The ``silicon_dg5'' system solves for the five equation density gradient model.
The quantities in parentheses are negative fluxes. The solution
variables for the above five equations are 
, 
,
, 
, and 
, respectively. The physical
constants 
and 
are defined as:
where l can be considered to be either the space dimensionality or
a fitting parameter; 
( 
) is the electron (hole)
effective mass.
Required Field Definitions
This system requires netdope to be defined after the structure is created with grid and deposit statements.
An implementation of the silicon_dg5 system is given below:
system name=silicon_dg5
+ sysvars=psi,sqrt_n,sqrt_p,phi_n,phi_p
+ term0=ndiv_fbm.lapflux(psi|psi)@{silicon,poly,oxide}
+ term1=nodal.nscd(electrons,holes,netdope|psi)@{silicon,poly}
+ term2=constraint.continuity(psi|psi)@{silicon/oxide,poly/oxide,silicon/poly}
+ term3=dirichlet.dg_dirichlet(netdope|psi,phi_n,phi_p)@{silicon/gate,poly/gat
e,silicon/back,silicon/source,silicon/drain,oxide/gate,silicon/substrate}
+ term4=ndiv_fbm.diffusion(bn,sqrt_n|sqrt_n)@{silicon,poly}
+ term5=-0.5*nodal.prod(sqrt_n,dphi_n|sqrt_n)@{silicon,poly}
+ term6=dirichlet.default_dirichlet(0|sqrt_n,sqrt_p)@{silicon/oxide,poly/oxide}
+ term7=ndiv_fbm.diffusion(bp,sqrt_p|sqrt_p)@{silicon,poly}
+ term8=0.5*nodal.prod(sqrt_p,dphi_p|sqrt_p)@{silicon,poly}
+ term9=ndiv_fbm.nqfflux(psi,phi_n,tl,mobn,electrons,edge|phi_n)@{silicon,poly}
+ term10=ndiv_fbm.nqfflux(psi,phi_p,tl,mobp,holes,edge|phi_p)@{silicon,poly}
+ tmpvars=electrons,holes,phin0,phip0,dphi_n,dphi_p,bn,bp,mobn,mobp
+ func0=prod(sqrt_n,sqrt_n|electrons)@{silicon,poly}
+ func1=prod(sqrt_p,sqrt_p|holes)@{silicon,poly}
+ func2=phiMB(electrons,psi,tl|phin0)@{silicon,poly}
+ func3=phiMB(holes,psi,tl|phip0)@{silicon,poly}
+ func4=sub(phin0,phi_n|dphi_n)@{silicon,poly}
+ func5=sub(phip0,phi_p|dphi_p)@{silicon,poly}
+ func6=6.35e-9*inverse(mn|bn)@{silicon,poly}
+ func7=6.35e-9*inverse(mp|bp)@{silicon,poly}
+ func8=mob0(electrons,holes,tl,netdope|mobn,mobp)@{silicon,poly}
+ init0="tl:${solve/bias/Tcelsius}+${library/physics/celsius}"
+ init1="edge:1"
+ init2="sqrt_n:sqrt(electrons)"
+ init3="sqrt_p:sqrt(holes)"
+ init4="mn:0.19"
+ init5="mp:0.49"