Theoretical and experimental study of MOS transistors nonuniformly doped by SILOX technique

Comparison of Simple Approximations and Numerical Solutions for the Threshold Voltage of Ion-Implanted Long-Channel MOSFET's

“…More sophisticated analytical techniques have, of course, been applied to predicting the threshold shifts due to nonuniform doping profiles [6]- [8]. For example, Brews [8] has introduced a simplified method of calculation which does not require a numerical solution to Poisson's equation; he invokes a charge-sheet approximation for the inversion layer and a modified depletion approximation for majority carriers.…”

“…Details of these simplifications are given in [ 1]. The drain current in this model is then given by (5) (6) where the electron density n and the hole density p are n = niexp(q(ir -On)/kT) (7) p = niexp(q(p -q)/IkT) (8) and where Shockley-Read-Hall recombination is given by R = -(pn-n'3 (9 TnO(n + ni) + Tpo(p +pi) (9) The symbols have their usual meaning as defined in [11].…”

“…This is then used to replace (8) and eliminate (6). If, in addition, the channel current is assumed to flow only in a one-dimensional sheet at the surface, the problem is reduced to solving (4) and In order to determine the threshold voltage, the drain current gate voltage characteristics were calculated using (11) and extrapolated to zero current in the triode region.…”