CN-121986257-A - Optical and X-ray metrology methods for patterned semiconductor structures with randomness

CN121986257ACN 121986257 ACN121986257 ACN 121986257ACN-121986257-A

Abstract

Methods and systems for determining random variations in one or more structures on a sample are provided. A method includes determining a characteristic of an output generated by an output acquisition subsystem for a structure formed on a sample and simulating the characteristic of the output using initial parameter values of the structure. The method also includes determining a parameter value of the structure formed on the sample as the initial parameter value of the simulated characteristic that results in a best match with the determined characteristic. The determined parameter values are responsive to random variations in parameters of the structure on the sample.

Inventors

D. J. Hackston
D. Sang Ke
C. Liman
JIN RENJIAO
CHEN BOXUE
Pu Xiaoyuan
T.G. Chiura
Jin Luorun
H. Shu Ai Bu
ZHOU HONGZHI

Assignees

科磊股份有限公司

Dates

Publication Date: 20260505
Application Date: 20241030
Priority Date: 20240201

Claims (20)

1. A system configured for determining random variations in one or more structures formed on a sample, comprising: an output acquisition subsystem configured for generating an output of one or more structures formed on the sample, and A computer subsystem configured for: Determining one or more characteristics of the output generated for the one or more structures; Simulating the one or more characteristics of the output using initial parameter values of the one or more structures, and Parameter values of the one or more structures formed on the sample are determined as the initial parameter values of the simulated one or more characteristics that result in a best match to the determined one or more characteristics, wherein the determined parameter values are responsive to random variations of one or more parameters of the one or more structures on the sample.
2. The system of claim 1, wherein the one or more characteristics of the output are responsive to random variation of the one or more parameters of the one or more structures formed on the sample according to an arbitrary statistical distribution of random degrees of freedom that is parameterized a priori by a user and sampled by a quasi-random or pseudo-random distribution defining one superunit structure that is larger than the one or more structures or a collection thereof.
3. The system of claim 1, wherein the computer subsystem is further configured for determining an arbitrary statistical distribution by sampling the arbitrary statistical distribution with an orthogonal pair defined by a quasi-random or pseudo-random number including an aperiodic degree of freedom of the arbitrary characteristic, wherein the arbitrary characteristic includes one or more of a correlation and a non-gaussian distribution.
4. The system of claim 1, wherein the random variation of the one or more parameters is parameterized by one number for each of the one or more parameters for each of the one or more structures, and wherein the one number is any single parameter.
5. The system of claim 4, wherein the probability distribution describing the random variation is a gaussian distribution, a double gaussian distribution, a uniform distribution, a skewed gaussian distribution, or a poisson distribution.
6. The system of claim 4, wherein describing the randomly varying probability distribution includes a correlation predetermined a priori by a user such that one value of the arbitrary single parameter for each geometric critical dimension parameter of the one or more parameters is sufficient to describe a correlated multi-parameter distribution.
7. The system of claim 1, wherein the simulation is performed using a supercell model having any number of unit cells in x and y directions, and wherein x and y are nominal periodic directions of the structure.
8. The system of claim 7, wherein the simulation is further performed using a set of independent instances of the superunit model, and wherein the simulation comprises averaging results of the simulation of the set according to a weighted average formula.
9. The system of claim 8, wherein the arbitrary number of values of the unit cells in the x and y directions and a size of the set are automated to achieve a predetermined accuracy, a predetermined speed, a predetermined robustness, or a combination thereof, of the result of the simulation.
10. The system of claim 8, wherein the superunit model or the set is designed to describe long-range correlations in the random variation of the one or more parameters of the one or more structures formed on the sample.
11. The system of claim 1, wherein the simulating comprises simulating the output using a forward model configured for performing a regression technique.
12. The system of claim 1, wherein the computer subsystem is further configured for identifying a first one of the one or more characteristics of the output that is more responsive to the output of at least one of the parameter values than a second one of the one or more characteristics of the output, and wherein determining the one or more characteristics, simulating the one or more characteristics, and determining the parameter values are performed using only the first one of the one or more characteristics.
13. The system of claim 1, further comprising one or more components executed by the computer subsystem, wherein the one or more components comprise an electromagnetic solver configured for performing the simulation.
14. The system of claim 1, further comprising one or more components executed by the computer subsystem, wherein the one or more components comprise a model-based machine learning model configured for fitting the one or more characteristics of the output that vary as a function of the initial parameter values.
15. The system of claim 1, wherein the simulation is performed using a machine learning model trained using synthetic and real spectra, and wherein the real spectra are collected using selected samples such that a statistical distribution describing the random variation is determined per die on a training sample.
16. The system of claim 1, wherein the computer subsystem is further configured for determining a probability distribution describing the random variation by collecting electrical test results from a plurality of devices within one die on an additional sample and generating an electrical test gaussian distribution from the electrical test results.
17. The system of claim 1, wherein the output is responsive to x-rays from the sample, and wherein the one or more characteristics of the output include diffuse scattering and diffraction order intensity.
18. The system of claim 17, wherein the simulating comprises calculating diffuse and specular scatter in response to the random variations by averaging results of electromagnetic simulations of a set of superunit profiles, determining diffuse scatter from the average results, and determining diffuse scatter detector signals by interpolation of the determined diffuse scatter.
19. The system of claim 18, wherein the simulating further comprises determining a diffraction detector signal from the average result and determining a full detector signal by combining the diffuse scattering detector signal with the diffraction detector signal.
20. The system of claim 17, wherein determining the one or more characteristics comprises removing diffraction orders from the outputs to thereby extract the one of the outputs that is responsive only to the diffuse scattering.

Description

Optical and X-ray metrology methods for patterned semiconductor structures with randomness Technical Field The present invention generally relates to methods and systems for determining information of a sample. Certain embodiments relate to optical and x-ray metrology methods for patterned semiconductor structures with randomness. Background The following description and examples are not admitted to be prior art by inclusion in this section. Manufacturing semiconductor devices such as logic and memory devices typically involves processing a substrate (e.g., a semiconductor wafer) using a large number of semiconductor manufacturing processes to form various features and multiple levels of the semiconductor device. For example, photolithography is a semiconductor manufacturing process that involves transferring a pattern from a reticle to a resist 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. Multiple semiconductor devices may be fabricated in an arrangement on a single semiconductor wafer and then separated into individual semiconductor devices. The metrology process is used at various steps during the semiconductor manufacturing process to monitor and control the process. The metrology process is different from the inspection process in that, unlike the inspection process in which defects are detected on a sample, the metrology process is used to measure one or more characteristics of a sample that cannot be determined using currently used inspection tools. For example, metrology processes are used to measure one or more characteristics of a sample, such as the dimensions (e.g., line width, thickness, etc.) of features formed on the sample during the process, so that the performance of the process can be determined from the one or more characteristics. Additionally, if one or more characteristics of the sample are unacceptable (e.g., outside a predetermined range of characteristics), the measurement of the one or more characteristics of the sample may be used to alter one or more parameters of the process such that additional samples manufactured by the process have acceptable characteristics. The metrology process is also different from the defect inspection process in that, unlike the defect inspection process in which defects detected by inspection are revisited in defect inspection, the metrology process may be performed at locations where defects have not been detected. In other words, unlike defect inspection, the location where the metrology process is performed on the sample may be independent of the results of the inspection process performed on the sample. In particular, the location at which the metrology process is performed may be selected independently of the inspection results. In addition, since the location on the sample at which the metrology is performed may be selected independently of the inspection results, unlike defect inspection in which the location on the sample at which defect inspection is to be performed cannot be determined until the inspection results of the sample are generated and available for use, the location at which the metrology process is performed may be determined before the inspection process has been performed on the sample. Metering methods and tools may vary in hardware and/or software. In addition, the metering methods and tools may vary depending on what type of measurement they are to be used for. Because of the nature of semiconductor structures that currently require measurements for metrology and process control, some type of modeling is typically required to determine parameter values for the structure from measured outputs or signals. One particular challenge in creating a suitable metrology method or tool is finding a way to model imperfect structures that are imperfect in an unknown manner. In fact, imperfections are often a concern in metrology. Thus, the need to consider such imperfections in the metrology model can be critical to the production of metrology methods and tools. Some currently used methods for calculating any deviation of the measured signal from perfect correlation among unit cells in a target semiconductor structure for x-ray diffraction include the use of debye-waler (DW) factors, which gives an empirical equation describing how randomness attenuates the scattering intensity. This approach cannot directly correlate DW factor values with complex geometry randomness values (e.g., CD sigma or slope sigma). This approach does not predict diffuse scattering for any context and only can predict certain simple contexts. Another currently used method involves the use of an active dielectric layer. However, such methods do not predict diffuse scattering. An additional approach is to use Born (Born) or a Distorted Wave Born Approximation (DWBA). This approach suffers from the deficie