Silicon-on-insulator (SOI) technology has been of interest since the 1970's due to advantages in device isolation and speed,
etc., over regular MOSFET's, , . A common difficulty with SOI technologies has been obtaining accurate SPICE
simulations of circuits that correctly model SOI device behavior, including the "kink" effect.
SPICE software requires current-voltage (I-V) formulae for the transistor elements in circuits, and modeling the I-V
relationships for SOI devices has introduced only small variations from the standard bulk MOSFET formulae, -. The latter,
at small channel lengths, now require up to 200 parameters in their descriptions. This formulation requires extensive test data
and identification, an expensive and time-consuming operation.
Among the efforts to reduce over-parametrization and return to a fundamental, physics-based description, we have been
developing the asymptotic analysis developed by Ward  .This work approached the partial differential equations governing
the flow of electrons and holes , in terms of
1. A perturbation expansion based on the small parameter measuring the ratio of depletion layer depth to channel length. The
first term in this expansion gives the ``quasi-one-dimensional approximation,'' which is the standard approximation usually
adopted, based on ``long channel'' arguments. Ward shows how to improve on this approximation to include source and
drain corner effects, but the analysis is limited to small drain voltages.
2. An asymptotic solution to the quasi-1-D equations based on the large parameter measuring the ratio of doping to the
This approach identifies the electron-rich inversion region as a thin boundary layer, and applies the method of matched
asymptotic expansions . This approach was introduced in semi-conductor physics by Please,  for the p-n junction, and