---
title: "Resonant Tunneling Transport Interactive Lab | Sandbox Physics"
description: "Can two barriers transmit better than one? At the right energies, yes."
canonical_url: "https://sandboxphysics.com/labs/resonant-tunneling-transport/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/resonant-tunneling-transport/"
last_modified: "2026-10-27"
---

Q015 · Barriers / resonance / current

# Resonant Tunneling Transport

**Can two barriers transmit better than one?** At the right energies, yes. Waves bouncing between the two barriers interfere so that their reflections cancel, and nearly all of the wave gets through. These resonances can be so narrow that a coarse energy scan steps right over them.

Move the barriers, tune the energy of the incoming electrons and count how many get through. Measure the transmission spectrum before estimating the current, because a narrow resonance can fall between your measurement points.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Electrons scatter elastically in one channel with two spin states. The effective mass is a uniform illustrative value, and the barriers are rectangular. The bias only changes how the reservoirs are filled; the potential stays fixed. The simulated single-electron counts, and the current estimated from them over a finite energy window, are kept separate from the model predictions. Self-consistent electrostatics of the device and inelastic scattering are not included.

02 / Counts first, then the curve

## Where does transmission return?

Model reference

$E/\mathrm{meV}$ · Blue: current records. Amber: last saved other sample. Dashed: optional model. Drag to inspect; the slider supports keyboard input.

At this probe setting

$\text{—}$

No recorded particles yet.

$\text{—}$

95% pointwise Wilson interval. It is not a simultaneous band and carries no guarantee under optional stopping.

Latest 60 raw outcomes

Blue: transmitted. Gray: reflected or absorbed. No hidden trajectory is recorded.

03 / What can these records tell us?

## A tall peak does not mean a large current.

This reservoir weighting is set separately from the counting run. A positive bias favors flow from left to right. The barriers keep their shape.

Inferred from the scan records

$\text{—}$

Independent model comparison

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Model only; nothing new is recorded

## The wave builds up between the barriers.

$x/\mathrm{nm}$ · Drag the right barrier; height is potential energy, not a physical wall. Dashed line: incident energy.

$|\psi|^2/|A_{\mathrm{in}}|^2$ · This is a stationary scattering state, not a normalized particle cloud or a trajectory. The vertical scale adjusts automatically and is labeled.

$\text{—}$

04 / Save the evidence

## Save before changing the experiment.

Eight frozen samples. Restoring inspects the original records; acquiring again starts a new run. CSV contains individual outcomes, scan membership and original settings.

Physical model, units and sources

$$
m^*=0.067m_e,\quad\mu_{L,R}=100\,\mathrm{meV}\pm eU/2
$$

Illustrative uniform effective mass, equal lead velocities, one spatial channel and two spin states. The source, nanostructure and collector are enlarged conceptually; raised gates mark potential regions. Ideal single-energy transmission trials are not a simulation of a real single-electron detector. Reservoir bias does not tilt the potential. No mass mismatch, many-body charging, phonons or full device current outside the displayed window.

[Olkhovsky, Recami & Zaichenko · double-barrier transmission, sections 2–3](https://arxiv.org/abs/quant-ph/0410128) · [Beenakker & van Houten · Landauer transport](https://www.lorentz.leidenuniv.nl/beenakkr/mesoscopics/topics/qpc/physics_today/node9.html)

Physics tutorial

## Resonant Tunneling Transport

**Background** Move the barriers, tune the energy of the incoming electrons and count how many get through. Measure the transmission spectrum before estimating the current, because a narrow resonance can fall between your measurement points.

**Why it matters** A boundary changes which waves are allowed, and a detector only ever records a finite sample.

Start with the essentials

- **Focus question**: Can two barriers transmit better than one?
- **One-sentence intuition**: Interference can cancel the reflections from the two barriers, but the width of that resonance matters just as much.

### Core mathematical model

#### Stationary scattering

$$
-\frac{\hbar^2}{2m^*}\psi^{\prime\prime}+V(x)\psi=E\psi
$$

The wavefunction and its derivative are continuous at each interface, and the effective mass is the same everywhere.

#### Flux conservation

$$
R+T=1
$$

Because the left and right leads are identical, the transmission equals the squared magnitude of the transmitted amplitude.

#### Landauer current over a finite energy window

$$
I_{[1,301]}=\frac{2e}{h}\int_{1\,\mathrm{meV}}^{301\,\mathrm{meV}}T(E)[f_L(E)-f_R(E)]\,dE
$$

Both spin channels contribute. The scan counts estimate the same integral with the trapezoidal rule. The bias changes the occupations, not the shape of the barriers.

### Common difficulties

#### What was measured?

**Typical misconception** The current readout comes from a separately simulated ammeter.

**Better mental model** The current is estimated from the recorded transmission counts and the given reservoir occupations. The model integral on a finer grid is shown separately as a reference.

#### An idealized model

**Typical misconception** Agreement here certifies a real device.

**Better mental model** Electrons scatter elastically in one channel with two spin states. The effective mass is a uniform illustrative value, and the barriers are rectangular. The bias only changes how the reservoirs are filled; the potential stays fixed. The simulated single-electron counts, and the current estimated from them over a finite energy window, are kept separate from the model predictions. Self-consistent electrostatics of the device and inelastic scattering are not included.

### Run the experiment

1. 01

   #### Predict

   Compare two barriers with one barrier removed. Predict whether two barriers can transmit more than one.

   **What to observe:** Keep the reference curve hidden until you have recorded data.

2. 02

   #### Scan and save

   Scan energy and save. Widen the well, scan again and compare the positions of the peaks.

   **What to observe:** A saved sample keeps the settings that produced it.

3. 03

   #### Find the limits

   Use thick barriers and a coarse scan, then refine the scan. More counts at points that miss the peak cannot recover it.

   **What to observe:** Counting noise and the bias from a coarse energy grid are two separate problems.

Physical conclusion

Electrons scatter elastically in one channel with two spin states. The effective mass is a uniform illustrative value, and the barriers are rectangular. The bias only changes how the reservoirs are filled; the potential stays fixed. The simulated single-electron counts, and the current estimated from them over a finite energy window, are kept separate from the model predictions. Self-consistent electrostatics of the device and inelastic scattering are not included.

Quantum & fields · Starter path

## Start from a single measurement

Predict an outcome, then count what the measurements actually give. The path starts with one qubit and moves on to wave packets, bound states and two-photon interference.

[Start here → **Quantum State & Born Measurement** Predict a probability, turn the analyzer, then compare your prediction with the measured frequency over many shots. Observe · 15 min](https://sandboxphysics.com/labs/qubit-state/)

1. [1 Quantum State & Born Measurement](https://sandboxphysics.com/labs/qubit-state/)
2. [2 Stern–Gerlach Sequence](https://sandboxphysics.com/labs/stern-gerlach-sequence/)
3. [3 Wave Packet & Uncertainty](https://sandboxphysics.com/labs/wave-packet-uncertainty/)
4. [4 Quantum Harmonic Oscillator](https://sandboxphysics.com/labs/quantum-harmonic-oscillator/)
5. [5 Which Path & Quantum Eraser](https://sandboxphysics.com/labs/quantum-eraser/)
6. [6 Hong–Ou–Mandel Two-Photon Interference](https://sandboxphysics.com/labs/hong-ou-mandel/)

[View the full path →](https://sandboxphysics.com/topics/quantum/#starter-path)