For a typical $n-p-n$ transistor, as shown in the figure we have the following data available
- $\mathrm{W}_{\mathrm{C}}=20 \mu \mathrm{m}$ and Collcetor doping $=5 \times 10^{18} / \mathrm{cc}$
- $\mathrm{W}_{\mathrm{E}}=1 \mu \mathrm{m}$ and Emitter doping $=10^{19} / \mathrm{cc}$
- Base doping $=5 \times 10^{15} / \mathrm{cc}$
- Minority carrier life time in the Base region is $\tau_{n}=5 \mu \mathrm{Sec}$.
Under Punch-through condition the $\mathrm{V}_{B C}=10 \mathrm{~V}+\mathrm{V}_{b i}$ volts.
Here $V_{b i}$ is the built in potential of Base-collector junction. Emitter Injection efficiency can be assumed as 1 for this transistor.
Evaluate Base Width $W_{B}$ and the current gain $\alpha$. [Standard data for this question is : $q=1.6 \times 10^{-19}$ coloumbs; $\frac{\mathrm{KT}}{q}=25 \; \mathrm{mV}$.
For silicon at $\mathrm{T}=300 \mathrm{~K}, \mathrm{D}_{n}=30 \mathrm{~cm}^{2} / \mathrm{sec}$; $\left.\mathrm{K}_{s} \in_{\mathrm{o}}=10^{-12} \mathrm{~F} / \mathrm{cm} ; \quad n_{i}=1.5 \times 10^{10} / \mathrm{cc}\right]$