Manufacturing tool calibration

Abstract

A method for calibrating a manufacturing system includes selecting, from a plurality of recipes, a calibration recipe including a first process parameter for performing a manufacturing process on a substrate, including for each recipe and for two or more substrates, characterization data representative of the manufacturing process performed on the two or more substrates using the recipe is received. And determining a second process parameter according to the first state and the second state of the substrate, and determining a process relationship between the first process parameter and the second process parameter of the formula. The calibration recipe is selected from the plurality of recipes based on a respective process relationship, a threshold change in the process relationship between the first process parameter and the second process parameter is determined, and the calibration recipe and the threshold change are provided for calibrating the manufacturing system.

Description

Technical Field

[0001] This specification relates to semiconductor systems, processes, and equipment. Background Technology

[0002] Plasma etching can be used in semiconductor processing to fabricate integrated circuits. Integrated circuits can be formed from layer structures comprising multiple (e.g., two or more) layers. Different etching gas chemistry (e.g., different gas mixtures) can be used to generate plasma in the processing environment, allowing a given etching gas chemistry to have increased precision and higher selectivity for the layer components to be etched. As integrated circuits continue to scale towards smaller features and increasing aspect ratios, the need for precise etching of layer structures is growing. Summary of the Invention

[0003] This manual describes techniques used for calibrating manufacturing tools.

[0004] These techniques broadly relate to methods for reducing variability between different manufacturing tools and / or different processing chambers within the same manufacturing tool. Variation is reduced by determining chamber variability in a manufacturing process performed by the manufacturing tool using optimized and well-characterized process parameter-sensitive formulations. The determined chamber variability is then used to generate offset parameters to align the manufacturing tool with a standardized manufacturing tool.

[0005] Generally, an innovative aspect of the subject matter described in this specification can be embodied in a method for temperature calibration of a manufacturing tool for semiconductor processing, comprising a system and a selection from multiple formulations of a calibration formulation including a first process parameter for performing a manufacturing process on a substrate. For each of the multiple formulations, the selection includes: receiving, by the system and for two or more substrates, characterization data representing a manufacturing process performed on two or more substrates using the formulation, wherein the manufacturing process for each of the two or more substrates includes different values ​​of the first process parameter, and wherein the characterization data representing the manufacturing process on each of the two or more substrates includes a first state of the substrate before the manufacturing process and a second state of the substrate after the manufacturing process. The system determines a second process parameter based on the first and second states of the substrate, and for the manufacturing process performed on two or more substrates using the formulation, determines a process relationship between the first and second process parameters of the formulation. The system selects a calibration formulation from the multiple formulations based on the corresponding process relationships of the multiple formulations. For the calibration formulation, the system determines a threshold variation of the process relationship between the first and second process parameters, and provides the calibration formulation and the threshold variation for calibrating the manufacturing system.

[0006] Other embodiments of this aspect include a corresponding system, a computer system, an apparatus, and a computer program recorded on one or more computer storage devices, each computer program being configured to perform the actions of the method.

[0007] As used herein, a substrate refers to a wafer or another carrier structure, such as a glass plate. The wafer may include semiconductor materials, such as silicon, GaAs, InP, or another semiconductor-based wafer material. The wafer may include insulating materials, such as silicon-on-insulator (SOI), diamond, etc. Sometimes, the substrate includes a film formed on the surface of the wafer / carrier structure. The film may be, for example, a dielectric film, a conductive film, or an insulating film. Various deposition techniques can be used to form films on the surface of the wafer, such as spin coating, atomic layer deposition (ALD), chemical vapor deposition (CVD), metal-organic chemical vapor deposition (MOCVD), molecular beam epitaxy (MBE), or other similar techniques for forming thin film layers on a wafer or another carrier structure. In some embodiments, the manufacturing tools described herein are plasma-based etching tools, wherein the etching process can be performed on the surface of the wafer / carrier structure and / or on a layer formed on the wafer.

[0008] The subject matter described in this specification can be implemented in these and other embodiments to achieve one or more of the following advantages. Implementing a calibration process to reduce chamber-to-chamber variability between manufacturing tools can result in improved yield and fidelity of manufactured components when using the same manufacturing process across two or more manufacturing tools. The calibration methods described in this specification can be used to reduce the variability of critical dimension (CD) (e.g., a specific dimension used by the end user to calibrate the fidelity and / or yield of an etching process) between manufactured structures etched by manufacturing tools with different deployments. Using the calibration methods described in this specification, the variability of etching rates under nominally identical conditions between manufacturing tools with different deployments can be reduced. Reducing variability between different manufacturing tools, such as temperature variability, can improve consistency between different manufacturing tools performing the same manufacturing process (e.g., using the same formulation).

[0009] Specifically, calibration methods can be used to measure and calibrate cryogenic etching processes performed on plasma-based etching tools, where the substrate temperature is maintained between approximately -150 and -20 degrees Celsius during the manufacturing process, for example, between approximately -90 and -20 degrees Celsius, or between approximately -150 and -90 degrees Celsius. The limitations of conventional temperature sensors operating in and / or having accuracy in cryogenic ranges can restrict the ability to perform temperature control during cryogenic etching processes. Furthermore, etching processes can have increased sensitivity to temperature fluctuations in cryogenic ranges, leading to greater variation in etching rates and lower fidelity in the resulting manufacturing process. Calibration processes can be used to determine the offset of the manufacturing tool relative to a set standardized tool and to provide a global (or local) offset to the feedback control of the manufacturing tool to align the performance of the manufacturing tool with the set standardized tool. In this way, the variability between manufacturing tools performing cryogenic manufacturing processes (e.g., cryogenic etching processes) can be reduced to less than approximately 1.5 degrees Celsius. Reducing variability between manufacturing tools can lead to reduced variability, greater utilization of field system groups, and improved yield and fidelity of processes performed by different manufacturing tools. While the remainder of the disclosure will identify specific calibration processes for etching-based manufacturing tools using the disclosed techniques, these systems and methods are equally applicable to a wide variety of other manufacturing tools and chambers, as is readily apparent. Therefore, the technique should not be considered limited to use only with the described etching manufacturing tools. Before describing systems and methods or operations with exemplary process sequences according to some embodiments of the present technique, this disclosure will discuss one possible system and chamber that can be used with the present technique. It should be understood that the technique is not limited to the described equipment, and the discussed processes can be performed in any number of processing chambers and systems. Attached Figure Description

[0010] Figure 1 A schematic cross-sectional view of an example plasma processing chamber is shown.

[0011] Figure 2 A block diagram of an example operating environment for a process variable calibration system is shown.

[0012] Figure 3 A flowchart of an example process for a process variable calibration system is shown.

[0013] Figure 4 A flowchart of another example process for a process variable calibration system is shown.

[0014] Figure 5 An example diagram of the process relationship is shown.

[0015] Figure 6 A general-purpose computer system is shown.

[0016] Similar reference numerals and designations in the various figures indicate similar elements. Detailed Implementation

[0017] This specification provides improved methods and components for manufacturing tool calibration. Embodiments of this disclosure include methods for reducing variability between different manufacturing tools and / or between different processing chambers of the same manufacturing tool. Variability is reduced by determining the chamber variability of a manufacturing process performed by the manufacturing tool using optimized and well-characterized process parameter-sensitive formulations. The determined chamber variability is used to generate offset parameters to align the manufacturing tool with a standardized manufacturing tool.

[0018] Figure 1 A schematic cross-sectional view of an example processing chamber 100 is shown, adapted for etching one or more layers of material on a substrate 103 (e.g., also referred to as a “wafer”) disposed within the processing chamber 100 (e.g., a plasma processing chamber). The processing chamber 100 includes a chamber body 105 defining a chamber volume 101 in which the substrate can be processed. The chamber body 105 has sidewalls 112 and a bottom 118 coupled to ground 126. The sidewalls 112 may include gaskets 115 to protect the sidewalls 112 and extend the time between maintenance cycles of the plasma processing chamber 100. The chamber body 105 supports a chamber cover assembly 110 to surround the chamber volume 101. The chamber body 105 may be made of, for example, aluminum or other suitable materials. A substrate inlet / outlet 113 is formed through the sidewalls 112 of the chamber body 105, which facilitates the movement of the substrate 103 into and out of the plasma processing chamber 100. Inlet / outlet 113 may be coupled to a transfer chamber and / or other chambers (not shown) of a substrate processing system, for example, to perform other processes on the substrate. Pump port 145 is formed through the bottom 118 of the chamber body 105 and connected to the chamber volume 101. A pumping device may be connected to the chamber volume 101 via pump port 145 to vent and control the pressure within the processing volume. The pumping device may include one or more pumps and throttle valves.

[0019] The chamber volume 101 includes a processing region 107, such as a station for processing a substrate. A substrate support 135 may be disposed in the processing region 107 of the chamber volume 101 to support the substrate 103 during processing. The substrate support 135 may include an electrostatic chuck 122 for holding the substrate 103 during processing. The electrostatic chuck (ESC) 122 may use electrostatic attraction to hold the substrate 103 on the substrate support 135. The ESC 122 may be powered by an RF power supply 125 integrated with matching circuitry 124. The ESC 122 may include electrodes 121 embedded within a dielectric body. The electrodes 121 may be coupled to the RF power supply 125 and may provide a bias voltage that attracts plasma ions formed by process gases in the chamber volume 101 to the ESC 122 and the substrate 103 located on the pedestal. The RF power supply 125 may be cyclically switched on and off, or pulsed, during processing of the substrate 103. To reduce the attraction of the ESC 122's sidewalls to the plasma and extend its maintenance life, the ESC 122 may have an isolator 128. Additionally, the substrate support 135 may have a cathode pad 136 to protect the sidewalls of the substrate support 135 from the plasma gas and extend the time between maintenance of the plasma processing chamber 100. Alternatively, in some embodiments, the ESC 122 may be powered by an applied pulsed DC voltage applied to the substrate, rather than by an RF power supply 125.

[0020] Electrode 121 may be coupled to DC power supply 150. Power supply 150 may provide a clamping voltage of approximately 200 volts to approximately 2000 volts to electrode 121. Power supply 150 may also include a system controller for controlling the operation of electrode 121 by directing DC current to electrode 121 to clamp and declamp substrate 103. ESC 122 may include a heater disposed within and connected to a power supply for heating the substrate, while a cooling base 129 supporting ESC 122 may include conduits for circulating heat transfer fluid to maintain the temperature of ESC 122 and substrate 103 disposed thereon. ESC 122 may be configured to operate within the temperature range required by the thermal budget of the components manufactured on substrate 103. For example, ESC 122 may be configured to maintain substrate 103 at a temperature of approximately -150°C or lower to approximately 500°C or higher, depending on the process being performed. Cover ring 130 may be disposed on ESC 122 and disposed along the periphery of substrate support 135. The cover ring 130 can be configured to confine the etching gas to a desired portion of the exposed top surface of the substrate 103, while shielding the top surface of the substrate support 135 from the plasma environment within the plasma processing chamber 100.

[0021] Gas panel 160 (e.g., also referred to herein as a “gas distribution manifold”) may be coupled to chamber body 105 via chamber cover assembly 110 via gas line 167 to supply process gases into chamber volume 101. Gas panel 160 may include one or more process gas sources 161, 162, 163, 164, and may additionally include inert gases, non-reactive gases, and reactive gases, as may be used for any number of suitable processes. Examples of process gases that may be supplied by gas panel 160 include, but are not limited to, hydrocarbon-containing gases, including methane, sulfur hexafluoride, silicon chloride, silicon tetrachloride, carbon tetrafluoride, and hydrogen bromide. Process gases that may be supplied by gas panel may include, but are not limited to, argon, chlorine, nitrogen, helium, or oxygen, sulfur dioxide, and any number of additional materials. In addition, process gases may include nitrogen, chlorine, fluorine, oxygen, or hydrogen-containing gases, including, for example, BCl3, C2F4, C4F8, C4F6, CHF3, CH2F2, CH3F, NF3, NH3, CO2, SO2, CO, N2, NO2, N2O, and H2, and any additional suitable precursors. Process gases from process gas sources (e.g., sources 161, 162, 163, 164) may be combined to form one or more etching gas mixtures. For example, gas panel 160 includes one or more process gas sources specific to oxide-based etching chemicals. In another example, gas panel 160 includes one or more process gas sources specific to nitride-based etching chemicals.

[0022] Gas panel 160 includes various valves, pressure regulators (not shown), and mass flow controllers (not shown) arranged relative to gas sources 161, 162, 163, 164 to control the flow rate of process gas from the gas sources. Valve 166 can control the flow rate of process gas from gas sources 161, 162, 163, 164 from gas panel 160. The operation of valves, pressure regulators, and / or mass flow controllers can be controlled by controller 165. Controller 165 can be operatively coupled to an electro-valve (EV) manifold (not shown) to control the actuation of one or more of the valves, pressure regulators, and / or mass flow controllers. Cover assembly 110 may include gas delivery nozzle 114. Gas delivery nozzle 114 may include one or more openings for introducing process gas from gas sources 161, 162, 163, 164 from gas panel 160 into chamber volume 101. After the process gas is introduced into the plasma processing chamber 100, the gas can be energized to form plasma. An antenna 148, such as one or more inductor coils, can be provided near the plasma processing chamber 100. An antenna power supply 142 can supply power to the antenna 148 via a matching circuit 141 to inductively couple energy (such as RF energy) to the process gas to maintain the plasma formed by the process gas within the chamber volume 101 of the plasma processing chamber 100. Alternatively, or in addition to the antenna power supply 142, process electrodes below and / or above the substrate 103 can be used to couple an RF power capacitor to the process gas to maintain the plasma within the chamber volume 101. The operation of the power supply 142 can be controlled by a controller (e.g., controller 165) that also controls the operation of other components in the plasma processing chamber 100.

[0023] The controller 165 can be used to control the process sequence, regulate the airflow from the gas panel 160 into the plasma processing chamber 100, and other process parameters. When the software routine is executed by a computing device having one or more processors (e.g., a central processing unit (CPU)) that communicates data with one or more memory storage devices, it transforms the computing device into a dedicated computer, such as a controller, that controls the plasma processing chamber 100 to perform the process according to this disclosure. The software routine can also be stored and / or executed by one or more other controllers that may be associated with the plasma processing chamber 100.

[0024] In some embodiments, controller 165 communicates data with characterization device 172. Characterization device 172 may include one or more sensors (e.g., image sensors) operable to collect processing data associated with processing chamber 100. For example, characterization device 172 includes an optical emission spectroscopy device configured to monitor signals, such as emitted light from plasma, within the processing area of ​​processing chamber 100. For example, the signal may be the dominant wavelength or the wavelength of highest intensity of the emitted light. The characteristics (e.g., wavelength and intensity) of the emitted light from the plasma within the processing area may depend in part on the etching gas mixture used to generate the plasma and the layer composition of the etched layer. For example, each etching gas mixture and the corresponding layer composition being etched may have their own signal characteristics. Emission wavelengths that are unique or distinct for each etching gas mixture and the corresponding layer composition can be monitored to determine the etching conditions of the etched layer. For example, etching the remaining thickness of the layer. The characteristics of the light emitted from the plasma may vary, for example, based on the etching process. For example, the intensity of the monitored signal may vary as material is removed from the processed layer. The characterization device 172 can be configured to collect processing data, including corresponding signals corresponding to the etching gas mixture used in substrate processing and the corresponding layer composition of the structure being processed in the processing chamber 100. The controller 165 can receive the processing data from the characterization device 172 and determine one or more actions to be performed based on the processing data.

[0025] In some embodiments, at the end of the etching process on the substrate, an automatic or semi-automatic robotic manipulator (not shown) can be used to transfer the substrate from the substrate support to the processing chamber, for example, via the substrate inlet / outlet 113. For example, the robotic manipulator can transfer the substrate to another chamber (or another location) to perform another step in the manufacturing process.

[0026] In some embodiments, the substrate may be transferred to a metrology chamber, for example, another chamber including one or more metrology tools. The metrology chamber may be coupled to the processing chamber, for example, via a substrate inlet / outlet 113. The metrology chamber may be an external metrology chamber, from which the substrate is removed from the processing chamber and provided. The metrology chamber may be configured to characterize the substrate before, during, and / or after performing a manufacturing process in the processing chamber. Sometimes, the metrology chamber may be configured to characterize the substrate between manufacturing processes. (See reference...) Figure 2 In more detail, the metering chamber can be configured to characterize an etching process performed on a substrate, for example, by characterizing a thin film formed on the substrate surface before and after the etching process in the processing chamber.

[0027] As used herein, the processing chamber 100 is a component of a manufacturing tool, such as a plasma etching tool. Sometimes, a manufacturing tool may include two or more processing chambers 100, each as described in reference... Figure 1 The configuration is described above. The manufacturing tool may include one or more additional auxiliary chambers, such as a loading lock, metering chamber, substrate cleaning / preparation chamber, transfer chamber, etc. In the case of a manufacturing process described herein as being performed by the manufacturing tool, it is understood that the manufacturing process may be performed within a processing chamber, for example... Figure 1 The processing chamber is 100.

[0028] Sometimes, a manufacturing process performed by a manufacturing tool using a formulation can lead to different results than a manufacturing process performed by different manufacturing tools using the same formulation. For example, variations in installed hardware, hardware aging / wear, changes in sensor calibration / offset, changes in manufacturing tool calibration / bias, or other variations between manufacturing tools can all cause inter-chamber variability in manufacturing processes performed using the same formulation. Furthermore, certain operating ranges may have increased sensitivity to one or more process parameters of the formulation, potentially increasing the variability of formulation results between chambers. To reduce inter-chamber variability, standardized (e.g., "gold standard") manufacturing tools can be used to establish calibration procedures and can also be used to reduce the variability of other manufacturing tools relative to standardized tools and between them.

[0029] Figure 2 An example operating environment 200 for a process variable calibration system 202 is shown. The process variable calibration system 202 includes a recipe selection module 204 and an offset generation module 206. The process variable calibration system 202 can receive multiple recipes 208 including corresponding process parameters 210 for performing a manufacturing process on a manufacturing tool 212. The manufacturing tool 212 can be a standardized system, such as a "gold standard" system (or an average set of standardized systems), against which other manufacturing tools 212 of the same model or model family can be calibrated. Different standardized systems can be used for corresponding different hardware configurations, such as different hardware subsystems. For example, a dielectric etching system may have a different standardized system than a conductor etching system.

[0030] The process variable calibration system 202 communicates with the manufacturing tool 212 via a network 214 (e.g., a local area network (LAN) or a wide area network (WAN), such as the Internet). One or more operations described with reference to the process variable calibration system 202 can be performed by one or more servers, such as a regional server and / or a cloud-based server. For example, the process variable calibration system can be fully hosted on a cloud-based server.

[0031] The process variable calibration system 202 communicates data with one or more metrology tools 216 via network 214. The metrology tools 216 can be used to characterize the substrate processed by manufacturing tool 212 before, during, and / or after the manufacturing process performed on the substrate using formulation 208. Sometimes, the metrology tool may be a subsystem of manufacturing tool 212, such as a metrology chamber within manufacturing tool 212. The metrology tool may be located outside the processing chamber of the manufacturing tool (e.g., processing chamber 100) and may include, for example, interferometry-based metrology tools or other thin-film measurement tools. The metrology tool may include an in-situ metrology tool. In some embodiments, the in-situ metrology tool may be located within a metrology chamber (e.g., an auxiliary chamber) connected to the processing chamber, for example, by a transfer chamber or loading lock. In some embodiments, the in-situ metrology tool may be located within the processing chamber of the manufacturing tool, for example, a temperature sensor (e.g., a thermocouple, an optical temperature sensor, a resistance-based temperature sensor, an etalon interferometer, etc.). In some embodiments, the metrology tool may be a system separate from manufacturing tool 212, for example, located outside the manufacturing tool. The metrology tool 216 can be used to generate characterization data 218 for one or more substrates.

[0032] In some embodiments, characterization data 218 includes measurements of substrate dimensions. For example, the thickness of one or more thin films formed on the wafer and / or the wafer thickness. Characterization data 218 may include measurements of substrate dimensions before and after manufacturing processes performed on the substrate using a formulation by manufacturing tools. For example, measurements of the thickness of the substrate (e.g., comprising one or more layers) before and after an etching process. Sometimes, characterization data 218 may include a wafer map that includes multiple measurement points across the substrate, e.g., such as... Figure 5 As shown. Characterization data 218 may include the central trend of multiple measurements of the substrate dimensions (e.g., average, mean, median, etc.). Characterization data 218 may include measurements of the substrate dimensions at the center point of the substrate (e.g., aligned with a central axis perpendicular to the substrate surface).

[0033] The recipe selection module 204 of the process variable calibration system 202 can access characterization data 218 generated for a substrate processed by the manufacturing tool 212 using process parameters 210 according to recipe 208, and generate a calibration procedure including selecting a calibration recipe from recipe 208 for calibrating the manufacturing tool. (Reference) Figure 4 Further details for selecting calibration recipes are described. The process variable calibration system 202 can store calibration procedures, including calibration recipes, in the calibration database 220.

[0034] The process variable calibration system 202 can provide calibration procedures from a calibration database 220, which includes calibration recipes for performing the calibration procedures, to one or more field manufacturing tools 224 via a network 214. As used herein, a field manufacturing tool 224 refers to a manufacturing tool having the same model or within the same family of manufacturing tools 212, and which is being prepared for deployment or deployed to a production environment.

[0035] In some embodiments, the process variable calibration system 202 may receive field characterization data 226, for example, via network 214. Field characterization data 226 includes characterization data collected from substrates processed using calibration recipes from calibration database 220 on a field manufacturing tool 224. The field manufacturing tool 224 may produce a set of substrates using calibration recipes, each substrate being processed according to a calibration procedure at different process parameter values ​​(e.g., at different temperature values). This set of substrates may be characterized, for example, by a metrology tool 216, and the field characterization data 226 is provided as input to the offset generation module 206. The offset generation module 206 determines, in response to the field characterization data 226, whether an offset of the field manufacturing tool is required (e.g., and provides an offset if required), as referenced. Figure 5 Further detailed description.

[0036] Although reference Figure 2 The description is of the operations performed by the process variable calibration system 202, but in some embodiments, some or all of the field calibration methods described may be performed on a regional version of the process variable calibration system 202 and / or by an offset generation program that operates as part of a regional controller (e.g., controller 165) on the field manufacturing tool 224.

[0037] In some embodiments, the system may generate a calibration procedure that includes selecting a calibration recipe from a plurality of available recipes, wherein a second process parameter (e.g., etch rate) exhibits a higher sensitivity (e.g., 2-3x, 5-10x, or greater) to a first process parameter (e.g., temperature) than to one or more other process parameters of the manufacturing technique performed using that recipe. For example, a calibration recipe for a cryogenic process may include a high sensitivity of the etching process to process temperature relative to other process parameters (e.g., plasma power, back gas cooling pressure, chamber pressure, etc.).

[0038] Figure 3 This is a flowchart of an example process 300 for manufacturing tool calibration. For convenience, process 300 will be described as being executed by a system of one or more computers located in one or more locations and appropriately programmed according to this specification. For example, an appropriately programmed process variable calibration system (e.g., Figure 2 The process variable calibration system 202) can execute process 300.

[0039] The process variable calibration system selects a calibration recipe (302) from multiple recipes that include a first process parameter for performing a manufacturing process on a substrate. Multiple recipes, such as recipe 208, may be for different types of manufacturing processes, such as dielectric etching, conductor etching, etc., where the manufacturing process may be specific to the substrate material. Each recipe may include a set of process parameters, such as process parameter 210, including, for example, process temperature, back gas pressure, plasma bias power, ion density, pressure in the process chamber, source power, etc. The process parameters may be adjustable relative to the recipe (e.g., selectable within a range). Sometimes, one of the process parameters may be optional, allowing the recipe to be used to perform multiple manufacturing processes on multiple substrates, where different process parameter values ​​are used to process each substrate. For example, the process temperature may be selected from a process temperature range (e.g., -90°C to -20°C, or -150°C to -90°C), where different process temperatures are used to process each substrate.

[0040] In some embodiments, the formulation may have a selectable range of process parameters. For example, the process temperature of the formulation may be selected from two or more process temperature ranges, such as -90 to -50 degrees Celsius and -60 to -20 degrees Celsius, or -150 to -90 degrees Celsius and -90 to -20 degrees Celsius, wherein each substrate may be processed using different process temperatures within the respective range. Sometimes, when compared to a second process temperature range for the same formulation, the etching rate of the substrate used for the formulation may have increased sensitivity to the process temperature of a first process temperature range. As described further in detail below, selecting a temperature range with increased sensitivity to the etching rate is advantageous for calibration procedures for calibrating process temperatures.

[0041] In some embodiments, a design of experiment (DOE) or another experiment-based or simulation-based design can be used to determine a given formulation from a set of formulations, for which a second process parameter exhibits a threshold dependence (e.g., sensitivity) on a first process parameter relative to one or more other process parameters. For example, simulation can be used to screen sensitive process parameters (e.g., plasma parameters) to generate a DOE. Furthermore, for a given formulation, a DOE can be used to determine a range of values ​​for a first process parameter, for which the second process parameter exhibits threshold sensitivity to the first process parameter relative to one or more other process parameters. For example, a set of formulation and process temperature values ​​can be determined, where the etching rate of the substrate exhibits threshold sensitivity to temperature, and where the corresponding sensitivity of the etching rate to other process parameters (e.g., plasma power, backplane gas pressure, ion density, etc.) is less than the threshold sensitivity, e.g., by an order of magnitude. In other words, a DOE can be used to select a range of values ​​for a formulation and a first process parameter (e.g., temperature) where the sensitivity of the second process parameter (e.g., etching rate) to variability in other process parameters is suppressed.

[0042] For each of the multiple formulations, a manufacturing process can be performed, for example, using standardized manufacturing tools. The manufacturing process can be performed on multiple substrates, for example, two or more substrates, where each substrate is treated using different values ​​of the formulation and given process parameters, while keeping other process parameters nominally fixed. For example, a group of two or more substrates (e.g., three or more, four or more substrates) can use the formulation and be etched in a plasma etching tool at different substrate process temperatures (e.g., as shown in the image). Figure 1 The above).

[0043] For each of a plurality of formulations, the system receives characterization data (304) representing a manufacturing process performed on two or more substrates using that formulation. The manufacturing process for each substrate or the two or more substrates includes different values ​​for a first process parameter, wherein the characterization data representing the manufacturing process on each of the two or more substrates includes a first state of the substrate before the manufacturing process and a second state of the substrate after the manufacturing process. For example, the manufacturing process may be an etching process. The characterization data may include, for example, measurements of the dimensions (e.g., thickness) of the substrate. For example, the characterization data may be a measured thickness of a thin film formed on the substrate. The characterization data may include dimensional measurements before and after the manufacturing process, for example, dimensional measurements before and after performing an etching process on the substrate.

[0044] In some embodiments, characterization data includes central trends (e.g., mean, median, pattern, etc.) of the measured dimensions of the substrate at multiple points on the substrate. For example, multiple measurements of the substrate dimensions can be collected using metrology tool 216 before and after the etching process using the formulation. In some embodiments, characterization data includes measurements of the center point of the substrate. For example, the dimensions of the center point of the substrate (e.g., aligned along a central axis) can be collected using metrology tool 216 before and after the manufacturing process.

[0045] For each of the multiple formulations, the system determines a second process parameter (306) based on a first state and a second state of the substrate. For example, the difference between the measured dimensions in the first state and the second state, such as before and after the etching process, can be used to calculate the thickness of the substrate etched. The second process parameter, such as the etching rate, can be extracted using the thickness of the substrate etched and the time of the etching process (e.g., from the formulation used to perform the manufacturing process).

[0046] For example, the etching rate can be determined as

[0047]

[0048] D1 and D2 are the measured dimensions before and after the etching process, respectively.

[0049] For each of a plurality of formulations and for a manufacturing process performed on two or more substrates using that formulation, the system determines a process relationship (308) between a first process parameter and a second process parameter of that formulation. To determine the process relationship between the first and second process parameters, the system can generate corresponding graphs of the first and second process parameters for two or more substrates processed using the formulation at different values ​​of the first process parameter. Figure 5 As shown, calibration data were collected for each of two or more substrates processed using multiple values ​​of the formulation and first process parameters. The etching rate of each substrate was calculated using Equation (1), where the etching rate range corresponding to the non-uniformity of the etching rate on the substrate surface is within... Figure 5 The deviation from the central trend of etching rate (e.g., average etching rate) is represented in the figure. The system can determine the process relationship, such as a linear fit, based on points corresponding to a curve of average etching rate versus process temperature. The slope of the linear fit of the data can then be used to determine the sensitivity of the second process parameter (e.g., etching rate) to the first process parameter (e.g., temperature). For example, a shallower slope may indicate a less sensitive relationship, while a steeper slope may indicate a more sensitive relationship between the second process parameter (e.g., etching rate) and the first process parameter (e.g., process temperature).

[0050] refer to Figure 3The system selects a calibration formulation from multiple formulations based on the corresponding process relationships of these formulations (310). For each of the multiple formulations, the system can generate a respective graph and determine the process relationship between a second process parameter and a first process parameter of the formulation. By comparing the slope of each generated graph corresponding to the respective formulation, the system can select a calibration formulation from the multiple formulations that has a threshold dependence of the second process parameter on the first process parameter (e.g., for a given substrate material composition). As described above, for each formulation, the system can perform a DOE to establish a sensitivity range, wherein the second process parameter has at least a threshold sensitivity to the first process parameter.

[0051] For a calibration recipe, the system determines a threshold variability (312) of the process relationship between a first process parameter and a second process parameter. The system may determine the variability of each variable sensitivity of the manufacturing process performed using the calibration recipe, such as the root mean square (RMS). Variable sensitivity may include the expected variability of process parameters, such as pressure control, plasma power, chamber gas pressure, ion density, etc., and the expected wafer-to-wafer inherent variability (e.g., provided by the wafer manufacturer). The threshold variability (e.g., representing the total chamber-to-chamber variability) is determined by combining (e.g., by adding) all individual subsystem variability and inherent wafer-to-wafer variability. Variations in individual subsystems may be determined by analyzing hardware performance (e.g., performance logs, self-tests, test procedures, etc.). Variations between wafers may be determined by metrological measurements, such as online metrology including ellipticization, CD-SEM, etc. Threshold variability may include, for example, the standard deviation from the nominal RMS variability. Threshold variability may include, for example, the percentage variance from the nominal RMS variability. In some embodiments, the determined threshold variability may be stored in calibration database 220 along with the corresponding calibration recipe and calibration procedure.

[0052] The system provides calibration recipes and threshold variability for calibrating the manufacturing system (314). In some embodiments, a calibration recipe is used to calibrate the manufacturing system. Calibration of the manufacturing system can be performed during the initial setup and qualification process of the manufacturing system in the field. In some embodiments, a calibration recipe can be used to recalibrate the manufacturing system. For example, the manufacturing system can be recalibrated in response to drifts observed in the manufacturing process that deviate from expected results (e.g., etch rate non-uniformity between process chambers). In another example, the manufacturing system can be recalibrated in response to changes in the configuration of the manufacturing system, such as replacing or reconfiguring a component. In some embodiments, the manufacturing system can be recalibrated periodically, for example, for quality control purposes.

[0053] The process variable calibration system can provide a calibration procedure to a field manufacturing tool, such as field manufacturing tool 224, including a calibration recipe selected based on one or more process parameters of the manufacturing tool. For example, a calibration procedure including a calibration recipe can be selected based on etching chemistry, substrate composition, process temperature, or another process parameter.

[0054] Figure 4 This is a flowchart of another example process 400 for calibrating manufacturing tools using a calibration procedure. For convenience, process 400 will be described as being executed by a system of one or more computers located in one or more locations and appropriately programmed according to this specification.

[0055] The system provides a calibration recipe to a manufacturing tool for performing a set of manufacturing processes on a corresponding substrate, each manufacturing process using a different first process parameter value from a set of first process parameter values ​​(402). The calibration recipe may be provided by a calibration procedure, such as instructions for implementing the calibration recipe to generate calibration data. For example, the process variable calibration system 202 may receive a request for a calibration procedure to calibrate the field manufacturing tool 224 (e.g., from a technician or end operator of the tool). The process variable calibration system 202 may select a calibration recipe from calibration data 220 to provide to the field manufacturing tool 224 and includes a calibration procedure for performing a set of manufacturing processes using the calibration recipe. For example, the set of manufacturing processes may include performing manufacturing processes on two or more substrates, each substrate being processed at a different process temperature within a temperature range. The calibration procedure may further include collecting field calibration data of the processed substrates, for example, using metrology tools described in this specification.

[0056] The system determines the dependence of the second process parameter of the manufacturing system on the first process parameter based on the substrate characterization data (404). In some embodiments, the field manufacturing tool 224 may provide field characterization data 226 of the process substrate to the process variable calibration system 202 via network 214. The offset generation module 206 may determine the process relationship between the second process parameter and the first process parameter. For example, the process relationship may be a linear relationship between etching rate and process temperature, where each processed substrate corresponds to a point on the process relationship graph, for example, as referenced. Figure 5 The system can generate a graph showing the relationship between etching rate and process temperature for a calibrated formulation and determine the process relationship. The system can also determine the variability of the process relationship between a first process parameter and a second process parameter based on the linearity of the field manufacturing tools.

[0057] In response to determining that the dependence of the second process parameter on the first process parameter is outside a threshold variation, the system generates an offset calibration value (406) for the manufacturing system. The system can generate calibration curves for the calibration recipe on a standardized chamber and determine the average etch rate and the sensitivity of the etch rate to the ESC temperature. For a given field manufacturing tool, the system can receive calibration data for the same calibration recipe and compare the etch rate differences between the field manufacturing tool and the standardized manufacturing tool. In other words, the system can compare the variability of the process relationship between the first process parameter and the second process parameter of the substrate group processed by the field manufacturing tool 224 with the threshold variability of the calibration recipe for a standard manufacturing tool (e.g., a "gold standard" tool). If the system determines that the variability of the process relationship is outside the threshold variability, the system can generate an offset for the field manufacturing tool.

[0058] In some embodiments, the system calculates the offset calibration value by dividing the etch rate difference between the field manufacturing tool and the standardized manufacturing tool (e.g., the average etch rate difference across multiple temperature points) by the temperature sensitivity determined for the calibration recipe.

[0059] In some embodiments, the offset calibration value may be determined based on the variability determined for the field manufacturing tool relative to a threshold variability of the standard manufacturing tool for the calibration recipe. For example, the threshold variability of the standard manufacturing tool for the calibration recipe may be set to X+ / -Y. For a variability value Z of the field manufacturing tool outside the variability range, for example, when Z is outside the range of Z > X+Y or Z < -XY, the offset calibration value A may be set as follows:

[0060] For Z > X + Y, A = ZY

[0061] For Z <X-Y,A=Y-Z

[0062] In this article, Z and Y can be absolute or percentage values ​​of nominal variability.

[0063] In some embodiments, the offset calibration value may be a global offset applied to a control system for one or more process parameters. A global temperature offset may be applied to a temperature control system for process temperatures, for example, as a setpoint change in a process control loop. For instance, the offset may be applied as a setpoint offset to the PID loop of a PID controller in a process temperature control system. In another example, the offset calibration value may be used to offset the reading of a temperature probe measuring process temperature (e.g., back-side substrate temperature) to a temperature process controller.

[0064] In some embodiments, the methods described above can be used, for example, to select a calibration formulation to calibrate different heating regions of the electrostatic chuck (ESC). For example, a formulation can be selected to perform zone-by-zone calibration, wherein characterization data is collected for each region of the substrate in a first state (before manufacturing) and a second state (after manufacturing) during the manufacturing process. Furthermore, the methods described herein can be used to facilitate micro-region tuning and / or extreme edge quantization of the substrate, wherein additional calibration data representing the etching process at each micro-region heater and / or edge of the substrate for the formulation can be collected. A combined etch rate offset map and etch rate map of the substrate can be compared with a gold etch rate uniformity map for the substrate and can be used to adjust the micro-region heaters. For example, the superposition of the two calibrations can be used to scale the offset of the micro-region heaters and determine which other variables may have a high impact, such as due to the location of the electrostatic chuck support structure, the type of support structure, and centering relative to the substrate.

[0065] In some embodiments, real-time in-situ temperature measurements (e.g., using interferometric etalons) can be combined with etch rate signals to establish a combined etch rate versus temperature model. This combined model can be used to generate real-time wafer temperature maps and to adjust process parameters in real-time during the manufacturing process. For example, the real-time wafer temperature map can be used in control loops, such as dead-loop feedforward control, to adjust setpoints for various components during the manufacturing process. In-situ metrology tools (e.g., interferometers) can be used to collect higher-density data points and establish denser temperature maps on the surface of the substrate. Real-time measurements can be used to build algorithms to automatically update offsets, for example, between processed substrates. Real-time measurements can be used to capture drift in the manufacturing tool between processing runs to achieve offsets more quickly and reduce inter-chamber variability (e.g., between manufacturing tools or between chambers of a manufacturing tool).

[0066] Figure 6 This is a block diagram of an example computer system 600 that can be used to perform the operations described above. For example, operations such as those performed by an electrostatic chuck model. System 600 includes a processor 610, memory 620, storage device 630, and input / output device 640. Each of components 610, 620, 630, and 640 may be interconnected, for example, using a system bus 650. Processor 610 is capable of processing instructions for execution within system 600. In one embodiment, processor 610 is a single-threaded processor. In another embodiment, processor 610 is a multi-threaded processor. Processor 610 is capable of processing instructions stored in memory 620 or on storage device 630.

[0067] Memory 620 stores information within system 600. In one embodiment, memory 620 is a computer-readable medium. In one embodiment, memory 620 is a volatile memory cell. In another embodiment, memory 620 is a non-volatile memory cell.

[0068] Storage device 630 provides mass storage for system 600. In one embodiment, storage device 630 is a computer-readable medium. In various embodiments, storage device 630 may include, for example, a hard disk drive, an optical disk drive, a storage device shared over a network by multiple computing devices (e.g., cloud storage devices), or some other mass storage device.

[0069] Input / output device 640 provides input / output operations for system 600. In one embodiment, input / output device 640 may include one or more of a network interface device (e.g., an Ethernet card), a serial communication device (e.g., an RS-232 port), and / or a wireless interface device (e.g., an 802.11 card). In another embodiment, input / output device may include a driver device configured to receive input data and send output data to peripheral device 660, such as a keyboard, printer, and display device. However, other embodiments, such as mobile computing devices, mobile communication devices, set-top box television client devices, etc., may also be used.

[0070] Despite Figure 6 An example processing system is described herein, but implementations of the subjects and functional operations described herein may be implemented in other types of digital electronic circuit systems, or in computer software, firmware, or hardware, including the structures disclosed herein and their structural equivalents, or in one or more combinations thereof.

[0071] The subjects and aspects of action and operation described in this specification, such as computing devices like controller 165 and processes performed by controller 165, such as controlling the switching of etching gases in a plasma processing chamber, can be implemented in digital electronic circuit systems, in tangibly embodied computer software or firmware, in computer hardware, including the structures disclosed in this specification and their structural equivalents, or combinations thereof. The subjects and aspects of action and operation described in this specification can be implemented as or in one or more computer programs, for example, one or more modules of computer program instructions encoded on a computer program carrier for execution by or control of the operation of a data processing device. The carrier can be a tangible, non-transitory computer storage medium. Alternatively or additionally, the carrier can be an artificially generated propagation signal, such as a machine-generated electrical, optical, or electromagnetic signal, generated to encode information for transmission to a suitable receiver device for execution by the data processing device. The computer storage medium can be a machine-readable storage device, a machine-readable storage substrate, a random or serial access storage device, or a combination thereof, or a portion thereof. Computer storage media are not transmitted signals.

[0072] The term "data processing device" encompasses all types of devices, apparatuses, and machines used for processing data, including programmable processors, computers, or multiple processors or computers. Data processing devices may include dedicated logic circuit systems such as FPGAs (Field-Programmable Gate Arrays), ASICs (Application-Specific Integrated Circuits), or GPUs (Graphics Processing Units). In addition to hardware, the device may also include code that creates the execution environment for computer programs, such as code constituting processor firmware, protocol stacks, database management systems, operating systems, or combinations thereof.

[0073] Computer programs can be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages; and they can be deployed in any form, including as stand-alone programs, such as as applications, or as modules, components, engines, subroutines or other units suitable for execution in a computing environment, which may include one or more computers interconnected by a data communication network in one or more locations.

[0074] A computer program may, but does not necessarily, correspond to a document in a file system. A computer program may be stored in a section of a document that holds other programs or data, for example, in one or more scripts stored in a markup language document, in a single document dedicated to the program in question, or in multiple coordinating documents, such as a document storing one or more modules, subroutines, or code portions.

[0075] The process and logic flow described in this specification can be executed by one or more computers that execute one or more computer programs to perform operations by manipulating input data and producing outputs. The process and logic flow can also be executed by a dedicated logic circuit system, such as an FPGA, ASIC, or GPU, or by a combination of a dedicated logic circuit system and one or more programmable computers.

[0076] A computer suitable for executing computer programs can be based on a general-purpose or special-purpose microprocessor, or both, and any other type of central processing unit (CPU). Generally, the CPU receives instructions and data from read-only memory (ROM) or random access memory (RAM), or both. The basic components of a computer are the CPU for executing instructions and one or more memory devices for storing instructions and data. The CPU and memory may be supplemented by or incorporated into a dedicated logic circuit system.

[0077] Generally, a computer will also include one or more mass storage devices, or be operatively coupled to one or more mass storage devices, and be configured to receive data from or transfer data to a mass storage device. Mass storage devices may be, for example, magnetic disks, magneto-optical disks, optical disks, or solid-state drives. However, a computer does not need to have such devices. Furthermore, a computer may be embedded in another device, such as a mobile phone, a personal digital assistant (PDA), a mobile audio or video player, a game console, a Global Positioning System (GPS) receiver, or a portable storage device, such as a universal serial bus (USB) flash drive, to name a few.

[0078] To provide interaction with a user, the subject matter described in this specification can be implemented on one or more computers having a display device for displaying information to the user, such as an LCD (liquid crystal display) monitor, or a virtual reality (VR) or augmented reality (AR) display, or being configured to communicate with it, and input devices for the user to provide input to the computer, such as a keyboard and pointing devices, such as a mouse, trackball, or touchpad. Other types of devices may also be used to provide interaction with the user; for example, feedback and responses provided to the user may be in any form of sensory feedback, such as visual, auditory, verbal, or tactile; and input from the user may be received in any form, including acoustic, verbal, or tactile input, including touch motion or gestures, or dynamic motion or gestures, or directional motion or gestures. Furthermore, the computer can interact with the user by sending documents to and receiving documents from the device used by the user; for example, by sending web pages to a web browser on the user's device in response to a request received from a web browser, or by interacting with an application running on the user's device (e.g., a smartphone or electronic tablet). In addition, computers can interact with users by sending text messages or other forms of information to personal devices (e.g., smartphones running messaging applications) and receiving response messages from users.

[0079] This specification uses the term "configured to" in connection with systems, devices, and computer program elements. A system of one or more computers configured to perform a specific operation or action means that software, firmware, hardware, or a combination thereof are installed on the system, which, in operation, causes the system to perform the operation or action. A computer program configured to perform a specific operation or action means that the one or more programs include instructions that, when executed by a data processing device, cause the device to perform the operation or action. A dedicated logic circuit system configured to perform a specific operation or action means that the circuit has electronic logic that performs the operation or action.

[0080] While this specification contains numerous specific implementation details, these should not be construed as limiting the scope of the claims as defined by the claims themselves, but rather as descriptions of features specific to particular embodiments of the invention. Certain features described in the context of individual embodiments may also be implemented in combination in a single embodiment. Conversely, various features described in the context of a single embodiment may also be implemented individually or in any suitable sub-combination in multiple embodiments. Furthermore, although features may be described above as functioning in certain combinations, even initially so claimed, in some cases one or more features from the claimed combination may be removed from that combination, and the claim may be directed to a sub-combination or a variation thereof.

[0081] Similarly, although operations are described in the accompanying drawings and recited in a specific order in the claims, this should not be construed as requiring such operations to be performed in the specific order or sequence shown, or requiring all of the shown operations to achieve the desired result. In some cases, multitasking and parallel processing may be advantageous. Furthermore, the separation of various system modules and components in the above embodiments should not be construed as requiring such separation in all embodiments, and it should be understood that the described program elements and systems can be largely integrated into a single software product or packaged into multiple software products.

[0082] Specific embodiments of the subject matter have been described. Other embodiments are within the scope of the following claims. For example, the actions described in the claims can be performed in different orders and still achieve the desired result. As an example, the process described in the figures does not necessarily require the specific order or sequence shown to achieve the desired result. In some cases, multitasking and parallel processing may be advantageous.

Claims

1. A method for calibrating a manufacturing system, the method comprising: A selection from multiple formulations includes a calibration formulation for performing a first process parameter on a substrate, wherein the selection includes: For each of the plurality of formulations: For two or more substrates, characterization data representing the manufacturing process performed on the two or more substrates using the formulation is received, wherein the manufacturing process for each of the two or more substrates includes different values ​​of the first process parameter, and wherein the characterization data representing the manufacturing process on each of the two or more substrates includes a first state of the substrate before the manufacturing process and a second state of the substrate after the manufacturing process. The second process parameters are determined based on the first state and the second state of the substrate; and For the manufacturing process performed on two or more substrates using the aforementioned formulation, determine the process relationship between the first process parameter and the second process parameter of the formulation; and The calibration formula is selected from the plurality of formulas based on the corresponding process relationships of the plurality of formulas; For the calibration formula, determine the threshold change in the process relationship between the first process parameter and the second process parameter; and The calibration formula and the threshold variation are provided for calibrating the manufacturing system.

2. The method of claim 1, wherein the first process parameter includes the substrate temperature of the substrate during the manufacturing process.

3. The method of claim 1, wherein the second process parameter includes the etching rate of the substrate during the manufacturing process.

4. The method of claim 1, wherein determining the process relationship comprises extracting the slope of the linear relationship between the first process parameter and the second process parameter of the manufacturing process performed on the two or more substrates.

5. The method of claim 1, wherein selecting the calibration formulation from the plurality of formulations comprises selecting a formulation from the plurality of formulations that has at least a threshold dependence between the first process parameter and the second process parameter.

6. The method of claim 5, wherein selecting the calibration formulation from the plurality of formulations comprises selecting the formulation from the plurality of formulations in which the second process parameter has the greatest dependence on the first process parameter.

7. The method of claim 6, wherein selecting the calibration formulation from the plurality of formulations includes selecting the formulation from the plurality of formulations in which the etching rate of the substrate is most dependent on the substrate temperature.

8. The method of claim 1, wherein the calibration formula further comprises a plurality of process parameters, and wherein selecting the calibration formula from the plurality of formulas comprises selecting a formula from the plurality of formulas in which the dependence of the second process parameter on the first process parameter is greater than the deterministic dependence of the second process parameter on each of the plurality of process parameters by a specified threshold amount.

9. The method of claim 1, wherein providing the calibration formula and the threshold variation for calibrating the manufacturing system comprises: The manufacturing system is provided with the calibration recipe for performing a set of manufacturing processes on a respective substrate using the calibration recipe, each manufacturing process using a different first process parameter value from a set of first process parameter values; The dependence of the second process parameter of the manufacturing system on the first process parameter is determined based on the characterization data of the substrate. as well as In response to determining that the dependence of the second process parameter on the first process parameter is outside the threshold variation, an offset calibration value for the manufacturing system is generated.

10. The method of claim 1, wherein, for two or more substrates, receiving the characterization data representing the manufacturing process performed on the two or more substrates using the formulation comprises: The formulation is used to perform the manufacturing process on the two or more substrates, wherein the manufacturing process for each of the two or more substrates includes different values ​​of the first process parameter; as well as Characterize the two or more substrates to extract the characterization data.

11. The method of claim 10, wherein the manufacturing process includes an etching process.

12. A system comprising: One or more computers and one or more storage devices, wherein instructions are stored on the one or more storage devices, the instructions being operable, when executed by the one or more computers, to cause the one or more computers to perform operations, the operations including: A selection from multiple formulations includes a calibration formulation for performing a first process parameter on a substrate, wherein the selection includes: For each of the plurality of formulations: For two or more substrates, characterization data representing the manufacturing process performed on the two or more substrates using the formulation is received, wherein the manufacturing process for each of the two or more substrates includes different values ​​of the first process parameter, and wherein the characterization data representing the manufacturing process on each of the two or more substrates includes a first state of the substrate before the manufacturing process and a second state of the substrate after the manufacturing process. The second process parameters are determined based on the first state and the second state of the substrate; and For the manufacturing process performed on two or more substrates using the aforementioned formulation, determine the process relationship between the first process parameter and the second process parameter of the formulation; and The calibration formula is selected from the plurality of formulas based on the corresponding process relationships of the plurality of formulas; For the calibration formula, determine the threshold change in the process relationship between the first process parameter and the second process parameter; and The calibration formula and the threshold variation are provided for calibrating the manufacturing system.

13. The system of claim 12, wherein the first process parameter includes the substrate temperature of the substrate during the manufacturing process.

14. The system of claim 12, wherein the second process parameter includes the etching rate of the substrate during the manufacturing process.

15. The system of claim 12, wherein determining the process relationship comprises extracting the slope of the linear relationship between the first process parameter and the second process parameter of the manufacturing process performed on the two or more substrates.

16. The system of claim 12, wherein selecting the calibration formula from the plurality of formulas comprises selecting a formula among the plurality of formulas that has at least a threshold dependence between the first process parameter and the second process parameter.

17. The system of claim 16, wherein selecting the calibration formula from the plurality of formulas comprises selecting the formula from the plurality of formulas in which the second process parameter has the greatest dependence on the first process parameter.

18. The system of claim 17, wherein selecting the calibration formulation from the plurality of formulations includes selecting the formulation from the plurality of formulations in which the etch rate of the substrate is most dependent on the substrate temperature.

19. The system of claim 12, wherein the calibration recipe further comprises a plurality of process parameters, and wherein selecting the calibration recipe from the plurality of recipes comprises selecting a recipe from the plurality of recipes in which the dependence of the second process parameter on the first process parameter is greater than the deterministic dependence of the second process parameter on each of the plurality of process parameters by a specified threshold amount.

20. One or more non-transitory computer storage media, said one or more non-transitory computer storage media being encoded with computer program instructions, said computer program instructions, when executed by said one or more computers, causing said one or more computers to perform operations, said operations including: A selection from multiple formulations includes a calibration formulation for performing a first process parameter on a substrate, wherein the selection includes: For each of the plurality of formulations: For two or more substrates, characterization data representing the manufacturing process performed on the two or more substrates using the formulation is received, wherein the manufacturing process for each of the two or more substrates includes different values ​​of the first process parameter, and wherein the characterization data representing the manufacturing process on each of the two or more substrates includes a first state of the substrate before the manufacturing process and a second state of the substrate after the manufacturing process. The second process parameters are determined based on the first state and the second state of the substrate; and For the manufacturing process performed on two or more substrates using the aforementioned formulation, determine the process relationship between the first process parameter and the second process parameter of the formulation; and The calibration formula is selected from the plurality of formulas based on the corresponding process relationships of the plurality of formulas; For the calibration formula, determine the threshold change in the process relationship between the first process parameter and the second process parameter; and The calibration formula and the threshold variation are provided for calibrating the manufacturing system.

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