Calculator Form
Example Data Table
These examples show typical engineering inputs and model outputs.
| Case | E (eV) | V0 (eV) | a (nm) | m*/me | Model | Regime | T | Current (A) |
|---|---|---|---|---|---|---|---|---|
| Case A | 0.6 | 1.4 | 1 | 0.19 | Exact Rectangular Barrier | Below barrier | 0.069661 | 1.116086e-8 |
| Case B | 0.9 | 1.6 | 1.5 | 0.25 | WKB Approximation | Below barrier | 0.001613 | 6.461654e-10 |
| Case C | 1.8 | 1.2 | 0.8 | 0.1 | Exact Rectangular Barrier | Above barrier | 0.808268 | 1.035990e-7 |
How to Use This Calculator
- Enter the electron energy in electron volts.
- Enter the barrier height and width.
- Set the effective mass ratio for the material system.
- Enter the incoming electron flux for current estimation.
- Select the exact model or the WKB method.
- Press the calculate button to view results above the form.
- Review transmission, decay, wavelength, and current values.
- Export the result as CSV or PDF when needed.
Formula Used
For a rectangular barrier, the key quantities are based on quantum wave behavior.
Below the Barrier
Decay constant:
κ = √(2m*(V0 - E)q) / ħ
WKB transmission:
T ≈ exp(-2κa)
Exact rectangular barrier transmission:
T = 1 / [1 + (V0² sinh²(κa)) / (4E(V0 - E))]
Above the Barrier
Internal wave number:
k2 = √(2m*(E - V0)q) / ħ
Exact transmission:
T = 1 / [1 + (V0² sin²(k2a)) / (4E(E - V0))]
Estimated Current
I = q × incident flux × T
Here, q is the electron charge, ħ is reduced Planck's constant, and all energy terms stay consistent within the chosen model.
Electron Tunneling in Engineering
Why This Effect Matters
Electron tunneling is a core quantum effect. It lets electrons cross barriers without enough classical energy. This behavior matters in nanoscale engineering. It appears in tunnel diodes, flash memory, scanning tunneling microscopes, Josephson junctions, and thin oxide devices. Accurate estimates help engineers compare materials, barrier widths, and operating voltages. A practical tunneling calculator reduces guesswork. It turns quantum equations into quick design checks. That saves time during device screening. It also supports early research, coursework, and feasibility reviews.
Inputs That Control Transmission
Three inputs drive most tunneling results. The first is electron energy. Higher electron energy usually raises transmission. The second is barrier height. A higher barrier blocks more particles. The third is barrier width. Even a small width increase can sharply reduce transmission. Effective mass also matters. A larger effective mass strengthens decay inside the barrier. Model choice matters too. The WKB approach is fast and useful for thick barriers. The exact rectangular barrier model is better for precise comparisons and resonance behavior above the barrier.
Outputs Engineers Can Use
This calculator reports more than one number. It shows tunneling probability, probability percent, decay constant, attenuation exponent, penetration depth, wave number, wavelength, transmitted flux, and estimated current. These outputs help engineers understand both physics and device impact. A tiny change in width can alter current by orders of magnitude. That sensitivity is why clean inputs matter. Engineers can test multiple cases and compare trends. The example table supports quick validation. The export options also help with reports, lab notes, and design reviews.
Practical Use in Design Work
Use this tool when you need fast insight into quantum transport across thin barriers. Start with realistic values from literature, datasheets, or simulations. Keep units consistent. Compare WKB and exact outputs when accuracy matters. Review the regime note before making decisions. If electron energy exceeds barrier height, wave behavior changes and transmission may oscillate. If the barrier is much higher than the electron energy, the decay constant becomes dominant. In real devices, temperature, image-force lowering, complex band structure, and nonideal interfaces can also matter. Still, this calculator gives a strong first-pass engineering estimate. It is useful for education and process development. It can also support sensitivity checks before detailed numerical simulation begins on real projects.
Frequently Asked Questions
1. What does electron tunneling mean?
Electron tunneling is a quantum process where an electron crosses an energy barrier that classical physics would treat as blocked. It becomes important in nanoscale devices and thin insulating layers.
2. When should I use the WKB option?
Use WKB for fast estimates when the barrier is thick and the electron energy stays below the barrier. It is useful for trend studies and early design screening.
3. When is the exact model better?
The exact rectangular barrier model is better when you want more precise results, especially near the barrier top or when transmission oscillations above the barrier matter.
4. Why does width change the result so much?
Tunneling depends exponentially on barrier width in the forbidden region. A small increase in width can strongly reduce transmission and current. That makes width one of the most sensitive inputs.
5. What is effective mass ratio?
It is the electron effective mass in the material divided by the free electron mass. Semiconductor materials often use effective mass because band structure changes carrier motion.
6. Is the current result a full device current?
No. It is a simple estimate based on incident electron flux and transmission probability. Real device current may also depend on density of states, temperature, contact effects, and geometry.
7. Can this calculator model every tunneling device?
No. It is best for first-pass engineering estimates with a rectangular barrier idea. Advanced devices may need image-force lowering, band bending, multi-layer barriers, or numerical transport solvers.
8. What units should I enter?
Enter electron energy and barrier height in eV, barrier width in nm, effective mass as m*/me, and incident flux in electrons per second. The calculator handles internal unit conversion.