| Summary: | 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formulated over 40 years ago, are based upon assumptions that are no longer valid.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.]
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