Model-based development of zone-based flow or heat distribution systems

Abstract

The embodiments disclosed herein include a method for optimizing zones in a fluid flow system. In an embodiment, the method includes the step of performing a baseline simulation for a fluid flow system and the step of performing a plurality of sensitivity simulations, each sensitivity simulation perturbing the flow rate through one of a plurality of pitch circles in the fluid flow system by an offset percentage. In an embodiment, the method further includes the step of generating a sensitivity matrix from the plurality of sensitivity simulations and the step of optimizing an objective function to enable grouping the plurality of pitch circles into a plurality of zones.

Description

Technology Field

[0001] This application claims priority to U.S. Patent Application No. 18 / 415,495 filed January 17, 2024, the entire contents of which are incorporated herein by reference.

[0002] The embodiments relate to the field of semiconductor manufacturing, and in particular to apparatuses and methods for simulating fluid flow systems and / or thermal systems to enable zone control optimization. Background Technology

[0003] In semiconductor fabrication environments, controlling the flow of fluids (e.g., gases) is a critical factor in providing process uniformity across the wafer surface. Typically, the flow of gases into a chamber is implemented via a showerhead containing multiple holes. These holes can be grouped into zones for easier control. However, determining which holes to provide for each zone is not a simple task. This is at least partially due to crosstalk between the gases flowing through each hole within the showerhead. In other words, altering the gas flow in a single hole can also affect process uniformity in the regions immediately below and near the hole. In addition to controlling fluid flow, thermal control can also be grouped into zones. These thermal zones also involve crosstalk issues that make delineation of the thermal zones difficult.

[0004] Existing solutions for flow control systems require physical models, extensive design of experiment (DoE), and other tests. This is a costly and time-consuming process, particularly when physical models are required for the many different processing tools within a semiconductor fabrication facility.

[0005] The embodiments disclosed herein include a method for optimizing zones in a fluid flow system. In an embodiment, the method includes the steps of performing a baseline simulation for a fluid flow system and performing a plurality of sensitivity simulations, each sensitivity simulation perturbs the flow rate through one of a plurality of pitch circles in the fluid flow system by an offset percentage. In an embodiment, the method further includes the steps of generating a sensitivity matrix from the plurality of sensitivity simulations and optimizing an objective function to enable grouping the plurality of pitch circles into a plurality of zones.

[0006] The embodiments disclosed herein include a method for optimizing zones in a heat control plate. In an embodiment, the method includes the step of performing a baseline simulation for the heat control plate and the step of performing a plurality of sensitivity simulations, each sensitivity simulation perturbing an energy input for one of a plurality of heating elements in the heat control plate by an offset percentage. In an embodiment, the method may further include the step of generating a sensitivity matrix from the plurality of sensitivity simulations and the step of optimizing an objective function to enable grouping the heating elements into a plurality of zones.

[0007] Embodiments may also include a method for optimizing zone grouping in a system having multiple inputs. In an embodiment, the method includes the step of performing a baseline simulation for the system, wherein the baseline simulation includes applying a uniform stimulus to each of the inputs. In an embodiment, the method further includes the step of performing multiple sensitivity simulations, wherein each sensitivity simulation perturbs the stimulus for one of the multiple inputs in the system by an offset percentage. In an embodiment, the method may further include the step of generating a sensitivity matrix from the multiple sensitivity simulations, and the step of optimizing an objective function to enable grouping the multiple inputs into multiple zones. Brief explanation of the drawing

[0008] FIG. 1 is an example of a plan view of a shower head having holes arranged in a plurality of pitch circles according to an embodiment. FIG. 2 is a cross-sectional example of a semiconductor processing tool including a showerhead similar to the showerhead illustrated in FIG. 1, according to an embodiment. FIGS. 3a to 3d are graphs depicting processing results on a wafer when different pitch circles are used to exemplify the effect of crosstalk in a system according to an embodiment. FIG. 4 is a process flowchart illustrating a process for optimizing zone grouping in a showerhead using a model-based approach according to an embodiment. FIG. 5 is a graph illustrating improvements in process uniformity when zone grouping is appropriately optimized according to an embodiment. FIG. 6 is an example plan view of a heating plate having a plurality of resistive heating elements according to an embodiment. FIG. 7 is a cross-sectional example of a semiconductor processing tool including a heating plate similar to the heating plate illustrated in FIG. 6, according to an embodiment. FIG. 8 is a process flowchart illustrating a process for optimizing zone grouping in a heating plate using a model-based approach according to an embodiment. FIG. 9 is a process flowchart illustrating a process for optimizing zone grouping in a system having inputs exhibiting crosstalk behavior according to an embodiment. FIG. 10 illustrates a block diagram of an exemplary computer system that can be used with a processing tool according to an embodiment. Specific details for implementing the invention

[0009] The systems described herein include systems and methods for simulating fluid flow systems and / or thermal systems to enable zone control optimization. In the following description, many specific details are presented to provide a thorough understanding of the embodiments. It will be apparent to those skilled in the art that the embodiments may be practiced without these specific details. In other cases, well-known aspects are not described in detail to avoid unnecessarily obscuring the embodiments. Furthermore, it should be understood that the various embodiments depicted in the accompanying drawings are exemplary representations and are not necessarily drawn to actual scale.

[0010] Various embodiments or aspects of the present disclosure are described herein. In some implementations, different embodiments are practiced separately. However, the embodiments are not limited to being practiced independently. For example, two or more different embodiments may be combined together to be practiced as a single device, process, structure, etc. In some cases, the entirety of the various embodiments may be combined together. In other cases, parts of a first embodiment may be combined with parts of one or more different embodiments. For example, a part of the first embodiment may be combined with a part of the second embodiment, or a part of the first embodiment may be combined with a part of the second embodiment and a part of the third embodiment.

[0011] The embodiments illustrated and discussed in connection with the drawings included herein are provided for the purpose of explaining some of the basic principles of the present disclosure. However, the scope of the present disclosure covers all related, potential, and / or possible embodiments, including embodiments different from the ideal and / or exemplary examples presented. The present disclosure also covers embodiments that incorporate and / or utilize components, devices, systems, etc. that are modern, future, and / or unknown at the time of writing of the present disclosure, as substitutes for functionally equivalent, similar, and / or similar components, devices, systems, etc. used in the embodiments illustrated and / or discussed herein for the purposes of explanation, illustration, and example.

[0012] As mentioned above, crosstalk between zones in fluid or thermal systems makes it difficult to control process uniformity. For example, changing the gas flow in one zone of a showerhead can also affect process uniformity in other nearby zones. In other words, improperly grouping inputs to the system can result in a system that is more difficult to adjust to achieve the desired process uniformity.

[0013] Accordingly, the embodiments disclosed herein may relate to a model-based approach for zone optimization in a system having multiple inputs that experience crosstalk. The use of a model-based approach offers significant advantages over existing solutions. One advantage is that there is no need to construct a physical model. This can be a time-saving and cost-saving benefit of the embodiments disclosed herein. Another advantage is that the model can be executed without extensive experimentation on actual processing tools. This reduces research and development costs and allows tools to be utilized for revenue-generating tasks. The model-based optimization approach described herein is also applicable to many types of tools, chambers, and / or environments. Accordingly, the benefits of the embodiments disclosed herein can be applied across semiconductor fabrication facilities (or any other manufacturing environment).

[0014] In the case of a shower head, each pitch circle may be an input containing multiple holes. Since the diameters of the pitch circles are not uniform, the number of holes within each pitch circle may also not be uniform. For example, the outer pitch circles will have more holes than the inner pitch circles. In the case of a heating plate, each input may be a resistive heater. The resistive heater may be a conductive trace having a ring-shaped path, but other resistive heater layouts may also be used. The diameters of each resistive heater may also not be uniform.

[0015] Process modeling according to embodiments of the present disclosure begins with the creation of a model. The model may be a digital representation of the physical structure of a system (e.g., showerhead, heating plate, etc.) compatible with simulation software to predict processing results (e.g., material deposition rates, etching rates, elemental concentrations, temperatures, etc.) on a substrate (e.g., wafer). The model is used to generate a baseline simulation.

[0016] In the case of a showerhead, baseline simulation may involve flowing gas through each of the holes of the showerhead at a uniform flow rate. After baseline simulation, multiple sensitivity simulations are executed on the model. Each sensitivity simulation perturbs the gas flow rate of one pitch circle of the showerhead at a time to determine the sensitivity of the system. A sensitivity matrix is ​​generated from the sensitivity simulation data. The sensitivity matrix can be incorporated into an objective function that is optimized to appropriately group the pitch circles into multiple zones.

[0017] For heating plates, baseline simulations may involve applying a uniform energy input to each resistive heater. After baseline simulations, multiple sensitivity simulations are executed on the model. Each sensitivity simulation perturbs the energy input to one of the resistive heaters at a time to determine the sensitivity of the system. A sensitivity matrix is ​​generated from the sensitivity simulation data. The sensitivity matrix can be incorporated into an objective function that is optimized to appropriately group the resistive heaters into multiple zones.

[0018] The embodiments disclosed herein explicitly describe showerhead embodiments and heating plate embodiments, but other embodiments are not limited. It should be recognized that modeling processes such as those described in more detail herein may be applicable to many different systems including fluid flow, heat transfer, or any other similarly behaving characteristics undergoing crosstalk between inputs.

[0019] Now, referring to FIG. 1, an example plan view of a shower head (120) according to an embodiment is shown. The shower head (120) may be used to distribute gas into a chamber such as a plasma chamber. The shower head (120) may include a substrate (122) having a plurality of holes (125), and the holes (125) pass through the substrate (122). In the embodiment shown in FIG. 1, the holes (125) are vertical holes that pass through the entire thickness of the substrate (122). However, in other embodiments, the gas flow paths may include horizontal sections, baffles, or other flow control features or structures to distribute gas from the top of the shower head (120) through the shower head (120) to the bottom of the shower head (120).

[0020] Although illustrated as a single monolithic substrate (122), other embodiments may include a showerhead (120) having a plurality of sub-components coupled together to form a larger substrate (122). The substrate (122) may comprise any suitable material or materials. For example, the substrate (122) may comprise aluminum, titanium, ceramics, etc. In other embodiments, the substrate (122) may have an outer coating on the bottom surface of the showerhead (120) to protect the showerhead (120) from a plasma environment.

[0021] In an embodiment, the holes (125) may be substantially uniform to each other. That is, each of the holes (125) may have substantially the same diameter. However, in other embodiments, holes (125) of non-uniform diameters may also be used. In an embodiment, the holes (125) may be arranged in a plurality of groups. For example, each group of FIG. 1 may include a ring of holes (125). Each ring of holes (125) may be referred to herein as a "pitch circle." For example, FIG. 1 has 12 pitch circles (and a single hole (125) at the center of the shower head (120)) to provide 13 distinct groups of holes (125). However, any number of pitch circles may be provided on the shower head (120). The pitch circles may be substantially concentric to each other.

[0022] The diameters of the pitch circles can be increased in a regular pattern (i.e., with a regular pitch). For example, for a 300 mm substrate, the suitable pitch between the pitch circles can be approximately 10 mm or more. In other embodiments, the spacing between the pitch circles may not be uniform. For example, the spacing between the pitch circles toward the center of the showerhead (120) may be smaller than the spacing between the pitch circles toward the outer edge of the showerhead (120).

[0023] In an embodiment, the first spacing between nearby holes (125) within the first pitch circle may be substantially similar to the second spacing between nearby holes (125) within the second pitch circle, which is larger than the first pitch circle. Since the second pitch circle has a larger circumference, there may be more holes (125) in the second pitch circle, which is larger than the first pitch circle. Accordingly, when a uniform gas flow is provided in each pitch circle, the flow rate through the individual holes may not be uniform. In the case of the first pitch circle and the second pitch circle described above, since there are more holes (125) in the second pitch circle, the holes (125) within the first pitch circle may have a higher flow rate than the holes (125) within the second pitch circle.

[0024] In some embodiments, the showerhead (120) is configured to enable a uniform gas flow to each of the pitch circles. In other embodiments, the showerhead (120) is configured to enable a non-uniform gas flow to each of the pitch circles. The ability to provide non-uniform gas flows enables greater control of process uniformity. Additionally, the non-uniform gas flows can be utilized to initiate sensitivity modeling that can be used for zone grouping optimization, as will be described in more detail below.

[0025] Now, referring to FIG. 2, a cross-sectional example of a tool (200) according to an embodiment is shown. The tool (200) may be a semiconductor processing tool, such as an etching tool, a deposition tool, an annealing tool, etc. (but is not limited thereto). In an embodiment, the tool (200) may include a chamber (210). The chamber (210) may be sealed by a cover including a showerhead (220). The showerhead (220) may be similar to the showerhead (120) described in more detail above. For example, the showerhead (220) may include a substrate (222) having holes (225), the holes (225) pass through the thickness of the substrate (222). The holes (225) may be arranged in circular rings, such as a plurality of pitch circles.

[0026] The gas may be contained around the upper side of the shower head (220) by an enclosure (217), etc. The enclosure (217) may include baffles or other flow-blocking components to direct and / or control the gas flow directed toward one or more of the pitch circles. A gas inlet (218) may supply gas (219) into the enclosure (217). The gas (219) may flow into the interior of the chamber (210) through the shower head (220). In an embodiment, the gas in the chamber (210) may be ionized, etc., to form a plasma within the chamber (210). In some embodiments, bias electrodes (not shown) may be used to initiate and maintain the plasma.

[0027] In an embodiment, a pedestal (212) may be provided below the showerhead (220). The pedestal (212) may include an electrostatic chuck (ESC) or other structure for securing a substrate (215) to the pedestal (212). The substrate (215) may be a wafer, such as a silicon wafer, or any other substrate suitable for processing within the chamber (210). The substrate (215) may have any form factor, such as a 300 mm wafer, a 450 mm wafer, or a wafer of a smaller or larger diameter.

[0028] In an embodiment, control of gas flow through the showerhead (220) can be used to improve process result uniformity across the surface of the substrate (215). Process uniformity may refer to the ability to have substantially the same measurable results across the surface of the substrate. For example, a measurement of a parameter at the center of the substrate (215) may be similar to a measurement of the same parameter near the edge of the substrate (215). Process uniformity can be applied to many different parameters. For example, it may be desirable to control the etching rate, deposition rate, elemental composition and / or concentration, layer thickness, etching profile uniformity, temperatures, etc., with high process uniformity across the substrate (215).

[0029] In some embodiments, the pitch circles of the showerhead are grouped into multiple zones. That is, two or more nearby pitch circles can be controlled together as a single zone. (Since this reduces the number of controllers required) this enables easier control and simplifies the design of the gas distribution assembly (e.g., within the enclosure (217)) because each pitch circle does not need to be controlled independently.

[0030] However, due to crosstalk between different pitch circles, optimizing zone grouping is not simple. For example, even if the pitch circle with the smallest diameter is close to the center of the substrate (215), the flow through the pitch circle will still affect the processing conditions and results near the edge of the substrate (215). Examples of these interrelated effects are illustrated in FIGS. 3a through 3d.

[0031] Now, referring to FIGS. 3a through 3d, the graphs represent the concentration (Y-axis) of a specific element on the substrate (i.e., sensitivity) at a radius (X-axis) increasing from the center of the substrate. However, the Y-axis can represent any measurable value depending on the specific application. For example, the Y-axis can also represent the etching rate, deposition rate, temperature, etc. Each graph represents the effect of flowing an equal amount of gas through a single pitch circle. For example, FIG. 3a is a line (331) showing the effect when the first (innermost) pitch circle is used independently. As illustrated, the effect is highest at the center of the substrate (point 0 mm) and gradually decreases toward the edge of the substrate (point 300 mm). FIG. 3b is the effect when the first intermediate pitch circle is used independently. As illustrated, the effect is high up to about 50 mm and then decreases toward the edge of the substrate (point 150 mm). FIG. 3c is the effect of the second intermediate pitch circle (having a larger diameter than the first intermediate pitch circle). As shown, the peak of sensitivity is provided around 100 mm and decreases toward the center (point 0 mm) and toward the edge of the substrate (point 150 mm). Finally, Fig. 3d shows the effect of the pitch circle near the edge of the substrate (point 150 mm). As shown, the effect is highest at the edge of the substrate (point 150 mm) and gradually decreases toward the center (point 0 mm).

[0032] As illustrated in the graphs of FIGS. 3a through 3d, each pitch circle contributes to the sensitivity of the substrate across the entire surface. In other words, there is no one-to-one relationship between the effect location and the positioning of the pitch circle. Accordingly, the embodiments disclosed herein utilize a form of matrix-based computation to optimize the appropriate zone grouping of the pitch circles by taking into account the various effects of each pitch circle across the surface of the substrate.

[0033] Now, referring to FIG. 4, a process flow diagram of a process (460) for optimizing zone grouping in a fluid flow system according to an embodiment is shown. In the embodiment, the fluid flow system may be a component of any type having a plurality of inputs, through which fluid flows. The process (460) may be used to group the inputs into zones to optimize the control of the process. For example, the fluid flow system may include a showerhead similar to the showerhead (120) described herein. The inputs of the showerhead may be a plurality of pitch circles.

[0034] In an embodiment, the process (460) may begin with an operation (461) that includes performing a baseline simulation of the fluid flow system. The baseline simulation is implemented by developing a model. The model may be a digital representation of the physical structure of the system (e.g., a showerhead) compatible with simulation software to predict processing results on the substrate (e.g., material deposition rates, etching rates, element concentrations, temperatures, etc.). In an embodiment, the model includes a plurality of holes, through which a fluid (e.g., a gas) flows. In some embodiments, the holes may be arranged in a plurality of pitch circles. In some embodiments, there may be 5 to 30 pitch circles. However, in some cases, a smaller or larger number of pitch circles may also be used.

[0035] After the model is developed, a baseline simulation is implemented. The baseline simulation may include simulating a uniform flow process through each hole in the system according to Equation (1), where is the flow rate through each hole, and is the total flow through the system, and is the total number of holes in the system. Baseline simulation is also used to generate baseline flow through each pitch circle using Equation (2), where is the flow rate through a given pitch circle, and is the number of holes within a given pitch circle (PC).

[0036] (1)

[0037] (2)

[0038] Subsequently, the results on the substrate are calculated to form the baseline matrix It is expressed as follows. The baseline matrix can be a single column (since there is only one baseline result) or can have an arbitrary number of rows (depending on how finely the desired data needs to be subdivided). For example, on a 300 mm wafer substrate, 150 mm from the center to the edge can be represented by 150 rows (i.e., one row for each millimeter from the center to the edge). Using this configuration, the baseline matrix can be a (150×1) matrix.

[0039] In an embodiment, the process (460) may continue to an operation (462) comprising running a plurality of sensitivity simulations. In an embodiment, each sensitivity simulation perturbs the flow through one of the plurality of pitch circles by an offset percentage. For example, if there are 12 pitch circles, there will be 12 sensitivity simulations. In each sensitivity simulation, the flow at one of the pitch circles will be perturbed, and the remaining pitch circles will maintain the baseline flow. The offset percentage can be any desired offset amount (positive or negative). For example, the offset percentage can be up to 1%, up to 5%, up to 10%, or up to 20% (all of these can be positive or negative percentages). In an embodiment, the flow through the perturbed pitch circle can be defined by Equation (3), where P is the offset percentage. Then, the results on the substrate are calculated to form a perturbation matrix It is expressed as such. The perturbation matrix can take the form of (150×C), where C is the number of pitch circles in the system.

[0040] (3)

[0041] In an embodiment, the process (460) obtains a sensitivity matrix from a plurality of sensitivity simulations. S It may continue with an operation (463) that includes generating the sensitivity matrix. S It can be generated through the use of equation (4). S is the perturbation matrix It can have the same form as (e.g., (150×C)).

[0042] (4)

[0043] In an embodiment, the process (460) may continue to an operation (464) comprising optimizing an objective function to enable grouping a plurality of pitch circles into a plurality of zones. Objective function is expressed by Equation (5). The objective function is for each column of the objective function matrix (i.e., for each pitch circle) dF It is minimized by calculating . In an embodiment, may refer to the mean value or a value based on experimental analysis when the model is corrected with experimental data.

[0044] (5)

[0045] After that, for each pitch circle, the dF The values ​​can be used to optimize zone assignment for pitch circles. For example, comparable dF Pitch circles having values ​​can be grouped together into zones. In one embodiment, the calculated dF A clustering algorithm may be used to group pitch circles into any desired number of zones based on values. Suitable clustering algorithms may include (but are not limited to) centroid-based or partition clustering, hierarchy-based clustering, distribution-based clustering, or density-based clustering. Depending on the results of optimization, each zone may contain a different number of pitch circles.

[0046] Now, referring to FIG. 5, a process uniformity graph is shown according to an embodiment, with concentration on the Y-axis and distance from the center of the substrate on the X-axis. Lines (531) depict the difference between the baseline result and the optimized result when a 3-zone optimization process similar to process (460) is used. Line (531A) is for the baseline case, and line (531B) is for the optimized case. As illustrated, the optimized line (531B) exemplifies a more uniform process result. Lines (532) depict the difference between the baseline result and the optimized result when a 4-zone optimization process similar to process (460) is used. Line (532A) is for the baseline case, and line (532B) is for the optimized case. As illustrated, the optimized line (532B) exemplifies a more uniform process result.

[0047] In addition to being applicable to fluid flow systems (e.g., flow of gases and liquids), the embodiments disclosed herein may also be applicable to heat transfer applications. For example, a heating plate for a chuck, or a ramp array for a thermal annealing system, may benefit from optimized zone groupings. An example of a heating plate configuration is shown in FIG. 6.

[0048] Now, referring to FIG. 6, an example plan view of a heating plate (640) according to an embodiment is shown. In an embodiment, the heating plate (640) may include a substrate (641). The substrate (641) may include ceramic, etc. A plurality of heating elements (645) may be provided within the substrate (641). For example, in some embodiments, the heating elements (645) may be embedded within the substrate (641). The heating elements (645) may be electrically conductive traces that generate heat through resistive heating when an electric current passes through the heating elements. In an embodiment, the heating elements (645) may be circular rings. In some embodiments, the rings may be concentric. Each heating element (645) may have a different diameter. Although concentric ring heating elements (645) are shown, embodiments are not limited to this heating element layout. For example, in other embodiments, serpentine traces, spiral traces, etc. may be used. The heating elements (645) may also include fluid channels for flowing heating and / or cooling heat fluid.

[0049] Now, referring to FIG. 7, a cross-sectional example of a tool (700) according to an embodiment is shown. The tool (700) may be a semiconductor processing tool, such as an etching tool, a deposition tool, an annealing tool, etc. (but is not limited thereto). In an embodiment, the tool (700) may include a chamber (710). The chamber (710) may be sealed by a cover including a showerhead (720). The showerhead (720) may be similar to the showerhead (120) described in more detail above. For example, the showerhead (720) may include a substrate (722) having holes (725), the holes (725) pass through the thickness of the substrate (722). The holes (725) may be arranged in circular rings, such as a plurality of pitch circles.

[0050] The gas may be contained around the upper side of the showerhead (720) by an enclosure (717), etc. The enclosure (717) may include baffles or other flow-blocking components to direct and / or control the gas flow directed toward one or more of the pitch circles. A gas inlet (718) may supply gas (719) into the enclosure (717). The gas (719) may flow into the interior of the chamber (710) through the showerhead (720). In an embodiment, the gas in the chamber (710) may be ionized, etc., to form a plasma within the chamber (710). In some embodiments, bias electrodes (not shown) may be used to initiate and maintain the plasma.

[0051] In an embodiment, a pedestal (712) may be provided below the showerhead (720). The pedestal (712) may include an ESC or other structure for securing the substrate (715) to the pedestal (712). In an embodiment, a heating plate (740) may be provided on the pedestal (712). Although illustrated as separate components, other embodiments may include a pedestal (712) having an integrated heating plate (740). The heating plate (740) may be similar to the heating plate (640) described in more detail above. For example, the heating plate (740) may include a substrate (741) having a plurality of embedded heating elements (745). The substrate (715) may be a wafer, such as a silicon wafer, or any other substrate suitable for processing within the chamber (710). The substrate (715) may have any form factor, such as a 300 mm wafer, a 450 mm wafer, or a wafer with a smaller or larger diameter.

[0052] In an embodiment, control of heat transfer across the surface of the substrate (715) by the heating plate (740) can improve process result uniformity across the surface of the substrate (715). Process uniformity may refer to the ability to have substantially the same measurable results across the surface of the substrate. For example, a measurement of a parameter at the center of the substrate (715) may be similar to a measurement of the same parameter near the edge of the substrate (715). Process uniformity can be applied to many different parameters. For example, it may be desirable to control the etching rate, deposition rate, elemental composition and / or concentration, layer thickness, etching profile uniformity, temperatures, etc., with high process uniformity across the substrate (715).

[0053] In some embodiments, the heating elements (745) of the heating plate (740) are grouped into multiple zones. That is, two or more nearby heating elements (745) can be controlled together as a single zone. (Since this reduces the number of variables that need to be controlled) this enables easier control and simplifies the design of the heating plate (740) because each individual heating element (745) does not need to be controlled independently.

[0054] However, due to crosstalk between different heating elements (745), optimizing zone grouping is not simple. For example, even if the smallest diameter heating element (745) is close to the center of the substrate (715), the flow rate through the smallest heating element will still affect the processing conditions and results near the edge of the substrate (715). Examples of these interrelated effects are similar to those illustrated in FIGS. 3a through 3d in relation to fluid flow control, which is described in more detail above.

[0055] Accordingly, the embodiments disclosed herein utilize a form of matrix-based computation to optimize appropriate zone grouping of heating elements (745) by taking into account various effects of each heating element (745) across the surface of the substrate (715).

[0056] Now, referring to FIG. 8, a process flowchart of a process (870) for optimizing zone grouping in a thermal system according to an embodiment is illustrated. In an embodiment, the thermal system may be any type of component having a plurality of inputs configured to generate heat (e.g., a heating plate), remove heat (e.g., a cooling plate), or generate and remove heat as well. The process (870) may be used to group the inputs into zones to optimize the control of the process. For example, the thermal system may include a heating plate similar to the heating plate (640) described herein. The inputs of the heating plate may be a plurality of heating elements.

[0057] In an embodiment, the process (870) may begin with an operation (871) that includes performing a baseline simulation for a heat control plate. The baseline simulation is implemented by developing a model. The model may be a digital representation of the physical structure of a system (e.g., a heat control plate) compatible with simulation software to predict processing results on a substrate (e.g., material deposition rates, etching rates, element concentrations, temperatures, etc.). In an embodiment, the model includes a plurality of heating elements. In some embodiments, the heating elements may be arranged in a plurality of concentric rings. In some embodiments, there may be 5 to 30 rings. However, in some cases, a smaller or larger number of rings may also be used.

[0058] After the model is developed, baseline simulations are implemented. Baseline simulations may involve simulating a process where the energy input per unit length of the trace for each heating element within the system is uniform. Accordingly, larger heating elements will generate more total heat than smaller heating elements, because more energy will be input to the larger heating elements to account for their larger circumferences compared to the smaller ones.

[0059] Subsequently, the results on the substrate are calculated to form the baseline matrix It is expressed as follows. The baseline matrix can be a single column (since there is only one baseline result) or can have an arbitrary number of rows (depending on how finely the desired data needs to be subdivided). For example, on a 300 mm wafer substrate, 150 mm from the center to the edge can be represented by 150 rows (i.e., one row for each millimeter from the center to the edge). Using this configuration, the baseline matrix can be a (150×1) matrix.

[0060] In an embodiment, the process (870) may continue to an operation (872) comprising executing a plurality of sensitivity simulations. In an embodiment, each sensitivity simulation perturbs the energy input for one of the plurality of heating elements by an offset percentage. For example, if there are 12 heating elements, there will be 12 sensitivity simulations. In each sensitivity simulation, the energy input for one of the heating elements will be perturbed, and the remaining heating elements will maintain the baseline energy input. The offset percentage can be any desired offset amount (positive or negative). For example, the offset percentage can be up to 1%, up to 5%, up to 10%, or up to 20% (all of these can be positive or negative percentages). Then, the results on the substrate are calculated to obtain a perturbation matrix It is expressed as follows. The perturbation matrix will have the form (150×C), where C is the number of pitch circles in the system.

[0061] In an embodiment, the process (870) obtains a sensitivity matrix from a plurality of sensitivity simulations. S It may continue with an operation (873) that includes generating the sensitivity matrix. S It can be generated using processes and expressions similar to expression (4). S is the perturbation matrix described above It can have the same form as (e.g., (150×C)).

[0062] In an embodiment, the process (870) may continue to an operation (874) comprising optimizing an objective function to enable grouping a plurality of heating elements into a plurality of zones. Objective function is expressed by Equation (6). The objective function is for each column of the objective function matrix (i.e., for each column element) dF It is minimized by finding .

[0063] (6)

[0064] After that, for each heating element, the dF The values ​​can be used to optimize zone assignment for heating elements. For example, similar dF Heating elements having values ​​can be grouped together into zones. In one embodiment, the calculated dF A clustering algorithm may be used to group heating elements into any desired number of zones based on their values. Suitable clustering algorithms may include (but are not limited to) centroid-based or partition clustering, hierarchy-based clustering, distribution-based clustering, or density-based clustering. Depending on the results of the optimization, each zone may contain a different number of heating elements.

[0065] In the embodiments described in more detail above, fluid flow systems and thermal systems are optimized. However, it should be recognized that any system having multiple inputs having mutual communication between the inputs may benefit from the embodiments disclosed herein. FIG. 9 is a general representation of a process for model-based zone grouping optimization that may be applicable to other applications and systems.

[0066] Now, referring to FIG. 9, a process flowchart of a process (980) for optimizing zone grouping in a system according to an embodiment is shown. In an embodiment, the system may be any type of component having a number of inputs prone to crosstalk, similar to those described in FIG. 3a through 3d above. The process (980) may be used to group the inputs into zones to optimize the control of the process. The inputs may refer to holes for enabling fluid flow, heating elements for generating heat, coolant loops for removing heat, ramps for generating heat, etc.

[0067] In an embodiment, the process (980) may begin with an operation (981) that includes performing a baseline simulation for the system. The baseline simulation is implemented by developing a model. The model created may be a digital model having functions similar to other models disclosed herein. In some embodiments, there may be 5 to 30 inputs. However, in some cases, fewer or more inputs may also be used.

[0068] After the model is developed, baseline simulations are implemented. Baseline simulations may involve simulating a uniform process across the system for stimuli for each input. For example, stimuli may refer to fluid flow rates, electrical power, coolant pulse durations, etc. Subsequently, results on the substrate are calculated to form a baseline matrix. It is expressed as such. The baseline matrix may be similar to other baseline matrices described in more detail in this specification.

[0069] In an embodiment, the process (980) may continue to an operation (982) comprising running a plurality of sensitivity simulations. In an embodiment, each sensitivity simulation perturbs the stimulus for one of the inputs by an offset percentage. For example, if there are 12 inputs, there will be 12 sensitivity simulations. In each sensitivity simulation, the stimulus for one of the inputs will be perturbed, and the remaining inputs will maintain baseline stimulus. The offset percentage can be any desired offset amount (positive or negative). For example, the offset percentage can be up to 1%, up to 5%, up to 10%, or up to 20% (all of these can be positive or negative percentages). Then, the results on the substrate are calculated and expressed as a perturbation matrix. The perturbation matrix may be similar to other perturbation matrices described in more detail herein.

[0070] In an embodiment, the process (980) may continue to an operation (983) comprising generating a sensitivity matrix from a plurality of sensitivity simulations. The sensitivity matrix may be generated and / or calculated through expressions and / or processes similar to any of the other sensitivity matrices described in more detail herein.

[0071] In an embodiment, the process (980) may continue to an operation (984) comprising optimizing an objective function to enable grouping multiple inputs into multiple zones. The objective function is for each column of the objective function matrix (i.e., for each input) dF It is minimized by finding . The objective function may be similar to any of the objective functions described in more detail in this specification.

[0072] After that, the calculated for each input dF The values ​​can be used to optimize zone assignment for heating elements. For example, similar dF Inputs having values ​​can be grouped together into zones using clustering algorithms, etc. Depending on the optimization results, each zone may contain a different number of inputs.

[0073] Now, referring to FIG. 10, a block diagram of an exemplary computer system (1000) of a processing tool according to an embodiment is illustrated. In an embodiment, the computer system (1000) is coupled to the processing tool and controls processing in the processing tool. The computer system (1000) may be connected (e.g., networked) to other machines in a Local Area Network (LAN), intranet, extranet, or the Internet. The computer system (1000) may operate as a server or client machine in a client-server network environment, or as a peer machine in a peer-to-peer (or distributed) network environment. The computer system (1000) may be a personal computer, a tablet personal computer, a set-top box (STB), a Personal Digital Assistant (PDA), a cellular phone, a web device, a server, a network router, a switch or a bridge, or any machine capable of executing a set of commands (sequentially or otherwise) that specify actions to be taken by said machine. Additionally, although only a single machine is exemplified for the computer system (1000), the term “machine” will also be taken to include any set of machines (e.g., computers) that individually or jointly execute a set (or a number of sets) of instructions to perform any one or more of the methods described herein.

[0074] A computer system (1000) may include a computer program product or software (1022), which has a non-transient machine-readable medium storing instructions that can be used to program the computer system (1000) (or other electronic devices) to perform a process according to the embodiments. The machine-readable medium includes any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computer). For example, a machine-readable (e.g., computer-readable) medium includes a machine-readable (e.g., computer-readable) storage medium (e.g., read-only memory (“ROM”), random access memory (“RAM”), magnetic disk storage media, optical storage media, flash memory devices, etc.), a machine-readable (e.g., computer-readable) transmission medium (electrical, optical, acoustic, or other forms of radio signals (e.g., infrared signals, digital signals, etc.)), etc.

[0075] In an embodiment, the computer system (1000) includes a system processor (1002) that communicates with each other via a bus (1030), a main memory (1004) (e.g., ROM (read-only memory), flash memory, DRAM (dynamic random access memory), such as SDRAM (synchronous DRAM) or RDRAM (Rambus DRAM), etc.), a static memory (1006) (e.g., flash memory, SRAM (static random access memory), etc.), and an auxiliary memory (1018) (e.g., a data storage device).

[0076] The system processor (1002) represents one or more general-purpose processing devices, such as a microsystem processor, a central processing unit, etc. More specifically, the system processor may be a complex instruction set computing (CISC) microsystem processor, a reduced instruction set computing (RISC) microsystem processor, a very long instruction word (VLIW) microsystem processor, or a system processor implementing other instruction sets, or a system processor implementing a combination of instruction sets. The system processor (1002) may also be one or more special-purpose processing devices, such as an application-specific integrated circuit (ASIC), a field programmable gate array (FPGA), a digital signal system processor (DSP), a network system processor, etc. The system processor (1002) is configured to execute processing logic (1026) for performing the operations described herein.

[0077] The computer system (1000) may further include a system network interface device (1008) for communicating with other devices or machines. The computer system (1000) may also include a video display unit (1010) (e.g., an LCD (liquid crystal display), an LED (light emitting diode display), or a CRT (cathode ray tube)), an alphanumeric input device (1012) (e.g., a keyboard), a cursor control device (1014) (e.g., a mouse), and a signal generating device (1016) (e.g., a speaker).

[0078] The auxiliary memory (1018) may include a machine-accessible storage medium (1031) (or more specifically, a computer-readable storage medium) in which one or more sets of instructions (e.g., software (1022)) embody any one or more of the methods or functions described herein are stored. The software (1022) may also reside in the main memory (1004) and / or in the system processor (1002) wholly or at least partially during the execution of the software (1022) by the computer system (1000), and the main memory (1004) and the system processor (1002) also constitute machine-readable storage media. The software (1022) may additionally be transmitted or received over the network (1061) through the system network interface device (1008). In an embodiment, the network interface device (1008) may operate using RF coupling, optical coupling, acoustic coupling, or inductive coupling.

[0079] Although the machine-accessible storage medium (1031) is depicted as a single medium in exemplary embodiments, the term “machine-readable storage medium” should be taken to include a single medium or multiple media (e.g., a centralized or distributed database, and / or associated caches and servers) that store one or more sets of instructions. The term “machine-readable storage medium” will also be taken to include any medium capable of storing or encoding a set of instructions for execution by a machine and enabling the machine to perform any one or more of the methods. Accordingly, the term “machine-readable storage medium” will be taken to include (but not be limited to) solid-state memories and optical and magnetic media.

[0080] In the foregoing specification, specific exemplary embodiments have been described. It will be apparent that various modifications may be made to these embodiments without departing from the scope of the following claims. Accordingly, the specification and drawings should be regarded as illustrative rather than restrictive.

Claims

Claim 1 A method for optimizing zones in a fluid flow system, comprising: performing a baseline simulation for the fluid flow system; performing a plurality of sensitivity simulations — each sensitivity simulation perturbs the flow rate through one of a plurality of pitch circles in the fluid flow system by an offset percentage —; generating a sensitivity matrix from the plurality of sensitivity simulations; and optimizing an objective function to enable grouping the plurality of pitch circles into a plurality of zones. Claim 2 In claim 1, the fluid flow system is a showerhead, method. Claim 3 A method according to claim 1, wherein the plurality of pitch circles comprises five or more pitch circles. Claim 4 A method according to claim 1, wherein the plurality of zones comprises three zones. Claim 5 A method according to claim 1, wherein the plurality of zones comprises four or more zones. Claim 6 A method according to claim 1, wherein the offset percentage is 5% or more. Claim 7 A method according to claim 1, wherein the offset percentage is a positive offset percentage or a negative offset percentage. Claim 8 In claim 1, the simulated flow rate through each hole in the fluid flow system during the baseline simulation is the same for all holes in the fluid flow system. Claim 9 A method according to claim 1, wherein a clustering algorithm is used to group the plurality of pitch circles into the plurality of zones. Claim 10 A method according to claim 1, wherein the fluid flow system is part of a plasma chamber. Claim 11 A method for optimizing zones in a heat control plate, comprising: performing a baseline simulation for the heat control plate; performing a plurality of sensitivity simulations — each sensitivity simulation perturbs an energy input for one of a plurality of heating elements in the heat control plate by an offset percentage —; generating a sensitivity matrix from the plurality of sensitivity simulations; and optimizing an objective function to enable grouping the heating elements into a plurality of zones. Claim 12 In claim 11, the heating elements are resistive heater rings, method. Claim 13 In claim 11, the heating elements are thermal fluid channels, method. Claim 14 In claim 11, the method wherein the plurality of zones comprises three or more zones. Claim 15 In claim 11, the method wherein the offset percentage is 5% or more. Claim 16 In claim 11, the method wherein the offset percentage is a positive offset percentage or a negative offset percentage. Claim 17 A method for optimizing zone grouping in a system having multiple inputs, comprising: performing a baseline simulation for the system — the baseline simulation includes applying a uniform stimulus to each of the inputs —; performing multiple sensitivity simulations — each sensitivity simulation perturbs the stimulus for one of the multiple inputs in the system by an offset percentage —; generating a sensitivity matrix from the multiple sensitivity simulations; and optimizing an objective function to enable grouping the multiple inputs into multiple zones. Claim 18 In claim 17, the system is a shower head, and the inputs are flow rates through holes within the shower head, method. Claim 19 In claim 18, the system is a heater plate, and the inputs are energy inputs into resistive heaters, method. Claim 20 In claim 17, the method, wherein the system is part of a semiconductor processing tool.

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