PtH2Pt nanojunction
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Experimental Motivation
- R. H. M. Smit, Y. Noat, C. Untiedt, N. D. Lang, M. C. van Hemert and J. M. van Ruitenbeek, Measurement of the conductance of a hydrogen molecule, Nature 419, 906 (2002). [PDF]
- M. Kiguchi, R. Stadler, I. S. Kristensen, D. Djukic, and J. M. van Ruitenbeek, Evidence for a single hydrogen molecule connected by an atomic chain, Phys. Rev. Lett. 98, 146802 (2007). [PDF]
NEGF+Tight-Binding modeling of electronic transport
NEGF+DFT for zero-bias transmission function
- Calculate zero-bias transmission function using pt_h2_trans.py script:
#Transport calculations using transport object following https://wiki.fysik.dtu.dk/gpaw/documentation/transport/negftransport.html
from ase import Atoms
from gpaw.transport.calculator import Transport
from gpaw.atom.basis import BasisMaker
from gpaw.occupations import FermiDirac
from gpaw.poisson import PoissonSolver
from gpaw.mixer import Mixer
from ase.visualize import view
a = 2.41 # Pt binding lenght
b = 0.90 # H2 binding lenght
c = 1.70 # Pt-H binding lenght
L = 7.00 # width of unit cell
# L-Lead scat region R-Lead
#------------ ------------------- -----------
# Pt--Pt--Pt-|-Pt--Pt-H-H-Pt--Pt-|-Pt--Pt--Pt
# 0 1 2 3 4 5 6 7 8 9 10 11
#------------ ------------------- -----------
atoms = Atoms('Pt5H2Pt5', pbc=( 0, 0,1), cell=[ L, L, 9 * a + b + 2 * c])
atoms.positions[:5, 2] = [i * a for i in range(5)]
atoms.positions[-5:, 2] = [i * a + b + 2 * c for i in range(4, 9)]
atoms.positions[5:7, 2] = [4 * a + c, 4 * a + c + b]
atoms.positions[:, 0:1] = L / 2.
atoms.center()
# setup leads
pl_atoms1 = range(3) # 3 atoms 0~2 is L-Lead
pl_atoms2 = range(9,12) # 3 atoms 9~11 is R-Lead
pl_cell1 = (L, L, 3 * a) # cell size of lead 3 Pt bonds
pl_cell2 = pl_cell1
# visulize device with ag
view(atoms)
t = Transport(h=0.3,
xc='PBE',
basis='szp(dzp)',
kpts=(1,1,1), #
occupations=FermiDirac(0.1),
mode='lcao',
poissonsolver=PoissonSolver(nn=2, relax='GS'),
txt='pt_h2_trans.txt',
mixer=Mixer(0.1, 5, weight=100.0),
pl_atoms=[pl_atoms1, pl_atoms2],
pl_cells=[pl_cell1, pl_cell2],
pl_kpts=(1,1,10), # lead is periodic along transport direction
plot_energy_range = [-4.,4.], # min and max energy of transmission
plot_energy_point_num = 201, # Number of energy points
#edge_atoms=[[0, 2], [0, 5]], # edge and mol_atoms should be
#mol_atoms=range(1,5), # specified to be able to restart.
#analysis_mode=True, # for restarting jobs
#scat_restart=True, # need to specify mol_atom
#lead_restart=True,
#guess_steps=1,
non_sc=True, #True = Normal DFT (default) for zero bias transmission, False = NEGF-DFT
)
atoms.set_calculator(t)
t.calculate_iv() # for zero-bias transmission, do not put any arguments
- Plot zero-bias transmission function using plot_trans.py script:
from gpaw.transport.analysor import Transport_Plotter
import numpy as np
import sys
from pylab import *
fd=0
plotter=Transport_Plotter(fd)
plotter.plot_setup()
# the following Emax , nE should be the same as specified in the transport calculations
Emax=3.0
Emin=-Emax
nE=201
bias_step=0
tc = plotter.tc(bias_step) # transmission
ee=np.linspace(Emin,Emax,nE) # Energy range specified in transport calculation
plot(ee, tc, 'b-o')
xlabel('Energy (eV)')
ylabel('Transmission')
show()
NEGF+DFT for I-V characteristics
- Calculate transmission function at finite bias voltage using pt_h2_iv.py script:
#Transport calculations using transport object following https://wiki.fysik.dtu.dk/gpaw/documentation/transport/negftransport.html
from ase import Atoms
from gpaw.transport.calculator import Transport
from gpaw.atom.basis import BasisMaker
from gpaw.occupations import FermiDirac
from gpaw.poisson import PoissonSolver
from gpaw.mixer import Mixer
from ase.visualize import view
a = 2.41 # Pt binding lenght
b = 0.90 # H2 binding lenght
c = 1.70 # Pt-H binding lenght
L = 7.00 # width of unit cell
# L-Lead scat region R-Lead
#------------ ------------------- -----------
# Pt--Pt--Pt-|-Pt--Pt-H-H-Pt--Pt-|-Pt--Pt--Pt
# 0 1 2 3 4 5 6 7 8 9 10 11
# | |
# C_i C_f
#------------ ------------------- -----------
# 0 1 2 0 1 2
# | |
# L_i R_f
atoms = Atoms('Pt5H2Pt5', pbc=( 0, 0,1), cell=[ L, L, 9 * a + b + 2 * c])
atoms.positions[:5, 2] = [i * a for i in range(5)]
atoms.positions[-5:, 2] = [i * a + b + 2 * c for i in range(4, 9)]
atoms.positions[5:7, 2] = [4 * a + c, 4 * a + c + b]
atoms.positions[:, 0:1] = L / 2.
atoms.center()
# setup leads
pl_atoms1 = range(3) # 3 atoms 0~2 is L-Lead
pl_atoms2 = range(9,12) # 3 atoms 9~11 is R-Lead
pl_cell1 = (L, L, 3 * a) # cell size of lead 3 Pt bonds
pl_cell2 = pl_cell1
# visulize device with ag
view(atoms)
t = Transport(h=0.3,
xc='PBE',
basis='szp(dzp)',
kpts=(1,1,1), #
occupations=FermiDirac(0.1),
mode='lcao',
poissonsolver=PoissonSolver(nn=2, relax='GS'),
txt='pt_h2_iv.txt',
mixer=Mixer(0.1, 5, weight=100.0),
pl_atoms=[pl_atoms1, pl_atoms2],
pl_cells=[pl_cell1, pl_cell2],
pl_kpts=(1,1,10), # lead is periodic along transport direction
plot_energy_range = [-4.,4.], # min and max energy of transmission
plot_energy_point_num = 201, # Number of energy points
edge_atoms=[[0, 2], [0, 11]], # Defining edge atoms in the form [[L_i, R_f][C_i, C_f]]
mol_atoms=range(3,9), # specified to be able to restart.
#analysis_mode=True, # for restarting jobs
#scat_restart=True, # need to specify mol_atom
#lead_restart=True,
guess_steps=1,
#non_sc=False, #True = Normal DFT (default)for zero bias transmission, False = NEGF-DFT
fixed_boundary=False
)
atoms.set_calculator(t)
t.calculate_iv(0.5, 3) # bias voltage set in the interval 0 to 0.5 eV using 3 steps: 0, 0.25 and 0.5 V
# could have 3rd argument specified the nth point of bias voltage to begin with
- Plot I-V characteristics using plot_iv.py script:
from gpaw.transport.analysor import Transport_Plotter
import numpy as np
from pylab import *
import sys
plotter = Transport_Plotter()
plotter.plot_setup()
nbias=2 #number of bias points to plot
bias, current = plotter.iv(nbias)
bias=np.abs(bias)
plot(bias, current, 'r-o')
xlabel('Bias Voltage (V)')
ylabel('Current (microA)')
show()
