Calculator inputs
Formula used
Electron affinity model: Ec = −χ + ΔEc + qφs + S. Ev = −χ − Eg − ΔEv + qφs + S.
Fermi-centered model: Ei = midgap + (kT / 2) ln(Nv / Nc). Ec = EF − (EF − Ei) − intrinsic offset + Eg / 2 + ΔEc. Ev = EF − (EF − Ei) − intrinsic offset − Eg / 2 − ΔEv.
Carrier estimates: n = Nc exp[−(Ec − EF) / kT]. p = Nv exp[−(EF − Ev) / kT]. Eg,effective = Ec − Ev.
The calculator treats electron-volts as energy units. It converts eV to joules using 1 eV = 1.602176634 × 10−19 J.
How to use this calculator
- Select a semiconductor preset or choose custom material values.
- Enter the band gap, electron affinity, temperature, and Fermi level.
- Choose the electron affinity model for vacuum referenced band edges.
- Choose the Fermi-centered model when EF − Ei is known.
- Add conduction or valence offsets for junction studies.
- Press the calculate button. Review the result above the form.
- Use the CSV or PDF buttons to save your result.
Example data table
| Material | Band gap Eg | Electron affinity χ | Typical use |
|---|---|---|---|
| Silicon | 1.12 eV | 4.05 eV | CMOS, solar cells, diodes |
| Germanium | 0.66 eV | 4.00 eV | Infrared devices, high mobility channels |
| Gallium arsenide | 1.42 eV | 4.07 eV | LEDs, lasers, RF devices |
| Gallium nitride | 3.40 eV | 4.10 eV | Power electronics, blue LEDs |
| 4H silicon carbide | 3.26 eV | 3.70 eV | High temperature power devices |
Understanding valence and conduction band energy
Why band edges matter
Valence and conduction band energies describe allowed electron states in a solid. The valence band holds the highest occupied states at low excitation. The conduction band holds states that can carry mobile electrons. Their separation is the band gap. A small gap supports easier excitation. A large gap resists thermal conduction and usually gives stronger insulation.
Energy references
Band edges need a reference. Many device drawings use the vacuum level. In that case, electron affinity places the conduction band below vacuum. The valence band sits one band gap below the conduction band. Other problems use the Fermi level or intrinsic level as the reference. This tool supports both methods, because laboratory notes often use different conventions.
Offsets and interfaces
Real devices rarely contain one ideal material. A junction may add a conduction band offset. It may also add a valence band offset. These offsets change barriers for electrons and holes. They are important in heterojunctions, quantum wells, solar cells, photodiodes, and transistors. The calculator lets you add both offsets separately. This helps compare interface designs without redrawing the full band diagram.
Temperature effects
Temperature affects carrier estimates through thermal energy kT. Higher temperature makes exponential carrier terms larger. It also changes the intrinsic carrier concentration estimate. This page does not model the temperature drift of the band gap itself. Enter a temperature corrected band gap when high precision is required. That keeps the calculation transparent and easy to audit.
Fermi level position
The Fermi level shows electron filling tendency. When it sits closer to the conduction band, the material often behaves n-type. When it sits closer to the valence band, the material often behaves p-type. If the Fermi level enters a band, simple nondegenerate formulas become approximate. The result warning helps identify that case.
Carrier estimates
The electron and hole concentrations use effective density of states values. They assume Boltzmann statistics and uniform material conditions. They are useful for quick checks, coursework, and early device design. They are not a replacement for full semiconductor simulation. Heavy doping, strong fields, traps, strain, and quantum confinement can require more advanced models.
Design checks
Before using the result, confirm the sign convention. Vacuum referenced energies often appear negative. Fermi referenced energies may look positive or negative, depending on the chosen zero. Compare only values that share one reference. For layered devices, calculate each material separately, then compare edges at the interface. Use measured offsets when possible. Literature offsets can vary with strain, composition, and surface preparation during calibration and reporting workflows in real samples.
Practical interpretation
Use the calculated Ec and Ev values to compare barriers, alignment, and optical transition energy. The joule conversion helps connect band energy with thermodynamics. The wavelength estimate links the gap to photon absorption or emission. Together, these outputs give a clear first view of semiconductor band structure.
FAQs
What is the conduction band energy?
It is the energy level where mobile electron states begin. Electrons promoted into this band can move through the material and contribute to electrical conduction.
What is the valence band energy?
It is the upper energy region filled by bound electrons in a semiconductor. Holes in this band can move and contribute to current flow.
What does band gap mean?
The band gap is the energy difference between the conduction band edge and valence band edge. It controls optical absorption, emission, and thermal carrier generation.
Which reference model should I use?
Use the electron affinity model for vacuum referenced diagrams. Use the Fermi-centered model when your problem gives Fermi level position relative to the intrinsic level.
Why is electron affinity negative in the formula?
Electron affinity measures how far the conduction band lies below the vacuum level. With vacuum set to zero, the conduction band is written as a negative energy.
Can I calculate heterojunction band offsets?
Yes. Enter a conduction band offset and a valence band offset. The calculator shifts each band edge and reports the new effective gap.
What does surface potential shift do?
It moves both band edges together. This can approximate electrostatic bending or a common potential shift in a simplified band diagram.
Are carrier concentrations exact?
No. They are estimates using effective density of states and Boltzmann factors. Heavy doping, degeneracy, traps, and quantum effects need more detailed modeling.
Why enter Nc and Nv?
Nc and Nv describe available states near the band edges. They are needed for electron, hole, and intrinsic carrier concentration estimates.
What happens if EF enters a band?
The material may be degenerate. The simple exponential carrier formulas become less accurate, so a Fermi-Dirac model may be needed.
Can this calculator help optical design?
Yes. The band gap wavelength estimate helps connect semiconductor energy with absorption or emission wavelength for LEDs, lasers, and photodiodes.