Computer-aided design and analysis of circuits and semiconductor – Nanotechnology related integrated circuit design
Reexamination Certificate
2002-02-26
2004-05-25
Siek, Vuthe (Department: 2825)
Computer-aided design and analysis of circuits and semiconductor
Nanotechnology related integrated circuit design
C716S030000
Reexamination Certificate
active
06742167
ABSTRACT:
CROSS REFERENCE TO RELATED APPLICATIONS
Applicants claim priority under 35 U.S.C. §119 GERMAN application No. 101 09 554.6 filed on Feb. 28, 2001.
BACKGROUND OF THE INVENTION
The invention relates to a method for determination of the electrical characteristics of an arrangement of conductor elements (conductor pieces) by means of a computer, wherein the conductor elements are at least partly dissected into segments which carry each a fraction of the total current through the related conductor element and wherein the electrical characteristics of the segments and the mutual electromagnetic couplings between the segments are modelled by means of partial impedance values which are assigned to the respective segments.
FIELD OF THE INVENTION
The invention further relates to a method for determination by means of a computer of the electrical behaviour of integrated high-frequency inductors as well as a computer program for the performing of the method in accordance with the invention.
In the field of modern microelectronics there is a trend towards smaller and smaller device dimensions and higher and higher clock rates. This leads to the development of microelectronic components requiring today a precise investigation of the high-frequency characteristics of the current carrying elements. The reason for this is that conditional on the high signal frequencies the dimensions of the conductor elements lay in the region above the skin depth, so that especially the ohmic resistance of the conductor elements will significantly depend on the frequencies of the signals to be carried. Integrated circuits normally contain a complicated arrangement of a multitude of conductor elements. The precise characterization of the electrical behaviour of such structures is of big importance because mutual inductive and capacitive couplings between the conductor elements will significantly influence the signal quality and therefore the system performance. Of special interest is the analysis of the impedance behaviour of integrated inductors as e. g. used in the modem mobile and satellite communication technology. Integrated micro-inductors are used for example in oscillators for mobile phones. The inductance and the ohmic resistance of such an inductor influences both the resonance frequency and the quality factor of the oscillator. A precise analysis of the impedance behaviour of such inductors is essential for rapid, cost effective and norm-fulfilling development of integrated circuits for the communication technology. During development of fast digital circuits it is also important to perform an analysis of the transmission characteristics of interconnects and of the interconnecting elements so that signal delay, signal cross talk, and tendencies to oscillate can be evaluated.
During development of integrated circuits in which inductors are used it is today common practice to manufacture complete inductor test fields in advance and to undertake them a characterization by measurement. This method is already disadvantageous because of the very high efforts which are caused by it. Moreover, for circuits which operate at high signal frequencies very small inductance values are needed. The dimensions of such inductors can be in the order of some tenth of microns. However, the measurement of such small impedances is difficult and the measurement results are error-prone due to the high tolerances of the available measurement instruments and due to the surrounding influence on the measurement arrangement which cannot be neglected.
Because of said reasons today one goes over to simulating the electrical characteristics of conductor arrangements before the manufacturing by means of computer-generated models. In this case methods are very powerful with which the impedance behaviour of a physical model of the related conductor arrangement is determined, wherein the model represents the real geometry of the conductor elements as close as possible. This power comes i. a. from such models allowing a broadband analysis and being applicable in both frequency domain and time domain. Therefore also non-linear effects can be analysed which are especially of big importance for circuits of the communication technology.
Such a method for calculation of the frequency-dependent resistance and inductance of an arrangement of conductor elements is proposed e. g. by Weeks et al. (IBM Journal of Research and Development, vol. 23, no. 6, pp. 652-660). The known method especially takes into account said high-frequency effects, e. g. skin effect and proximity effect. For this it is necessary to model the current density distribution inside the conductor elements. In said document for this it is proposed to dissect the conductor elements into segments which are straight and parallel to each other and which each carry a fraction of a total current through the related conductor element. There it is assumed that the current density inside the separate segments is constant. However, because the current density varies from segment to segment, the overall current density distribution of the related conductor elements is thereby reproduced as a discrete model. The known method is based on the theory of partial impedances (cf A. E. Ruehli, “Inductance Calculation in a Complex Integrated Circuit Environment”, IBM Journal of Research and Development, vol. 16, pp. 417-481). With this it is possible to assign a set of partial impedance values to every separate segment with which the electrical properties of the segments and the mutual electromagnetic couplings between the segments can be fully described. The partial impedance values depend only on the geometric arrangement and the form of the segments and can be easily calculated. Even complex conductor geometries can be easily handled by performing a suitable dissection into segments. From the viewpoint of mathematics the determination of the impedance in a network of conductor elements can be done by the known method of partial impedances by solving linear equation systems. The actual analysis of the network then is done by inversion of corresponding matrices whose matrix elements are the partial impedance values of the segments. These matrices contain on the diagonal the resistances of the segments and their self-inductances. Outside the diagonal the complex symmetrical matrices contain the mutual inductance values between different segments. If a frequency dependent impedance analysis is to be performed, for every frequency to be examined an inversion of the impedance matrix has to be performed because the complex partial impedance values are naturally frequency dependent.
With the known method the said high frequency effects can be examined because those are modelled by the mutual inductive couplings between the segments. Thus it is possible to e. g. determine the frequency dependent resistance of a conductor arrangement with a given geometry. For the analysis of inductances it is important that the frequency dependence of the self inductances of the conductor elements can also be calculated with high accuracy.
With the known method, the dimension of the linear equation systems (analysis in the frequency domain) or the coupled differential equation systems (analysis in the time domain) to be solved depends on the number of segments, as described above. The application of the method is therefore limited to those cases where the arrangement of conductor elements to be examined can be modelled by dissection into a few hundred segments with sufficient accuracy. For complex conductor arrangements the known method is slow and extremely memory intensive. In addition, during examination of high signal frequencies an extremely fine dissection of the conductor elements has to be performed, because a correct modelling of the high-frequency effects can only be performed if the dimensions of the segments are smaller than the corresponding skin depth.
SUMMARY OF THE INVENTION
Starting from that, the invention is based on the problem to improve the known method of modelling the impedance behaviour of a n
Collard & Roe P.C.
Siek Vuthe
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