Accurate Thermal Analysis, Including Thermal Coupling Of On-Chip Hot Interconnect

How to efficiently and accurately calculating the temperature increase on millions of wires due to self-heat.


Driven by rapid advancement in mobile/server computing and automotive/communications, SoCs are experiencing a fast pace of functional integration along with technology scaling. Advanced low power techniques are widely used, while meeting higher performance requirements using a variety of packaging technologies. The Internet of Things (IoT) is further opening up new applications with connected devices and systems, where low power, high performance and reliability are paramount. Because the impact of temperature on power, performance and reliability is huge, accurate thermal analysis is a requirement for the design flow.

In advanced process technologies such as finFET or FD-SOI, the wire width and spacing are reduced and the current density is increased, leading to increases in wire temperature (∆T) on wires. Typically, in addition to thermal coupling from devices to wires, this is due to self-heating and thermal coupling among wires, and can impact a chip’s reliability and performance. Power due to self-heat is defined as I²R, where I (current) can be I^AVG or I^RMS on power/ground wire and IRMS on signal wire.

A traditional methodology uses uniform worst-case temperatures across the chip for electromigration (EM) sign-off. This method can be pessimistic for the devices/wires not in thermal hotspots, but also may fail to take a local hot wire into account. Therefore, estimating the realistic temperature of wires is necessary for ensuring reliability while optimizing the wire design. Due to the large number of wires in a modern chip, applying a direct thermal field solution such as Finite Element Method (FEM) across all wires is not feasible. This blog describes an innovative method for efficiently and accurately calculating the temperature increase on millions of wires due to self-heat. Also outlined is the thermal-aware EM methodology that considers both self-heat and the chip-package-system (CPS) thermal environment.

Wire temperatures of a chip are critical data that are used to determine the allowable currents on wires that meet the expected Mean-Time-To-Failure (MTTF) as described in Black’s equation (Figure 1). This is used to predict EM reliability failure of a metal wire, which over time results in undesired open or short circuits. Wire/device temperature impacts power (particularly leakage power, which is an exponential function of temperature), resistance, EM limit, and consequently, EM, IR/dynamic voltage drop, signal integrity, ESD, and timing.

Figure 1: Thermal impact on electromigration.

Accurate estimation of the steady-state temperature of a wire over thousands of clock cycles in peak power operation requires the following inputs:

1. Power of CMOS devices when they are in actual operating state (i.e. switching or idle mode);
2. Thermal environment of a chip in a package, such as thermal conductivity distribution, including multi-die heating for 3D-IC design, and variations of the CPS configurations, and
3. The self-heat component of a wire, which is typically caused by self-heat-induced heating and thermal coupling between wires from the average or root-mean-square (RMS) current that flows through the wire.

Typically, the device heating is the dominant part of a chip’s total power consumption. Chip-level power analysis tools, such as ANSYS RedHawk or Totem, generate Chip Thermal Model (CTM), which represents the impact of device heating in terms of fine grid power maps, together with the detailed channel area and its power. ANSYS Sentinel-TI is a FEM tool that models and solves thermal profiles of a chip(s) in IC package such as in SoC or 3D-IC. The model uses CTM power, as well as system thermal boundary conditions from a board-level CPS analysis or a system-level thermal analysis, using ANSYS Icepak, a system-level thermal solutions using Computational Fluid Dynamics (CFD) simulation. CTM includes temperature-dependent leakage power on devices and metal distribution data of the interconnect layers.

Even though self-heating of wires in a chip’s interconnect layers constitute a small portion of the total power, as the technology scales to 16/14/10nm and below, both current density and electrical resistances on wires increase, leading to a significant rise in local self-heating and temperature. Because the number of wire segments on a chip is usually in the hundreds of millions, it is difficult to solve self-heating using a field solver such as FEM or CFD. RedHawk and Totem use a novel and efficient approach to calculate a wire’s temperature rise, as well as the thermal coupling effects. For accurate EM analysis, the base temperature from CTM flow is used together with the temperature rise on wires due to self-heating and thermal coupling.

Thermal coupling due to self-heat on devices and wires is illustrated in Figure 2. The increase in self-heat (ΔT) of each Back End of Line (BEOL) wire buried in a dielectric media is pre-characterized using ANSYS Mechanical, a general-purpose FEM tool. The pre-characterization process takes geometry and physical factors into consideration. These factors include current, electrical resistance and geometry of the wires, thickness of the dielectric layer, positioning and thermal conductivity of the dielectric, and content of the neighboring metal. Temperature decay behavior in the dielectric is a key component in the calculation of thermal coupling among wires. With ΔT and temperature decay characteristics, the thermal coupling among wires is readily and efficiently calculated using linear superposition method (Ref. S. Span, N. Chang, ECTC. 2015).

CPS thermal simulation results of an SoC or 3D-IC using Icepak generated boundary conditions illustrated in Figure 3. An FEM and/or CFD field solvers are used for thermal convection and radiation outside the conductive solid boundaries of CPS. The final thermal-aware EM analysis is performed using fine wire resolution (Figure 4) and temperature levels compatible to a realistic CPS environment. This method allows designers to easily identify and fix wires with high EM limit violations during the chip design sign-off flow.

Figure 2: Thermal coupling due to self-heating on devices and wires.

Figure 3: 3D-IC package (right) in CPS environment with thermal boundary condition from CFD (left).

Figure 4. EM limit percentage on signal wires with CPS thermal environment and wire self-heating considerations.

In the self-heat pre-characterization process, FEM is used to create detailed 3D modeling of a wire in a dielectric layer on a silicon substrate. An example of the analysis model and the typical temperature profile of a wire, including the decay profile into the dielectric media, are illustrated in Figure 5. This type of simulation serves as the base for efficiently predicting the temperature rise on each wire with a given wire geometry and environment configuration. The temperature decay behaviors for the above simulation are characterized using models similar to those in Figure 6.

Thermal coupling among the wires is obtained by using wire arrays with the parameters for wire sizes, pitches, elevations/locations of the heating wire, and decay directions. The thermal coupling results show the temperature rises due to the self-heating in wires. Reliability of wires is a function of the final temperature of a chip, which is a function of the thermal influence across chip-package-system using temperature-dependent CTM power maps. After iterations in the CPS environment, the temperature and power converge, showing consistent temperature profile and power map (Figure 7). For multi-chip and 3D-IC designs, CTM and CPS approach provides convergence of on-chip temperature profiles simultaneously. The converged thermal profile combined with wire thermal coupling deliver a complete solution for thermal-aware EM analysis.

Figure 5: 3D finite element model for charaterizing temperature rise of a wire in dielectric layers.

Figure 6: Temperature decay from wire with self-heating embedded in dielectric layers.

The base temperatures on layers and wires due to device or Front End of Line (FEOL) heating (Figures 2 and 7) are calculated using CTM based thermal analysis (Figure 3).

Figure 7. FEOL device power from CTM (right) and thermal profile on chip layers as base temperature for wires.

In summary, with advanced process technologies including finFETs, as the power density of SoCs increases, so does the thermal-induced electromigration within the chip, which is a major reliability issue. Instead of applying the traditional uniform worst-case temperature based methodology, ANSYS has developed an innovative technique that uses the self-heat-induced ΔT and thermal coupling of wires for accurately and efficiently calculating the wire temperature of the hundreds of millions of nanometer wires in a SoC today. ANSYS offers a thermal-aware EM methodology that uses both self-heat and chip-package-system thermal environment enabling designers to create the most reliable ICs for markets such as mobile, communication and automotive.

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