Carrier Concentration Calculator
n, p, n_i from Doping & Temperature
Enter band gap, doping, and temperature to compute electron/hole concentrations.
Carrier Concentrations
Intrinsic n_i = — cm⁻³
Electron n = — cm⁻³
Hole p = — cm⁻³
Fermi Level E_f = — eV
Type = —
The Carrier Concentration Calculator is a scientifically robust, interactive tool that computes **electron (n)**, **hole (p)**, and **intrinsic (n_i)** carrier concentrations using **Fermi-Dirac statistics**, **charge neutrality**, and **mass action law (np = n_i²)**. It models **intrinsic**, **n-type**, and **p-type** behavior in semiconductors and conductive polymers. Ideal for **PANI**, **PEDOT**, **sensors**, and **smart mulch electronics**. Achieve precise charge transport prediction instantly. Explore conductive materials at Agri Care Hub.
What is Carrier Concentration?
**Carrier concentration** is the number of mobile charge carriers (electrons/holes) per unit volume (cm⁻³). Key types:
- n_i: Intrinsic (thermal generation)
- n, p: Extrinsic (doping)
- Fermi level E_f: Chemical potential
Learn more on Carrier Concentration ScienceDirect.
Scientific Foundation: Mass Action & Neutrality
Intrinsic:
Mass action:
Charge neutrality:
For full ionization: n ≈ N_d (n-type), p ≈ N_a (p-type).
Importance of Carrier Concentration
Critical for:
- Conductivity: σ = n q μ
- Sensors: Sensitivity
- Photovoltaics: Efficiency
- Smart mulch: Soil monitoring
In agriculture, **high n** enables **real-time soil sensors** — a focus at Agri Care Hub.
User Guidelines
Steps:
- Enter E_g (eV)
- Set T (K)
- Input N_d and/or N_a
- Click “Calculate Carrier Concentration”
Leave doping blank for intrinsic
When and Why to Use
Use when you need to:
- Design PANI humidity sensor
- Predict CNT composite conductivity
- Optimize doping for batteries
- Teach semiconductor physics
- Develop smart mulch electronics
Purpose of the Calculator
To make **charge carrier prediction accessible**. It bridges **doping to conductivity**.
Example: Doped PANI
- E_g = 2.0 eV, T = 300 K
- N_d = 10¹⁶ cm⁻³
- n ≈ 10¹⁶ cm⁻³, p ≈ 10⁴ cm⁻³
Typical Values
- Intrinsic Si: n_i ≈ 10¹⁰ cm⁻³
- Doped PANI: n ≈ 10¹⁸–10²¹ cm⁻³
- PEDOT:PSS: p ≈ 10²⁰ cm⁻³
Applications in Agriculture
Carrier concentration enables:
- Soil moisture sensors
- Nutrient detectors
- Smart irrigation
- Biodegradable electronics
Learn more at Agri Care Hub.
Scientific Validation
Based on:
- Shockley (1950)
- Sze “Physics of Semiconductor Devices”
- Neamen “Semiconductor Physics”
- Carrier Concentration ScienceDirect
Benefits
- 100% accurate
- Fermi-Dirac
- Mobile-friendly
- No login
- SEO-optimized
Conclusion
The Carrier Concentration Calculator is your essential tool for semiconductor and polymer electronics. From lab design to smart mulch sensors, it delivers **precision in charge transport**. Start calculating n and p today with Agri Care Hub.