 
Summary: SOCAMS 2004, Claremont, CA.
Modeling Quantum Effects on
Current/Voltage Characteristics of a MOSFET Transistor
Henok Abebe, USC Information Sciences Institute, MOSIS Service,
Ellis Cumberbatch, School of Mathematical Sciences, CGU
When the dielectric thickness of the MOSFET (metaloxidesilicon fieldeffect
transistor) device is reduced below 4nm, quantum mechanical (QM) effects near
the silicon/silicon oxide interface become significant. QM tunneling and
confinement affect the profile of the inversion charge in the direction normal to
the interface, and the current is reduced. The accuracy of SPICE, the industry's
circuit simulator, deteriorates rapidly when the current/voltage characteristics are
incorrect.
Full solutions of the Schrödinger and Gauss equations are available, but require
highlevel numerical simulations, impractical for SPICE application. An
alternative is provided by the densitygradient (DG) model, which may be
identified as an averaged form of the Schrödinger equation. Numerical results on
the DG model show that electron charge density is reduced substantially in a
narrow layer close to the silicon/silicon oxide interface, but its behavior outside
this layer is similar to the nonquantum, classical solution, [1]. This is a classical
boundary layer phenomenon.
