U.S. patent application Ser. Nos. 09/283,392, 09/283,393, now U.S. Pat. No. 6,289,298, and Ser. No. 09/283,395 were filed concurrently herewith.
1. Technical Field
This invention is related to the design of optimized metalization structures and, more particularly, to modeling of electromagnetic interactions in metalization structures in electrical circuits to simulate their electrical characteristics in circuits from their physical characteristics.
2. Background of the Invention
It is desirable to be able to model quickly and accurately the electrical characteristics of metalization structures, such as inductors, interconnects and the like. To obtain of these electrical characteristics requires a detailed determination of the charge and current distributions everywhere in the metalization structure. Because of very rapid three dimensional variation in charge and current density with position in known metalization structures and because these variations strongly affect the electrical characteristics of the metalization structures, an accurate and fast process for determining the charge and current distributions and the interactions between those distributions is required in order properly to determine the electrical characteristics of, inductors or other systems of metals. One family of techniques that has been used for this purpose effects a uniform or three-dimensional mesh of the entire metalization structure. However, these processes are very inefficient, i.e., slow, when employed in an attempt to model metalization structures that are largely planar as in integrated circuit melatization structures. Another family of techniques is the so-called two dimensional or quasi two dimensional processes that are significantly faster than the three dimensional processes in arriving at a model, but yield very inaccurate results for many integrated circuit metalization structures fabricated on conductive substrates.
These and other problems and limitations of prior known modeling arrangements and methods are overcome by employing a basis function decomposition process for modeling the charge and/or current distributions and the interactions of those distributions on metalization structures arising from voltages and currents flowing in the metalization structures. Then, the charge and/or current distributions and their interactions are employed to obtain the electrical characteristics of a metalization structure.
In one embodiment of the invention, representative sub units of the metalization structure are selected, the charge and current distributions are determined in those representative sub units, the self and mutual interactions are determined of those sub units and, then, those self and mutual interactions are used as an initial solution to describe all interactions between similar metalization sub units in the overall system of metals. These interactions are then employed to determine the impedance and admittance of each of the sub units. The impedances and admittances of the sub units are combined to obtain the overall metalization structure to be fabricated. Then, the electrical characteristics of the overall metal structure are determined.
In another embodiment of the invention, the metal structure is decomposed into sub units. Repeated or representative ones of the sub units are determined and, then, decomposed into smaller sub unit elements. Sub unit impedances and admittances are determined for the sub units by using the current and/or charge distributions and their self and mutual interactions for the sub unit elements. Then, the impedances and admittances for the sub units are combined to obtain the overall metalization structure to be fabricated. Finally, the electrical characteristics are generated of the overall metalization structure.