Electrostatic simulations with Palace

Electrostatic simulations with Palace#

Here, we show how Palace may be used to perform electrostatic simulations. For a given geometry, one needs to specify the terminals where to apply potential, similar to ./elmer_01_electrostatic.py. This effectively solves the mutual capacitance matrix for the terminals and the capacitance to ground. For details on the physics, see [1].

Installation#

See Palace – Installation for installation or compilation instructions. Gplugins assumes palace is available in your PATH environment variable.

Alternatively, Singularity / Apptainer containers may be used. Instructions for building and an example definition file are found at Palace – Build using Singularity/Apptainer. Afterwards, an easy install method is to add a script to ~/.local/bin (or elsewhere in PATH) calling the Singularity container. For example, one may create a palace file containing

#!/bin/bash
singularity exec ~/palace.sif /opt/palace/bin/palace "$@"

Geometry, layer config and materials#

Hide code cell source 
import os
from math import inf
from pathlib import Path

import gdsfactory as gf
import pyvista as pv
from gdsfactory.components.interdigital_capacitor import (
    interdigital_capacitor,
)
from gdsfactory.generic_tech import LAYER, get_generic_pdk
from gdsfactory.technology import LayerStack
from gdsfactory.technology.layer_stack import LayerLevel
from IPython.display import display

from gplugins.common.types import RFMaterialSpec
from gplugins.palace import run_capacitive_simulation_palace

gf.config.rich_output()
PDK = get_generic_pdk()
PDK.activate()

We employ an example LayerStack used in superconducting circuits similar to [1].

layer_stack = LayerStack(
    layers=dict(
        substrate=LayerLevel(
            layer=LAYER.WAFER,
            thickness=500,
            zmin=0,
            material="Si",
            mesh_order=99,
        ),
        bw=LayerLevel(
            layer=LAYER.WG,
            thickness=200e-3,
            zmin=500,
            material="Nb",
            mesh_order=2,
        ),
    )
)
material_spec: RFMaterialSpec = {
    "Si": {"relative_permittivity": 11.45},
    "Nb": {"relative_permittivity": inf},
    "vacuum": {"relative_permittivity": 1},
}

simulation_box = [[-200, -200], [200, 200]]
c = gf.Component()
cap = c << interdigital_capacitor()
c.add_ports(cap.ports)
substrate = gf.components.bbox(c, layer=LAYER.WAFER)
c << substrate
c.plot()

Running the simulation#

We use the function run_capacitive_simulation_palace(). This runs the simulation and returns an instance of ElectrostaticResults containing the capacitance matrix and a path to the mesh and the field solutions.

help(run_capacitive_simulation_palace)

Note

The meshing parameters and element order shown here are very lax. As such, the computed capacitances are not very accurate.

results = run_capacitive_simulation_palace(
    c,
    layer_stack=layer_stack,
    material_spec=material_spec,
    n_processes=1,
    element_order=1,
    simulation_folder=Path(os.getcwd()) / "temporary",
    mesh_parameters=dict(
        background_tag="vacuum",
        background_padding=(0,) * 5 + (700,),
        port_names=c.ports,
        default_characteristic_length=200,
        resolutions={
            "bw": {
                "resolution": 15,
            },
            "substrate": {
                "resolution": 40,
            },
            "vacuum": {
                "resolution": 40,
            },
            **{
                f"bw__{port}": {  # `__` is used as the layer–port delimiter for Palace
                    "resolution": 20,
                    "DistMax": 30,
                    "DistMin": 10,
                    "SizeMax": 14,
                    "SizeMin": 3,
                }
                for port in c.ports
            },
        },
    ),
)
display(results)

if results.field_file_location:
    pv.start_xvfb()
    pv.set_jupyter_backend("trame")
    field = pv.read(results.field_file_location)
    field_slice = field.slice_orthogonal(z=layer_stack.layers["bw"].zmin * 1e-6)

    p = pv.Plotter()
    p.add_mesh(field_slice, scalars="E", cmap="turbo")
    p.show_grid()
    p.camera_position = "xy"
    p.enable_parallel_projection()
    p.show()

Bibliography#

[1]

Ivica Smolić and Bruno Klajn. Capacitance matrix revisited. Progress In Electromagnetics Research B, 92:1–18, 2021. URL: http://www.jpier.org/PIERB/pier.php?paper=21011501 (visited on 2023-08-17), doi:10.2528/PIERB21011501.

[2]

Fabian Marxer, Antti Vepsäläinen, Shan W. Jolin, Jani Tuorila, Alessandro Landra, Caspar Ockeloen-Korppi, Wei Liu, Olli Ahonen, Adrian Auer, Lucien Belzane, Ville Bergholm, Chun Fai Chan, Kok Wai Chan, Tuukka Hiltunen, Juho Hotari, Eric Hyyppä, Joni Ikonen, David Janzso, Miikka Koistinen, Janne Kotilahti, Tianyi Li, Jyrgen Luus, Miha Papic, Matti Partanen, Jukka Räbinä, Jari Rosti, Mykhailo Savytskyi, Marko Seppälä, Vasilii Sevriuk, Eelis Takala, Brian Tarasinski, Manish J. Thapa, Francesca Tosto, Natalia Vorobeva, Liuqi Yu, Kuan Yen Tan, Juha Hassel, Mikko Möttönen, and Johannes Heinsoo. Long-distance transmon coupler with cz-gate fidelity above 99.8 %. PRX Quantum, 4(1):010314, 2023. URL: https://link.aps.org/doi/10.1103/PRXQuantum.4.010314 (visited on 2023-08-17), doi:10.1103/PRXQuantum.4.010314.