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.. _tdgl_fem:
TDGL, London, and FEM normal-state analysis
===========================================

In this set of tutorials, we will cover conversion of ``qnngds.Device`` to ``skfem.mesh.MeshTri1``, ``tdgl.Device``, and ``superscreen.Device`` for analysis of device properties.

First, let's analyze a structure with femwell/skfem to visualize the current density of our device
in the normal state.

.. code-block:: python
   :linenos:

   import qnngds as qg
   import matplotlib.pyplot as plt
   from qnngds.analysis.fem import (
       make_mesh,
       solve_laplace,
       visualize_mesh,
       visualize_current,
   )
   
   snspd = qg.devices.snspd.basic(size=(3, 3))
   

we can create a mesh as so:

.. code-block:: python
   :linenos:

   mesh = make_mesh(device=snspd, layer=(1, 0), tolerance=0.01)
   visualize_mesh(mesh)
   plt.show()


.. image:: qg_analysisfemmesh.png
Now, let's analyze the current density by solving the laplace equation

.. code-block:: python
   :linenos:

   result = solve_laplace(mesh)
   visualize_current(result, ("1", "2"))
   plt.show()


.. image:: qg_analysisfemj.png

The current density is normalized to the current density at the excitation ports.

Next, we will show how to generate a ``tdgl.Device``

.. code-block:: python
   :linenos:

   from qnngds.analysis.tdgl import make_tdgl_device
   
   device = make_tdgl_device(
       device=snspd,
       coherence_length=0.005,
       london_lambda=0.35,
       thickness=0.01,
       gamma=23.8,
       layer=(1, 0),
   )
   fig, ax = device.draw()
   plt.show()


.. image:: qg_analysistdgldraw.png

We can use this object to do tdgl simulations, check out the `py-tdgl docs <https://py-tdgl.readthedocs.io/en/latest/>`_
for more info and examples.

In some cases, we may be interested in modeling screening effects and Meissner currents in multi-layer structures.
Note that py-tdgl `can simulate screening <https://py-tdgl.readthedocs.io/en/latest/notebooks/screening.html>`_,
but is limited to a single layer. In order to simulate screening on multiple layers, we can use
`superscreen <https://superscreen.readthedocs.io/en/latest/>`_.

First, let's create a gated diode device with a 5 nm thick layer having :math:`\lambda = 0.33` μm penetration depth
and a 40 nm thick layer having :math:`\lambda = 0.4` μm penetration depth, separated by 45 nm spacer.

.. code-block:: python
   :linenos:

   import superscreen as sc
   from qnngds.analysis.superscreen import make_superscreen_device
   
   qg.pdk.get_generic_pdk().activate()
   diode = qg.devices.diode.gated(
       channel_spec=qg.devices.diode.basic(
           layer=(1, 0),
       ),
       gate_spec=qg.geometries.optimal_hairpin(
           width=1,
           pitch=3,
           layer=(10, 0),
       ),
   )
   scdev = make_superscreen_device(
       diode,
       london_lambda={(1, 0): 0.33, (10, 0): 0.4},
       thickness={(1, 0): 0.005, (10, 0): 0.04},
       z0={(1, 0): 0, (10, 0): 0.05},
       min_refine_points=1000,
   )
   fig, ax = scdev.draw(figsize=(6, 4))
   _ = scdev.plot_polygons(ax=ax, legend=True)
   plt.show()


.. image:: qg_analysissuperscreendev.png

Now, we can simulate a 1 mA bias current flowing through the upper hairpin "gate"


.. code-block:: python
   :linenos:

   Ibias = "1 mA"
   scdev.make_mesh(max_edge_length=0.25)
   solutions = sc.solve(
       scdev,
       terminal_currents={
           "(10, 0)_0": {"port_(10, 0)_g1": Ibias, "port_(10, 0)_g2": f"-{Ibias}"}
       },
       iterations=10,
       progress_bar=True,
   )


Evaluating the solution at a distance of 10 nm (5 nm above the bottom film), we can plot
the field distribution due to the current flowing through the upper layer.


.. code-block:: python
   :linenos:

   eval_region = sc.Polygon(points=sc.geometry.box(12, 6))
   eval_mesh = eval_region.make_mesh(min_points=2000)
   fig, ax = solutions[-1].plot_field_at_positions(
       eval_mesh, zs=0.01, figsize=(6, 4), symmetric_color_scale=True, cmap="coolwarm"
   )
   for film in scdev.films.values():
       film.plot(ax=ax, color="k", ls="--", lw=1)
   plt.show()


.. image:: qg_analysissuperscreenhz.png

We can also use superscreen to compute the current density in a wire.
Let's reuse the same ``snspd`` device from earlier that we analyzed with femwell:

.. code-block:: python
   :linenos:

   scdev = make_superscreen_device(
       device=snspd,
       london_lambda=0.33,
       thickness=0.005,
       min_refine_points=1000,
   )
   scdev.make_mesh(max_edge_length=0.25)
   Ibias = f"{snspd.ports[1].width} uA"
   solutions = sc.solve(
       scdev,
       terminal_currents={
           "(1, 0)_0": {"port_(1, 0)_1": Ibias, "port_(1, 0)_2": f"-{Ibias}"}
       },
       iterations=10,
       progress_bar=True,
   )
   fig, ax = solutions[-1].plot_currents(films=["(1, 0)_0"])
   _ = scdev.plot_polygons(ax=ax[0], color="w", ls="--", lw=1)
   plt.show()


.. image:: qg_analysissuperscreenj.png