Band Bending From Potential Guide
Band bending links electrical potential to energy movement inside a semiconductor. A surface voltage changes the local electrostatic potential. Bands move because electron energy equals negative charge times potential. This calculator converts that potential change into electron volt shifts. It also estimates depletion width, maximum electric field, and surface charge. These extra values help in device checks.
Why The Result Matters
Band bending is important in diodes, MOS structures, sensors, contacts, and surface studies. A positive surface potential can bend electron energy bands downward. A negative potential can bend them upward. The exact direction depends on the chosen sign convention. Engineers use the result to compare surface states, doping levels, and barrier changes.
Key Inputs
The surface potential is the main input. The reference potential is usually the bulk potential. Their difference gives the bending potential. Temperature sets the thermal voltage. Doping concentration sets the space charge strength. Relative permittivity describes how strongly the material stores electric field. Intrinsic carrier concentration helps estimate the Fermi potential.
Using The Advanced Outputs
Energy shift in joules is useful for physics notes. Energy shift in electron volts is easier to read. For a single electronic charge, one volt equals one electron volt of energy shift. Depletion width is based on the depletion approximation. It is best for abrupt and uniformly doped regions. Surface charge gives the charge per unit area. Electric field estimates the strongest field near the surface.
Practical Checks
Use consistent units before entering values. The calculator accepts centimeters and meters for doping. It converts values internally. Very high doping reduces depletion width. Large potential increases field and charge. Results are estimates, not full device simulations. They ignore quantum effects, traps, interface layers, and mobile charge details. For final design, compare these outputs with measured C V data or a numerical solver.
Good Use Cases
This tool is helpful for quick semiconductor homework, lab reports, and early device sizing. It can compare silicon, germanium, gallium arsenide, or custom materials. It also shows formulas beside results, so the calculation stays transparent. Save the CSV or PDF when you need a record. Recheck all signs before sharing the result. This keeps each estimate simple, traceable, and audit ready.