Philips Unified Mobility Model

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Model

proc mobility.philips {} {

#------------------------
# 1. Lattice Scattering
#------------------------

set T_0 300.0
set T_Lattice 300.0
#Phosphorus
set mu_e_max 1414.0
set mu_min_e 68.5
set theta_e 2.285
set N_eref 9.2e16
set alpha_e 0.711
#Boron
set mu_h_max 470.5
set mu_min_h 44.9
set theta_h 2.247
set N_href 2.23e17
set alpha_h 0.719
term add name=mu_eL eqn = "$mu_e_max*(($T_Lattice/$T_0)^(-$theta_e))"
term add name=mu_hL eqn = "$mu_h_max*(($T_Lattice/$T_0)^(-$theta_h))"
term add name=mu_eN eqn = "(($mu_e_max^2)/($mu_e_max-$mu_min_e))*(($T_Lattice/$T_0)^(3*$alpha_e-1.5))"
term add name=mu_hN eqn = "(($mu_h_max^2)/($mu_h_max-$mu_min_h))*(($T_Lattice/$T_0)^(3*$alpha_h-1.5))"
term add name=mu_ec eqn = "(($mu_e_max*$mu_min_e)/($mu_e_max-$mu_min_e))*(($T_Lattice/$T_0)^0.5)"
term add name=mu_hc eqn = "(($mu_h_max*$mu_min_h)/($mu_h_max-$mu_min_h))*(($T_Lattice/$T_0)^0.5)"

#-------------------------------
# High-Concentration Clustering
#-------------------------------

set c_D 0.21
set c_A 0.5
set N_refD 7.2e20
set N_refA 4.0e20 
term add name=ND_clus eqn = "ND*(1+(1/($c_D+(($N_refD/ND)^2))))"
term add name=NA_clus eqn = "NA*(1+(1/($c_A+(($N_refA/NA)^2))))"
term add name=N_esc eqn = "ND_clus + NA_clus + Hole"
term add name=N_hsc eqn = "ND_clus + NA_clus + Elec"

#---------------------
# Screening Parameter
#---------------------

set me_div_m0 1.0
set mh_div_m0 1.258
set f_CW 2.459
set f_BH 3.828
term add name=Pe eqn = "(($f_CW/(3.97*10^13*(N_esc^(-2/3)))+$f_BH/(((1.36*10^20)/(Elec+Hole))*$me_div_m0))^-1)*(($T_Lattice/$T_0)^2)"
term add name=Ph eqn = "(($f_CW/(3.97*10^13*(N_hsc^(-2/3)))+$f_BH/(((1.36*10^20)/(Elec+Hole))*$mh_div_m0))^-1)*(($T_Lattice/$T_0)^2)"

#------------------------------
# Minority Impurity Scattering
#------------------------------

set a_g 0.89233
set b_g 0.41372
set c_g 0.005978
set alpha_g 0.28227
set alphaprime_g 0.72169
set beta_g 0.19778
set gamma_g 1.80618
set m0_div_me 1.0
set m0_div_mh 0.794913
term add name=G_Pe eqn = "1-$a_g/(($b_g+Pe*(($m0_div_me*($T_Lattice/$T_0))^$alpha_g))^$beta_g)+$c_g/((Pe*(($m0_div_me*($T_Lattice/$T_0))^$alphaprime_g))^$gamma_g)"
term add name=G_Ph eqn = "1-$a_g/(($b_g+Ph*(($m0_div_mh*($T_Lattice/$T_0))^$alpha_g))^$beta_g)+$c_g/((Ph*(($m0_div_mh*($T_Lattice/$T_0))^$alphaprime_g))^$gamma_g)"

#--------------------------
# Electron-Hole Scattering
#--------------------------

set me_div_mh 0.794913
set mh_div_me 1.258
term add name=F_Pe eqn = "(0.7643*(Pe^0.6478)+2.2999+6.5502*$me_div_mh)/(Pe^0.6478+2.367-0.8552*$me_div_mh)"
term add name=F_Ph eqn = "(0.7643*(Ph^0.6478)+2.2999+6.5502*$mh_div_me)/(Ph^0.6478+2.367-0.8552*$mh_div_me)"

#--------------------------
# Final Model Equations
#--------------------------

term add name=N_e_sceff eqn = "ND_clus+G_Pe*NA_clus+Hole/F_Pe"
term add name=N_h_sceff eqn = "NA_clus+G_Ph*ND_clus+Elec/F_Ph"
term add name=mu_e_DAeh eqn = "mu_eN*(N_esc/N_e_sceff)*(($N_eref/N_esc)^$alpha_e)+mu_ec*((Elec+Hole)/N_e_sceff)"
term add name=mu_h_DAeh eqn = "mu_hN*(N_hsc/N_h_sceff)*(($N_href/N_hsc)^$alpha_h)+mu_hc*((Elec+Hole)/N_h_sceff)"
term add name=Emob_Philips eqn = "(mu_e_DAeh*mu_eL)/(mu_e_DAeh+mu_eL)"
term add name=Hmob_Philips eqn = "(mu_h_DAeh*mu_hL)/(mu_h_DAeh+mu_hL)"
}

Notes

Reference: D. B. M. KLAASSEN, A UNIFIED MOBILITY MODEL FOR DEVICE SIMULATION Solid-State Electronics Vol. 35, No. 7, pp. 953 959, 1992

INPUTS Required:

1. ND - Donors
2. NA - Acceptors
3. Elec - Electrons
4. Hole - Holes

OUTPUT Terms:

1. Emob_Philips - Electron Mobility
2. Hmob_Philips - Hole Mobility

ND and NA must be at least 1.0 for all regions