A combined theory of the micromagnetic and Monte Carlo simulations is established to analyze the thermal property of a nano-sized magnetic grain. The Langevin equation of a grain's magnetic moment is the Landau-Lifshitz equation augmented by a "random-field" term representing the thermal-agitated force. The angular distribution of the magnetic moment of the grain is studied via its time evolution process. The switching of the magnetic moment vector between two energy-minimum states is observed. A simple analytical expression is obtained for the simulated attempt frequency f0, which is related to the magnetic constant of the nano-grain, and agrees well with the phenomenological value.

RF noise in quarter-micron nMOSFETs is analysed on the device level based on Shockley's impedance field method. The impact of different transport models and physical parameters is discussed in detail. Well-calibrated drift-diffusion and energy-balance models give very similar results for noise current spectral densities and noise figures. We show by numerical simulations with the general-purpose device simulator DESSIS_ISE that the hot-electron effect on RF noise is unimportant under normal operating conditions and that thermal substrate noise is dominant below 0.5 GHz. The contribution of energy-current fluctuations to the terminal noise is found to be negligible. Application of noise sources generated in bulk full-band Monte Carlo simulations changes the noise figures considerably, which underlines the importance of proper noise source models for far-from-equilibrium conditions.

We propose a new sampling method for 2D and 3D implicit surfaces. The method is based on a stochastic process defined by the Langevin equation with a Gaussian random-force term. Our Langevin equation describes a stochastic-dynamical particle, which develops in time confined around the sampled implicit surface with small width. Its numerically generated solutions can be easily moved onto the surface strictly with very few iteration of the Newton correction. The method is robust in a sense that an arbitrary number of sample points can be obtained starting from one simple initial condition. It is because (1) the time development of the stochastic-dynamical particle does not terminate even when it reaches the sampled implicit surface, and (2) there is non-zero transition probability from one disconnected component to another. The method works very well for implicit surfaces which are complicated topologically, mathematically, and/or in shape. It also has some advantageous features in rendering 3D implicit surfaces. Many examples of applying our sampling method to real 2D and 3D implicit surfaces are presented.