Question #42012

A semiconductor diode is forward-biased at a constant current. The voltage $V$ across the diode is given by $V(T) = \frac{E_g(T)}{e} - \beta T$, where $E_g(T)$ is the temperature-dependent band gap energy, $e$ is the elementary charge, and $\beta = 1.2 \times 10^{-3} \text{ V/K}$. The band gap energy follows the empirical relation $E_g(T) = E_g(0) - \alpha T^2$, where $\alpha = 1.5 \times 10^{-6} \text{ eV/K}^2$. The diode is used as a temperature sensor by measuring $V$ with a digital voltmeter having a least count of $4.2 \text{ mV}$. What is the minimum temperature change $\Delta T$ (the 'blind spot') that the voltmeter can resolve at an operating temperature of $T = 300 \text{ K}$?