Plasma Hypermodel Integrating Feature-Scale Profile Models for Accelerating Etch Process Development

Abstract

Plasma parameters at the surface of the wafer are determined based on the plasma process conditions using a plasma hyper-model. A post-processing profile can be predicted at the surface of the wafer using a feature-scale profile model. The correlation in the plasma hyper-model can be recalibrated if the post-processing profile deviates from the convergence criteria of the experimental reference.

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority to provisional patent application Ser. No. 63 / 414,603, filed Oct. 10, 2022, the disclosure of which is incorporated herein by reference.

[0002] The present disclosure relates to semiconductor manufacturing. [Background technology]

[0003] The fabrication of semiconductor devices, such as logic and memory devices, typically involves processing semiconductor wafers using a number of fabrication processes to form the various features and layers of the semiconductor devices. For example, lithography is a semiconductor fabrication process that involves transferring a pattern from a reticle to a photoresist disposed on a semiconductor wafer. Additional examples of semiconductor fabrication processes include, but are not limited to, chemical mechanical polishing (CMP), etching, deposition, and ion implantation. An arrangement of multiple semiconductor devices fabricated on a single semiconductor wafer can be separated into individual semiconductor devices.

[0004] Many of these fabrication processes use plasma. For example, plasma etching, ion implantation, and plasma-enhanced chemical vapor deposition (PECVD) all generate plasma as part of their operation. The operating settings for these processes can be based on simulations of plasma parameters.

[0005] In previous methods, a rigorous physics-based plasma model was used to simulate the plasma in an etch reactor to obtain plasma parameters at the wafer surface, such as radical flux and ion energy. These plasma parameters were then imported into a feature-scale profile model to predict the resulting etch profile. This previous method used two separate models—a rigorous physics-based plasma model and a feature-scale profile model—that ran in tandem. Each model was calibrated separately, and data was manually transferred from the plasma model to the profile model. Beyond this manual transfer, there was little communication or interaction between the rigorous physics-based plasma model and the feature-scale profile model. The surface chemistry in the feature-scale profile model and the plasma chemistry in the rigorous physics-based plasma model could not be co-optimized. It was also not possible to implement a numerical algorithm to calibrate the two separate models. As a result, the iterative approach of looping between the two models for calibration was time-consuming and inefficient. [Prior art documents] [Patent documents]

[0006] [Patent Document 1] U.S. Patent Application Publication No. 2022 / 0171373 [Patent Document 2] International Publication No. 2021 / 154747 Summary of the Invention [Problem to be solved by the invention]

[0007] Therefore, new methods and systems are needed. [Means for solving the problem]

[0008] In a first embodiment, a method is provided. The method includes receiving plasma process conditions with a processor and using the processor to determine plasma parameters at a surface of a wafer based on the plasma process conditions using a plasma hyper-model. The plasma process conditions may include one or more of pressure, gas chemistry, temperature, flow rate, source power, bias power, source power, or pulse conditions.

[0009] The method may further include inputting the plasma parameters into a feature-scale profile model and predicting, using a processor, a post-processing profile of the surface of the wafer using the feature-scale profile model. The post-processing profile may be compared to an experimental reference using the processor. The correlation of the plasma hyper-model may be recalibrated using the processor if the post-processing profile falls outside the convergence criteria of the experimental reference. The experimental reference may be a TEM image or an XSEM image.

[0010] The plasma hypermodel may include matrices that are multiplied by the plasma process conditions.

[0011] The plasma conditions may be for an etching process, a deposition process, or an ion implantation process.

[0012] The method may further include exposing the wafer to a plasma using plasma process conditions in a plasma processing apparatus.

[0013] A non-transitory computer-readable medium storing a program may be configured to instruct a processor to perform the method of the first embodiment.

[0014] A system is provided in a second embodiment. The system includes a plasma processing apparatus having a plasma chamber, a stage disposed within the plasma chamber configured to hold a wafer, and a plasma generation system. The plasma processing apparatus can be an etching apparatus, a deposition apparatus, or an ion implantation apparatus. A processor is in electronic communication with the plasma processing apparatus. The processor is configured to receive plasma process conditions and determine plasma parameters at the surface of the wafer based on the plasma process conditions using a plasma hypermodel. The plasma process conditions can include one or more of pressure, gas chemistry, temperature, flow rate, source power, bias power, source power, or pulse conditions.

[0015] The processor may be further configured to input the plasma parameters into a feature-scale profile model and predict a post-processing profile of the surface of the wafer using the feature-scale profile model. The processor may be configured to compare the post-processing profile with an experimental reference. The processor may also be configured to recalibrate the correlation of the plasma hyper-model if the post-processing profile deviates from the convergence criteria of the experimental reference. The experimental reference may be a TEM image or an XSEM image.

[0016] The plasma hypermodel may include matrices that are multiplied by the plasma process conditions.

[0017] The processor can be configured to send instructions to the plasma processing device to generate a plasma at plasma process conditions. [Brief explanation of the drawings]

[0018] For a fuller understanding of the nature and objects of the present disclosure, reference should be made to the following detailed description taken in conjunction with the accompanying drawings.

[0019] [Figure 1]1 is a flowchart of one embodiment of a calibration process based on integration of a plasma hyper-model and a feature-scale profile model according to the present disclosure. [Figure 2] FIG. 1 is a block diagram of an exemplary system according to the present disclosure. [Figure 3] 1 shows contour plots of correlations in the Ar / Cl plasma hypermodel between process conditions (power and pressure) and plasma parameters at the wafer surface, calibrated based on XSEM images from different process conditions. DETAILED DESCRIPTION OF THE INVENTION

[0020] Although the claimed subject matter is described in terms of certain embodiments, other embodiments, including embodiments that do not provide all of the advantages and features described herein, are also within the scope of this disclosure. Various structural, logical, process step, and electrical changes may be made without departing from the scope of the disclosure. Accordingly, the scope of the disclosure is defined solely by reference to the appended claims.

[0021] In embodiments disclosed herein, a plasma hyper-model is integrated with a feature-scale profile model for process development. Based on process conditions, the plasma hyper-model generates plasma parameters at the wafer surface, which are used as inputs to the feature-scale profile model to predict feature profiles. Thus, the plasma hyper-model and the feature-scale profile model can be co-optimized. The integration of the plasma hyper-model and the feature-scale profile model can enable model calibration and process optimization, from macroscopic process conditions such as power and pressure to microscopic feature metrology such as critical dimensions and sidewall angles.

[0022] The plasma hyper-model has adjustable parameters instead of the large, fixed parameter set of rigorous physics-based plasma models. Integration of the plasma hyper-model with the feature-scale profile model allows metrology references to be used to calibrate both the plasma hyper-model and the feature-scale profile model through numerical algorithms based on experimental references, such as transmission electron microscope (TEM) and cross-sectional scanning electron microscope (XSEM) images. TEM and XSEM images are more accessible than plasma parameters at the surface of an operating plasma reactor. Once calibrated, the plasma hyper-model and the feature-scale profile model can be used to predict profiles at other process conditions. The plasma hyper-model can capture both linear and nonlinear relationships between reactor knobs (e.g., power and pressure) and plasma parameters (e.g., energy and flux) at the wafer surface in different forms (e.g., linear, quadratic, or cross terms).

[0023] Computational model process development relies on the accuracy and efficiency of the model. High-fidelity, high-efficiency models can improve high-volume manufacturing by taking process conditions tuned by the knobs of a process reactor as inputs and predicting feature profiles as outputs.

[0024] Previous methods used both reactor-scale and feature-scale modeling in tandem to achieve high-fidelity and efficient models. In reactor-scale plasma modeling, used to model the plasma in an etch reactor using a rigorous physics-based approach, the process conditions tuned by reactor knobs (e.g., power and pressure) were the inputs. Physical equations for transport, kinetics, and electromagnetism, as well as chemical reactions for gas-phase and surface reactions, were solved. The outputs were plasma parameters (e.g., flux and energy) at the wafer surface. In feature-scale profile modeling, used to model the evolution of the feature profile using a rigorous physics-based approach, the outputs of reactor-scale modeling, which are plasma parameters, were used as inputs. Plasma particle transport and surface reactions were modeled with the resulting etch feature profile as the output.

[0025] As disclosed herein, a plasma hypermodel is used in place of reactor-scale plasma modeling to correlate process conditions with plasma parameters at the wafer surface. The correlations are based on empirical assumptions. Their coefficients can be calibrated based on a cost function defined by the difference between the modeling results and an experimental reference. The plasma hypermodel is integrated with a rigorous physics-based profile model for model calibration. An iterative regression approach for calibration is shown in method 100 of FIG. 1. Using process conditions as input, the plasma hypermodel generates plasma parameters at the wafer surface based on the correlations contained therein. These plasma parameters can be used to predict post-processing profiles (e.g., post-etch profiles) as input for subsequent feature-scale models. A cost function based on the difference between the model-predicted profile and an experimental reference (e.g., a TEM or XSEM image) can be evaluated. If the evaluation results meet preset convergence criteria, model calibration is complete and can be used for process optimization. If the evaluation results do not meet the convergence criteria, numerical algorithms can be used to recalibrate both the correlations within the plasma hypermodel and the transport and surface reactions in the feature-scale profile model. This process can be repeated until the feature profiles predicted from the plasma hyper-model and the feature-scale profile model meet a convergence criterion.

[0026] A hypermodel refers to the correlation or mapping between two data sets (i.e., input data and output data) or multiple data sets. The input data can be the control knobs of a physical system (e.g., a plasma processing device such as a plasma etcher), and the output data are the parameters (e.g., plasma flux, ion energy, temperature) that an engineer wants to control through the control knobs. A hypermodel can be a matrix or multiple matrices multiplied together.

[0027] Compared to conventional methods that may only allow process engineers to iterate on plasma recipes on a weekly basis, embodiments disclosed herein may allow process engineers to iterate on plasma recipes more frequently. For example, plasma recipes can be iterated on a daily basis using embodiments disclosed herein. Conventional methods typically required both rigorous physics-based plasma modeling, which typically required several days to complete, and rigorous physics-based etch modeling. Process engineers manually transferred the output of the plasma modeling as input to the etch modeling. Embodiments disclosed herein replace the rigorous physics-based plasma modeling with a plasma hypermodel that can be completed in less than one second. The flow shown in FIG. 1 can automate the calibration process for both the plasma hypermodel and the rigorous physics-based modeling in the feature-scale profile model, thereby improving efficiency and allowing process engineers to iterate recipes for optimal profile control on a daily basis instead of weekly.

[0028] In the plasma hyper-model, a matrix operator A is assumed to correlate process conditions x with plasma parameters y at the wafer surface in the form y = Ax + b with an adjustable bias b. These correlations can be expressed, for example, in the following form:

number

[0029] The above equation shows a linear form of the vector x, but it can also have the following cross-term form:

number

[0030] The vector x can also have the following quadratic form:

number

[0031] The vector x can also have a combination of linear, quadratic, and cross terms, as shown below.

number

[0032] The coefficients in matrix A and vector b can be adjusted to obtain plasma parameters that result in a simulated etch profile that matches the experimental reference. After the matrix A and vector b in the plasma hyper-model and the transport and surface reactions in the feature-scale profile model are calibrated, they can be used to predict profiles for other process conditions. The calibrated plasma hyper-model and feature-scale profile model can be used inversely to search for optimal process conditions based on the desired feature profile.

[0033] A hypermodel correlates input parameters, which are typically different physical parameters (power, pressure, frequency, temperature, etc.) with different physical units and different orders of magnitude and range of values. For example, power can be from 1 W to 10,000 W, and frequency can be from 1 kHz to 100 MHz. Output parameters can have different units, magnitudes (e.g., plasma flux is 1015 cm -2 s -1 From 1018cm -2 s -1 and the ion energy can be from 10 eV to 10,000 eV). Given the differences in units, magnitudes, and ranges of both input and output parameters, it can be difficult to efficiently perform calculations using or calibrate hypermodels without a processor.

[0034] 1, plasma process conditions are received at a processor at 101. The plasma process conditions may include, for example, one or more of pressure, gas chemistry, temperature, flow rate, source power, bias power, source power, pulse conditions (e.g., pulse frequency or pulse duty cycle), or other parameters. The processor may determine an output based on the plasma process conditions using a plasma hypermodel at 102. In one embodiment, plasma parameters at the surface of the wafer are determined using the plasma hypermodel. The plasma hypermodel may include a matrix that is multiplied by the plasma process conditions.

[0035] The plasma parameters determined by the plasma hypermodel may include, for example, one or more of the following: neutral radical flux, ion flux, ion energy, ion angle, or other parameters. In certain plasma processing systems, such as plasma etching systems with multiple power control knobs, the plasma may exhibit a double-peak or multi-peak distribution of ions. In these complex conditions, the hypermodel may also be used to determine the low-energy ion peak, the high-energy ion peak, the flux of the low-energy ion peak, and / or the flux of the high-energy ion peak.

[0036] The plasma parameters are input into a feature-scale profile model at 103. The feature-scale profile model may be KLA's PROETCH physics-based dry etch simulator or other model. A processor may execute the feature-scale profile model. The feature-scale profile model may predict a post-processing profile for the surface of the wafer at 103 from the plasma parameters generated by the plasma hypermodel and from the pre-processing profile shown at 105. Although disclosed with etching, method 100 may be applied to other plasma processing techniques, such as deposition or ion implantation.

[0037] The feature-scale profile model may be used for research or development in semiconductor manufacturing to develop new techniques, processes, or process flows for new structures, new materials, or new technology nodes.

[0038] A feature-scale profile model can model the evolution of features on a semiconductor wafer under exposure to energetic and reactive species generated in a plasma. In one example, a feature-scale profile model can input a hard mask profile and underlying material from a scanning electron microscope (SEM) image or design file. A feature-scale profile model can also input a photoresist profile and underlying film stack from a lithography simulator (e.g., PROLITH, developed by KLA). The incoming geometry is discretized as a collection of voxels in 3D space, with each voxel tagged with a material identifier. The evolution of this voxel mesh over time due to interaction with the plasma is tracked to predict the post-processing profile. Other methodologies are possible for the feature-scale profile model; this is just one example.

[0039] As shown in FIG. 1 , the processor may compare the post-processing profile to an experimental reference at 105. If the post-processing profile deviates from the convergence criteria of the experimental reference, a recalibration process may be initiated. The correlation of the plasma hyper-model and / or the feature-scale profile model may be adjusted. If the post-processing profile is within or equal to the convergence criteria, the calibration is complete, as shown at 106.

[0040] The convergence criterion can be that the cost is less than a user-set threshold. The cost is calculated based on the difference between the feature scale profile model's simulation results and an experimental reference. For example, for a bow critical dimension (CD), the experimental reference is 20 nm. The feature scale profile model gives 25 nm. The cost is calculated as a function of the difference (i.e., 25 nm - 20 nm). This difference can be multiplied by one or more factors, such as standard deviation or stochastic noise, as part of the function.

[0041] Adjustable parameters in the hypermodel can include, for example, linear and power coefficients for the assumed correlation between input and output parameters. Adjustable parameters in the feature-scale profile model can include, for example, surface reaction parameters (e.g., sticking coefficient, sputter yield, threshold energy, etc.) or plasma operating conditions (e.g., power, pressure, frequency, temperature, process time, process steps, etch recipe, etc.).

[0042] The experimental reference can be, for example, a TEM or XSEM. In addition to these TEM and XSEM images, other references can be, for example, critical dimensions at different heights, characteristic sizes (e.g., neck CD, bow CD, bottom CD, etch depth, mask remaining thickness, etc.), ideal profiles, or target profiles (e.g., rectilinear or anisotropic profiles).

[0043] If the post-processing profile is within or equal to the convergence criteria of the experimental reference, the calibration may be complete. The processor may send instructions to expose the wafer to plasma using plasma process conditions in the plasma processing apparatus.

[0044] Although a processor has been described for exemplary features of the method of FIG. 1 , it will be understood that such an arrangement should not be construed as limiting the invention to such features. The method may be implemented in software, firmware, hardware, or a combination thereof. In one aspect, the method is implemented in software as an executable program and executed by one or more special-purpose or general-purpose digital computer(s), such as a personal computer (e.g., an IBM-compatible, Apple-compatible, workstation, or mainframe computer). The method steps may be implemented by a server or computer on which the software modules reside or partially reside.

[0045] Generally, in terms of hardware architecture, as will be appreciated by those skilled in the art, such a computer includes a processor, memory, and one or more input and / or output (I / O) devices (or peripherals) communicatively coupled via a local interface. The local interface may be, for example, but not limited to, one or more buses or other wired or wireless connections, as known to those skilled in the art. The local interface may have additional elements, such as controllers, buffers (caches), drivers, repeaters, and receivers, to enable communication. Furthermore, the local interface may include address, control, and / or data connections to enable appropriate communication between other computer components.

[0046] The processor(s) can be programmed to perform the functions of the embodiment of Figure 1. The processor(s) are hardware devices for executing software, particularly software stored in a memory. The processor(s) can be a custom-made or commercially available processor, a main processing unit (CPU or GPU), a coprocessor among multiple processors associated with a computer, a semiconductor-based microprocessor (in the form of a microchip or chipset), a microprocessor, or generally any device for executing software instructions.

[0047] The memory is associated with the processor(s) and may include any one or combination of volatile memory elements (e.g., random access memory (RAM, such as DRAM, SRAM, SDRAM)) and non-volatile memory elements (e.g., ROM, hard drive, tape, CD-ROM, etc.). Furthermore, the memory may incorporate electronic, magnetic, optical, and / or other types of storage media. The memory may have a distributed architecture where various components are located remotely from each other but are still accessed by the processor(s).

[0048] The software in the memory may include one or more individual programs, each of which includes an ordered list of executable instructions for implementing logical functions to implement the functionality of a module. In the example above, the software in the memory includes one or more components of the method and is executable on a suitable operating system (O / S).

[0049] The present disclosure may include components provided as a source program, an executable program (object code), a script, or any other entity containing a set of instructions to be executed. In the case of a source program, the program must be converted via a compiler, assembler, interpreter, or the like, which may or may not be contained in memory, to operate properly in conjunction with the O / S. Furthermore, methodologies implemented in accordance with the present teachings may be expressed as (a) an object-oriented programming language having classes of data and methods, or (b) a procedural programming language having routines, subroutines, and / or functions, such as, but not limited to, C, C++, Pascal, Basic, Fortran, Cobol, Ped, Java, and Ada.

[0050] An additional embodiment relates to a non-transitory computer-readable medium storing program instructions executable on a processor to perform a computer-implemented method for calibrating plasma process conditions as disclosed herein. In particular, an electronic data storage unit or other storage medium may include the non-transitory computer-readable medium including program instructions executable on a processor. The computer-implemented method may include any step(s) of any method(s) described herein.

[0051] Each step of the method may be performed as described herein. The method may also include any other step(s) that may be performed by a processor and / or computer subsystem(s) or system(s) described herein. The steps may be performed by one or more computer systems that may be configured according to any of the embodiments described herein. Furthermore, the above-described method may be performed by any of the system embodiments described herein.

[0052] 2 is a block diagram of a system 200. The system 200 includes a plasma processing apparatus 206 having a plasma chamber 201, a stage 203 within the plasma chamber 201 that holds a wafer 202, and a plasma generation system 204. The plasma generation system 204 may be an RF plasma generation system, an inductively coupled plasma (ICP) generation system, or another type of ion source. The plasma processing apparatus 206 may be an ion implanter, such as an etcher, a deposition system, a plasma doping system, or other plasma processing apparatus. Ion implanters having a beam line with beam optics may also benefit from the embodiments disclosed herein.

[0053] The processor 205 is in electronic communication with other components of the plasma generating system 204 or plasma processing device 206. Although the processor 205 is illustrated as a single functional block for ease of explanation, in reality the processor 205 may include multiple interconnected processors with appropriate interfaces for receiving and outputting the signals shown in the figures and described herein.

[0054] The processor 205 may be part of the plasma processing device 206 or may be separate from the plasma processing device 206. For example, the processor 205 may be located on a system or other server within a semiconductor manufacturing facility. The processor 205 may be used offline from the plasma processing device 206.

[0055] The processor 205 may be programmed to perform some or all of the steps of the method of Figure 1. In this manner, the processor 205 may receive plasma process conditions and use the plasma hyper-model to determine plasma parameters at the surface of the wafer 202. The processor 205 may also be configured to input the plasma parameters into a feature-scale profile model and use the feature-scale profile model to predict a post-processing profile of the surface of the wafer 202.

[0056] The processor 205 may be configured to compare the post-processing profile to an experimental reference (e.g., a TEM image or an XSEM image). The processor 205 may also be configured to recalibrate the correlation of the plasma hypermodel if the post-processing profile falls outside the convergence criteria of the experimental reference.

[0057] If the post-processing profile is within the convergence criteria, or is within or equal to the convergence criteria, the processor 205 may optionally be configured to send instructions to the plasma processing device 206 to generate plasma in the plasma chamber 201 at plasma process conditions.

[0058] Although described in conjunction with plasma processing equipment, embodiments disclosed herein can be operated on or in conjunction with metrology, inspection, or review equipment. This can include optical-based, ion-beam-based, X-ray-based, or electron-beam-based systems. The ion-beam-based imaging subsystem can be a focused ion beam (FIB) system, a helium ion microscope (HIM) system, or a secondary ion mass spectrometry (SIMS) system. Such systems can be used to generate images of test wafers, including, for example, those having pre-processing profiles or references (e.g., pre-etch and post-etch profiles, pre-deposition and post-deposition profiles, or pre-implant and post-implant profiles) to be used for comparison with post-processing profiles.

[0059] The following examples are presented to illustrate the present disclosure and are not intended to be limiting.

[0060] Example 1

[0061] When using Ar / Cl plasma in a silicon etching process, the process conditions include pressure, power, pulse frequency, and duty cycle. The plasma parameters at the wafer surface that directly affect the etching profile include at least flux, energy, and angle. The empirical correlation between plasma parameters and process conditions is assumed as follows: Ion Flux: Flux イオン = a × pressure + b Fraction of energetic ion flux: fraction 高エネルギーイオン =c×power+d Fraction of low energy ion flux: fraction 低エネルギーイオン =1-fraction 高エネルギーイオン Radical Flux: Flux Cl = e × pressure + f High ion energy: Energy 高エネルギーイオン = g × power + h × pressure + i Low ion energy: Energy 高エネルギーイオン = j × power + k × pressure + l

[0062] The above equation can be expressed in the following matrix form:

number

[0063] The coefficients in matrix A and vector b can be adjusted to match experimental references. Contours of the correlations established based on the plasma hypermodel are shown in Figure 3. These correlations in the Ar / Cl plasma hypermodel were calibrated based on XSEM images from different process conditions using the iterative approach shown in Figure 1, along with the silicon etching mechanism developed in the feature-scale profile model (PROETCH from KLA).

[0064] Example 2

[0065] Self-aligned double patterning (SADP) is characterized by lithography at twice the desired pitch, followed by spacer deposition, spacer etch-back, and core etching processes. Double patterning and multi-patterning techniques scale technology nodes while posing challenges in spacer uniformity.

[0066] An example of a feature-scale profile model is PROETCH, developed by KLA. PROETCH is a three-dimensional, physics-based plasma dry etching simulator that describes the processes occurring during plasma etching processes, including the propagation of energetic and thermal species through the feature, physical and chemical sputtering of material, thermal etching, and surface passivation. Inputs can include etch recipes and incoming geometries. Outputs can include 3D etch profiles, local flux distributions in the feature layer, and surface composition. PROETCH can be integrated with PROLITH, a lithography simulator developed by KLA for process control.

[0067] Silicon can be etched by Ar / Cl plasma. The surface sites of the SADP can include hard mask (HM), Si, SiCl (collectively passivated surface states), and SiO (stop layer). The reaction mechanism can include: [Table 1]

[0068] Overlay metrology targets in DRAMs during shallow trench isolation (STI) etching, patterned using SADP, were investigated using PROETCH for shallow trench isolation masks. Each process introduces non-uniformities, resulting in, for example, variations in the hard mask used for the final etching step to form the gate. Optimization of the etch profile and etch process for specific plasma operating conditions was investigated. Mask sputtering, bowing, tapered front, and aspect ratio dependent etching can occur during STI etching.

[0069] In one study, a sensitivity analysis of the model was performed using a parametric study of the mechanism parameters. Physical sputtering primarily contributes to material removal at the bottom and etch front. Chemical sputtering affects both lateral etching at the sidewalls and vertical etching at the bottom. Chlorination promotes vertical etching because bare sites are converted to SiCl, which has a lower removal threshold. Parametric studies of plasma parameters (e.g., flux and energy) show the combined effect of multiple reactions with specific plasma parameters. Chlorine radicals contribute to chlorination and thermal etching (enhancing undercutting). Ions contribute to vertical etching and a linear profile. Increasing ion energy increases the number of ions above the threshold for both chemical and physical sputtering. Etch by-product redeposition can affect direct deposition when etch by-products are recaptured by the surface without desorbing from the feature. Etch by-product redeposition can affect indirect redeposition after interaction with the gas phase when etch by-products desorb from the feature, are sputtered by gas-phase species, and then deposited back into the feature. The angular yield curve (dependence of yield on incident ion angle) depends on factors such as ion energy, material type, surface roughness, etc. As the incident ion energy increases, the angular yield curve transitions from a shape resembling chemical sputtering (peak at normal incidence) to a shape resembling physical sputtering (peak at 60 degrees incidence).

[0070] Calibration was then performed using the method shown in FIG. 1 and described herein. The inputs were the process conditions, pre-processing profile, and post-processing profile (e.g., pre-etch and post-etch profiles). The reaction mechanism and plasma hypermodel were calibrated. The cost metric was the difference between the model-determined profile and the experimental profile. The PROETCH algorithm was used as the feature-scale profile model.

[0071] The pre-etch profile may be an SEM image that can show the hard mask formed by lithography, etching, and / or deposition. The pre-etch profile may be an actual experimental profile, but the pre-etch profile may also be a design image (desired profile).

[0072] A plasma hypermodel was used to correlate process conditions (e.g., power, pressure) with plasma parameters (e.g., flux, energy). Subset data was used for model calibration. Interpolation and extrapolation of the calibrated model were used as validation. A combination of conditions was selected to cover a wide range of parameters in two dimensions. Both characteristic sizes and critical dimensions were included in the cost with user-defined weights. Validation was performed at conditions different from the calibration set. Both interpolation and extrapolation (or hybrid) were used as validation conditions. The validation results showed good agreement with the experimental data for both characteristic sizes and critical dimensions.

[0073] Process optimization demonstrated forward and inverse problems. For the forward problem, output performance (e.g., etch rate, profile, selectivity) could be predicted under specific process conditions (e.g., power, pressure, frequency) by using a calibrated model. This reduces experimental trials and shortens development cycles. For the inverse problem, the search for process conditions for optimal etch performance achieved linear profiles, increased throughput, and minimized aspect ratio dependent etching.

[0074] Using the calibrated model, extrapolation in the time domain was performed with a fixed etch depth. End point detection (EPD) was used to stop the simulation after the etch front reached a preset depth. CD and profile can be visualized to select optimal process conditions.

[0075] The inverse solveability of the model can be demonstrated if the process conditions given by the model's inverse problem converge to the vicinity of the design of experiments (DOE) process performed to generate the target profile. A linear profile (uniform critical dimension) was used as the target / cost for optimizing the process conditions. With different time tolerances, the optimization converged to different conditions. The characteristic dimensions (bow and bottom CD) were used as indicators for optimizing the process recipe for the linear profile. A tolerance window was set to allow the profile to vary within the DOE tolerance range. PROETCH optimized the process conditions to close the gap in the bottom CD while maintaining the bow CD within the tolerance range.

[0076] A rigorous physics-based etching model (PROETCH) was developed and validated for the use case of STI etching in an SADP process. A reaction mechanism was developed based on XSEM images of DOE conditions for Si etching with Ar / Cl2 plasma. An empirical plasma hypermodel was implemented to correlate process conditions (e.g., power, pressure) with plasma parameters (e.g., flux, energy). PROETCH provided etch profiles for conditions interpolated or extrapolated over the DOE range and was used in process development to explore process conditions that could meet user-defined criteria for optimal etch performance.

[0077] Although the present disclosure has been described with respect to one or more particular embodiments, it will be understood that other embodiments of the present disclosure may be practiced without departing from the scope of the present disclosure. Accordingly, the present disclosure is deemed to be limited only by the appended claims and their reasonable interpretation.

Claims

1. 1. A method comprising: receiving plasma process conditions at a processor; using the processor to determine plasma parameters at the surface of the wafer based on the plasma process conditions using a plasma hypermodel; A method comprising:

2. The method of claim 1 , wherein the plasma process conditions include one or more of pressure, gas chemistry, temperature, flow rate, source power, bias power, source power, or pulse conditions.

3. inputting the plasma parameters into a feature scale profile model; using the processor to predict a post-processing profile of the surface of the wafer using the feature scale profile model; The method of claim 1 further comprising:

4. The method of claim 3 , further comprising using the processor to compare the processed profile to an empirical reference.

5. 5. The method of claim 4, further comprising recalibrating the correlation of the plasma hypermodel using the processor, wherein the processed profile falls outside the convergence criteria of the experimental reference.

6. The method of claim 4 , wherein the experimental reference is a TEM image or an XSEM image.

7. The method of claim 1 , wherein the plasma hyper-model comprises a matrix that is multiplied by the plasma process conditions.

8. The method of claim 1 , wherein the plasma conditions are for an etching process, a deposition process, or an ion implantation process.

9. The method of claim 1 , further comprising exposing the wafer to a plasma using the plasma process conditions in a plasma processing apparatus.

10. A non-transitory computer-readable medium storing a program configured to instruct the processor to perform the method of claim 1.

11. 1. A system comprising: A plasma processing apparatus, a plasma chamber; a stage disposed within the plasma chamber configured to hold a wafer; a plasma generation system; a plasma processing apparatus including: a processor in electronic communication with the plasma processing device, the processor comprising: receiving plasma process conditions; a processor configured to determine plasma parameters at the surface of the wafer based on the plasma process conditions using a plasma hypermodel; A system comprising:

12. The system of claim 11 , wherein the plasma processing device is an etching device, a deposition device, or an ion implantation device.

13. The system of claim 11 , wherein the plasma process conditions include one or more of pressure, gas chemistry, temperature, flow rate, source power, bias power, source power, or pulse conditions.

14. the processor: inputting the plasma parameters into a feature-scale profile model; The system of claim 11 , further configured to predict a post-processing profile of the surface of the wafer using the feature-scale profile model.

15. The system of claim 14 , wherein the processor is further configured to compare the processed profile to an empirical reference.

16. 16. The system of claim 15, wherein the processor is further configured to recalibrate the correlation of the plasma hypermodel, and the processed profile deviates from the convergence criteria of the experimental reference.

17. The system of claim 15 , wherein the experimental reference is a TEM image or an XSEM image.

18. The system of claim 11 , wherein the plasma hyper-model comprises a matrix that is multiplied by the plasma process conditions.

19. The system of claim 11 , wherein the processor is further configured to send instructions to the plasma processing device to generate a plasma at the plasma process conditions.

Images