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An analytical expression for the current in short-base transistors

Publication Type:

Journal Article

Source:

Solid-State Electron. (UK), Volume 38, Number 8, p.1431 - 6 (1995)

URL:

http://dx.doi.org/10.1016/0038-1101(94)00292-N

Keywords:

bipolar transistors;Boltzmann equation;carrier mobility;minority carriers;

Abstract:

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 collector or by backscattering into the emitter. These exit velocities are shown to deviate from the Maxwellian value of 2vR, where vR is the Richardson velocity, due to the angular anisotropy of the non-equilibrium distribution. The new exit velocities are then used to improve the Schottky boundary conditions for thermionic emission at the junctions to the base. A current-balancing approach is then employed, using these junction currents and a diffusion current for base transport, to develop an analytical expression for the collector current. The diffusivity used in the base-transport current is an average of the spatially dependent diffusivity which is required to keep the current constant by compensating for the non-linearity of the minority-carrier-electron profile in the base. This non-linearity increases as the basewidth is reduced. The presence, in the resulting analytical expression for the current, of a correction factor associated with both the exit velocities of the carriers and the average value of the basewidth-dependent diffusivity, 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 BTE

Notes:

short-base transistors;Boltzmann transport equation;boundary values;collector absorption;backscattering;exit velocities;Maxwellian value;Richardson velocity;angular anisotropy;Schottky boundary conditions;thermionic emission;current-balancing approach;diffusion current;junction currents;collector current;spatially dependent diffusivity;minority-carrier-electron profile;basewidth-dependent diffusivity;