Modeling of lossy multiregion substrates in microelectronic circuits using time‐domain surface integral equations

Abstract

In the BiCMOS process, the trade-off in specifications of all kind of circuits can be fully utilized for possible circuit designs. In this paper, the trade-off between the NF and linearity for LNA circuit design have been tested and verified. A good choice in the first stage of the LNA design is an HBT for a better NF, and the last stage is an MOS for better linearity. Furthermore, the circuits (HBT-MOS) designed in this paper are very useful for integration with other subcircuits in 5-6-GHz receivers IC due to its powersaving characteristic and better figure of merit. With the modern microelectronic industry entering a new era featuring progressively higher speed and more highly integrated mixed-signal systems on chip, accurate modeling of distributed electromagnetic behavior of sections, which may include signal traces, power planes, substrates, and so forth, is crucial during the design flow. Driven by broadband and nonlinear circuit design [1][2][3][4][5], time-domain coupled electromagnetic and circuit simulation has been gaining popularity. In particular, integral-equation methods [6 -14] have proven to be useful since radiation conditions are built in and only surface meshing and modeling is needed. In this work, the time-domain integral equation (TDIE) method is enhanced to model realistic loss behavior in substrates, which is a crucial component for quality-factor prediction of integrated passives, as well as potentially for thermal pattern prediction. The EM simulation environment in emerging and future 3D integrated circuits is characterized by multiple piecewise homogeneous regions. Each region is comprised of lossy materials, which may or not have a strong impact on the overall performance. In general, for higher speed and higher sensitivity systems such as RF and analog methods, the loss is a crucial factor in determining system specifications and performance. The TDIE approach has been shown to work with lossy material [15][16][17][18] wherein the Green's functions, besides possessing delta functions in time, also include a broadly exponentially decaying 'wake'. This leads to the implementation issue that the spatial integrals at retarded times have to be replaced by temporal convolutions. This convolution brings not only coding complexity, but also increases the computational cost dramatically [15,17].In the presented work, the multiregion substrate geometry is addressed with a TDIE solver. An equivalent-surface approach for each region is used along with the following method to tackle the lossy medium Green's function. To circumvent the difficulty caused by the convolution in time, the decaying 'wake' in the Green's function is approximated by a sum of decaying exponentials via Prony's method. It is shown that for circuit dimensions and realistic losses, the decaying 'wake' changes slowly with the variation of the distance between the source and observation point. This allows the creation and use of an exponential fitting table for discrete distances. The use of the exponential models permits t...

MOT Solution of the PMCHWT Equation for Analyzing Transient Scattering from Conductive Dielectrics

“…Methods to efficiently compute these convolutions are proposed in [5] and [6] and are not described here.…”

“…The method to compute this convolution is one of the contributions of this work and is described next. This method represents (20) in terms of [type-1 convolution], which can be computed efficiently using existing methods [5], [6]. To this end, first, the auxiliary function is approximated using…”

“…Because of the "operator scaling" introduced in the equations to eliminate a temporal convolution, this scheme cannot be directly applied to scatterers with volumes of different conductivity. In [6], an MOT scheme for solving the electric field SIE enforced on interfaces between volumes of different conductivity is proposed. However, this scheme suffers from the problem of interior resonances if any one of the volumes is lossless [8].…”

“…However, their application to lossy dielectric and PEC scatterers residing in a lossy/dispersive medium has been very limited [2]- [6]. This is simply due to the fact that Green function of such a medium has a temporal tail [7].…”

“…This is simply due to the fact that Green function of such a medium has a temporal tail [7]. Consequently, computation of the convolution of the Green function and currents becomes very costly, and the resulting marching-on-in-time (MOT)-based TDSIE solvers have to be accelerated using blocked fast Fourier transform Manuscript (blocked-FFT) [3], plane-wave time domain (PWTD) [4], and/or Prony-series [5], [6] schemes. The first MOT scheme [2] developed for lossy dielectrics solves four coupled TDSIEs constructed in tangential and normal components of the fields on the interface between the lossy scatterer and the lossless background medium.…”