Method for determining the dimensions of elements in subsurface topography, scanning probe microscopy system, and computer program

Abstract

The present specification relates to a method for determining dimensions of features of a subsurface topography of a sample, the features having spatial periodicity. The subsurface topography is acquired using scanning probe microscopy. The method includes obtaining measurements of an acoustic output signal at at least N locations to generate a position-dependent subsurface topography signal. The method includes providing an auto-correction matrix by performing a correlation of the subsurface topography signal for each additional location to result in an auto-correction matrix having size N*N. The method then includes performing an eigenvalue decomposition to obtain eigenvalues ​​of the matrix and selecting a subset of the eigenvalues ​​with the largest values. A frequency estimation function is constructed therefrom, and at least one output value indicative of the spatial periodicity is obtained from the frequency estimation function. The present specification also describes a scanning probe microscopy system and a computer program product.

Description

[Technical Field]

[0001] The present invention relates to a method for determining the dimensions of one or more subsurface elements from the results of subsurface topography measurements of a sample, wherein the subsurface topography includes one or more elements having spatial periodicity, the subsurface topography measurements are obtained using a scanning probe microscopy system, and the method includes the steps of: applying an acoustic input signal to a sample using a transducer; sensing an acoustic output signal at a plurality of locations on the surface of the sample using a probe, wherein the probe includes a cantilever and a probe tip, the probe tip is in contact with the surface, and the acoustic output signal represents a sound wave corresponding to the acoustic input signal that can be measured on the surface; and obtaining a measurement of the acoustic output signal for each of the plurality of locations. [Background technology]

[0002] Acoustic scanning probe microscopy (SPM) methods offer promising techniques for investigating the subsurface topography of different types of samples. For example, acoustic AFM methods may be applied to investigate the subsurface elements of biological samples without destroying the sample itself. Another example concerns investigating the embedded topography of semiconductor samples to identify manufacturing defects or malfunctions or to evaluate manufacturing quality, for example, to ensure that dimensions are machined correctly.

[0003] Generally, these acoustic SPM methods can be classified in terms of the physical principles governing subsurface sensing. Low-frequency acoustic SPM applies acoustic signals up to, for example, 200 megahertz (MHz), and is based on the principle that, at such frequencies, the sample's response is particularly governed by the elasticity of the sample's material below the surface. Where an element exists below the surface, the elasticity differs slightly, resulting in a different response in the contact stiffness of the SPM probe tip. Thus, an element below the surface can feel as if it were an object under a pillow. However, the detection depth range is limited, and therefore, structures embedded at deep positions below the surface (e.g., more than 200 micrometers deep) cannot be detected in this way.

[0004] On the other hand, high-frequency acoustic signal moment measurements (SPMs) generally operate with signals exceeding approximately 500 MHz, for example, up to 100 gigahertz (GHz), and are based on the principle that these signals are scattered by elements embedded within the sample. SPM probes generally do not sense such high-frequency signals. Therefore, to measure such signals, the acoustic output signal must be converted to a lower frequency to enable sensing. This is done by applying a heterodyne acoustic signal consisting of two high frequencies (within the range shown above) having different frequencies within the probe's movable detection range. In this case, the output signal contains frequency components at different frequencies, making it possible to sense the characteristics of the signal.

[0005] While the above sensing methods can detect and visualize subsurface elements, achieving sufficient accuracy in determining the dimensions of detected elements remains challenging. Noise and artifacts can also hinder accurate determination. The ability to accurately determine dimensions is crucial in several applications, such as detecting critical dimensions or overlay errors in semiconductor manufacturing processes. [Overview of the project] [Problems that the invention aims to solve]

[0006] The object of the present invention is to provide a method for determining the dimensions of subsurface elements that improves the accuracy of determining the dimensions of subsurface elements by at least partially eliminating the above-mentioned drawbacks. [Means for solving the problem]

[0007] For this purpose, a method for determining the dimensions of one or more subsurface elements from subsurface topography measurements of a sample is provided herein, wherein the subsurface topography measurements are obtained using a scanning probe microscopy system, and the method comprises the steps of: applying an acoustic input signal to a sample using a transducer; sensing an acoustic output signal at a plurality of locations on the surface of the sample using a probe, wherein the probe comprises a cantilever and a probe tip, the probe tip is in contact with the surface, and the acoustic output signal represents a sound wave corresponding to the acoustic input signal that is measurable on the surface; and obtaining a measurement of the acoustic output signal for each of the plurality of locations, and providing a position-dependent subsurface topography signal based on the measurement of at least some of the plurality of locations. The method further includes steps of: providing an autocorrection matrix by performing a correlation of the subsurface topography signal for each of the at least part of the multiple positions with respect to each of the further positions of the at least part of the multiple positions using a position-shifted version of the subsurface topography signal shifted by a distance equal to the distance between each position and the further position, resulting in an autocorrection matrix of size N*N; performing an eigenvalue decomposition of the autocorrection matrix to obtain a plurality of eigenvalues ​​and selecting a subset of the eigenvalues ​​having the maximum value from the eigenvalues; constructing a frequency estimation function from the subset of eigenvalues; and obtaining at least one output value from the frequency estimation function that exhibits spatial periodicity.

[0008] This invention is based on the insight that subsurface topography often includes periodicity or regularity that can be used to more accurately determine the dimensions of such subsurface elements. This is true, for example, in the semiconductor industry. For instance, in many situations, subsurface topography of a wafer includes at least periodicity with respect to a regular pattern of devices arranged side by side with dicing lanes inserted between them to allow for the separation of individual structures. Furthermore, in many situations, the subsurface topography of individual devices includes one or more regular or periodic structures. Such periodicity may be used to apply analytical techniques that allow for more accurate dimensional determination even in the presence of noise or artifacts.

[0009] In this invention, a multiple signal classification (MUSIC) algorithm is applied to obtain such periodic characteristics. Having such characteristics makes it possible to more accurately determine the dimensions of elements or structures. The MUSIC algorithm generates an automatic correction matrix by correlating the subsurface topography signal with itself. By determining the eigenvalues, the largest eigenvalue is considered to indicate a periodic structure in the subsurface topography, while the smallest eigenvalue is considered to arise from noise and other disturbances. This method may include ranking the eigenvalues, although this is not mandatory. This system can immediately determine the largest eigenvalue and calculate periodicity from it.

[0010] In some embodiments, the method includes the step of obtaining a fitted periodic function by fitting at least one periodic function having the same periodicity as the spatial periodicity shown by at least one output value. Such fitted data may be used to enable the calculation of dimensions or the modeling of subsurface topography. The latter is useful when the method is applied in a method for determining overlay errors or alignment errors, and the subsurface topography needs to be modeled and compared with the on-surface topography of the sample.

[0011] In some of these embodiments, the method further includes, for at least some of the plurality of positions, using a post-fitted periodic function to calculate an expected value of the acoustic output signal to provide an expected value for at least the N positions, and for at least some of the plurality of positions, generating a correlation matrix by performing a correlation between the subsurface topography signal and each expected value to provide a correlation matrix having size N*N, performing an eigenvalue decomposition of the correlation matrix to obtain a plurality of further eigenvalues, selecting a further subset of eigenvalues having a maximum value from the further eigenvalues, constructing a further frequency estimation function from the further subset of eigenvalues, and obtaining at least one further output value indicative of spatial periodicity from the further frequency estimation function. The additional iteration described above may be performed once or multiple times to improve the determined spatial periodicity characteristics. Thus, according to some embodiments, the above method steps may be repeated one or more times to obtain an improved estimate of spatial periodicity.

[0012] In some embodiments, the method includes calculating one or more dimensions of the subsurface element based on the determined spatial periodicity. In some embodiments, these dimensions include at least one of a group including the pitch of the periodic structure, the width of the subsurface element, the line width roughness, the critical dimension, and the element spacing.

[0013] Further, in some embodiments, the method includes applying at least one periodic function, and the method further includes using the post-fitted periodic function to determine one or more positions of at least one of a minimum value, a maximum value, or a zero-crossing of the post-fitted periodic function. For example, in some embodiments, the post-fitted periodic function includes a sine wave fit.

[0014] In some specific embodiments, this method is applied to a method for monitoring overlay or alignment during a semiconductor manufacturing process. In these embodiments, the method is a method for monitoring at least one of the overlay or alignment of a first layer and a second layer of a semiconductor substrate using a scanning probe microscopy system, the method comprising the steps of scanning the substrate surface in at least one scanning direction using a probe tip of the scanning probe microscopy system to obtain surface topography and subsurface topography, the method of any one or more of the above claims is carried out, thereby further yielding output values ​​indicating spatial periodicity, the method generates at least one pattern template, matches the measured surface topography with at least one pattern template, and the measured in at least one scanning direction The process further includes the steps of determining a first candidate pattern representing a first topography, obtaining a second candidate pattern representing a measured subsurface topography in at least one scanning direction, wherein the second candidate pattern is obtained by fitting at least one periodic function having the same periodicity as the spatial periodicity, determining one or more elemental properties of device elements in the first topography from the first candidate pattern, determining one or more elemental properties of device elements in the second topography from the second candidate pattern, and calculating one or more overlay parameters or alignment parameters using the determined elemental properties of the first and second topography. Based on the determined periodicity, a topography candidate pattern may be generated that accurately follows the subsurface topography and enables the determination of overlay errors or alignment errors during the process.

[0015] A second aspect of the present invention provides a scanning probe microscopy system configured to carry out the method of any one or more of the above claims, the system comprising a substrate carrier for supporting a sample and comprising a transducer for applying an acoustic input signal to the sample, the system further comprising a scan head comprising a probe, the probe comprising a cantilever and a probe tip, and comprising at least one actuator configured such that at least one of the substrate carrier or the scan head scans the probe relative to the sample such that the probe tip contacts the sample, the system further comprising a sensor for enabling the acquisition of a subsurface topography signal comprising measurements of at least N positions on the surface of the sample, by acquiring an acoustic output signal representing a sound wave corresponding to an acoustic input signal that is measurable on the surface of the sample, and the system further comprising an analysis system or being communicably connected to an analysis system The system comprises a memory and a controller, the memory being configured to store instructions that, when loaded into the memory, enable the controller to determine one or more dimensions of a substrate element having spatial periodicity, and to make the determination, the instructions enable the controller to perform the steps of: providing an autocorrection matrix by performing a correlation of the subsurface topography signals to each of the further positions of at least some of the multiple positions using a position-shifted version of the subsurface topography signal that has been shifted by a distance equal to the distance between each of the multiple positions and the further positions for each of the multiple positions, resulting in an autocorrection matrix having size N*N; performing an eigenvalue decomposition of the autocorrection matrix to obtain a plurality of eigenvalues ​​and selecting a subset of the eigenvalues ​​having the maximum value from the eigenvalues; constructing a frequency estimation function from the subset of eigenvalues; and obtaining at least one output value from the frequency estimation function that indicates spatial periodicity.

[0016] In a third aspect of the present invention, there is provided a computer program product including instructions that, when loaded into a memory of an analysis system related to a scanning probe microscopy system, enable a controller of the analysis system to execute the method according to the first aspect.

[0017] The present invention will be further clarified by describing some specific embodiments of the present invention with reference to the accompanying drawings. The detailed description presents examples of possible implementations of the present invention, but should not be considered as describing only the embodiments within the scope. The scope of the present invention is defined within the scope of the claims, and the description is considered exemplary and does not limit the present invention.

Brief Description of the Drawings

[0018] [Figure 1] FIG. schematically shows the configuration of a system according to an embodiment of the present invention for implementing the method according to an embodiment of the present invention. [Figure 2] FIG. schematically shows how a subsurface device element can be visualized using a scattering-based subsurface scanning probe microscopy method applied using the system shown in FIG. 1. [Figure 3] FIG. schematically shows the method according to an embodiment of the present invention. [Figure 4A] FIG. shows the results of the method of the present invention executed on a wafer. [Figure 4B] FIG. shows the results of the method of the present invention executed on a wafer. [Figure 5] FIG. schematically shows a semiconductor device configuration measured using the method according to an embodiment of the present invention. [Figure 6] FIG. visualizes four signal channels obtained for topography and subsurface measurements. [Figure 7A] FIG. shows an example of sine wave fitting in the method according to an embodiment of the present invention. [Figure 7B]This figure shows an example of sinusoidal wave fitting in a method according to one embodiment of the present invention. [Figure 8] This figure shows raw and filtered visualizations of topographic and subsurface measurements obtained using the method in one embodiment of the present invention. [Figure 9] This figure schematically illustrates the determination of overlay errors for two elements in a test sample based on a method according to one embodiment. [Modes for carrying out the invention]

[0019] The propagation of mechanical waves (ultrasound) in materials inherently depends on the material's mechanical properties, such as density, shape, and modulus of elasticity. Therefore, the analysis of such wave propagation has been studied in the literature for decades, whether in the medical field (e.g., ultrasound) or in non-destructive testing of inert materials, in order to non-destructively determine the properties of the propagation medium.

[0020] The development of the semiconductor industry is generally governed by Moore's Law, which predicts that the number of transistors in dense integrated circuits will double every two years. This presents significant technical challenges as it demands smaller integrated circuits with complex multilayer devices.

[0021] Overlay measurement is a control of pattern alignment in the semiconductor industry. Any type of misalignment can lead to short circuits and connection failures. Figure 5 shows an example of a device configuration 75 in which overlay measurement is required. In this illustrated device configuration 75, the open rectangles 76 represent surface elements, and the dashed rectangles 77 represent subsurface elements. Current measurement techniques are based on optical methods, but such methods are limited because devices may have opaque layers. The object of the present invention is to detect subsurface elements 77 embedded in the structure using an ultrasonic non-destructive evaluation method and to estimate the overlay between the surface elements 76 and the subsurface elements 77. This method can be used for both defect inspection and process control.

[0022] Figure 1 schematically shows a scanning probe microscopy (SPM) system suitable for applying the method according to the present invention. The SPM system in Figure 1 allows a sample 5, which can be fixed to a sample carrier (not shown), to be investigated using scanning probe microscopy techniques. System 1 is suitable for performing both surface topography and subsurface topography measurements. System 1 comprises at least a probe 8 consisting of a cantilever 9 and a probe tip 10, the probe tip 10 generally mounted on a scan head (not shown) together with an actuator for scanning the probe 8 against the sample 5 and bringing the probe tip 10 into contact with the surface of the sample 5. In some cases, the SPM system may be suitable for operating in various operating modes, such as contact mode, non-contact mode, or tapping mode, as will be understood by those skilled in the art. To investigate the sample 5, the probe tip 10 is brought into contact with the surface of the sample 5, and, for example, surface topography or subsurface topography is measured. Sensing of subsurface elements in sample 5 to enable subsurface topography analysis is performed, for example, using a transducer 12 in contact with sample 5 in system 1 of Figure 1, which is located below sample 5. Although the system shown in Figure 1 is bottom-acting, the present invention can also be applied using a top-acting system, in which case the acoustic signal is applied from the top of the surface of sample 5. The transducer 12 may be operated in combination with sensing by probe 8, as will be further described below. The transducer 12 provides an acoustic signal to be applied to sample 5. Furthermore, a binding layer 13 may be present to allow the acoustic signal to be coupled into the sample. The binding layer 13 may be a grease, gel, or any other material that allows the acoustic signal to be efficiently coupled into sample 5. The transducer 12 below sample 5 provides an acoustic signal and may be connected to an acoustic generator 14.

[0023] In the example in Figure 1, the acoustic generator 14 consists of an arbitrary waveform generator (AWG) 15 and an amplifier 16 that provides a gigahertz acoustic input signal to a splitter 17. The splitter 17 provides a portion of the signal to an oscilloscope 20. The remainder of the signal is provided to a transducer 12 via a circulator 18. Any portion of the acoustic signal reflected by internal elements in the sample may be received again via the transducer in the circulator 18, which provides this portion of the signal to the oscilloscope 20. The acoustic generator 14 continuously emits a signal at a probing frequency in the gigahertz range (GHz), and the signal is modulated by the resonant frequency of a cantilever 9 in the kilohertz range (kHz). The transducer 12 may have a diameter of, for example, 100 μm and may be fixed to a silicon delay line. The silicon delay line may be larger and 550 μm thick. This delay line is used to "construct" a plane wave.

[0024] The cantilever 9 captures the motion on the surface of sample 5, induced by a plane wave in response to an applied acoustic signal, as an out-of-plane (perpendicular) displacement of the probe tip 10. Any motion of the probe tip 10 perpendicular to the surface of sample 5 may be sensed, for example, using an optical sensor (not shown). The optical sensor may include, for example, a light beam deflector, which is common in SPM systems such as System 1. The optical sensor generates raw sensor data 21, from which four signal channels, namely a surface topography signal 22, a surface topography error signal 23, a subsurface amplitude signal 26, and a subsurface phase signal 27, may be obtained using an analyzer (not shown). The subsurface signals 26 and 27 are downmixed from the sample-tip interaction using the heterodyne principle described above, and thus the signals 26 and 27 are extracted at a specific resonant frequency using a locking amplifier 25. In this case, the frequency is determined / selected before scanning to maximize the signal-to-noise ratio (SNR). This is not strictly necessary (any shift, or even no shift in some cases, is possible), but the measurement may be performed with some degree of shift (approximately 30° to 40°) to decorrelated the scattering from the AFM plane-movement. System 1, shown in Figure 1, allows for the detection of surface topography and further subsurface topography of sample 5. Subsurface elements cannot be observed from either surface topography channel 22 or surface topography channel 23. However, some scattering patterns can be detected from the subsurface amplitude 26 signal and phase 27 signal. Overlay errors and alignment errors may be detected by comparing the surface topography and subsurface topography, as will be further described below.

[0025] Figure 2 schematically illustrates the principle of subsurface topography measurement using an SPM system, for example, system 1 shown in Figure 1. In this example, sensing is performed using an applied acoustic signal having a center frequency within a high-frequency range (>500 MHz and gigahertz range), as described below, in which case the sensing mechanism is dominated by scattering, for example, a center frequency at 1 GHz. An ultrasonic source 12 (transducer 12 in Figure 1) provides an acoustic input signal to sample 5. The acoustic signal may be applied to any desired portion of sample 5, but in this example, it is applied to the bottom of sample 5 opposite the sample surface. If an element 30 is present inside sample 5, the acoustic signal 29 is locally dispersed by the element 30. Thus, downstream of element 30, disturbances 31 propagate to the surface of sample 5. The acoustic signal 29' contains any disturbances 31 and can be sensed by the probe tip 10 of probe 8.

[0026] Subsurface topography measurements may be performed using SPM with acoustic input signals in various different frequency ranges. However, the sensing mechanism differs depending on the frequency of the acoustic signal applied to sample 5. At low frequencies, for example, typically up to 200 MHz, the elastic properties of the sample 5 material dominate, enabling the sensing of subsurface elements. That is, at such frequencies, subsurface elements are generally "sensed" due to differences in elastic properties at the location where the subsurface elements exist. This can be deduced from the output signal showing the movement of the probe tip 10 lateral to the surface of sample 5. At high frequencies of the acoustic input signal, generally around 500 MHz, the elastic properties no longer play a role because the sample 5 material is inert at such frequencies. Instead, the acoustic signal 29 propagates through sample 5 as shown in Figure 2 and is scattered by obstacles encountered. That is, sensing at such frequencies is performed by measuring the acoustic signal received after it has propagated through sample 5. Low-frequency elastic-based sensing provides a good SNR for the layer immediately below the surface of sample 5, but is limited to relatively small penetration depths. Therefore, it is not possible to perform topographic measurements of deeper layers below the surface of sample 5 using such low-frequency sensing methods. High-frequency scattering-based sensing methods are more suitable for sensing deeper layers below the surface of sample 5. However, obtaining information about the dimensions of subsurface elements from such measurements presents problems, assuming a low SNR. The method of the present invention overcomes this problem, as described below.

[0027] The sensitivity of the probe 8 to the vibrations it receives is limited by the probe's characteristics, such as its dimensions and design, as well as its material. The probe's resonant frequency, which defines the probe's operating range, is generally much lower than the aforementioned acoustic frequencies (generally lower than 2 MHz), thereby placing the aforementioned acoustic frequencies outside this range. To enable sensing, the acoustic input signal 29 may be a heterodyne signal consisting of two (or more) frequencies with a frequency difference that is within the operating range of the probe 8. Mixing both frequencies creates signal components at different frequencies, which can be sensed. Thus, the movement of the probe tip 10 is affected by both the acoustic signal 29' and the disturbance 31. As a result, the surface amplitude 26 and subsurface phase 27 of the acoustic signal 29' may be determined by analyzing the movement of the probe tip 10 using the rocking amplifier 25 in Figure 1, from which a subsurface topography can be derived.

[0028] Considering the semiconductor device 75 in Figure 5, as an example, the surface area 80 of the device 75 is scanned and analyzed. The results of visualizing the four channels 22, 23, 26, and 27 are shown in Figure 6 as 80-1, 80-2, 80-3, and 80-4. In 80-1, the topography signal 22 is visualized across the entire sensed region, and bar-shaped elements 76 are shown on the topography. In 80-2, the topography error signal 23 is visualized across the entire sensed region, and bar-shaped elements 76 are also shown on the topography. In 80-3, the subsurface amplitude signal 26 is visualized across the entire sensed region, and in this case too, bar-shaped elements 76 are shown on the topography, and further subsurface bar-shaped elements 77 are indistinctly shown. In 80-4, the subsurface phase signal 27 is visualized across the entire region where it was sensed, and in this case a rod-shaped element 76 is shown on the topography, and a subsurface rod-shaped element 77 is shown very indistinctly. The four visualized channels 22, 23, 26, and 27 in Figure 6 may be used as inputs to a method according to one embodiment of the present invention to enable the detection of the dimensions of subsurface elements (e.g., rods 77).

[0029] Figure 3 shows a data processing method for processing data from an atomic microscopy system, in which ultrasonic excitation is performed in addition to topographic measurements to determine subsurface elements. This method may be applied, for example, during the manufacturing of semiconductor wafers containing multiple semiconductor devices. Applying scanning probe microscopy methods such as atomic microscopy (AFM) makes it possible to measure critical dimensions and determine overlay errors and alignment errors during wafer manufacturing. In industrial processes, this method may be applied to perform quality inspection or to enable correction of industrial processes to ensure desired quality.

[0030] The method in Figure 3 begins in step 50, where measurements are received from the AFM system, which then applies ultrasonic excitation to identify or map subsurface elements in addition to performing topographic measurements on the surface of the substrate sample. For example, step 50 may be performed using the SPM system 1 in Figure 1. Step 50 receives raw data from system 1, for example, raw data 21 acquired from the optical sensor of system 1, from which four channels are generated, for example, a surface topography signal 22, a surface topography error signal 23, a subsurface amplitude signal 26, and a subsurface phase 27. For example, the visualized channels in Figure 6 may be acquired. In step 52, at least two of the channels are selected, i.e., at least one of the topography channels 22 or 23 and one of the subsurface channels 26 or 27. This is necessary because relevant information about subsurface topographic elements 77 may be contained in either the subsurface amplitude channel 26 or the subsurface phase channel 27.

[0031] In step 53, the data acquired from system 1 is preprocessed. Data preprocessing and cleaning are performed because, as can be observed in Figure 6, the signal can become quite noisy, making overlay extraction more complex. For example, preprocessing step 53 involves data flattening and kx -k y Steps such as filter processing (i.e., any filter processing in the wavenumber domain of two-dimensional Fourier transform) may be included. After the preprocessing step 53, a position-dependent measurement value map may be obtained from the data. An example thereof is shown in FIG. 4A, which shows an image 62 of the subsurface amplitude signal 26 such as the image 80-3 of FIG. 6. FIG. 4B shows a graph 64 of the signal column curve 65 located at 1221 nanometers (nm) from the image of FIG. 4A. Considering FIGS. 4A and 4B, the scattering pattern is difficult to extract, and it is impossible to estimate the subsurface element pitch and width without some additional processing.

[0032] According to the present invention, in order to enable accurate estimation of the dimensions of subsurface elements, a position-dependent subsurface topography signal is acquired. This may be a one-dimensional or two-dimensional position-dependent signal. For this example, assuming a one-dimensional position-dependent subsurface topography signal, this signal includes measurements over a line or column in the topography. For example, the signal shown in the graph 64 of FIG. 4B. In some embodiments, a plurality of such one-dimensional position-dependent subsurface topography signals may be acquired. For example, referring to the image 62 in FIG. 4A, for each column x of interest i a one-dimensional position-dependent subsurface topography signal may be acquired. In this case, 500 nm < x < 1350 nm. For each column x i if the two-dimensional position-dependent subsurface topography signal is shown as (x, y), the one-dimensional position-dependent subsurface topography signal s(x i ) provides the signal component (amplitude 26 or phase 27, selected in step 52) of the image containing the acoustic information. The one-dimensional signal s(xi) may consist of, for example, a total of N positions y i (measurement points).

[0033] Of course, in the above, the focus was on the subsurface topography signal, but the same could be done for the surface topography signals 22 and / or 23. These signals are also used together in each of the following method steps 53, 54, 55, 56, and 57 (even if not specifically mentioned below).

[0034] Using this position-dependent subsurface topography signal, assuming that the subsurface element contains at least one or more elements with spatial periodicity, for each of the N positions y where measurements are available i of the same subsurface topography signal s(x i ), the correlation of the subsurface topography signal s(x i ) with other positions y i is performed to calculate the autocorrection matrix, and autocorrection is applied in step 54. Thus, for each point in the one-dimensional position-dependent subsurface topography signal s(x i ), the correlation with the position-shifted version of this same position-dependent subsurface topography signal is calculated. The result of step 54 provides an autocorrection matrix R × of dimension N xx N (where E is the expected value and T is the transpose). R xx (s(x i )) = E(s(x i ), s(x i )) (Equation 1) T Here, note that in FIG. 3, the autocorrection matrix is shown to be slightly different (using R(x n ) for x n and applying the Hermitian matrix R(x n ) H ).

[0035] ​As will be appreciated by those skilled in the art, an auto - correction matrix may be applied to identify periodicity in any signal. In the present invention, an auto - correction matrix is applied to identify periodicity in the position - dependent subsurface topography signal. Further, although step 54 has been described for a one - dimensional position - dependent subsurface topography signal, the same may also be applied to a two - dimensional subsurface topography signal, i.e., a topography map. Above, the auto - correction is for a plurality of columns x in the region of interest (e.g., the region within image 4A, where 500nm < x < 1350nm) i for each column of the one - dimensional position - dependent subsurface topography signal s(x i ) associated with that column. Considering 1 ≤ i ≤ M for x i , this results in M different auto - correction matrices. However, it is also possible to directly perform two - dimensional auto - correction on the signal s(x, y) at once over the entire region.

[0036] Next, in step 55, the method consists of an eigenvalue decomposition step of the obtained auto - correction matrix. The auto - correction matrix R xx is a Hermitian matrix, which means that it is possible to perform eigenvalue decomposition. Then, the auto - correction matrix can be rewritten as follows based on its eigenvalues and eigenvectors. R xx (s(x i ))ν(x i ) = λ(x i )ν(x i ) (Equation 2)

[0037] λ and ν are the eigenvalues and eigenvectors of the auto - correction matrix, respectively. Step 55 may include a diagonalization step to determine the eigenvalues of the auto - correction matrix of step 54. When sorting the eigenvalues in descending order, it is possible to separate the eigenvalues into two sub - spaces, i.e., the eigenvalues corresponding to the signal (element) subspace and the eigenvalues corresponding to the noise subspace. This results in the following equation.

[0038]

Number

[0039] In the above equation, N S This corresponds to the number of signal components (in the example of Figure 5 where the diffraction grating is perfectly periodic, N S N = 1) N This corresponds to the total number of eigenvalues. Of course, it is not necessary to actually sort the eigenvalues. If the number of periodicities in the signal is known (as in this example: 1), then the number of maximum eigenvalues ​​is N. S The periodicity may be immediately recognizable from the set of eigenvalues. In this example, since there is only one periodicity, it is sufficient to select the largest eigenvalue as the eigenvalue associated with the periodicity of the design in Figure 5. In other situations, multiple different periodicities may arise by mixing several elements. Therefore, as input to this method, based on the design blueprint, the number of known periodicities in the design can be provided to enable eigenvalue selection. If this is not available, other selection criteria may be applied as well, for example, selecting an eigenvalue that is significantly larger than the mean, or larger than a threshold, or at least larger than the mean plus three times the standard deviation of the 50% smallest eigenvalue (i.e., identifying outliers, while assuming a normal distribution of eigenvalues ​​associated with noisy signals). Here, various selection criteria may be applied.

[0040] The signal subspace and the noise subspace are orthogonal. Based on this hypothesis, the MUSIC algorithm may perform projections on different eigenvalues ​​corresponding to noise in the signal subspace. These projections should tend to be zero due to the orthogonality of the two subspaces. MU The pseudospectral estimator shown may be defined as the reciprocal of this projection, and this quantity tends to move toward infinity at the signal location. In step 56, peaks are extracted from this estimator to obtain the topographic or subsurface channel spatial components. The projector in this case can be a simple Fourier transform (denoted as FT) projector.

[0041]

number

[0042] Alternatively, in some embodiments, other estimators defined from the signal's autocorrection matrix can be used, such as the maximum likelihood based on the projection of weighted eigenvalues ​​by the estimator's eigenvalues, which yields less accurate results.

[0043]

number

[0044] The present invention is not limited to the above-described estimators, and alternative estimators may be similarly used to determine periodic characteristics such as the pitch, width, or linewidth roughness (LWR) of the rod 77.

[0045] The spatial periodicity determination step described above assigns different element pitches and widths to each of the subsurface topographs of sample 5. Furthermore, since this step can be performed on several traces, it can be used to estimate line width roughness (LWR) or defects in sample 5. In all different tests performed by the inventors, the pitch estimation error was at most 1 pixel off. This means that this dimensional extraction based on spatial periodicity estimation is highly accurate, can be used on large scales, and can be used with noisy data or environments.

[0046] In some cases, according to some embodiments, after estimation in step 56, it is possible to perform sinusoidal fitting or other periodic function (e.g., square wave signal for topography) on all estimated signals in step 57. A post-fit periodic function having the same periodicity as the spatial periodicity obtained from the estimation step is applied. Figures 7A and 7B show sinusoidal fittings 82 and 83 for the topography signal (Figure 7A) and the subsurface signal (Figure 7B), respectively. 2The value represents the residual component of the fit.

[0047] In some cases, as shown by arrow 60 in Figure 3, this method may then repeat another cycle, which is restarted in step 54, and instead of automatic correction of the post-fit periodic function (which provides no information), a correlation is taken between the actual signal and the post-fit periodic function. This can improve the accuracy of the fitted data and allow for a more accurate estimation of the periodicity characteristics.

[0048] Furthermore, in any step 58, the method may continue by creating a two-dimensional map including the post-fitted profile, for example, to obtain a visual representation of the overlay estimation. Figure 8 shows images of the raw topography signal 22 (image 85), the topography signal 22 filtered using the method of the present invention (image 86), the raw subsurface amplitude signal 26 (image 87), and the subsurface amplitude signal 26 filtered using the method of the present invention (image 88). In detail, the latter two images 87 and 88 show a significant improvement in the subsurface signal 26, thereby directly enabling accurate determination of subsurface element dimensions (e.g., the width of the bar element 77).

[0049] Overlay and alignment may already be determined from the results of estimation step 56 without such visualization after one process or one or more iterations. To determine the accuracy and validity of the overlay, it is possible to compare the lines (one is sufficient, but more increase accuracy) between the topography and the acquired subsurface channel results. The overlay can be estimated using several possibilities, namely by comparing the maximum or minimum values ​​of the fitted signal, or by extracting zero crossings (up or down). Figure 9 shows an example of the latter. In Figure 9, the zero crossings of bars 76 and 77 between approximately 1.0 micrometers and 2.2 micrometers in the y-direction of the underlying data of images 86 and 88 are shown in graph 90 x iAll values ​​(i.e., all pixels in the x-direction) are plotted. Plot 91 is the upward zero crossing for the filtered topography signal 22, plot 92 is the upward zero crossing for the filtered subsurface amplitude signal 26, plot 93 is the downward zero crossing for the filtered topography signal 22, and plot 94 is the downward zero crossing for the filtered subsurface amplitude signal 26. Furthermore, the average levels are indicated by the average level 95 for the upward zero crossing of the filtered topography signal 22, the average level 96 for the upward zero crossing of the filtered subsurface amplitude signal 26, the average level 97 for the downward zero crossing of the filtered topography signal 22, and the average level 98 for the downward zero crossing of the filtered subsurface amplitude signal 26. These levels clearly show the overlay discrepancies (e.g., between levels 97 and 98) for the investigated target bars 76 and 77.

[0050] The present invention has been described in relation to several specific embodiments. It will be understood that the embodiments shown in the drawings and described herein are for illustrative purposes only and do not limit the present invention in any way. The operation and configuration of the present invention are expected to be apparent from the above description and the accompanying drawings. It will be apparent to those skilled in the art that the present invention is not limited to any embodiments described herein and that modified embodiments are possible to be devised within the scope of the appended claims. Furthermore, the alteration of mechanisms is considered to be inherently disclosed and within the scope of the present invention. Moreover, any components and elements of the various embodiments disclosed may be combined or incorporated into other embodiments if deemed necessary, desired, or preferred, without departing from the scope of the present invention as defined in the claims.

[0051] In the claims, reference numerals should not be construed as limiting the claims. The terms “composes” and “includes,” as used in this description or the appended claims, should not be construed as exclusive or exhaustive, but rather as inclusive. Accordingly, the expression “composes” as used herein does not exclude the existence of other elements or steps in addition to those enumerated in any claim. Furthermore, the words “a” and “an” should not be construed as limiting to “only one,” but rather as meaning “at least one,” and not as excluding plural. Features not specifically or expressly described or claimed may be additionally included in the structure of the invention within the scope of the invention. Expressions such as “means for ~” should be read as “components configured to ~” or “members configured to ~,” and should be construed as including equivalents of the disclosed structure. The use of expressions such as “significant,” “preferred,” and “particularly preferred” does not limit the invention. Additions, deletions, and modifications within the scope of what is known to those skilled in the art can generally be made without departing from the spirit and scope of the invention, as determined by the claims. The present invention may be implemented in forms other than those specifically described herein and is limited only by the appended claims. [Explanation of Symbols]

[0052] 1 System 5 samples 8 probes 9. Cantilever 10 probe tips 12 transducers, ultrasonic sources 13 Bonding layer 14. Sound Generator 15. Waveform Generator (AWG) 16 Amplifier 17 Splitter 18 Circulator 20 Oscilloscopes 21 Raw sensor data 22 Surface Topography Signals 23 Subsurface topography error signals 25 Locking Amplifiers 26 Subsurface amplitude signal 27 Subsurface phase 29. Acoustic signals 29' Acoustic signal 30 elements 31 External Disturbances 60 Arrows 62 images 64 Graphs 65 Signal Column Curve 75 device configuration, semiconductor devices 76 Surface Elements 77 Subsurface elements 80 surface area 82, 83 Sine wave fitting Images 85, 86, 87, 88 90 Graphs Plots 91, 92, 93, and 94 95, 96, 97, 98 Average level

Claims

1. A method for determining the dimensions of one or more subsurface elements from the results of subsurface topography measurements of a sample, wherein the subsurface topography measurements are obtained using a scanning probe microscopy system, and the method is: The steps include applying an acoustic input signal to the sample using a transducer, A step of sensing an acoustic output signal at multiple locations on the surface of the sample using a probe, wherein the probe includes a cantilever and a probe tip, the probe tip is in contact with the surface, and the acoustic output signal represents a sound wave corresponding to the acoustic input signal that can be measured on the surface; A step of obtaining a measurement value of the acoustic output signal for each of the plurality of positions, and providing a position-dependent subsurface topography signal based on the measurement values ​​of at least some of the plurality of positions, wherein at least some of the plurality of positions include N positions. The subsurface element includes one or more elements having spatial periodicity, and the method is The steps of providing an autocorrection matrix by performing a correlation of the subsurface topography signal with respect to each of the further positions of at least some of the plurality of positions using a position-shifted version of the subsurface topography signal shifted by a distance equal to the distance between each of the positions and the further positions, thereby yielding an autocorrection matrix of size N*N, The steps include: performing eigenvalue decomposition of the aforementioned automatic correction matrix to obtain multiple eigenvalues, and selecting a subset of the eigenvalues ​​that has the maximum value from the aforementioned eigenvalues; The steps include constructing a frequency estimation function from the aforementioned subset of eigenvalues, A method further comprising the step of obtaining at least one output value representing the spatial periodicity from the frequency estimation function.

2. The method according to claim 1, further comprising the step of fitting at least one periodic function having the same periodicity as the spatial periodicity indicated by the at least one output value to obtain a fitted periodic function.

3. For each of the multiple positions, at least some of the positions, the expected value of the acoustic output signal is calculated using the fitted post-periodic function to obtain expected values ​​for at least the N positions. The steps include generating a correlation matrix by performing a correlation between the subsurface topography signal and each expected value for each of the plurality of positions, thereby obtaining a correlation matrix of size N*N, The steps include: performing eigenvalue decomposition of the correlation matrix to obtain a number of further eigenvalues, and selecting a further subset of the eigenvalues ​​having the maximum value from the further eigenvalues; The steps include constructing a further frequency estimation function from the aforementioned further subset of eigenvalues, The method according to claim 2, further comprising the step of obtaining at least one further output value representing the spatial periodicity from the further frequency estimation function.

4. The method according to claim 3, further comprising the steps of fitting the at least one periodic function, calculating the expected value, generating the correlation matrix, performing the eigenvalue decomposition, selecting a further subset of the eigenvalues, constructing the further frequency estimation function, and repeating the steps of obtaining the at least one further output value one or more times to obtain an estimate with improved spatial periodicity.

5. The method according to any one of claims 1 to 4, further comprising the step of calculating the dimensions of one or more subsurface elements based on the determined spatial periodicity.

6. The method according to any one of claims 1 to 5, wherein the dimension includes at least one from the group including the pitch of the periodic structure, the width of the subsurface elements, the line width roughness, the limit dimension, and the element spacing.

7. The method according to claim 2, further comprising the step of determining one or more locations of the minimum value, maximum value, or zero crossing of the fitted post-periodic function using the fitted post-periodic function.

8. The method according to claim 2, wherein the fitted periodic function includes sinusoidal fitting.

9. A method for monitoring at least one of the overlay or alignment between a first layer and a second layer of a semiconductor substrate using a scanning probe microscopy system, The step includes scanning the substrate surface in at least one scanning direction using the probe tip of the scanning probe microscopy system to obtain surface topography and subsurface topography, When obtaining the subsurface topography, the method according to any one of claims 1 to 8 is carried out, thereby further yielding an output value that shows spatial periodicity. The aforementioned method, The steps include generating at least one periodic function, comparing the acquired surface topography with the at least one periodic function, and determining a first candidate pattern representing the first measured topography in at least one scanning direction, A step of obtaining a second candidate pattern representing the acquired subsurface topography in at least one scanning direction, wherein the second candidate pattern is obtained by fitting at least one periodic function having the same periodicity as the spatial periodicity, The steps include determining one or more elemental characteristics of device elements in the first topography from the first candidate pattern, The steps include determining one or more elemental characteristics of device elements in the second topography from the second candidate pattern, A method further comprising the step of calculating one or more overlay parameters or alignment parameters using the determined elemental properties of the first and second topographs.

10. A scanning probe microscopy system configured to carry out the method according to any one of claims 1 to 9, the system comprising a substrate carrier for supporting a sample, the substrate carrier comprising a transducer for applying an acoustic input signal to the sample, the system further comprising a scan head comprising a probe, the probe comprising a cantilever and a probe tip, and at least one actuator configured on the substrate carrier or the scan head to scan the probe relative to the sample such that the probe tip contacts the sample, the system further comprising a sensor for enabling the acquisition of a subsurface topography signal comprising measurements of at least N positions on the surface of the sample, by acquiring an acoustic output signal representing a sound wave corresponding to an acoustic input signal, which is measurable on the surface of the sample, The system further comprises an analysis system, or is communicably connected to the analysis system, and the analysis system comprises a memory and a controller. The memory is configured to store instructions that, when loaded into the memory, enable the controller to determine the dimensions of one or more subsurface elements having spatial periodicity, and in order to make the determination, the instructions enable the controller to The steps of providing an autocorrection matrix by performing the correlation of the subsurface topography signal with respect to each of the further positions of at least some of the plurality of positions using a position-shifted version of the subsurface topography signal shifted by a distance equal to the distance between each of the positions and the further positions, thereby yielding an autocorrection matrix of size N*N, The steps include: performing eigenvalue decomposition of the aforementioned automatic correction matrix to obtain multiple eigenvalues, and selecting a subset of the eigenvalues ​​that has the maximum value from the aforementioned eigenvalues; The steps include constructing a frequency estimation function from the aforementioned subset of eigenvalues, A scanning probe microscopy system that enables the performance of the step of obtaining at least one output value exhibiting the spatial periodicity from the frequency estimation function.

11. The scanning probe microscopy system according to claim 10, wherein the instruction enables the controller to perform the step of fitting at least one periodic function having the same periodicity as the spatial periodicity indicated by the at least one output value to obtain a fitted periodic function.

12. The aforementioned instruction further allows the controller to: For each of at least some of the plurality of positions, the expected value of the acoustic output signal is calculated using the fitted post-periodic function to obtain expected values ​​for at least the N positions. The steps include generating a correlation matrix by performing a correlation between the subsurface topography signal and each expected value for each of the plurality of positions, thereby obtaining a correlation matrix of size N*N, The steps include: performing eigenvalue decomposition of the correlation matrix to obtain a plurality of further eigenvalues, and selecting a further subset of the eigenvalue having the maximum value from the further eigenvalues; The steps include constructing a further frequency estimation function from the aforementioned further subset of eigenvalues, The scanning probe microscopy system according to claim 11, which enables the step of obtaining at least one further output value indicating the spatial periodicity from the further frequency estimation function.

13. The scanning probe microscopy system according to any one of claims 10 to 12, wherein the instruction further enables the controller to perform the step of calculating the one or more dimensions of the subsurface element based on the determined spatial periodicity.

14. The scanning probe microscopy system according to claim 13, wherein the dimensions include at least one from the group consisting of the pitch of the periodic structure, the width of the subsurface elements, the line width roughness, the critical dimension, and the element spacing.

15. A computer program product comprising instructions, wherein when the instructions are loaded into the memory of an analysis system associated with a scanning probe microscopy system, the controller of the analysis system enables the analysis system to perform the method according to any one of claims 1 to 9.

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