Mass Action Law Check
Check the mass action law by comparing the electron-hole product against the square of the intrinsic carrier concentration.
Description
Check the mass action law by comparing the electron-hole product against the square of the intrinsic carrier concentration.
Mass Action Law Check is a focused tool for the following task. Check the mass action law by comparing the electron-hole product against the square of the intrinsic carrier concentration. It reports np product, Deviation percent from the values you provide rather than inventing measurements, coefficients, or professional judgment that are not part of the input.
When to use Mass Action Law Check
Use this semiconductor calculation for first-order device, material, fabrication, interconnect, packaging, or reliability estimates when every coefficient and unit convention is known.
- Electron concentration (cm^-3)
- Required number in cm^-3. Electron concentration n.
- Hole concentration (cm^-3)
- Required number in cm^-3. Hole concentration p.
- Intrinsic concentration (cm^-3)
- Required number in cm^-3. Intrinsic carrier concentration ni.
The cited overview of Semiconductor device supplies background for the terminology and domain context used by this tool.1
How Mass Action Law Check works
Check the mass action law by comparing the electron-hole product against the square of the intrinsic carrier concentration. Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.
- np product (cm^-6)
- Returned number in cm^-6. Product of the electron and hole concentrations.
- Deviation percent (%)
- Returned number in %. Relative deviation of the product from the squared intrinsic concentration.
Limitations and assumptions
- Material composition, geometry, process history, temperature, electric field, bias, interfaces, parasitics, and fitted parameter ranges can invalidate a compact semiconductor model.
- Electron concentration must be at least 5e-324.
- Hole concentration must be at least 5e-324.
- Intrinsic concentration must be at least 5e-324.
- Use finite inputs in the displayed units, preserve source measurements and assumptions, and independently verify consequential decisions.
Alternative or Complementary approaches
Compare the estimate with measured process data, current device documentation, and a higher-fidelity circuit, field, thermal, quantum, or TCAD model when the decision requires it.
References
-
Semiconductor device — Wikipedia contributors
Similar or alternative tools
- N-Type Carrier Concentration Calculator
Solve the n-type charge-neutrality relation n = (ND + sqrt(ND² + 4·ni²))/2 for equilibrium electron concentration. ND is ionized donor concentration in cm⁻³ and ni is intrinsic concentration in cm⁻³, both per volume.
- 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.
- Charge Neutrality Carrier Solver
Solve the exact charge-neutrality relations n = (Nd-Na+√((Nd-Na)²+4ni²))/2 and p = ni²/n for equilibrium electron and hole concentrations. Nd, Na, ni in cm⁻³.