WO2012120465A1

WO2012120465A1 - Multi-terminal self and mutual inductance network extraction for superconductive integrated circuits

Info

Publication number: WO2012120465A1
Application number: PCT/IB2012/051080
Authority: WO
Inventors: Coenrad Johann FOURIE
Original assignee: Stellenbosch University
Priority date: 2011-03-08
Filing date: 2012-03-08
Publication date: 2012-09-13

Abstract

A method and system is provided for determining self- and mutual inductances in three-dimensional multi-terminal superconductive integrated circuits (1), based on modifying the standard version of FastHenry. The method includes, but is not limited to, the steps of discretizing (12) the network geometry into a numerical model (14); creating a netlist describing at least a network of inductors associated with the conductive tracks between the terminals as well as mutual inductances between these inductors; calculating a current density distribution (19) over the network geometry for each terminal; calculating a total signed current flowing in at least those elements connected to terminals for each current density distribution; calculating signed terminal currents for every terminal (20); determining a branch current matrix including the signed terminal currents and signed branch currents as calculated for each current density distribution (21); and determining an inductance matrix from the branch current matrix (23).

Description

MULTI-TERMINAL SELF AND MUTUAL INDUCTANCE NETWORK EXTRACTION FOR SUPERCONDUCTIVE INTEGRATED CIRCUITS

FIELD OF THE INVENTION

This invention relates to multi-terminal superconductive networks. In particular, the invention relates to a method and system for calculating the self and mutual inductances in superconductive multi-terminal networks.

BACKGROUND TO THE INVENTION

Electrical inductance is probably the most important electrical parameter of superconductive integrated circuits (ICs). At present, these inductances are calculated with analytical approximations which are typically inaccurate. Analytical approximations are also not possible when the circuits have ground plane holes, which is most often the case with modern ICs. In addition, analytical techniques typically only work for the most basic network shapes and fail for micrometre-sized integrated circuit structures, which could have complicated, three-dimensional geometries which are frequently arranged in multiple layers.

Other, software based methods of calculating inductances in integrated circuits have also been developed. These methods involve the computer simulation and analysis of the integrated circuits with freely available programs such as: Lmeter, 3D-MLSI and FastHenry.

Lmeter was developed by Paul Bunyk et al., but is only a two-dimensional method that cannot account for modern circuit structures which include three- dimensional geometries and holes in the ground plane. Lmeter is typically two orders of magnitude faster than FastHenry for similar problems. 3D-MLSI on the other hand can handle three-dimensional geometries, but is restricted to planar geometries and is slow in comparison to other techniques. 3D-MLSI is most frequently used for high temperature (monolayer) Superconductive Quantum Interference Devices (SQUIDs).

FastHenry was adapted to include equations governing electrical and magnetic fields in superconductors (FastHenry 3.0wr, from Whiteley Research), and although this gives three-dimensional solutions, the inductances are only calculated in a point-to-point fashion. In addition, FastHenry is also relatively slow.

FastHenry is a three-dimensional solver that only calculates inductances for simple networks with single inductances. It calculates the frequency- dependent impedances between defined terminals in a geometry input file (typically a ".inp" file). The results it obtains are written to an impedance matrix, from which the self- and mutual inductances between a number of inductors can be calculated through frequency division, provided that each inductor has only one terminal and that no two inductors are electrically connected. FastHenry by its own is, however, not useful for networks that contain multiple terminals in an interconnected geometry.

All the programs mentioned above suffer from a variety of problems including that they cannot handle three-dimensional networks, are very slow, that they cannot handle mutual inductances and/or multi-terminal network inductances, or a combination of these.

In the remainder of this specification the term "discretization" should be interpreted to refer to the process of transferring continuous models and equations into their discrete counterparts. The term "discretizing" shall have a corresponding meaning. SUMMARY OF THE INVENTION

In accordance with this invention there is provided a method for determining self- and mutual inductances between terminals of a superconductive integrated circuit network comprising a plurality of terminals interconnected by means of superconductive tracks and arranged in a predefined network geometry, the method including the steps of

discretizing the network geometry into a numerical model consisting of x, y and z-directed elements, the numerical model including definitions of the terminals;

creating a netlist describing at least a network of inductors associated with the conductive tracks between the terminals as well as mutual inductances between these inductors;

calculating a current density distribution over the network geometry for each terminal by means of a three-dimensional computational electromagnetic (3D-CEM) modelling analysis conducted on the numerical model by sequentially exciting each terminal at a predefined frequency and amplitude while short circuiting all other terminals;

calculating a total signed current flowing in at least those elements connected to terminals for each current density distribution;

calculating signed terminal currents for every terminal by summing current contributions from all elements connected to that terminal for each current density distribution;

calculating signed branch currents through all inductors of the network of inductors not terminating in terminals using the signed terminal currents with Kirchhoff s current law for each current density distribution;

determining a branch current matrix including the signed terminal currents and signed branch currents as calculated for each current density distribution; and

determining an inductance matrix from the branch current matrix by means of singular value decomposition (SVD) using at least the predefined frequency and amplitude. Further features of the invention provide for the 3D-CEM modelling analysis to be a method-of-moment analysis; for the method-of-moment analysis to be conducted by means of FastHenry; for the numerical model and netlist to be used to create a circuit geometry input file from the circuit elements in combination with definitions for the terminals; and for the circuit geometry input file to be a .inp file.

Still further features of the invention provide for the steps of calculating a current density distribution over the network geometry for each terminal to further include the step of adapting the open source software code associated with FastHenry to output a current density file containing a current density matrix for every excited terminal node in the network geometry; discarding the standard FastHenry output which is typically referenced as 'zc.mat'; and inducing a current density file dump with the "-d grids" command to FastHenry. The adapted FastHenry returns "3.0wr+su" when prompted to return a version by software implementing the invention.

The invention further provides a system comprising a processor and an electronic memory module in data communication with the processor on which is stored machine instructions configured to cause the processor to determine self- and mutual inductances between terminals of a superconductive integrated circuit network comprising a plurality of terminals interconnected by means of superconductive tracks and arranged in a predefined network geometry in accordance with the method referred to above.

The invention still further provides a program storage device readable by a machine, embodying a program of instructions executable by the machine to perform method steps for determining self- and mutual inductances between terminals of a superconductive integrated circuit network comprising a plurality of terminals interconnected by means of superconductive tracks and arranged in a predefined network geometry, in accordance with the method referred to above.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings:-

Figure 1 is a diagram showing a simplified superconductor integrated circuit track between three terminals;

Figure 2 is a diagram showing the track of Figure 1 discretized into elements;

Figure 3 is a network of inductors representing the inductive contributions of the constituent portions of the track of Figure 1 ;

Figure 4 is a matrix of self- and mutual inductances between the inductors shown in Figure 3; and

Figure 5 is a flow diagram illustrating a method for determining self- and mutual inductances between terminals of a superconductive integrated circuit network in accordance with the invention.

DETAILED DESCRIPTION WITH REFERENCE TO THE DRAWINGS

In this detailed description the freeware software FastHenry, as mentioned in the background section of this specification, will be used to explain the invention. It should, however, be noted that the invention is by no means limited to the use of FastHenry and that any suitable method-of-moment analysis tool may be used to implement the invention. In addition, the term "netlist" should be understood to be a text file representation of a circuit which emphasises the connections between the different circuit elements, in the present case inductors.

A very simplified example of a three-dimensional superconductive integrated circuit (IC) network (1 ) is shown in Figure 1 . The network (1 ) includes three terminals (T1 ), (T2) and (T3) that are interconnected by means of a superconductive track (2) which is arranged in a three-dimensional, T-shaped network geometry (3).

As the track is superconductive, it does not, for practical purposes at least, have any real resistance when electricity flows through it between the terminals, as is the case with all superconductive tracks. Each portion of the track does, however, have an associated inductance which can be represented by the network of inductors shown in Figure 3. In Figure 3, an inductor (L1 ) is positioned between terminal T1 and an internal node (4) which is simulated at a point where the three arms of the track converge (5) in the network geometry (3). Inductor (L2) is positioned between the internal node (4) and terminal T2 and inductor (L3) is positioned between the internal node (4) and terminal T3. In addition to the direct inductances between the terminals, referred to as self inductances, there are also mutual inductances between the various inductors. The combination of self- and mutual inductances of the tracks in the geometry can be represented in an inductive matrix as shown in Figure 4.

It is the calculation of these self- and mutual inductance values with which this invention is concerned.

In order to calculate the self- and mutual inductances of the circuit geometry the steps shown in the flow diagram of Figure 5 are followed. At a step (10), an IC layout file, in this example a Graphic Database System II ("GDSII") file, is read into a computer. The GDSII file format is the industry standard for data exchange of IC layout artwork. It is a binary file format representing planar geometric shapes, text labels, and other information about the layout in hierarchical form. Other file formats used to read an IC layout into a computer for the purposes of this invention are the Caltech Intermediate Form (CIF) and AutoCAD Drawing Interchange Format (DXF). The data can be used to reconstruct the whole or part of the artwork (network geometry) to be used in sharing layouts, transferring artwork between different tools, or creating photomasks. In addition to the layout file, a technology file is read in at step (1 1 ). The technology file includes information on the mask-to-layer mapping from GDSII artwork to eventual integrated circuit structures, layer names, numbers and order, layer properties including thickness and London penetration depth, and discretization parameters such as element size and number of elements constituting a layer thickness.

The entire network geometry (3) is then discretized at step (12) by slicing the network geometry into x, y and z-directed elements (13). The network geometry (3) as discretized into elements (13) is shown in more detail in Figure 2. In multi-layered network geometries, all layers are discretized in such a way. The discretized network geometry is thereby represented by a numerical model made up of the elements (13). The numerical model also includes definitions of all the terminals, specifically indicating where they are situated and which elements they are connected to.

In addition, a numerical node grid is generated at step (14), which specifies all the nodes in the network geometry (3), with elements always connected between two nodes (13). At step (15) all the elements (13) represented by the numerical model are connected with the nodes in the numerical node grid. This data is then used to generate a FastHenry geometry input file in ".inp" format at step (16), which is then inputted to the FastHenry software program along with definitions for the terminals. It should be appreciated that the terminals may have any shape or size, from a single node to a line of nodes to a two-dimensional figure.

FastHenry is then executed on the input file once at step (17) in the normal way to calculate the frequency-dependent impedances of the modelled geometry. However, due to the fact that the geometry (3) includes multiple terminals that are interconnected, the FastHenry results are essentially meaningless. FastHenry typically gives an error instead of a solution. The normal FastHenry solution, which is typically in a "zc.mat" file is then discarded at step (18).

As part of its calculations, FastHenry, however, solves the current density distribution over the entire network geometry (3). This is done by calculating a current density distribution over the network geometry (3) for each terminal by exciting one terminal at a time while grounding all the other terminals and then solving the current density distribution for that terminal by means of a three-dimensional computational electromagnetic (3D-CEM) modelling analysis conducted on the numerical model. The terminals are excited sequentially by simulating the application of a signal of a known frequency and amplitude to the terminal while all the other terminals remain grounded.

By invoking the "-d grids" command of FastHenry, or any command with a similar result in any altered version of FastHenry, a current density file dump can be invoked. This command causes FastHenry to write a current density matrix for every excited terminal to a file at step (19). The current density files are typically in a "jimag.mat" format. Due to a change to the standard, publically available FastHenry code, these "jimag.mat" files are created for every excited terminal, whereas the standard code only saves it for one excited terminal and thereby makes inductance extraction as done with this invention, and at this speed, impossible. In order to differentiate the adapted FastHenry code from the standard code, it returns a version string when prompted with the "-v" command line parameter, which is "3.0wr+su" for the 32-bit version, and "3.0wr+su64" for the 64-bit version.

At step (20), the current density files and the numerical model, which contains information on the cross-sectional dimensions of all elements, are then used to calculate a total signed current flowing in each of the elements, in particular those elements that are connected to terminals, for each current density file. These signed currents are calculated for each current density distribution file, which implies it is calculated for each excited terminal. These singed element currents are then used to calculate signed terminal currents for every terminal by summing current contributions from all elements connected to that terminal. As before, this is done for each calculated current density distribution and, accordingly, for each excited terminal.

After having calculated the singed terminal currents for each excited terminal, all signed branch currents in the remainder of the network geometry is calculated. This is done by using the signed terminal currents in combination with Kirchhoffs current law at step (21 ) for each current density distribution. The signed branch currents, signed terminal currents and a netlist of all the inductors in the network of inductors which describes both the self- and mutual inductances between the different portions of the track (2), as calculated for each excited terminal, are then used to calculate a single branch current matrix and voltage loop matrix for the entire geometry.

Finally, at step (23), a singular value decomposition (SVD) is conducted on the branch current matrix using at least the predefined excitation signal voltage amplitudes and frequencies. This yields an inductance matrix which contains all the self- and mutual inductances between the terminals of the entire network geometry.

The above description is by way of example only and it should be appreciated that numerous changes and modifications may be made to the embodiment described without departing from the scope of the invention. In particular, it is foreseen that any suitable software applications may be used to conduct the various calculation steps.

The invention provides a fast and accurate way of calculating the inductances of multi-terminal networks of three-dimensional superconductive integrated circuit structures. The invention exploits existing tools such as FastHenry in a way that allows it to calculate self- and mutual inductances of multi-terminal networks with any number of interconnected inductances, something which was not previously possible with the existing tools. The results have been found to be accurate even in geometries that include ground plane holes and three-dimensional geometries, mutually coupled inductors in the presence of ground plane holes, and inductor networks that may include mutual coupling in the total absence of ground planes (such as in monolayer high-temperature superconductor processes). In addition, the solution speeds obtainable are comparable to those of other tools that are considered to be fast, such as, for example, Lmeter, for similar circuit structures. These speeds have been measured in the order of ten times faster for representative test sets, and up to one hundred times faster for some larger circuits, than results obtained by using FastHenry in the way that it was intended.

Claims

CLAIMS:

1 . A method for determining self- and mutual inductances between terminals of a superconductive integrated circuit network comprising a plurality of terminals interconnected by means of superconductive tracks and arranged in a predefined network geometry, the method including the steps of

calculating a total signed current flowing in at least those elements connected to terminals for each current density distribution; calculating signed terminal currents for every terminal by summing current contributions from all elements connected to that terminal for each current density distribution;

calculating signed branch currents through inductors of the network of inductors not terminating in terminals using the signed terminal currents with Kirchhoffs current law for each current density distribution;

determining a branch current matrix including the signed terminal currents and signed branch currents as calculated for each current density distribution; and determining an inductance matrix from the branch current matrix by means of singular value decomposition (SVD) using at least the predefined frequency and amplitude.

2. A method as claimed in claim 1 in which the 3D-CEM modelling analysis is a method-of-moment analysis.

3. A method as claimed in claim 2 in which the method-of-moment analysis is conducted by means of FastHenry.

4. A method as claimed in one any of the preceding claims which includes using the numerical model and netlist to create a circuit geometry input file from the circuit elements in combination with definitions for the terminals.

5. A method as claimed in claim 4 in which the circuit geometry input file is a .inp file.

6. A method as claimed in any one of the preceding claims in which the steps of calculating a current density distribution over the network geometry for each terminal includes the step of adapting the software code associated with FastHenry to output a current density file containing a current density matrix for every excited terminal node in the network geometry.

7. A method as claimed in any one of the preceding claims in which the step of calculating a current density distribution over the network geometry for each terminal includes the step of discarding the standard FastHenry output which is typically referenced as 'zc.mat'.

8. A method as claimed in any one of the preceding claims in which the step of calculating a current density distribution over the network geometry for each terminal includes the step of inducing a current density file dump with the "-d grids" command to FastHenry.

9. A system for determining self- and mutual inductances between terminals of a superconductive integrated circuit network comprising a plurality of terminals interconnected by means of superconductive tracks and arranged in a predefined network geometry, comprising a processor; and

an electronic memory module in data communication with the processor on which is stored machine instructions configured to cause the processor to

discretize the network geometry into a numerical model consisting of x, y and z-directed elements, the numerical model including definitions of the terminals;

create a netlist describing at least a network of inductors associated with the conductive tracks between the terminals as well as mutual inductances between these inductors;

calculate a current density distribution over the network geometry for each terminal by means of a three-dimensional computational electromagnetic (3D-CEM) modelling analysis conducted on the numerical model by sequentially exciting each terminal at a predefined frequency and amplitude while grounding all other terminals;

calculate a total signed current flowing in at least those elements connected to terminals, for each current density distribution;

calculate signed terminal currents for every terminal by summing current contributions from all elements connected to that terminal for each current density distribution;

calculate signed branch currents through inductors of the network of inductors not terminating in terminals using the signed terminal currents with Kirchhoffs current law for each current density distribution;

determine a branch current matrix including the signed terminal currents and signed branch currents as calculated for each current density distribution; and

determine an inductance matrix from the branch current matrix by means of singular value decomposition (SVD) using at least the predefined frequency and amplitude.

10. A program storage device readable by a machine, embodying a program of instructions executable by the machine to perform method steps for determining self- and mutual inductances between terminals of a superconductive integrated circuit network comprising a plurality of terminals interconnected by means of superconductive tracks and arranged in a predefined network geometry, the method steps comprising:

calculating a current density distribution over the network geometry for each terminal by means of a three-dimensional computational electromagnetic (3D-CEM) modelling analysis conducted on the numerical model by sequentially exciting each terminal at a predefined frequency and amplitude while grounding all other terminals;

determining an inductance matrix from the branch current matrix by means of singular value decomposition (SVD) using at least the predefined frequency and amplitude.