src/material/SiGe/SiGe_mob_Lombardi.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: July 26, 2007                                               */
  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: Si(1-x)Ge(x). (in fact, use parameters for Si instead.)
  23
  24
  25 #include "PMI.h"
  26
  27 class GSS_Mob_Lombardi : public PMIS_Mobility
  28 {
  29 private:
  30   PetscScalar EXN1_LSM;
  31   PetscScalar EXN2_LSM;
  32   PetscScalar EXN3_LSM;
  33   PetscScalar EXN4_LSM;
  34   PetscScalar EXN8_LSM;
  35   PetscScalar MUN0_LSM;
  36   PetscScalar MUN1_LSM;
  37   PetscScalar MUN2_LSM;
  38   PetscScalar CRN_LSM;
  39   PetscScalar CSN_LSM;
  40   PetscScalar BN_LSM;
  41   PetscScalar CN_LSM;
  42   PetscScalar DN_LSM;
  43
  44   PetscScalar EXP1_LSM;
  45   PetscScalar EXP2_LSM;
  46   PetscScalar EXP3_LSM;
  47   PetscScalar EXP4_LSM;
  48   PetscScalar EXP8_LSM;
  49   PetscScalar MUP0_LSM;
  50   PetscScalar MUP1_LSM;
  51   PetscScalar MUP2_LSM;
  52   PetscScalar CRP_LSM;
  53   PetscScalar CSP_LSM;
  54   PetscScalar BP_LSM;
  55   PetscScalar CP_LSM;
  56   PetscScalar DP_LSM;
  57   PetscScalar PC_LSM;
  58
  59   // parameters for parallel field modification
  60   PetscScalar BETAN;
  61   PetscScalar BETAP;
  62   PetscScalar T300;
  63
  64   void Mob_Lombardi_Init()
  65   {
  66     EXN1_LSM=6.800000E-01;
  67     EXN2_LSM=2.000000E+00;
  68     EXN3_LSM=2.500000E+00;
  69     EXN4_LSM=1.250000E-01;
  70     EXN8_LSM=2.000000E+00;
  71     MUN0_LSM=5.220000E+01*cm*cm/V/s;
  72     MUN1_LSM=4.340000E+01*cm*cm/V/s;
  73     MUN2_LSM=1.417000E+03*cm*cm/V/s;
  74     CRN_LSM=9.680000E+16*pow(cm,-3);
  75     CSN_LSM=3.430000E+20*pow(cm,-3);
  76     BN_LSM=4.750000E+07*cm/s;
  77     CN_LSM=1.740000E+05*K*cm/s*pow(V/cm,PetscScalar(-2.0/3.0))*pow(cm,3*EXN4_LSM);
  78     DN_LSM=5.820000E+14*cm*cm/V/s*pow(V/cm,EXN8_LSM);
  79
  80     EXP1_LSM=7.190000E-01;
  81     EXP2_LSM=2.000000E+00;
  82     EXP3_LSM=2.200000E+00;
  83     EXP4_LSM=3.170000E-02;
  84     EXP8_LSM=2.000000E+00;
  85     MUP0_LSM=4.490000E+01*cm*cm/V/s;
  86     MUP1_LSM=2.900000E+01*cm*cm/V/s;
  87     MUP2_LSM=4.705000E+02*cm*cm/V/s;
  88     CRP_LSM=2.230000E+17*pow(cm,-3);
  89     CSP_LSM=6.100000E+20*pow(cm,-3);
  90     BP_LSM=9.930000E+06*cm/s;
  91     CP_LSM=8.840000E+05*K*cm/s*pow(V/cm,PetscScalar(-2.0/3.0))*pow(cm,3*EXP4_LSM);;
  92     DP_LSM=2.050000E+14*cm*cm/V/s*pow(V/cm,EXN8_LSM);
  93     PC_LSM=9.230000E+16*pow(cm,-3);
  94
  95     BETAN = 2.000000E+00;
  96     BETAP = 1.000000E+00;
  97     T300  = 300.0*K;
  98   }
  99   //---------------------------------------------------------------------------
 100   // Electron low field mobility
 101   PetscScalar ElecMobLowField(const PetscScalar &Tl) const
 102   {
 103     PetscScalar Na = ReadDopingNa();
 104     PetscScalar Nd = ReadDopingNd();
 105     PetscScalar N_total = Na+Nd+1e0*pow(cm,-3);
 106     PetscScalar mu_max = MUN2_LSM*pow(Tl/T300,-EXN3_LSM);
 107     return MUN0_LSM+(mu_max-MUN0_LSM)/(1+pow(N_total/CRN_LSM,EXN1_LSM))-MUN1_LSM/(1+pow(CSN_LSM/N_total,EXN2_LSM));
 108   }
 109   AutoDScalar ElecMobLowField(const AutoDScalar &Tl) const
 110   {
 111     PetscScalar Na = ReadDopingNa();
 112     PetscScalar Nd = ReadDopingNd();
 113     PetscScalar N_total = Na+Nd+1e0*pow(cm,-3);
 114     AutoDScalar mu_max = MUN2_LSM*pow(Tl/T300,-EXN3_LSM);
 115     return MUN0_LSM+(mu_max-MUN0_LSM)/(1+pow(N_total/CRN_LSM,EXN1_LSM))-MUN1_LSM/(1+pow(CSN_LSM/N_total,EXN2_LSM));
 116   }
 117
 118   //---------------------------------------------------------------------------
 119   // Hole low field mobility, Analytic model
 120   PetscScalar HoleMobLowField(const PetscScalar &Tl) const
 121   {
 122     PetscScalar Na = ReadDopingNa();
 123     PetscScalar Nd = ReadDopingNd();
 124     PetscScalar N_total = Na+Nd+1e0*pow(cm,-3);
 125     PetscScalar mu_max = MUP2_LSM*pow(Tl/T300,-EXP3_LSM);
 126     return MUP0_LSM*exp(-PC_LSM/N_total)+mu_max/(1+pow(N_total/CRP_LSM,EXP1_LSM))-MUP1_LSM/(1+pow(CSP_LSM/N_total,EXP2_LSM));
 127   }
 128   AutoDScalar HoleMobLowField(const AutoDScalar &Tl) const
 129   {
 130     PetscScalar Na = ReadDopingNa();
 131     PetscScalar Nd = ReadDopingNd();
 132     PetscScalar N_total = Na+Nd+1e0*pow(cm,-3);
 133     AutoDScalar mu_max = MUP2_LSM*pow(Tl/T300,-EXP3_LSM);
 134     return MUP0_LSM*exp(-PC_LSM/N_total)+mu_max/(1+pow(N_total/CRP_LSM,EXP1_LSM))-MUP1_LSM/(1+pow(CSP_LSM/N_total,EXP2_LSM));
 135   }
 136
 137   //---------------------------------------------------------------------------
 138   // Electron surface mobility, acoustical phono scattering and roughness scattering
 139   PetscScalar ElecMobSurface(const PetscScalar &Tl,const PetscScalar &Et) const
 140   {
 141     PetscScalar Na = ReadDopingNa();
 142     PetscScalar Nd = ReadDopingNd();
 143     PetscScalar N_total = Na+Nd+1e0*pow(cm,-3);
 144     PetscScalar ET = Et+1.0*V/cm;
 145     PetscScalar mu_ac = BN_LSM/ET + CN_LSM*pow(N_total,EXN4_LSM)/Tl*pow(ET,PetscScalar(-1.0/3.0));
 146     PetscScalar mu_sr = DN_LSM*pow(ET,-EXN8_LSM);
 147     return 1.0/(1.0/mu_ac+1.0/mu_sr);
 148   }
 149   AutoDScalar ElecMobSurface(const AutoDScalar &Tl,const AutoDScalar &Et) const
 150   {
 151     PetscScalar Na = ReadDopingNa();
 152     PetscScalar Nd = ReadDopingNd();
 153     PetscScalar N_total = Na+Nd+1e0*pow(cm,-3);
 154     AutoDScalar ET = Et+1.0*V/cm;
 155     AutoDScalar mu_ac = BN_LSM/ET + CN_LSM*pow(N_total,EXN4_LSM)/Tl*pow(ET,PetscScalar(-1.0/3.0));
 156     AutoDScalar mu_sr = DN_LSM*pow(ET,-EXN8_LSM);
 157     return 1.0/(1.0/mu_ac+1.0/mu_sr);
 158   }
 159
 160   //---------------------------------------------------------------------------
 161   // Hole surface mobility, acoustical phono scattering and roughness scattering
 162   PetscScalar HoleMobSurface(const PetscScalar &Tl,const PetscScalar &Et) const
 163   {
 164     PetscScalar Na = ReadDopingNa();
 165     PetscScalar Nd = ReadDopingNd();
 166     PetscScalar N_total = Na+Nd+1e0*pow(cm,-3);
 167     PetscScalar ET = Et+1.0*V/cm;
 168     PetscScalar mu_ac = BP_LSM/ET + CP_LSM*pow(N_total,EXP4_LSM)/Tl*pow(ET,PetscScalar(-1.0/3.0));
 169     PetscScalar mu_sr = DN_LSM*pow(ET,-EXP8_LSM);
 170     return 1.0/(1.0/mu_ac+1.0/mu_sr);
 171   }
 172   AutoDScalar HoleMobSurface(const AutoDScalar &Tl,const AutoDScalar &Et) const
 173   {
 174     PetscScalar Na = ReadDopingNa();
 175     PetscScalar Nd = ReadDopingNd();
 176     PetscScalar N_total = Na+Nd+1e0*pow(cm,-3);
 177     AutoDScalar ET = Et+1.0*V/cm;
 178     AutoDScalar mu_ac = BP_LSM/ET + CP_LSM*pow(N_total,EXP4_LSM)/Tl*pow(ET+1.0*V/cm,PetscScalar(-1.0/3.0));
 179     AutoDScalar mu_sr = DN_LSM*pow(ET,-EXP8_LSM);
 180     return 1.0/(1.0/mu_ac+1.0/mu_sr);
 181   }
 182
 183
 184 public:
 185
 186   //---------------------------------------------------------------------------
 187   // Electron mobility
 188   PetscScalar ElecMob(const PetscScalar &p, const PetscScalar &n, const PetscScalar &Tl,
 189                       const PetscScalar &Ep, const PetscScalar &Et, const PetscScalar &Tn) const
 190   {
 191     PetscScalar vsat = (2.4e7*cm/s)/(1+0.8*exp(Tl/(2*T300)));
 192     PetscScalar mu0  = 1.0/(1.0/ElecMobLowField(Tl)+1.0/ElecMobSurface(Tl,Et));
 193     return mu0/pow(1+pow(mu0*fabs(Ep)/vsat,BETAN),1.0/BETAN);
 194   }
 195   AutoDScalar ElecMob(const AutoDScalar &p, const AutoDScalar &n, const AutoDScalar &Tl,
 196                       const AutoDScalar &Ep, const AutoDScalar &Et, const AutoDScalar &Tn) const
 197   {
 198     AutoDScalar vsat = (2.4e7*cm/s)/(1+0.8*exp(Tl/(2*T300)));
 199     AutoDScalar mu0  = 1.0/(1.0/ElecMobLowField(Tl)+1.0/ElecMobSurface(Tl,Et));
 200     return mu0/pow(1+pow(mu0*fabs(Ep)/vsat,BETAN),1.0/BETAN);
 201   }
 202
 203   //---------------------------------------------------------------------------
 204   // Hole mobility
 205   PetscScalar HoleMob (const PetscScalar &p, const PetscScalar &n, const PetscScalar &Tl,
 206                        const PetscScalar &Ep, const PetscScalar &Et, const PetscScalar &Tp) const
 207   {
 208     PetscScalar vsat = (2.4e7*cm/s)/(1+0.8*exp(Tl/(2*T300)));
 209     PetscScalar mu0  = 1.0/(1.0/HoleMobLowField(Tl)+1.0/HoleMobSurface(Tl,Et));
 210     return mu0/pow(1+pow(mu0*fabs(Ep)/vsat,BETAP),1.0/BETAP);
 211   }
 212   AutoDScalar HoleMob(const AutoDScalar &p, const AutoDScalar &n, const AutoDScalar &Tl,
 213                       const AutoDScalar &Ep, const AutoDScalar &Et, const AutoDScalar &Tp) const
 214   {
 215     AutoDScalar vsat = (2.4e7*cm/s)/(1+0.8*exp(Tl/(2*T300)));
 216     AutoDScalar mu0  = 1.0/(1.0/HoleMobLowField(Tl)+1.0/HoleMobSurface(Tl,Et));
 217     return mu0/pow(1+pow(mu0*fabs(Ep)/vsat,BETAP),1.0/BETAP);
 218   }
 219
 220 // constructor
 221 public:
 222   GSS_Mob_Lombardi(const PMIS_Environment &env):PMIS_Mobility(env)
 223   {
 224     Mob_Lombardi_Init();
 225   }
 226
 227   ~GSS_Mob_Lombardi(){}
 228 }
 229 ;
 230
 231 /*---------------------------------------------------------------
 232  *  the interface function called by material databse controller
 233  *  and it setup Lucent mobility model
 234  */
 235 extern "C"
 236 {
 237   PMIS_Mobility* PMIS_SiGe_Mob_Lombardi (const PMIS_Environment& env)
 238   {
 239     return new GSS_Mob_Lombardi(env);
 240   }
 241 }