Gunn Diode Simulator (2D): Space-Time Domain & v(E) Phase Plot

Bias & Material

Applied field E_avg 4.0 kV/cm

Doping density N꜀ 1.0 ×10¹⁵ cm⁻³

Device length L 8 μm

Simulation speed 1.0×

Live Readouts

Terminal current density J

— kA/cm²

Domain transit frequency

— GHz

Peak domain field

— kV/cm

How it works — and why this view is different

This 2D companion runs the exact same finite-difference solver as the 3D version — the Ridley–Watkins–Hilsum / Gunn transferred-electron effect, integrated from first principles instead of animated as a scripted wave:

v(E) = (μ₀E + v_sat·(E/E꜀)⁴) / (1 + (E/E꜀)⁴)

Continuity:  ∂n/∂t = −∂(nv)/∂x + D·∂²n/∂x²
Poisson:     ∂E/∂x = (q/ε)·(n − N꜀)
Circuit:     (1/L)·∫E dx  =  E_avg  (fixed terminal bias)

The 3D scene only ever shows the field profile at the current instant, as a row of bars. Here the left panel is a space-time waterfall: every row is one snapshot of E(x) across the device, and rows scroll downward as time advances — so the traveling high-field domain shows up directly as a bright diagonal streak crossing from cathode (top of each row, left) to anode (right), repeating once per transit. That trace is the same kind of space-time plot used in real transferred-electron-device literature and cannot be read off a single instantaneous bar chart.

The top-right panel plots the analytic Copeland velocity–field curve v(E) and overlays a live scatter of every grid cell's own (Eᵢ, vᵢ) — this is the mechanism the 3D view never draws explicitly: once E passes E꜀≈3.2 kV/cm the points sit on the falling branch of the curve, the direct signature of negative differential mobility that makes a uniform current sheet unstable and nucleates the domain.

The bottom-right panel is a scrolling oscilloscope of the terminal current density J(t) — each domain transit produces one current pulse, and the spacing between pulses is exactly 1/f, the transit-time frequency reported at left.

μ₀ ≈ 8000 cm²/V·s — low-field Γ-valley mobility; v_sat ≈ 1×10⁷ cm/s — velocity once most electrons sit in the heavy L valley; E꜀ ≈ 3.2 kV/cm — the RWH threshold field for GaAs.
A short doping notch at the cathode re-triggers a new domain each time the previous one exits at the anode — visible in the waterfall as evenly spaced streaks.
f ≈ v_domain/L: shortening device length L raises the transit frequency toward the X-band (8–12 GHz) range used in real GaAs Gunn oscillators and radar sources — watch the waterfall streaks get closer together as you shorten L.
Diffusion coefficient D = μ₀·k_BT/q ≈ 207 cm²/s (Einstein relation, 300 K) smooths domain edges; the 64-cell explicit solver is sub-stepped every frame at a diffusion-limited Δt for numerical stability.

Space-time domain E(x,t)v(E) phase plot · J(t) oscilloscope

— below threshold —

Low field Near threshold Domain peak Operating points / J(t)