Effects of quasi-ballistic base transport on the high-frequency characteristics of bipolar transistors

High-frequency transport in bipolar transistors with quasi-ballistic base widths (on the order of a minority-carrier scattering length) is examined by using the approach of Grinberg and Luryi (1992) to solve the Boltzmann transport equation (BTE). By considering the phase angle of the dynamic distribution function in wave-vector space, it is shown that the ballistic mechanism of decay in the common-base current gain becomes important even for base widths in the quasi-ballistic regime. Simple expressions, which correctly yield both the magnitude and phase of all the forward characteristics, as predicted by the BTE, up to the intrinsic transit frequency, are found by combining the results from a one-flux approach with the well-known expressions of Thomas and Moll (1958). Expressions for the reverse small-signal parameters are also found by applying a "moving boundary condition" to the basic one-flux equations of Shockley (1962).