A method for evolution of a conical etching interface based on geometric visibility constraints

Abstract

This invention discloses a method for the evolution of a tapered etching interface based on geometric visibility constraints, comprising: for each interface point, radiating outwards from the interface at a direction perpendicular to the vertical direction... θ The visibility of an interface point is determined by the angle of the ray; for the interface points determined to be visible, their etching rate is set; the etching rate is then substituted into the Narrow Band calculation flow to perform the tapered etching interface evolution. This invention transfers the concept of geometric visibility to tapered etching to construct its velocity function, achieving numerically stable and expected tapered interface evolution. The final result has an accuracy error of less than 5% compared with mainstream international commercial software. It is applicable to etching interface evolution problems in 3D process simulation, including but not limited to anisotropic etching, tapered etching, and multi-material etching processes, and is especially suitable for process simulation scenarios with geometric occlusion, suspended structures, or complex spatial morphologies.

Description

Technical Field

[0001] This invention relates to the field of semiconductor process simulation technology, and in particular to a method for the evolution of a tapered etching interface based on geometric visibility constraints. Background Technology

[0002] As semiconductor devices evolve towards three-dimensional structures, high aspect ratios, and multi-material processes, the influence of structural morphology on the manufacturing process becomes increasingly complex. Three-dimensional process simulation has become a crucial tool in process development and process window evaluation. Compared to high-precision simulation methods based on physical particle transport, rapid process simulation methods based on interface evolution (Level Set) are widely used in process path exploration and layout-related effect analysis due to their high computational efficiency and strong parameter controllability.

[0003] In etching process simulation, a tapered etching model is typically introduced to characterize the sidewall tilting phenomenon caused by ion incident directionality or process conditions in actual processes. However, describing tapered etching behavior solely by constructing a single continuous etching rate function related to the interface normal direction and material properties is difficult to achieve the expected interface evolution and satisfy numerical stability under complex three-dimensional structural conditions, especially in the presence of suspended structures, shading effects, or multi-material interactions. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a method for the evolution of a conical etching interface based on geometric visibility constraints. By introducing a geometric visibility judgment mechanism, the method makes hierarchical decisions on etching accessibility and etching rate during the etching process, thereby achieving stable and physically consistent conical etching interface evolution under complex three-dimensional structural conditions.

[0005] This invention provides the following solutions:

[0006] This invention provides a method for the evolution of a tapered etching interface based on geometric visibility constraints, the method comprising:

[0007] S1. For each interface point, determine whether it is visible by emitting rays from it outward at an angle θ to the vertical direction. The determination process is as follows: determine whether each ray emitted from the interface point is blocked by the interface. If all rays are not blocked, the point is visible; if any ray is blocked, the point is not visible.

[0008] S2. For interface points that are determined to be visible, set their etching rate to the base etching rate, i.e., the relative rate is 1; for interface points that are determined to be invisible, set their etching rate to the cone etching rate, i.e., the relative rate is the lateral ratio r. When the lateral ratio r is 0, the etching rate is 0.

[0009] S3. Substitute the etching rate into the Narrow Band calculation process to perform the evolution of the tapered etching interface.

[0010] Furthermore, in step S1, when determining whether an interface point is visible, for the two-dimensional case, the interface point emits only two rays; for the three-dimensional case, all emitted rays form a conical surface, and m rays emitted from m directions are selected.

[0011] Furthermore, m can be 4 to 10.

[0012] Furthermore, step S3 includes the following processes:

[0013] S3.1. Given that at the initial time t0, the evolution time t is equal to the distance field φ=0 and the etching velocity F on the wavefront;

[0014] S3.2 Initialize the range field of n layers (band; because n is generally less than 10, the band is relatively narrow, so it is called narrow band) inside and outside the wavefront;

[0015] S3.3 Calculate the velocity field within the narrow band ;

[0016] S3.4 Calculate the range field within the narrow band at time t=t+Δt using the Level set time discretization formula;

[0017] S3.5 If the evolution time t reaches the preset time t final If the wavefront is successfully extracted, the evolution ends; otherwise, determine whether the wavefront has evolved to the edge of the narrow band. If so, return to step S3.1; otherwise, return to step S3.3.

[0018] Furthermore, step S3.3 calculates the velocity field using the following formula. :

[0019] (1);

[0020] in, It is a temporary range field used to calculate the velocity field within a narrow band, derived from the range field on the wavefront. This condition and formula The velocity field within the entire narrow band is obtained by simultaneous calculation of the etching velocity F on the wave surface and equation (1). .

[0021] Furthermore, step S3.4 calculates the distance field using the following formula:

[0022] (2);

[0023] in, It is the derivative of the distance field with respect to time. Equation (2) is discretized using first-order explicit time discretization, i.e. According to the distance field at the current moment Find the distance field at the next moment. .

[0024] The beneficial effects of this invention based on its technical solution are as follows:

[0025] (1) This invention transfers the concept of geometric visibility to the construction of its velocity function in conical etching, which can achieve numerical stability and results that meet expectations for the evolution of the conical interface. The final result has an accuracy error of less than 5% compared with mainstream international commercial software.

[0026] (2) Unlike traditional visibility etching, which judges whether the geometric visibility is blocked along the entire range from the interface point to the ion emission source, the visibility judgment proposed in this invention for tapered etching only focuses on whether the interface is blocked locally, that is, whether the rays emitted from the interface point are blocked after traveling through several voxel units. Due to the greatly reduced range, the computational efficiency of this method is not significantly worse than that of using a single continuous velocity function.

[0027] (3) The present invention is applicable to the etching interface evolution problem in three-dimensional process simulation, including but not limited to anisotropic etching, conical etching and multi-material etching processes, and is especially applicable to process simulation scenarios with geometric occlusion, suspended structure or complex spatial morphology. Attached Figure Description

[0028] To more clearly illustrate the technical solutions in the embodiments of this specification or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0029] Figure 1 This is a flowchart illustrating a method for the evolution of a tapered etching interface based on geometric visibility constraints, provided by the present invention.

[0030] Figure 2 This is a schematic diagram of the Narrow Band calculation process.

[0031] Figure 3 This is a diagram illustrating visibility determination.

[0032] Figure 4 This is a schematic diagram of the cone-shaped etching effect. Detailed Implementation

[0033] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention are within the protection scope of the embodiments of the present invention.

[0034] To achieve conical etching at target sidewall tilt angles θ (ranging from 0° to 90°), previous attempts included constructing a single continuous etching rate function related to the interface normal direction and material properties. However, verification revealed that this method could not produce the expected etching interface evolution results under different target tilt angles θ, and it was prone to evolution failure under complex 3D structural conditions. Analysis of the expected interface evolution results showed that its characteristics were similar to those of visibility etching.

[0035] Based on this conclusion, this embodiment provides a method for the evolution of a tapered etching interface based on geometric visibility constraints, referring to... Figure 1 The method includes:

[0036] S1. For each interface point, determine its visibility by observing the rays it emits outward from the interface at an angle θ (θ is the inclination angle of the target sidewall) to the vertical direction. In the two-dimensional case, the interface point emits exactly two rays; in the three-dimensional case, all emitted rays form a conical surface, and eight rays emitted in eight directions can be selected.

[0037] The determination process is as follows: determine whether each ray emanating from the interface point is blocked by the interface. If all rays are not blocked, the point is visible; if any ray is blocked, the point is not visible.

[0038] S2. For interface points that are determined to be visible, set their etching rate to the base etching rate, i.e., the relative rate is 1; for interface points that are determined to be invisible, set their etching rate to the cone etching rate, i.e., the relative rate is the lateral ratio r. When the lateral ratio r is 0, the etching rate is 0.

[0039] S3. Substitute the etching rate into the Narrow Band calculation process to perform the evolution of the tapered etching interface, referring to... Figure 2 This includes the following processes:

[0040] S3.1. Given that at the initial time t0, the evolution time t is equal to the distance field φ = 0 and the velocity F on the wavefront;

[0041] S3.2 Initialize the range field within the narrow band, i.e., inside and outside the n layers of the wavefront;

[0042] S3.3 Calculate the velocity field within the narrow band;

[0043] S3.4 Calculate the range field within the narrow band at time t = t + Δt using the Level set time discretization formula, where Δt is the differential time;

[0044] S3.5 If the evolution time t reaches the preset time t final If the wavefront is successfully extracted, the evolution ends; otherwise, determine whether the wavefront has evolved to the edge of the narrow band. If so, return to step S3.1; otherwise, return to step S3.3.

[0045] Reference Figure 3 The following explanation will be based on the case where the lateral ratio r is 0 (Lateral Ratio = lateral etching rate / vertical etching rate = 0). Figure 3 The two-dimensional diagram shows the initial interface (black dashed line) and the target interface (red solid line). Conical etching is essentially trapezoidal etching in two dimensions. Since the angle between the rays emanating from the interface points and the vertical direction is θ, the final evolution tends to result in a slope with an angle of θ. This is because interface points with a normal angle (the angle between the interface normal and the vertical direction) less than (90°-θ) are visible (as shown in points 1 and 4), representing basic etching. Since r=0, this is a vertical etching with a rate of 1. However, interface points with a normal angle greater than or equal to (90°-θ), such as vertical sidewalls (as shown in points 2 and 3), are invisible, and their rate is 0. Therefore, when an interface with a normal angle less than (90°-θ) evolves to a normal angle greater than or equal to (90°-θ), that interface point becomes stationary, ultimately forming a slope with an angle of θ, thus achieving conical etching.

[0046] Figure 4 This is a tapered etching interface obtained by using the process evolution of this embodiment.

[0047] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0048] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0049] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for the evolution of a conical etched interface based on geometric visibility constraints, characterized in that, The method includes: S1. For each interface point, determine whether it is visible by emitting rays from it outward at an angle θ to the vertical direction. The determination process is as follows: determine whether each ray emitted from the interface point is blocked by the interface. If all rays are not blocked, the point is visible; if any ray is blocked, the point is not visible. S2. For interface points that are determined to be visible, set their etching rate to the base etching rate, i.e., the relative rate is 1; for interface points that are determined to be invisible, set their etching rate to the cone etching rate, i.e., the relative rate is the lateral ratio r. When the lateral ratio r is 0, the etching rate is 0. S3. Substitute the etching rate into the Narrow Band calculation process to perform the evolution of the tapered etching interface.

2. The method for evolving a tapered etching interface based on geometric visibility constraints according to claim 1, characterized in that: In step S1, when determining whether an interface point is visible, for the two-dimensional case, the interface point emits only two rays; for the three-dimensional case, all emitted rays form a conical surface, and m rays emitted from m directions are selected.

3. The method for the evolution of a tapered etching interface based on geometric visibility constraints according to claim 2, characterized in that: m can be 4~10.

4. The method for the evolution of a tapered etching interface based on geometric visibility constraints according to claim 1, characterized in that: Step S3 includes the following processes: S3.

1. Given that at the initial time t0, the evolution time t is equal to the distance field φ=0 and the etching velocity F on the wavefront; S3.2 Initialize the range field within the narrowband, i.e., inside and outside the n layers of the wavefront; S3.3 Calculate the velocity field within the narrow band ; S3.4 Calculate the range field within the narrow band at time t=t+Δt using the Level set time discretization formula; S3.5 If the evolution time t reaches the preset time t final If the wavefront is successfully extracted, the evolution ends; otherwise, determine whether the wavefront has evolved to the edge of the narrow band. If so, return to step S3.1; otherwise, return to step S3.

3.

5. The method for evolving a tapered etching interface based on geometric visibility constraints according to claim 4, characterized in that: Step S3.3 Calculate the velocity field using the following formula : （1）； in, It is a temporary range field used to calculate the velocity field within a narrow band, derived from the range field on the wavefront. This condition and formula The velocity field within the entire narrow band is obtained by simultaneous calculation of the etching velocity F on the wave surface and equation (1). .

6. The method for evolving a tapered etching interface based on geometric visibility constraints according to claim 4, characterized in that: Step S3.4 Calculate the range field using the following formula: （2）； in, It is the derivative of the distance field with respect to time. Equation (2) is discretized using first-order explicit time discretization, i.e. According to the distance field at the current moment Find the distance field at the next moment. .

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