Work function with trapezoidal approximation at junction Calculator
The junction work function is approximated by a trapezoidal barrier when a bias is applied.
Formula first
Overview
The applied voltage tilts the barrier, so the effective barrier height is the average work function minus half the bias drop.
Symbols
Variables
=
Apply it well
When To Use
When to use: Use this when the wavefunction must be matched across a finite barrier or finite well.
Why it matters: The tunneling picture explains why wavefunctions oscillate in allowed regions and decay exponentially in forbidden regions.
Avoid these traps
Common Mistakes
- Using an oscillatory solution where the energy is below the barrier.
- Forgetting to match both the wavefunction and its derivative at the boundaries.
- Underestimating how quickly the tunneling signal drops with barrier width.
- Treating the barrier height as unchanged when a finite bias is present.
One free problem
Practice Problem
How does applying a bias voltage across a junction affect the shape of the potential barrier in a trapezoidal approximation?
Solve for:
Hint: Consider the relationship between electrostatic potential and the tilt of the potential energy landscape.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Engineering LibreTexts, finite square well and tunneling-barrier notes, accessed 2026-04-09
- Peverati, The Live Textbook of Physical Chemistry 2, quantum weirdness/tunneling section, accessed 2026-04-09
- Engineering LibreTexts, field enhanced emission and tunnelling effects, accessed 2026-04-09
- NIST CODATA
- IUPAC Gold Book
- Wikipedia: Work function
- Wikipedia: Electronvolt
- Introduction to Solid State Physics by Charles Kittel