Improved concepts for predicting the electrical behavior of bipolar structures in silicon

Most bipolar device models, based upon doping profiles and upon numerical solutions to coupled, nonlinear equations for semiconductor devices, contain empirical methods for computing the effective intrinsic carrier concentration niemobility, and lifetime. These methods usually are based upon electrical measurements, assume that the majority hole (electron) mobility equals the minority hole (electron) mobility at high doping densities, use Boltzmann statistics, and assume that the carrier lifetime is much greater than the carrier transit time. More physically correct concepts are reported in this paper and are applied to bipolar transistors in silicon. These concepts use the perturbed densities of states and nonparabolic bands which arise from a quantum mechanical description of bandgap narrowing to compute separately nieand the carrier mobility, use minority carrier lifetimes which agree much better with measured lifetimes in processed silicon, and use Fermi-Dirac statistics. When these concepts are incorporated into a device analysis code such as SEDAN¹and then used to compute the dc common-emitter gain of two n-p-n transistors, the predicted gains agree very well with the measured gains. In addition, these concepts offer potential improvements in predicting the temperature dependence of the gain.