Question #76782

A semiconductor diode is used as a temperature sensor. When driven by a constant forward current, the voltage $V$ across the diode is given by the relation: $V(T) = \frac{E_g(T)}{e} - \eta T$ where $e$ is the elementary charge, $T$ is the absolute temperature, and $\eta = 4.0 \times 10^{-3} \text{ V/K}$. The band gap energy $E_g(T)$ of the semiconductor varies with temperature as: $E_g(T) = E_{g0} - \alpha T^2$ where $E_{g0} = 1.2 \text{ eV}$ and $\alpha = 2.0 \times 10^{-5} \text{ eV/K}^2$. The diode voltage is measured using a digital voltmeter with a least count of $\Delta V = 0.48 \text{ mV}$. What is the minimum temperature change $\Delta T$ (the "blind spot") that this sensor can detect at an ambient temperature of $T = 300 \text{ K}$?