src/material/SiGe/SiGe_mob_Lucent.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: Si(1-x)Ge(x). (in fact, use parameters for Si instead.)
  23
  24
  25 #include "PMI.h"
  26
  27 class GSS_Mob_Lucent : public PMIS_Mobility
  28 {
  29 private:
  30   // parameters for Lucent 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 transvers field modification
  54   PetscScalar AN_LUC;
  55   PetscScalar AP_LUC;
  56   PetscScalar BN_LUC;
  57   PetscScalar BP_LUC;
  58   PetscScalar CN_LUC;
  59   PetscScalar CP_LUC;
  60   //PetscScalar DN_LUC;
  61   //PetscScalar DP_LUC;
  62   PetscScalar FN_LUC;
  63   PetscScalar FP_LUC;
  64   PetscScalar KN_LUC;
  65   PetscScalar KP_LUC;
  66   PetscScalar EXN4_LUC;
  67   PetscScalar EXP4_LUC;
  68   PetscScalar EXN9_LUC;
  69   PetscScalar EXP9_LUC;
  70   // parameters for parallel field modification
  71   PetscScalar BETAN;
  72   PetscScalar BETAP;
  73
  74   void Mob_Lucent_Init()
  75   {
  76     MMNN_UM = 5.220000E+01*cm*cm/V/s;
  77     MMXN_UM = 1.417000E+03*cm*cm/V/s;
  78     NRFN_UM = 9.680000E+16*pow(cm,-3);
  79     ALPN_UM = 6.800000E-01;
  80     TETN_UM = 2.285000E+00;
  81     NRFD_UM = 4.000000E+20*pow(cm,-3);
  82     CRFD_UM = 2.100000E-01;
  83
  84     MMNP_UM = 4.490000E+01*cm*cm/V/s;
  85     MMXP_UM = 4.705000E+02*cm*cm/V/s;
  86     NRFP_UM = 2.230000E+17*pow(cm,-3);
  87     ALPP_UM = 7.190000E-01;
  88     TETP_UM = 2.247000E+00;
  89     NRFA_UM = 7.200000E+20*pow(cm,-3);
  90     CRFA_UM = 5.000000E-01;
  91
  92     NSC_REF = 3.97e13*pow(cm,-2);
  93     CAR_REF = 1.36e20*pow(cm,-3);
  94     me_over_m0 = 1.0;
  95     mh_over_m0 = 1.258;
  96     me_over_mh = 1.0/1.258;
  97     T300    = 300.0*K;
  98
  99     EXN4_LUC = 2.330000E-02;
 100     EXP4_LUC = 1.190000E-02;
 101     EXN9_LUC = 7.670000E-02;
 102     EXP9_LUC = 1.230000E-01;
 103     AN_LUC   = 2.580000E+00;
 104     AP_LUC   = 2.180000E+00;
 105     BN_LUC   = 3.610000E+07*cm/s;
 106     BP_LUC   = 1.510000E+07*cm/s;
 107     CN_LUC   = 1.700000E+04*cm*cm/V/s*pow(V/cm,PetscScalar(1.0/3.0))*pow(cm,3*EXN4_LUC);
 108     CP_LUC   = 4.180000E+03*cm*cm/V/s*pow(V/cm,PetscScalar(1.0/3.0))*pow(cm,3*EXP4_LUC);
 109     //DN_LUC=3.580000E+18*cm*cm/V/s*pow(V/cm,rn);
 110     //DP_LUC=4.100000E+15*cm*cm/V/s*pow(V/cm,rp);
 111     FN_LUC   = 6.850000E-21*pow(cm,3*(1-EXN9_LUC));
 112     FP_LUC   = 7.820000E-21*pow(cm,3*(1-EXP9_LUC));
 113     KN_LUC   = 1.700000E+00;
 114     KP_LUC   = 9.000000E-01;
 115
 116     BETAN = 2.000000E+00;
 117     BETAP = 1.000000E+00;
 118
 119   }
 120   //---------------------------------------------------------------------------
 121   // Electron low field bulk mobility
 122   PetscScalar ElecMobPhilips(const PetscScalar &p,const PetscScalar &n,const PetscScalar &Tl) const
 123   {
 124     PetscScalar mu_lattice = MMXN_UM*pow(Tl/T300,-TETN_UM);
 125     PetscScalar mu1 = MMXN_UM*MMXN_UM/(MMXN_UM-MMNN_UM)*pow(Tl/T300,3*ALPN_UM-1.5);
 126     PetscScalar mu2 = MMXN_UM*MMNN_UM/(MMXN_UM-MMNN_UM)*sqrt(T300/Tl);
 127     PetscScalar Na  = ReadDopingNa()+1e0*pow(cm,-3);
 128     PetscScalar Nd  = ReadDopingNd()+1e0*pow(cm,-3);
 129     PetscScalar Nds = Nd*(1.0+1.0/(CRFD_UM+(NRFD_UM/Nd)*(NRFD_UM/Nd)));
 130     PetscScalar Nas = Na*(1.0+1.0/(CRFA_UM+(NRFA_UM/Na)*(NRFA_UM/Na)));
 131     PetscScalar Nsc = Nds+Nas+fabs(p);
 132
 133     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);
 134     PetscScalar pp1 = pow(P,PetscScalar(0.6478));
 135     PetscScalar F   = (0.7643*pp1+2.2999+6.5502*me_over_mh)/(pp1+2.3670-0.8552*me_over_mh);
 136     //PetscScalar G   = 1-0.89233/pow(0.41372+P*pow(Tl/T300/me_over_m0,PetscScalar(0.28227)),PetscScalar(0.19778))+0.005978/pow(P*pow(Tl/T300/me_over_m0,PetscScalar(0.72169)),PetscScalar(1.80618));
 137     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));
 138     PetscScalar Nsce = Nds+Nas*G+fabs(p)/F;
 139     PetscScalar mu_scatt = mu1*(Nsc/Nsce)*pow(NRFN_UM/Nsc,ALPN_UM)+mu2*(fabs(n+p)/Nsce);
 140     return 1.0/(1.0/mu_lattice+1.0/mu_scatt);
 141   }
 142   AutoDScalar ElecMobPhilips(const AutoDScalar &p,const AutoDScalar &n,const AutoDScalar &Tl) const
 143   {
 144     AutoDScalar mu_lattice = MMXN_UM*pow(Tl/T300,-TETN_UM);
 145     AutoDScalar mu1 = MMXN_UM*MMXN_UM/(MMXN_UM-MMNN_UM)*pow(Tl/T300,3*ALPN_UM-1.5);
 146     AutoDScalar mu2 = MMXN_UM*MMNN_UM/(MMXN_UM-MMNN_UM)*sqrt(T300/Tl);
 147     PetscScalar Na  = ReadDopingNa()+1e0*pow(cm,-3);
 148     PetscScalar Nd  = ReadDopingNd()+1e0*pow(cm,-3);
 149     PetscScalar Nds = Nd*(1.0+1.0/(CRFD_UM+(NRFD_UM/Nd)*(NRFD_UM/Nd)));
 150     PetscScalar Nas = Na*(1.0+1.0/(CRFA_UM+(NRFA_UM/Na)*(NRFA_UM/Na)));
 151     AutoDScalar Nsc = Nds+Nas+fabs(p);
 152
 153     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);
 154     AutoDScalar pp1 = pow(P,PetscScalar(0.6478));
 155     AutoDScalar F   = (0.7643*pp1+2.2999+6.5502*me_over_mh)/(pp1+2.3670-0.8552*me_over_mh);
 156     //PetscScalar G   = 1-0.89233/pow(0.41372+P*pow(Tl/T300/me_over_m0,PetscScalar(0.28227)),PetscScalar(0.19778))+0.005978/pow(P*pow(Tl/T300/me_over_m0,PetscScalar(0.72169)),PetscScalar(1.80618));
 157     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));
 158     AutoDScalar Nsce = Nds+Nas*G+fabs(p)/F;
 159     AutoDScalar mu_scatt = mu1*(Nsc/Nsce)*pow(NRFN_UM/Nsc,ALPN_UM)+mu2*(fabs(n+p)/Nsce);
 160     return 1.0/(1.0/mu_lattice+1.0/mu_scatt);
 161   }
 162
 163   //---------------------------------------------------------------------------
 164   // Hole low field bulk mobility
 165   PetscScalar HoleMobPhilips(const PetscScalar &p,const PetscScalar &n,const PetscScalar &Tl) const
 166   {
 167     PetscScalar mu_lattice = MMXP_UM*pow(Tl/T300,-TETP_UM);
 168     PetscScalar mu1 = MMXP_UM*MMXP_UM/(MMXP_UM-MMNP_UM)*pow(Tl/T300,3*ALPP_UM-1.5);
 169     PetscScalar mu2 = MMXP_UM*MMNP_UM/(MMXP_UM-MMNP_UM)*sqrt(T300/Tl);
 170     PetscScalar Na  = ReadDopingNa()+1e0*pow(cm,-3);
 171     PetscScalar Nd  = ReadDopingNd()+1e0*pow(cm,-3);
 172     PetscScalar Nds = Nd*(1.0+1.0/(CRFD_UM+(NRFD_UM/Nd)*(NRFD_UM/Nd)));
 173     PetscScalar Nas = Na*(1.0+1.0/(CRFA_UM+(NRFA_UM/Na)*(NRFA_UM/Na)));
 174     PetscScalar Nsc = Nds+Nas+fabs(n);
 175
 176     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);
 177     PetscScalar pp1 = pow(P,PetscScalar(0.6478));
 178     PetscScalar F   = (0.7643*pp1+2.2999+6.5502/me_over_mh)/(pp1+2.3670-0.8552/me_over_mh);
 179     //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);
 180     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));
 181     PetscScalar Nsce = Nas+Nds*G+fabs(n)/F;
 182     PetscScalar mu_scatt = mu1*(Nsc/Nsce)*pow(NRFP_UM/Nsc,ALPP_UM)+mu2*(fabs(n+p)/Nsce);
 183     return 1.0/(1.0/mu_lattice+1.0/mu_scatt);
 184   }
 185   AutoDScalar HoleMobPhilips(const AutoDScalar &p,const AutoDScalar &n,const AutoDScalar &Tl) const
 186   {
 187     AutoDScalar mu_lattice = MMXP_UM*pow(Tl/T300,-TETP_UM);
 188     AutoDScalar mu1 = MMXP_UM*MMXP_UM/(MMXP_UM-MMNP_UM)*pow(Tl/T300,3*ALPP_UM-1.5);
 189     AutoDScalar mu2 = MMXP_UM*MMNP_UM/(MMXP_UM-MMNP_UM)*sqrt(T300/Tl);
 190     PetscScalar Na  = ReadDopingNa()+1e0*pow(cm,-3);
 191     PetscScalar Nd  = ReadDopingNd()+1e0*pow(cm,-3);
 192     PetscScalar Nds = Nd*(1.0+1.0/(CRFD_UM+(NRFD_UM/Nd)*(NRFD_UM/Nd)));
 193     PetscScalar Nas = Na*(1.0+1.0/(CRFA_UM+(NRFA_UM/Na)*(NRFA_UM/Na)));
 194     AutoDScalar Nsc = Nds+Nas+fabs(n);
 195
 196     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);
 197     AutoDScalar pp1 = pow(P,PetscScalar(0.6478));
 198     AutoDScalar F   = (0.7643*pp1+2.2999+6.5502/me_over_mh)/(pp1+2.3670-0.8552/me_over_mh);
 199     //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);
 200     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));
 201     AutoDScalar Nsce = Nas+Nds*G+fabs(n)/F;
 202     AutoDScalar mu_scatt = mu1*(Nsc/Nsce)*pow(NRFP_UM/Nsc,ALPP_UM)+mu2*(fabs(n+p)/Nsce);
 203     return 1.0/(1.0/mu_lattice+1.0/mu_scatt);
 204   }
 205
 206   //---------------------------------------------------------------------------
 207   //the surface acoustical phono scattering and roughness scattering for electron
 208   PetscScalar ElecMobLombardi(const PetscScalar &p,const PetscScalar &n,const PetscScalar &Tl,const PetscScalar &Et) const
 209   {
 210     PetscScalar Na = ReadDopingNa();
 211     PetscScalar Nd = ReadDopingNd();
 212     PetscScalar N_total = Na+Nd+1e0*pow(cm,-3);
 213     PetscScalar ET = Et+1.0*V/cm;
 214     PetscScalar mu_ac = BN_LUC/ET + CN_LUC*pow(N_total,EXN4_LUC)*pow(Tl/T300,-KN_LUC)*pow(ET,PetscScalar(-1.0/3.0));
 215     PetscScalar r = AN_LUC + FN_LUC*fabs(n+p)/pow(N_total,EXN9_LUC);
 216     PetscScalar DN_LUC=3.580000E+18*cm*cm/V/s*pow(V/cm,r);
 217     PetscScalar mu_sr = DN_LUC*pow(ET,-r);
 218     return 1.0/(1.0/mu_ac+1.0/mu_sr);
 219   }
 220   AutoDScalar ElecMobLombardi(const AutoDScalar &p,const AutoDScalar &n,const AutoDScalar &Tl,const AutoDScalar &Et) const
 221   {
 222     PetscScalar Na = ReadDopingNa();
 223     PetscScalar Nd = ReadDopingNd();
 224     PetscScalar N_total = Na+Nd+1e0*pow(cm,-3);
 225     AutoDScalar ET = Et+1.0*V/cm;
 226     AutoDScalar mu_ac = BN_LUC/ET + CN_LUC*pow(N_total,EXN4_LUC)*pow(Tl/T300,-KN_LUC)*pow(ET,PetscScalar(-1.0/3.0));
 227     AutoDScalar r = AN_LUC + FN_LUC*fabs(n+p)/pow(N_total,EXN9_LUC);
 228     AutoDScalar DN_LUC=3.580000E+18*cm*cm/V/s*pow(V/cm,r);
 229     AutoDScalar mu_sr = DN_LUC*pow(ET,-r);
 230     return 1.0/(1.0/mu_ac+1.0/mu_sr);
 231   }
 232
 233   //---------------------------------------------------------------------------
 234   //the surface acoustical phono scattering and roughness scattering for hole
 235   PetscScalar HoleMobLombardi(const PetscScalar &p,const PetscScalar &n,const PetscScalar &Tl,const PetscScalar &Et) const
 236   {
 237     PetscScalar Na = ReadDopingNa();
 238     PetscScalar Nd = ReadDopingNd();
 239     PetscScalar N_total = Na+Nd+1e0*pow(cm,-3);
 240     PetscScalar ET = Et+1.0*V/cm;
 241     PetscScalar mu_ac = BP_LUC/ET + CP_LUC*pow(N_total,EXP4_LUC)*pow(Tl/T300,-KP_LUC)*pow(ET,PetscScalar(-1.0/3.0));
 242     PetscScalar r = AP_LUC + FP_LUC*fabs(n+p)/pow(N_total,EXP9_LUC);
 243     PetscScalar DP_LUC=4.100000E+15*cm*cm/V/s*pow(V/cm,r);
 244     PetscScalar mu_sr = DP_LUC*pow(ET,-r);
 245     return 1.0/(1.0/mu_ac+1.0/mu_sr);
 246   }
 247   AutoDScalar HoleMobLombardi(const AutoDScalar &p,const AutoDScalar &n,const AutoDScalar &Tl,const AutoDScalar &Et) const
 248   {
 249     PetscScalar Na = ReadDopingNa();
 250     PetscScalar Nd = ReadDopingNd();
 251     PetscScalar N_total = Na+Nd+1e0*pow(cm,-3);
 252     AutoDScalar ET = Et+1.0*V/cm;
 253     AutoDScalar mu_ac = BP_LUC/ET + CP_LUC*pow(N_total,EXP4_LUC)*pow(Tl/T300,-KP_LUC)*pow(ET,PetscScalar(-1.0/3.0));
 254     AutoDScalar r = AP_LUC + FP_LUC*fabs(n+p)/pow(N_total,EXP9_LUC);
 255     AutoDScalar DP_LUC=4.100000E+15*cm*cm/V/s*pow(V/cm,r);
 256     AutoDScalar mu_sr = DP_LUC*pow(ET,-r);
 257     return 1.0/(1.0/mu_ac+1.0/mu_sr);
 258   }
 259
 260 public:
 261
 262   //---------------------------------------------------------------------------
 263   // Electron mobility
 264   PetscScalar ElecMob(const PetscScalar &p, const PetscScalar &n, const PetscScalar &Tl,
 265                       const PetscScalar &Ep, const PetscScalar &Et, const PetscScalar &Tn) const
 266   {
 267     PetscScalar vsat = (2.4e7*cm/s)/(1+0.8*exp(Tl/(2*T300)));
 268     PetscScalar mu0  = 1.0/(1.0/ElecMobPhilips(p,n,Tl)+1.0/ElecMobLombardi(p,n,Tl,Et));
 269     PetscScalar mu = 2*mu0/(1+pow(1+pow(2*mu0*fabs(Ep)/vsat,BETAN),1.0/BETAN));
 270     return mu;
 271   }
 272   AutoDScalar ElecMob(const AutoDScalar &p, const AutoDScalar &n, const AutoDScalar &Tl,
 273                       const AutoDScalar &Ep, const AutoDScalar &Et, const AutoDScalar &Tn) const
 274   {
 275     AutoDScalar vsat = (2.4e7*cm/s)/(1+0.8*exp(Tl/(2*T300)));
 276     AutoDScalar mu0  = 1.0/(1.0/ElecMobPhilips(p,n,Tl)+1.0/ElecMobLombardi(p,n,Tl,Et));
 277     AutoDScalar mu = 2*mu0/(1+pow(1+pow(2*mu0*fabs(Ep)/vsat,BETAN),1.0/BETAN));
 278     return mu;
 279   }
 280
 281   //---------------------------------------------------------------------------
 282   // Hole mobility
 283   PetscScalar HoleMob (const PetscScalar &p, const PetscScalar &n, const PetscScalar &Tl,
 284                        const PetscScalar &Ep, const PetscScalar &Et, const PetscScalar &Tp) const
 285   {
 286     PetscScalar vsat = (2.4e7*cm/s)/(1+0.8*exp(Tl/(2*T300)));
 287     PetscScalar mu0  = 1.0/(1.0/HoleMobPhilips(p,n,Tl)+1.0/HoleMobLombardi(p,n,Tl,Et));
 288     PetscScalar mu = 2*mu0/(1+pow(1+pow(2*mu0*fabs(Ep)/vsat,BETAP),1.0/BETAP));
 289     return mu;
 290   }
 291   AutoDScalar HoleMob(const AutoDScalar &p, const AutoDScalar &n, const AutoDScalar &Tl,
 292                       const AutoDScalar &Ep, const AutoDScalar &Et, const AutoDScalar &Tp) const
 293   {
 294     AutoDScalar vsat = (2.4e7*cm/s)/(1+0.8*exp(Tl/(2*T300)));
 295     AutoDScalar mu0  = 1.0/(1.0/HoleMobPhilips(p,n,Tl)+1.0/HoleMobLombardi(p,n,Tl,Et));
 296     AutoDScalar mu = 2*mu0/(1+pow(1+pow(2*mu0*fabs(Ep)/vsat,BETAP),1.0/BETAP));
 297     return mu;
 298   }
 299
 300
 301   // constructor
 302 public:
 303   GSS_Mob_Lucent(const PMIS_Environment &env):PMIS_Mobility(env)
 304   {
 305     Mob_Lucent_Init();
 306   }
 307
 308   ~GSS_Mob_Lucent(){}}
 309 ;
 310
 311 /*---------------------------------------------------------------
 312  *  the interface function called by material databse controller
 313  *  and it setup Lucent mobility model
 314  */
 315 extern "C"
 316 {
 317   PMIS_Mobility* PMIS_SiGe_Mob_Lucent (const PMIS_Environment& env)
 318   {
 319     return new GSS_Mob_Lucent(env);
 320   }
 321 }