A. Setting up LeadDeviceLead
You can set up the regions , , and in the structural
configuration shown in Fig. 29 in the following way:
The geometrical structure of the central region is specified by the following keywords 'Atoms.Number' and 'Atoms.SpeciesAndCoordinates':
Atoms.Number 18 <Atoms.SpeciesAndCoordinates 1 C 3.000 0.000 0.000 2.0 2.0 ..... 18 C 28.500 0.000 0.000 2.0 2.0 Atoms.SpeciesAndCoordinates>
The geometrical structure of the left lead region is specified by the following keywords 'LeftLeadAtoms.Number' and 'LeftLeadAtoms.SpeciesAndCoordinates':
LeftLeadAtoms.Number 3 <LeftLeadAtoms.SpeciesAndCoordinates 1 C -1.500 0.000 0.000 2.0 2.0 2 C 0.000 0.000 0.000 2.0 2.0 3 C 1.500 0.000 0.000 2.0 2.0 LeftLeadAtoms.SpeciesAndCoordinates>
The geometrical structure of the right lead region is specified by the following keywords 'RightLeadAtoms.Number' and 'RightLeadAtoms.SpeciesAndCoordinates'
RightLeadAtoms.Number 3 <RightLeadAtoms.SpeciesAndCoordinates 1 C 30.000 0.000 0.000 2.0 2.0 2 C 31.500 0.000 0.000 2.0 2.0 3 C 33.000 0.000 0.000 2.0 2.0 RightLeadAtoms.SpeciesAndCoordinates>This is the case of carbon chain which is demonstrated in the previous subsection. The central region is formed by 18 carbon atoms, and the left and right regions and contains three carbon atoms, respectively, where every bond length is 1.5 Å. Following the geometrical specification of device and leads, OpenMX will construct an extended central region as shown in Fig. 29. The Green function for the extended central region is self-consistently determined in order to take account of relaxation of electronic structure around the interface between the central region and the region . In addition, we impose two conditions so that the central Green function can be calculated in the NEGF method :
Although the specification of unit cells for the regions , , and is not required, it should be noted that some periodicity is implicitly assumed. The construction of infinite leads is made by employing the unit cells used in the band structure calculations by the step 1, and the informations are stored in a file '*.hks'. Also, due to the structural configuration shown in Fig. 29, the unit vectors on the bc-plane for the left and right leads should be consistent. Thus, the unit vector on the bc-plane for the extended central region is implicitly assumed to be same as that of the leads. Within the structural limitation, you can set up the structural configuration.
The unit in the specification of the geometrical structure can be given by
Atoms.SpeciesAndCoordinates.Unit Ang # Ang|AU
How OpenMX analyzes the geometrical structure can be confirmed by the standard output as shown below:
<TRAN_Calc_GridBound> ******************************************************* The extended cell consists of Left0-Center-Right0. The cells of left and right reads are connected as. ...|Left2|Left1|Left0-Center-Right0|Right1|Right2... Each atom in the extended cell is assigned as follows: where '12' and '2' mean that they are in 'Left0', and '12' has overlap with atoms in the Left1, and '13' and '3' mean that they are in 'Right0', and '13' has overlap with atoms in the 'Right1', and also '1' means atom in the 'Center'. ******************************************************** Atom1 = 12 Atom2 = 2 Atom3 = 1 Atom4 = 1 Atom5 = 1 Atom6 = 1 Atom7 = 1 Atom8 = 1 Atom9 = 1 Atom10 = 1 Atom11 = 1 Atom12 = 1 Atom13 = 1 Atom14 = 1 Atom15 = 1 Atom16 = 1 Atom17 = 1 Atom18 = 1 Atom19 = 1 Atom20 = 1 Atom21 = 3 Atom22 = 13
The NEGF calculation of the step 2 is performed by the keyword 'scf.EigenvalueSolver'
For the NEGF calculation the following keywords are newly added.
NEGF.filename.hks.l lead-chain.hks NEGF.filename.hks.r lead-chain.hks NEGF.Num.Poles 100 # defalut=150 NEGF.scf.Kgrid 1 1 # defalut=1 1 NEGF.bias.voltage 0.0 # default=0.0 (eV) NEGF.bias.neq.im.energy 0.01 # default=0.01 (eV) NEGF.bias.neq.energy.step 0.02 # default=0.02 (eV)
An explanation for each keyword is given below.
NEGF.filename.hks.l lead-chain.hks NEGF.filename.hks.r lead-chain.hks
NEGF.Num.Poles 100 # defalut=150
NEGF.scf.Kgrid 1 1 # defalut=1 1
NEGF.bias.voltage 0.0 # default=0.0 (eV)
NEGF.bias.neq.im.energy 0.01 # default=0.01 (eV) NEGF.bias.neq.energy.step 0.02 # default=0.02 (eV)
Intrinsic chemical potential (eV) of the leads Left lead: -7.752843837400 Right lead: -7.752843837400 add voltage = 0.0000 (eV) to the left lead: new ChemP (eV): -7.7528 add voltage = 0.5000 (eV) to the right lead: new ChemP (eV): -7.2528 Parameters for the integration of the non-equilibrium part lower bound: -8.706843837400 (eV) upper bound: -6.298843837400 (eV) energy step: 0.020000000000 (eV) number of steps: 120The total number of energy points where the Green function is evaluated is given by the sum of the number of poles and the number of energy points on the real axis determined by the two keywords 'NEGF.bias.neq.im.energy' and 'NEGF.bias.neq.energy.step', and you should notice that the computational time is proportional to the total number of energy points.
C. SCF criterion
In the NEGF method, the SCF criterion given by the keyword
'scf.criterion' is applied to the residual norm
between the input and output charge densities 'NormRD', while in the other
cases 'dUele' is monitored.
D. Gate bias voltage
In our implementation, the gate voltage is treated by adding
an electric potential defined by
NEGF.gate.voltage 1.0 # default=0.0 (in eV)
E. Density of States (DOS)
In the NEGF calculation, the density of states can be calculated by setting the following keywords:
Dos.fileout on # on|off, default=off NEGF.Dos.energyrange -15.0 25.0 5.0e-3 #default=-10.0 10.0 5.0e-3 (eV) NEGF.Dos.energy.div 200 # default=200 NEGF.Dos.Kgrid 1 1 # default=1 1