Method for thermal simulation

• US 8,539,408 B1
• Filed: 07/29/2009
• Issued: 09/17/2013
• Est. Priority Date: 07/29/2008
• Status: Expired due to Fees

• Current Assignee: Clarkson University (Union Graduate College)
• Original Assignee: Clarkson University (Union Graduate College)
• Inventors: Helenbrook, Brian T., Cheng, Ming-Cheng
• Primary Examiner(s): Siek, Vuthe
• Assistant Examiner(s): LEE, ERIC D
• Application Number:
  US12/462,078
• Time in Patent Office: 1,511 Days
• Field of Search: 716/110
• US Class Current: 716/110
• CPC Class Codes: G06F 2119/08 Thermal analysis or thermal optimisation
• CPC Class Codes: G06F 30/367 Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods

Abstract

The invention of novel methods is described for efficient and accurate thermal simulation of a structure that can be primarily constructed using building blocks. These structures may include, but not limited to, semiconductor chips, photovoltaic/solar panels, battery packs, etc. The methods are formulated in hierarchical function spaces, rather than the physical space and provide three-dimensional (3D) steady-state and transient temperature profiles of the structure, which are as detailed as full-scale numerical simulation, using substantially less computational degrees-of-freedom (DOF). The number of DOF required is comparable to that of lumped thermal models, yet no ad-hoc modeling assumptions related to geometry, dimensions, temperature profiles, or heat flow paths are required. The methods can be applied to evaluate temperature profiles at different levels of granularity. The methods can also be implemented in various computer-aided-design (CAD) or electronic-design-automation (EDA) tools for different technologies to perform electro-thermal simulations.

Claims

1. A method for steady state and transient thermal simulation of a block-based structure or system comprising the acts of:

selecting building blocks for a technology;

performing a detailed numerical simulation of each selected block;

constructing a reduced-order thermal model of each block using either one of the following techniques;

(i) generating interior and boundary thermal modes of said reduced-order model from detailed numerical simulation data for each selected block and using interior and boundary thermal modes to enforce a coupling of modal solutions between said blocks;

or

(ii) generating thermal modes of said reduced-order model from detailed numerical simulation data for said entire domain of each selected block and using a discontinuous method to enforce a coupling of modal solutions between said blocks;

storing thermal modes and model parameters of said constructed reduced-order thermal models for said selected building blocks in a library for said selected technology;

constructing said reduced-order thermal model for said block-based structure from said generated thermal models for individual blocks in said library;

wherein said acts perform a steady state and a transient thermal simulation of said structure;

further wherein said thermal modes are basis functions of a function space;

further wherein said thermal simulation is performed in said function space, where a temperature for each thermal mode in said function space is calculated; and

further wherein said acts are performed using a computer.

2. The method of claim 1 wherein said structure or system can be constructed primarily using a number of standard building blocks wherein said standard building blocks are said selected blocks whose thermal modes and model parameters are stored in said library for a technology;

further wherein each different technology requires a different set of standard building blocks stored in a library for said technology.

3. The method of claim 2 further comprising the acts of:

selecting and storing standard building blocks with different sizes, thermal modes and model parameters with different temperature resolutions in said libraries of a technology for simulation of different levels of resolution and efficiency.

4. The method of claim 1 further comprising the act of:

determining whether said simulation requires one or more non-standard blocks wherein said non-standard building blocks refer to those which are not selected as standard building blocks.

5. The method of claim 1 further comprising the acts of:

generating one or more reduced-order thermal models for non-standard building blocks; and

constructing said reduced-order thermal model for said structure from said generated thermal models for individual blocks in said library with some or no non-standard building blocks wherein said reduced-order model refers to a method that transforms partial differential equations into said function space represented by a finite number of basis functions in order to reduce numerical degrees of freedom (DOF) required to solve said equations;

further wherein said thermal simulation of said structure based on said reduced-order model involves solving an ordinary matrix differential equation in said function space representing heat flow in said structure and further wherein in steady state, said ordinary matrix differential equation reduces to a matrix equation.

6. The method of claim 5 further comprising the act of generating thermal models for a particular group of non-standard blocks that deviate from a standard one.

7. The method of claim 6 further comprising the acts of generating one or more reduced-order thermal models for said group of non-standard building blocks;

and

constructing said reduced-order thermal model for said structure from said standard building blocks with one or more said generated thermal models for said group of non-standard building blocks.

8. The method of claim 1 wherein said method can be applied to structure materials with nonlinear thermal conductivities and/or specific heats that vary with temperature.

9. The method of claim 8 further comprising the act of applying one or more reduced-order thermal models to perform thermal simulation of said structure in a circuit simulator, accounting for nonlinear thermal resistances and/or capacitances induced by said nonlinear thermal conductivities and/or nonlinear specific heats in said structure materials wherein said thermal simulation of said structure in a circuit simulator based on said reduced-order model involves solving a thermal circuit in said function space representing heat flow in said structure;

further wherein nodes or circuit nodes in said circuit represent said thermal modes in said function space and node temperatures are calculated in said thermal circuit simulation.

10. The method of claim 1 wherein said method can be applied to any block-based system or structure

further wherein said block-based system refers to any kind of structures or systems that can be primarily constructed using said standard building blocks, including but not limited to planar semiconductor integrated circuits (IC'"'"'s) or chips, 3D stacked IC'"'"'s, 3D stacked dies, 3D packages, optical interconnects, nanowire interconnects, photonic IC'"'"'s chips, stacked-cell battery packs, LED lighting, MEMS, NEMS, and photovoltaic modules, panels or arrays, including nanotechnology and/or biotechnologies.

11. The method of claim 1 further comprising the act of applying said method to a single-block system or a system with several coupled blocks, wherein a multi-block system comprises standard building blocks with some or no non-standard blocks.

12. The method of claim 1 further comprising the acts of using said technique (i) using said interior and boundary thermal modes of each block to enforce thermal coupling across adjoining blocks in a multi-block system.

13. The method of claim 1 further comprising the acts of using said technique (ii) using said discontinuous method to enforce thermal coupling across adjoining blocks in a multi-block system.

14. The method of claim 1 further comprising the act of applying reduced-order thermal models of several smaller-size blocks to generate a thermal model for a larger-size block wherein said blocks may include standard or non-standard building blocks.

15. The method of claim 1 further comprising the act of using a higher-resolution reduced-order thermal model of a block to generate a lower-resolution thermal model for said block wherein said block may include standard or non-standard building blocks.

16. The method of claim 1 further comprising the acts of applying said reduced-order thermal models to perform electro-thermal simulation of said structure in a circuit simulator, accounting for nonlinear thermal resistances and/or capacitances induced by nonlinear thermal conductivities and/or nonlinear specific heats in said materials for electro-thermal simulation wherein said electro-thermal simulation performs self-consistent calculations accounting for influences of temperature on electric characteristics and of electric power dissipation on the temperature distribution of said structure.

17. The method of claim 1 further comprising the act of coupling said reduced-order thermal models self-consistently with any other models, methods or CAD or EDA tools to perform thermal, electro-thermal, electro-magnetic-thermal, electro-chemical-thermal, electro-opto-thermal, or electromechanical-thermal simulations.

18. The method of claim 1 further comprising the act of applying said reduced-order thermal models to a semiconductor structure, including a single- or multiple-device structure, one or more interconnect structures, one or more standard cells, one or more functional circuit blocks, one or more dies, or a mix of any combination of these selected blocks.

19. The method of claim 1 wherein said building blocks can be placed together to construct a thermal model of a larger semiconductor structure, which may include some non-standard blocks.

20. The method of claim 1 further comprising the act of applying said method to conventional planar, 3D stacked IC, 3D packages, photonic, MEMS, microwave, millimeter-wave and other emerging semiconductor technologies, including system in packages (SiPs), through silicon vias (TSVs), stacked multi-chip modules, stacked dies and nanotechnology.

21. The method of claim 1 further comprising the act of applying said method to a stacked-cell battery pack.

22. The method of claim 1 wherein said selected building blocks may include:

one or more battery cells;

part of a case or a whole case that packs said cells;

part of or all spacing material(s) between said case and cells,

one or more built-in protection circuit blocks and/or a mix of any combination of said selected blocks.

23. The method of claim 22 wherein a reduced-order thermal model of a battery pack is generated using said models of said selected blocks with some or no non-standard blocks.

24. The method of claim 23 wherein said battery pack includes any energy storage system using cells or units, such as galvanic cells, voltaic piles, electrolytic cells, fuel cells, biofuel cells, flow cells, and ultracapacitors.

25. The method of claim 1 wherein said method is applied to a photovoltaic module, array or panel.

26. The method of claim 25 wherein said selected building blocks comprise one or more photovoltaic cells;

one or more modules;

one or more built-in protection circuit blocks;

one or more solar panels;

or a mix of any combination of said selected blocks.

27. The method of claim 26 further comprising the act of:

generating reduced-order thermal models of a photovoltaic module, panel, or array using the models of said selected blocks with some or no non-standard blocks.

28. The method of claim 27 wherein said photovoltaic cells comprises any type of photovoltaic cells based on crystalline, thin-film, multi-junction, quantum-well, quantum-wire, quantum-dot, and nanoparticle structures.

29. A non-transitory computer readable medium containing an executable program for performing steady state and transient thermal simulation of said block-based structure or system where said program performs the acts of:

selecting building blocks or standard building blocks for a technology;

performing a detailed numerical simulation of each selected block;

generating interior and boundary thermal modes of a reduced-order model from detailed numerical simulation data for each block;

constructing said reduced-order thermal model of each block using its interior and boundary thermal modes to enforce a coupling of modal solutions between said blocks;

storing thermal modes and model parameters of said constructed reduced-order thermal models for said selected blocks in a library for said selected technology;

and constructing said reduced-order thermal model for said block-based structure from said generated thermal models for individual blocks in said library; and

wherein said acts perform a steady state and a transient thermal simulation of said structure;

further wherein said thermal modes are basis functions of a function space; and

further wherein said thermal simulation is performed in said function space, where a temperature for each thermal mode in said function space is calculated.

30. A non-transitory computer readable medium containing an executable program for performing steady state and transient thermal simulation of a block-based structure or system where the program performs the acts of:

selecting building blocks or standard building blocks for a technology,

performing a detailed numerical simulation of each selected block,

generating thermal modes of a reduced-order model for each block from detailed numerical simulation data for said entire domain of each selected block,

constructing said reduced-order model of each block using a discontinuous method to enforce a coupling of modal solutions between said blocks;

storing said thermal modes and model parameters of said constructed reduced order model for said selected building blocks in a library for said selected technology;

and

constructing said reduced-order thermal model for said block-based structure from said generated thermal models for individual blocks in said library; and

wherein said acts perform a steady state and a transient thermal simulation of said structure;

further wherein said thermal modes are basis functions of a function space; and

further wherein said thermal simulation is performed in said function space, where a temperature for each thermal mode in said function space is calculated.

31. A method for steady state and transient thermal simulation of a block based structure or system comprising the acts of:

selecting building blocks or standard building blocks for a technology;

performing a detailed numerical simulation of each selected block;

constructing a reduced-order thermal model of each block using either one of the following techniques;

(i) generating interior and boundary thermal modes of said reduced-order model from detailed numerical simulation data for each selected block and using interior and boundary thermal modes to enforce a coupling of modal solution between said blocks;

or

(ii) generating thermal modes of said reduced-order model from detailed numerical simulation data for said entire domain of each selected block and using a discontinuous method to enforce said coupling of modal solutions between said blocks;

storing thermal modes and model parameters of said constructed reduced-order thermal models for said selected building blocks in a library for said selected technology;

constructing said reduced-order thermal model for said block-based structure from said generated thermal models for individual blocks in said library; and

wherein said acts perform a steady state and a transient thermal simulation of said structure;

further wherein said thermal modes are basis functions of a function space;

further wherein said thermal simulation is performed in said function space, where a temperature for each thermal mode in said function space is calculated

further wherein said structure or system can be constructed primarily using a number of standard building blocks wherein said standard building blocks are said selected blocks whose thermal modes and model parameters are stored in said library for a technology;

further wherein each different technology requires a different set of standard building blocks stored in a library for said technology;

further comprising selecting and storing standard building blocks with different sizes, thermal modes and model parameters with different temperature resolutions in said libraries of a technology for simulation of different levels of resolution and efficiency; and

further wherein said acts are performed using a computer.