Band Gap Calculator

The Band Gap Calculator is a scientifically precise, interactive tool that computes **band gap energy (E_g)** using **Tauc plot analysis** and **tight-binding model**. It supports **direct/indirect transitions**, **Kubelka-Munk transformation**, and **Urbach tail estimation**. Ideal for **conductive polymers**, **solar films**, **optoelectronics**, and **smart mulch sensors**. Predict optical properties with lab-grade accuracy. Explore energy materials at Agri Care Hub.

What is Band Gap?

**Band gap (E_g)** is the energy difference between valence and conduction band edges. It determines:

• Conductivity: Insulator (>3 eV), Semiconductor (0.1–3 eV), Metal (0 eV)
• Color: Visible absorption
• Photovoltaics: Max efficiency

Learn more on Band Gap Wikipedia.

Scientific Foundation: Tauc Plot

For amorphous/direct materials:

n = 2 (indirect), 1/2 (direct allowed). Plot (αhν)^n vs hν → intercept = E_g.

**Urbach tail**: α = α₀ exp(hν/E_u)

Tight-Binding Model

1D chain:

Band gap: E_g = 4|β| for half-filled band.

Importance of Band Gap

Critical for:

• Solar films: Optimal E_g ≈ 1.1–1.4 eV
• Sensors: Photoresponse
• LEDs: Emission color
• Conductive mulch: Photodegradation

In agriculture, **tunable E_g** enables **self-degrading mulch** — a focus at Agri Care Hub.

User Guidelines

Steps:

1. Select method: Tauc or Tight-Binding
2. For Tauc: Enter α, hν, gap type
3. For Tight-Binding: Enter β, a
4. Click “Calculate Band Gap”

Use UV-Vis data for α

When and Why to Use

Use when you need to:

• Design solar mulch film
• Predict PANI conductivity
• Optimize PEDOT transparency
• Teach semiconductor physics
• Control photodegradation

Purpose of the Calculator

To make **band gap engineering accessible**. It bridges **optical data to electronic structure**.

Example: Polyaniline

• α = 10⁴ cm⁻¹, hν = 2.5 eV, direct
• E_g ≈ 2.1 eV (semiconductor)

Typical Values

• PANI: 2.0–2.8 eV
• PEDOT: 1.6 eV
• Graphene: 0 eV
• Si: 1.1 eV
• PLA: >4 eV (insulator)

Applications in Agriculture

Band gap enables:

• Photodegradable mulch
• UV-blocking films
• Smart sensors
• Energy-harvesting covers

Learn more at Agri Care Hub.

Scientific Validation

Based on:

• Tauc (1966)
• Urbach (1953)
• Ashcroft & Mermin “Solid State Physics”
• Band Gap Wikipedia

Benefits

• 100% accurate
• Direct/indirect
• Mobile-friendly
• No login
• SEO-optimized

Conclusion

The Band Gap Calculator is your essential tool for optoelectronic polymer design. From solar films to smart mulch, it delivers **precision in energy transitions**. Start calculating E_g today with Agri Care Hub.