This is the same metal–insulator–metal nanocapacitor as the 3D model, redrawn as a 2D band diagram instead of a rendered plate stack. The top strip is the electron energy-band cross-section along the tunneling axis; the bottom strip is the design-space trade-off curve every chip designer actually reads off.
Capacitance density: C/A = ε₀εr / d
Equivalent oxide
thickness (EOT): EOT = d · (3.9 / εr)
WKB tunneling
current density: J ≈ J₀·V·exp(−2κd), κ = √(2m*qφB) / ħ
In the band diagram, the flat regions left and right are the metal electrodes (filled Fermi sea, sea level offset by the applied bias V); the raised block of height φB is the dielectric barrier, width d. A traveling wavefunction ψ(x) enters the barrier oscillating, decays as exp(−κ·x) through it, and exits with reduced amplitude on the far side — its transmitted probability |ψ|² = exp(−2κd) is exactly the exponential in the leakage-current formula above, so the visible decay of the wave envelope is the same physics as the current readout, not a separate cartoon.
The lower strip sweeps d from 0.5–5 nm for the selected material and plots log₁₀J against C/A, tracing the actual capacitance–vs–leakage trade-off curve; thin reference curves for the other five dielectrics stay visible so a high-κ film's advantage (same C/A, far lower J) is visually obvious. The bright dot marks the current (d, V) operating point.
- Dielectric dropdown — swaps εr and barrier height φB used by every formula and redraws the barrier block height and trade-off family.
- Thickness slider — the physical film thickness d, 0.5–5 nm; widens or narrows the barrier block and slides the operating dot along the trade-off curve.
- Voltage slider — the bias V; tilts the right electrode's Fermi level and scales plate-charge markers and the wave's emission rate (J is linear in V in this low-field WKB model).
- Tunneling wave — toggles the animated decaying wave packets; their emission rate is tied to the computed J, exactly like the 3D model's animated electrons.
The prefactor J₀ and effective mass m* = 0.4·mₑ are fixed, illustrative constants shared across all six materials — only εr, φB and d change per selection — so the simulator isolates the real trade-off (capacitance vs. leakage vs. material) rather than fitting any single fabrication process.