Method for predicting resist deformation

Patent metadata

Field	Value
Publication number	US-2022075275-A1
Application number	US-201917416314-A
Country	US
Kind code	A1
Filing date	Dec 13, 2019
Priority date	Dec 31, 2018
Publication date	Mar 10, 2022
Grant date	—

Abstract

A method for determining a deformation of a resist in a patterning process. The method involves obtaining a resist deformation model of a resist having a pattern, the resist deformation model configured to simulate a fluid flow of the resist due to capillary forces acting on a contour of at least one feature of the pattern; and determining, via the resist deformation model, a deformation of a resist pattern to be developed based on an input pattern to the resist deformation model.

First claim

1 . A method comprising:
obtaining a resist deformation model for a resist of a patterning process, the resist deformation model configured to simulate a fluid flow of the resist due to capillary forces acting on a contour of at least one feature of a pattern of the resist; and determining, via a hardware processor and the resist deformation model, a deformation of a resist pattern to be developed based on an input pattern to the resist deformation model.

2 . The method of claim 1 , wherein the resist deformation model is based on Navier-Stokes flow equations, and wherein the fluid flow is characterized by a Stokes flow and/or a Hele-Shaw flow, and wherein the fluid flow is characterized by a fundamental solution that decays with distance to a particular location in the resist, and that is either regular in the resist or only singular at the location in the resist.

3 . The method of claim 1 , wherein the determining the deformation comprises:
defining a plurality of vertices along the contour of the at least one feature; determining a capillary force at a given vertex of the plurality of vertices; and determining a velocity flow field of the fluid flow due to the capillary force based on a superposition of a velocity response at one or more of the plurality of the vertices, and based on a boundary condition, wherein the velocity response is due to a capillary force acting at a vertex adjacent to the given vertex.

4 . The method of any of claim 3 , wherein the defining the plurality of vertices comprises distributing the plurality of vertices to make them evenly spaced while conserving an area or a volume of the contour of the at least one feature, wherein the capillary force acting on the given vertex is a sum of tensions on either side of the given vertex.

5 . The method of claim 3 , wherein the velocity response is characterized by Stokeslet, wherein a Stokeslet represents a velocity flow field due to a point force in a Stokes flow.

6 . The method of claim 3 , wherein the determining the velocity flow field further comprises:
decomposing the velocity flow field into a squeeze flow and a higher order velocity flow; applying a boundary condition corresponding to the squeeze flow; and removing the squeeze flow from the velocity flow field based on the boundary condition corresponding to the squeeze flow.

7 . The method of claim 6 , wherein the squeeze flow is a flow of resist due to a net inward flux or a net outward flux through resist domain boundaries, causing a large scale migration of features in the resist pattern.

8 . The method of claim 6 , wherein applying the boundary condition corresponding to the squeeze flow comprises:
setting a flow rate through a boundary of a resist domain to zero; and/or setting a velocity across a boundary of the resist domain to a no-flux condition.

9 . The method of claim 7 , wherein a total inward flow rate through the resist domain boundaries is set to zero by providing a rotlet of selected strength at one or more corners of a boundary of the resist domain.

10 . The method of claim 3 , wherein the determining a velocity flow field further comprises obtaining a velocity at the given vertex along the contour of the at least one feature based on velocities of all other vertices caused due to the capillary force at each of the other vertices by multiplication with Stokeslets, and wherein contributions to the velocity flow field due to features far away from the given vertex are neglected.

11 . The method of claim 3 , further comprising:
determining forces at a partial area within the resist; and obtaining a deformation of an entire area of the resist based on a simulation of the resist deformation model using the forces at the partial area.

12 . The method of claim 1 , wherein the input pattern is a design pattern, a resist image, a mask pattern, and/or an aerial image, wherein the resist is a negative tone resist or a positive tone resist, chemically or not-chemically amplified, and wherein further the input pattern is a grayscale image and/or a binary image.

13 . The method of claim 1 , further comprising:
computing, using the resist deformation model, a critical dimension between a pair of locations disposed on a boundary of the at least one feature in the developed resist pattern; and calculating an error between the computed critical dimension and a measured critical dimension of an actual developed resist pattern, wherein the calculating the error comprises comparing, using a cross-correlation matrix, between printed wafer data and a simulated image.

14 . The method of claim 1 , wherein the deformation is determined at a plurality of locations, each location corresponding to a point that lies on a boundary of a developed portion of the developed resist pattern for the input pattern.

15 . A non-transitory computer program product comprising machine-readable instructions therein, the instructions, when executed by processor system, configured to cause the processor system to at least:
obtain a resist deformation model for a resist of a patterning process, the resist deformation model configured to simulate a fluid flow of the resist due to capillary forces acting on a contour of at least one feature of a pattern of the resist; and determine, via the resist deformation model, a deformation of a resist pattern to be developed based on an input pattern to the resist deformation model.

16 . The computer program product of claim 15 , wherein the resist deformation model is based on Navier-Stokes flow equations, and wherein the fluid flow is characterized by a Stokes flow and/or a Hele-Shaw flow, and wherein the fluid flow is characterized by a fundamental solution that decays with distance to a particular location in the resist and that is either regular in the resist or only singular at the location in the resist.

17 . The computer program product of claim 15 , wherein the instructions configured to cause the processor system to determine the deformation are further configured to cause the processor system to:
define a plurality of vertices along the contour of the at least one feature; determine a capillary force at a given vertex of the plurality of vertices; and determine a velocity flow field of the fluid flow due to the capillary force based on a superposition of a velocity response at one or more of the plurality of the vertices, and based on a boundary condition, wherein the velocity response is due to a capillary force acting at a vertex adjacent to the given vertex.

18 . The computer program product of claim 15 , wherein the instructions configured to cause the processor system to define the plurality of vertices are further configured to cause the processor system to distribute the plurality of vertices to make them evenly spaced while conserving an area or a volume of the contour of the at least one feature, wherein the capillary force acting on the given vertex is a sum of tensions on either side of the given vertex.

19 . The computer program product of claim 15 , wherein the instructions are further configured to cause the processor system to:
compute, using the resist deformation model, a critical dimension between a pair of locations disposed on a boundary of the at least one feature in the developed resist pattern; and calculate an error between the computed critical dimension and a measured critical dimension of an actual developed resist pattern, wherein the calculating the error comprises comparing, using a cross-correlation matrix, between pr

Assignees

• Asml Netherlands Bv

Inventors

• Batistakis Chrysostomos
• Jeurissen Roger Josef Maria
• Winkels Koen Gerhardus

Classifications

• G06F2119/18

  Manufacturability analysis or optimisation for manufacturability · CPC title

• G06F2111/10

  Numerical modelling · CPC title

• G06F30/398 Primary

  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) · CPC title

• G06F30/3308

  using simulation · CPC title

• G06F30/28

  using fluid dynamics, e.g. using Navier-Stokes equations or computational fluid dynamics [CFD] · CPC title