Compact models for the high-frequency characteristics of modern bipolar transistors
Creators: name: Vaidyanathan, Mani
Publisher: name: University of British Columbia
Year: 2009

description: Modern bipolar transistors are characterized by shrinking dimensions (now on the order of a mean-free path length for carrier scattering), reduced parasitics (particularly in heterojunction devices), and increasing cutoff frequencies (now over 100 GHz). As a result, the classical models used for transistor analysis and design, many of which were originally formulated over 40 years ago, are based upon assumptions that are no longer valid. This thesis deals with the reexamination and improvement of such models, particularly those used to describe the high-frequency characteristics. A new method of describing high-frequency carrier transport through the base of a bipolar transistor, known as the "one-flux method," is critically analyzed. It is shown that the basic one-flux equations are essentially equivalent to the classical drift-diffusion equations, and that the use of the one-flux approach to describe high-frequency transport in modern thin-base devices is essentially equivalent to employing the usual drift-diffusion equations with appropriately chosen boundary conditions. It is pointed out that while the flux approach does provide both compact, analytical expressions and useful aids for visualization, there is an inherent difficulty that exists in deriving values for the required backscattering coefficients on a rigorous, physically correct basis. A solution of the Boltzmann transport equation (BTE) in the base, and for highfrequency input signals, is carried out in order to obtain a fundamental, physical insight into the effects of carrier transport on the high-frequency operation of modern thinbase (or "quasi-ballistic") transistors, and to test the merit of recently suggested oneflux expressions for the intrinsic high-frequency characteristics of such devices. It is shown that both the common-base current gain and the dynamic distribution function are affected by a "ballistic" degradation mechanism, in addition to a "diffusive" degradation mechanism, and that, as a result, expressions from the one-flux approach alone cannot adequately model the device characteristics. Expressions which involve a combination of the one-flux expressions with the well-known expressions of Thomas and Moll are suggested for the forward characteristics, and these are then shown to agree with the BTE solutions. Expressions for the reverse parameters are derived by applying the "moving boundary approach" of Early and Pritchard to the basic one-flux equations of Shockley. Expressions for the extrapolated maximum oscillation frequency (commonly denoted fmax) of modern heterojunction bipolar transistors (HBTs) are systematically developed from a general-form, high-frequency equivalent circuit. The circuit employs an arbitrary network to model the distributed nature of the base resistance and collector-base junction capacitance, and includes the parasitic resistances of the emitter and collector. The values of fmax as found by extrapolation of both Mason's unilateral gain and the maximum available gain to unity, at —20 dB/decade, are considered. It is shown that the fmax of modern HBTs can be written in the form [equation], where fτ is the common-emitter, unity-current-gain frequency, and where (RC)eff is a general time constant that includes not only the effects of base resistance and collector-base junction capacitance, but also the effects of the parasitic emitter and collector resistances, and the device's dynamic resistance (given by the reciprocal of the transconductance). Simple expressions are derived for (RC)eff, and these are applied to two state-of-the-art devices recently reported in the literature. It is demonstrated that, in modern HBTs, (RC)eff can differ significantly from the effective base-resistance-collector-capacitance product conventionally assumed to determine fmax. [Scientific formulae used in this abstract could not be reproduced.]