# US 2014/0208280 A1 · Modeling mechanical behavior with layout-dependent material properties

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- Number: US 2014/0208280 A1
- Document ID: US20140208280A1
- Status: Published application
- Kind: A1
- Application number: 13/745,732
- Filed: 2013-01-18
- Published: 2014-07-24
- Earliest claimed: 2013-01-18
- Assignees: Synopsys, Inc.
- Applicants: Synopsys, Inc.
- Inventors: Xiaopeng Xu; Dasarapu Vinay Kumar; Xi-Wei Lin
- Web page: https://patentgrep.com/patent/US20140208280A1

## CPC

- G06F 30/398: Design verification or optimisation, e.g. using design rule check [DRC], layout versus schematics [LVS] or finite element methods [FEM] (optical proximity correction [OPC] design processes G03F1/36)
- G06F 30/20: Design optimisation, verification or simulation (optimisation, verification or simulation of circuit designs G06F30/30)
- G06F 30/39: Circuit design at the physical level (physical level design for reconfigurable circuits G06F30/347)
- G06F 2119/08: Thermal analysis or thermal optimisation
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)

## Abstract

Computer-implemented techniques for modeling the mechanical behavior of integrated circuits using layout-dependent material properties are disclosed. The back end of line wiring that connects an integrated circuit to a substrate undergoes stresses and strains due to many heating and cooling cycles during a chip's packaging and lifecycle. Depending on integrated circuit design style, there may be vastly different thermal profiles across the integrated circuit. The mechanical behavior caused by the thermal cycles of the wire, vias, and insulators comprising the BEOL materials is simulated. Extraction of the integrated circuit structural information, regarding the BEOL materials, yields anisotropic information. Layout-dependent material volume fractions are computed using integrated circuit structural information. Anisotropic mechanical properties are determined based on the structural information. Mechanical responses are calculated based on the anisotropic material properties and the calculated material-volume fractions.

## Claims

### Claim 1

A computer-implemented method for design analysis comprising:
obtaining a design and integrated circuit structural information for the design;
extracting, using one or more processors, anisotropic information from the integrated circuit structural information;
computing layout dependent material volume fractions using the integrated circuit structural information;
determining anisotropic mechanical properties based on the anisotropic information; and
calculating mechanical responses, based on interconnecting layers that undergo stress due to thermal coefficients of expansion, based on the anisotropic mechanical properties and the layout dependent material volume fractions.

### Claim 2 (depends on 1)

The method of claim 1 wherein the computing layout dependent material volume fractions includes computing a dependent material volume fraction for one layer.

### Claim 3 (depends on 2)

The method of claim 2 wherein the one layer includes an interconnect layer, a via layer, or a region of interest.

### Claim 4 (depends on 3)

The method of claim 3 wherein the design includes a plurality of layers.

### Claim 5 (depends on 1)

The method of claim 1 wherein the design is three dimensional.

### Claim 6 (depends on 1)

The method of claim 1 wherein the structural information is included in an interconnect technology file (ITF).

### Claim 7 (depends on 1)

The method of claim 1 wherein the structural information includes one or more of vertical geometry information, material thickness, or layout dimensions.

### Claim 8 (depends on 1)

The method of claim 1 wherein the structural information includes one or more of metallization thickness, metallization resistivity, dielectric thickness, dielectric permeability, metallization width, or metallization length.

### Claim 9 (depends on 1)

The method of claim 1 wherein the layout dependent material volume fractions are computed based on evaluation of three-dimensional structures.

### Claim 10 (depends on 1)

The method of claim 1 wherein the layout dependent material volume fractions comprise an amount of metal included within a three-dimensional volume.

### Claim 11 (depends on 1)

The method of claim 1 wherein the anisotropic mechanical properties are determined using an averaging scheme.

### Claim 12 (depends on 11)

The method of claim 11 wherein the averaging scheme includes serial averaging.

### Claim 13 (depends on 11)

The method of claim 11 wherein the averaging scheme includes parallel averaging.

### Claim 14 (depends on 1)

The method of claim 1 wherein the calculating of mechanical responses is for a specified layer.

### Claim 15 (depends on 1)

The method of claim 1 wherein the calculating mechanical responses is for a plurality of layers.

### Claim 16 (depends on 1)

The method of claim 1 wherein the calculating mechanical responses is for a specified region.

### Claim 17 (depends on 1)

The method of claim 1 further comprising determining critical parameters for the integrated circuit structural information.

### Claim 18 (depends on 17)

The method of claim 17 wherein the critical parameters include one or more of layer composition, volume, direction, or layer level.

### Claim 19 (depends on 1)

The method of claim 1 further comprising determining volumes from coordinate and thickness information in the design.

### Claim 20 (depends on 1)

The method of claim 1 further comprising determining local material properties from the critical parameters and three-dimensional volumes.

### Claim 21 (depends on 1)

The method of claim 1 wherein the design includes a semiconductor chip.

### Claim 22 (depends on 21)

The method of claim 21 wherein the design further includes a package.

### Claim 23 (depends on 22)

The method of claim 22 further comprising modeling mechanical interaction between the semiconductor chip and the package.

### Claim 24 (depends on 1)

The method of claim 1 wherein the design includes through-silicon vias.

### Claim 25 (depends on 1)

The method of claim 1 further comprising calculating mechanical responses for a plurality of interconnect layers or via layers in the design where each layer is considered individually.

### Claim 26 (depends on 1)

The method of claim 1 wherein one or more of interconnect line directions, local pattern densities, or level of layers is analyzed to determine anisotropic mechanical properties.

### Claim 27 (depends on 1)

The method of claim 1 wherein the extracting anisotropic information is based on information from technology files and design files.

### Claim 28 (depends on 1)

The method of claim 1 wherein the calculating mechanical responses are based on anisotropic material dependencies and layout dependent material properties.

### Claim 29

A computer system for design analysis comprising:
a memory which stores instructions;
one or more processors coupled to the memory wherein the one or more processors are configured to:
obtain a design and integrated circuit structural information for the design;
extract anisotropic information from the integrated circuit structural information;
compute layout dependent material volume fractions using the integrated circuit structural information;
determine anisotropic mechanical properties based on the anisotropic information; and
calculate mechanical responses, based on interconnecting layers that undergo stress due to thermal coefficients of expansion, based on the anisotropic mechanical properties and the layout dependent material volume fractions.

### Claim 30

A computer program product embodied in a non-transitory computer readable medium for design analysis comprising:
code for obtaining a design and integrated circuit structural information for the design;
code for extracting anisotropic information from the integrated circuit structural information;
code for computing layout dependent material volume fractions using the integrated circuit structural information;
code for determining anisotropic mechanical properties based on the anisotropic information; and
code for calculating mechanical responses, based on interconnecting layers that undergo stress due to thermal coefficients of expansion, based on the anisotropic mechanical properties and the layout dependent material volume fractions.

### Claim 31 (depends on 30)

The computer program product of claim 30 further comprising code for determining volumes from coordinate and thickness information.

### Claim 32 (depends on 30)

The computer program product of claim 30 further comprising code for modeling mechanical interaction between a semiconductor chip included in the design and a package.

### Claim 33 (depends on 30)

The computer program product of claim 30 further comprising code for calculating mechanical responses for a plurality of interconnect layers or via layers in the design where each layer is considered individually.

### Claim 34 (depends on 29)

The system of claim 29 wherein the one or more processors are further configured to determine volumes from coordinate and thickness information for the design.

### Claim 35 (depends on 29)

The system of claim 29 wherein the one or more processors are further configured to model mechanical interaction between a semiconductor chip included in the design and a package.

### Claim 36 (depends on 29)

The system of claim 29 wherein the one or more processors are further configured to calculate mechanical responses for a plurality of interconnect layers or via layers in the design where each layer is considered individually.