|Linearity of SiGe HBTs has been widely studied nowadays. The accuracy on modeling of the third order intercept point (IP3) always puts strict requirements on compact models that can reproduce measured IP3 characteristics in advanced SiGe HBT technologies. In this dissertation, two options of collector-base (CB) depletion capacitance model have been presented to correctly model IP3 peak and high injection base-collector capacitance (CBC) for a common-emitter SiGe HBT. A new technique to implement Volterra series with complete Mextram model is proposed. A new extended avalanche model with excellence in wide temperature range and current dependence at high injection has been verified to have improved IP3 dependence for common-base SiGe HBT.
For common-emitter SiGe HBT, the measured and simulated magnitude, real and imaginary part of third order output current (i2,3rd) are compared near the IP3 peak. The simulated i2,3rd from Mextram 504.12 shows that its imaginary part dominates over the real part and is much higher than measurement. This points to CBC modeling as an issue for IP3 peak modeling. Two new options of CB depletion capacitance model are then presented to correctly model the bias dependence of peak IP3. Also, the influence of each CB depletion capacitance model on peak cut-off frequency (fT) and high injection CBC are examined.
For common-base SiGe HBT, the avalanche model plays a critical role in accuracy of modeling IP3 dependence on both VCB and IE. An avalanche factor (M-1) model with improved CB voltage VCB and collector current IC dependence is first developed, which semi-empirically models the decrease of M-1 with increasing current. This was implemented in the official release of Mextram 505.00. To further improve the description of current dependence of M-1, another model is developed based on modeling the evolution of the peak electric field. This allows a more physical description of the decrease of M-1 at relatively lower IC, and the rise of M-1 at high IC when the electrical CB junction interface shifts from the original metallurgical junction to the epi-layer/buried layer interface. Parameters are also introduced to model the transition region between the low IC and high IC cases. This new extended avalanche model enables accurate fitting of the emitter current dependence of base current at high VCB up to a high level of injection above peak fT roll-off, which was not possible with existing avalanche models.
To understand the VCB and VBE dependences of IP3, as well as to identify the physical mechanisms of IP3 peak, a Volterra series analysis program is developed with a modified circuit topology that more closely resembles that of an ideal transistor equivalent circuit where the base-emitter and base-collector voltages control all circuit elements. Symbolic analysis is carried out to yield analytically the first order derivatives of all circuit elements on the two control voltages. Higher order derivatives are evaluated using numerical differentiation, with special attention paid to the handling of self heating. The validity of the Volterra series analysis program is verified by comparison with harmonic balance simulations at a lower RF power level.
A unique advantage of Volterra series is that nonlinearities from various circuit elements can be turned on and off individually, in a fashion similar to linear circuit analysis. The responses add to each other, and IP3 peak occurs when the responses cancel each other. Among 25 nonlinearities, the main current nonlinearity (IN) including epi-layer high injection effect and the avalanche current nonlinearity (IAVL) are found to dominate. The cancellation between
these two dominant nonlinearities leads to IP3 peaks for both VCB dependence and VBE dependence.
A detailed evaluation is made on the IP3 modeling capability of Mextram 504.12, 505.00, and the newly developed extended avalanche model. The main difference lies in commonbase configuration at high VCB and IE. The new model overall allows much more accurate DC modeling, much improved VCB dependence modeling, and much improved VBE/IE dependence modeling.