Abstract: The previous report (XI) gave the electrochemical-potential theory of the Bipolar Field-Effect Transistors.This report (XII) gives the drift-diffusion theory.Both treat 1-gate and 2-gate,pure-base and impure-base,and thin and thick base.Both utilize the surface and bulk potentials as the parametric variables to couple the voltage and current equations.In the present drift-diffusion theory,the very many current terms are identified by their mobility multiplier for the components of drift current,and the diffusivity multiplier for the components of the diffusion current.Complete analytical drift-diffusion equations are presented to give the DC current-voltage characteristics of four common MOS transistor structures.The drift current consists of four terms:1-D (One-Dimensional) bulk charge drift term,1-D carrier space-charge drift term,1-D E2X(transverse electric field) drift term,2-D drift term.The diffusion current consists of three terms:1-D bulk charge diffusion term,1-D carrier space-charge diffusion term,and 2-D diffusion term.The 1-D E2X drift term was missed by all the existing transistor theories,and contributes significantly,as much as 25% of the total current when the base layer is nearly pure.The 2-D terms come from longitudinal gradient of the longitudinal electric field,which scales as the square of the Debye to Channel length ratio, at 25nm channel length with nearly pure base,(LD/L)2=1E6,but with impurity concentration of 1E18cm-3,(LD/L)2=1E-2.

Key words: bipolar field-effect transistor theory, surface potential, drift and diffusion theory, single-gate impure-base, double-gate impure-base