Design the collector doping concentration and collector width to meet a punchthrough voltage specification.
Consider a uniformly doped silicon bipolar transistor with a metallurgical base width of 0.5 \mu \mathrm{m} and a base doping of N_{B}=10^{16} \mathrm{~cm}^{-3}. The punch-through voltage is to be V_{p t}=25 \mathrm{~V}.