2. Creating the FD-SOI `device`

2.1. Requirements

2.1.1. Software components

QTCAD

2.1.2. Python script

qtcad/examples/practical_application/FDSOI/setup_fdsoi_device.py

2.1.3. References

Mesh generation using QTCAD Builder

2.2. Briefing

The file presented in this section is not meant to be run. Instead, it contains quantities and a function that are imported by other scripts in this practical application tutorial series. In particular, the function get_double_dot_fdsoi defined here is used to create the FD-SOI Device object. This function is analogous to the identically named function defined in A double quantum dot device in a fully-depleted silicon-on-insulator transistor.

2.4. Default values

We then define some default values that will be used in the different scripts.

# Default values
V_qd        = 0.75              # Default quantum dot potential (V)
V_set       = 1.25              # Default SET potential (V)
scaling     = 1e-9              # scaling factor for the mesh

These provide the default voltages to be applied to the single-electron transistor (SET) and quantum dot gates (plunger_gate_1_bnd and plunger_gate_2_bnd, respectively) and also define the length scale of the mesh.

2.6. Creating the device

Finally, we define the function that creates and returns the FD-SOI device model.

# Function to create the FD-SOI device
def get_double_dot_fdsoi(mesh_file_name: str="refined_dqdfdsoi.msh",
                        V_qd: float=V_qd, V_set: float=V_set) -> Device:
    """Create a Device object for the FD-SOI structure.

    Args:
        V_qd (float): Potential for the qubit quantum-dot regions.
        V_set (float): Potential for the SET region.
        mesh_file_name (str): Filename of the mesh file.

    Returns:
        Device: The constructed Device object.
        list[str]: List of qubit quantum-dot region names.
        list[str]: List of SET region names.
    """
    # Create the mesh
    script_dir           = pathlib.Path(__file__).parent.resolve()
    path_mesh            = script_dir / "meshes"
    mesh_file            = path_mesh / mesh_file_name
    mesh                 = Mesh(scaling, mesh_file)

    # Define the device object
    dvc = Device(mesh, conf_carriers='e')
    dvc.set_temperature(0.1)

    # Create the regions
    dvc.new_region("oxide", mt.SiO2)
    dvc.new_region("oxide.QD1", mt.SiO2)
    dvc.new_region("oxide.QD2", mt.SiO2)
    dvc.new_region("channel", mt.Si)
    dvc.new_region("channel.QD1", mt.Si)
    dvc.new_region("channel.QD2", mt.Si)
    dvc.new_region("source", mt.Si, ndoping=1e20*1e6)
    dvc.new_region("drain", mt.Si, ndoping=1e20*1e6)

    # Set up boundary conditions
    Ew = mt.Si.Eg/2 + mt.Si.chi # Midgap
    dvc.new_gate_bnd("barrier_gate_1_bnd", 0.5, Ew)
    dvc.new_gate_bnd("plunger_gate_1_bnd", V_set, Ew)
    dvc.new_gate_bnd("barrier_gate_2_bnd", 0.5, Ew)
    dvc.new_gate_bnd("plunger_gate_2_bnd", V_qd, Ew)
    dvc.new_gate_bnd("barrier_gate_3_bnd", 0.5, Ew)
    dvc.new_ohmic_bnd("source_bnd")
    dvc.new_ohmic_bnd("drain_bnd")
    dvc.new_frozen_bnd("back_gate_bnd", -0.5, mt.Si, 1e15*1e6,
        "n", 46*1e-3*ct.e)

    # Create the double quantum dot region
    SET_region_list = ["oxide.QD1", "channel.QD1"]
    QD_region_list = ["oxide.QD2", "channel.QD2"]

    return dvc, SET_region_list, QD_region_list

This function starts by generating the Mesh object using the specified mesh file. It then creates an instance of the Device class and sets up the material stack of the device by defining the different regions and assigning them appropriate materials. Next, it applies appropriate boundary conditions to the surfaces representing the gate contacts. The plunger-gate voltages are set according to the function arguments. In contrast, barrier-gate voltages are all set to a value of \(0.5\,\mathrm{V}\). This value of barrier-gate voltage was shown in Tunnel coupling in a double quantum dot in FD-SOI—Part 2: Tuning the barrier gate to lead to minimal tunneling between different regions of the device, allowing the quantum dots to be well-defined and isolated. Finally, the get_double_dot_fdsoi function creates lists identifying the quantum-dot and SET regions that will later be used when solving the Schrödinger equation before returning the created Device object along with these lists.

2.7. Full code

__copyright__ = "Copyright 2022-2025, Nanoacademic Technologies Inc."

import pathlib
from qtcad.device import materials as mt
from qtcad.device import constants as ct
from qtcad.device.mesh3d import Mesh
from qtcad.device import Device

# Default values
V_qd        = 0.75              # Default quantum dot potential (V)
V_set       = 1.25              # Default SET potential (V)
scaling     = 1e-9              # scaling factor for the mesh

# Visualization parameters
normal = (0., 0., 1.) # the plane of the slice is normal to the z axis
origin = (0., 0., -1. * scaling) # the slice is inside the Si quantum well

# Function to create the FD-SOI device
def create_fdsoi_device(mesh_file_name: str="refined_dqdfdsoi.msh",
                        V_qd: float=V_qd, V_set: float=V_set) -> Device:
    """Create a Device object for the FD-SOI structure.

    Args:
        V_qd (float): Potential for the quantum dot regions.
        V_set (float): Potential for the SET region.
        mesh_file_name (str): Filename of the mesh file.

    Returns:
        Device: The constructed Device object.
        list[str]: List of quantum dot region names.
        list[str]: List of SET region names.
    """
    # Create the mesh
    script_dir           = pathlib.Path(__file__).parent.resolve()
    path_mesh            = script_dir / "meshes"
    mesh_file            = path_mesh / mesh_file_name
    mesh                 = Mesh(scaling, mesh_file)

    # Define the device object
    dvc = Device(mesh, conf_carriers='e')
    dvc.set_temperature(0.1)

    # Create the regions
    dvc.new_region("oxide", mt.SiO2)
    dvc.new_region("oxide.QD1", mt.SiO2)
    dvc.new_region("oxide.QD2", mt.SiO2)
    dvc.new_region("channel", mt.Si)
    dvc.new_region("channel.QD1", mt.Si)
    dvc.new_region("channel.QD2", mt.Si)
    dvc.new_region("source", mt.Si, ndoping=1e20*1e6)
    dvc.new_region("drain", mt.Si, ndoping=1e20*1e6)

    # Set up boundary conditions
    Ew = mt.Si.Eg/2 + mt.Si.chi # Midgap
    dvc.new_gate_bnd("barrier_gate_1_bnd", 0.5, Ew)
    dvc.new_gate_bnd("plunger_gate_1_bnd", V_set, Ew)
    dvc.new_gate_bnd("barrier_gate_2_bnd", 0.5, Ew)
    dvc.new_gate_bnd("plunger_gate_2_bnd", V_qd, Ew)
    dvc.new_gate_bnd("barrier_gate_3_bnd", 0.5, Ew)
    dvc.new_ohmic_bnd("source_bnd")
    dvc.new_ohmic_bnd("drain_bnd")
    dvc.new_frozen_bnd("back_gate_bnd", -0.5, mt.Si, 1e15*1e6, 
        "n", 46*1e-3*ct.e)

    # Create the double quantum dot region
    SET_region_list = ["oxide.QD1", "channel.QD1"]
    QD_region_list = ["oxide.QD2", "channel.QD2"]

    return dvc, SET_region_list, QD_region_list

2. Creating the FD-SOI device