BJT Base Width Modulation Calculator
Quantify BJT base-width modulation (Early effect) from the reverse-biased collector-base junction: fractionalChange = (sqrt(Vbi+VCB)-sqrt(Vbi))·sqrt(2·εSi/(q·NA)) / Wb, with Vbi=builtInVoltageV>0 V, VCB=collectorBaseVoltageV>=0 V, NA=acceptorDopingPerCm3>0 cm^-3, Wb=baseWidthUm>0 um, εSi=11.7·ε0 F/cm, q=1.602e-19 C. Uses stable sqrt difference; checks total voltage finiteness and depletion-factor overflow. One-sided abrupt-junction approximation neglecting emitter side and non-uniform doping; valid for NA not too low and moderate VCB; result >=0, zero when VCB=0.
Description
Estimate fractional BJT neutral-base narrowing caused by collector-base reverse bias.
Quantify BJT base-width modulation (Early effect) from the reverse-biased collector-base junction: fractionalChange = (sqrt(Vbi+VCB)-sqrt(Vbi))·sqrt(2·εSi/(q·NA)) / Wb, with Vbi=builtInVoltageV>0 V, VCB=collectorBaseVoltageV>=0 V, NA=acceptorDopingPerCm3>0 cm^-3, Wb=baseWidthUm>0 um, εSi=11.7·ε0 F/cm, q=1.602e-19 C. Uses stable sqrt difference; checks total voltage finiteness and depletion-factor overflow. One-sided abrupt-junction approximation neglecting emitter side and non-uniform doping; valid for NA not too low and moderate VCB; result >=0, zero when VCB=0.
When to use BJT Base Width Modulation Calculator
- Estimate fractional BJT neutral-base narrowing caused by collector-base reverse bias.
- 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
A value approaching one indicates the depletion change is consuming the modeled neutral base and the small-change interpretation is breaking down.
ΔWB/WB = [√(Vbi+VCB)−√Vbi]·√[2εSi/(qNA)] / WB Interpreting the result
A value approaching one indicates the depletion change is consuming the modeled neutral base and the small-change interpretation is breaking down.
Assumptions and limitations
- The formula uses a one-sided abrupt collector-base junction with uniform base doping and excludes emitter depletion, grading, and high injection.
- Use parameters measured for the same material, geometry, temperature, and operating regime whenever the result informs engineering work.