# TCAD guide `gsim.tcad` solves Poisson and electron/hole drift-diffusion on a 2D cross-section of a doped silicon device with [DEVSIM](). Each bias point returns the carrier concentrations, the terminal currents and the small-signal capacitance and admittance of the swept contact. The cross-section is meshed by the same native-2D pipeline as the Palace mode solver, so the charge solve and the RF and optical solves see the same mesh. Use `Simulation` to configure and solve, and `BiasSweepResult` to read the result. The [PN junction notebook]() walks through a complete C(V) extraction. ## Install DEVSIM is optional. Install the `tcad` extra: ```bash pip install "gsim[tcad]" ``` It brings `devsim` and `scipy-openblas32`, which gives DEVSIM a BLAS/LAPACK library on Linux, Windows and macOS. On macOS it needs macOS 15 or later on Apple silicon, the only macOS wheel DEVSIM ships. `import gsim.tcad` works without DEVSIM; `solve()` and `sweep()` raise an error naming the extra. ## Configure and solve The simulation is set up by physical concern, like `gsim.fdtd.Simulation`: ```python from gsim import tcad sim = tcad.Simulation() sim.geometry(component, stack=stack) sim.domain(plane="x=0", window=(-25.0, -15.0), margin_x=3.0, margin_y=3.0, z_above=2.0, z_below=1.0) sim.materials(temperature_k=300.0, mobility=tcad.MobilityModel.masetti_silicon()) sim.doping.add(tcad.StepDoping(region="p_rib", dopant_type="acceptor", concentration_cm3=1e18)) sim.doping.add(tcad.StepDoping(region="n_rib", dopant_type="donor", concentration_cm3=1e18)) sim.contacts.add(name="anode", semiconductor="p_rib", electrode="metal_p") sim.contacts.add(name="cathode", semiconductor="n_rib", electrode="metal_n") sim.interfaces.add(name="junction", region_a="p_rib", region_b="n_rib") sim.solver(mesh_preset="coarse", refined_mesh_size_um=0.05, relative_error=1e-8) sim.mesh(output_dir="./tcad") point = sim.solve(1.0, contact="cathode") # BiasPoint sweep = sim.sweep([0.0, 0.5, 1.0, 2.0], contact="cathode") # BiasSweepResult ``` A positive bias on the n-side contact reverse-biases the junction. The other contacts are at 0 V: one swept by an earlier solve is ramped back first. Between bias points the swept contact is ramped in `solver.bias_step_v` steps, and a bias must be a finite voltage. Calling a concern applies several settings at once and validates them together; a failed call changes nothing. Single attributes can also be assigned, `sim.solver.relative_error = 1e-8`, and a whole concern replaced by a model or a mapping, `sim.materials = {"temperature_k": 350.0}`. The constructor takes the same concerns as keyword arguments: ```python sim = tcad.Simulation( domain={"plane": "x=0", "window": (-25.0, -15.0)}, doping=[tcad.StepDoping(region="p_rib", dopant_type="acceptor", concentration_cm3=1e18)], contacts=[{"name": "anode", "semiconductor": "p_rib", "electrode": "metal_p"}], solver={"mesh_preset": "coarse"}, ) ``` ## Concerns Lengths are in µm, concentrations in cm⁻³, voltages in V, frequencies in Hz and temperatures in K. Field names carry their unit. - `geometry(component, *, stack=None)`: the gdsfactory component and its layer stack, a `LayerStack`, a stack YAML path, or `None` for the active PDK. - `domain(...)`: `plane` (`"x="` or `"y="`); `window` and `window_z`, `(min, max)` clips of the domain in µm; the airbox `margin_x`, `margin_y`, `z_above`, `z_below` in µm. - `materials(...)`: `temperature_k` (300 K); `semiconductor`, the DEVSIM material of the doped Regions (`"Silicon"`); `mobility`, a `MobilityModel` (Masetti silicon); `insulators`, Region to static relative permittivity. - `doping`: the doping profiles, with `add(profile)`, `remove(profile)`, `clear()`, iteration and `len()`. - `contacts`: `add(name=, semiconductor=, electrode=)`, `remove(name)`, `sim.contacts[name]`, iteration. - `interfaces`: `add(name=, region_a=, region_b=)`, `remove(name)`, `sim.interfaces[name]`, iteration. - `solver(...)`: mesh resolution (`mesh_preset`, `refined_mesh_size_um`, `max_mesh_size_um`, `refinement_boxes`), Newton convergence (`absolute_error`, `relative_error`, `max_iterations`, `bias_step_v`, `extended_precision`), the small-signal frequencies (`small_signal_freq_hz`, `junction_freq_hz`) and `claim_devsim_namespace`. ### Doping A profile names the mesh Region it applies to and its dopant type. `StepDoping` is uniform inside an optional box, `GaussianDoping` and `ImplantDoping` are analytic implants, `TableDoping` interpolates a sampled profile (a SIMS depth profile, a process simulator's output) and `CallableDoping` evaluates a function of `(x, y)` in µm. Profiles on the same Region add up; donors and acceptors compensate in the net doping and add up as scatterers in the mobility. ### Contacts, interfaces and insulators Every Region of the device takes one role, and the declarations state it: - A **doped Region** carries at least one doping profile. It holds the potential and both carrier densities. - A **Contact** is where an electrode meets a doped Region: an ohmic contact whose bias the solve sets. `semiconductor` is the doped Region it injects into; `electrode` is the Region on the other side, the metal or any Region that is neither doped nor insulating. - An **Interface** is where two doped Regions meet. Potential and carriers are continuous across it; it carries no bias. Declare one between every pair of touching doped Regions: two touching doped Regions without one are refused, since no carrier would cross between them. - An **insulator** is a Region in `materials.insulators`. It joins the electrostatic solve with its own permittivity and holds no carriers. Without any, Poisson is solved in the doped silicon alone and its boundary is a zero-normal-field wall; with the oxide declared, the field may fringe around the junction through it. The interfaces an insulator shares with its neighbours are bound automatically. A Region is doped or insulating, never both. A Contact against a declared insulator is refused: one curve cannot be both a Contact and a semiconductor-insulator interface. Each Contact and Interface becomes a line group of that name on the mesh, so contact and interface names are unique across both. ## Mesh, then solve `mesh(output_dir=...)` writes the native-2D mesh in µm and its copy in cm that DEVSIM loads, and returns a `TCADMesh` with both paths and the mesh's physical groups. `output_dir` is required on the first call and remembered afterwards. Resolution comes from the `solver` concern. The DEVSIM device is built on the first solve, and `mesh()` is never called implicitly. What a later change invalidates depends on the concern: - **Mesh inputs**: `geometry`, `domain`, `contacts`, `interfaces`, and the solver's mesh fields. `mesh()` records them. A solve after any of them changed raises `ValueError("... changed since mesh(); call mesh() again")`. - **Device inputs**: `materials`, `doping`, and the other solver fields. A change drops the DEVSIM device and its bias state; the next solve builds it again on the existing mesh. ## Results A DEVSIM 2D device is 1 cm deep, so extensive quantities are per cm of device length; each has a per-metre counterpart. ```python sweep.voltages # V sweep.capacitance_f_per_cm # small-signal C(V) sweep.capacitance_f_per_m sweep.admittance_s_per_cm # complex admittance at solver.junction_freq_hz sweep.junction_branch() # series-RC fit: r_s_ohm_m, c_j_f_per_m point = sweep.points[-1] point.currents_a_per_cm # DC terminal current per contact point.carriers.electrons_cm3, point.carriers.holes_cm3 # per mesh node point.carriers.x_um, point.carriers.y_um # in-plane and vertical node coordinates ``` The capacitance comes from an AC solve at the quasi-static `small_signal_freq_hz`. The admittance comes from a second AC solve at `junction_freq_hz`, high enough that the capacitive current dominates the junction's DC leakage and far below the branch's own RC rolloff, so `junction_branch()` reads the series resistance of the doped slab and the junction capacitance a loaded-line RF model needs. `tcad.compare_capacitance` evaluates the depletion-approximation capacitance (Sze) at the same biases and reports the relative deviation; `tcad.estimate_depletion_width_um` reads the depletion width off a 1D cut of the carrier map. The comparison uses the solve's own silicon constants (below) for whatever the `PNJunctionConfig` leaves at its defaults. ## Silicon constants The solve takes DEVSIM's silicon parameters, with one change: the intrinsic carrier density follows the temperature. - **Permittivity:** static relative permittivity 11.1, DEVSIM's value (`gsim.tcad.silicon.SILICON_RELATIVE_PERMITTIVITY`). The RF and optical stacks use 11.9 for silicon. - **Intrinsic density:** `n_i(T) = n_i(300 K) (T/300)^1.5 exp(E_g(300)/2kT_300 - E_g(T)/2kT)`, with Varshni's band gap and DEVSIM's `n_i(300 K) = 1e10` cm⁻³ (`gsim.tcad.silicon.intrinsic_density_cm3`). A 300 K solve is DEVSIM's own; away from 300 K the built-in voltage falls with temperature as it should. - **Temperature:** `materials.temperature_k` sets the thermal voltage, the intrinsic density and the SRH trap densities. The Masetti mobility is its 300 K fit at every temperature. ## Limits - DEVSIM keeps meshes, devices and its circuit in one process-wide namespace. By default each device setup claims it (`solver.claim_devsim_namespace`), so one charge-transport device is live at a time. - The physics is DEVSIM's Scharfetter-Gummel drift-diffusion for silicon, with Shockley-Read-Hall recombination and the doping-dependent mobility of `materials.mobility`. There is no field-dependent mobility (velocity saturation), no impact ionisation and no quantum correction. - Contacts, interfaces and insulators are declared, never inferred from the layer stack.