New Analytic Determination of the Frequency Dependence of Current Gain and Power Gain in HBTs Applied to their High-Frequency Optimization and Study of Velocity Overshoot Effects in Precollectors Using Analytic Descriptions

Graduate Students : Dave Pehlke*, Don Sawdai
Professor D. Pavlidis
U.S.Army Research Office DAAL03-92-G-0109, Bell Northern Research

This work has resulted in a new approach to the analytic expression of current gain and power gain of Heterojunction Bipolar Transistors (HBTs), along with new and highly accurate expressions for their respective unity intercept frequencies, fT and fMAX. In order to determine the intercept frequencies for fT and fMAX for HBTs when they exist above the highest frequency of measurement systems, single pole extrapolation techniques from the highest measurable frequency are used. This extrapolation is found to be a pessimistic benchmark for the actual current gain intercept fT, and often is inaccurate in cases where the first order zero of the h21(s) transfer function is low enough in frequency to extend the region of positive current gain out well beyond the extrapolated fT intercept frequency. The analytic calculation of the h21(s) pole and zero frequencies is used to explain non-idealities in gain roll-off for -(h21)^2 and provides the basis for accurate extrapolation criteria in determining fT. The validity of extrapolation for the Maximum Available Gain (Gmax) and Unilateral Gain (U) are described analytically, along with the transit time effect of resonances in U and the accurate description of the condition for resonance and resonance frequencies. These analytic approaches for the exact calculation of intercept frequencies are then applied toward analytic approaches for the high-speed optimization of HBTs, and the fundamental limitations to their small-signal switching performance at those higher frequencies.

A first complete equivalent circuit model is developed to account for velocity overshoot in the pre-collector region of HBTs, and provides the first analytic tool for accurate transit delay optimization in that region. Analytic expressions for the pre-collector transport factor a(omega) are incorporated into the base transport factor, a(omega), expression of the HBT T-Model equivalent circuit yielding a new analytic expression for the HBT pre-collector transit delay time, Tau(PCD). A new analytic two region model for the velocity profile of electrons in GaAs has been developed and analyzed as applied to the pre- collector region of HBTs. The profile was investigated to demonstrate that for a given peak velocity, v(p), the ideal peak placement for minimum delay is in the middle of the pre-collector thickness.

The HBT pre-collector transit delay is calculated from the peak velocity (v(p)) and vSAT of the velocity profile. Constant average velocity models are often used for this, and may significantly overestimate the transit times of this region by as much as 65%. This model has been used to demonstrate clear evidence of the overshoot effect in measured HBTs, and has been applied as part of an equivalent circuit parameter extraction formalism to successfully find peak velocities, mean free times to the peak velocity and transit delays in experimental devices.

The extent to which velocity overshoot effects improve the small-signal high- frequency performance of HBTs has been investigated in an analytic approach that allows parametric evaluation on the basis of any given technology, geometry, etc. The increase in speed is normalized to technical and geometric factors and is studied over a wide range of electric field values. The analysis demonstrates that even for power devices under relatively large electric fields, state-of-the-art technologies will be significantly impacted by the non-uniform velocity distributions within the HBT pre-collector region. Studies along these lines are currently extended towards InP-based HBTs in order to calculate velocity overshoot in such devices.

Current gain vs. frequency for an AlGaAs/GaAs HBT evaluated using analytical modeling techniques. The results show the proper etrapolation precudure from the f(3dB), along with the conventionally quoted fT form the last measured point (fTQuoted) and the analytically calculated actual intercept frequency fTAct. The quoted fTQuoted is neither the proper extrapolation frequency, nor the actual intercept, but provide a coservative benchmark for that actual intercept frequency fTAct.

Parameter extraction bias dependent results for the total forward transit delay time Tau(F), the pre-collector signal delay time Tau(PCD), and the base transit time Tau(B), all calculated from measured S-parameters. Analytic velocity overshoot modeling has been applied to experimentaly characterized AlGaAs/GaAs HBTs for this purpose. The pre-collector transit delay time Tau(PCD) increases rapidly with base collector reverse bias as a result of diminishing velocity overshoot.

Current Research Programs: HBTs

Current Research Programs

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