Pump-probe, THZ time-domain spectroscopy for semiconductor metrology

Abstract

A system and methods for characterizing a semiconductor sample by terahertz (THz) time-domain spectroscopy (TDS), the system configured to implement methods including: directing an optical pump pulse, having one or more optical pump parameters, onto a region of the sample, thereby inducing a transient change within the region; directing a terahertz (THz) probe pulse to the region of the sample at a controlled time delay relative to the optical pump pulse; detecting the THz response signal from the transmission or reflection of the THz probe pulse from the region of the sample; and determining from the THz response signal at least one characteristic of the sample indicated by the transient change induced by the optical pump pulse..

Description

PUMP-PROBE, THZ TIME-DOMAIN SPECTROSCOPY FOR SEMICONDUCTOR METROEOGYFIEED OF THE INVENTION

[0001] The present invention relates generally to metrology for semiconductors, and in particular to characterization of physical and electrical field properties of semiconductors.BACKGROUND

[0002] Semiconductor process control and metrology is a fast-evolving field crucial for developing and manufacturing advanced logic and memory devices. As semiconductor devices become ever smaller and more complex in structure, while incorporating more layers, materials, and functions, it is essential to find process control techniques that can support their fabrication at scale. These include dimensional metrology methods such as ellipsometry and reflectometry, and material metrology methods such as X-ray photoelectron spectroscopy (XPS) and Raman scattering. In addition, optical techniques such as timedomain spectroscopy (TDS) have emerged as powerful tools for characterizing ultrafast material responses, offering a complementary modality for evaluating the electrical and optical behavior of complex semiconductor structures.

[0003] However, as device architectures continue to evolve, traditional metrology tools increasingly fall short in providing access to the electrical performance of the actual structures being built. In many cases, electrical properties — such as local resistivity, leakage, or transient carrier dynamics — are strongly influenced by buried interfaces, material interfaces, or device geometry, and cannot be reliably inferred from measurements on blanket films or isolated test structures.

[0004] Accordingly, there is a need for metrology techniques that can probe electrical behavior on fully or partially fabricated device structures, without relying on contact electrodes or destructive methods. Such techniques should be compatible with standardprocess flows, analyzing response of device components as formed in situ. A measurement approach that meets these requirements would provide valuable visibility into electronic properties during semiconductor fabrication.SUMMARY

[0005] The present invention provides a system and method for pump-probe terahertz (THz) time-domain spectroscopy (TDS) configured for non-contact, time-resolved metrology of semiconductor samples. The system includes an optical pump source configured to generate ultrashort optical pulses that are directed onto a selected region of a sample to induce transient changes in its electrical or dielectric properties. A THz probe pulse is then directed to the same region at a controlled time delay following the pump excitation. The reflected or transmitted THz response is collected and analyzed to determine the sample’s transient response. This configuration enables measurement of dynamic phenomena such as carrier generation, recombination, and transport, with sub-picosecond temporal resolution. The optical pump source may be a femtosecond or picosecond laser, with optical paths split to support both pump excitation and synchronized triggering of THz generation and detection.

[0006] The system architecture incorporates multiple optical paths that may be implemented with beam splitters, delay lines, and focusing optics configured to control spatial and temporal alignment of the pump and probe pulses. THz generation and detection components are integrated into the system and triggered by optical pulses with tunable, controlled delay. The THz emitter optics direct the probe pulse onto the sample, while the detector optics collect the THz response and guide it to a gated THz detector. By systematically varying the time delay between pump and probe, a time-domain waveform of the sample’s THz response may be determined. This time-resolved signal may be transformed to the frequency domain and compared to physical or computational models toextract parameters such as carrier lifetime, mobility, and permittivity. The system is suitable for operation on structured device regions enabling characterization of semiconductor materials and devices during the manufacturing process.BRIEF DESCRIPTION OF DRAWINGS

[0007] For a better understanding of various embodiments of the invention and to show how the same may be carried into effect, reference is made, by way of example, to the accompanying drawings. Structural details of the invention are shown to provide a fundamental understanding of the invention, the description, taken with the drawings, making apparent to those skilled in the art how the several forms of the invention may be embodied in practice. In the figures:

[0008] Fig. 1 is a block diagram of a system for pump-probe, terahertz (THz) timedomain spectroscopy (TDS) for semiconductor metrology, in accordance with embodiments of the present invention;

[0009] Fig. 2 is a graph of change in THz reflectivity over time, following optical pump excitation, illustrating carrier lifetime in doped silicon;

[0010] Fig. 3 is a graph of THz spectral responses at different pump-probe delays, showing spectral evolution due to varying excitation levels;

[0011] Figs. 4A-4C demonstrate simulated electric field distributions within and around a structure of a semiconductor wafer under different optical pump polarizations, based on Rigorous Couples Wave Analysis (RCWA);

[0012] Fig. 5 is a graph of a time-domain THz signal showing distinguishable reflections from the top and bottom surfaces of a semiconductor sample; and

[0013] Fig. 6 is a flow diagram depicting a process for characterizing semiconductor metrology, the process including pump-probe, THz TDS, in accordance with embodiments of the present invention.DETAILED DESCRIPTION

[0014] Embodiments of the present invention provide systems and methods for semiconductor metrology based on terahertz time-domain spectroscopy. Conventional spectroscopic techniques for semiconductor devices involve directing broadband light onto a sample and detecting the scattered light with wavelength resolution, allowing for analysis of material and structural properties. In the terahertz spectral range, the reflection and transmission of electromagnetic radiation are governed by the material’s complex refractive index, which is itself determined by key electronic properties such as carrier concentration, effective mass, and mobility. Changes in these parameters alter the material’s THz response, making it possible to extract electronic characteristics by analyzing the reflected or transmitted signal. As such, THz spectroscopy enables non-contact, frequency-resolved electrical characterization of semiconductor materials and device structures.

[0015] The present invention extends these methods by introducing controlled optical pump excitation prior to THz probing, allowing the system to induce and temporally resolve transient changes in the sample's electrical and dielectric properties. By varying the time delay between pump and probe pulses, the invention enables direct measurement of ultrafast carrier dynamics, such as charge carrier generation, diffusion, recombination, and trapping. This capability allows for time-resolved mapping of electronic behavior in situ, revealing effects that are inaccessible to steady-state measurements and enabling advanced diagnostic capabilities for process monitoring and device evaluation.

[0016] Fig. 1 is a block diagram illustrating an exemplary system 100 for pump-probe, THz time-domain spectroscopy (TDS) for semiconductor metrology, in accordance with embodiments of the present invention. The system 100 is configured to direct an optical pump pulse from an optical pump source 110 onto a region of a sample 120, to follow the opticalpump pulse with a THz probe pulse at a controlled time delay, and to detect and analyze theTHz probe pulse after its interaction with the sample.

[0017] The optical pump source provides one or more high-intensity, short-duration optical pulses that are directed towards the sample to induce a transient change in the sample's properties, such as generating free charge carriers. In addition, the optical pulses are typically split and conditioned so as to also provide triggers for THz illumination and THz detection.

[0018] The optical pump source 110 is typically an ultrashort pulse laser. For example, it may be a femtosecond Ti:Sapphire laser capable of generating optical pulses with durations in the femtosecond or picosecond range. Other types of sources include an Ytterbium-doped fiber laser, or an Erbium-doped fiber laser. These pulses typically have a central wavelength in the near-infrared (e.g., -800 nm or -1030 nm or -1550 nm) but can be selected based on the desired interaction with the semiconductor sample, as described further hereinbelow.

[0019] A first beam splitter (BS 1) 130 may split the optical beam between an “excitation path” 132 and a “trigger” path 130, which leads to a second beam splitter (BS2) 140. The second beam splitter 140 may then split the pulse between two further paths, for triggering the THz emission and the THz detection (i.e., “collection”) respectively. The beam splitters can be, for example, partially reflective mirrors, pellicle beam splitters, and / or dichroic mirrors, chosen for appropriate splitting ratio and minimal pulse distortion. Alternatively, other known methods for pulse synchronization may also be implemented, to synchronize excitation and trigger pulses.

[0020] From the first beam splitter (BS1) 130, the excitation path (directing the optical excitation pulse) passes through pump optics 136, which include one or more elements such as filters, lenses, polarization components, frequency converters and reflectors. These elements are configured to achieve desired pulse parameters, such as intensity, spot size, angle of incidence, and polarization. Elements may include one or more lenses to achieve adesired numerical aperture (NA), so as to achieve the desired spot size on the sample.Focusing elements may also include, for example, off-axis parabolic mirrors (OAPs). Typically, dimensions and materials for the optic elements are selected according to parameters that include the wavelength of the pump pulse and the desired spot size.

[0021] The focused and filtered pump pulse (indicated as optical pulse 138) then impinges on the sample 120, causing carrier excitation that alters the sample’s electric field and optical properties, which can then be measured by their effect on the transmission and / or reflection of THz radiation.

[0022] The sample may be any material or device structure whose properties are to be characterized, such as bulk semiconductors, thin films, or patterned semiconductor devices. A sample stage, not shown, typically holds the sample and may allow for automated and / or manual X, Y, Z translation and rotation of the sample, to facilitate sample analysis that targets specific regions at pre-determined angles. Alternatively, or additionally, the optical pump source and the pump optics, as well as the other THz elements of system 100, may be configured for automated and / or manual translation and rotation.

[0023] The second optical path from BS1, the trigger path 134, is typically split, as described above, by BS2, to paths for triggering THz emission (i.e., THz “generation”) and for triggering THz detection.

[0024] The THz emission and detection paths typically include an emitter trigger delay line 144 and a detector trigger delay line 154, which control the timing of the THz pulse generation and detection relative to the optical pump pulse. These delay lines may comprise retroreflectors mounted on precision motorized translation stages, or alternative elements such as variable path length fiber optics or acousto-optic scanners for rapid delay variation. The emitter delay triggers a THz emitter 146, which may be a photoconductive antenna (PCA) based on low-temperature-grown GaAs (LT-GaAs) or other materials, or a nonlinearoptical crystal (e.g., ZnTe, GaP, LiNbOs), plasma-based emitter, or spintronic THz emitter.When illuminated by the optical pulse, the emitter typically radiates a broadband THz pulse via photocarrier acceleration or optical rectification.

[0025] The THz pulse is typically filtered and focused by emitter optics 148, which may include lenses, polarizers, or off-axis parabolic mirrors (OAPs) made of materials such as high-resistivity float-zone silicon (HRFZ-Si) or TPX™. The THz pulse (indicated as pulse 150) is directed onto the region of the sample 120 that is (or will be) excited by the optical pump pulse. The interaction with the sample modifies the THz pulse based on the transient state of the sample, generating a reflected or transmitted THz response signal 160, with altered amplitude, phase, or polarization.

[0026] The THz response signal 160 is typically collected by detector optics 168 and directed to a THz detector (e.g., a PCA or electro-optic sampling crystal). Detector optics may include any one or more of the elements described above with respect to the emitter optics, such as , lenses, polarizers, and OAPs. The THz detector is typically gated by a delayed optical pulse from the detector trigger delay line. The delay may be scanned over a range (starting with an initial delay offset), to acquire a time-domain waveform of the signal. This allows analysis of dynamic electrical properties of the sample based on the interaction of the THz probe with the transient carrier distribution.

[0027] In various embodiments, the THz illumination and detection paths may incorporate optical and mechanical components that enable adjustment of key system parameters. For example, the system may be configured to operate in either a reflection or transmission geometry, depending on sample structure and metrology requirements. The angle of incidence of the THz beam onto the sample can be varied using adjustable mounts or goniometers integrated into the emitter and detector optics. Polarization control in the THz path may be implemented by inserting polarizing elements, such as wire-grid polarizers orpolarization rotators, in either the illumination or collection path. Numerical aperture (NA) and resulting spot size may be controlled by selecting appropriate focusing elements, such as lenses or off-axis parabolic mirrors, and by adjusting the THz beam path through mechanical translation or aperture control.

[0028] The configurable elements of the THz path described above may be employed in support of multiple measurement schemes implemented by the system. In one scheme, the system may acquire the THz frequency spectrum at a fixed pump-probe delay, enabling frequency-domain characterization of the sample. Although the fixed pump-probe delay corresponds to a transient excitation state rather than equilibrium, such a measurement enables rapid, high-throughput assessment of sample properties across process conditions or devices, making the measurement suitable for inline monitoring or defect screening. The reduced acquisition time relative to full time -resolved scans supports efficient implementation in production environments.

[0029] In another measurement scheme, the THz spectrum may be acquired at multiple pump-probe delays to capture the temporal evolution of the spectral response. The system may alternatively record the peak amplitude of the time-domain signal at each of a series of delays, generating a simplified decay profile suitable for extracting parameters such as carrier lifetime. In yet another scheme, the system may perform relative measurements by comparing the THz signal from a pumped region to that from an unpumped or reference condition, optionally using a lock-in amplifier synchronized to the pump pulse. Spatially resolved measurements may also be implemented by scanning the position of the optical pump relative to the THz probe, allowing data to be collected over different regions of the sample surface. These measurement modes may be selected based on sample characteristics and the type of electrical property to be extracted, and the selected mode or modes may be executed independently or in combination within a measurement cycle.

[0030] Similarly, the pump optics may be configured to provide control over one or more optical pump parameters, including the wavelength (e.g., by using tunable laser sources or optical parametric amplifiers), pulse duration (e.g., via dispersion compensation or pulse shaping), and intensity (e.g., by using variable attenuators or neutral density filters). The polarization of the pump beam may be controlled using polarizers or waveplates inserted in the optical path. The spot size and angle of incidence on the sample can be adjusted by modifying the focusing optics and sample orientation, or by mounting optical components on translation and rotation stages. These configuration options may be selected manually or controlled via software to implement a desired excitation condition, either statically or as part of a dynamic scanning or optimization procedure.

[0031] The THz detector 166 may also be a photoconductive antenna (PC A), similar in principle to a PCA emitter, or other technologies known in the art, such as an electro-optic sampling crystal (e.g., ZnTe, GaP) used in conjunction with a balanced photodiode pair. The delay line controls the arrival time of the optical pulse at the detective, relative to the timing of the pulse reaching the emitter. By repeating the process for multiple delay increments, the waveform of the THz response can be sampled in the time domain. The THz detector 166 typically generates an electrical signal proportional to the electric field of the THz response signal 160, at the moment it is gated by the delayed optical pulse. The electrical signal from the THz detector is typically received by a processor 170. The processor is typically configured to perform signal processing, including acquiring, digitizing, and processing the detected signal as a function of the delay to reconstruct a time-domain waveform of the THz response 160. Further processing, such as Fourier transformation may be applied to obtain a frequency spectrum, which may be compared with reference signals, or model-based spectrum, to determine characteristics of the sample 120 related to the transient changes induced by the optical pump pulse.

[0032] By varying the delay introduced by the detector delay line 154, the system 100 can measure the sample's response at different times after excitation, allowing for the characterization of dynamic processes such as charge carrier generation, relaxation, and recombination. Control of the delay is typically automated by processor control, by methods known in the art, as are other system elements of the system, such as elements of the pump pulse, THz generation and THz collection optics, to effect automated control of optic parameters, such as polarization, spot size, and angle of incidence.

[0033] Fig. 2 is a graph demonstrating transient reflectivity response of semiconductor samples, from which a measure of carrier lifetime can be extracted. The graph shows three traces of change in THz reflectivity over time, following optical pump excitation, for three samples with different respective levels of doping (one, an undoped sample, the others with two different doping levels). The traces show an initial rise in reflectivity immediately after excitation, corresponding to the generation of free carriers by the pump pulse, followed by a gradual decay back to the baseline level as carriers recombine or are otherwise removed from the excited state. Each trace is generated by systematically varying the time delay between the optical pump and the THz probe pulses, while detecting the reflected THz signal at each delay interval. At each delay step, the system measures the electric field amplitude of the reflected THz pulse, allowing the change in reflectivity to be plotted as a function of time after excitation.

[0034] The time-resolved measurement provides direct, non-contact access to dynamic electronic properties of semiconductor structures, enabling a quantitative evaluation of recombination rates and other transient behaviors that affect device performance. Because the measurements are made without electrical contacts or destructively modifying the sample, in situ electrical characterization of active device regions can be performed during or after fabrication, enhancing process monitoring and device diagnostics.

[0035] Fig. 3 is a graph of THz spectra measured at different pump-probe delay times, showing how the spectral response of a semiconductor sample evolves following optical excitation. Each curve represents the frequency-domain THz reflectivity of the sample at a specific time delay after the pump pulse, revealing changes in the material’s optical properties as excited carriers relax or recombine. The spectra are obtained by recording the time-domain THz response at each delay and applying a Fourier transform to extract the corresponding frequency components. The system's controlled variation of the pump-probe delay, combined with synchronized THz emission and detection, enables acquisition of these time-resolved spectra. Differences between the spectral curves at various delays reflect the dynamic evolution of the sample’s dielectric function, which is sensitive to parameters such as carrier concentration, mobility, and scattering mechanisms. This spectral information complements time-domain measurements by enabling identification of frequency -dependent effects and supporting model-based extraction of electronic and material properties. The ability to resolve both spectral and temporal changes enhances the system’s diagnostic capability for evaluating ultrafast phenomena in complex semiconductor structures.

[0036] Figs. 4A-4C demonstrate effects of the optical pump pulse polarization on the electric field of a structure of a semiconductor device. Fig. 4A shows a schematic 3D view of the structure, indicating with arrows the structure’s length and width, respectively. Figs. 4B-4C show simulated electric field distributions within the structure, for two different polarizations of the pump pulse. The simulation was performed by Rigorous Coupled-Wave Analysis (RCWA), though other techniques known in the art may have been applied. In Fig. 4B, the electric field is simulated with the pump polarization aligned along the length of the structure, while in Fig. 4C, the polarization is aligned along the width. The resulting electric field patterns differ significantly, demonstrating an anisotropic response of the sample, which may arise from directional variations in material properties, device geometry, or both. Thevariation illustrates how the spatial distribution of excited carriers can be modulated by the polarization direction of the optical pump.

[0037] This ability to control where and how strongly carriers are excited enables selective probing of localized material responses, offering enhanced sensitivity to orientation-dependent or region- specific electrical behaviors in semiconductor devices. As described below, the parameters of the optical pump pulse can thus be modified to cause charge carrier responses that are optimized for the characterization of different areas of a targeted region of a semiconductor sample.

[0038] Fig. 5 is a graph of a time-domain THz signal showing two distinct reflection peaks corresponding to different interfaces within a semiconductor sample. The first peak represents the reflection from the top surface of the sample, while the second peak corresponds to a reflection from a deeper interface, such as the bottom surface or an internal layer. These reflections are temporally separated due to the difference in optical path length and are captured by scanning multiple detector delays to record the reflected THz electric field over time. Because the system collects the time-domain waveform of the reflected THz pulse, it can resolve multiple internal reflections based on their arrival times. This allows for isolation and analysis of layer- specific signals, enabling the characterization of buried features and depth-dependent variations in optical or electronic properties. By distinguishing reflections from different depths, the system supports non-destructive probing of multilayer structures and facilitates detection of process-induced variations or defects within complex semiconductor devices.

[0039] Fig. 6 is a flow chart illustrating an exemplary process 600 for characterizing a semiconductor sample using pump-probe terahertz time-domain spectroscopy. The sequence of operations begins with optional model-based simulation and pump parameter selectionand continues through optical excitation, THz probing, signal detection, and parallel analysis steps that may be used to extract material and electronic properties.

[0040] At a preparation step 602, which includes optional simulation-based configuration, a structural model of the semiconductor sample may be obtained, and a simulation of electromagnetic scattering may be simulated for optical excitation by an optical pump pulse, over a range of optical pump parameters. Such a simulation may be performed, for example, by Rigorous Coupled-Wave Analysis (RCWA), typically implemented by an RCWA engine configured to simulate the interaction between an optical pump pulse and the model. Based on the simulation results, one or more optical pump parameters — such as polarization, intensity, wavelength, and pulse duration — may be selected to achieve an excitation effect corresponding with a desired measurement objective. For example, as described above, the excitation may be designed to optimize the characterization of different areas or features of a targeted region of the sample under inspection.

[0041] The main measurement process then proceeds through steps 604 to 610. In step 604, an optical pump pulse, with selected parameters, is directed onto a region of the semiconductor sample to induce a transient change in its electrical or dielectric properties. In step 606, a THz probe pulse is directed onto the same region of the sample at a controlled time delay relative to the optical pump pulse.

[0042] In step 608, a THz response signal is detected after the interaction of the THz probe pulse with the sample, i.e., after reflection from or transmission through the sample. The detection may be implemented with a gated THz detector synchronized with a delayed optical trigger pulse.

[0043] In step 610, the probe and detection process is optionally repeated over a range of pump-probe delays to sample the evolution of the transient response.

[0044] The detected THz signals may then be analyzed by the processor (described above) in a step 620, which may include parallel or partially parallel processing sub-steps. These sub-steps include the types of analysis described above, including steps indicated in the figure as steps 622-628.

[0045] In step 622, the decay of the THz signal amplitude over successive pump-probe delays may be processed to extract information about the recombination dynamics of photoexcited carriers. This is done by plotting the amplitude of the detected THz signal as a function of the pump-probe delay time and fitting the resulting decay curve to a mathematical model. Depending on the physical characteristics of the sample, the decay may be modeled by fitting it to a theoretical model. By way of example, simple models include a singleexponential function — characterized by a uniform recombination rate — or a stretched exponential function, which accounts for a distribution of recombination rates due to material inhomogeneities or trap states. In each case, the fitting process yields a characteristic carrier lifetime parameter, which quantifies the average time that carriers remain in the excited state before recombining.

[0046] In step 624, the time-domain THz signal detected at one or more pump-probe delays may be converted to the frequency domain by applying a Fourier transform. This yields the complex frequency-dependent response of the sample, including both amplitude and phase information across the THz spectrum. The resulting spectrum is then analyzed using physical models, such as the Drude or Drude-Smith model, which describe the dielectric function or complex conductivity of the material as a function of parameters including carrier concentration, mobility, and effective mass. By fitting the measured spectral data to one of these models, it is possible to extract quantitative values for these parameters. For example, the low-frequency amplitude and shape of the spectrum are sensitive to carrier concentration, while spectral broadening relates to carrier mobility via scattering time. Theeffective mass appears in the model as a scaling factor influencing the spectral curvature and conductivity amplitude. This analysis enables non-contact determination of key electrical properties of the sample under both static and dynamic excitation conditions.

[0047] In step 626, the detected THz signal from a photoexcited (pumped) region of the sample may be compared to a reference signal acquired under non-excited (unpumped) conditions. This comparison may be performed in the time domain, frequency domain, or both. The differential signal reveals the net effect of the pump-induced carrier excitation on the THz response. To improve measurement sensitivity, a lock-in amplifier synchronized with the pump modulation may be used to extract only the signal components associated with the pump-induced change. The differential THz response — whether in amplitude, phase, or spectral shape — is then used as input to models or empirical comparisons to derive physical properties such as carrier lifetime (via decay tracking across delays), carrier concentration (from changes in reflectivity or transmission), and mobility (from relative changes in spectral width). This method is particularly useful for isolating small changes in highly absorptive or reflective samples where absolute measurements may be difficult to interpret directly.

[0048] In step 628, features may be extracted from the measured THz signal — either in the time domain (e.g., peak amplitude, rise time, decay slope) or frequency domain (e.g., bandwidth, resonance shifts, spectral slope) — and used as input to a trained machine learning model. The model is typically developed using a dataset of simulated or experimentally characterized samples, where ground truth values for carrier properties are known. During analysis, the extracted features from the test sample are passed to the model, which infers one or more physical characteristics based on learned correlations. Depending on the architecture and training of the model, this approach can be used to estimate carrier concentration, mobility, effective mass, and lifetime, either individually or jointly. Machine learning analysis is particularly advantageous when physical models are insufficientlyaccurate due to structural complexity, material heterogeneity, or nonlinear excitation effects.It also enables fast, high-throughput property extraction once trained, supporting real-time process control or large-scale spatial mapping.

[0049] In step 630, the carrier properties derived from the previous analysis steps — such as carrier concentration, mobility, effective mass, and carrier lifetime — are used to characterize the electrical behavior of the semiconductor sample. These extracted parameters may be compared to values predicted by physical models, derived from simulation, or obtained from reference samples or process targets. The purpose of such comparison is to evaluate whether the sample meets design specifications, to detect deviations caused by process variation, or to identify the presence of material defects, interface degradation, or unintended doping effects. For instance, a reduction in mobility compared to expected values may indicate increased impurity scattering or lattice damage, while shortened carrier lifetime may suggest elevated recombination due to trap states or surface defects.

[0050] Such comparisons can be applied not only to absolute values but also to trends across different regions, layers, or time delays. In dynamic measurements, temporal evolution of the extracted characteristics can be analyzed to assess carrier dynamics, such as recombination pathways or diffusion behavior. In frequency -domain analysis, deviations in spectral response may be matched to known signatures of physical mechanisms, such as plasmonic effects or phonon coupling. These evaluations support multiple use cases, including process window monitoring, in-line defect detection, material selection, and design verification for advanced semiconductor devices. The ability to non-destructively obtain and interpret these electrical parameters directly on device structures, rather than on surrogate test structures, represents a key advantage of the present method.

[0051] In step 632, the process steps — from optical excitation through signal acquisition and analysis — may be repeated across multiple locations on the surface of the semiconductorsample to create a spatial map of characteristics. This may be achieved by scanning the position of the optical pump pulse, the THz probe pulse, or both, relative to the sample. At each location, the relevant THz response signal is recorded and processed to extract electrical and material characteristics as described in the processing steps of step 620. It may be noted that typically the spot size of the pump pulse is focused to be smaller than the spot size of the THz pulse, such that moving a more focused pump pulse to different locations across a surface of the sample can facilitate higher resolution mapping of sample characteristics.

[0052] The resulting data from multiple locations is then compiled to form a spatial map of sample characteristics such as carrier lifetime, concentration, or mobility. This mapping enables the identification of spatially localized defects, gradients in material quality, process non-uniformities, or lithographic variation within complex device structures or wafer-level patterns. It also allows correlation of electrical properties with physical layout or process history, supporting advanced diagnostics and yield analysis.

[0053] In short, the flow chart of Fig. 6 outlines a flexible and comprehensive method for characterizing semiconductor samples using pump-probe THz time-domain spectroscopy. The process accommodates both model-driven and measurement-driven parameter selection, supports multiple acquisition schemes and analysis techniques, and enables extraction of key electrical properties with sub-picosecond time resolution and micrometer- scale spatial precision. By integrating temporal, spectral, relative, and machine learning-based analyses, the system can evaluate transient carrier dynamics and material responses directly on structured device regions. Through comparative evaluation and spatial mapping, the method supports in-line process monitoring, material validation, and fault localization in advanced semiconductor manufacturing.

[0054] Advantages of the invention include:• high temporal resolution enabling observation of transient electronic phenomena such as carrier generation, diffusion, recombination, and trapping;• non-contact, non-destructive metrology applicable to advanced semiconductor structures, including patterned wafers and thin films;• tunability of pump and probe parameters (e.g., wavelength, delay, spot size, polarization, angle of incidence), allowing targeted measurement of specific material responses;• capability to spatially resolve local material properties within small metrology pads or device regions by using a tightly focused optical pump;• analysis in both time and frequency domains providing methods for calculating range of material and device properties;• flexible system architecture supporting multiple configurations (e.g., transmission, reflection, variable angle) to optimize sensitivity for various applications;• integration with computational models or machine learning techniques to extract quantitative parameters from complex spectral or temporal signatures.

[0055] It is to be understood that processing elements shown or described herein are preferably implemented by one or more computers in computer hardware and / or in computer software embodied in a non-transitory, computer-readable medium in accordance with conventional techniques, such as employing a computer processor, a memory, I / O devices, and a network interface, coupled via a computer bus or alternate connection arrangement.

[0056] Unless otherwise described, the terms “processor” and “device” are intended to include any processing device, such as, for example, one that includes a CPU (central processing unit) and / or other processing circuitry (e.g., GPUs), and may refer to more thanone processing device. Various elements associated with a processing device may be shared by other processing devices.

[0057] The term “memory” as used herein is intended to include memory associated with a processor or CPU, such as, for example, RAM, ROM, a fixed memory device (e.g., hard drive), a removable memory device (e.g., diskette, tapes), flash memory, etc. Such memory may be considered a computer readable storage medium.

[0058] In addition, phrases “input / output devices” or “I / O devices” may include one or more input devices (e.g., keyboard, mouse, scanner, HUD, etc.) for entering data to the processing unit, and / or one or more output devices (e.g., speaker, display, printer, HUD, AR, VR, etc.) for presenting results associated with the processing unit.

[0059] Embodiments of the invention may include a system, a method, and / or a computer program product. The computer program product may include a computer readable storage medium (or media) having computer readable program instructions thereon for causing a processor to carry out aspects of the invention.

[0060] The computer readable storage medium can be a tangible device that can retain and store instructions for use by an instruction execution device. The computer readable storage medium may be, for example, but is not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. A non- exhaustive list of more specific examples of the computer readable storage medium includes the following: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disk (DVD), Blue-Ray, magnetic tape, Holographic Memory, a memory stick, a floppy disk, a mechanically encoded device such as punch-cardsor raised structures in a groove having instructions recorded thereon, and any suitable combination of the foregoing. A computer readable storage medium, as used herein, is not to be construed as being transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission media (e.g., light pulses passing through a fiber-optic cable), or electrical signals transmitted through a wire.

[0061] Computer readable program instructions described herein can be downloaded to respective computing / processing devices from a computer readable storage medium or to an external computer or external storage device via a network, for example, the Internet, a local area network, a wide area network and / or a wireless network. A network adapter card or network interface in each computing / processing device may receive computer readable program instructions from the network and forwards the computer readable program instructions for storage in a computer readable storage medium within the respective computing / processing device.

[0062] Computer readable program instructions for carrying out operations of the invention may be assembler instructions, instruction-set-architecture (ISA) instructions, machine instructions, machine dependent instructions, microcode, firmware instructions, state-setting data, or either source code or object code written in any combination of one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C++ or the like, and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The computer readable program instructions may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user's computer through any type of network,including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider). In some embodiments, electronic circuitry including, for example, programmable logic circuitry, field-programmable gate arrays (FPGA), or programmable logic arrays (PLA) may execute the computer readable program instructions by utilizing state information of the computer readable program instructions to personalize the electronic circuitry, in order to perform aspects of the invention.

[0063] Where aspects of the invention are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention, it will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer readable program instructions.

[0064] These computer readable program instructions may be provided to a processor of a general-purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions / acts specified in the flowchart and / or block diagram block or blocks. These computer readable program instructions may also be stored in a non-transient, computer readable storage medium that can direct a computer, a programmable data processing apparatus, and / or other devices to function in a particular manner, such that the computer readable storage medium having instructions stored therein may include an article of manufacture including instructions which implement aspects of the function / act specified in the flowchart and / or block diagram block or blocks.

[0065] The computer readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other device to produce a computer implemented process, such that the instructions which execute on the computer, other programmable apparatus, or other device implement the functions / acts specified in the flowchart and / or block diagram block or blocks.

[0066] Any flowchart and block diagrams included herein illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of instructions, which may include one or more executable instructions for implementing the specified logical function(s). In some alternative implementations, the functions noted in the block may occur out of the order shown herein. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and / or flowchart illustration, and combinations of blocks in the block diagrams and / or flowchart illustration, can be implemented by special purpose hardware-based systems that perform the specified functions or acts or carry out combinations of special purpose hardware and computer instructions.

[0067] The descriptions of the various embodiments of the invention have been presented for purposes of illustration, but are not intended to be exhaustive or limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terminology used herein was chosen to best explain the principles of the embodiments, the practical application or technical improvement over technologies found inthe marketplace, or to enable others of ordinary skill in the art to understand the embodiments disclosed herein.

[0068] EXAMPLES

[0069] The present invention may include the following exemplary configurations.

[0070] Example 1 is a method for characterizing a semiconductor sample. Steps of the method may include: a) directing an optical pump pulse, having one or more optical pump parameters, onto a region of the sample, thereby inducing a transient change within the region; b) directing a terahertz (THz) probe pulse to the region of the sample at a controlled time delay relative to the optical pump pulse; c) detecting the THz response signal from the transmission or reflection of the THz probe pulse from the region of the sample; and d) determining from the THz response signal at least one characteristic of the sample indicated by the transient change induced by the optical pump pulse.

[0071] As example 2 of the invention includes the steps of example 1 and, prior to directing the optical pump pulse to the region of the sample, additional steps include: i) obtaining a model representing a structure of the sample; ii) executing a simulation of an interaction between the optical pump pulse and the model to estimate the transient change to be induced when directing the optical pump pulse onto the region of the sample; and iii) selecting the one or more optical pump parameters of the optical pump pulse to obtain the estimated transient change.

[0072] An example 3 includes the features of example 2, and when selecting the one or more optical pump parameters comprises simulating the interaction for multiple sets of potential optical pump parameters to identify a set that achieves a desired excitation effect.

[0073] An example 4 includes the features of either example 2 or 3, and execution of the simulation is performed by Rigorous Coupled-Wave Analysis (RCWA).

[0074] An example 5 includes the features of any one of the above examples and the one or more optical pump parameters are selected from a group consisting of: a polarization state, an intensity, a wavelength, a pulse duration, a spot size, and combinations thereof.

[0075] An example 6 includes the features of any one of the above examples, and wherein determining from the THz response signal at least one characteristic of the sample comprises: i) generating a THz frequency spectrum from the THz response signal; and ii) comparing the THz frequency spectrum to a physical model result or a reference spectrum to determine an electrical property of the sample.

[0076] An example 7 includes the features of any one of the above examples, and the THz probe pulse is directed to the region of the sample at a plurality of controlled time delays, the THz response signal is detected for each delay, and a temporal decay characteristic is determined from the resulting THz response signals.

[0077] An example 8 includes the features of example 7, and the at least one characteristic of the sample includes a charge carrier lifetime derived from the temporal decay characteristic.

[0078] An example 9 includes the features of examples 7 or 8, and determining the temporal decay characteristic comprises identifying a peak signal amplitude of each of the multiple THz response signals to determine a sequence of peak signal amplitudes, and deriving the temporal decay from the sequence.

[0079] An example 10 includes the features of any one of the above examples, and further includes performing a relative measurement by comparing the THz response signal with a reference THz signal detected from a non-pumped region of the sample, to identify the at least one characteristic.

[0080] An example 11 includes the features of example 10, and the relative measurement utilizes a lock-in amplifier synchronized with the optical pump pulse.

[0081] An example 12 includes the features of any one of the above examples, and analyzing the THz response signal to determine the at least one characteristic comprises applying a trained machine learning model to correlate features extracted from the THz response signal with the at least one characteristic.

[0082] An example 13 includes the features of any one of the above examples, and further includes spatially scanning one or both of the optical pump pulse and the THz probe pulse across a surface of the sample, and repeating the measurement and analysis at multiple locations, to map the at least one characteristic over an area of the sample.

[0083] An example 14 includes the features of any one of the above examples, and the at least one characteristic comprises one or more of: charge carrier mobility, charge carrier concentration, or charge carrier effective mass.

[0084] An example 15 includes the features of any one of the above examples, wherein the sample is a multilayer sample and the at least one characteristic is associated with a given layer identified by analyzing timing differences in the THz response signal corresponding to reflections from different interfaces within the sample

[0085] A further example 16 of the present invention is a unit for TDS metrology that includes: a) a laser source configured to generate an optical pulse to cause a temporal redistribution of charge carriers in a region of the sample; b) a terahertz (THz) emitter, optically coupled to the laser source, configured to generate a THz pulse in response the optical pulse after a controlled first delay, via an emitter delay line; c) a THz detector, optically coupled to the laser source, configured to receive a THz response signal generated by interaction of the THZ pulse with the region of the sample after a controlled second delay, via a detector delay line, and to generate an electrical signal representative of a timedependent electric field of the THz response signal; and d) a processing unit communicatively coupled to the THz detector, the processing unit programmed to analyze the electrical signalto determine at least one property of the sample, wherein the at least one property is indicated by the interaction of the THz pulse with the temporal redistribution of charge carriers in the region of the sample, and wherein the processor is further programmed to output the at least one property to characterize the sample.

[0086] An example 17 of the present is a unit including the elements of example 16 and the processing unit is configured to determine the at least one property by performing at least one of: i) generating a frequency-domain representation of the THz response signal and comparing it to a physical or empirical model (as described above with respect to example 6); ii) determining a temporal decay characteristic from a sequence of THz response signals acquired at a plurality of controlled time delays (as described above with respect to examples 7-9); iii) performing a relative comparison of the THz response signal to a reference signal acquired under non-excited conditions (as described above with respect to examples 10-11); and iv) applying a trained machine learning model to features extracted from the THz response signal (as described above with respect to example 12).

[0087] An example 18 of the present invention is a non-transitory computer readable medium that stores instructions for semiconductor metrology, for characterizing a semiconductor sample by terahertz (THz) time-domain spectroscopy (TDS). The instructions include steps of: a) directing an optical pump pulse, having one or more optical pump parameters, onto a region of the sample, thereby inducing a transient change within the region;b) directing a terahertz (THz) probe pulse to the region of the sample at a controlled time delay relative to the optical pump pulse; c) detecting a THz response signal resulting from interaction of the THz probe pulse with the region of the sample; d) analyzing the THz response signal to determine at least one characteristic of the sample; and e) outputting a result indicative of the at least one characteristic of the sample.

[0088] In an example 19, the instructions of claim 18 for analyzing the THz response include instructions for at least one of: i) generating a frequency-domain representation of the THz response signal and comparing it to a physical or empirical model; ii) determining a temporal decay characteristic from a sequence of THz response signals acquired at a plurality of controlled time delays; iii) performing a relative comparison of the THz response signal to a reference signal acquired under non-excited conditions; and iv) applying a trained machine learning model to features extracted from the THz response signal

Claims

CLAIMS1. A method for characterizing a semiconductor sample, comprising: a) directing an optical pump pulse, having one or more optical pump parameters, onto a region of the sample, thereby inducing a transient change within the region; b) directing a terahertz (THz) probe pulse to the region of the sample at a controlled time delay relative to the optical pump pulse; c) detecting the THz response signal from the transmission or reflection of the THz probe pulse from the region of the sample; and d) determining from the THz response signal at least one characteristic of the sample indicated by the transient change induced by the optical pump pulse.

2. The method of claim 1, further comprising, prior to directing the optical pump pulse to the region of the sample: i) obtaining a model representing a structure of the sample; ii) executing a simulation of an interaction between the optical pump pulse and the model to estimate the transient change to be induced when directing the optical pump pulse onto the region of the sample; and iii) selecting the one or more optical pump parameters of the optical pump pulse to obtain the estimated transient change.

3. The method of claim 2, wherein selecting the one or more optical pump parameters comprises simulating the interaction for multiple sets of potential optical pump parameters to identify a set that achieves a desired excitation effect.

4. The method of claim 2, executing the simulation comprises applying Rigorous Coupled- Wave Analysis (RCWA).

5. The method of claim 1, wherein the one or more optical pump parameters are selected from a group consisting of: a polarization state, an intensity, a wavelength, a pulse duration, a spot size, and combinations thereof.

6. The method of claim 1, wherein determining from the THz response signal at least one characteristic comprises: i) generating a THz frequency spectrum from the THz response signal; and ii) comparing the THz frequency spectrum to a physical model result or a reference spectrum to determine an electrical property of the sample as the at least one characteristic.

7. The method of claim 1, wherein directing the THz probe pulse to the region of the sample is repeated for a plurality of controlled time delays, wherein detecting the THz response signal is performed for each of said controlled time delays to detect multiple THz response signals, and further comprising determining a temporal decay characteristic from the multiple THz response signals obtained at said controlled time delays.

8. The method of claim 7, wherein the at least one characteristic of the sample comprises a charge carrier lifetime derived from the temporal decay characteristic.

9. The method of claim 7, wherein determining the temporal decay characteristic comprises identifying a peak signal amplitude of each of the multiple THz response signals to determine a sequence of peak signal amplitudes, and wherein the temporal decay characteristic is determined by changes in the peak signal amplitudes.

10. The method of claim 1, further comprising performing a relative measurement of comparing the THz response signal with a reference THz signal detected from a non-pumped region of the sample, to identify the at least one characteristic.

11. The method of claim 10, wherein the relative measurement utilizes a lock-in amplifier synchronized with the optical pump pulse.

12. The method of claim 1, wherein analyzing the THz response signal to determine the at least one characteristic of the sample comprises applying a trained machine learning (ML) model to correlate features extracted from the THz response signal with the at least one characteristic of the sample.

13. The method of claim 1, further comprising spatially scanning one or both of the optical pump pulse and the THz probe pulse across a surface of the sample, and repeating the directing of the optical pump pulse, the directing of the terahertz (THz) probe pulse, and the detecting and analysis of the THz response signal, at multiple locations, to map the at least one characteristic of the sample over an area of the surface.

14. The method of claim 1, wherein the at least one characteristic is one or more characteristics in a group of characteristics consisting of: charge carrier mobility, charge carrier concentration, charge carrier effective mass, and combinations thereof.

15. The method of claim 1, wherein the sample is a multilayer sample, and wherein the at least one characteristic is one or more characteristics associated with a given layer of the sample, the layer being identified by analyzing timing differences in the THz response signal corresponding to reflections from different interfaces within the sample.

16. A metrology unit for time-domain spectroscopy (TDS), for characterizing a semiconductor sample, comprising: a) a laser source configured to generate an optical pulse to cause a temporal redistribution of charge carriers in a region of the sample; b) a terahertz (THz) emitter, optically coupled to the laser source, configured to generate a THz pulse in response the optical pulse after a controlled first delay, via an emitter delay line;c) a THz detector, optically coupled to the laser source, configured to receive a THz response signal generated by interaction of the THZ pulse with the region of the sample after a controlled second delay, via a detector delay line, and to generate an electrical signal representative of a time-dependent electric field of the THz response signal; and d) a processing unit communicatively coupled to the THz detector, the processing unit programmed to analyze the electrical signal to determine at least one property of the sample, wherein the at least one property is indicated by the interaction of the THz pulse with the temporal redistribution of charge carriers in the region of the sample, and wherein the processor is further programmed to output the at least one property to characterize the sample.

17. The metrology unit of claim 16, wherein the processing unit is configured to determine the at least one property by performing at least one of: i) generating a frequency-domain representation of the THz response signal and comparing it to a physical or empirical model; ii) determining a temporal decay characteristic from a sequence of THz response signals acquired at a plurality of controlled time delays; iii) performing a relative comparison of the THz response signal to a reference signal acquired under non-excited conditions; and iv) applying a trained machine learning model to features extracted from the THz response signal.

18. A non-transitory computer readable medium that stores instructions for semiconductor metrology, for characterizing a semiconductor sample by terahertz (THz) time-domain spectroscopy (TDS), the instructions including steps of: a) directing an optical pump pulse, having one or more optical pump parameters, onto a region of the sample, thereby inducing a transient change within the region;b) directing a terahertz (THz) probe pulse to the region of the sample at a controlled time delay relative to the optical pump pulse; c) detecting a THz response signal resulting from interaction of the THz probe pulse with the region of the sample; d) analyzing the THz response signal to determine at least one characteristic of the sample; and e) outputting a result indicative of the at least one characteristic of the sample.

19. The non-transitory computer readable medium of claim 18, wherein the step of analyzing the THz response includes instructions for at least one of: i) generating a frequency-domain representation of the THz response signal and comparing it to a physical or empirical model; ii) determining a temporal decay characteristic from a sequence of THz response signals acquired at a plurality of controlled time delays; iii) performing a relative comparison of the THz response signal to a reference signal acquired under non-excited conditions; and iv) applying a trained machine learning model to features extracted from the THz response signal.

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