Model-based acousto-optic depth metrology of sample

Abstract

A method for lossless depth profiling includes projecting a pulsed pump beam into a sample, projecting a pulsed probe beam into the sample, and sensing light returning from the sample to obtain a measurement signal. Each probe pulse is configured to undergo Brillouin scattering from the primary acoustic pulse caused by a directly preceding pump pulse so as to scatter from the primary acoustic pulse at a respective depth within the sample. The method further includes executing an optimization algorithm configured to receive as an input a measurement signal and / or a processed signal obtained from the measurement signal, and outputting a value characterizing the structural parameter (s) of the sample by minimizing a cost function indicative of a difference between the measurement signal and an analog signal obtained using a forward model that simulates scattering of the pulsed probe beam from at least the primary acoustic pulse.

Description

Technical Field

[0001] The present disclosure generally relates to non-destructive metrology of samples. Background Art

[0002] As design rules shrink, process control of semiconductor samples becomes increasingly complex due to the need to perform metrology on smaller and smaller structures. Current state-of-the-art non-destructive techniques for semiconductor sample metrology primarily rely on scanning electron microscopy, optical critical dimension (OCD) scatterometry, and / or small-angle X-ray scattering (SAXS). While each of these techniques has its own advantages, there remains an unmet need in the art for fast, non-destructive techniques for semiconductor sample metrology that offer increased accuracy. Summary of the Invention

[0003] According to some embodiments of the present disclosure, aspects of the present disclosure relate to non-destructive metrology of samples. More particularly, but not exclusively, according to some embodiments of the present disclosure, aspects of the present disclosure relate to non-destructive acousto-optic based depth metrology of semiconductor samples.

[0004] Therefore, according to one aspect of some embodiments, a method for non-destructive acousto-optic depth measurement of a sample is provided. The method comprises the following operations:

[0005] - Projecting a pulsed pump beam into the sample to be analyzed: each pump pulse in the pulsed pump beam is configured to be absorbed in the analyzed sample so as to cause the formation of at least a corresponding primary acoustic pulse propagating within the analyzed sample.

[0006] - Projecting a pulsed probe beam into the analyzed sample: each probe pulse in the pulsed probe beam is configured to undergo Brillouin scattering from a primary acoustic pulse at a corresponding depth within the analyzed sample, the Brillouin scattering being caused by a corresponding pump pulse directly preceding the probe pulse, so as to probe the analyzed sample over at least one depth range (i.e., the depths at which the probe pulses are respectively scattered from the primary acoustic pulse).

[0007] - obtaining a measurement signal by sensing light comprising a portion of the pulsed probe beam returning from the profiled sample.

[0008] - subjecting the measurement signal to processing to obtain a processed signal.

[0009] - executing an optimization algorithm configured to (i) receive as input the processed signal and (ii) output a set of structural parameters characterizing the profiled sample by minimizing a cost function indicative of the difference between the processed signal and a simulated signal obtained using a forward model that simulates scattering of a probe pulse from at least the primary acoustic pulse.

[0010] According to some embodiments of the method, in each iteration of the optimization algorithm, the optimization algorithm updates a guess for a set of structural parameters and updates the simulation signal based on the guess.

[0011] According to some embodiments of the method, the sample includes a through-hole extending from a top surface of the sample into the sample, each of the pump beam and the probe beam is projected onto the top surface, and a set of structural parameters at least partially characterizes an average geometry of the through-hole.

[0012] According to some embodiments of the method, a set of structural parameters quantifies at least the dependence of the average area of ​​the through-holes on the depth within the profiled sample.

[0013] According to some embodiments of the method, the depth of the through-hole is at least about 1 μm.

[0014] According to some embodiments of the method, the wavelength of the probe pulse is at least about two times greater than a nominal distance between adjacent vias.

[0015] According to some embodiments of the method, each of the pump pulses is configured to be absorbed in an absorbing slice of the profiled sample such that after formation of the primary acoustic pulse each of the primary acoustic pulses propagates away from the absorbing slice.

[0016] According to some embodiments of the method, the profiled sample consists of a single material.

[0017] According to some embodiments of the method, the profiled sample includes a plurality of layers, the plurality of layers including an absorbing layer and at least one other layer including an absorbing slice, such that, in addition to each primary acoustic pulse, a corresponding secondary acoustic pulse is formed as a result of partial reflection of the primary acoustic pulse from a boundary between adjacent layers. The forward model additionally accounts for the formation of the secondary acoustic pulses by additionally simulating scattering of the probe pulse from at least some of the secondary acoustic pulses.

[0018] According to some embodiments of the method, the absorbent slice consists of a top sub-layer (segment) of the bulk, on top of which a layered structure comprising the rest of the layers is arranged.

[0019] According to some embodiments of the method, the body is made of or includes silicon, and / or the remainder of the layer is composed of, made of and / or includes silicon oxide, silicon germanium, silicon nitride, an oxide-nitride-oxide (ONO) mixture stack, and / or a combination and / or mixture of the above.

[0020] According to some embodiments of the method, pump pulses and probe pulses are projected alternately.

[0021] According to some embodiments of the method, each of the probe pulses is delayed relative to an immediately preceding pump pulse by a respective time delay, the time delays being varied so as to facilitate probing the profiled sample over at least one depth range.

[0022] According to some embodiments of the method, the layered structure includes at least two layers. The time delay is varied such that some of the probe pulses are first scattered from the primary acoustic pulse, respectively, within a top layer of the layered structure, and other of the probe pulses are first scattered from the primary acoustic pulse, respectively, within a bottom layer of the layered structure, the bottom layer being adjacent to the absorbing layer.

[0023] According to some embodiments of the method, the frequency of the probe pulse is such that the profiling sample is substantially transparent to the probe pulse.

[0024] According to some embodiments of the method, the pump beam is a laser beam and / or the probe beam is a laser beam.

[0025] According to some embodiments of the method, the pump beam and the probe beam originate from the same laser source.

[0026] According to some embodiments of the method, wherein the profiled sample comprises a through hole, in the forward model the profiled sample is simulated by a laterally uniform sample having a refractive index n(z) equal to an effective refractive index n of the profiled sample as predetermined based on at least reference data related to the profiled sample. eff (z).

[0027] According to some embodiments of the method, the initial guess input into the forward model in a first iteration of the optimization algorithm is derived taking into account at least reference data of the profiled sample and / or previously obtained calibration data related to the profiled sample.

[0028] According to some embodiments of the method, in the forward model, each of the simulated acoustic pulses is modeled by a semi-transparent mirror traveling at the local speed of sound.

[0029] According to some embodiments of the method, the forward model is derived using an optical transfer matrix method.

[0030] According to some embodiments of the method, the values ​​of the model parameters of the forward model are tuned using machine learning techniques based at least on reference data of the profiled sample.

[0031] According to some embodiments of the method, the reference data includes design data of the profiled sample and / or ground truth data of samples having the same or similar design intent as the profiled sample.

[0032] According to some embodiments of the method, the calibration data is obtained by performing the operations of projecting a pulsed pump beam, projecting a pulsed probe beam, and sensing light returned from the profiled sample with respect to one or more scribe lines of the profiled sample.

[0033] According to some embodiments of the method, the method further comprises an initial operation of calibrating model parameter values ​​of the forward model based on the calibration data.

[0034] According to some embodiments of the method, the cost function is a sum of squares and the optimization algorithm is a Levenberg-Marquardt algorithm.

[0035] According to some embodiments of the method, the processed signal is indicative of a contribution of Brillouin oscillations to the measurement signal.

[0036] According to some embodiments of the method, the processing signal quantifies at least a dependence of the Brillouin frequency and / or the Brillouin amplitude of the Brillouin oscillations on the (scattering) depth within the profiled sample.

[0037] According to some embodiments of the method, in which the pump beam and the probe beam originate from the same laser source, the envelope of the pump beam is amplitude modulated, and in order to obtain the processing signal or as part of obtaining the processing signal, the measurement signal is demodulated using a lock-in amplifier, which is fed with the modulation frequency of the envelope.

[0038] According to some embodiments of the method, when obtaining the processed signal, the thermo-optical contribution to the measurement signal is removed.

[0039] According to some embodiments of the method, the pump pulse has a different wavelength than the probe pulse, and an optical filter is used to filter out a return component of the pump beam when obtaining the measurement signal.

[0040] According to some embodiments of the method, the profiled sample is or includes a V-NAND, a DRAM, or a 3D DRAM, or a preliminary structure at an intermediate manufacturing stage of a V-NAND, a DRAM, or a 3D DRAM.

[0041] According to some embodiments of the method, the profiled sample is or forms part of a preliminary structure of a patterned wafer or is at an intermediate fabrication stage of a patterned wafer.

[0042] According to some embodiments of the method, wherein (i) the profiled sample includes vias, wherein (ii) in executing the optimization algorithm, an initial guess is input into the optimization algorithm, and wherein (iii) a set of structural parameters quantifies the dependence of an average area of ​​the vias on depth within the profiled sample, to obtain the initial guess, a short-time Fourier transform (STFT) is applied to the processed signal to extract a preliminary estimate of the dependence of the Brillouin frequency on the time delay. Based on the preliminary estimate of the dependence of the Brillouin frequency on the time delay, the dependence of the average area of ​​the vias on the depth is extracted.

[0043] According to some embodiments of the method, wherein the profiled sample comprises a plurality of layers, an iterative process is applied to obtain an initial guess, wherein the processed signal is modeled by a sinusoidal series whose terms correspond to respective contributions to the processed signal from Brillouin scattering of the primary acoustic pulse and at least some of the secondary acoustic pulses within each of the layers.

[0044] According to some embodiments of the method, a set of structural parameters comprises a plurality of sub-sets of structural parameters, such that each sub-set of structural parameters comprises a set of non-overlapping vertical increments {Δz i} i At least one vertical localization parameter related to one of i is the i-th vertical increment Δz within the sample i The height of (the index in curly brackets is used to indicate that the index is generally a running index). i Each of the executions starts at z1 and proceeds sequentially upwards, so that at the i-th execution, the optimization algorithm (i) receives as input the following: i =∑ j≤i Δz j / v s (z j ) of the processed signal, where v s (z j ) represents the area around z j speed of sound, and / or until time t i The method comprises the steps of: (i) determining a processed signal derived from the measurement signal and, optionally, any previously obtained value of at least one vertical localization parameter, and (ii) outputting a corresponding value of the at least one vertical localization parameter.

[0045] According to some embodiments of the method, the operation of subjecting the measurement signal to processing comprises, as a subsequent sub-operation, applying a bridge architecture to the initial processed signal, thereby obtaining a (final) processed signal. The initial processed signal is a product of all sub-operations of the operation of subjecting the measurement signal to processing that precedes the subsequent sub-operation.

[0046] According to one aspect of some embodiments, a system for non-destructive acousto-optic depth measurement of a structure is provided. The system comprises:

[0047] - (Acousto-optical) measurement setup for:

[0048] ■ Projecting a pulsed pump beam onto the sample to be profiled such that each pump beam of the pulsed pump beam is absorbed in the profiled sample and causes the formation of at least a corresponding primary acoustic pulse that propagates within the profiled sample.

[0049] ■ Projecting a pulsed probe beam into the analyzed sample such that each probe pulse in the pulsed probe beam undergoes Brillouin scattering from a primary acoustic pulse at a corresponding depth within the analyzed sample, the Brillouin scattering being caused by a corresponding pump pulse directly preceding the probe pulse, so as to detect the analyzed sample over at least one depth range (i.e., the depths at which the probe pulses are respectively scattered from the primary acoustic pulse).

[0050] ■ The measurement signal is obtained by sensing light comprising a portion of the pulsed probe beam returning from the profiled sample.

[0051] - a processing circuit system for executing an optimization algorithm configured to (i) receive as input a processed signal derived from the measurement signal, and (ii) output a set of structural parameters characterizing the analyzed sample by minimizing a cost function indicative of the difference between the processed signal and a simulated signal obtained using a forward model that simulates scattering of a probe pulse from at least a primary acoustic pulse.

[0052] According to some embodiments of the system, the processing circuitry is further configured to derive the processed signal from the measurement signal.

[0053] According to some embodiments of the system, the optimization algorithm is configured to update a guess for a set of structural parameters after each iteration of the optimization algorithm, and to update the simulation signal based on the guess.

[0054] According to some embodiments of the system, a measurement setup includes a light generating device and at least one light sensor. The light generating device is configured to generate a pulsed pump beam and a pulsed probe beam. The at least one light sensor is configured to measure an intensity of light incident on the at least one light sensor, thereby obtaining a measurement signal.

[0055] According to some embodiments of the system, at least one light sensor is configured to sense light from the profiled sample in each of a plurality of optical modes specified by one or more of wavelength and polarization.

[0056] According to some embodiments of the system, the at least one light sensor comprises a plurality of light sensors and / or a light sensor array.

[0057] According to some embodiments of the system, the measurement setup further comprises a controller configured to command and coordinate the operation of components of the measurement setup.

[0058] According to some embodiments of the system, the pump beam is a laser beam and / or the probe beam is a laser beam.

[0059] According to some embodiments of the system, the light generating device comprises a laser source, and each of the pump beam and the probe beam originates from the laser source.

[0060] According to some embodiments of the system, the light generating device further comprises an optical modulator configured to amplitude modulate the pump light beam, and the processing circuitry comprises a lock-in amplifier configured to demodulate the measurement signal using the modulation frequency of the pump light beam to obtain the processing signal or as part of obtaining the processing signal.

[0061] According to some embodiments of the system, the modulation frequency of the pump beam is less than about 10 MHz.

[0062] According to some embodiments of the system, the sample includes a through-hole extending from a top surface of the sample into the sample. The measurement setup is configured to project each of the pump beam and the probe beam onto the top surface. A set of structural parameters at least partially characterizes an average geometry of the through-hole.

[0063] According to some embodiments of the system, a set of structural parameters quantifies at least a dependence of an average area of ​​the through-holes on a depth within the profiled sample.

[0064] According to some embodiments of the system, the depth of the through-hole is at least about 1 μm.

[0065] According to some embodiments of the system, the wavelength of the probe pulse is at least about two times greater than a nominal distance between adjacent vias.

[0066] According to some embodiments of the system, each of the pump pulses is configured to be absorbed in an absorbing slice of the profiled sample such that after formation of the primary acoustic pulse each of the primary acoustic pulses propagates away from the absorbing slice.

[0067] According to some embodiments of the system, the profiled sample consists of a single material.

[0068] According to some embodiments of the system, the profiled sample includes a plurality of layers, the plurality of layers including an absorbing layer and at least one other layer including an absorbing slice, such that, in addition to each primary acoustic pulse, a corresponding secondary acoustic pulse is formed as a result of partial reflection of the primary acoustic pulse from a boundary between adjacent layers. The forward model additionally accounts for the formation of the secondary probe pulses by additionally simulating scattering of a pulsed probe beam from at least some of the secondary acoustic pulses.

[0069] According to some embodiments of the system, the absorbent slice consists of a top sublayer of the body, on top of which a layered structure comprising the rest of the layers is arranged.

[0070] According to some embodiments of the system, the body is made of or includes silicon, and / or the remainder of the layer is composed of, made of and / or includes silicon oxide, silicon germanium, silicon nitride, an oxide-nitride-oxide (ONO) mixture stack, and / or a combination and / or mixture of the above.

[0071] According to some embodiments of the system, the measurement setup is configured to alternately project pump pulses and probe pulses.

[0072] According to some embodiments of the system, the measurement setup is configured to delay each probe pulse by a controllably variable time interval relative to an immediately preceding pump pulse so as to facilitate probing the profiling sample over at least one depth range.

[0073] According to some embodiments of the system, wherein profiling the sample includes a layered structure mounted on top of a body including an absorbing slice, and the layered structure includes at least two layers, the time interval is varied such that some of the probe pulses are first scattered from the primary acoustic pulse, respectively, within a top layer of the layered structure, and other of the probe pulses are first scattered from the primary acoustic pulse, respectively, within a bottom layer of the layered structure, the bottom layer being adjacent to the absorbing layer.

[0074] According to some embodiments of the system, the frequency of the probe pulse is such that the layered structure is substantially transparent to the probe pulse.

[0075] According to some embodiments of the system, in the forward model, the profiled sample is simulated by a laterally uniform sample whose refractive index n(z) is equal to the effective refractive index n(z) of the profiled sample as predetermined based on reference data related to the profiled sample. eff (z).

[0076] According to some embodiments of the system, the initial guess input into the forward model in a first iteration of the optimization algorithm is derived taking into account at least reference data of the profiled sample and / or previously obtained calibration data related to the profiled sample.

[0077] According to some embodiments of the system, the reference data includes design data of the profiled sample and / or ground truth data of samples having the same or similar design intent as the profiled sample.

[0078] According to some embodiments of the system, in the forward model, each of the simulated acoustic pulses is modeled by a semi-transparent mirror traveling at the local speed of sound.

[0079] According to some embodiments of the system, the forward model is derived using an optical transfer matrix method.

[0080] According to some embodiments of the system, the tuned values ​​of the model parameters of the forward model are obtained by applying a machine learning tool to reference data of at least the profiled sample.

[0081] According to some embodiments of the system, at least some of the calibration data is obtained by depth profiling one or more scribes of a profiled sample using the system.

[0082] According to some embodiments of the system, at least some model parameters of the forward model are obtained based on or also based on calibration data of the profiled sample.

[0083] According to some embodiments of the system, the cost function is a sum of squares and the optimization algorithm is a Levenberg-Marquardt algorithm.

[0084] According to some embodiments of the system, the processed signal is indicative of a contribution of Brillouin oscillations to the measurement signal.

[0085] According to some embodiments of the system, the processed signal quantifies at least a dependence of a Brillouin frequency and / or a Brillouin amplitude of the Brillouin oscillations on a (scattering) depth within the profiled sample.

[0086] According to some embodiments of the system, the processing circuitry is configured to remove thermo-optical contributions to the measurement signal as part of obtaining the processed signal.

[0087] According to some embodiments of the system, the measurement setup further comprises an optical filter configured to filter out a return component of the pump light beam.

[0088] According to some embodiments of the system, the profiled sample is or includes a V-NAND, DRAM, or 3D DRAM, or a preliminary structure at an intermediate manufacturing stage of a V-NAND, DRAM, or 3D DRAM.

[0089] According to some embodiments of the system, the profiled sample is or forms part of a preliminary structure of a patterned wafer or is at an intermediate fabrication stage of a patterned wafer.

[0090] According to some embodiments of the system, in which a set of structural parameters quantifies the dependence of the average area of ​​the through-holes on the depth within the profiled sample in order to obtain an initial guess of the dependence of the average area of ​​the through-holes on the depth within the profiled sample, the processing circuit system is configured to apply a short-time Fourier transform (STFT) to the processed signal to extract a preliminary estimate of the dependence of the Brillouin frequency on the time delay.

[0091] According to some embodiments of the system, wherein the profiled sample comprises a plurality of layers, to obtain the initial guess, the processing circuitry is configured to apply an iterative process whereby the processed signal is modeled by a sinusoidal series whose terms correspond to respective contributions to the processed signal from Brillouin scattering of the primary acoustic pulse and at least some of the secondary acoustic pulses within each of the layers.

[0092] According to some embodiments of the system, a set of structural parameters comprises a plurality of sub-sets of structural parameters such that each sub-set of structural parameters comprises a set of non-overlapping vertical increments {Δz i} i At least one vertical localization parameter related to one of i is the i-th vertical increment Δz within the sample i The processing circuit system is configured to i Each of the optimisation algorithms executes, starting at z1 and proceeding sequentially upwards, such that at the i-th execution, the optimisation algorithm (i) receives as input the following: i =∑ j≤i Δz j / v s (z j ) processing signal, where v s (z j ) represents the area around z j speed of sound, and / or until time t i The method comprises the steps of: (i) determining a processed signal derived from the measurement signal and, optionally, any previously obtained value of at least one vertical localized parameter, and (ii) outputting a corresponding value of the at least one vertical localized parameter.

[0093] According to some embodiments of the system, the processing circuitry is configured to apply a bridging architecture to the initial processed signal as part of obtaining the processed signal.The initial processed signal is obtained by initially processing the measurement signal.

[0094] According to one aspect of some embodiments, a non-transitory computer-readable storage medium is provided, wherein the storage medium stores instructions for causing a system for non-destructive acousto-optic depth metrology of structures (such as the system described above) to perform the method described above on a (profiling) sample.

[0095] According to one aspect of some embodiments, a non-transitory computer-readable storage medium is provided. The storage medium stores instructions that cause one or more processors to execute an optimization algorithm configured to (i) receive as input a processed signal derived from a measurement signal associated with an analyzed sample, and (ii) output a set of structural parameters characterizing the analyzed sample. The measurement signal is obtained by:

[0096] Projecting a pulsed pump beam into the sample to be analyzed: each pump pulse in the pulsed pump beam is configured to be absorbed in the sample to be analyzed so as to induce formation of at least a corresponding primary acoustic pulse that propagates within the sample. Projecting a pulsed probe beam into the sample to be analyzed: each probe pulse in the pulsed probe beam is configured to undergo Brillouin scattering from the primary acoustic pulse at a corresponding depth within the sample to be analyzed, the Brillouin scattering being caused by the corresponding pump pulse immediately preceding the probe pulse, so as to probe the sample over at least one depth range.

[0097] - sensing light comprising a portion of the pulsed probe beam returning from the profiled sample.

[0098] The optimization algorithm involves minimizing a cost function indicative of the difference between the processed signal and a simulated signal obtained using a forward model that simulates scattering of a probe pulse from at least the primary acoustic pulse.

[0099] Certain embodiments of the present disclosure may include some, all, or none of the above advantages. One or more other technical advantages may be apparent to those skilled in the art from the accompanying drawings, description, and claims. Furthermore, although specific advantages have been enumerated above, various embodiments may include all, some, or none of the enumerated advantages.

[0100] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure relates. In the event of a conflict, the patent specification (including definitions) shall prevail. As used herein, the indefinite articles "a" and "an" mean "at least one" or "one or more" unless the context clearly indicates otherwise.

[0101] Unless otherwise specifically stated, as will be apparent from this disclosure, it will be understood that, according to some embodiments, terms such as "processing," "computing," "calculating," "determining," "estimating," "assessing," "gauging," and the like may refer to the actions and / or procedures of a computer or computing system, or similar electronic computing device, that manipulate and / or transform data represented as physical (e.g., electronic) quantities within the computing system's registers and / or memory into other data similarly represented as physical quantities within the computing system's memory, registers, or other such information storage, transmission, or display devices.

[0102] Embodiments of the present disclosure may include devices for performing the operations herein. Devices may be specially constructed for specific purposes, or may include general-purpose computers selectively activated or reconfigured by computer programs stored in (multiple) general-purpose computers. Such computer programs may be stored in computer-readable storage media, such as, but not limited to, any type of disk, including floppy disks, optical disks, CD-ROMs, magneto-optical disks, read-only memories (ROMs), random access memories (RAMs), electrically programmable read-only memories (EPROMs), electrically erasable programmable read-only memories (EEPROMs), magnetic or optical cards, flash memory, solid-state disks (SSDs), or any other type of medium suitable for storing electronic instructions and capable of being coupled to a computer system bus.

[0103] The program and display proposed herein are essentially independent of any specific computer or other equipment. Various general-purpose systems can be used together with the program according to the present invention, or it can be confirmed that it is convenient to construct a more specialized device to perform (a plurality of) desired methods. (A plurality of) desired structures of various these systems are apparent from the following description. In addition, the embodiments of the present disclosure are not described with reference to any specific programming language. It will be appreciated that various programming languages ​​can be used to implement the teachings of the present disclosure as described herein.

[0104] Aspects of the present disclosure may be described in the general context of computer-executable instructions (such as program modules) executed by a computer. Generally speaking, program modules include routines, programs, objects, components, data structures, etc. that perform specific tasks or implement specific abstract data types. The disclosed embodiments may also be practiced in a distributed computing environment, where tasks are performed by remote processing devices linked through a communication network. In a distributed computing environment, program modules may be located in local and remote computer storage media (including memory storage devices). BRIEF DESCRIPTION OF THE DRAWINGS

[0106] Certain embodiments of the present disclosure are described herein with reference to the accompanying drawings. The description, along with the accompanying drawings, makes it clear to one skilled in the art how certain embodiments may be practiced. The accompanying drawings are for illustrative purposes only and are not intended to illustrate the structural details of the embodiments in more detail than is necessary for a basic understanding of the present disclosure. For clarity, some objects depicted in the drawings are not drawn to scale. Furthermore, two different objects in the same drawing may be drawn at different scales. Specifically, the scale of some objects may be greatly exaggerated compared to other objects in the same drawing.

[0107] The patent or application file contains at least one drawing printed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.

[0108] In the attached figure:

[0109] Figure 1 A flow chart of a computer-implemented method for non-destructive acousto-optic depth metrology of a structure is presented, according to some embodiments.

[0110] Figures 2A to 2D Schematically depicts the Figure 1 Some embodiments of the method Figure 1 The method is applied to different stages of the structure.

[0111] Figure 3A and Figure 3B Schematically depicts the Figure 1 Some embodiments of the method Figure 1 The method is applied to different stages of the structure.

[0112] Figure 4 is based on Figure 1 Flowchart of some embodiments of the method of measuring data processing operations for determining a set of structural parameters of a structure, the measuring data processing operations corresponding to Figure 1 A specific embodiment of a method of measuring data processing operations.

[0113] Figure 5A Describes the basis Figure 1 Some embodiments of the method of bridging an analog gap between an analog signal and an actual signal by implementing an encoder-decoder-based computing architecture Figure 1 The measurement data obtained by the measurement operation of the method are derived.

[0114] Figure 5B Depicts a system configured for training according to some embodiments Figure 5A The autoencoder of the encoder.

[0115] Figure 5C Depicts a method for training according to some embodiments Figure 5A The decoder of the autoencoder.

[0116] Figure 6 A flow chart of a computer-implemented method for non-destructive acousto-optic depth metrology of a layered structure is presented, the method corresponding to Figure 1 A specific embodiment of the method.

[0117] Figures 7A to 7G Schematically depicts the Figure 6 Some embodiments of the method Figure 6 The method is applied at different stages of the hierarchical structure.

[0118] Figure 8A graphical representation of the scattering of a probe pulse from an acoustic pulse within a hierarchical structure in the context of a forward model is provided, in accordance with some embodiments, where each acoustic pulse is modeled by a semi-transparent mirror traveling at the local speed of sound.

[0119] Figure 9 is an example according to some embodiments Figure 8 Time-depth plot of the formation and propagation of an acoustic pulse in the forward model.

[0120] 10A to 10C Schematically depicts the Figure 6 Some embodiments of the method Figure 6 The method is applied at different stages of the hierarchical structure.

[0121] Figure 11 Describes the basis Figure 6 In some embodiments of the method, the voltage signal is varied according to Figure 6 The method is projected on 10A to 10C The layered structure varies with the time delay Δt between successive probe pulses and the directly preceding pump pulse.

[0122] Figure 12 A computerized system for non-destructive acousto-optic depth metrology according to some embodiments is presented.

[0123] Figure 13 A computerized system for non-destructive acousto-optic depth metrology is presented, the computerized system corresponding to Figure 12 A specific embodiment of the system. DETAILED DESCRIPTION

[0124] The principles, uses, and implementations of the teachings herein may be better understood with reference to the accompanying description and drawings. After reading the description and drawings presented herein, those skilled in the art will be able to implement the teachings herein without undue effort or experimentation. In the accompanying drawings, like reference numerals refer to like parts throughout.

[0125] State-of-the-art non-destructive techniques for semiconductor sample metrology rely primarily on scanning electron microscopy, optical critical dimension (OCD) scatterometry, or small-angle X-ray scattering (SAXS). Scanning electron microscopy allows for high-resolution (two-dimensional) imaging of the top surface of a sample (e.g., a semiconductor sample), but can be poor at detecting or distinguishing subsurface structural features and deeply buried portions. In contrast, OCD scatterometry is generally sensitive to buried structural features (assuming the sample is optically transparent), but often fails to characterize buried structures: if two or more parameters of a buried structure change simultaneously, OCD scatterometry may not be able to distinguish them. For example, as long as the optical path length traversing the light beam remains constant (e.g., if the size and refractive index of the buried structure change simultaneously), no changes will be detected.

[0126] Recently, a novel non-destructive depth metrology method has been developed. The method is based on inducing an acoustic pulse within the sample and Brillouin scattering of a pulsed probe beam from the acoustic pulse. The acoustic pulse is caused by localized heating of the sample due to absorption of a pulsed pump beam projected on the sample. The measurement signal is obtained by sensing the return portion of the probe beam. The measurement signal can be analyzed to extract features that characterize the excited (Brillouin) oscillations, such as the Brillouin frequency shift or the amplitude of the Brillouin oscillations. The extracted features can be analyzed to determine the structural parameters of the sample.

[0127] The present application advantageously discloses an improved technique for analyzing a measurement signal based on an optimization involving a forward model. The forward model simulates the scattering of a probe pulse from an induced acoustic pulse. In addition, the present application teaches how to account for multiple scattering events of a single probe pulse. More specifically, in a layered structure, an induced first acoustic pulse (called a "primary") can then induce multiple secondary acoustic pulses by partial reflections of the first acoustic pulse from the boundaries between adjacent layers. A single probe pulse will thereby be scattered not only from the primary acoustic pulse (Brillouin), but also from the secondary acoustic pulse (Brillouin), which will appear as additional oscillatory contributions to the measurement signal. These additional contributions make the extraction of features (such as the Brillouin frequency shift or the amplitude of the Brillouin oscillations) more challenging. The present application discloses various methods of using a forward model to address this challenge. Finally, the present application discloses ways in which the parameters of the forward model can be calibrated using scribing data.

[0128] In order to make the description clearer, certain symbols (e.g., letters) may be used throughout the description specifically to mark specific types of parameters and / or quantities. For example, the letter v is used to represent the speed of sound within the sample (or the local speed of sound when the sample is inhomogeneous), and the letter u is used to represent the depth within the sample or the scattering depth within the sample (e.g., the depth of Brillouin scattering of an acoustic pulse propagating from the sample by a probe pulse). The symbol, F, is used to represent the formation of an acoustic pulse within the sample due to the absorption of an (optical) pump pulse within the sample. The symbol Δt is used to represent the time interval by which the incidence of the (optical) probe pulse on the sample is delayed relative to the incidence of the immediately preceding pump pulse. Such symbols should not be interpreted as being associated with the specific embodiment in which they are first introduced in the text. That is, the use of such symbols in the context of one embodiment does not carry over to another embodiment unless it is implicit from the text that the properties being described are general. Specifically, for example, in the context of the first embodiment, "speed of sound v", "depth u", "formation time T" may be introduced. F " and "time delay Δt", which may subsequently be referred to as "sound speed v", "depth u", "formation time, F", and "time delay Δt" (or simply "v" and "u", respectively) in the description of the first embodiment. Thereafter, in the context of the second embodiment, "sound speed v", "depth u", "formation time, F", and "time delay Δt" may be reintroduced, and unless otherwise stated or implied, properties described in the context of the first embodiment are not assumed to be relevant in the context of the second embodiment.

[0129] method

[0130] Figure 1 A flow chart of a method 100 for non-destructive acousto-optic depth metrology of a structure is presented, according to some embodiments. The method 100 includes:

[0131] Operation 110, wherein a pulsed pump beam is projected into a (profiled) sample comprising a structure to be tested. Each of the pump pulses in the pulsed pump beam is configured to be absorbed in the sample so as to induce the formation of at least a corresponding primary acoustic pulse that propagates within the test structure.

[0132] An operation 120 is provided in which a pulsed probe beam is projected into the sample. Each probe pulse in the probe beam is configured to undergo Brillouin scattering from a primary acoustic pulse at a corresponding depth within the sample, the Brillouin scattering being caused by a corresponding pump pulse immediately preceding the probe pulse, such that the sample is probed over at least a range of depths.

[0133] - Operation 130, wherein a measurement signal is obtained by measuring the intensity of light comprising a portion of the pulsed probe beam returning from the sample.

[0134] - Operation 140, wherein the measurement signal is subjected to processing to obtain a processed signal.

[0135] Operation 150, wherein an optimization algorithm is executed. The optimization algorithm is configured to (i) receive at least the processed signal as input, and (ii) output a set of structural parameters characterizing the test structure by minimizing a cost function indicative of a difference between the processed signal and a simulated signal. The simulated signal is obtained using a forward model that simulates scattering of a probe pulse from at least a primary acoustic pulse within the test structure.

[0136] In each iteration of the optimization algorithm, the optimization algorithm updates a guess for a set of structural parameters and updates the simulation signal based on the guess.

[0137] Method 100 can be used as follows Figure 12 and Figure 13 It can be implemented by any of the systems described in the description or a system similar thereto.

[0138] According to some embodiments, the test structure is or includes one or more semiconductor materials. According to some embodiments, the test structure is disposed on a body (e.g., a silicon body). According to some embodiments, the sample is a patterned wafer, e.g., in one of the fabrication stages of a patterned wafer, and the test structure is embedded on the wafer.

[0139] According to some embodiments, each of the pump pulses is configured to be absorbed in a slice of the sample (referred to as the "absorbing slice") such that the corresponding induced primary acoustic pulse propagates within the sample away from the absorbing slice. According to some embodiments, and for example, Figure 2B and Figure 7B As depicted in , the absorbing slice can be embedded in the sample. Non-limiting examples include embodiments where the sample comprises a semiconductor structure (i.e., a test structure) mounted on a body (e.g., a silicon body), wherein the absorbing slice constitutes a thin layer within the body. The absorbing slice can be adjacent to the semiconductor structure. According to some embodiments, and as Figure 3A As depicted in , the absorbing slice may be exposed on top of the test structure: non-limiting examples include embodiments where the test structure is made of silicon (Si) or silicon germanium (SiGe).

[0140] According to some embodiments, the test structure may include a through-hole extending from the top surface of the sample into the test structure. The set of structural parameters may characterize at least an average geometry of the through-hole. According to some embodiments, the depth of the through-hole may be at least about 1 μm.

[0141] The term "group" should be understood to encompass not only multi-element groups (e.g., including multiple structural parameters) but also single-element groups. The elements of a group can represent datums (e.g., the value of a structural parameter) or data (e.g., the values ​​of multiple structural parameters). A relevant example of the latter case is the case where the elements of a group (e.g., a set of structural parameters related to a test structure) represent functions (e.g., the average transverse cross-sectional area of ​​a through-hole as a function of the depth within the test structure). According to some embodiments, a set of structural parameters may include one or more functions that specify the dependence of one or more physical properties of the test structure on the depth within the test structure. As a non-limiting example, in an embodiment in which the test structure includes a through-hole, the one or more physical properties may include the average (averaged relative to the through-hole) area of ​​the transverse cross-section of the through-hole. Optionally, the one or more physical properties may additionally include one or more parameters (in addition to the average area) that specify the average shape of the transverse cross-section of the through-hole (e.g., the magnitude of the axis of the ellipse when the transverse cross-section of the through-hole is predetermined or otherwise known to be substantially elliptical). According to some embodiments where the transverse cross-section of the through-holes is predetermined or otherwise known to be substantially circular, the one or more physical characteristics may consist of an average diameter of the through-holes.

[0142] In accordance with some embodiments, the pump beam is a laser beam. Selectable parameters of the pump beam may include one or more of the following: a frequency of the pump pulses, a number of pump pulses, a duration of each pump pulse, a duration of the pump beam, a time interval between consecutive pump pulses, a modulation frequency of the pump beam, and a polarization of the pump beam. Specifically, in embodiments in which the absorbing slice is buried and not exposed, the parameters of the pump beam may be selected to ensure that the pump beam is absorbed substantially only in the absorbing slice in operation 110. To this end, the frequency of the pump beam and, optionally, in accordance with some embodiments, the polarization of the pump beam may be selected such that the pump beam is substantially transparent with respect to a substance located between the top of the test structure and the absorbing slice. In accordance with some embodiments, the wavelength of the pump pulses may be in the ultraviolet range.

[0143] According to some embodiments, the probe beam is a laser beam. Selectable parameters of the probe beam may include one or more of the following: the frequency of the probe pulses, the number of probe pulses, the duration of each probe pulse, the polarization of the probe beam, and the time interval between consecutive probe pulses. The duration of each probe pulse may be selected to be shorter than the characteristic time scale of the thermo-optic effect and the period of the acoustic pulse (or more precisely, the period of the higher frequency component of the acoustic pulse). According to some such embodiments, the duration of each of the pump pulses and / or the probe pulses is shorter than 10 picoseconds. According to some embodiments, the wavelength of the probe pulses may be selected to be in the visible range or the infrared range.

[0144] According to some embodiments, the pump beam and the probe beam can be prepared using the same laser source, for example, using a beam splitter that is used to split an initial laser beam (e.g., a pulsed laser beam) into a pump beam and a probe beam. According to some such embodiments, the pump beam can be amplitude modulated to facilitate isolating the contribution of the return portion of the probe beam to the measurement signal. The modulation frequency can be less than the bandwidth of the optical sensor. According to some embodiments, the modulation frequency can be in the range of 0.1 MHz to 10 MHz.

[0145] According to some embodiments, the pump beam may have a different wavelength than the probe beam. These include embodiments in which the pump beam and the probe beam are prepared using the same laser source: as a non-limiting example, after passing through a beam splitter, a harmonic generation unit and a filter may be used to change the frequency of one of the two beams leaving the beam splitter from the fundamental frequency (i.e. defined by the output of the laser source) to one of its higher harmonics. According to some embodiments in which the pump beam is amplitude modulated, the carrier of the pump pulses may have a different wavelength than the probe pulses. According to some such embodiments, when obtaining the measurement signal, a filter may be used to filter out the return component of the pump beam (while allowing the return component of the probe beam to pass through the filter). Additionally or alternatively, after demodulating the measurement signal (as described below), a low-pass or high-pass filter may be used to remove the contribution of the return component of the pump beam to the demodulated signal, depending on whether the frequency of the pump beam is higher or lower than that of the probe beam.

[0146] According to some embodiments, the measurement signal of operation 130 consists of a sequence of measured intensities. The number of measured intensities in the sequence may depend on the bandwidth B of the optical sensor used to implement operation 130 and the duration of the projected light beams (i.e., the pump beam and the probe beam). According to some such embodiments, the rate of probe pulses may be greater than the bandwidth of the optical sensor used in operation 130 to obtain the measurement signal. Thus, in such embodiments, each of the measured intensity values ​​(constituting the measurement signal) will include contributions from the return portions of each of a plurality of consecutively projected probe pulses within a time interval equal to 1 / B. In other words, after demodulating and cleaning the measurement signal to isolate the contribution of induced Brillouin oscillations thereto, each of the resulting processed intensity values ​​will correspond to the average of the contributions of each of the corresponding plurality of return portions incident on the optical sensor within a time interval equal to 1 / B. Such averaging may potentially reduce the signal-to-noise ratio.

[0147] According to some embodiments in which the test structure includes through-holes (vertically extending holes) arranged in a two-dimensional array, the pulsed probe beam can be linearly polarized along a transverse direction that is perpendicular to the longitudinal dimension of the through-holes. More specifically, according to some embodiments in which the through-holes are arranged in a rectangular array (e.g., as Figure 2AIn some embodiments described in FIG. 5 , in order to increase the width of the first lateral direction (e.g., along the Figure 2A The pulsed probe beam can be measured along the second transverse direction (e.g., along the y-axis in FIG. Figure 2A In one embodiment, the detection portion of the optical fiber is polarized along an x-axis (in the x-axis), and the second transverse direction is perpendicular to the first transverse direction. The first transverse direction extends parallel to the direction in which the columns of the rectangular array are arranged. The second transverse direction extends parallel to the direction in which the rows of the rectangular array are arranged. Similarly, in order to increase the measurement sensitivity along the second transverse direction, the pulsed detection beam can be polarized along the first transverse direction. Polarizing the detection pulse parallel to the first transverse direction may result in an uneven intensity distribution of the detection pulse within the detection portion, wherein the intensity is maximum along the rows of the through-holes. Conversely, polarizing the detection pulse parallel to the second transverse direction may result in an uneven intensity distribution of the detection pulse within the detection portion, wherein the intensity is maximum along the columns of the through-holes.

[0148] To facilitate the description by way of non-limiting examples, additional reference is made to Figures 2A to 2D . Figure 2A A partial perspective view of a (dissected) sample 200 is provided, wherein the front portion of the sample 200 is removed to show the internal structure of the sample 200. The sample 200 includes a test structure 202 (e.g., a semiconductor structure) and a body 204 (e.g., a silicon substrate). The test structure 202 is positioned on top of the body 204. According to some embodiments, and as Figures 2A to 2D , test structure 202 is shown to include through-holes 212 (e.g., empty holes) extending from a top surface 214 of test structure 202 into test structure 202. As a non-limiting example, assume that each of through-holes 212 extends longitudinally (and vertically) into test structure 202 and has a circular transverse cross-section whose area decreases with depth. According to some embodiments, and as Figure 2A As depicted in FIG, the through holes 212 may be arranged in a periodic two-dimensional array. According to some such embodiments, the two-dimensional array is rectangular, wherein the through holes 212 are arranged parallel to two orthogonal axes (e.g., according to FIG. Figure 2A , the rows and columns of the coordinate system depicted in , are the x-axis and y-axis respectively).

[0149] See also Figures 2B to 2D , Figures 2A to 2D Schematically depicts the application of the method 100 according to some embodiments of the method 100 to the test structure 202, or more precisely to the (probing) portion 220 of the test structure 202 (at Figure 2A) and depicted by a double-dashed line. The detection portion 220 may be shaped as a cylinder whose diameter is defined by the beam diameter of the pump beam projected on the top surface 214 in operation 110. In order to fully detect the detection portion 220, the beam diameter of the detection beam may be selected in operation 120 to be at least equal to or substantially equal to the beam diameter of the pump beam. According to some embodiments, and as Figure 2A As depicted in FIG, the detection portion 220 includes a plurality of through holes from the through hole 212.

[0150] Figure 2A and Figure 2B A pump pulse 201 is shown projected onto top surface 214 in accordance with some embodiments. Pump pulse 201 forms part of a pulsed pump beam projected onto test structure 202 in accordance with operation 110. Pump pulse 201 is configured to penetrate into test structure 202 and propagate within test structure 202 onto body 204. Pump pulse 201 is further configured to be absorbed by body 204. Slice 224 (also referred to as an "absorption slice") indicates a region within body 204 in which substantially all of pump pulse 201 (or, in embodiments in which a non-negligible portion of pump pulse 201 is reflected from body 204, substantially all of the transmitted portion of pump pulse 201) has been absorbed. Absorption slice 224 is adjacent to test structure 202. The thickness of absorption slice 224 depends on the absorption length of pump pulse 201 in body 204.

[0151] Absorption of pump pulse 201 by absorbing slice 224 results in heating of absorbing slice 224. Heating of absorbing slice 224 results in expansion of absorbing slice 224, as indicated by double-headed arrow E. The expansion of absorbing slice 224 results in the formation of primary acoustic pulse 211 and additional acoustic pulse 213, each of which propagates away from absorbing slice 224. Primary acoustic pulse 211 propagates within test structure 202 in the direction of the negative z-axis (i.e., toward top surface 214). As primary acoustic pulse 211 propagates within test structure 202, the local mass density is temporarily modified where primary acoustic pulse 211 is momentarily localized. Due to the photoelastic effect, this temporary modification of the density results in a corresponding temporary (local) modification of the refractive index. Additional acoustic pulse 213 can propagate within body 204 in the direction of the positive z-axis.

[0152] Figure 2C Depicts the Figure 2BA cross-sectional view of probe portion 220 at a later time is shown. Absorbing slice 224 has cooled and is therefore no longer colored black. Each of primary acoustic pulse 211 and additional acoustic pulse 213 has propagated away from absorbing slice 224. According to some embodiments, probe pulse 221 is shown projected onto top surface 214. Probe pulse 221 forms part of a pulsed probe beam projected onto test structure 202 according to operation 120. Specifically, as described above, the pulsed probe beam and the pulsed pump beam (including pump pulse 201) can be prepared using the same laser source. Due to optical diffraction limit considerations, according to some embodiments, the wavelength of probe pulse 221 can be at least approximately two times greater than the distance between adjacent vias (adjacent vias from via 212, such as first via 212a and second via 212b). A transmitted portion 223 of probe pulse 221 penetrates test structure 202. A reflected portion 225 of probe pulse 221 reflects from top surface 214. The transmitted portion 223 travels in the direction of the body 204 and is Brillouin scattered from the primary acoustic pulse 211, as Figure 2C 2. Transmissive portion 229 corresponds to the portion of scattering portion 227 that is transmitted out of test structure 202 through top surface 214.

[0153] As used herein, the terms "reflection" and "transmission" should be understood to encompass partial reflection and partial transmission, respectively.

[0154] In order not to hinder Figure 2C , the primary acoustic pulse 211 is present only between the first through-hole 212a and the second through-hole 212b. However, it should be understood that the lateral extent of the primary acoustic pulse 211 is not limited to this, and that propagation of the primary acoustic pulse 211 occurs throughout the detection portion 220. Similarly, the arrows representing the transmissive portion 223, the scattering portion 227, and the transmissive portion 229 are present only between the first through-hole 212a and the second through-hole 212b. However, it should be understood that the lateral extent of the transmissive portion 223, the scattering portion 227, and the transmissive portion 229 is not limited to this, and that propagation of the transmissive portion 223, the scattering portion 227, and the transmissive portion 229 occurs throughout the detection portion 220.

[0155] The depth to which the transmitted portion 223 is scattered (Brillouin) from the primary acoustic pulse 211 within the test structure 202 depends on the time delay of the probe pulse 221 relative to the preceding pump pulse (i.e., pump pulse 201). More precisely, the depth u (i.e., the vertical distance from the top surface 214) to which the probe pulse 221 is Brillouin scattered from the primary acoustic pulse 211 is determined by Δt≈T F +(u max -u) / v is related to the time delay. T F is the formation time of the primary acoustic pulse 211. maxis the distance from the top surface 214 to the body 204 (in general, z=u+a, where a is a constant. If the coordinate system is chosen so that the xy plane coincides with the top surface 214, then a=0 and z=u). v represents the speed of sound in the test structure 202. Here, as a non-limiting example, it is assumed that, except for the presence of the through hole 212, the test structure 202 is uniform so that the speed of sound therein does not vary with depth. Figure 8 The more general case is addressed in the description of the method.

[0156] According to some embodiments, pump pulses and probe pulses can be alternately projected onto the probe portion 220 such that, for each k, the kth probe pulse is projected after the kth pump pulse and before the (k+1)th probe pulse. Furthermore, each of the probe pulses can be delayed relative to the immediately preceding pump pulse by a respective time interval that varies from one pair of probe-pump pulses to the next, so as to facilitate probing the test sample over at least a range of depths. Specifically, in such embodiments, each of the probe pulses "probes" the test structure at a respective depth.

[0157] Figure 2D A cross-sectional view of the probe portion 220 is depicted after projecting a later pump pulse (not shown) onto the probe portion 220 according to operation 110, the later pump pulse being included in the same pulsed pump beam as the pump pulse 201. The later pump pulse follows the pump pulse 201. The pump pulse 201 and the later pump pulse may or may not be consecutive. The later pump pulse is absorbed in the absorbing slice 224, thereby causing heating of the absorbing slice 224 and forming a primary acoustic pulse 211' and an additional acoustic pulse 213' that propagate away from the absorbing slice within the test structure 202 and the body 204, respectively, as described above in Figure 2B Described in the description.

[0158] A probe pulse 221' is shown projected onto the top surface 214 according to operation 120. The probe pulse 221' may be included in the same pulsed probe beam as the probe pulse 221. A transmitted portion 223' of the probe pulse 221' penetrates the test structure 202 into the detection portion 220. A reflected portion 225' of the probe pulse 221' reflects from the top surface 214. The transmitted portion 223' travels in the direction of the body 204 and is Brillouin scattered from the primary acoustic pulse 211', as shown in FIG. Figure 2D2 is indicated by scattered portion 227 in FIG. Transmitted portion 229′ corresponds to the portion of scattered portion 227′ that is transmitted out of test structure 202 through top surface 214. Probe pulse 221′ is delayed relative to the later pump pulse by a time delay Δt′, which is greater than Δt (the time delay of probe pulse 221 relative to pump pulse 201). Thus, the depth u′ at which probe pulse 221′ is scattered from primary acoustic pulse 211′ is less than u (the depth at which probe pulse 221 is scattered from primary acoustic pulse 211).

[0159] In order not to hinder Figure 2D , the primary acoustic pulse 211′ and the arrows representing the transmissive portion 223′, the scattered portion 227′, and the transmissive portion 229′ are present only between the first through-hole 212a and the second through-hole 212b. However, it should be understood that the lateral extent of each of the primary acoustic pulse 211′, the transmissive portion 223′, the scattered portion 227′, and the transmissive portion 229′ is not limited thereto, and that propagation of the primary acoustic pulse 211′, the transmissive portion 223′, the scattered portion 227′, and the transmissive portion 229′ occurs throughout the detection section 220.

[0160] Generally speaking, the return portion of the probe pulse will also include secondary acoustic pulses due to the presence of the secondary acoustic pulses induced within the body 204 (e.g., Figure 2C and Figure 2D The corresponding scattered part is not in Figure 2C and Figure 2D . These contributions may be distinguished from contributions due to scattering within the test structure 202 and, according to some embodiments, not taken into account when determining a set of structural parameters (related to the test structure 202). As a non-limiting example, the body may be composed of silicon and the test structure (mounted on the body) may be composed of an oxide. Since the refractive indices of silicon and oxide in the visible range are approximately 4 and 1.45, respectively, and the speed of sound is approximately 8,400 m / sec in silicon and approximately 4,600 m / sec in oxide, the ratio of the Brillouin frequencies of silicon to oxide is approximately 5. Thus, a low-pass filter is employed to filter out contributions to the measurement signal (or more precisely, the demodulated signal) that are caused by scattering of the acoustic pulse within the body.

[0161] Although Figures 2A to 2DWhile the diameter of the through-hole 212 is depicted as decreasing substantially linearly with depth, skilled artisans will readily recognize that the methods and systems of the present disclosure may be applied to detect other through-hole geometries. These include, for example, straight through-hole geometries (i.e., through-hole geometries in which the diameter (or diameters when the through-hole transverse cross-section is elliptical rather than circular) is constant), or through-hole geometries in which the change in diameter (or diameters) of the through-hole (with increasing depth) is non-monotonic (e.g., initially increasing and then decreasing, e.g., as in Figure 3A and Figure 3B The through-hole geometry is depicted in FIG.

[0162] Figure 3A and Figure 3B Depicted are two different stages in an implementation of the method 100 for a test structure 302 (included in the profiling sample 300 ), or more precisely, a probe portion 320 of the test structure 302 , according to some specific embodiments thereof. Figure 3A A partial perspective view of a test structure 302 is provided, wherein a front portion of the test structure 302 is removed to show the internal structure of the test structure 302. As a non-limiting example, the test structure 302 is shown to include a through hole 312 that protrudes into the test structure 302 from a top surface 314 of the test structure 302. According to some embodiments, and as Figure 3A and Figure 3B , test structure 302 is similar to test structure 202, but may differ from test structure 202, e.g., in material composition and / or depth of via 312. According to some embodiments, test structure 302 may have a uniform composition (until the presence of via 312), e.g., be made of silicon (Si) or silicon germanium (SiGe).

[0163] According to some embodiments, Figure 3A 3. Pump pulse 301 is shown as projected onto top surface 314. Pump pulse 301 forms part of a pulsed pump beam projected onto test structure 302 according to operation 110. Pump pulse 301 is configured to be absorbed by test structure 302. In an embodiment, wherein Figure 3A and Figure 3B As depicted in FIG, the test structure 302 is made of a single material, and the wavelength of the pump pulse 301 can be selected so that the absorption coefficient of the test structure 302 is high for this wavelength. In embodiments where the test structure 302 is layered ( Figure 3A and Figure 3BIn the embodiment (not depicted in the drawings), the wavelength of pump pulse 301 can be selected such that the absorption coefficient of the top layer of test structure 302 is high for this wavelength. Thus, pump pulse 301 is absorbed in a top slice 324 (referred to as the "absorbing slice") of test structure 302. The top surface of absorbing slice 324 is formed by top surface 314. The thickness of absorbing slice 324 depends on the absorption length of pump pulse 301 in test structure 302, or in the top layer of test structure 302 in embodiments in which test structure 302 is layered.

[0164] Absorption of pump pulse 301 by absorbing slice 324 results in heating of absorbing slice 324, which in turn causes absorbing slice 324 to expand, as indicated by double-headed arrow E'. The expansion of absorbing slice 324 results in the formation of a (primary) acoustic pulse 311 that propagates in the direction of the (positive) z-axis. As acoustic pulse 311 propagates within test structure 302, it temporarily changes the local mass density where acoustic pulse 311 is temporarily localized. Due to the photoelastic effect, this temporary change in density causes a corresponding temporary (local) change in the refractive index.

[0165] Figure 3B Depicts the Figure 3A 312a and 312b are compared to a cross-sectional view of the test structure 302 at a later time. The absorbing slice 324 has cooled and is therefore no longer colored black. The acoustic pulse 311 has propagated away from the absorbing slice 324. According to some embodiments, the probe pulse 321 is shown as being projected onto the top surface 314. The probe pulse 321 forms part of a pulsed probe beam that is projected onto the test structure 302 according to operation 120. In particular, as described above, the pulsed probe beam and the pulsed pump beam can be prepared using the same laser source. Due to optical diffraction limit considerations, according to some embodiments, the wavelength of the probe pulse 321 can be at least about two times greater than the distance between adjacent through-holes (adjacent through-holes from through-hole 312, such as the first through-hole 312a and the second through-hole 312b). A transmitted portion 323 of the probe pulse 321 penetrates the test structure 302. A reflected portion 325 of the probe pulse 321 is reflected from the top surface 314. The transmitted portion 323 is Brillouin scattered from the acoustic pulse 311, as Figure 3B 3. Transmissive portion 329 corresponds to the portion of scattering portion 327 that is transmitted out of test structure 302 through top surface 314.

[0166] In order not to hinder Figure 3B, the acoustic pulse 311 and the arrows representing the transmissive portion 323, the scattering portion 327, and the transmissive portion 329 are present only between the first through-hole 312a and the second through-hole 312b. However, it should be understood that the lateral extent of each of the acoustic pulse 311, the transmissive portion 323, the scattering portion 327, and the transmissive portion 329 is not limited thereto, and that the propagation of the acoustic pulse 311, the transmissive portion 323, the scattering portion 327, and the transmissive portion 329 occurs throughout the detection portion 320.

[0167] The depth to which the transmitted portion 323 is scattered (Brillouin) from the acoustic pulse 311 within the test structure 302 depends on the time delay of the probe pulse 321 relative to the delay of the preceding pump pulse. More precisely, the depth u to which the transmitted portion 323 is scattered (Brillouin) from the acoustic pulse 311 is determined by Δt≈T F +u / v is related to the time delay.Here, as a non-limiting example, it is assumed that the test structure 302 is homogeneous except for the presence of the through-hole 312, so that the speed of sound in the test structure 302 does not vary with depth.

[0168] According to some embodiments, pump pulses and probe pulses may be alternately projected onto test structure 302 , substantially as described above in the description of sample 200 .

[0169] Although Figure 3A and Figure 3B , the diameter of the through hole 312 is depicted as first decreasing and then increasing with depth, a skilled artisan will readily recognize that the methods and systems of the present disclosure may be applied to detect other through hole geometries, such as, for example, straight through hole geometries or through hole geometries such as Figures 2A to 2D The through-hole geometry depicted in .

[0170] In general, the frequency of the returned portion (e.g., transmitted portion 229 or 329) of a probe pulse (e.g., probe pulse 221 or probe pulse 321) that exits the test structure after Brillouin scattering in the test structure will be different from the frequency of the directly reflected portion (e.g., reflected portion 225 or 325) of the probe pulse. This so-called "Brillouin frequency shift" (also simply referred to as the "Brillouin frequency") depends on the local refractive index (or local effective refractive index, e.g., when the test structure includes a via) and the local speed of sound within the test structure, as well as the frequency (or equivalently, wavelength) of the probe pulse. Due to the interference of the Brillouin scattered portion of the probe beam (or each of the Brillouin scattered portions of the probe beam, e.g., when the test structure is layered) with the reflected portion of the probe beam, the Brillouin frequency shift manifests as an oscillatory contribution (referred to as a "Brillouin oscillation") to the returned portion of the probe beam. Here, "reflected portion of the probe beam" means the portion of the probe beam that is reflected from the test structure (e.g., from the top surface of the test structure) and is not transmitted into the test structure (i.e., does not enter the test structure). Thus, by measuring the Brillouin frequency shift, localized information about the geometry and material composition of the test structure can be derived.According to some embodiments, additional information can be derived from other parameters characterizing the induced Brillouin oscillations (eg, the amplitude of the Brillouin oscillations).

[0171] According to some embodiments, in order to fully probe the test structure, operations 110-130 can be performed sequentially with respect to each of a plurality of probe portions (such as probe portion 220). According to some embodiments, the measurement data of each probe portion can be processed separately so that the obtained set of structural parameters is related only to the probe portion. Alternatively, according to some embodiments, the measurement data from each of the plurality of probe portions can be processed jointly. According to some such embodiments, the measurement signals from all of the plurality of probe portions can be considered to derive some or all of the key parameters. In some such embodiments in which the probe portions are nominally identical, the obtained set of structural parameters can correspond to an average of the structural parameters related to each of the probe portions from the plurality of probe portions.

[0172] Referring to operation 140, according to some embodiments, derivation of the processed signal may involve extracting key parameters characterizing induced Brillouin oscillations from the measured signal, and more particularly, the dependence of at least some of these key parameters on the time delay (or equivalently, the Brillouin scattering depth). Specifically, derivation may involve extracting the dependence of the Brillouin frequency shift on the time delay. According to some embodiments, operation 140 may include an initial sub-operation in which the measured signal is converted to a digital signal (e.g., using an analog-to-digital converter).

[0173] According to some embodiments, the pulsed pump beam (of operation 110) may be modulated to facilitate substantial removal of, or at least reduction of, noise and background signals from the measurement signal, thereby isolating the contribution of Brillouin oscillations to the measurement signal. More specifically, according to some such embodiments, and as described in greater detail below, a lock-in amplifier may be used in operation 140 to demodulate the measurement signal and thereby isolate the Brillouin oscillation contribution. Specifically, key parameters may be extracted after demodulation.

[0174] According to some embodiments, operation 140 may further include one or more of the following after demodulation: (i) removal or at least attenuation of thermo-optical contributions to the measurement signal, as described in detail below in the system subsection, (ii) laser noise reduction (e.g., using a reference channel), and (iii) selective filtering of undesired ranges in the Fourier transform of the demodulated signal, and optionally, other digital signal processing operations, such as extraction from the demodulated signal of a spectrogram.

[0175] The forward model is configured to receive as input a set of structural parameters and output corresponding simulated signals. The simulated signals are intended to simulate the processed signals of operation 140 (i.e., when the input set of structural parameters matches the GT data). According to some such embodiments, the simulated signals may specify simulated values ​​of the key parameters. According to some embodiments, the forward model of operation 150 may be or be combined with a computer simulation that simulates Brillouin scattering of the probe pulse from the acoustic pulse within the test structure.

[0176] More precisely, the structural parameters that the forward model is configured to receive in each iteration of the optimization algorithm may consist of or at least include the structural parameters to be determined by method 100. In contrast to these structural parameters (i.e., the structural parameters may be fed as input to the forward model in each iteration), other structural parameters may be fixed (e.g., defined by the user based on design data and / or GT data). According to some embodiments, the values ​​of these (fixed) structural parameters may be initially set (i.e., input to the forward model before the first iteration) without subsequent updates. Other (physical) parameters of the forward model may also be initially known or known to a sufficiently high degree of accuracy and thus not updated from one iteration to the next. These non-updated parameters of the forward model are referred to as "fixed parameters," and according to some embodiments, the fixed parameters may include some or all of the following: (i) when the profiled sample includes through-holes, the average spacing (i.e., the average distance between the centers of adjacent through-holes); (ii) when the profiled sample is layered, the thickness and / or material composition of the layers; (iii) the lattice geometry (e.g., rectangular, hexagonal); (iv) the refractive index values ​​of the various materials included in the test structure and / or the sound velocity values ​​in said materials; (v) the transmission coefficients and reflection coefficients characterizing the boundaries between adjacent layers (when the profiled sample is layered); (vi) the wavelength, intensity, and / or duration of the pump and probe pulses, and / or the time delay between consecutive pulses; (vii) the focus of the pump beam and / or the focus of the probe beam; (viii) when polarized, the polarization of the pump and probe beams; (ix) the location(s) on the profiled sample at which the pump and / or probe beams impinge; and (x) parameters characterizing the measurement setup (e.g., the bandwidth and / or gain of the photosensor). According to some embodiments, and as described below in Figure 4 As elaborated in detail in the description of , the values ​​of some or all of the non-fixed parameters of the forward model (optionally including the structural parameters to be determined) can be restricted to corresponding value ranges.

[0177] According to some embodiments, the values ​​of some of the fixed parameters may be determined in a calibration operation, which is performed before operation 140 or, optionally, before operation 130, as described below. According to some such embodiments, one or more of the fixed parameters may specify parameter values ​​of the parameterized analog signal.

[0178] According to some embodiments in which the forward model is or is combined with a computer simulation, the computer simulation can be configured to: (i) initially receive parameters characterizing a probe pulse incident on the test structure and each of the acoustic pulse(s) propagating within the test structure (including parameters specifying the location of the acoustic pulse within the test structure, e.g., when the probe pulse strikes the test structure); and (ii) output at least a Brillouin frequency shift characterizing the induced Brillouin oscillations. More generally, the computer simulation can be configured to output a plurality of key parameters characterizing the Brillouin oscillations or at least some of the Brillouin oscillations. The parameters characterizing the probe pulse and the acoustic pulse(s) are selectable to at least allow simulation of the probing of the test structure at each of a plurality of depths according to the provisions of method 100. Additional selectable parameters can include, for example, the wavelength and duration of the probe pulse, and the phase of the return component of the probe pulse. According to some embodiments, the values ​​of some of the selectable parameters are determined in real time (e.g., prior to operation 150) based on the processed signal using machine learning tools. As a non-limiting example, the decay response of the envelope of the processed signal can be determined in real time using machine learning tools.

[0179] Parameters characterizing the test structure may also be selectable at least within respective ranges, the parameters specifying the expected geometry and material composition of the test structure (and thereby the refractive index and acoustic velocity, or multiple refractive indices and / or acoustic velocities when layered). More specifically, each structural parameter may be selectable within a respective range that reflects deviations from an expected value of the structural parameter (e.g., specified by the design data for the test structure) due to, for example, manufacturing imperfections.

[0180] According to some alternative embodiments, where the forward model is or is combined with a computer simulation, the computer simulation can be configured to additionally receive as input parameters characterizing the pump pulse and the probe pulse. In such embodiments, the computer simulation additionally simulates the formation of the acoustic pulse(s). The parameters of the pump pulse (e.g., wavelength and duration of the pump pulse) and the time interval by which the probe pulse is delayed relative to the pump pulse can be selectable. According to some embodiments, the computer simulation can be configured to receive as input parameters characterizing the pulsed pump beam and the pulsed probe beam, in which case the computer simulation additionally simulates the formation of the acoustic pulses caused by each of the pump pulses in the pulsed pump beam.

[0181] Reference data related to the dissected sample can be considered to derive the forward model. The reference data can include one or more of the following: design data of the sample (e.g., a computer-aided design (CAD) model), ground truth (GT) data of a sample with the same and / or similar design intent as the dissected sample (referred to as a "GT sample"). The GT data can be obtained by subjecting the GT sample to destructive measurements. Non-limiting examples of relevant destructive measurement techniques include using transmission electron microscopy (TEM) for thin sections extracted from GT samples and / or cut slices of GT samples (e.g., using focused ion beam extraction). Most generally, the reference data can refer to any information indicative of the internal geometry and material composition of the dissected sample. According to some embodiments, the forward model can be derived by additionally considering associated measurement data (i.e., measurement data associated with the GT data) obtained by performing operations 110-130 on a sample with the same and / or similar design intent as the dissected sample (consisting of or including the GT sample). In embodiments where the GT samples include GT samples having a different design intent than the profiled samples, derivation of the forward model may include interpolation from the GT data and associated measurement data related to these GT samples (i.e., the GT samples having a different design intent than the profiled samples). According to some such embodiments, the interpolation may involve application of a k-nearest neighbor (k-NN) algorithm.

[0182] According to some embodiments, in the forward model, the test structure comprising the vertically extending through-hole is modeled by a laterally uniform structure having a refractive index equal to n eff (z) - the effective refractive index of the test structure estimated before performing method 100 (with respect to the test structure) based on the model of the test structure. The model may be constructed using reference data available before performing method 100. According to some embodiments, n eff (z) is equal to the average refractive index obtained by averaging the transverse cross-sections of the model at the vertical coordinate z (which quantifies the depth). That is,

[0183]

[0184] n0 is the refractive index of air or vacuum. n1(z) is the refractive index of the material present at z (i.e., excluding air when operating under non-vacuum conditions). Note that, most generally, n1(z) depends on z, e.g., in embodiments where the test structure is layered and / or where the density of the material or one or more compositions of the material varies with depth. r is the (average) distance between the centers (i.e., vertically extending central axes) of adjacent holes along the same row of through holes (e.g. Figure 2A d in x ).dc is the (average) distance between the centers of adjacent vias along the same column of vias (e.g. Figure 2A d in y ). A via (z) is the (average) transverse cross-sectional area of ​​the (single) through-hole at z. In the embodiment where the transverse cross-section of the through-hole is circular, n eff (z) depends on a single physical property of the vias: the average diameter of the vias at z.

[0185] According to some embodiments, in the forward model, the acoustic pulse propagating within the test structure is modeled by a reflector. More specifically, in embodiments where the test structure is non-layered (e.g., test structure 202, test structure 302), the primary acoustic pulse can be modeled by a reflector that moves at the local speed of sound in the direction of propagation of the primary acoustic pulse. Alternatively, according to some embodiments where the test structure is layered such that multiple acoustic pulses are generated within the test structure, the acoustic pulse can be modeled by a semi-transparent reflector, as described below in Figure 8 and Figure 9 In the description about Figure 6 The method described.

[0186] According to some embodiments, the forward model can be trained using training data comprising GT data (i.e., GT data of GT samples) and associated measurement data. The (associated) measurement data can be obtained by performing operations 110-130 on the GT samples. More specifically, according to some embodiments, the values ​​of the model parameters of the forward model can be tuned based on the training data using optimization techniques (as known in the art of machine learning). According to some embodiments, line data (defined below) can be used when training the forward model.

[0187] According to some embodiments, the values ​​of the model parameters of the forward model may be tuned based on calibration data associated with the profiled sample (e.g., prior to operation 150). According to some such embodiments, and as explained in detail below, method 100 may include an initial calibration operation (the operation at Figure 1), wherein calibration data is obtained. According to some embodiments, the calibration operation may include performing method 100 on one or more scribe lines of the profiled sample. Here, the term "scribe line" is used in an expanded manner to refer to an area of ​​the profiled sample that is laterally uniform (and thus free of vias) but is otherwise similar to the test structure (in terms of material composition and, when layered, in terms of the thickness of the layers and their material composition). For example, according to some embodiments in which the profiled sample is a patterned wafer that includes areas including vias to be profiled using method 100, the scribe lines may be composed of via-free areas between areas including vias. The via-free areas correspond to areas that were not drilled during the manufacture of the patterned wafer. According to some embodiments, in order to minimize the impact of process variations on the calibration operation, the scribe line(s) that are closest to (e.g., adjacent to) the test structure may be selected.

[0188] In a homogeneous medium, the Brillouin frequency f B By f B =2v s ·n m / λ prob Given. m is the refractive index of the medium. s is the speed of sound in the medium. prob is the wavelength of the probe pulse. Using equation (1), it follows that in the region including the through-hole, f B (z) can be approximated as having the form corresponds to the Brillouin frequency distribution that would be obtained in the case of a region without a through hole (i.e. the dependence of the Brillouin frequency on depth). c(z) depends on n0, n1(z), d r and d c . This can be determined by performing method 100 on one or more scribe lines near the test structure. Once determined, to calibrate the forward model.

[0189] Note that in embodiments where the test structure consists of layers, will generally be a piecewise function. Furthermore, when vias are included, the layer is uniform, with will be constant (i.e. is constant within a layer). For example, in an embodiment where the test structure comprises N layers (which are uniform except for the inclusion of the vias), There will be a set of N Brillouin frequencies Definition. For every 1≤i≤N, is the Brillouin frequency associated with the i-th layer, as obtained in the absence of the through-hole.

[0190] Additionally or alternatively, in accordance with some embodiments in which the test structure is layered and includes through-vias, the calibration data may specify one or more of: the concentration of material within each layer, the refractive index of the solid portion of the layer, the speed of sound within the solid portion, the refractive index and transmission coefficient characterizing the boundaries between adjacent layers (as determined by implementing method 100 with respect to one or more scribing lines), and the average distance(s) between the centers of adjacent through-vias.

[0191] According to some embodiments, the initial guess in operation 150 may be selected taking into account at least reference data and / or calibration data of the profiled sample.

[0192] According to some embodiments, a set of structural parameters comprises a plurality of sub-sets of structural parameters. Each sub-set of structural parameters comprises a plurality of non-overlapping vertical increments from a set of non-overlapping vertical increments. At least one (vertically localized) parameter related to the corresponding increment in i represents the i-th vertical increment Δz within the test structure i A relevant example of a vertical localization parameter is the (lateral) area of ​​the through-hole at a given height. According to some such embodiments, the optimization algorithm is i Each of the executions starts at z1 and proceeds sequentially up to smaller z within the test structure. i (Right now ). In the i-th execution, the optimization algorithm (i) receives the following as input: until time t i =∑ j≤i Δz j / v s (z j ) a processed signal derived from the measurement signal, and optionally any previously obtained value of a vertical localization parameter, and (ii) outputting the value of the ith vertical localization parameter. s (z) represents the local sound speed at z.

[0193] Figure 4 A flow diagram of operation 400 is presented, which corresponds to a specific embodiment of operation 150. Operation 400 includes:

[0194] - Sub-operation 410, in which an initial guess of N structural parameters of the test structure is selected

[0195] - Sub-operation 420, where a forward model (e.g., an interpolator) is used to predict the To obtain analog signals (u represents the depth within the test structure).

[0196] - Sub-operation 430, depending on the analog signal Did not converge to the processed signal m(u), where guess Based on analog signal The processed signal m(u) is updated by the measurement signal m(u). The processed signal is derived (in operation 140) from the measurement signal obtained in operation 130.

[0197] - Sub-operation 440, depending on the analog signal has converged to the processed signal, where the output guess

[0198] According to some embodiments, N=1 (i.e., a single structural parameter is to be estimated), in which case is a one-dimensional vector (i.e. scalar).

[0199] According to some embodiments, the convergence criterion for operations 430 and 440 is given by That is, when hour, is considered to converge to m(u), and when hour, is considered not to have converged to m(u). is the cost function to be minimized. The double vertical bars represent the norm (e.g., L 1 or L 2 ). ε is a positive constant whose value can be predetermined based on the required estimation accuracy of a set of structural parameters of the test structure. More generally, according to some embodiments, the convergence criterion can be given by Given by , where F is a function of the signal or a transform of the signal (e.g., a standard Fourier transform or a short-time Fourier transform). Alternatively, according to some embodiments, the convergence criterion may be given by given. is the difference between the last guess (i.e., the guess obtained in the most recent iteration) and the immediately preceding guess (i.e., the guess obtained in the iteration immediately preceding the most recent iteration). Failure to converge may indicate a fault in the measurement setup, a fault in the algorithm, and / or a defective profiled sample. Thus, according to some embodiments, operation 400 is aborted if convergence is not achieved after a predefined number of iterations. Alternatively, according to some embodiments, a last guess is output if convergence is not achieved after a predefined number of iterations. According to some such embodiments, operation 400 is aborted if one or more values ​​of the structural parameters specified by the output guess fall outside a corresponding expected value range.

[0200] According to some embodiments, in operation 430, an optimization algorithm may be used to update the guess According to some embodiments, the optimization algorithm can be an algorithm known in the literature, such as a stochastic gradient descent algorithm. According to some embodiments, where the cost function is the sum of squares (or more precisely, the squared differences), the optimization algorithm can be a nonlinear least squares algorithm, such as the Levenberg-Marquardt algorithm. Other options may include, for example, extensions of the gradient descent algorithm, such as the adaptive moment estimation algorithm (Adam) or the Nesterov accelerated adaptive moment estimation algorithm (Nadam). In addition to the sum of squares, these last options are also related to other cost functions, such as the sum of absolute differences.

[0201] According to some embodiments, in sub-operation 430, according to Update guess, where Is the final analog signal (i.e. is a vector function of the last updated guess) and the measured signal m(u). According to some such embodiments, where J is at The Jacobian matrix (i.e. Updated using gradient descent). Alternatively, according to some embodiments, a Hessian matrix may be employed instead of J or in addition to J.

[0202] The initial guess can be determined based on the design intent of the test sample (e.g., test structure 202 or test structure 302). The determination can be further informed by physical modeling and / or data acquired in past embodiments of method 100 regarding samples having the same or similar intended design as the profiled sample, optionally supplemented by GT data related to the test sample. According to some embodiments, the determination can take into account the processing signal. More specifically, and as explained in detail below, the initial guess can be determined based on a preliminary analysis of the processing signal, whereby the time dependence of the processing signal obtained is approximately related to the depth dependence of the average area of ​​the through-hole.

[0203] Alternatively, according to some embodiments, the initial guess can be randomly selected from a set of guesses. Each guess in the set can be determined based on the design intent of the test sample and optionally other relevant data as described in the previous paragraph. As a non-limiting example, according to some embodiments, the "guess" value of each structural parameter (as specified by the guess) is selected to fall within a preselected number of standard deviations (e.g., one σ) from the expected mean value of the structural parameter.

[0204] According to some embodiments, the values ​​of the non-fixed parameters of the forward model can be restricted to a corresponding value range by adding a suitable penalty term to the cost function. As a non-limiting example, according to some embodiments, the cost function can be modified to have the form When for every 1≤i≤N, hour, in and Define g separately i The lower and upper bounds of the corresponding value range to be clamped. Otherwise, where λ is a positive constant.

[0205] According to some embodiments, the forward model of operation 420 may be or be combined with a computer simulation, as described above in the description of operation 150 of method 100 .

[0206] In practice, there may potentially be an inherent gap between the simulated signal and the processed signal due to factors that are not taken into account by the forward model according to some embodiments. Such factors may include uncontrollable factors and / or may be due to measurement setup parameters that are not taken into account (at least not to a sufficient degree of accuracy). Examples of uncontrollable factors include temperature changes and various types of noise, whether ambient noise or noise in the measurement setup (e.g. laser noise, jitter and / or acceleration of the platform used to translate the mirror in the variable delay line). Examples of measurement setup parameters that are not taken into account according to some embodiments may include laser focus offset. According to some embodiments, other measurement setup parameters (such as the positions of various components of the measurement setup) may not be known to a sufficient degree of accuracy to not contribute to the simulation gap. Simulation gaps may also occur due to only considering some of the secondary acoustic pulses in the forward model and / or due to other approximations, such as modeling the acoustic pulses by moving a semi-transparent mirror. In principle, the simulation gap can be bridged using a neural network (NN) trained based on GT data and associated measurement data. However, since GT data are typically very limited (e.g., extracted from about ten or about twenty samples), standard deep learning models / artificial intelligence models (e.g., transformers) that typically require large amounts of GT data may not be applicable.

[0207] Figure 5A Describes the basis Figure 1 Some embodiments of the method of the present invention are configured to bridge an analog gap (when present) between an analog signal and an actual signal by implementing an encoder-decoder-based computing architecture. Figure 1 The measurement data obtained by the operations 110-130 of the method are derived. Here, the "actual signal" means the measurement signal after the processing described above in the description of operation 140. More specifically, Figure 5AA bridge (architecture) 500 is depicted. The bridge 500 may comprise a (first) encoder 510, a converter 520 and a (first) decoder 530. As explained in detail below, according to some embodiments, the converter 520 may be constituted by a NN or linear regression algorithm.

[0208] In the operation of the bridge 500, the actual signal A Input to encoder 510 (and hence to bridge 500). Actual signal A The first latent space representation output by the encoder 510 (indicated by arrow 505) is input into the converter 520. The converter 520 converts the first latent space representation into a second latent space representation (indicated by arrow 515). The second latent space representation is input into the decoder 530, which in turn outputs the distilled signal S .

[0209] The bridge 500 is trained so that the dimensionality of the first latent space is significantly reduced (e.g., reduced by two orders of magnitude) relative to the dimensionality of the space of the actual signal. The dimensionality of the second latent space can be equal to or smaller than the dimensionality of the first latent space.

[0210] According to some embodiments, the bridge 500 may be incorporated into operation 140. In such embodiments, during the initial processing of the measurement signal (i.e., during the Figures 5A to 5C After the processing of the measurement signal (described in detail above in the description of operation 140), the initial processed signal (i.e., the actual signal) is input into the bridge 500. The output of the bridge 500 (i.e., the distilled signal) may constitute the (final) processed signal, which is then used in operation 150 to update the guess and establish convergence.

[0211] Figure 5B A (first) autoencoder 540 for training an encoder 510 according to some embodiments is depicted. The autoencoder 540 comprises an encoder 510 and a second decoder 510'. The autoencoder 540 is trained on a set of real signals. Each of them is trained under conditions that are specific to him. For example, Figure 5B As shown, the actual signal input to the autoencoder 540 A k (from the group) is also outputted hereby. More specifically, the actual signal A k Encoded by encoder 510, thereby obtaining the actual signal A k Latent space representation ofR k . The latent space is represented by R k The second decoder 510' then outputs the original actual signal (ie, the actual signal A k According to some embodiments, the dimensionality of the latent space may be at least an order of magnitude smaller than the dimensionality of the space of the actual signal.

[0212] Figure 5C A second autoencoder 550 is depicted for training the first decoder 530 according to some embodiments. The second autoencoder 550 includes a second encoder 530′ and a first decoder 530. The second autoencoder 550 is trained on a set of analog signals. Each of the distilled signals is trained on its own condition. Figure 5C As shown, the analog signal input to the second autoencoder 550 S k (from said group) is also outputted thereby. More specifically, the analog signal S k The analog signal is encoded by the second encoder 530' to obtain S k Latent space representation of R k ′. The latent space is represented by R k ' is input to the first decoder 530, which then outputs the original analog signal (i.e., the analog signal S k According to some embodiments, the dimensionality of the latent space may be at least an order of magnitude smaller than the dimensionality of the space of the analog signal.

[0213] Once the (first) encoder 510 and the (first) decoder 530 have been trained, the bridge 500 (or more precisely, the converter 520) can be trained using labeled training data. The training data can be obtained by performing operations 110-130 on each of a plurality of samples (also referred to as "GT samples"), thereby obtaining measurement signals respectively related to each of the GT samples. Each of the measurement signals is then processed as described above in the description of operation 140. Subsequently, each of the GT samples is subjected to destructive measurement (e.g., using TEM to analyze a thin section extracted from the GT sample) to obtain GT data for the GT sample. Optionally, after processing the GT data for each GT sample, the GT data for each GT sample is input into a forward model to obtain a corresponding simulation signal. The training data includes labeled input signal-output signal pairs. Each input signal-output signal pair includes a processed signal related to a corresponding one of the GT samples and a simulation signal obtained based on the GT data of the (same) GT sample. After training the bridge 500, a (first) test subset of the training data can be used to evaluate the performance of the bridge 500. The evaluation can be performed by (i) applying the bridge 500 on each of the input signals, and (ii) computing the distance between the distilled signal output by the bridge 500 and the corresponding simulated signal (i.e., obtained using a forward model with the GT data as input).

[0214] According to some embodiments in which operation 140 is combined with the bridge 500, the training data may further include a second test subset comprising (additional) label pairs. Each of the additional label pairs may include one of the input signals of the first test subset and the corresponding GT data. After training the bridge 500, the additional label pairs may be used to evaluate the performance of the optimization algorithm of operation 150. The evaluation may be performed by (i) implementing the optimization algorithm on each of the input signals (of the additional label pairs), and (ii) calculating the distance between the (final) guess output by the optimization algorithm and the corresponding GT data.

[0215] According to some embodiments, the scribing data may be used as part of training and / or testing of the bridge 500 .

[0216] According to some embodiments, the optimization algorithm can be configured to receive as input a first difference signal given by or indicative of the difference between a first reference signal and a processed signal (obtained in operation 140). The first reference signal corresponds to the processed signal obtained by performing operation 140 on a measurement signal, which in turn is obtained by performing operations 110-130 on a reference sample or a reference structure in the profiled sample (whose structural parameters are known to a sufficient degree of accuracy). In such embodiments, the simulated signal output by the forward model can be subtracted from a second reference signal associated with the reference sample / structure (e.g., a second simulated signal or a distilled signal obtained from the first reference signal) to obtain a second difference signal. The optimization algorithm can be configured to minimize the distance between the first difference signal and the second difference signal. As a non-limiting example, the reference structure can be constituted by a line drawn on the profiled sample.

[0217] Figure 6 A flow chart of a method 600 for non-destructive acousto-optic depth metrology of a stratified sample according to some embodiments is presented. The method 600 corresponds to a specific embodiment of the method 100. The method 600 includes:

[0218] Operation 610 involves projecting a pulsed pump beam into a profiled sample comprising a layered structure to be tested (i.e., a structure comprising multiple layers) (the layered structure is also referred to as a "test structure"). Each of the pump pulses in the pump beam is configured to be absorbed in a slice of the profiled sample (also referred to as an "absorption slice") to induce a corresponding primary acoustic pulse that propagates within the layered structure and across the layers of the layered structure. Secondary acoustic pulses are generated by partial reflections of the primary acoustic pulse from a boundary between adjacent layers of the layered structure.

[0219] Operation 620 includes projecting a pulsed probe beam into the sample. Each probe pulse in the pulsed probe beam is configured to undergo Brillouin scattering from a primary acoustic pulse at a corresponding depth within the layered structure, the Brillouin scattering being caused by a corresponding pump pulse immediately preceding the probe pulse, such that the layered structure is probed over at least a depth range.

[0220] - Operation 630, wherein a measurement signal is obtained by measuring the intensity of light comprising a portion of the pulsed probe beam returning from the profiled sample.

[0221] - Operation 640, wherein the measurement signal is subjected to processing to obtain a processed signal.

[0222] Operation 650 involves executing an optimization algorithm. The optimization algorithm is configured to (i) receive at least the processed signal as input, and (ii) output a set of structural parameters representing the hierarchical structure by minimizing a cost function. The cost function indicates a difference between the processed signal and a simulated signal. The simulated signal is obtained using a forward model that simulates scattering of the probe pulse from the primary acoustic pulse and at least some of the secondary acoustic pulses within the hierarchical structure.

[0223] In each iteration of the optimization algorithm, the optimization algorithm updates a guess for a set of structural parameters and updates the simulation signal based on the guess.

[0224] Method 600 may be used as follows Figure 12 and Figure 13 It can be implemented by any of the systems described in the description or a system similar thereto.

[0225] According to some embodiments, the layered structure may include a via extending from a top surface of the layered structure into the layered structure (nominally perpendicular to the layers) and onto the body. According to some such embodiments, the depth of the via may be at least about 1 μm.

[0226] According to some embodiments, the body may be made of or include silicon. According to some embodiments, at least some of the rest of the layer (i.e., in addition to the body) may consist of, be made of, and / or include silicon oxide (SiO2), silicon germanium (SiGe), silicon nitride (e.g., Si3N4), an oxide-nitride-oxide (ONO) mixture stack, and / or combinations and / or mixtures thereof.

[0227] According to some non-limiting examples, the layered structure may be or include V-NAND (vertical NAND; also known as "3D NAND"), DRAM (dynamic random access memory), or 3D DRAM. According to some embodiments, the layered structure may be a preliminary structure in one of the manufacturing stages of V-NAND, DRAM, or 3D DRAM.

[0228] According to some embodiments, operations 610-630 may be implemented as specified in the description of operations 110-130 of method 100. Specifically, the pulsed pump beam and the pulsed probe beam may be implemented as specified in the description of operations 110 and 120 of method 100, respectively, according to some embodiments of method 100. Figures 2A to 2D Prepared as specified in the description.

[0229] To facilitate the description by way of non-limiting examples, additional reference is made to Figures 7A to 7G . Figures 7A to 7G Depicted are different stages in an implementation of method 600 according to some specific embodiments thereof. Figure 7A A cross-sectional view of a (dissected) sample 700 according to some embodiments is provided. The sample 700 includes a layered structure 702 to be tested (e.g., a semiconductor structure including a plurality of layers; also referred to as a "test structure") and a body 704 (e.g., a silicon substrate). The layered structure 702 is positioned on top of the body 704. As a non-limiting example, the layered structure 702 includes two types of layers 708: a first layer 708a and a second layer 708b. The first layer 708a and the second layer 708b are alternately disposed on top of each other. The second layer 708b may differ from the first layer 708a in terms of material composition (i.e., components and corresponding concentrations or relative concentrations) and / or total concentration (i.e., mass density). According to some embodiments, the first layer 708a may be composed of a first refractive index n A Characterized by the second layer 708b, and the second refractive index n B ≠n A Additionally or alternatively, according to some embodiments, the speed of sound in the second layer 708b may be different from the speed of sound in the first layer 708a.

[0230] According to some embodiments, and as Figures 7A to 7G , the layered structure 702 is shown to include through-holes (e.g., empty holes) 712 that protrude into the layered structure 702 from a top surface 714 of the layered structure 702. As a non-limiting example, assume that each of the through-holes 712 protrudes longitudinally (and vertically) into the layered structure 702 and has a circular transverse cross-section whose area decreases with depth. According to some embodiments, the through-holes 712 can be arranged in a periodic two-dimensional array. According to some such embodiments, the two-dimensional array is rectangular, wherein the through-holes 712 are arranged parallel to two orthogonal axes (e.g., according to Figure 7A , the rows and columns of the coordinate system depicted in , are the x-axis and y-axis respectively).

[0231] Figure 7A 708a1, 708a2, and 708b1 are also indicated. Layer 708a1 is the bottommost layer of first layer 708a (and the bottommost layer of all layers). Layer 708a2 is the second-bottommost layer of first layer 708a. Layer 708b1 is the bottommost layer of second layer 708b and is sandwiched between layers 708a1 and 708a2.

[0232] Figures 7B to 7ESchematically depicts the successive stages of the generation and propagation of an acoustic pulse within a layered structure 702, or more precisely, a detection portion (not numbered) of the layered structure 702, according to some embodiments. The detection portion may be shaped as a cylinder whose diameter is defined by the smaller of two beam diameters: (i) a pump beam (e.g., comprising) projected onto the top surface 714; Figure 7B The pump pulse 701 shown in FIG. 7 is a beam diameter, and (ii) a probe beam projected onto the top surface 714 (e.g., comprising Figures 7F to 7G The beam diameter of the probe pulse 721' is shown.

[0233] See also Figure 7B , according to some embodiments, pump pulses 701 are shown as projected onto top surface 714. Also indicated by double-headed arrow D p 701. Pump pulse 701 forms the portion of the pulsed pump beam projected onto layered structure 702 according to operation 610. Pump pulse 701 is configured to penetrate into layered structure 702 and propagate within layered structure 702 onto body 704. Pump pulse 701 is further configured to be absorbed by body 704. Slice 724 (also referred to as an "absorption slice") indicates a region within body 704 where substantially all of pump pulse 701 (or, in embodiments where a non-negligible portion of pump pulse 701 is reflected from body 704, substantially all of the transmitted portion of pump pulse 701) has been absorbed. Absorption slice 724 is adjacent to layered structure 702. The thickness of absorption slice 724 depends on the absorption length of pump pulse 701 in body 704.

[0234] Absorption of the pump pulse 701 by the absorbing slice 724 results in heating and expansion of the absorbing slice 724 and thus formation of the primary acoustic pulse 711 and the additional acoustic pulse 713, substantially as described above in Figure 2B Each of the primary acoustic pulse 711 and the additional acoustic pulse 713 propagates away from the absorbing slice 724. The primary acoustic pulse 711 travels within the layered structure 702 in the direction of the negative z-axis (i.e., toward the top surface 714). The additional acoustic pulse 713 can travel within the body 704 in the direction of the positive z-axis.

[0235] Figure 7C Depicts the Figure 7B Compared to the layered structure 702 at a later time, the absorbing slice 724 has cooled and is therefore no longer colored black. Each of the primary acoustic pulse 711 and the additional acoustic pulse 713 has propagated away from the absorbing slice 724. The primary acoustic pulse 711 is shown as being localized in the bottommost portion of the layer 708 (i.e., layer 708a1).

[0236] Figure 7D Depicts the Figure 7CCompared to the hierarchical structure 702 at a later time. Each of the primary acoustic pulse 711 and the additional acoustic pulse 713 has propagated (with Figure 7C 8b1). A primary acoustic pulse 711 (or, more precisely, the portion of the primary acoustic pulse 711 that is not reflected from the boundary between layer 708a1 and layer 708b1) is shown as being localized in layer 708b1. Also shown is a (first) secondary acoustic pulse 715. Secondary acoustic pulse 715 is briefly localized in layer 708a1 and is seen to propagate toward body 704. Secondary acoustic pulse 715 corresponds to the reflected portion of primary acoustic pulse 711 that is generated by the passage of primary acoustic pulse 711 from layer 708a1 into layer 708b1.

[0237] Figure 7E Depicts the Figure 7D Compared to the layered structure 702 at a later time, the primary acoustic pulse 711 (or more precisely, the portion of the primary acoustic pulse 711 that is not reflected from the boundary between layer 708b1 and layer 708a2) is shown as being localized in layer 708a2 (with additional acoustic pulse 713 at Figure 7E 708a1 and the main body 704). Secondary acoustic pulse 715 (or more precisely, the portion of secondary acoustic pulse 715 that was not reflected from the boundary between layer 708a1 and main body 704) has passed into main body 704. Also shown is (second) secondary acoustic pulse 717. Secondary acoustic pulse 717 is shown as being briefly localized in layer 708b1 and propagating toward main body 704. Secondary acoustic pulse 717 corresponds to the reflected portion of primary acoustic pulse 711, which was generated by the passage of primary acoustic pulse 711 from layer 708b1 into layer 708a2. Finally, (third) secondary acoustic pulse 719 is shown. Secondary acoustic pulse 719 is briefly localized in layer 708a1 and is seen to propagate away from main body 704. Secondary acoustic pulse 719 corresponds to the reflected portion of secondary acoustic pulse 715, which was generated by the passage of secondary acoustic pulse 715 into main body 704.

[0238] Figure 7F and Figure 7G The scattering of the probe pulse from the acoustic pulse within the layered structure 702 is schematically depicted. Figure 7F, according to some embodiments, a probe pulse 721' is shown as being projected onto the top surface 714. The probe pulse 721' forms part of a pulsed probe beam that is projected onto the layered structure 702 according to operation 620 after formation of a primary acoustic pulse 711' that propagates within the layered structure 702 in the direction of the negative z-axis towards the top surface 714. As described above, according to operation 610, the primary acoustic pulse 711' is induced by a pump pulse (not shown) that directly precedes the probe pulse 721'. In particular, as already described above, the pulsed probe beam and the pulsed pump beam (including the pump pulse that induced the primary acoustic pulse 711') can be prepared using the same laser source. A transmitted portion 723' of the probe pulse 721' penetrates the layered structure 702. A reflected portion 725' of the probe pulse 721' is reflected from the top surface 714. The transmitted portion 723' travels in the direction of the body 704 and is Brillouin scattered from the primary acoustic pulse 711', as Figure 7F 729' corresponds to the portion of scattered portion 727' that is transmitted out of layered structure 702 through top surface 714. The depth to which transmitted portion 723' is scattered (Brillouin) from primary acoustic pulse 711' within layered structure 702 depends on the time interval Δt1 by which probe pulse 721' is delayed relative to the immediately preceding pump pulse.

[0239] Figure 7F Also indicated in FIG 7 is an additional acoustic pulse 713′ caused by the same pump pulse as the primary acoustic pulse 711′. The additional acoustic pulse 713′ travels within the body 704 in the direction of the positive z-axis.

[0240] See also Figure 7G , according to some embodiments, a probe pulse 721″ is shown as being projected onto the top surface 714. The probe pulse 721″ is delayed relative to an immediately preceding pump pulse (not shown) by a time interval Δt2 ≥ Δt1. Thus, the transmitted portion 723″ (i.e., the portion of the probe pulse 721″ that is transmitted into the layered structure 702) is Brillouin scattered at a smaller depth within the layered structure 702 than the transmitted portion 723′. More specifically, the transmitted portion 723″ is Brillouin scattered from a primary acoustic pulse 711″ caused by the pump pulse that immediately precedes the probe pulse 721″. The primary acoustic pulse 711″ propagates in the direction of the negative z-axis toward the top surface 714 and is shown as being briefly localized in the layer 708b1. Secondary acoustic pulse 715″ propagates in a direction toward the positive z-axis of body 704 and is shown as being briefly localized in layer 708a1. Secondary acoustic pulse 715″ corresponds to a reflected portion of primary acoustic pulse 711″ that occurs as primary acoustic pulse 711″ passes from layer 708a1 into layer 708b1.

[0241] Figure 7GAlso indicated are an additional acoustic pulse 713" (partially shown) and a reflected portion 725" of the probe pulse 721" that is reflected from the top surface 714. The additional acoustic pulse 713" is caused by the same pump pulse as the primary acoustic pulse 711" and is shown traveling within the body 704 in the direction of the positive z-axis. The scattered portion 727" corresponds to the portion of the transmitted portion 723" that is Brillouin scattered from the primary acoustic pulse 711". The transmitted portion 729" corresponds to the portion of the scattered portion 721" that is transmitted out of the sample 700 through the top surface 714. The transmitted portion 731" corresponds to the portion of the transmitted portion 723" that is not scattered from the primary acoustic pulse 711". The transmitted portion 731" is scattered from the secondary acoustic pulse 715" (Brillouin), as shown in FIG. Figure 7G ” is indicated by the scattered portion 733” in the image. The scattered portion 733” travels in the direction of the negative z-axis toward the top surface 714 and is scattered from the primary acoustic pulse 711” (Brillouin). The transmitted portion 735” corresponds to the portion of the scattered portion 733” that is not scattered from the primary acoustic pulse 711”. The transmitted portion 735” travels in the direction of the negative z-axis toward the top surface 714. The transmitted portion 731” corresponds to the portion of the transmitted portion 735” that is transmitted out of the layered structure 702 through the top surface 714.

[0242] Figure 7F and Figure 7G Portions of the transmitted portion and the scattered portion reflected from the boundary between the first layer 708a and the second layer 708b are not indicated in FIG.

[0243] See again Figure 7F , the probe pulse 721 ′ (or more precisely, the transmitted portion 723 ′) is scattered from the primary acoustic pulse 711 ′ to a depth u1 via Δt1 ≈ T F +(u max -u1) / v a Related to time delay. T F is the formation time of the primary sound pulse. max is the distance from the top surface 714 to the body 704. a is the speed of sound in the first layer 708a. Figure 7G The detection pulse 721" (or more precisely, the transmitted portion 723") is scattered from the primary acoustic pulse 711" by Brillouin at a depth u2 via Related to time delay. b is the speed of sound in the second layer 708b. w1 is the thickness (vertical extent) of each of the first layers 708a. The depth u3 of the Brillouin scattering of the transmitted portion 731″ from the secondary acoustic pulse 715″ is measured via Δt2≈T F +(u3+2w1-u max ) / v a Related to time delay.

[0244] According to some embodiments, pump pulses and probe pulses may be alternately projected onto sample 700 , substantially as described above in the description of sample 200 .

[0245] Due to optical diffraction limit considerations, according to some embodiments, the wavelength of the probe pulse may be at least about two times greater than the distance between adjacent vias (eg, via 712a and via 712b).

[0246] Although Figures 7A to 7G , the diameter of the through-hole 712 is depicted as decreasing substantially linearly with depth, a skilled artisan will readily recognize that the methods and systems of the present disclosure may be applied to profile other through-hole geometries, such as, for example, geometries in which the through-hole has an elliptical cross-section, straight through-hole geometries, or through-hole geometries in which the change in through-hole diameter is non-monotonic.

[0247] The forward model of operation 650 may be or be combined with a computer simulation that simulates Brillouin scattering of the probe pulse from the acoustic pulse within the layered structure. The computer simulation may constitute the process described above in the context of operation 150 of method 100 (and in Figure 4 A specific embodiment of the computer simulation described in the description of FIG) is provided, with the additional proviso that the test structure is layered and that the simulated acoustic pulses simulate secondary acoustic pulses (e.g., secondary acoustic pulses 715, 717, and 719) in addition to simulating primary acoustic pulses (e.g., primary acoustic pulse 711).

[0248] According to some embodiments, in order to reduce the computational load of the computer simulation, acoustic pulses having energies below a selectable threshold energy may be ignored.

[0249] In the same manner as described above with respect to operation 150 of method 100, according to some embodiments, in a computer simulation, a layered structure including vertically extending through-holes (e.g., layered structure 702) is modeled by a laterally uniform structure having a refractive index that is equal to the effective refractive index of the layered structure estimated before performing method 600 based on the model of the layered structure (with respect to the layered structure).

[0250] According to some embodiments, and as described below in Figure 8 and Figure 9 As described in detail in the description of , in a computer simulation, acoustic pulses propagating within a layered structure are modeled by semi-transparent mirrors. Each of the acoustic pulses is modeled by a semi-transparent mirror moving at the local speed of sound in the direction of propagation of the acoustic pulse.

[0251] Alternatively, according to some embodiments, the computer simulation applies an optical transmission matrix approach to a model of the layered structure (eg, a laterally uniform structure that models the actual layered structure in embodiments where the actual layered structure includes through-holes).

[0252] See also Figure 8 As mentioned above, according to some embodiments of method 600, in a computer simulation, an acoustic pulse is modeled by a semi-transparent mirror. Most generally, each time a new acoustic pulse is formed, whether due to heating or reflection, a corresponding semi-transparent mirror is formed. Equivalently, when a semi-transparent mirror passes from one medium (e.g., a layer) to another medium (e.g., a layer) of different density, a new semi-transparent mirror is (additionally) formed, said new semi-transparent mirror traveling away from the "original" semi-transparent mirror.

[0253] Figure 8 A schematic diagram of a (dissected) sample 800 according to some embodiments is depicted. Sample 800 includes a layered structure 802 to be tested and a body 804 on which the layered structure 802 is disposed. As a non-limiting example, the layered structure 802 includes a first layer 808a and a second layer 808b, with the first layer 808a disposed on the second layer 808b. The second layer 808b can differ from the first layer 808a in terms of material composition and / or concentration (i.e., mass density). Also indicated are a top surface 814 of the layered structure 802, an absorbent slice 824 included in the body 804 and adjacent to the layered structure 802, a first boundary 842 between the body 804 and the layered structure 802, and a second boundary 844 between the first layer 808a and the second layer 808b. The first boundary 842 constitutes the top surface of the absorbent slice 824.

[0254] A semi-transparent (first) mirror 811, a semi-transparent (second) mirror 813, and a semi-transparent (third) mirror 815 are shown superimposed on a schematic diagram of the sample 800. The first mirror 811 is depicted as "propagating" within the second layer 808b in the direction of the top surface 814 (i.e., in the direction of the negative z-axis). The second mirror 813 is depicted as "propagating" within the body 804 away from the layered structure 802. The third mirror 815 is depicted as "propagating" within the first layer 808a in the direction of the body 804. The first mirror 811 and the second mirror 813 correspond to the primary acoustic pulse and the additional acoustic pulse, respectively. The primary acoustic pulse and the additional acoustic pulse are caused by the vibration of the absorbing slice 824 within the body 804, which is caused by the heating of the absorbing slice 824. According to the measurement operation 110, the heating is generated by the projection of the pump pulse (not shown) on the top surface 814, essentially as described above in Figure 7B and Figure 7CThe third reflector 815 corresponds to a secondary acoustic pulse that constitutes a reflected portion of the primary acoustic pulse, the secondary acoustic pulse being generated by partial reflection of the primary acoustic pulse from the second boundary 844, substantially as described above in Figure 7D The description of sound pulses 711 and 715 is described in detail.

[0255] Also shown is a (simulated) probe pulse 821 superimposed on the schematic diagram of sample 800, along with a (simulated) transmitted portion 823 and a (simulated) reflected portion 825 of probe pulse 821. As indicated by a (simulated) scattered portion 827 and a (simulated) transmitted portion 831, transmitted portion 823 is partially reflected from first reflector 811. Due to the Doppler effect, the frequency of scattered portion 827 shifts. This frequency shift is consistent with the Brillouin frequency shift that would be obtained in a realistic setting corresponding to the computer simulation. (Simulated) scattered portion 833 indicates the portion of transmitted portion 831 that is reflected from first reflector 811.

[0256] The degree of reflectivity and transmittance of each of the mirrors can be determined based on the physical properties of the sample 800 (specified by the reference data) and prior knowledge of the physics of acoustic wave propagation in such a profiled sample (e.g., the speed of sound). In this regard, it is noted that the reflectivity and transmittance of a mirror can differ depending on whether the mirror is located within the first layer 808a or the second layer 808b, reflecting the differences in physical properties (e.g., density) between the layers. According to some embodiments in which the density of the test structure varies continuously with a depth coordinate within the layer, the reflectivity and transmittance of the mirror can also vary continuously with the depth coordinate when moving through the layers.

[0257] Most generally, a semi-transparent mirror can be double-sided in the sense of comprising two reflective (and semi-transparent) surfaces. As an example, in addition to the top surface 851a of the first mirror 811 being (partially) reflective, the bottom surface 851b of the first mirror 811 can also be considered (partially) reflective, so that the return portion of the projected probe pulse will include a contribution resulting from triple scattering: in addition to the first portion of the scattered portion 833 being transmitted through the first mirror 811 (as indicated by the (modeled) transmitted portion 835), the second portion of the scattered portion 833 undergoes a partial (second) reflection from the bottom surface 851b. This doubly reflected portion (not shown) is partially reflected a third time from the top surface (not numbered) of the third mirror 815. The triply reflected portion (not shown) is partially transmitted through the first mirror 811 and then exits the layered structure 802 through the top surface 814.

[0258] Alternatively, according to some embodiments, for example, to reduce the computational load of computer simulations, at least some of the mirrors (e.g., mirrors formed later) may be considered single-sided in the sense of having only one reflective surface. As a non-limiting example, according to some embodiments, only the top surface (not numbered) of the third reflector 815 may be reflective, while both the top surface 851a and the bottom surface 851b (of the first reflector 811) may be reflective. According to some embodiments, and as Figure 8 As depicted in , all mirrors can be considered as single-sided.

[0259] Figure 9 is a time-depth plot illustrating the propagation and formation of an acoustic pulse in an exemplary semi-transparent mirror model, according to some embodiments. The horizontal axis represents the time t from the formation of the first reflector 811 and the second reflector 813. The vertical axis represents the height h measured from the first boundary 842 in the direction of the negative z-axis. (Segmented) line 911 represents the trajectory of the first reflector 811 within the layered structure 802. Line 913 represents the trajectory of the second reflector 813 within the main body 804. (Segmented) line 915 represents the trajectory of the third reflector 815 within the layered structure 802 and the main body 804. Line 911 includes three straight line segments: a first segment 911a, a second segment 911b, and a third segment 911c. The respective slopes of the first segment 911a and the second segment 911b are different. The first segment 911a extends between points (t=0, h=0) and (t=t1, h=h1). The second segment 911b extends between points (t=t1, h=h1) and (t=t3>t1, h=H), where H is the height of the layered structure 802 (i.e., the distance between the main body 804 and the top surface 814). At t=t1, the first reflector 811 reaches the second boundary 844. At t=t3>t1, the first reflector 811 reaches the top boundary of the layered structure 802. The third segment 911c represents the trajectory of the first reflector 811 after the first reflector 811 reflects from the top boundary of the layered structure 802. Due to the fact that the speed of sound in the second layer 808b is greater than the speed of sound in the first layer 808a, the second segment 911b is more inclined than the first segment 911a. At t=t1, the first reflector 811 reaches the second boundary 844, causing the first segment 911a to diverge into the second segment 911b and line 915 (or equivalently, forming the second reflector 815).

[0260] Similar to line 911, line 915 is also segmented. Line 915 includes two straight line segments with different respective slopes: a first segment 915a extends between points (t=t1, h=h1) and (t=t2>t1, h=0). A second segment 915b extends from point (t=t2>t1, h=0). At t=t2, the second reflector 815 reaches the first boundary 842, causing the first segment 915a to diverge into the second segment 915b and line 917. Line 917 represents the semi-transparent (fourth) reflector ( Figure 8 The fourth reflector corresponds to a secondary acoustic pulse generated by the reflection of the secondary acoustic pulse corresponding to the third reflector 815 from the second boundary 844.

[0261] According to some embodiments, an initial guess of the average transverse cross-sectional area of ​​the through-holes in the layered structure can be obtained by an iterative process. The iterative process is performed on the measurement signals related to the layered structure (e.g., obtained in operations 610-630), and more precisely, on the processed signals obtained from the measurement signals (e.g., obtained in operation 640). In the iterative process, the estimated Brillouin frequency distribution of the first layer is used to estimate the Brillouin frequency distribution of the second layer adjacent to the first layer. The estimated Brillouin frequency distributions of the first and second layers are used to estimate the Brillouin frequency distribution of the third layer adjacent to the second layer, and so on. To facilitate the description, the case of two layers is first described. 10A to 10C Depicted is a hierarchical structure 1002 to be tested according to some embodiments. More specifically, Figure 10A A cross-sectional view of a sample 1000 (dissected) is presented. In addition to a layered structure 1002 (also referred to as a "test structure"), the sample 1000 also includes a body 1004 (e.g., a silicon body) on which the layered structure 1002 is mounted. By way of non-limiting example, the layered structure 1002 is shown as including two layers: a first layer 1008a and a second layer 1008b. The first layer 1008a is sandwiched between the body 1004 and the second layer 1008b. The layered structure 1002 additionally includes a through-hole 1012 extending vertically from a top surface 1014 of the layered structure 1002 to the body 1004.

[0262] According to operation 610 of method 600, a pump pulse 1001 is shown projected onto (e.g., perpendicular to) a top surface 1014 of a layered structure 1002. Pump pulse 1001 forms part of a pulsed pump beam projected onto layered structure 1002. Pump pulse 1001 is configured to penetrate into layered structure 1002 and propagate within layered structure 1002 onto body 1004. Pump pulse 1001 is further configured to be absorbed by body 1004. Slice 1024 (also referred to as an "absorption slice") indicates a region (e.g., a thin region) within body 1004 where substantially all of pump pulse 1001 (or, in embodiments where a non-negligible portion of pump pulse 1001 is reflected from body 1004, substantially all of the transmitted portion of pump pulse 1001) is absorbed. Absorption slice 1024 is adjacent to layered structure 1002. The thickness of the absorption slice 1024 depends on the absorption length of the pump pulse 1001 in the body 1004 .

[0263] Absorption of the pump pulse 1001 by the absorbing slice 1024 results in heating of the absorbing slice 1024. Heating of the absorbing slice 1024 causes the absorbing slice 1024 to expand, as indicated by the double-headed arrow E". The expansion of the absorbing layer 1024 results in the formation of a primary acoustic pulse 1011 and an additional acoustic pulse 1013, each of which propagates away from the absorbing slice 1024. The primary acoustic pulse 1011 propagates within the layered structure 1002 in the direction of the negative z-axis (i.e., toward the top surface 1014). The additional acoustic pulse 1013 may propagate within the body 1004 in the direction of the positive z-axis.

[0264] Figure 10B Presented with Figure 10A Compared to a cross-sectional partial view of sample 1000 at a later time: absorbing slice 1024 has cooled, and each of primary acoustic pulse 1011 and additional acoustic pulse 1013 has propagated away from absorbing slice 1024. Primary acoustic pulse 1011 is shown propagating within first layer 1008a. As primary acoustic pulse 1011 travels through layered structure 1002, the local mass density is temporarily modified where primary acoustic pulse 1011 is temporarily localized. This temporary modification of the local mass density results in a corresponding temporary (local) modification of the refractive index due to the photoelastic effect.

[0265] Figure 10B 6 is further depicted in FIG6 , in accordance with some embodiments, as a probe pulse 1021 projected onto the top surface 1014. The probe pulse 1021 forms part of a pulsed probe beam projected onto the layered structure 1002 in accordance with operation 620 of method 600. As described above, the pulsed probe beam and the pulsed pump beam (including the pump pulse 1001) can be prepared using the same laser source.

[0266] A transmitted portion 1023 of the probe pulse 1021 penetrates the layered structure 1002. A reflected portion 1025 of the probe pulse 1021 reflects from the top surface 1014. The transmitted portion 1023 is Brillouin scattered from the primary acoustic pulse 1011, as indicated by scattered portion 1027. A transmitted portion 1029 corresponds to the portion of the scattered portion 1027 that exits the layered structure 1002 through the top surface 1014. The depth to which the transmitted portion 1023 (Brillouin) is scattered from the primary acoustic pulse 1011 within the layered structure 1002 depends on the time delay of the probe pulse 1021 relative to the delay of the preceding pump pulse (i.e., pump pulse 1001).

[0267] See also Figure 10C In accordance with some embodiments, a probe pulse 1021′ is shown projected onto top surface 1014. Probe pulse 1021′ is delayed relative to an immediately preceding pump pulse (not shown) by a time interval that is greater than the time delay of probe pulse 1021 relative to pump pulse 1001. Thus, transmitted portion 1023′ (i.e., the portion of probe pulse 1021′ that is transmitted into layered structure 1002) Brillouin scatters at a smaller depth within layered structure 1002 than transmitted portion 1023′. More specifically, transmitted portion 1023′ Brillouin scatters from primary acoustic pulse 1011′ caused by the pump pulse immediately preceding probe pulse 1021′. Primary acoustic pulse 1011′ is shown propagating within second layer 1008b in a direction toward the negative z-axis of top surface 1014. Secondary acoustic pulse 1015′ is shown propagating within first layer 1008a in a direction toward the positive z-axis of body 1004. The secondary acoustic pulse 1015' corresponds to a reflected portion of the primary acoustic pulse 1011' that is generated when the primary acoustic pulse 1011' passes from the first layer 1008a into the second layer 1008b.

[0268] Figure 10C Also indicated is a reflected portion 1025' of the probe pulse 1021' that is reflected from the top surface 1014. The scattered portion 1027' corresponds to the portion of the transmitted portion 1023' that is Brillouin scattered from the primary acoustic pulse 1011'. The transmitted portion 1029' corresponds to the portion of the scattered portion 1027' that is transmitted out of the layered structure 1002 through the top surface 1014. The transmitted portion 1031' corresponds to the portion of the transmitted portion 1023' that is not scattered from the primary acoustic pulse 1011'. The transmitted portion 1031' is scattered from the secondary acoustic pulse 1015' (Brillouin), as shown in FIG. Figure 10C1014. The transmitted portion 1035' corresponds to the portion of the scattered portion 1033' that is not scattered from the primary acoustic pulse 1011'. The transmitted portion 1035' travels in the direction of the negative z-axis toward the top surface 1014. The transmitted portion 1037' corresponds to the portion of the transmitted portion 1035' that is transmitted out of the layered structure 1002 through the top surface 1014.

[0269] See also Figure 11 , Figure 11 is a graph depicting the variation of the voltage signal with the time delay Δt between the successively projected probe pulse and the directly preceding pump pulse (e.g., probe pulse 1021 and pump pulse 1001). The voltage signal corresponds to the expected Brillouin oscillation contribution to the measurement signal, which would be obtained by implementing method 600 with respect to layered structure 1002 in the absence of noise and measurement setup imperfections. Two different behaviors are visible: Up to a time delay Δt=Δt′ (indicated by the vertical dashed line), the voltage signal has a well-defined frequency. For time delays greater than Δt′, the voltage signal resembles an amplitude modulated signal (i.e., an AM signal). That is, the voltage signal can be viewed as the sum of two voltage signals with slightly different frequencies. Δt′=w a / v a , where w a is the thickness (vertical extent) of the first layer 1008a and v a is the speed of sound within the first layer 1008a (i.e., the propagation speed of the primary acoustic pulse within the first layer 1008a). Until a time delay Δt′ from the formation of the primary acoustic pulse, only a single acoustic pulse (i.e., the primary acoustic pulse; e.g., primary acoustic pulse 1011) propagates within the layered structure 1002. Therefore, a probe pulse delayed by a time delay less than Δt′ is scattered only once within the layered structure 1002. More specifically, until the time delay Δt′, a voltage signal is generated by scattering within the first layer 1008a (and only within the first layer 1008a), e.g., Figure 10B For a time delay greater than Δt′, initially, two acoustic pulses (e.g., primary acoustic pulse 1011′ and secondary acoustic pulse 1015′) propagate within the layered structure 1002, and a probe pulse is scattered from each acoustic pulse. More specifically, for a time delay greater than Δt′, a voltage signal is generated by scattering within each of the first layer 1008a and the second layer 1008b, e.g., Figure 10C Depicted in.

[0270] Thus, to obtain an initial guess, a short-time Fourier transform (STFT) can be performed over the time interval (T F, Δt′) is applied to process the signal. Based on the STFT, the Brillouin frequency distribution of the first layer 1008a is estimated. More specifically, the function The frequency of the Brillouin oscillations (caused at a certain time by scattering within the first layer 1008a, as measured from the corresponding primary acoustic pulses generated) is estimated to be equal to the time delay Δt. Next, using the relation Equation (1) estimates the dependence of the average lateral cross-sectional area of ​​the vias in the first layer 1008a on depth. Here represents the effective refractive index within the first layer 1008a (as estimated from the above relationship). a is the distance from the subject 1004.

[0271] For time delays greater than Δt′, for the purpose of obtaining an initial guess, the processed signal is (preliminarily) assumed to be

[0272] form. Estimate the frequency of the Brillouin oscillation caused by scattering within the second layer 1008b. The STFT can be applied to process the signal within the time interval (Δt′, Δt″), where Δt″=Δt′+min{w a / v a , w b / v b}w b is the thickness of the second layer 1008b. b is the speed of sound in the second layer 1008b. Based on STFT and estimate This is then used to estimate the depth dependence of the average lateral cross-sectional area of ​​the vias within the second layer 1008b in substantially the same manner as described above with respect to the first layer 1008a.

[0273] According to some embodiments, the values ​​of a1 and a2 can be learned in real time based on the processed signals using machine learning tools. According to some embodiments, the ratio a2 / a1 can be approximately equal to the reflection coefficient of the transition from the second layer 1008b to the first layer 1008a, which depends on the material composition of the layers 1008a and 1008b.

[0274] Although Figures 10A to 11The description has been made in the context of depth profiling of a test structure comprising two layers, but the skilled person will readily recognize the generalization to a test structure comprising N ≥ 3 layers. For example, in the case of three layers, for the purpose of obtaining an initial guess, for the time delay Δt such that the primary acoustic pulse has passed into the third layer (i.e., the top layer), the processed signal is (preliminarily) assumed to be Mode. and It can be determined as described above. Estimate the frequency of the Brillouin oscillations caused by scattering within the third layer. The STFT is applied to process the signal in the time interval where the primary sound pulse exists in the third layer. and estimate This is then used to estimate the depth dependence of the average lateral cross-sectional area of ​​the vias within the third layer.

[0275] According to some embodiments, an iterative process may also be applied on the scribing data as part of a calibration operation to determine (i.e., the Brillouin frequency distribution associated with the scribe line). Thus, in such an embodiment, determining This is equivalent to determining a set of N Brillouin frequencies Where index i denotes a layer (and N is the number of layers). According to some embodiments, as part of obtaining the Brillouin frequency distribution, an STFT may be applied to process the signal as described above. Alternatively, according to some embodiments, as part of obtaining the Brillouin frequency distribution, a Fast Fourier Transform (FFT) may be applied to process the signal.

[0276] system

[0277] According to an aspect of some embodiments, there is provided a computerized system for non-destructive acousto-optic depth metrology of layered structures. Figure 12 A block diagram of such a computerized system (computerized system 1200) according to some embodiments is presented. System 1200 includes an acoustic-optical measurement setup 1202 and a processing circuit system 1204. Measurement setup 1202 includes a light generating device 1212 and a light sensor 1214 (or more generally, one or more light sensors). Measurement setup 1202 may further include a controller 1218 that is functionally associated with the components of measurement setup 1202 and / or communicatively associated with processing circuit system 1204.

[0278] The light generating device 1212 is configured to generate an (optical) pulsed pump beam indicated by arrow A1, which is directed onto the (profiling) sample 40. Each pump pulse in the pulsed pump beam is configured to be absorbed by the sample 40 so as to form a corresponding (primary) acoustic pulse within the sample 40, as specified above in the description of operations 110 and 610 of methods 100 and 600, respectively. The light generating device 1212 is further configured to project an (optical) pulsed probe beam indicated by arrow A2 onto the sample 40 substantially simultaneously with the pulsed pump beam. Each probe pulse in the pulsed probe beam is configured to penetrate into the sample 40 and Brillouin scatter from the last formed (primary) acoustic pulse (up to the time), as specified above in the description of operations 120 and 620 of methods 100 and 600, respectively. Each detection pulse can be delayed by a corresponding time interval relative to the immediately preceding pump pulse so as to be Brillouin scattered by the last generated (primary) acoustic pulse at a corresponding depth within the sample 40, thereby allowing detection of the sample 40 over a range of depths and facilitating three-dimensional analysis of the sample 40.

[0279] It should be understood that sample 40 does not form part of system 1200.

[0280] Light sensor 1214 is configured to obtain a measurement signal by measuring the intensity of light, indicated by arrow A3, returned from sample 40. The measurement signal is relayed from light sensor 1214 to processing circuitry 1204, as indicated by arrow A4. Processing circuitry 1204 is configured to process the measurement signal to obtain information indicative of the three-dimensional geometry and / or material composition of sample 40, as described below.

[0281] According to some embodiments, and as Figure 12 As depicted in FIG, light generating device 1212 may include a light source (not shown), such as a laser source, for generating both a pulsed pump beam and a pulsed probe beam. According to some embodiments, the laser source may be a visible laser source or an infrared laser source.

[0282] According to some embodiments, the light generating device 1212 further includes a pump modulator (not shown), and the processing circuit system 1204 includes a lock-in amplifier (not shown). The pump modulator is configured to amplitude modulate the pulsed pump beam to facilitate using the lock-in amplifier to isolate the contribution of the Brillouin oscillation component of the return portion of the pulsed probe beam to the measurement signal, as detailed above in the description of method 100 and as described below. Figure 13 as further specified in the description.

[0283] According to some embodiments, light generating device 1212 can be configured to allow for controllable setting of the polarization of the generated pulsed pump beam and / or the polarization of the generated pulsed probe beam. According to some such embodiments, light generating device 1212 can include one or more polarizers (not shown). Additionally, according to some embodiments, light generating device 1212 can be configured to allow for controllable setting of the intensity of the pulsed pump beam and the intensity of the pulsed probe beam and / or the beam diameter of each of the above beams.

[0284] Controller 1218 can be configured to control and synchronize the operation of various components of measurement setup 1202. Specifically, controller 1218 can be configured to allow for setting values ​​for selectable preparation parameters of the pulsed pump beam and the pulsed probe beam, as well as the impact position of the pulsed pump beam on the profiled sample (e.g., sample 40). Non-limiting examples of selectable preparation parameters include polarization, the intensity of each of the pulsed pump beam(s) and the pulsed probe beam(s), and / or the angle of incidence of each of these beams, and, in some embodiments, the time delay between successive pump and probe pulses. Additionally, controller 1218 can be configured to allow for setting operating parameters of light sensor 1214. For example, in some embodiments, the bandwidth of the output signal of light sensor 1214 can be adjusted by controller 1218. In some embodiments, in which measurement setup 1202 includes a polarization filter (not shown), which is functionally associated with controller 1218 and configured to transmit only return light of a specific polarization through the polarization filter, the polarization (e.g., vertical, horizontal, right-handed circular, or left-handed circular) can be selected by controller 1218.

[0285] Processing circuitry 1204 may include one or more processors and, optionally, volatile and / or non-volatile memory components (not shown). According to some embodiments, and as mentioned above, processing circuitry 1204 may further include a lock-in amplifier. Processing circuitry 1204 is configured to execute software stored thereon or remotely executed, the software being configured to determine a set of structural parameters of sample 40 based at least on the measurement data relayed from light sensor 1214. The set of structural parameters may indicate at least the internal geometry and / or material composition of sample 40. To determine the set of structural parameters of sample 40, according to some embodiments, processing circuitry 1204 (i.e., the one or more processors therein) may be configured to execute optimization algorithm(s), as described above in the descriptions of operations 150 (including specific embodiments thereof consisting of operation 400) and 650 of methods 100 and 600, respectively.

[0286] According to some embodiments, the processing circuit system 1204 may be further configured to run software (e.g., signal processing software) stored thereon or remotely run software before executing the algorithm(s), the software being configured to extract a processed signal indicating the contribution of Brillouin oscillations to the measured signal from the measured signal. According to some such embodiments, where the measurement setup 1202 includes a pump modulator and the processing circuit system 1204 includes a lock-in amplifier, the processed signal may be composed of a demodulated signal obtained using the lock-in amplifier. According to some embodiments, the software may be further configured to extract values ​​of key parameters from the processed signal, as described above in the description of operations 140 and 640 of methods 100 and 600, respectively. In this regard, it is noted that the extraction of the key parameters may involve the use of an algorithm configured to enhance the processed signal and / or the measured signal. According to some embodiments, the processing circuit system 1204 may be configured to extract the STFT of the processed signal.

[0287] According to some embodiments, processing circuitry 1204 can be configured to suppress laser noise in the measurement signal based on noise correlation between the pump beam and the probe beam. According to some embodiments, processing circuitry 1204 can be configured to apply a low-pass filter and / or a high-pass filter to selectively remove undesired frequency ranges in the Fourier transform of the measurement signal or the demodulated signal. For example, as described above in the description of method 100, in embodiments where the profiled sample includes a silicon body on which a test structure is mounted, a low-pass filter can be used to remove contributions to the measurement signal due to scattering of the probe beam from an acoustic pulse propagating within the body. Additionally, according to some embodiments, processing circuitry 1204 can be configured to apply: (i) a fitting algorithm to remove or at least attenuate thermal-optical contributions to the measurement signal, and / or (ii) a low-pass filter to average out the thermal-optical contributions.

[0288] According to some embodiments, processing circuitry 1204 may be configured to execute bridge 500 .

[0289] The memory component may store information specifying expected ranges of values ​​for various physical parameters. The physical parameters may include structural parameters to be determined, as well as other physical parameters whose values ​​can be inferred from the measurement data. As an example, the memory component may store a frequency range within which the extracted Brillouin frequency is expected to fall. According to some embodiments, failure of a measured value to fall within a corresponding expected value range may indicate a malfunction in the measurement setup and / or a defect in the profiled sample. Similarly, according to some embodiments, failure of a determined value of a structural parameter to fall within a corresponding expected value range may indicate a software malfunction and / or a defect in the profiled sample.

[0290] According to some embodiments, processing circuitry 1204 and controller 1218 may be housed in a common housing, for example, when implemented by a single computer.

[0291] According to some embodiments, system 1200 may further include an analog-to-digital converter (ADC; not shown) configured to convert an analog signal obtained by light sensor 1214 into a digital signal. According to some such embodiments, light sensor 1214 may be equipped with an ADC. Additionally or alternatively, according to some embodiments, controller 1218 and / or processing circuitry 1204 may include one or more ADCs.

[0292] Figure 13 Schematically depicted is a computerized system 1300, which corresponds to a specific embodiment of system 1200. System 1300 includes an acousto-optic measurement setup 1302 and processing circuitry 1304, which correspond to specific embodiments of acousto-optic measurement setup 1202 and processing circuitry 1304, respectively. Also depicted is a (profiled) sample 80, including a (test) structure 82, being profiled by system 1300. Sample 80 corresponds to a specific embodiment of sample 40. It should be understood that sample 80 and structure 82 are not included in system 1300. Measurement setup 1302 includes a light generating device 1312, a light sensor 1314, and an optional controller 1318, which correspond to specific embodiments of light generating device 1212, light sensor 1214, and controller 1218, respectively. Also indicated is a platform 1320 (eg, an xyz platform) on which the sample 80 is placed.

[0293] Light generating device 1312 may include a laser source 1322 (i.e., a laser generator), a variable delay line 1358, and a (first) beam splitter 1362. Laser source 1322 is configured to generate a pulsed laser beam comprising a plurality (i.e., a series of) laser pulses. According to some embodiments, laser source 1322 may be a visible laser source or an infrared laser source. Variable delay line 1358 is configured to delay the laser pulses (and more generally, the laser pulse train) transmitted thereto by a controllably selectable time delay (i.e., a time interval). According to some embodiments, and as Figure 13, the light generating device 1312 can further include a pump modulator 1356, and the processing circuitry 1304 can include a lock-in amplifier 1366 in addition to the processor(s) 1368. According to some embodiments, and as explained in detail below, the pump modulator 1356 can be configured to amplitude modulate the pump beam transmitted into the pump modulator 1356 to facilitate isolating the contribution of the Brillouin oscillation component of the returning portion of the probe beam incident on the sample (e.g., sample 80) to the measurement signal.

[0294] According to some embodiments, and as Figure 13 As depicted in FIG, the light generating device 1312 may further include an objective lens 1342, a second beam splitter 1346, and a third beam splitter 1348. According to some embodiments, and as Figure 13 As depicted in , the measurement setup 1302 may further include an optical filter 1352 .

[0295] In operation, laser source 1322 generates a laser beam comprising a plurality of laser pulses. To facilitate description, the operation of measurement setup 1302 is described with respect to a single laser pulse in the laser beam: nth laser pulse 1301n (in the laser beam generated by laser source 1322). Each group of M consecutively generated laser pulses can be generated within a corresponding time frame of size 1 / B, where B is the bandwidth of light sensor 1314 (such that 1 / B is its temporal resolution). As a result, the rate of probe pulses will be greater than the bandwidth of light sensor 1314, so that each of the intensity values ​​comprising the measurement signal obtained by light sensor 1314 includes contributions from the return portion of each of the plurality of probe pulses, which are projected consecutively within the time frame 1 / B.

[0296] The nth laser pulse 1301n is split by a first beam splitter 1362 into two parts: a first (nth) pulse portion 1303n1 and a second (nth) pulse portion 1303n2. The first pulse portion 1303n1 is transmitted to a pump modulator 1356 and thereby amplitude modulated to produce an nth pump pulse 1305n. The second pulse portion 1303n2 is transmitted to a variable delay line 1358, thereby being delayed by a corresponding time interval Δt′, thereby producing an nth detection pulse 1315n. The modulation frequency used by the pump modulator 1356 to modulate the first pulse portion (as part of the modulation of the pulsed pump beam) is relayed (e.g., by a controller 1318) to a lock-in amplifier 1366.

[0297] Alternatively, according to some embodiments, variable delay line 1358 may be configured to change the path length in increments. According to some such embodiments, multiple probe pulses may be delayed by the same time delay.

[0298] According to some embodiments, and as Figure 13 As depicted in , the nth pump pulse 1305n can be focused by the objective lens 1342 (optionally after passing through a second beam splitter 1346) before impinging on the structure 82. Similarly, according to some embodiments, and as Figure 13 As depicted in , the nth probe pulse 1315n may be focused by an objective lens 1342 before impinging on the structure 82 (optionally after passing through a third beam splitter 1348 and being reflected by a second beam splitter 1346).

[0299] The first returning nth pulse 1325n (indicated by the dashed line) corresponds to a portion of the nth probe pulse 1315n that is reflected from the structure 82. Figure 13 , first returned nth pulse 1325n travels onto filter 1352 (optionally after being reflected by second beam splitter 1346 and passed through third beam splitter 1348). Second returned nth pulse 1335n (indicated by the double-dashed line) may correspond to a portion of nth pump pulse 1305n that returns (is reflected and / or scattered) from structure 82. According to some embodiments, and as Figure 13 As depicted in , the second returning nth pulse 1335n travels onto the filter 1352 (optionally after being reflected by the second beam splitter 1346 and passing through the third beam splitter 1348).

[0300] The nth filtered pulse 1345n corresponds to the output of optical filter 1352. From optical filter 1352, nth filtered pulse 1345n travels to light sensor 1314. In embodiments where, as described above, M>1 laser pulses are projected consecutively within time frame 1 / B, light sensor 1314 does not distinguish between different filtered pulses within a group of M consecutive filtered pulses and therefore measures the combined intensity of the M filtered pulses. Thus, light sensor 1314 measures nth filtered pulse 1345n along with M-1 additional filtered pulses to obtain a single intensity value. Alternatively, according to some embodiments where only a single laser pulse is generated in each time frame 1 / B, light sensor 1314 measures the intensity of nth filtered pulse 1345n to obtain the nth intensity value.

[0301] The measurement signal (i.e. the measured intensity value, optionally after processing) is sent to a lock-in amplifier 1366. The lock-in amplifier 1366 uses the modulated signal to obtain a demodulated signal (i.e. the measurement signal after processing), in which contributions due to background signals and / or noise are suppressed and Brillouin oscillations are evident.

[0302] The demodulated signal is relayed to processor(s) 1368. Processor(s) 1368 are configured to process the demodulated signal to determine a set of structural parameters characterizing structure 82, as described above in the description of operations 150 and 650 of methods 100 and 600, respectively, and in the description of processing circuitry 1204 of system 1200. According to some embodiments, processor(s) 1368 may be configured to perform operations using the demodulated signal. Figure 4 4. The optimization algorithm of FIG. 8 is then executed (i.e., operation 400), optionally after additional processing (e.g., as specified by operations 140 and 640 of methods 100 and 600, respectively), thereby constituting an input to the optimization algorithm. According to some embodiments, the additional processing may include removing thermo-optical contributions to the measurement signal. Additionally or alternatively, in embodiments in which the sample 80 comprises a silicon body on which the test structure is mounted, low-pass filtering may be utilized to filter out contributions to the Brillouin oscillations due to scattering of acoustic pulses from within the body. The additional processing may also include applying an STFT to the processed signal to extract a preliminary estimate of the dependence of the Brillouin frequency on the time delay, as described above in Figures 10A to 11 According to some embodiments, the processor(s) 1368 may be configured to execute the bridge 500 .

[0303] According to some embodiments, the light generating device 1312 may further include a harmonic generation unit (not shown). The harmonic generation unit may be positioned between the first beam splitter 1362 and the pump modulator 1356. The inclusion of the harmonic generation unit allows the frequency of the pump beam to be varied relative to the frequency of the probe beam. For example, using the harmonic generation unit, the pump beam may be prepared at a frequency that is, for example, a second harmonic or a third harmonic relative to the fundamental frequency (i.e., the frequency of the laser beam generated by the laser source 1322). To this end, according to some embodiments, the light generating device 1312 may further include an optical filter (not shown) positioned between the harmonic generation unit and the pump modulator 1356. The optical filter may be configured to selectively filter light passing through the filter at one or more higher harmonics (i.e., having a higher frequency than the first harmonic). Additionally or alternatively, according to some embodiments, the processor(s) 1368 may be configured to subject the demodulated signal to low-pass filtering to filter out contributions of reflected portions of the pump beam to the demodulated signal. Additionally or alternatively, according to some embodiments, the harmonics generating unit may be positioned between the first beam splitter 1362 and the variable delay line 1358 .

[0304] As used herein, the term "beam" in reference to a light beam (such as a laser beam) may refer to a continuous wave light beam or a pulsed light beam (train of light pulses) according to some embodiments.

[0305] In the description and claims of this application, the words "include" and "have" and their forms are not limited to the list of members that can be associated with the words.

[0306] As used herein, the term "substantially" may be used to specify that a first property, quantity, or parameter is close to or equal to a second or target property, quantity, or parameter. For example, a first object and a second object may be said to have "substantially the same length" when the length of the first object measures at least 80% (or some other predefined threshold percentage) and no more than 120% (or some other predefined threshold percentage) of the length of the second object. Specifically, situations in which the first object and the second object have the same length are also encompassed by the statement that the first object and the second object have "substantially the same length."

[0307] According to some embodiments, a target quantity may refer to an optimal parameter, which can, in principle, be obtained using mathematical optimization software. Thus, for example, when the value of the parameter is equal to at least 80% of the maximum possible value (or some other predefined threshold percentage), the value assumed by the parameter may be said to be "substantially equal to" the maximum possible value that the parameter can assume. Specifically, the situation in which the value of the parameter is equal to the maximum possible value is also encompassed by the statement that the value assumed by the parameter is "substantially equal to" the maximum possible value that the parameter can assume.

[0308] As used herein, the term "about" can be used to specify a value of a quantity or parameter (e.g., the length of an element) as being within a continuous range of values ​​in the neighborhood of (and including) a given (stated) value. According to some embodiments, "about" can specify a value of a parameter as being between 80% and 120% of the given value. For example, the statement "the length of the element is equal to about 1 m" is equivalent to the statement "the length of the element is between 0.8 m and 1.2 m." According to some embodiments, "about" can specify a value of a parameter as being between 90% and 110% of the given value. According to some embodiments, "about" can specify a value of a parameter as being between 95% and 105% of the given value.

[0309] As used herein, the terms "substantially" and "about" are interchangeable according to some embodiments.

[0310] To facilitate the description, a three-dimensional Cartesian coordinate system (with orthogonal axes x, y, and z) is introduced in some of the drawings. Note that the orientation of the coordinate system relative to the depicted objects may vary from one drawing to another. In addition, the symbol can be used to represent axes pointing "out of the page", while the symbol Can be used to represent axes pointing "inside the page".

[0311] Referring to the drawings, in the block diagrams and flow charts, optional elements and operations may be depicted by dashed lines, respectively.

[0312] It will be appreciated that certain features of the present disclosure that, for the sake of clarity, are described in the context of separate embodiments may also be provided in combination in a single embodiment. Conversely, various features of the present disclosure that, for the sake of brevity, are described in the context of a single embodiment may also be provided separately or in any suitable subcombination or as appropriate in any other described embodiment of the present disclosure. Any feature described in the context of an embodiment is not to be considered an essential feature of that embodiment unless expressly designated as such.

[0313] Although the operations in the disclosed methods may be described in a particular order according to some embodiments, the methods of the present disclosure may include some or all of the described operations performed in a different order. The methods of the present disclosure may include some or all of the described operations. No specific operation in the disclosed methods is considered to be an essential operation of the method unless explicitly specified as such.

[0314] Although the present disclosure has been described in conjunction with specific embodiments of the present disclosure, it is apparent that there may be numerous alternatives, modifications, and variations that will be apparent to those skilled in the art. Thus, the present disclosure encompasses all such alternatives, modifications, and variations that fall within the scope of the appended claims. It should be understood that the application of the present disclosure is not necessarily limited to the details of construction and arrangement of components and / or methods set forth herein. Other embodiments may be practiced, and the embodiments may be implemented in various ways.

[0315] The phraseology and terminology employed herein are for descriptive purposes and should not be construed as limiting. The citation or identification of any reference in this application should not be construed as an admission that such reference is available as prior art to the present disclosure. Section headings are used herein to facilitate understanding of this specification and should not be construed as necessarily limiting.

Claims

1. A system for non-destructive acoustic and optical depth measurement of a structure, the system comprising: A measurement setup, the measurement setup being used to: projecting a pulsed pump beam onto a sample to be profiled such that each of the pulsed pump beams is absorbed in the profiled sample and causes the formation of at least a corresponding primary acoustic pulse that propagates within the profiled sample; projecting a pulsed probe beam into the profiled sample such that each probe pulse in the pulsed probe beam experiences Brillouin scattering from the primary acoustic pulse at a respective depth within the profiled sample, the Brillouin scattering being caused by a respective pump pulse immediately preceding the probe pulse, so as to probe the profiled sample over at least one depth range; as well as obtaining a measurement signal by sensing light comprising a portion of said pulsed probe beam returning from said profiled sample; as well as A processing circuit system for executing an optimization algorithm configured to (i) receive as input a processed signal derived from the measurement signal and (ii) output a set of structural parameters characterizing the profiled sample by minimizing a cost function indicative of the difference between the processed signal and a simulated signal obtained using a forward model simulating the scattering of the probe pulse from at least the primary acoustic pulse. 2 . The system of claim 1 , wherein the optimization algorithm is configured to update a guess for the set of structural parameters after each iteration of the optimization algorithm and to update the simulation signal based on the guess.

3. The system of claim 1, wherein the measurement setup comprises a light generating device and at least one light sensor; wherein the light generating device is configured to generate the pulsed pump beam and the pulsed probe beam; and The at least one light sensor is configured to measure the intensity of light incident on the at least one light sensor, thereby obtaining the measurement signal.

4. The system of claim 3, wherein the light generating device comprises a laser source, and wherein each of the pump beam and the probe beam originates from the laser source.

5. The system of claim 4 , wherein the light generating device further comprises an optical modulator configured to amplitude modulate the pump light beam, and wherein the processing circuit system comprises a lock-in amplifier configured to demodulate the measurement signal using the modulation frequency of the pump light beam to obtain the processing signal, or as part of obtaining the processing signal.

6. The system of claim 1, wherein the profiling sample comprises a through hole extending from a top surface of the profiling sample into the profiling sample; wherein the measurement setup is configured to project each of the pump beam and the probe beam onto the top surface; wherein the set of structural parameters quantifies at least the dependence of the average area of ​​the through-holes on the depth within the profiled sample; and The wavelength of the probe pulse is at least about two times greater than a nominal distance between adjacent through holes.

7. The system of claim 1, wherein each of the pump pulses is configured to be absorbed in an absorbing slice of the profiled sample such that, after the primary acoustic pulse is formed, each of the primary acoustic pulses propagates away from the absorbing slice.

8. The system of claim 7, wherein the profiled sample comprises a plurality of layers, the plurality of layers comprising an absorbing layer and at least one other layer, the absorbing layer comprising the absorbing slice, such that in addition to each primary acoustic pulse, a corresponding secondary acoustic pulse is formed as a result of partial reflection of the primary acoustic pulse from a boundary between adjacent layers; wherein said forward model additionally accounts for said forming of said secondary probe pulses by additionally simulating said scattering of said pulsed probe beam from at least some of said secondary acoustic pulses; wherein the absorbent slice consists of a top sublayer of the body on top of which a layered structure comprising the rest of the layer is arranged; and The frequency of the detection pulse is such that the layered structure is substantially transparent to the detection pulse.

9. The system of claim 1, wherein the measurement setup is configured to alternately project the pump pulses and the probe pulses; and Wherein the measurement setup is configured to delay each probe pulse by a controllably variable time interval relative to the immediately preceding pump pulse so as to facilitate probing of the profiled sample over the at least one depth range.

10. The system of claim 6, wherein in the forward model, the profiled sample is simulated by a transversely uniform sample whose refractive index n(z) is equal to an effective refractive index n(z) of the profiled sample predetermined based on reference data related to the profiled sample. eff (z); and The reference data may include design data of the analyzed sample and / or ground truth data of a sample having the same or similar design intent as the analyzed sample.

11. The system of claim 1 , wherein the initial guess input into the forward model in a first iteration of the optimization algorithm is derived taking into account at least reference data for the profiled sample and / or previously obtained calibration data related to the profiled sample; and The reference data may include design data of the analyzed sample and / or ground truth data of a sample having the same or similar design intent as the analyzed sample.

12. The system of claim 1 , wherein in the forward model, each of the simulated acoustic pulses is modeled by a semi-transparent mirror traveling at the local speed of sound; or The forward model is derived using the optical transfer matrix method.

13. The system of claim 11, wherein at least some of the calibration data is obtained by depth profiling one or more scribe lines of the profiled sample using the system.

14. The system of claim 1, wherein the processed signal indicates a contribution of Brillouin oscillations to the measured signal; and Wherein the processed signal quantifies at least a dependence of a Brillouin frequency and / or a Brillouin amplitude of a Brillouin oscillation on the scattering depth within the profiled sample.

15. The system of claim 1, wherein the profiled sample is or includes a V-NAND, a DRAM, or a 3D DRAM, or a preliminary structure at an intermediate manufacturing stage of a V-NAND, a DRAM, or a 3D DRAM.

16. The system of claim 1, wherein the profiled sample is or forms part of a preliminary structure of a patterned wafer or an intermediate fabrication stage of a patterned wafer.

17. A system according to claim 6, wherein in order to obtain an initial guess of the dependence of the average area of ​​the through-holes on the depth within the profiled sample, the processing circuit system is configured to apply a short-time Fourier transform (STFT) to the processed signal to extract a preliminary estimate of the dependence of the Brillouin frequency on the time delay.

18. The system of claim 17 wherein the profiled sample comprises a plurality of layers, wherein to obtain the initial guess, the processing circuitry is configured to apply an iterative process whereby the processed signal is modeled by a sinusoidal series whose terms correspond to respective contributions to the processed signal from Brillouin scattering of the primary acoustic pulses and at least some of the secondary acoustic pulses within each of the layers.

19. The system of claim 1, wherein the set of structural parameters comprises a plurality of sub-sets of structural parameters, each sub-set of structural parameters comprising a set of non-overlapping vertical increments {Δz i } i At least one vertical localization parameter related to one of i is the i-th vertical increment Δz within the sample i height; and wherein the processing circuitry is configured relative to the z i Each of the optimisation algorithms executes the optimisation algorithm, starting at z1 and proceeding sequentially upwards, such that at the i-th execution, the optimisation algorithm (i) receives as input the following: i =∑ j≤i Δz j / v s (z j ) of the processed signal, wherein v s (z j ) represents the area around z j speed of sound, and / or until time t i a processed signal obtained from said measurement signal, and optionally, any previously obtained value of said at least one vertical localisation parameter, and (ii) outputting a corresponding value of said at least one vertical localisation parameter.

20. A method for non-destructive acousto-optic depth measurement of a sample, the method comprising the following operations: Projecting a pulsed pump beam onto a sample to be analyzed: each pump pulse in the pulsed pump beam is configured to be absorbed in the analyzed sample so as to cause the formation of at least a corresponding primary acoustic pulse propagating within the analyzed sample; projecting a pulsed probe beam into the profiled sample: each probe pulse in the pulsed probe beam being configured to undergo Brillouin scattering from the primary acoustic pulse at a respective depth within the profiled sample, the Brillouin scattering being caused by a respective pump pulse immediately preceding the probe pulse, so as to probe the profiled sample over at least one depth range; obtaining a measurement signal by sensing light comprising a portion of said pulsed probe beam returning from said profiled sample; subjecting the measurement signal to processing to obtain a processed signal; as well as An optimization algorithm is executed, the optimization algorithm being configured to (i) receive the processed signal as input and (ii) output a set of structural parameters characterizing the profiled sample by minimizing a cost function indicative of the difference between the processed signal and a simulated signal obtained using a forward model simulating the scattering of the probe pulse from at least the primary acoustic pulse.

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