Application of Mixedmode Simulation to High Frequency Bipolar Characterization


The high frequency analog performance of silicon bipolar transistors has, until recently, been characterized by lumped element models. These models have been used to define high frequency parameters such as the unity gain cut-off frequency fT and the maximum oscillation frequency fmax [1]. In consequence many approximations have been incorporated such as the effects of the substrate capacitance, variable base resistance, collector series resistance and distributed collector capacitance.

In this article the high frequency performance of bipolar transistors has been characterized through the application of Silvaco's ATLAS software suite for coupled device and circuit simulation. Commonly referred to as mixedmode simulation, this simulator allows direct extraction, from the amplifier circuits, of the high frequency parameters fT and fmax [2]. As a result of the physical basis of the ATLAS device simulation all parasitic effects are inherently taken into account. The predicted fT and fmax will therefore be based solely on the physical device model, rather than extracted SPICE parameters.


Simulation of High Frequency Parameters

The fT may be calculated using mixedmode based upon a simple rf amplifier circuit. As in the definition of fT the collector of the transistor is shorted to ground and an ac voltage source is connected to the base terminal. When the frequency of the ac source is varied over a large range the small signal current gain is found to vary. Figure 1 shows the simulated variation of the current gain with frequency, for a fully oxide isolated bipolar transistor, and a predicted fT of approximately 5 GHz.


Figure 1. Variation of the small signal current gain with
frequency, using mixedmode simulation, of a fully oxide
isolated bipolar transistor.


The mixedmode simulator can, in a similar manner, be used to calculate the maximum frequency of oscillation based upon the power transfer through a typical rf amplifier circuit. The rf amplifier circuit can also be designed so that the input and output impedances are matched. This ensures maximum power transfer through the transistor to achieve the highest possible fmax. Figure 2 shows the calculated input and output powers over a range of frequencies for the previous fully oxide isolated bipolar transistor. When the input power is equal to the output power, the maximum oscillation frequency has been reached, which from Figure 2 is approximately 10 GHz.


Figure 2. Mixedmode simulation of the input and output powers,
and the resultant f
max,of a rf amplifier circuit for fully
oxide isolated bipolar transistors.


Due to the inherent physical basis of the simulation, mixedmode automatically accounts for many important effects such as the substrate capacitance. The effect of the substrate capacitance on fmax can be illustrated by simulating a junction isolated transistor which has a much higher collector-substrate capacitance. Figure 3 shows the simulated input and output powers for this transistor and predicts a fmax of approximately 5 GHz, which is significantly lower than that for the fully oxide isolated device.


Figure 3. Mixedmode simulation of the input and output
powers, and the resultant f
max, of a rf amplifier circuit
with junction isolated bipolar transistors.



The MixedMode simulation of fT may also be used to calculate the base resistance, rb, of the bipolar transistor [2]. From the hybrid πequivalent circuit the input power, Pin, from an ac source is developed across the base resistance and the parallel combination of rπ and Cπ. For frequencies above 10GHz the input impedance is entirely due to the base resistance. This impedance is easily calculated based upon Pin= rb*ib2where ib is the base current. Figure 4
shows the simulated variation of the input impedance with frequency for different levels of base current. At high frequencies the impedance tends to a constant value equal to the base resistance.


Figure 4. Dependence of input impedance on
frequency for different base currents.



Mixedmode Simulation of Ring Oscillators

In practice the most reliable method to determine the frequency response of bipolar transistors is to find the oscillation frequency of a ring of ECL inverters, called a ring oscillator. In such a case the assumption that the output and input impedances of the circuit are matched may not apply. Physically the oscillations are generated as a result of the positive feedback of noise which is always present within semiconductor devices. However, the low level of noise within the simulation is insufficient to achieve oscillation. The final state of the circuit is simply a stable dc condition at the switching voltage. To initiate oscillations within the mixedmode simulator, the node voltages of one ECL gate are held constant during an initial dc simulation. This dc solution is then used to set the initial conditions for a transient analysis with all of the terminal voltages allowed to vary. The transient analysis is then capable of simulating the oscillations within the circuit. Figure 5 shows the results for a mixedmode simulation of a three stage ECL ring oscillator where the individual bipolar transistors are fully oxide isolated. The ring oscillator example can also be used to demonstrate the importance of oxide isolation for high frequency design. Repeating the ring oscillator simulation but with junction isolated bipolar transistors, the oscillations shown in Figure 6 were obtained. These results clearly indicate the importance of substrate capacitance in the high frequency operation of bipolar transistors.


Figure 5. Variation of output voltage with time for a 3 stage ECL
ring oscillator using fully oxide isolated bipolar transistors.


Figure 6. Variation of output voltage with time for a 3 stage ECL
ring oscillator using junction isolated bipolar transistors.




Coupled device and circuit simulation allows the high frequency circuit behavior of modern bipolar transistors to be accurately modeled, without the limitations imposed by standard bipolar SPICE models. Indeed, it offers new possibilities not only for the extraction of standard SPICE parameters, such as base resistance, but also improved understanding of the internal device conditions during the operation of the circuit.



[1] D.J.Roulston, "Bipolar Semiconductor Devices", McGraw-Hill, 1990.

[2] G.A.Armstrong and W.D.French, "High Speed Bipolar Transistor Design on BESOI Substrates by Mixed-Mode Simulation", 6th International Symposium on IC Technology, Systems & Applications", Singapore, September, 1995.