Author´s reply

Prof. Parker makes the point that a properly designed model should not predict thermal instability or have multiple solutions in a device that is thermally stable, and, if it does, the model is not doing its job. The issue addressed in the original letter [ibid., vol. 12, pp. 88??89, Mar. 2002] goes a bit beyond this, however. Since self-heating models are inherently nonlinear, and many model designers seem unable to avoid equating complexity with accuracy, it is almost inevitable that multiple solutions can occur, under some conditions. A harmonic-balance analysis searches over a wide range of its independent variables (usually voltage components) to find a solution, so multiple solutions, even at unrealistic temperatures, are likely to be discovered. Models are frequently formulated to work in the expected range of temperatures, and often are not robust outside of that range. Another concern is the existence of indistinct solutions, which can lead to convergence failure in harmonic-balance analysis. The example presented by Prof. Parker can be modified to make it ill conditioned. Details are given.