P-Type Carrier Concentration Calculator
Solve the p-type charge-neutrality relation p = (NA + sqrt(NA² + 4·ni²))/2 for equilibrium hole concentration. NA is ionized acceptor concentration and ni is intrinsic concentration in cm⁻³.
Description
Solve equilibrium hole concentration for uncompensated p-type material from ionized acceptor and intrinsic concentrations.
Solve the p-type charge-neutrality relation p = (NA + sqrt(NA² + 4·ni²))/2 for equilibrium hole concentration. NA is ionized acceptor concentration and ni is intrinsic concentration in cm⁻³.
When to use P-Type Carrier Concentration Calculator
- Solve equilibrium hole concentration for uncompensated p-type material from ionized acceptor and intrinsic concentrations.
- Compare fabrication or device scenarios while holding coefficients and unit conventions constant.
- Check a hand calculation before moving to a higher-fidelity process, circuit, or TCAD model.
How the calculation works
The exact quadratic approaches ni at zero acceptor concentration and NA when acceptors dominate.
p = NA/2 + √[(NA/2)² + ni²] Interpreting the result
The exact quadratic approaches ni at zero acceptor concentration and NA when acceptors dominate.
Assumptions and limitations
- The result assumes equilibrium mass action, one acceptor species, complete ionization, and no donor compensation.
- Use parameters measured for the same material, geometry, temperature, and operating regime whenever the result informs engineering work.