PN Diode: Ideality Factor from ln I versus V
Unknown silicon diode at known T. Measure forward I at several V and recover n from a fit of ln I versus V.
Goal
Determine n from I ≈ I₀ exp(V/(n V_T)). The slope of ln I versus V is 1/(n V_T), so n = 1/(slope · V_T).
Equipment
- Unknown Si diode
- Known T
- DC source
- Ammeter
Experiment
Theory
Shockley’s equation is I = I₀ (e^{V/(n V_T)} − 1) with V_T = k_B T/e. In strong forward bias the −1 is negligible and ln I is linear in V. The bench hides I₀, n and live I. T (and therefore V_T) is known. An ammeter reports I after you record. This is an I–V lab, not a band cartoon.
Procedure
- Temperature T is fixed and known. You only change the forward voltage V. Stay in strong forward bias (about 0.50–0.72 V).
- Record. An ammeter logs I with small noise. There is no live I, I₀ or n.
- The notebook computes ln I. Repeat for at least 6 voltages.
- Fit ln I versus V; n = 1 / (slope · V_T). Compare with the reference.
Conclusion
The fitted ideality agrees with the hidden diode. Main uncertainties: ammeter noise and neglecting the −1 in the Shockley law.