRFD_UM+(NRFD_UM/Nd)*(NRFD_UM/Nd)));
 158     PetscScalar Nas = Na*(1.0+1.0/(CRFA_UM+(NRFA_UM/Na)*(NRFA_UM/Na)));
 159     AutoDScalar Nsc = Nds+Nas+fabs(n);
 160
 161     AutoDScalar P   = 1.0/(2.459/(NSC_REF/pow(Nsc,PetscScalar(2.0/3.0)))+3.828/(CAR_REF/fabs(n+p)*mh_over_m0))*(Tl/T300)*(Tl/T300);
 162     AutoDScalar pp1 = pow(P,PetscScalar(0.6478));
 163     AutoDScalar F   = (0.7643*pp1+2.2999+6.5502/me_over_mh)/(pp1+2.3670-0.8552/me_over_mh);
 164     //PetscScalar G = 1-0.89233/pow(0.41372+P*pow(Tl/T300/mh_over_m0,0.28227),0.19778)+0.005978/pow(P*pow(Tl/T300/mh_over_m0,0.72169),1.80618);
 165     AutoDScalar G   = 1-4.41804/pow(39.9014+P*pow(Tl/T300/mh_over_m0,PetscScalar(0.0001)),PetscScalar(0.38297))+0.52896/pow(P*pow(T300/Tl*mh_over_m0,PetscScalar(1.595787)),PetscScalar(0.25948));
 166     AutoDScalar Nsce = Nas+Nds*G+fabs(n)/F;
 167     AutoDScalar mu_scatt = mu1*(Nsc/Nsce)*pow(NRFP_UM/Nsc,ALPP_UM)+mu2*(fabs(n+p)/Nsce);
 168     return 1.0/(1.0/mu_lattice+1.0/mu_scatt);
 169   }
 170 public:
 171
 172   //---------------------------------------------------------------------------
 173   // Electron mobility
 174   PetscScalar ElecMob(const PetscScalar &p, const PetscScalar &n, const PetscScalar &Tl,
 175                       const PetscScalar &Ep, const PetscScalar &Et, const PetscScalar &Tn) const
 176   {
 177     PetscScalar vsat = (2.4e7*cm/s)/(1+0.8*exp(Tl/(2*T300)));
 178     PetscScalar mu0  = ElecMobPhilips(p,n,Tl);
 179     return mu0/pow(1+pow(mu0*fabs(Ep)/vsat,BETAN),1.0/BETAN);
 180   }
 181   AutoDScalar ElecMob(const AutoDScalar &p, const AutoDScalar &n, const AutoDScalar &Tl,
 182                       const AutoDScalar &Ep, const AutoDScalar &Et, const AutoDScalar &Tn) const
 183   {
 184     AutoDScalar vsat = (2.4e7*cm/s)/(1+0.8*exp(Tl/(2*T300)));
 185     AutoDScalar mu0  = ElecMobPhilips(p,n,Tl);
 186     return mu0/pow(1+pow(mu0*fabs(Ep)/vsat,BETAN),1.0/BETAN);
 187   }
 188
 189   //---------------------------------------------------------------------------
 190   // Hole mobility
 191   PetscScalar HoleMob (const PetscScalar &p, const PetscScalar &n, const PetscScalar &Tl,
 192                        const PetscScalar &Ep, const PetscScalar &Et, const PetscScalar &Tp) const
 193   {
 194     PetscScalar vsat = (2.4e7*cm/s)/(1+0.8*exp(Tl/(2*T300)));
 195     PetscScalar mu0  = HoleMobPhilips(p,n,Tl);
 196     return mu0/pow(1+pow(mu0*fabs(Ep)/vsat,BETAP),1.0/BETAP);
 197   }
 198   AutoDScalar HoleMob(const AutoDScalar &p, const AutoDScalar &n, const AutoDScalar &Tl,
 199                       const AutoDScalar &Ep, const AutoDScalar &Et, const AutoDScalar &Tp) const
 200   {
 201     AutoDScalar vsat = (2.4e7*cm/s)/(1+0.8*exp(Tl/(2*T300)));
 202     AutoDScalar mu0  = HoleMobPhilips(p,n,Tl);
 203     return mu0/pow(1+pow(mu0*fabs(Ep)/vsat,BETAP),1.0/BETAP);
 204   }
 205
 206 // constructor
 207 public:
 208   GSS_Mob_Philips(const PMIS_Environment &env):PMIS_Mobility(env)
 209   {
 210     Mob_Philips_Init();
 211   }
 212   ~GSS_Mob_Philips(){}
 213 }
 214 ;
 215
 216 /*---------------------------------------------------------------
 217  *  the interface function called by material databse controller
 218  *  and it setup Philips mobility model
 219  */
 220 extern "C"
 221 {
 222   PMIS_Mobility* PMIS_Si_Mob_Philips (const PMIS_Environment& env)
 223   {
 224     return new GSS_Mob_Philips(env);
 225   }
 226 }