The Transistor — Question 2

Question 2

Emitter injection and base transport jointly determine transistor gain

For a simplified NPN device, electron injection efficiency is $\gamma=.995$ and the fraction of injected electrons crossing the neutral base is $\alpha_T=.990$. Neglect leakage, so $I_C=\gamma\alpha_T I_E$.

1. Find alpha and beta.

2. If a thinner base raises $\alpha_T$ to .997 while gamma is unchanged, calculate the new beta and the base-current fraction of emitter current.

Question 2 - Solution

Emitter injection and base transport jointly determine transistor gain

(a) Method and calculation

$$\boxed{\alpha=\gamma\alpha_T=.98505}.$$$$\boxed{\beta=\alpha/(1-\alpha)=65.89}.$$

(b) Interpretation and further calculation

$$\alpha_{\mathrm{new}}=.995(.997)=.992015\Rightarrow\boxed{\beta_{\mathrm{new}}=124.23}.$$$$\boxed{I_B/I_E=1-\alpha_{\mathrm{new}}=.007985=.7985\%}.$$

Physical check

Base recombination and unwanted hole injection both consume base current. Improving only one process eventually leaves the other as the gain limit.