AN ANALYTICAL EXPRESSION FOR THE CURRENT IN SHORT-BASE TRANSISTORS

An exact solution of the Boltzmann transport equation (BTE) for short- base transistors is used to provide boundary values for the velocities of carriers which exit the base, either by absorption at the collecto r or by backscattering into the emitter. These exit velocities are sho wn to deviate from the Maxwellian value of 2v(R), where v(R) is the Ri chardson velocity, due to the angular anisotropy of the non-equilibriu m distribution. The new exit velocities are then used to improve the S chottky boundary conditions for thermionic emission at the junctions t o the base. A current-balancing approach is then employed, using these junction currents and a diffusion current for base transport, to deve lop an analytical expression for the collector current. The diffusivit y used in the base-transport current is an average of the spatially de pendent diffusivity which is required to keep the current constant by compensating for the non-linearity of the minority-carrier-electron pr ofile in the base. This non-linearity increases as the basewidth is re duced. The presence, in the resulting analytical expression for the cu rrent, of a correction factor associated with both the exit velocities of the carriers and the average value of the basewidth-dependent diff usivity, distinguishes this equation from one that has appeared in the recent literature. The analytical expression yields results which are in near-exact agreement with those from a numerical solution of the B TE.