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Diode current at 100°C (eta 1.8)

Short answer

The forward voltage drops 144 mV from 20°C to 100°C. With VT(100°C)=32.15 mV, ηVT=57.9 mV, current rises to I≈1 mA×exp(144/57.9)≈12 mA.

A diode conducts 1mA at 20°C. If it is operated at 100°C, what will be its current? Given data are: η = 1.8 and negative temperature coefficient value = -1.8 mV/°C.

For a fixed diode current the forward voltage falls with temperature at about -1.8 mV/°C. If the applied voltage stays the same, the current rises exponentially.

Given

I1 = 1 mA at 20 °C, T2 = 100 °C, η = 1.8, temperature coefficient = -1.8 mV/°C.

Steps

ΔV  = -1.8 mV/°C × (100 - 20) = -144 mV
VT (100 °C) = 8.617×10⁻⁵ × 373.15 = 32.15 mV
η VT = 1.8 × 32.15 = 57.9 mV

I2 = I1 × exp(|ΔV|/(η VT))
   = 1 mA × exp(144/57.9) = 1 mA × exp(2.49)
   ≈ 12.0 mA

Answer: I ≈ 12 mA at 100 °C (about 12 times the 20 °C value).

Assumption: VT is taken at 100 °C; using VT = 25 mV gives ≈ 24.5 mA instead.

✓ Answer checked by Claude Opus 5.5 (high effort)

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