Doped silicon heater

Contents

Doped silicon heater#

Hide code cell source

 
from collections import OrderedDict

import matplotlib.pyplot as plt
import numpy as np
from shapely.geometry import LineString, Polygon
from skfem import Basis, ElementTriP0, Mesh
from skfem.io import from_meshio

from femwell.mesh import mesh_from_OrderedDict
from femwell.thermal import solve_thermal

Simulating the doped silicon heater in [1]. First we set up the mesh:

w_sim = 8 * 4
h_clad = 2.8
h_box = 2
w_core = 0.5
h_core = 0.22
w_buffer = 0.8
h_buffer = 0.09
h_heater = h_buffer
w_heater = 1
offset_heater = 2.2

polygons = OrderedDict(
    bottom=LineString([(-w_sim / 2, -h_box), (w_sim / 2, -h_box)]),
    core=Polygon(
        [
            (-w_core / 2, 0),
            (-w_core / 2, h_core),
            (w_core / 2, h_core),
            (w_core / 2, 0),
        ]
    ),
    slab_l=Polygon(
        [
            (-w_core / 2 - w_buffer, 0),
            (-w_core / 2 - w_buffer, h_buffer),
            (-w_core / 2, h_buffer),
            (-w_core / 2, 0),
        ]
    ),
    slab_r=Polygon(
        [
            (+w_core / 2 + w_buffer, 0),
            (+w_core / 2 + w_buffer, h_buffer),
            (+w_core / 2, h_buffer),
            (+w_core / 2, 0),
        ]
    ),
    heater_l=Polygon(
        [
            (-w_core / 2 - w_buffer - w_heater, 0),
            (-w_core / 2 - w_buffer - w_heater, h_heater),
            (-w_core / 2 - w_buffer, h_heater),
            (-w_core / 2 - w_buffer, 0),
        ]
    ),
    heater_r=Polygon(
        [
            (w_core / 2 + w_buffer + w_heater, 0),
            (w_core / 2 + w_buffer + w_heater, h_heater),
            (w_core / 2 + w_buffer, h_heater),
            (w_core / 2 + w_buffer, 0),
        ]
    ),
    clad=Polygon(
        [
            (-w_sim / 2, 0),
            (-w_sim / 2, h_clad),
            (w_sim / 2, h_clad),
            (w_sim / 2, 0),
        ]
    ),
    box=Polygon(
        [
            (-w_sim / 2, 0),
            (-w_sim / 2, -h_box),
            (w_sim / 2, -h_box),
            (w_sim / 2, 0),
        ]
    ),
)

resolutions = dict(
    core={"resolution": 0.01, "distance": 1},
    clad={"resolution": 0.4, "distance": 1},
    box={"resolution": 0.4, "distance": 1},
    heater_l={"resolution": 0.01, "distance": 1},
    heater_r={"resolution": 0.01, "distance": 1},
)

mesh = from_meshio(mesh_from_OrderedDict(polygons, resolutions, default_resolution_max=0.4))

And then we solve it!

basis0 = Basis(mesh, ElementTriP0(), intorder=4)
thermal_conductivity_p0 = basis0.zeros()
for domain, value in {
    "core": 90,
    "box": 1.38,
    "clad": 1.38,
    "slab_l": 55,
    "slab_r": 55,
    "heater_l": 55,
    "heater_r": 55,
}.items():
    thermal_conductivity_p0[basis0.get_dofs(elements=domain)] = value
thermal_conductivity_p0 *= 1e-12  # 1e-12 -> conversion from 1/m^2 -> 1/um^2

power = 25.2e-3
current = np.sqrt(
    power * 1e5 * (polygons["heater_l"].area + polygons["heater_r"].area) * 1e-12 / 320e-6
)
print(current)

basis, temperature = solve_thermal(
    basis0,
    thermal_conductivity_p0,
    specific_conductivity={"heater_l": 1e5, "heater_r": 1e5},
    current_densities={
        "heater_l": current / (polygons["heater_l"].area + polygons["heater_r"].area),
        "heater_r": current / (polygons["heater_l"].area + polygons["heater_r"].area),
    },
    fixed_boundaries={"bottom": 303},
)

fig, ax = plt.subplots(subplot_kw=dict(aspect=1))
for subdomain in mesh.subdomains.keys() - {"gmsh:bounding_entities"}:
    mesh.restrict(subdomain).draw(ax=ax, boundaries_only=True)
basis.plot(temperature, shading="gouraud", ax=ax)

from mpl_toolkits.axes_grid1 import make_axes_locatable

divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="5%", pad=0.05)
plt.colorbar(ax.collections[0], cax=cax)
plt.show()

0.0011905880899790657
../../_images/13b2980652bf3b8965cc0877becead6f695707a86d2f2d17ec434ff8ed32cdfb.png

Bibliography#

[1]

Maxime Jacques, Alireza Samani, Eslam El-Fiky, David Patel, Zhenping Xing, and David V. Plant. Optimization of thermo-optic phase-shifter design and mitigation of thermal crosstalk on the SOI platform. Optics Express, 27(8):10456, April 2019. URL: https://doi.org/10.1364/oe.27.010456, doi:10.1364/oe.27.010456.

Contents