Multi-scale, multi-physics analysis for device, chip, package, and board level

The computer integrated circuitmn (IC) is inundated with electromagnetic signals. These signals are omnipresent at the device, chip, package, and board level. The length-scales vary from nanometers to centimeters. The physics also changes significantly over these length-scales. It is clear that multi-scale, multi-physics analyses are needed to understand future generation IC's.

Computational electromagnetics (CEM) research is important for producing simulation software that has been used for virtual prototyping and the design of major micro- and nano-electronic components. Solving electromagnetics problem is a challenging task, especially when it involves multi-scale and multi-physics structures.

In this presentation, we will give a brief introduction to the three physics of electromagnetic fields: circuit physics, wave physics, and ray physic. Then we will give an overview of past and recent progress in large scale computing in electromagnetics by our research group, and discuss various methods to overcome multi-scale problems. We will give a brief overview of the circuit physics, and wave physics and their relationship to computation.

We first discuss large scale computing result from our group as well as other groups in the world using the multi-level fast multipole algorithm (MLFMA). We will discuss the use of self-box inclusion preconditioner, and parallel computing.

The development of the mixed-form fast multipole algorithm (MF-FMA) is essential to capture both circuit physics and wave physics problems. This is essential for solving multi-scale problems. We will discuss the equivalence principle algorithm (EPA) to capture the multi-scale physics of complex structures. In this method, complex structures are partitioned into parts by the use of equivalence surfaces. The interaction of electromagnetic field with structures within the equivalence surface is done through scattering operators working via the equivalence currents on the equivalence surfaces. The solution within the equivalence surface can be obtained by various numerical methods. Then the interaction between equivalence surfaces is obtained via the use of translation operators. When accelerated with the mixed-form fast multipole method, large multi-scale problems involving several million unknowns can be solved in this manner.

We will also discuss the augmented electric field integral equation (A-EFIE) approach in solving the low-frequency breakdown problem as encountered in circuits in electronic packaging. In this method, the EFIE is augmented with an additional charge unknown, and an additional continuity equation relating the charge to the current. The resultant equation, after proper frequency normalization, is frequency stable down to very low frequency. This method does not suffer from the low-frequency breakdown, but it does have the low-frequency inaccuracy problem, which can be solved by perturbation method. We will also discuss the augmentation of EPA (A-EPA) to avoid low frequency breakdown, and the hybridization of EPA, A-EPA, and A-EFIE to tackle some multi-scale problems. The applications of these techniques to nano-electronics will be discussed.

If time permits, we will discuss simulation, modeling, and theory at the device level.