Physical Electronics Underlying Junction Transistor Characteristics

In most transistors which are useful to engineering, densities of electrons and holes are low enough so that random energies have the classical Maxwell-Boltzmann distribution. Also, the customary large ratios of majority-to-minority carrier densities result in majority-carrier flow occurring in response to electric gradients, and minority-carrier flow by diffusion due to concentration gradients. Steps using these principles to derive junction transistor volt-ampere characteristic equations are: 1) interface contact potential determination, 2) expression of emitter and collector currents in terms of random-motion interface penetration, 3) boundary-value solution of the diffusion-flow differential equation, to give minority-carrier density distributions, 4) expression of currents in terms of at-interface density distribution gradients, 5) elimination of at-interface minority-carrier densities between 2) and 4), giving the Ebers and Moll volt-ampere equations. These equations show how base thickness, diffusion lengths, and relative majority carrier densities in emitter, base, and collector affect the characteristics. The residual collector current is found to be a measure of electron-hole pair generation. The relation of this current to surface energy states, and to the associated double layer of charge at and near the surface, is discussed.