Question #43838

In a particular p-n junction diode, Zener (quantum tunneling) and Avalanche (impact ionization) breakdown mechanisms compete. The diode enters breakdown when the reverse bias voltage reaches the lower of the two threshold voltages, $V_Z$ or $V_A$.

The Zener threshold voltage $V_Z$ is directly proportional to the semiconductor's energy band gap $E_g(T)$. The Avalanche threshold voltage $V_A$ increases linearly with temperature due to enhanced phonon scattering, given by $V_A(T) = V_0 [1 + \beta (T - T_0)]$.

At $T_0 = 300\text{ K}$, both mechanisms have an identical threshold voltage of $V_0 = 6.00\text{ V}$. The energy band gap at $300\text{ K}$ is $E_g(300\text{ K}) = 1.20\text{ eV}$, and it varies with temperature as $E_g(T) = E_g(T_0) - \alpha (T - T_0)$, where $\alpha = 4.0 \times 10^{-4}\text{ eV/K}$. The temperature coefficient for the Avalanche mechanism is $\beta = 2.0 \times 10^{-3}\text{ K}^{-1}$.

What is the actual breakdown voltage of the diode at $T = 400\text{ K}$ and $T = 200\text{ K}$, respectively?