CN-121997545-A - Electromigration stress modeling method and device for embedded power rail

CN121997545ACN 121997545 ACN121997545 ACN 121997545ACN-121997545-A

Abstract

The invention discloses an electromigration stress modeling method and device for an embedded power rail, relates to the technical field of embedded power rails, and aims to solve the problem of low fidelity in modeling simulation of the embedded power rail in the prior art. The modeling method comprises the steps of constructing a two-dimensional grain boundary structure based on grain boundary line segment coordinate data of an embedded power rail, determining included angle parameters between grain boundary directions and current directions of all grain boundaries in the two-dimensional grain boundary structure, constructing a target electromigration stress model based on the included angle parameters, and solving the target electromigration stress model to obtain electromigration stress distribution of the embedded power rail. The invention is used for improving the fidelity of modeling simulation of the embedded power rail.

Inventors

SUN ZEYU
TONG WEIJIE
LI ZHIQIANG
XU QINZHI
LIU JIANYUN
CAO HE

Assignees

中国科学院微电子研究所

Dates

Publication Date: 20260508
Application Date: 20251219

Claims (10)

1. The electromigration stress modeling method of the embedded power rail is characterized by comprising the following steps of: Constructing a two-dimensional grain boundary structure based on grain boundary line segment coordinate data of the embedded power rail; Determining included angle parameters between the grain boundary direction and the current direction of each grain boundary in the two-dimensional grain boundary structure; Constructing a target electromigration stress model based on the included angle parameter; and solving the target electromigration stress model to obtain the electromigration stress distribution of the embedded power rail.
2. The method of modeling electromigration stress of a buried power rail of claim 1, wherein constructing a target electromigration stress model based on the included angle parameter comprises: Substituting an included angle cosine value in the included angle parameter into an electron wind force item of atomic flux in a pre-constructed initial electromigration stress model to obtain the target electromigration stress model.
3. The method of modeling electromigration stress of a buried power rail of claim 2, wherein prior to constructing a two-dimensional grain boundary structure based on grain boundary line segment coordinate data of the buried power rail, the method further comprises constructing the initial electromigration stress model; constructing the initial electromigration stress model, comprising: the Korhonen equation that will apply to grain boundary structures: Determining an initial electromigration stress model; Wherein, the Is stress; Time is; Is bulk modulus; Is atomic flux; ; Is an electronic wind power item; is a stress gradient term; Is the atomic diffusion coefficient; Is the initial electron wind power; is atomic volume; is the boltzmann constant; Is the temperature; Is a stress gradient; Substituting the included angle cosine value in the included angle parameter into an electron wind force item of atomic flux in a pre-constructed initial electromigration stress model, wherein the method comprises the following steps: substituting the cosine value of the included angle into the initial electronic wind power to obtain corrected electronic wind power: ; substituting the corrected electron wind force into the electron wind force item in the atomic flux to obtain the target electromigration stress model, The corrected electronic wind power is used; Is the effective charge number; Is a meta-charge; Is resistivity; is the current density; Is an included angle in the included angle parameters; is the cosine value of the included angle.
4. The method of modeling electromigration stress in a buried power rail of claim 1, wherein determining an included angle parameter between a grain boundary direction and a current direction of each grain boundary in the two-dimensional grain boundary structure comprises: Extracting characteristic line segments in each grain boundary by adopting a first automatic script written by numerical calculation software; taking the direction of the characteristic line segment as the grain boundary direction of the corresponding grain boundary, and calculating the included angle between the characteristic line segment and the current direction; And associating the included angle of each grain boundary with a corresponding grain boundary serial number, and solidifying the included angle into the included angle parameter which can be identified by a physical field simulation platform, wherein the grain boundary serial number is used for positioning a grain boundary domain corresponding to the cosine value of the included angle.
5. The method of modeling electromigration stress of a buried power rail of claim 4, wherein prior to constructing a target electromigration stress model based on the included angle parameters, the method further comprises: Binding each included angle parameter with a corresponding entity grain boundary in the physical field simulation platform through a linkage interface between the numerical calculation software and the physical field simulation platform by adopting the second automation script to form a mapping relation between the included angle parameter and the entity grain boundary; And solidifying the two-dimensional grain boundary structure, the included angle parameter and the mapping relation together into a model file, wherein the model file is used for providing the readable included angle parameter and the mapping relation when the physical field simulation platform builds the target electromigration stress model.
6. The method of modeling electromigration stress in a buried power rail of claim 4, wherein extracting feature segments in each grain boundary comprises: the two-dimensional grain boundary structure consists of a plurality of polygons, each polygon corresponds to one grain boundary, and the grain boundary polygon data comprises all vertex coordinates of the polygon corresponding to each grain boundary; selecting two target vertexes representing the dominant extension direction of the corresponding grain boundaries from all vertex coordinates corresponding to each grain boundary; And connecting the two target vertexes, and taking the formed line segments as the characteristic line segments corresponding to the grain boundaries.
7. The method of modeling electromigration stress of a buried power rail of claim 4, wherein constructing a two-dimensional grain boundary structure based on grain boundary line segment coordinate data of the buried power rail comprises: Importing the coordinate data of the grain boundary line segments into the numerical calculation software, and setting physical thickness by adopting a second automation script written by the numerical calculation software; Calculating the length of each grain boundary line segment, filtering invalid short line segments with the length smaller than a preset threshold value, and calculating the offset perpendicular to the normal direction to generate a plurality of polygons with thickness; Eliminating overlapping areas among different polygons in the polygons with the thickness, and screening effective areas with areas larger than a preset area; Collecting all effective areas to form the two-dimensional grain boundary structure.
8. The method of modeling electromigration stress of a buried power rail of claim 4, wherein prior to solving the target electromigration stress model, the method further comprises performing a preprocessing step; Performing a preprocessing step comprising: in the physical field simulation platform, an automatic triangle grid is adopted to perform grid division on a simulation domain of the target electromigration stress model, and grid parameters are set; After grid division is completed, setting material parameters and electrical parameters in a parameter module of the physical field simulation platform, wherein the material parameters comprise initial atomic diffusion coefficients, and the initial atomic diffusion coefficients of internal crystal boundaries are larger than those of the crystal boundaries at the interfaces; Setting model boundary conditions and model initial conditions based on physical characteristics of the target electromigration stress model, wherein atomic fluxes of all boundaries are set to be zero flux, and initial stress is uniformly set to be 0; Aiming at the time sequence analysis requirement of stress evolution, setting the stepping time and the total simulation duration of the simulation solving parameters.
9. The method of modeling electromigration stress of a buried power rail of claim 5, wherein prior to solving the target electromigration stress model, the method further comprises performing model loading and parameter configuration; Model loading and parameter configuration are performed, including: loading the model file in the physical field simulation platform; Setting the target electromigration stress model in a partial differential equation module of the physical field simulation platform, and taking the partial differential equation module as a core carrier for stress evolution solution; According to the mapping relation, each included angle parameter is related to a variable library in the partial differential equation module so as to realize that each grain boundary domain can call the corresponding included angle parameter during simulation; and setting flux source parameters in the partial differential equation module by combining the expression of the atomic flux in the target electromigration stress model, wherein the flux source parameters comprise an x-axis direction flux source and a y-axis direction flux source.
10. Electromigration stress modeling apparatus for a buried power rail, comprising: The first construction module is used for constructing a two-dimensional grain boundary structure based on grain boundary line segment coordinate data of the embedded power rail; The determining module is used for determining included angle parameters between the grain boundary direction and the current direction of each grain boundary in the two-dimensional grain boundary structure; The second construction module is used for constructing a target electromigration stress model based on the included angle parameters; and the solving module is used for solving the target electromigration stress model to obtain electromigration stress distribution of the embedded power rail.

Description

Electromigration stress modeling method and device for embedded power rail Technical Field The invention relates to the technical field of embedded power supply rails, in particular to an electromigration stress modeling method and device for an embedded power supply rail. Background As chip interconnect linewidths continue to shrink, current density has increased significantly, and Electromigration (EM) issues have become a critical reliability bottleneck in advanced integrated circuit back-end packaging. To continue to push technology nodes toward 2nm and beyond, the industry is actively deploying back-powered network (Backside Power Delivery Network, BSPDN) architectures. The architecture effectively separates signals and Power wiring by migrating a Power supply network to the back of a transistor, remarkably relieves the problem of front-end wiring congestion, effectively reduces voltage drop, and improves the index of overall Power consumption-Performance-Area (PPA). The embedded power rail (Buried Power Rail, BPR) serves as a core component in the BSPDN architecture, serving the key role of transferring power from the back-side metal layer to the front-side active devices. The structure is buried in a shallow trench isolation (Shallow Trench Isolation, STI) region under the transistor, enabling low resistance power supply through high aspect ratio metal channels. However, BPR structures are more prone to EM failure problems at high current densities due to their extremely narrow linewidths, limited heat dissipation channels, and complex process constraints. Therefore, there is a need to develop high-fidelity physical modeling simulation methods for BPR structural characteristics for evaluation of electromigration reliability thereof. Disclosure of Invention The invention aims to provide a method and a device for modeling electromigration stress of a buried power rail, which are used for solving the problem of low fidelity of the method for modeling electromigration stress of the buried power rail in the prior art. In order to achieve the above object, the present invention provides the following technical solutions: in a first aspect, the present invention provides a method of modeling electromigration stress in a buried power rail, comprising: Constructing a two-dimensional grain boundary structure based on grain boundary line segment coordinate data of the embedded power rail; determining included angle parameters between the grain boundary direction and the current direction of each grain boundary in the two-dimensional grain boundary structure; Constructing a target electromigration stress model based on the included angle parameters; And solving the target electromigration stress model to obtain the electromigration stress distribution of the embedded power rail. Optionally, constructing the target electromigration stress model based on the included angle parameter includes: substituting an included angle cosine value in the included angle parameter into an electron wind force item of atomic flux in a pre-constructed initial electromigration stress model to obtain a target electromigration stress model. Optionally, before constructing the two-dimensional grain boundary structure based on the grain boundary line segment coordinate data of the embedded power rail, the method further comprises constructing an initial electromigration stress model; Constructing an initial electromigration stress model, comprising: the Korhonen equation that will apply to grain boundary structures: ; Determining an initial electromigration stress model; Wherein, the Is stress; Time is; Is bulk modulus; Is atomic flux; ; Is an electronic wind power item; is a stress gradient term; Is the atomic diffusion coefficient; Is the initial electron wind power; is atomic volume; is the boltzmann constant; Is the temperature; Is a stress gradient; Substituting the included angle cosine value in the included angle parameter into an electron wind force item of atomic flux in a pre-constructed initial electromigration stress model, wherein the method comprises the following steps: Substituting the cosine value of the included angle into the initial electronic wind power to obtain corrected electronic wind power: ; substituting the corrected electron wind power into an electron wind power item in atomic flux to obtain a target electromigration stress model, The corrected electronic wind power is used; Is the effective charge number; Is a meta-charge; Is resistivity; is the current density; Is an included angle in the included angle parameters; is the cosine value of the included angle. Optionally, determining an included angle parameter between a grain boundary direction and a current direction of each grain boundary in the two-dimensional grain boundary structure includes: Extracting characteristic line segments in each grain boundary by adopting a first automatic script written by numerical calculation software; tak