Atomic scale grid for modeling semiconductor structures and fabrication processes

Patent metadata

Field	Value
Publication number	US-10102318-B2
Application number	US-201715841238-A
Country	US
Kind code	B2
Filing date	Dec 13, 2017
Priority date	Sep 5, 2014
Publication date	Oct 16, 2018
Grant date	Oct 16, 2018

Abstract

Roughly described, a system for simulating a temporal process in a body includes a meshing module to impose a grid of nodes on the body, the grid having a uniform node spacing which is less than the quantum separation distance in silicon. A system of node equations is provided, including at least one node equation for each of a plurality of nodes of the grid. The node equations describe behavior of at least one physical quantity at that node through each time step of the process. An iterating module iterates through the time steps to determine values for physical quantities of the body at the end of the simulation period. Preferably one particle of the body is assigned to each node of the grid. For moving boundary processes, boundary movement can be represented simply by changing the particle type assigned to various nodes of the grid as the boundary advances.

First claim

The invention claimed is:

1. A computer readable medium having stored thereon in a non-transitory manner, a plurality of software code portions defining logic for simulating a temporal process in a body, the logic comprising:
imposing a uniform grid of nodes on the body, the grid having three independent dimensions and having a uniform node spacing which is less than the quantum separation distance in silicon;
providing a system of node equations, including at least one node equation for each of a plurality of nodes of the grid, the node equation or equations for each particular one of the nodes describing behavior of at least one physical quantity of the body at the particular node through each of a first plurality of time steps of the process; and
iterating through the first plurality of the time steps to determine values for at least a subset of the physical quantities of the body at the end of the first plurality of time steps.

2. The computer readable medium of claim 1 , wherein the temporal process comprises a semiconductor fabrication process step.

3. The computer readable medium of claim 1 , wherein the temporal process comprises charge movement in a semiconductor material.

4. The computer readable medium of claim 1 , wherein the uniform node spacing is a value that is within 10% of 0.27 nanometers.

5. The computer readable medium of claim 4 , wherein the uniform node spacing is 0.27 nanometers.

6. The computer readable medium of claim 1 , wherein the three independent dimensions are mutually orthogonal.

7. The computer readable medium of claim 1 , wherein the system of node equations includes a system of discrete time probability equations,
and wherein iterating through a first plurality of time steps comprises, at each time step in the first plurality of time steps, randomly determining a particle quantity change at each particular one of the nodes in the plurality of nodes in accordance with the probability equation for the particular node.

8. The computer readable medium of claim 7 , wherein the plurality of nodes of the grid includes all nodes of the grid.

9. The computer readable medium of claim 7 , wherein the system of node equations further includes a system of discrete time continuity equations, at least one of the discrete time continuity equations for each node of the grid,
and wherein the code portions further define logic for iterating through a second plurality of the time steps, and at each time step in the second plurality of time steps, solving the system of continuity equations as a set of simultaneous equations.

10. The computer readable medium of claim 1 , wherein the system of node equations includes a system of first node equations each describing behavior of a first physical quantity of the body at each of the nodes in the plurality of nodes through each time step in the first plurality of time steps, and a system of second node equations each describing behavior of a second physical quantity of the body at each of the nodes in a second plurality of the nodes of the grid through each time step in a second plurality of time steps of the process, each of the first node equations being dependent upon values of the second physical quantity and each of the second node equations being dependent upon values of the first physical quantity,
and wherein the code portions further define logic for iterating through the second plurality of the time steps to determine values for the second physical quantity of the body at the end of a second plurality of time steps.

11. The computer readable medium of claim 10 , wherein at least one of the time steps in the second plurality of time steps differs from all of the time steps in the first plurality of time steps.

12. The computer readable medium of claim 10 , wherein the second plurality of time steps is interspersed with the first plurality of time steps,
and wherein the iteration through the second plurality of time steps alternates with the iteration through the first plurality of time steps.

13. The computer readable medium of claim 10 , wherein the system of first node equations comprises a system of discrete time continuity equations, at least one of the discrete time continuity equations for each node of the grid,
and wherein the system of second node equations comprises a system of discrete time probability equations, at least one of the discrete time probability equations for each node of the grid.

14. The computer readable medium of claim 1 , wherein the body comprises a plurality of different particle types, each having different values for at least a first material property, at least one of the node equations being dependent upon the value for the first material property at each of the nodes,
and wherein imposing a uniform grid of nodes on the body comprises assigning exactly one particle of the body to each of the nodes.

15. The computer readable medium of claim 14 , wherein a first portion of the grid is imposed on a first portion of the body, the first portion of the body having particles disposed in a crystal lattice structure whose node positions differ from the node positions in the first portion of the uniform grid.

16. The computer readable medium of claim 14 , wherein a first one of the particle types comprises a molecule having a plurality of constituent atoms,
and wherein assigning exactly one particle of the body to each of the nodes comprises assigning one instance of the molecule to each of a number of the nodes.

17. The computer readable medium of claim 14 , wherein a first portion of the grid is imposed on a portion of the body composed essentially of multiple instances of a first compound, the first compound having a plurality of constituent elements in a particular ratio,
and wherein assigning exactly one particle of the body to each of the nodes comprises assigning the constituent elements individually to the nodes in the first portion of the grid in the same proportion as the particular ratio.

18. The computer readable medium of claim 14 , wherein a first portion of the grid is imposed on a portion of the body composed essentially of a mixture of particles of a plurality of types in respective particle ratios,
and wherein assigning exactly one particle of the body to each of the nodes comprises assigning the particles of the mixture individually to the nodes in the first portion of the grid in the same proportions as in the mixture.

19. The computer readable medium of claim 1 , wherein the code portions further define logic for reporting to a user values determined for the subset of physical quantities at one or more nodes in the grid.

20. A computer readable medium having stored thereon in a non-transitory manner, a plurality of software code portions defining logic for simulating a temporal process in a body, the body comprising particles of a plurality of different particle types each having a different value for at least a first material property, the logic comprising:
assigning exactly one particle of the body to each of a plurality of nodes in a uniform grid of nodes imposed on the body, the grid having three independent dimensions and having a uniform node spacing;
providing a system of discrete time probability node equations, at least one of the node equations for each of the plurality of nodes of the grid, each of the node equations describing probability of a predetermined physical event type occurring at the respective node of the grid during a predetermined time period, in dependence upon the value f

Assignees

• Synopsys Inc

Inventors

• Moroz Victor
• Smith Stephen Lee

Classifications

• G06F2111/12

  Symbolic schematics · CPC title

• G06F30/30

  Circuit design · CPC title

• G06F30/20 Primary

  Design optimisation, verification or simulation (optimisation, verification or simulation of circuit designs G06F30/30) · CPC title

• G06F2111/10

  Numerical modelling · CPC title

• G05B19/41885

  characterised by modeling, simulation of the manufacturing system · CPC title