The micro-mechanism of molten pool and metal droplet sputtering are significant to the material erosion caused by breaking or making arcs especially for high-power switching devices. In this paper, based on Navier-Stokes equations for incompressible viscous fluid and potential equation for electric field, a 2D axially symmetric simplified hydrodynamic model was built to describe the formation of the molten metal droplet sputtering and molten pool under arc spot near electrode region. The melting process was considered by the relationship between melting metal volumetric percentage and temperature, a free surface of liquid metal deformation was solved by coupling moving mesh and the automatic re-meshing. The simulated metal droplet sputtering and molten pool behaviors are presented by the temperature and velocity distribution sequences. The influence mechanism of pressure distribution and heat flux on the formation of molten pool and metal droplet sputtering has been analyzed according to the temperature distribution and sputtering angles. Based on the simulation results, we can distinguish two different models of the molten metal droplet sputtering process: edge ejection and center ejection. Moreover, a new explanation is proposed based on calculated results with arc spot pressure distribution in the form of both unimodal and bimodal. It shows that the arc spot pressure distribution plays an important role in the metal droplet ejected from molten pool, the angle of the molten jet drop can be decreased along with the increment of the arc spot pressure.

The precision of magnetic field calculation is crucial to predict the arc behavior using magnetohydrodynamic (MHD) model. A integrated calculation method is proposed to couple the calculation of magnetic field and fluid dynamics based on the commercial software ANSYS and FLUENT, which especially benefits to take into account the existence of the ferromagnetic parts. An example concerning air arc is presented using the method.

In this work it is shown for the first time how to calculate in advance by momentum-based noise simulation for stationary Monte Carlo (MC) device simulations the CPU time, which is necessary to achieve a predefined error level. In addition, analytical expressions for the simulation-time factor of terminal current estimation are given. Without further improvements of the MC algorithm MC simulations of small terminal currents are found to be often prohibitively CPU intensive.

The validity of the expression for the electron energy flux is evaluated by using the Monte Carlo simulation. The drift, divergence, and scattering terms are directly calculated from changes in the physical values of particles. Each term composing the momentum and energy conservation equations can be reproduced by indirect calculation of the expression for the term that is a function of other physical values. However, it is found that a parameter in electron heat conductivity has to be adjusted to reproduce the direct calculation of the energy flux. Namely, the parameter of the Wiedemann-Franz law for heat conductivity should be chosen so that the underestimations of the drift and diffusion terms in the energy flux equation cancel each other. It is shown that the parameter influences the electron temperature in a 50-nm gate nMOSFET.

A Schottky contact model was implemented as a boundary condition for Monte Carlo device simulations. Unlike the ideal ohmic contact, the thermal equilibrium is unnecessary around the Schottky contact. Therefore, the wide region with high impurity concentration around the contact is not required to maintain the thermal equilibrium, which means that it is possible to avoid assigning a lot of particles to the low-field region. The validity of the present boundary condition for contacts was verified by simulating a rectifying characteristic of a Schottky barrier diode. As an application example using the present contact model, we simulated transport in n+nn+ structures with sub-0.1 µm channel lengths. We observed direction dependence of the electron velocity dispersion, which indicates that the direction dependence of the diffusion constant or the carrier temperature should be taken into account in the hydrodynamic simulation for sub-0.1 µm devices.

The consequences of energy transport related effects like velocity overshoot on the performance of bipolar transistors have already been studied previously. So far however most of the applied models were only 1D and it remained unclear whether such effects would have a significant influence on important quantities like ECL gate delay accessible only on the circuit level. To the authors' best knowledge in this paper for the first time the consequences of energy transport related effects on the circuit level are investigated in a rigorous manner by mixed level device/circuit simulation incorporating full 2D numerical hydrodynamic models on the device level.

Numerical simulation of the hydrodynamic semiconductor device equations requires powerful numerical schemes. A Space-time Galerkin/Least-Squares finite element formulation, that has been successfully applied to problems of fluid dynamic, is proposed for the solution of the hydrodynamic device equations. Similarity between the equations of fluid dynamic and semiconductor devices is discussed. The robustness and accuracy of the numerical scheme are demonstrated with the example of a single electron carrier submicron silicon MESFET device.

A Monte Carlo calculation is performed to examine the transport coefficients of the electron gas under an inhomogeneous electric field. The expressions constructed from the M. C. results are then incorporated into the hydrodynamic formulation to calculate the internal characteristics of a silicon BJT device. The calculated results agree well with the Monte Carlo prediction.