Multi-physics: Heater
Highlighted features: heat_only shapes, fem_resolution, current, heat, the thermo-optic shift of a mode, and the heater power for a \(\pi\) phase shift.
This code example is licensed under the BSD 3-Clause License.
import emodeconnection as emc
import matplotlib.pyplot as plt
from scipy.interpolate import LinearNDInterpolator
## Simulation parameters
wavelength = 1550 # [nm]
dx, dy = 10, 10 # [nm] optical resolution
w_core, h_core = 500, 220 # [nm] Si core
w_trench = 800 # [nm] cladding on each side of the core in the optical window
h_bclad, h_tclad = 2000, 1200 # [nm] SiO2 below and above the core
w_pt, h_pt = 1000, 140 # [nm] Pt heater
current = 10e-3 # [A] heater current
h_air = 500 # [nm] air above the heater in the thermal domain
h_substrate, w_substrate = 10e3, 10e3 # [nm] Si substrate (thermal domain only)
opt_width, opt_height = w_core + 2 * w_trench, h_bclad + h_core + h_tclad
heat_width, heat_height = w_substrate, h_substrate + opt_height + h_air
## Connect and initialize EMode
em = emc.EMode()
em.settings(
wavelength=wavelength,
x_resolution=dx,
y_resolution=dy,
num_modes=1,
background_material='Air',
window_width=opt_width,
window_height=opt_height,
)
## Layer stack: heat_only shapes are excluded from the optical mesh. The
## thermal domain is the union of every shape; every exposed surface is
## insulating and the bottom of the substrate is held at 298 K.
em.shape(name='substrate', material='Si', height=h_substrate, fem_resolution=200, heat_only=True)
em.shape(name='BOX', material='SiO2', height=h_bclad, fem_resolution=200)
em.shape(
name='core',
material='Si',
fill_material='SiO2',
mask=w_core,
height=h_core,
etch_depth=h_core,
fem_resolution=50,
)
em.shape(name='tclad', material='SiO2', height=h_tclad, fem_resolution=200)
em.shape(
name='heater',
material='Pt',
width=w_pt,
height=h_pt,
fem_resolution=50,
current=current,
heat_only=True,
)
## Cold mode
em.FDM()
em.report()
n_cold = em.get('effective_index')[0]
## Thermal solve: a wider window so the substrate spans the full thermal domain
em.settings(window_width=heat_width, window_height=heat_height)
heat_data = em.heat(boundary_temperature=298, boundaries=['bottom'])
T = heat_data['temperature']
# heat() returns its mesh in the optical window's frame, so the core sits at the
# same y here as it does in the layer stack.
core_point = LinearNDInterpolator(heat_data['p'].T, T)((0.0, h_bclad + h_core / 2))
print(f'Maximum temperature: {T.max():.1f} K')
print(f'Core temperature rise: {core_point - 298:.1f} K')
## Heated mode: FDM folds the temperature field into the permittivity through dn_dT
em.settings(window_width=opt_width, window_height=opt_height)
em.FDM()
em.report()
n_hot = em.get('effective_index')[0]
dn = n_hot - n_cold
## Heater power per length and the power for a pi phase shift (independent of length)
Pt = em.get('Pt')
rho = Pt['resistivity'] * 1e-9 # [Ohm*nm] -> [Ohm*m]
area = w_pt * h_pt * 1e-18 # [m^2]
power_per_length = current**2 * rho / area # [W/m]
P_pi = power_per_length * wavelength * 1e-9 / (2 * abs(dn)) # [W]
print(f'Heater power: {power_per_length:.1f} mW/mm') # 1 W/m is 1 mW/mm
print(f'Effective index shift: {dn:.2e}')
print(f'Power for a pi phase shift: {P_pi * 1e3:.1f} mW')
## Temperature map, with the FEM mesh drawn over it
fig, ax = plt.subplots()
im = ax.tripcolor(
heat_data['p'][0], heat_data['p'][1], heat_data['t'].T, T, cmap='plasma', shading='gouraud'
)
ax.triplot(heat_data['p'][0], heat_data['p'][1], heat_data['t'].T, color='w', lw=0.15, alpha=0.4)
ax.set_aspect('equal')
ax.set_xlabel('x [nm]')
ax.set_ylabel('y [nm]')
fig.colorbar(im, ax=ax, label='Temperature [K]')
fig.savefig('heater_temperature.png', dpi=150, bbox_inches='tight')
em.plot()
em.close()
Console output:
EMode3D 1.0.4 - email
Meshing completed in 0.8 sec
Solving modes completed in 4.2 sec
Wavelength: 1550.0 nm
Mode # n_eff TE % Loss (dB/m)
-------- -------- ------ -------------
TE-0 2.446865 98.3 % 0.000
Solving heat completed in 0.2 sec
Meshing completed in 0.8 sec
Solving modes completed in 4.4 sec
Wavelength: 1550.0 nm
Mode # n_eff TE % Loss (dB/m)
-------- -------- ------ -------------
TE-0 2.451263 98.4 % 0.000
Exited EMode
Maximum temperature: 347.9 K
Core temperature rise: 20.5 K
Heater power: 75.0 mW/mm
Effective index shift: 4.40e-03
Power for a pi phase shift: 13.2 mW
Figures:
