  Due to significant manufacturing process variations, the performance of
integrated circuits (ICs) has become increasingly uncertain. Such uncertainties
must be carefully quantified with efficient stochastic circuit simulators. This
paper discusses the recent advances of stochastic spectral circuit simulators
based on generalized polynomial chaos (gPC). Such techniques can handle both
Gaussian and non-Gaussian random parameters, showing remarkable speedup over
Monte Carlo for circuits with a small or medium number of parameters. We focus
on the recently developed stochastic testing and the application of
conventional stochastic Galerkin and stochastic collocation schemes to
nonlinear circuit problems. The uncertainty quantification algorithms for
static, transient and periodic steady-state simulations are presented along
with some practical simulation results. Some open problems in this field are
discussed.
