Salvador Ortiz

An improved long distance treatment for mutual inductance

This paper examines the controversy between two approaches to inductance extraction: loop versus partial treatments for integrated circuit applications. We advocate the first one, and explicitly show that the alternative demands monopole-like magnetic configurations as well as dense inductance matrices. We argue that the uncertainties in the loop inductance treatment associated with possibly unknown return paths are in fact negligible for frequencies where inductance effects are important. Within the loop formulation, we develop an efficient way of computing mutual inductances between loops in terms of the field generated by a magnetic dipole. We derive easily computable analytical formulas. On numerical simulations, this dipole approximation (DA) shows good accuracy when compared to FastHenry, down to distances smaller than 30 /spl mu/m for 90-nm lithography. The DA leads naturally to selection rules for discarding the coupling for certain geometrical configurations, an experimentally verifiable prediction.

Mutual inductance extraction and the dipole approximation

The present work is centered in the controversy between two approaches to inductance extraction: loop vs. partial treatments for IC applications. We advocate for the first one, justifying this claim in terms of representing more realistically the physical situation, as well as having better sparseness properties. We argue that the drawbacks of loop inductance treatment are small for frequencies above 1 GHz. Within the loop inductance formulation, we develop an efficient way of calculating mutual inductances between loops in terms of the field generated by a magnetic dipole. On numerical simulations, the dipole approximation shows good accuracy when compared to FastHenry, down to distances of 30μ for 0.13μ processes. The dipole approximation leads naturally to selection rules for discarding certain couplings that can be experimentally verified.

Fullwave volumetric Maxwell solver using conduction modes

We present a gridless method for solving the interior problem for a set of conductors in an homogeneous dielectric, at sufficiently high frequencies, valid for conductor lengths that are not small compared to the minimum wavelength, and transverse dimensions that are large compared to the skin depth. For IC applications, we cover the regime 10-100 GHz and the inclusion of all relevant wire dimensions. We decompose the electromagnetic field in terms of the eigenfunctions of the Helmholtz equation for three dimensional current distributions inside the conductors. Using a relatively small number of modes per conductor we obtain results comparable to filament or mesh decompositions using a much larger dimensionality for the resulting linear problem. The method is an extension to the fullwave regime of a method introduced in (Daniel et al., 2001)

Efficient implementation of conduction modes for modelling skin effect

We present an efficient approach for computing the impedance matrix of a system of conductors, in the quasi-magneto static domain, suitable for frequency analysis well above the skin effect threshold. The method is based on the current decomposition in terms of conduction modes (CM) rather than the widespread filament decomposition. The memory gains using CM were already known to be large. Our main contribution is to improve the efficiency so as to achieve performance ratios that are significantly better than those resulting from using filament decomposition for the same accuracy. As the frequency increases the improvements become noteworthy. These gains result from optimally rendering two dimensional integration approaches involving the Coulomb Green function in combination with linear combinations of exponentials to the particular landscape of each of the constituent terms.

Mutual inductance between intentional inductors: closed form expressions

We present closed form analytical expressions for the mutual inductance between intentional inductors. The formalism is applicable for border to border separations that are longer than 0(1/10) of the inductor radius. The results are exact in leading order multi-pole expansion for the magnetic field generated by a superposition of current loops, acting on an external device. The derived expressions are simple analytical formulae. We present examples for the closed form expressions for a number of configurations used by RF designers including non Manhattan devices. The computational complexity of the result is linear with the number of segments. Detailed comparisons against standard methods are included, the CPU gains are two orders of magnitude. The formulae are useful for quick estimation of magnetic noise parameters during RF circuit layout synthesis