Project Summary
===============

Python codes provides a class object to simply calculate quantum mechanical transmission probability across arbitrary potential barriers by using the piece wise constant method. If you have a need to implement transmission probability into your code, it might be helpful.

There are several books and papers describing the piece wise constant method. I referred to specifically a paper by Ando and Itoh [#foot_1]_ along with a paper by Tsu and Esaki [#foot_2]_ and a book by Ferry and Goodnick [#foot_3]_.

Example
-------
Tunneling through 5 barriers

.. |fig1| image:: 5barriers.png
    :width: 50%
.. |fig2| image:: 5barriersbias02.png
    :width: 50%
.. |TC| image:: 5barriersTC.png
    :width: 50%

+-----------+-----------+
| |fig1|    | |fig2|    |
|           |           |
| Potential | Biased at |
| structure | -0.2 (V)  |
+-----------+-----------+

Result:

As can be seen, for 5 barriers without bias, the resonant energies are split into quadruplets. For n barriers, there should be n-1 fold splitting at resonant energies [#foot_2]_.


|TC|

.. [#foot_1] Ando, Yuji, and Tomohiro Itoh. "Calculation of transmission tunneling current across arbitrary potential barriers." Journal of applied physics 61.4 (1987): 1497-1502.

.. [#foot_2] Tsu, R., and Leo Esaki. "Tunneling in a finite superlattice." Applied Physics Letters 22.11 (1973): 562-564.

.. [#foot_3] Ferry, David, and Stephen Marshall Goodnick. Transport in nanostructures. No. 6. Cambridge university press, 1997.

Usage
-----
Set up a desired structure in a separate python module just like below (my5barriers.py for example).

The main part is to set up:

#. potential (eV)
#. thickness (nm)
#. effective_mass (m_0 electron free mass)

.. code:: python

    # list of effective masses from www.ioffe.ru/SVA/NSM/Semicond/index.html
    m = {'GaAs': 0.063,
         'AlxGa1-xAs': lambda x: 0.063+0.083*x,
         'AlAs': 0.146,
         'InN': 0.11,
         'GaN': 0.20,
         'InxGa1-xN': lambda x: 0.2+x*(0.11-0.2),
         'InAs': 0.023}

    # Set Up structure Here ---------------------------------------
    # potential (eV)
    # thickness (nm)
    # effective_mass (m_0 electron free mass)
    # Multiple Barriers
    potential = [0.0, 0.4, 0.0, 0.4, 0.0, 0.4, 0.0, 0.4, 0.0, 0.4, 0.0]
    thickness = [4, 2, 6, 2, 6, 2, 6, 2, 6, 2, 4]
    effective_mass = [m['GaAs'], m['GaAs'], m['GaAs'], m['GaAs'],
                      m['GaAs'], m['GaAs'], m['GaAs'], m['GaAs'], m['GaAs'],
                      m['GaAs'], m['GaAs']]

Then, in the main module (myTransmissionCoefficient.py), import the module describing the structure 'as myStr', e.g.

>>> import my5barriers as myStr

Now create an object

>>> RTD = QuantumTransmissionCoefficientCalculator(20)

The number 20 indicates the subdivision which is useful when applying bias. Check the structure described in the module by

>>> RTD.plot_structure()

Currently, it shows only the potential structure, no effective mass.

Create an numpy array E describing the energy range of interest

>>> import numpy as np
>>> import nu
>>> E = np.linspace(0.01, .5, 1000)*nu.eV

where nu is a custom module dealing with units. In this case, nu.eV = 1.602176565e-19.

Now you can have a transmission coefficient in the desired energy range.

>>> TC = RTD.compute(E)

See :ref:`ch-ref-doc` for more details.