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}.
The maximum collector doping concentration can be determined from Equation (12.54) as
\begin{aligned}V_{p t}=\frac{e x_{B O}^{2}}{2 \epsilon_{s}} \cdot \frac{N_{B}\left(N_{C}+N_{B}\right)}{N_{C}} \\ \end{aligned} (12.54)
\begin{aligned}25=\frac{\left(1.6 \times 10^{-19}\right)\left(0.5 \times 10^{-4}\right)^{2}\left(10^{16}\right)\left(N_{C}+10^{16}\right)}{2(11.7)\left(8.85 \times 10^{-14}\right) N_{C}}\end{aligned}
or
12.94=1+\frac{10^{16}}{N_{C}}
which yields
N_{C}=8.38 \times 10^{14} \mathrm{~cm}^{-3}
Using this \mathrm{n}-type doping concentration for the collector, we can determine the minimum width of the collector region such that the depletion region extending into the collector will not reach the substrate and cause breakdown in the collector region. We have, using the results of Chapter 7,
x_{d C}=x_{C}=5.97 \mu \mathrm{m}
Comment
From Figure 7.15, the expected avalanche breakdown voltage for this junction is greater than 300 \mathrm{~V}. Obviously punch-through will occur before the normal breakdown voltage in this case. For a larger punch-through voltage, a larger metallurgical base width will be required, since a lower collector doping concentration is becoming impractical. A larger punch-through voltage will also require a larger collector width in order to avoid premature breakdown in this region.
