Consequently, nonlinear frequency domain techniques like harmonic balance are widely used to solve such problems. However, current harmonic balance tools are circuit simulators which use either analytic or lumped models for the semiconductor devices. These models are not based on numerical solution of the underlying semiconductor equations, and are thus not as accurate nor nearly as predictive as full numerical device simulation. Because it is the nonlinear active devices which are ultimately responsible for the distortion present in the system, an accurate physical model of the device is extremely important, both for accurately simulating the distortion and for examining the internal operation of the device with a view towards optimizing device structure.
We have developed a harmonic balance version of the PISCES semiconductor device simulator to give the device and circuit designer accurate, physically based insight into device operation. This two-dimensional device simulation tool solves the drift-diffusion system of semiconductor equations in the frequency domain, using the full complement of PISCES physical models. A mixed-mode circuit capability is also present to model linear parasitics and packaging outside the device. We have successfully employed this code to simulate intermodulation distortion in a silicon RF power BJT at a center frequency of 1.5GHz, with tone spacing of 30kHz. The wide range of frequencies present in such an analysis would necessitate the integration over at least 105 periods of the 1.5GHz sinusoid, with spacing fine enough to resolve its harmonics. Such an analysis would be many orders of magnitude more time-consuming than its harmonic balance counterpart.
To handle the inherently large size of frequency domain 2D device analysis, we have also developed a nonlinear relaxation scheme to efficiently solve the time-dependent harmonic balance semiconductor equations. This scheme overcomes the extreme memory problems posed by conventional fully-coupled Newton-Raphson methods, while at the same time substantially decreasing the computation time and maintaining robust convergence. As a result, nonlinear frequency domain physically-based device analysis is brought well within the computing power of ordinary desktop workstations.