1. Apparatus comprising: a porous dielectric element comprising a dielectric containing no silicon-oxygen bonds but having gas pockets dispersed in the dielectric, wherein the dielectric of the porous dielectric element is a dielectric formed of SixCyHz.
2. The apparatus according to claim 1, wherein the porous dielectric element has a porosity of greater than 10%.
3. The apparatus according to claim 1, wherein the dielectric of the porous dielectric element contains no oxygen atoms.
4. The apparatus according to claim 1 wherein the porous dielectric element is a component of an integrated circuit.
5. The apparatus according to claim 1 wherein the component of the integrated circuit is an inter-level dielectric of a metallization level.
6. The apparatus according to claim 4, wherein the dielectric of the porous dielectric element has a porosity of greater than 10%
7. The apparatus according to claim 4, wherein the dielectric of the porous dielectric element contains no oxygen atoms.
8. Apparatus comprising: a porous dielectric element comprising a dielectric containing no silicon-oxygen bonds but having gas pockets dispersed in the dielectric, wherein the dielectric of the porous dielectric element is a dielectric formed by SixCyHz, and wherein SixCyHzis dimethylphenylsilane.
9. The apparatus according to claim 1, wherein the porous dielectric element has a dielectric constant of 3.0 or less and the dielectric has a dielectric constant of 3.5 or less.
10. The apparatus according to claim 1, wherein the dielectric of the porous dielectric element is permeable to hydrofluoric acid.
11. The apparatus according to claim 1, wherein a volume of the gas dispersed in the dielectric is between 10% and 40% of an overall volume of the porous dielectric element.
12. The apparatus according to claim 1, wherein the gas pockets define a porosity of between 10% and 40%.
13. The apparatus according to claim 1, wherein the porous dielectric element contains no materials of a SiwOxCyHz type.
14. The apparatus according to claim 1 wherein the gas pockets in the porous dielectric element formed by dissolution of a minor dielectric material phase dispersed within the dielectric of the porous dielectric element.
15. The apparatus according to claim 14 wherein the minor dielectric material phase is of a SiO2, SiwOxCyHz or siloxane type that is removed in the dissolution by attacking silicon-oxygen bonds present in the minor dielectric material phase.
16. Apparatus comprising: a porous dielectric element comprising a dielectric containing no silicon-oxygen bonds but having gas pockets dispersed in the dielectric formed by dissolution of a minor dielectric material phase dispersed within the dielectric of the porous dielectric element, wherein the minor dielectric material phase is of a SiwOxCyHz type that is removed in the dissolution by attacking silicon-oxygen bonds present in the minor dielectric material phase, and wherein the SiwOxCyHz type is tetraethylorthosilicate.
17. Apparatus comprising: a porous dielectric element comprising a dielectric containing no silicon-oxygen bonds but having gas pockets dispersed in the dielectric formed by dissolution of a minor dielectric material phase dispersed within the dielectric of the porous dielectric element, wherein the minor dielectric material phase is of a siloxane type that is removed in the dissolution by attacking silicon-oxygen bonds present in the minor dielectric material phase, and wherein the siloxane is of the decamethylcyclopentasiloxane type.
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.
1. A computer based method to generate a posynomial model for the performance characteristics of a system based on numerical data of these performance characteristics by indirectly or directly fitting the posynomial model to the numerical data.
2. The method according to claim 1, wherein directly fitting includes fitting a posynomial template to the numerical data by constrained optimization of a goal function using conjugate gradient descent, the posynomial template comprising arbitrary real exponents.
3. The method according to claim 1, wherein the fitting includes fitting a signomial model to the numerical data followed by an automatic recasting into a posynomial model.
4. The method according to claim 3, wherein the the signomial model is an nth order polynomial.
5. The method according to claim 1, wherein fitting includes directly fitting a posynomial template to the numerical data, the posynomial template comprising arbitrary real exponents.
6. The method according to claim 1, wherein the posynomial is a linear summation of at least two monomials.
7. The method according to claim 1, wherein said numerical data is obtained by at least one of measurement, simulation, and observation.
8. The method according to claim 1, wherein the system is physical system.
9. The method according to claim 8, wherein said system is an electronic circuit or a semiconductor device or a micro electro-mechanical system (MEMS).
10. The method according to claim 1, wherein the system displays linear or nonlinear performance behavior.
11. The method according to claim 1, wherein the posynomial model is a specification independent model or a sparse model.
12. A model residing in a memory device, the model being for performance characteristics of a system based on numerical data of these performance characteristics and the model having been obtained by indirectly or directly fitting the posynomial model to the numerical data.
13. A method to size or optimize an electronic circuit, a semiconductor device or a micro electro-mechanical system (MEMS) based on a posynomial model, the model being for performance characteristics of the circuits device or system based on numerical data of these performance characteristics and the model been obtained by indirectly or directly fitting the posynomial model to the numerical data.
14. The method according to claim 13, wherein the posynomial model is updated adaptively during the sizing or optimization iteration.
15. The method according to claim 1, wherein posynomial model is obtained without analytically analyzing the system andor without casting the resulting analytic equations in posynomial format andor without approximating them in posynomial format or without a-priori generation of a simplified equation or equations.
16. The method of claim 15, wherein the generation of the posynomial performance parameter model is based on a numerical SPICE-like simulation.
17. An electronic circuit, a semiconductor device or a micro-electro-mechanical system obtained by the method of claim 13.
18. A computer system comprising a memory and a processor for generating a posynomial model for the performance characteristics of a system based on numerical data of these performance characteristics, comprising means for indirectly or directly fitting the posynomial model to the numerical data.
19. The computer system according to claim 18, wherein the means for fitting includes means for fitting a signomial model to the numerical data followed by an automatic recasting into a posynomial model.
20. The computer system according to claim 18, wherein the means for fitting includes means for directly fitting a posynomial template to the numerical data, the posynomial template comprising arbitrary real exponents.
21. The computer system according to claim 18, wherein the posynomial is a linear summation of at least two monomials.
22. The computer system according to claim 18, further comprising input means for inputting the numerical data is obtained by measurement andor simulation andor observation.
23. The computer system according to claim 18, further comprising geometric programming means.
24. A computer program product which when executed on a computer system having a memory and a processor generates a posynomial model for the performance characteristics of a system based on numerical data of these performance characteristics, comprising means for indirectly or directly fitting the posynomial model to the numerical data.
25. The computer program product according to claim 24, further comprising code for executing a means for fitting a signomial model to the numerical data followed by an automatic recasting into a posynomial model when the code is executed on the computer system.
26. The computer program product according to claim 24, further comprising code for executing means for directly fitting a posynomial template to the numerical data, the posynomial template comprising arbitrary real exponents, when the code is executed on the computer system.
27. The computer program product according to claim 24, wherein the posynomial is a linear summation of at least two monomials.
28. The computer program product according to claim 24, further comprising code for executing a geometric program when the code is executed on the computer system.
29. A data carrier storing a computer program product according to claim 24.
30. A method for modeling of a first system, comprising: transmitting from a near location a description of the first system to a remote location where a processing engine carries out the method in accordance with claim 1, and receiving at a near location a representation of the model.
31. A method for modeling of a first system, comprising: transmitting from a near location a description of the first system to a remote location where a processing engine carries out the method in accordance with claim 1, and receiving at a near location a value relating to at least one parameter related to the first system.
32. A method for modeling of a first system, comprising: transmitting from a near location a description of the system to a remote location where a processing engine carries out the method in accordance with claim 1, and receiving at a near location a value relating to at least one parameter related to a second system which is dependent upon the first system.
33. The method according to claim 30, wherein the first system is a physical system and the parameter is a physical parameter.
34. The method according to claim 32, wherein the second system is a physical system and the parameter is a physical parameter.