Enhanced Lombardi Model

Model

proc mobility.lombardi {} {

# (using default coefficents for silicon)
set T_lattice 300.0
set T0 300.0
set B_e 4.75e7
set B_h 9.925e6
set C_e 5.8e2
set C_h 2.947e3
set N0 1.0
set lambda_e 0.1250
set lambda_h 0.0317
set k_e 1.0
set k_h 1.0
set delta_e 5.82e14
set delta_h 2.0546e14
set eta_e 5.82e30
set eta_h 2.0546e30

term add name=F_trans eqn = "(abs(dot(DevPsi,x*1.0e-4)) + 1.0e-10)"
#term add name=F_trans eqn = "1.0"

# surface contribution due to acoustic phonon scattering
term add name=mu_phonon_e eqn = "($B_e/F_trans)+($C_e*(((ND+NA)/$N0)^$lambda_e))/((F_trans^(1/3))*(($T_lattice/$T0)^($k_e)))" 
term add name=mu_phonon_h eqn = "($B_h/F_trans)+($C_h*(((ND+NA)/$N0)^$lambda_h))/((F_trans^(1/3))*(($T_lattice/$T0)^($k_h)))" 

# surface roughness scattering
term add name=mu_surface_e eqn = "(((F_trans^2)/$delta_e+((F_trans^3)/$eta_e))^-1)"
term add name=mu_surface_h eqn = "(((F_trans^2)/$delta_h+((F_trans^3)/$eta_h))^-1)" 

term add name=Emob_Lombardi eqn = "(mu_surface_e*mu_phonon_e)/(mu_surface_e+mu_phonon_e)+1" 
term add name=Hmob_Lombardi eqn = "(mu_surface_h*mu_phonon_h)/(mu_surface_h+mu_phonon_h)+1"
} 

Notes

Reference: C. Lombardi et al., "A Physically Based Mobility Model for Numerical Simulation of Nonplanar Devices." IEEE Transactions on Computer-Aided Design, vol. 7, no. 11, pp. 1164-1171, 1988.

INPUTS Required:

1. ND - Donors

2. NA - Acceptors

3. DevPsi - Electrostatic Potential

OUTPUT Terms:

1. Emob_Lombardi - Electron Mobility

2. Hmob_Lombardi - Hole Mobility