Back ground charge and the corrections in the charged systems

[umar]

Dear all,
     when we apply the net chareg in quantum-wise do we have the same amount of background charge to neutralized it.
   as far as i know about SIESTA when we apply the net charge (NetCharge = 1 ) there have two things
1. the Madelung correction
2. applying the SimulateDoping .true.
    the Madelung correction  term (automatically applied) only can be applicable for the (SC, BCC, and FC).
    the 2nd option we use as to simulate the impurity..
  (Infect I am confused about SIESTA also)
What we have here in quantum-wise can some body help me

when we are giving the net charge is background charge is applied automatically.
is there any correction terms ?
what is the theory ?  is there any reference ie.  tutorial or some background theory manual.

cheers 
umar farooq

[Anders Blom]

I can't really comment on SIESTA but here is how it's done in ATK. If you want to simulate a truly charged cell, you give the keyword charge=XXX. In this case you need to use the Multipole Poisson solver, and ATK will internally apply the relevant corrections. For doping, you can see some of the latest tutorials for more details. In short, you give the opposite charge as your intended doping as a "compensation charge" on each atom. For instance, if your cell volume is V (can be computed via bulk_configuration.bravaisLattice().unitCellVolume()) and you want a doping of 1e20 cm^-3 and you have N atoms, then the compensation charge on each atom should be 1e20*V(in cm^3)/N. Example code for doped bulk Si:

Code: python

lattice = FaceCenteredCubic(5.431*Angstrom)
elements = [Silicon, Silicon]
fractional_coordinates = [[ 0.  ,  0.  ,  0.  ],
                          [ 0.25,  0.25,  0.25]]

bulk_configuration = BulkConfiguration(
    bravais_lattice=lattice,
    elements=elements,
    fractional_coordinates=fractional_coordinates
    )

# Convert doping to total charge in unit cell volume
# and set up compensation charge
cell_volume = lattice.unitCellVolume()
cm = Units.m/100
doping = 1e20/(cm**3)
charge = float(doping*cell_volume)
n_si = len(bulk_configuration.elements())

# Note opposite sign!!!
compensation_charge = -charge/n_si
bulk_configuration.setExternalPotential(AtomicCompensationCharge((Silicon, compensation_charge)))

The charge will then automatically be balanced to create a neutral system, so you shold not give the "charge" keyword in this case (unless you want a charged, doped cell).

[umar]

dear sir,
 Actually i have to simulate the nano-ribbon.
 it seems that in this case the charge will be distributed all in the space (unit cell) which is mostly empty, in ribbon care ?
is it good options ?
I think that I need to add the background only surrounding the atoms.
 
thanks,


umar farooq

[Anders Blom]

That is more a matter of definition of doping concentration. You can always renormalize the doping to the active volume (or in your case active area), instead of using the total cell volume.

[umar]

 it mean that
AtomicCompensationCharge((Silicon, compensation_charge)
will assign the compensation charge only to the Silicon atoms, it nothing to do with the volume of the vint cell ..  Volume or Area is just the  matter of calculation of concentration, am i right ?
thanks

[Anders Blom]

The compensation charges are always assigned to atoms, yes. But the amount of charge you apply should correspond to the doping you want, and how you compute that depends on the volume, since doping concentration * volume = charge = the total compensation charge (summed over all atoms).