[ase-users] I-V curve from ase.transport

[Mikkel Strange]

Dear Vincent,

1) the method "get_transmission" calculates the transmission (unit-less).
In the zero-bias and zero temperature limit, the conductance is G = G_0 * T(E_F), where E_F is the Fermi-level.

2) At a quick glance your method "get_current" looks ok, but perhaps the current should just be returned
in units of 2e/h?, i.e. without the factor "2. * units._e / units._hplanck".
Also, one could perhaps try to use/extend the Fermi-distribution  all ready in tools.py?

Best wishes,
Mikkel
________________________________
From: ase-users-bounces at listserv.fysik.dtu.dk [ase-users-bounces at listserv.fysik.dtu.dk] on behalf of Vincent Pohl via ase-users [ase-users at listserv.fysik.dtu.dk]
Sent: Friday, November 04, 2016 4:10 PM
To: ase-users at listserv.fysik.dtu.dk
Subject: [ase-users] I-V curve from ase.transport

Dear ASE users,

I want to compute I-V curves for an electron transport though a nanojunction. I have used the transport module of ASE to compute the transmission function. Afterwards, I wrote a function to evaluate the current as a function of the bias (See below). I am very new in the field, and I am not quiet sure, if I have understood everything correctly:

1) Am I right in assuming that the function "T = calc.get_transmission()" computes the quantum conductance (G(E) in units of G_0 = 2e^2/h) and not the transmission function which is unitless? If I am right, isn't the name of the function quiet misleading?

2) Concerning my function to compute the I-V curve (get_current, see below), can anyone please check its correctness? I am not quiet sure, if I have used the correct formula, and if I have handled the ase.units correctly.

If everything is correct, shall I add the function to the ASE transport module and commit the changes. I think such a function might be very useful.

Thank you very much in advance for your help.

With best regards,
Vincent

----------------------------------

from __future__ import division
from ase.transport.calculators import TransportCalculator
from scipy import integrate
import numpy as np
from ase import units
import pylab as plt

h = np.array((0,)).reshape((1,1))
h1 = np.array((0, -1, -1, 0)).reshape(2,2)
energies = np.arange(-3, 3, 0.1)
tcalc = TransportCalculator(h=h, h1=h1, energies=energies)
G_E = tcalc.get_transmission() # Quantum conductance in units of G_0=2e^2/h
T_E = 2 * G_E                  # Transmission function (Unitless)

def get_current(bias, E, T_E, T = 0):
    '''Returns the current as a function of the
    bias voltage.

    **Parameters:**
    bias : {float, (M,) ndarray}, units: V
      Specifies the bias voltage.
    E : {(N,) ndarray}, units: eV
      Contains energy grid of the transmission function.
    T_E {(N,) ndarray}, units: unitless
      Contains the transmission function.
    T : {float}, units: K, optional
      Specifies the temperature.

    **Returns:**
    I : {float, (M,) ndarray}, units: A
      Contains the electric current.
    '''
    if not isinstance(bias, float):
        bias = bias[np.newaxis]
        E = E[:, np.newaxis]
        T_E = T_E[:, np.newaxis]
    assert T >= 0., 'Negative temperature given!'
    if T==0:
        fl = (E - bias / 2. <= 0).astype(int)
        fr = (E + bias / 2. <= 0).astype(int)
    else:
        beta = 1. / (units.kB * T)
        fl = 1. / (1. + np.exp(beta * (E - bias / 2.)))
        fr = 1. / (1. + np.exp(beta * (E + bias / 2.)))
    E = units._e * E
    I = 2. * units._e / units._hplanck * integrate.simps((fl - fr) * T_E, x=E, axis=0)
    return I

bias = np.arange(0, 2, .1)
plt.plot(bias, get_current(bias, energies, T_E, T = 0.))
plt.xlabel('U [V]')
plt.ylabel('I [A]')
plt.show()

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