Coupling of Solid-State and Electromagnetic Equations for Simulation of Wireless Packaged Geometries

Abstract

I. IntroductionThe accurate design and optimization of state-of-the-art wireless devices requires a simulator that can model both active and passive devices. Various solid-state models exist for these types of devices [1] and have been previously integrated with electromagnetic simulators (EMS), such as FDTD [2, 3, 4]. However, most of the prior implantations of this coupling have been limited in application due to the fact that the application of the CFL conditions [1] and stability requirements for the two models yields disparate time steps often with several orders of magnitude difference [2, 3]. The active device simulator (DS) has the smallest time and space stepping. The use of these values for the whole simulator makes the computational and memory requirements prohibitive for modeling an active device with integrated passives in a package. One alternative approach includes the lumped-element model of the device, but that method requires a priori knowledge of the device performance [5]. The novel approach proposed in this paper involves the development of a fully adaptive scheme in time-and space-domain that allows for the simultaneous timedomain simulation of the devices using different time and space discretization steps for the two sets of equations depending on the local details and the field variations.

An efficient method for the coupling of a fully-explicit Time-Domain solid-state hydrodynamic simulator with FDTD EM solvers

“…The novel method shown here extends the basic tenets of Vee's Leapfrog method in space and time Maxwell's Curl equation discretization to the HDM [6,7]. If one accepts that the equations can be sufficiently decoupled to stagger the gridding in space, the staggering of these variables in time is the next natural extension.…”

“…The collision terms in each of these equations describe the average carrier-carrier, carrierlattice interaction. In a multi-band device the collision term in the conservation of mass would allow for the loss or gain of mass due to the carriers' transition from one energy band to approaches to discretize the highly coupled non-linear model shown in (1 )- (6) were typically based on the staggering of the scalars and vector parameters at full and half nodal points or setting all variables at the nodal points at the same time step. This approximation is based on the assumption the variables are unable to be decoupled in time causing the model to be 2 nd order accurate in space, but only 1st order accurate in time.…”