Method and apparatus for characterizing membranes

Abstract

The method includes generating a source beam of heterodyne light toward the test layer such that the source beam is incident on the test layer at a first angle of incidence. The source beam is polarized to form a reference beam. The portion of the source beam reflected by the test layer is polarized, thereby forming a test beam. An intensity signal of the reference beam and an intensity signal of the test beam are measured. A difference between the phase of the intensity signal of the test beam and the phase of the intensity signal of the reference beam is determined. The refractive index, extinction coefficient, and thickness of the test layer are determined based on a difference between the phase of the intensity signal of the test beam and the phase of the intensity signal of the reference beam. The embodiment of the invention also relates to a method and a device for characterizing the membrane.

Description

Technical Field

[0001] Embodiments of this application relate to methods and apparatus for characterizing membranes. Background Technology

[0002] Many modern tools used for characterizing semiconductor device layers and / or layers used in semiconductor device fabrication utilize optics for non-contact measurements. One such optics is a reflectometer, which measures reflectivity resulting from the interaction of incident light radiation with the test layer. Another such optics is an interferometer, which measures interference resulting from the interaction of incident light radiation with the test layer. Yet another such optics is an ellipsometer, which measures elliptic polarization resulting from the interaction of incident light radiation with the test layer. Summary of the Invention

[0003] Some embodiments of this application provide a method for characterizing a film, comprising: generating a first source beam of heterodyne light directed toward a first test layer, such that the first source beam is incident on the first test layer at a first incident angle; polarizing the first source beam to form a first reference beam, and polarizing a portion of the first source beam reflected by the first test layer to form a first test beam; measuring an intensity signal of the first reference beam and measuring an intensity signal of the first test beam; determining a difference between the phase of the intensity signal of the first test beam and the phase of the intensity signal of the first reference beam; and determining the refractive index, extinction coefficient, and thickness of the first test layer based on the difference between the phase of the intensity signal of the first test beam and the phase of the intensity signal of the first reference beam.

[0004] Other embodiments of this application provide a method for characterizing a film, comprising: generating a first source beam of heterodyne light toward a sample including a first test layer using a heterodyne light source; polarizing a first portion of the first source beam using a first analyzer to form a first reference beam; measuring an intensity signal of the first reference beam using a first optical sensor; expanding a second portion of the first source beam using a beam expander to form an expanded beam, wherein the expanded beam is incident on the first test layer at a first incident angle, and a portion of the expanded beam is reflected by the first test layer to form a first reflected beam; polarizing the first reflected beam using a second analyzer to form a first test beam; measuring a first intensity signal of the first test beam using a first pixel of a second optical sensor, and measuring a second intensity signal of the first test beam using a second pixel of the second optical sensor. The method involves determining the difference between the phase of the first intensity signal of the first test beam and the phase of the intensity signal of the first reference beam, and determining the difference between the phase of the second intensity signal of the first test beam and the phase of the intensity signal of the first reference beam; determining the refractive index, extinction coefficient, and thickness of the first test layer in a first region along the first test layer based on the difference between the phase of the first intensity signal of the first test beam and the phase of the intensity signal of the first reference beam, and determining the refractive index, extinction coefficient, and thickness of the first test layer in a second region along the first test layer spaced from the first region based on the difference between the phase of the second intensity signal of the first test beam and the phase of the intensity signal of the first reference beam.

[0005] Some embodiments of this application provide an apparatus for characterizing a film, comprising: a heterodyne light source configured to generate a first source beam of heterodyne light directed toward a first test layer; a beam splitter located between the heterodyne light source and the first test layer, configured to reflect a first portion of the first source beam and transmit a second portion of the first source beam; a first analyzer configured to polarize the first portion of the first source beam to form a first reference beam; a first photodetector configured to measure the intensity of the first reference beam, wherein the first analyzer is located between the beam splitter and the first photodetector; and a beam expander located between the beam splitter and the first test layer, configured to expand and collimate the second portion of the first source beam from... The extended beam is formed; a second analyzer is configured to partially polarize the extended beam reflected by the first test layer to form a first test beam; a second photosensitive sensor includes a first pixel and a second pixel configured to measure the intensity of the first test beam, wherein the second analyzer is located between the first test layer and the second photosensitive sensor; and a characterization circuit is coupled to the first photosensitive sensor and the second photosensitive sensor and configured to determine the difference between the phase of the intensity of the first test beam and the phase of the intensity of the first reference beam, and to determine the refractive index, extinction coefficient and thickness of the first test layer based on the difference between the phase of the intensity of the first test beam and the phase of the intensity of the first reference beam. Attached Figure Description

[0006] Various aspects of the embodiments of this disclosure will be best understood from the following detailed description when read in conjunction with the accompanying drawings. It should be noted that, in accordance with standard industry practice, the various components are not drawn to scale. In fact, for clarity of discussion, the dimensions of the various components may be arbitrarily increased or decreased.

[0007] Figure 1 Block diagrams of some embodiments of an apparatus for measuring the thickness, refractive index, and extinction coefficient of a sample are shown.

[0008] Figure 2 The diagram shows some embodiments of the test intensity signal and the reference intensity signal.

[0009] Figure 3 It shows Figure 1 Block diagrams of some other embodiments of the device.

[0010] Figure 4 The diagram illustrates some embodiments of the first test intensity signal, the second test intensity signal, and the reference intensity signal.

[0011] Figure 5Figures illustrating some embodiments of the distribution of thickness, refractive index, and extinction coefficient of a layer used for a sample are shown.

[0012] Figure 6 It shows Figure 3 Block diagrams of some other embodiments of the device.

[0013] Figure 7 , Figure 8 and Figure 9 It shows Figure 6 Block diagrams of some other embodiments of the device.

[0014] Figure 10 , Figure 11 , Figure 12 and Figure 13 Cross-sectional views of some embodiments of the sample are shown.

[0015] Figure 14 Figures illustrating some embodiments of the distribution of thickness, refractive index, and extinction coefficient of multiple layers used in a sample are shown.

[0016] Figure 15 , Figure 16 and Figure 17 Block diagrams are shown of some embodiments of methods for determining the refractive index, extinction coefficient, and thickness of a sample.

[0017] Figure 18 , Figure 19 and Figure 20 Block diagrams are shown of some other embodiments of methods for determining the refractive index, extinction coefficient, and thickness of a sample.

[0018] Figure 21 , Figure 22 and Figure 23 Block diagrams are shown of some other embodiments of methods for determining the refractive index, extinction coefficient, and thickness of a sample.

[0019] Figure 24 Flowcharts are shown for some embodiments of methods for determining the distribution of refractive index, extinction coefficient, and thickness of layers across the surface of a sample. Detailed Implementation

[0020] The following disclosure provides numerous different embodiments or instances for implementing various features of the provided subject matter. Specific examples of components and arrangements are described below to simplify embodiments of this disclosure. Of course, these are merely examples and are not intended to be limiting. For example, in the following description, forming a first component on or over a second component may include embodiments where the first and second components are in direct contact, and may also include embodiments where an additional component may be formed between the first and second components, such that the first and second components are not in direct contact. Furthermore, reference numerals and / or characters may be repeated in various instances of embodiments of this disclosure. This repetition is for simplicity and clarity and does not in itself indicate a relationship between the various embodiments and / or configurations discussed.

[0021] Furthermore, for ease of description, this document uses spatial relative terms such as “below,” “under,” “lower,” “above,” and “upper” to describe the relationship between one element or component and another (or other elements or components) as shown in the figures. In addition to the orientations depicted in the figures, spatial relative terms are intended to include different orientations of the device during use or operation. The device may be oriented in other ways (rotated 90 degrees or in other orientations), and the spatial relative descriptors used herein can be interpreted accordingly.

[0022] Semiconductor device fabrication typically involves the formation and / or use of thin layers (e.g., thin films). Some thin layers are disposed on or over a substrate (e.g., thin dielectric layers, thin conductive layers, thin semiconductor layers, etc.), while others are freestanding (e.g., thin skins for photolithography). Characterizing these thin layers can be an important part of semiconductor device fabrication. For example, determining the thickness, refractive index, extinction coefficient, and / or other properties of these thin layers can be important for performance evaluation, quality control, etc.

[0023] In some instances, the thickness, refractive index, and extinction coefficient of the test layer can be determined using a spectral ellipsometric process. Spectral ellipsometrics involves simulating (e.g., estimating) the structure of the test layer. A light source generates a linearly polarized beam directed toward a point along the test layer. The linearly polarized beam is incident on the test layer at that point, and the test layer reflects the ellipsometric beam. The change in polarization is measured by polarizing the reflected beam using an analyzer and measuring the intensity of the polarized reflected beam using a light sensor. The thickness, refractive index, and extinction coefficient of the test layer are then determined based on the measured change in polarization and a model of the test layer.

[0024] One challenge with spectral elliptic polarization (SNP) is the need for accurate models to precisely determine the thickness, refractive index, and extinction coefficient of the test layer based on measured variations in polarization, and accurately simulating the test layer can be difficult. Therefore, the likelihood of inaccurate results from SNP may increase. Another challenge is that environmental factors (e.g., vibration, air disturbance, etc.) can affect the polarization of the beam between the light source and the test layer, and between the test layer and the photosensor, potentially influencing the variations in polarization measured by the photosensor. This can reduce the robustness of SNP.

[0025] In various embodiments of this disclosure, the thickness, refractive index, and extinction coefficient of the test layer are determined using heterodyne reflection measurement techniques and common-path interferometry to improve accuracy and robustness. The process includes generating a source beam of heterodyne light using a heterodyne source. A first portion of the source beam is polarized by a first analyzer to form a reference beam. The polarization by the first analyzer causes the source beam to self-interfere, and thus the reference beam exhibits self-interferometry. The self-interferometry of the reference beam is measured by measuring the intensity signal of the reference beam using a first optical sensor. A second portion of the source beam is incident on the test layer. The incident beam is reflected by the test layer and then polarized by a second analyzer to form a test beam. The polarization by the second analyzer causes the reflected beam to self-interfere (e.g., common-path interferometry), and thus the test beam exhibits self-interferometry. The self-interferometry of the test beam is measured by measuring the intensity signal of the test beam using a second optical sensor. The difference between the phase of the intensity signal of the test beam and the phase of the intensity signal of the reference beam is determined. Next, the thickness, refractive index, and extinction coefficient of the test layer are determined based on the difference between the phase of the intensity signal of the test beam and the phase of the intensity signal of the reference beam.

[0026] This heterodyne reflection measurement technique / interferometry does not rely on precise simulation of the test layer to accurately measure its thickness, refractive index, and extinction coefficient. Therefore, measurement accuracy can be improved. Furthermore, because this process utilizes common-path heterodyne interferometry, environmental factors have a reduced impact on the measurement intensity of the reference and test beams. Therefore, measurement robustness can be improved.

[0027] Figure 1 Block diagram 100 shows some embodiments of an apparatus for measuring the thickness, refractive index, and extinction coefficient of sample 108.

[0028] The device includes a heterodyne light source 102, a beam splitter 104, a first analyzer 110, a second analyzer 112, a first optical sensor 114, a second optical sensor 116, and a characterization circuit 118.

[0029] A beam splitter 104 is located between the heterodyne light source 102 and the sample 108. A first analyzer 110 is located directly between the beam splitter 104 and the first optical sensor 114. A second analyzer 112 is located directly between the sample 108 and the second optical sensor 116. A characterization circuit 118 is coupled to both the first and second optical sensors 114. For example, a first input terminal of the characterization circuit 118 is coupled to the output terminal of the first optical sensor 114, and a second input terminal of the characterization circuit 118 is coupled to the output terminal of the second optical sensor 116.

[0030] Sample 108 includes a test layer (e.g., Figures 10 to 13 Layer 1002). In some embodiments, the test layer is stand-alone (e.g., as shown in the figure). Figure 10 (As shown in the diagram). In some other embodiments, the test layer is located on the substrate (e.g., as shown in the diagram). Figure 11 (as shown in the diagram). In some embodiments, sample 108 includes a plurality of independent test layers stacked on top of one another (e.g., as shown in the diagram). Figure 12 (as shown in the illustration). In some other embodiments, sample 108 includes multiple test layers stacked on top of each other on a substrate (e.g., as shown in the illustration). Figure 13 (as shown in the image).

[0031] Heterodyne source 102 generates a source beam 130 of heterodyne light directed toward sample 108. Source beam 130 includes S-polarized light (e.g., light with an electric field polarized perpendicular to the incident plane) and P-polarized light (e.g., light with an electric field polarized parallel to the incident plane). The phase difference between the phase of the S-polarized light and the phase of the P-polarized light in source beam 130 is modulated.

[0032] Beam splitter 104 reflects a first portion of source beam 130, thereby forming beam splitter reflected beam 134. First analyzer 110 polarizes beam splitter reflected beam 134, causing the S-polarized and P-polarized light of beam splitter reflected beam 134 to interfere with each other (e.g., common path interference), thereby forming reference beam 140 (e.g., a beam generated due to interference). First optical sensor 114 measures the intensity of reference beam 140 over a period of time, which is determined by… Figure 2 Reference beam intensity signal I ref As shown.

[0033] Beam splitter 104 transmits a second portion of source beam 130, thereby forming incident beam 132. Sample 108 reflects a portion of incident beam 132, thereby forming sample reflected beam 136. This interaction with sample 108 (e.g., reflection) may affect the phase difference between S-polarized and P-polarized light. For example, it may cause the phase difference between the S-polarized and P-polarized light in sample reflected beam 136 to differ from the phase difference between the S-polarized and P-polarized light in incident beam 132. Second analyzer 112 polarizes sample reflected beam 136, causing the S-polarized and P-polarized light of sample reflected beam 136 to interfere with each other (e.g., common path interference), thereby forming test beam 138 (e.g., a beam generated due to interference). Second optical sensor 116 measures the intensity of test beam 138 over a period of time, which is determined by... Figure 2 The test beam intensity signal I test As shown.

[0034] Characterization circuit 118 determines the reference beam intensity signal I ref phase It indicates the phase difference between the S-polarized and P-polarized light of the reference beam 140. Characterization circuit 118 determines the test beam intensity signal I. test phase It indicates the phase difference between the S-polarized and P-polarized light of the test beam 138.

[0035] In addition, the characterization circuit 118 determines the test beam intensity signal I. test phase and reference beam intensity signal I ref phase phase difference between By measuring the test beam intensity signal I test phase Subtract the reference beam intensity signal I ref phase The portion of the phase difference between the S-polarized and P-polarized light of the test beam 138 caused by its interaction with the sample 108 can be determined. The effect of the sample 108 on the phase difference between the S-polarized and P-polarized light of the test beam 138 is used to determine several characteristics of the sample 108. For example, the characterization circuit 118 is based on the phase difference. Determine the refractive index, extinction coefficient, and thickness of the layer in sample 108.

[0036] Because this heterodyne reflection measurement technique using a common-path heterodyne interferometry process does not rely on accurately simulating sample 108 to precisely measure its thickness, refractive index, and extinction coefficient, the accuracy of the measurement can be improved. Furthermore, because this process utilizes common-path heterodyne interferometry, environmental factors (e.g., vibration, air disturbance, etc.) have a reduced impact on the process results. Therefore, the robustness of the measurement can be improved.

[0037] Another challenge with spectral elliptic polarization is that, because the incident beam strikes the sample at a single point along the sample, the measurements only indicate the thickness, refractive index, and extinction coefficient at that single point along sample 108. Therefore, the thickness, refractive index, and extinction coefficient at other points along sample 108 are unknown, and the variation of these parameters along sample 108 is also unknown.

[0038] In some instances, the distribution of the thickness, refractive index, and extinction coefficient of sample 108 across the surface of sample 108 can be determined using a surface scanning ellipsometry across sample 108. However, scanning can be slow, and environmental variations during scanning can reduce the accuracy of the measurement.

[0039] In various embodiments of this disclosure, heterodyne reflection measurement is performed in two dimensions using a common-path heterodyne interferometry process to immediately determine the distribution of the thickness, refractive index, and extinction coefficient of sample 108 across the surface of sample 108 (e.g., without having to scan across the surface of sample 108). Therefore, the speed and accuracy of determining the distribution of the thickness, refractive index, and extinction coefficient of sample 108 can be increased.

[0040] Figure 3 It shows Figure 1 Block diagram 300 of some embodiments of the device, wherein a beam expander 202 is located between a beam splitter 104 and a sample 108, and a second photosensor 116 includes a plurality of photodetectors.

[0041] For example, the second light sensor 116 includes a pixel array comprising a plurality of pixels, each pixel including a photodetector (e.g., a first pixel including a first test photodetector 206, and a second pixel including a second test photodetector 208). In some embodiments, the second light sensor 116 is an image sensor, such as, for example, a charge-coupled device (CCD) camera, a complementary metal-oxide-semiconductor (CMOS) camera, etc. In some embodiments, the second light sensor 116 includes a single reference photodetector 204. In some embodiments, the photodetector is or includes a photodiode, etc.

[0042] Source beam 130 includes multiple rays (e.g., first ray 130a and second ray 130b). A first portion of the rays in source beam 130 is reflected by beam splitter 104, thereby forming rays in beam splitter reflected beam 134 (e.g., first ray 134a and second ray 134b). The rays in beam splitter reflected beam 134 are polarized by first analyzer 110, thereby forming rays in reference beam 140 (e.g., first ray 140a and second ray 140b). First photosensor 114 measures the intensity of the rays in reference beam 140 over time. For example, rays 140a and 140b are incident on reference photodetector 204 of first photosensor 114, and reference photodetector 204 measures the intensity signals of rays 140a and 140b, which are then analyzed by... Figure 4 Reference beam intensity signal I ref As shown.

[0043] A second portion of the light from the source beam 130 is transmitted by the beam splitter 104, thereby forming the light from the incident beam 132 (e.g., first ray 132a and second ray 132b). The beam expander 202 expands and collimates the light from the incident beam 132, thereby forming an expanded incident beam 220 with expanded and collimated rays (e.g., first ray 220a and second ray 220b). For example, the beam expander 202 expands the distance between rays 132a and 132b and collimates rays 132a and 132b, thereby forming rays 220a and 220b, respectively. The expanded incident beam 220 is incident on the sample 108 at multiple points along the sample 108, such that the surface of the sample 108 is covered by the expanded incident beam 220. For example, the first ray 220a of the extended incident beam 220 is incident on the sample 108 at a first point 210 along the sample 108, and the second ray 220b of the extended incident beam 220 is incident on the sample 108 at a second point 212 along the sample 108, spaced apart from the first point 210.

[0044] Sample 108 reflects portions of the extended incident beam 220 at multiple points along sample 108. Therefore, the sample-reflected beam 136 comprises multiple rays (e.g., a first ray 136a and a second ray 136b). For example, ray 136a is emitted from the first point 210 along sample 108 due to reflection of a portion of the extended incident beam 220 at the first point 210. Similarly, ray 136b is emitted from the second point 212 along sample 108 due to reflection of a portion of the extended incident beam 220 at the second point 212.

[0045] The light reflected from the sample beam 136 is polarized by the second analyzer 112, thereby forming the light of the test beam 138 (e.g., first ray 138a and second ray 138b). The second photosensor 116 measures the intensity of the light of the test beam 138 over time. For example, ray 138a is incident on the first test photodetector 206 of the second photosensor 116, and the first test photodetector 206 measures the intensity signal of ray 138a, which is determined by... Figure 4 The first test beam intensity signal I test-1 As shown. Similarly, light 138b is incident on the second test photodetector 208 of the second photosensor 116, and the second test photodetector 208 measures the intensity signal of light 138b, which is determined by... Figure 4 The second test beam intensity signal I test-2 As shown.

[0046] Characterization circuit 118 determines the phase of the test intensity signal measured by the photodetector of the first optical sensor 114. For example, characterization circuit 118 determines the phase of the test intensity signal I measured by the first test photodetector 206 of the second optical sensor 116. test-1 phase (Intensity of the first ray 138a of the test beam 138) and the intensity signal I measured by the second test photodetector 208 of the second photosensor 116. test-2 phase (Indicating the intensity of the second ray 138b of the test beam 138).

[0047] Characterization circuit 118 determines the phase difference between the phase of the intensity signal and the phase of the reference intensity signal. For example, characterization circuit 118 determines the intensity signal I of the first ray 138a of test beam 138. test-1 phase and the intensity signal I of reference beam 140 ref phase phase difference between Furthermore, the characterization circuit 118 determines the intensity signal I of the second ray 138b of the test beam 138. test-2 phase and the intensity signal I of reference beam 140 ref phase phase difference between

[0048] Characterization circuit 118 determines the refractive index, extinction coefficient, and thickness of sample 108 at multiple regions along sample 108 based on the phase difference between the phase of the intensity signal and the phase of a reference intensity signal. For example, characterization circuit 118 determines the thickness based on the intensity signal I of the first ray 138a of test beam 138. test-1 phase and the intensity signal I of reference beam 140 ref phase phase difference between To determine the refractive index, extinction coefficient, and thickness of the layer in a first region along sample 108 (within which the first point 210 is located). Furthermore, the characterization circuit 118 is based on the intensity signal I of the second ray 138b of the test beam 138. test-2 phase and the intensity signal I of reference beam 140 ref phase The second phase difference between To determine the refractive index, extinction coefficient, and thickness of the layer in the second region of the sample 108 (where the second point 212 is located).

[0049] By including a beam expander 202 between the beam splitter 104 and the sample 108, and by including multiple photodetectors at the second photosensor 116, the distribution of the thickness, refractive index, and extinction coefficient of the sample 108 across its surface can be determined immediately. Therefore, the speed and accuracy of determining the distribution of the thickness, refractive index, and extinction coefficient of the sample 108 can be increased.

[0050] Although Figure 2 The beam of light is shown to have two rays, and Figure 2 The second light sensor 116 is shown to have two light detectors, but it should be understood that the light beam may have some other number of light rays, and the second light sensor 116 may have some other number of light detectors or pixels.

[0051] Figure 5 Figure 500 shows some embodiments of the distribution of thickness, refractive index, and extinction coefficient of a layer used for sample 108.

[0052] exist Figure 5In the illustrated embodiment, the second light sensor 116 has four pixels, and therefore four measurements are performed using the four photodetectors of the second light sensor 116 (corresponding to four regions along the sample 108). For example, this distribution includes: a first refractive index n1, a first extinction coefficient k1, and a first thickness t1, corresponding to a first region along the sample 108; a second refractive index n2, a second extinction coefficient k2, and a second thickness t2, corresponding to a second region along the sample 108 located adjacent to the first region in a first direction 502; a third refractive index n3, a third extinction coefficient k3, and a third thickness t3, corresponding to a third region along the sample 108 located adjacent to the first region in a second direction 504 transverse to the first direction 502; and a fourth refractive index n4, a fourth extinction coefficient k4, and a fourth thickness t4, corresponding to a fourth region along the sample 108 located adjacent to the second region in the second direction 504 and adjacent to the third region in the first direction 502.

[0053] Although Figure 5 The simplified embodiment shown illustrates the characteristics measured at four regions along sample 108, but it should be understood that more measurements can be taken at some larger number of regions along sample 108 to increase the resolution of the distribution.

[0054] Figure 6 It shows Figure 3 A block diagram 600 of some embodiments of the device shows that the characterization circuit 118 includes a first phase measurement circuit 602, a second phase measurement circuit 604, a phase difference circuit 606, and a calculation circuit 608.

[0055] A first phase measurement circuit 602 is coupled to a first optical sensor 114. For example, the input terminal of the first phase measurement circuit 602 is coupled to the output terminal of the first optical sensor 114. A second phase measurement circuit 604 is coupled to a second optical sensor 116. For example, the input terminal of the second phase measurement circuit 604 is coupled to the output terminal of the second optical sensor 116. A phase difference circuit 606 is coupled to both the first phase measurement circuit 602 and the second phase measurement circuit 604. For example, the first input terminal of the phase difference circuit 606 is coupled to the output terminal of the first phase measurement circuit 602, and the second input terminal of the phase difference circuit 606 is coupled to the output terminal of the second phase measurement circuit 604. A calculation circuit 608 is coupled to the phase difference circuit 606. For example, the input terminal of the calculation circuit 608 is coupled to the output terminal of the phase difference circuit 606.

[0056] The first phase measurement circuit 602 receives the reference intensity signal I from the reference photodetector 204 of the first optical sensor 114. ref And determine the reference intensity signal I ref phase The second phase measurement circuit 604 receives a test intensity signal (e.g., I) from the photodetector of the second optical sensor 116. test-1 I test-2 ), and determine the phase of the test intensity signal (e.g., The phase difference circuit 606 receives the test intensity signal (e.g., The phase and reference intensity signal I) ref The phase of the signal, and determine the test intensity signal (e.g., Phase and reference intensity signals The phase difference between the phases (e.g., The calculation circuit 608 receives the phase difference (e.g., Furthermore, the refractive index, extinction coefficient, and layer thickness of sample 108 at multiple regions along sample 108 are determined based on the phase difference.

[0057] Furthermore, in some embodiments, the heterodyne source 102 includes a laser source 610, an electro-optic (EO) modulator 612, an amplifier 614, and a function generator (FG) 616. The laser source 610 generates a laser beam 620 comprising multiple rays (e.g., a first ray 620a and a second ray 620b). The laser beam 620 includes S-polarized light and P-polarized light. The EO modulator 612 receives the laser beam 620 and a modulation signal 622, and modulates the laser beam 620 according to the modulation frequency of the modulation signal 622 (e.g., modulating the phase difference between the S-polarized and P-polarized light of the laser beam 620), thereby forming a source beam 130. The frame rate of the second optical sensor 116 is at least twice the modulation frequency. The function generator 616 generates a baseband signal 624, and the amplifier 614 amplifies the baseband signal 624, thereby forming the modulation signal 622.

[0058] In some embodiments, the linear polarization direction of the laser beam 620 is set to be at a 45-degree angle to the first axis (e.g., the ingress page), the fast axis of the EO modulator 612 is set to be along the first axis, the fast axis of the sample 108 is set to be along the first axis, and the transmission axes of the analyzers 110 and 112 are set to be at a 45-degree angle to the first axis.

[0059] Figure 7 It shows Figure 6 Block diagram 700 also includes some embodiments of the device, including a first actuator 702 and a second actuator 708.

[0060] Sample 108 is disposed on the first actuator 702. Second analyzer 112 and second optical sensor 116 are disposed on the second actuator 708.

[0061] A first actuator 702 rotates the sample 108 about axis 704, as indicated by arrow 706, to adjust the incident angle of the extended incident beam 220 on the sample 108. A second actuator 708 rotates a second analyzer 112 and a second photosensor 116 about axis 704 to adjust the angles of the second analyzer 112 and the second photosensor 116 based on the angle of the sample 108 (e.g., based on the reflection angle of the sample reflected beam 136), such that the sample reflected beam 136 passes through the second analyzer 112 and the test beam 138 is incident on the second photosensor 116. In some embodiments, the second actuator 708 rotates the second analyzer 112 and the second photosensor 116 about axis 704 by moving along transport path 710 (as indicated by arrow 712) and by rotating at axis 714 (as indicated by arrow 716). In some embodiments, axis 704 is positioned along the center of the surface of the sample 108.

[0062] Figure 8 It shows Figure 6 Block diagram 800 also includes some embodiments of the device comprising a reflector 802, a first actuator 702, a second actuator 804, and a third actuator 806.

[0063] A reflector 802 is located between a beam splitter 104 and a beam expander 202. A beam expander 202 is located between a reflector 802 and a sample 108. The sample 108 is mounted on a first actuator 702. A beam expander 202 and a third actuator 806 are mounted on a second actuator 804. A reflector 802 is mounted on the third actuator 806.

[0064] An incident beam 132 is incident on a reflector 802, and the reflector 802 reflects the incident beam 132 toward the beam expander 202. A first actuator 702 rotates the sample 108 about an axis 704, as indicated by arrow 706; a second actuator 804 rotates the beam expander 202 and a third actuator 806 (and therefore the reflector 802) about an axis 704, as indicated by arrow 814; and a third actuator 806 rotates the reflector 802 about an axis 809, as indicated by arrow 808, to adjust the angle of incidence of the expanded incident beam 220 on the sample 108 and to orient the sample reflected beam 136 toward the second analyzer 112 and the second photosensor 116, such that the sample reflected beam 136 passes through the second analyzer 112 and the test beam 138 is incident on the second photosensor 116. In some embodiments, the second actuator 804 rotates the beam expander 202 and the third actuator 806 about axis 704 by moving along transport path 810 (as indicated by arrow 812) and by rotating at axis 809 (as indicated by arrow 814). In some embodiments, axis 809 is positioned along the center of the surface of mirror 802. In some embodiments, the positions of the second analyzer 112 and the second photosensor 116 are fixed.

[0065] Figure 9 It shows Figure 6 Block diagram 900 also includes some embodiments of the device, including mirror 802, actuator 804, actuator 806, and actuator 708.

[0066] A reflector 802 is located between a beam splitter 104 and a beam expander 202. A beam expander 202 is located between a reflector 802 and a sample 108. A beam expander 202 and an actuator 806 are arranged on an actuator 804. A reflector 802 is arranged on an actuator 806. A second analyzer 112 and a second optical sensor 116 are arranged on an actuator 708.

[0067] Actuator 804 rotates beam expander 202 and third actuator 806 (and therefore mirror 802) about axis 704, as indicated by arrow 814, and actuator 806 rotates mirror 802 about axis 809, as indicated by arrow 808, to adjust the incident angle of the expanded incident beam 220 on sample 108. Actuator 708 rotates second analyzer 112 and second photosensor 116 about axis 704 to adjust the angles of second analyzer 112 and second photosensor 116 based on the incident angle of the expanded incident beam 220 (e.g., based on the reflection angle of the sample reflected beam 136), such that the sample reflected beam 136 passes through second analyzer 112 and test beam 138 is incident on second photosensor 116. In some embodiments, the position of sample 108 is fixed.

[0068] Figure 10 , Figure 11 , Figure 12 , Figure 13 Cross-sectional views 1000, 1100, 1200, and 1300 are shown for some embodiments of sample 108.

[0069] In some embodiments, the sample 108 is located on or supported by the sample holder 1004. In some embodiments (e.g., such as...) Figure 10 As shown in the illustration, sample 108 is a "freestanding" single thin layer 1002. In some other embodiments (e.g., as shown in the illustration), sample 108 is a "freestanding" single thin layer 1002. Figure 11 As shown in the diagram, sample 108 includes a single thin layer 1002 and a substrate 1102 on which the single thin layer 1002 is disposed. In some other embodiments (e.g., as shown in the diagram), sample 108 includes a single thin layer 1002 and a substrate 1102 on which the single thin layer 1002 is disposed. Figure 12 As shown in the diagram, sample 108 includes multiple "freestanding" thin layers (e.g., thin layer 1002, thin layer 1202 below thin layer 1002, and thin layer 1204 below thin layer 1202). In some other embodiments (e.g., as shown in the diagram), sample 108 includes multiple "freestanding" thin layers (e.g., thin layer 1002, thin layer 1202 below thin layer 1204). Figure 13 As shown in the diagram, sample 108 includes multiple thin layers (e.g., thin layers 1002, 1202, 1204) and a substrate 1102 on which the thin layers are disposed. In some embodiments, the freestanding layers may be or form a thin film for photolithography (e.g., extreme ultraviolet (EUV) lithography). In some embodiments, the layers on the substrate may be conductive layers, semiconductor layers, dielectric layers, etc.

[0070] Figure 14 Figure 1400 shows some embodiments of the distribution of thickness, refractive index, and extinction coefficient of multiple layers used for sample 108.

[0071] exist Figure 14 In the illustrated embodiment, the second light sensor 116 has four pixels, and therefore four measurements are performed using the four photodetectors of the second light sensor 116 (corresponding to four regions along each of the three layers of the sample 108). For example, the distribution of the first layer includes four refractive indices n1-n4, four extinction coefficients k1-k4, and four thicknesses t1-t4. Similarly, the distribution of the second layer below the first layer includes four refractive indices n5-n8, four extinction coefficients k5-k8, and four thicknesses t5-t8. Similarly, the distribution of the third layer below the second layer includes four refractive indices n9-n1-n2-n3-n4. 12 Four extinction coefficients k9-k 12 and four thicknesses t9-t 12 .

[0072] Although Figure 14The simplified embodiment shown illustrates properties measured at four regions along a sample with three layers, but it should be understood that more measurements can be taken at a larger number of regions along the sample 108 to increase the resolution of the distribution, and it should be understood that the sample may have some other number of layers.

[0073] Figure 15 , Figure 16 , Figure 17 Block diagrams 1500, 1600, and 1700 show some embodiments of methods for determining the refractive index, extinction coefficient, and thickness of sample 108. Figure 18 , Figure 19 , Figure 20 Block diagrams 1800, 1900, and 2000 show some other embodiments of the method for determining the refractive index, extinction coefficient, and thickness of sample 108, respectively. Figure 21 , Figure 22 , Figure 23 Block diagrams 2100, 2200, and 2300 show some other embodiments of the method for determining the refractive index, extinction coefficient, and thickness of sample 108. Although the method is described... Figures 15 to 23 However, it should be understood that Figures 15 to 23 The structures disclosed in the document are not limited to such methods, but can exist independently as structures independent of methods.

[0074] First, a first measurement is performed using a first source beam 130-1 of heterodyne light at a first incident angle. In some embodiments (e.g., as...) Figures 15 to 17 As shown in the diagram, the sample 108 is rotated to a first sample position about axis 704 using actuator 702, with the angle of incidence (e.g., the angle between the ray of the first source beam 130-1 and a line perpendicular to the surface of the sample 108) set as a first incident angle. Analyzer 112 and optical sensor 116 are rotated about axis 704 by actuator 708 to a first sensor position based on the first sample position. In some other embodiments (e.g., as shown in the diagram), the sample 108 is rotated to a first sensor position based on the first sample position. Figures 18 to 20 As shown in the diagram, the sample 108 is rotated to a first sample position by using actuator 702 about axis 704, the beam expander 202 and reflector 802 are rotated to a first source position by using actuator 804 about axis 704, and the reflector 802 is rotated to a first reflector position by using actuator 806 about axis 809, with the incident angle set to a first incident angle. In some other embodiments (e.g., as shown in the diagram), the incident angle is set to a first incident angle. Figures 21 to 23As shown in the diagram, the beam expander 202 and the reflector 802 are rotated to a first source position by using actuator 804 about axis 704, and the reflector 802 is rotated to a first reflector position by using actuator 806 about axis 809, with the incident angle set to a first incident angle. Analyzer 112 and light sensor 116 are rotated to a first sensor position based on the first source position by actuator 708 about axis 704.

[0075] With the actuator position already set, the heterodyne light source 102 generates a beam pointing toward the first test layer (e.g., ...). Figures 10 to 13 The first source beam 130-1 of the sample 108 (layer 1002). The first source beam 130-1 includes S-polarized light and P-polarized light, wherein the phase difference between the S-polarized light and the P-polarized light is modulated (e.g., according to the modulation frequency of the modulation signal).

[0076] Beam splitter 104 reflects a first portion of the first source beam 130-1, thereby forming a first beam splitter reflected beam 134-1. First analyzer 110 polarizes the first beam splitter reflected beam 134-1, thereby forming a first reference beam 140-1. First optical sensor 114 measures the intensity signal of the first reference beam 140-1. First phase measurement circuit 602 determines the phase of the intensity signal of the first reference beam 140-1.

[0077] Beam splitter 104 transmits a second portion of the first source beam 130-1, thereby forming a first incident beam 132-1. Beam expander 202 expands and collimates the first incident beam 132-1, thereby forming a first expanded incident beam 220-1. In some embodiments (e.g., as...) Figures 18 to 20 and Figures 21 to 23 As shown in the diagram, the reflector 802 reflects the first extended incident beam 220-1 toward the beam expander 202 and the sample 108.

[0078] The first extended incident beam 220-1 is incident on the sample 108 at a first incident angle. A portion of the first extended incident beam 220-1 is reflected by the sample 108, thereby forming a first sample reflected beam 136-1.

[0079] The second analyzer 112 polarizes the first sample reflected beam 136-1, thereby forming a first test beam 138-1. A photodetector (e.g., a pixel) of the second photosensor 116 measures the intensity of the first test beam 138-1. For example, the first test photodetector 206 measures a first intensity signal of the first test beam 138-1 (e.g., corresponding to a first ray of the first test beam emitted along a first region of the sample), and the second pixel measures a second intensity signal of the first test beam 138-1 (e.g., corresponding to a second ray of the first test beam emitted along a second region of the sample). A second phase measurement circuit 604 determines the phase of the intensity signal of the first test beam 138-1. For example, the second phase measurement circuit 604 determines the phase of the first intensity signal of the first test beam 138-1 (measured by the test photodetector 206) and the phase of the second intensity signal of the first test beam 138-1 (measured by the test photodetector 208).

[0080] Phase difference circuit 606 determines the phase difference (e.g., a first phase difference) between the phase of the intensity signal of the first test beam 138-1 and the phase of the intensity signal of the first reference beam 140-1. For example, phase difference circuit 606 determines the phase difference between the phase of the first intensity signal of the first test beam 138-1 (measured by test photodetector 206) and the phase of the intensity signal of the first reference beam 140-1, and determines the phase difference between the phase of the second intensity signal of the first test beam 138-1 (measured by test photodetector 208) and the phase of the intensity signal of the first reference beam 140-1.

[0081] Next, a second measurement is performed using the second source beam 130-2 of the heterodyne light at a second incident angle. In some embodiments (e.g., as...) Figures 15 to 17 As shown in the diagram, the sample 108 is rotated to a second sample position about axis 704 using actuator 702, and the incident angle is adjusted to a second incident angle. Analyzer 112 and optical sensor 116 are rotated about axis 704 by actuator 708 to a second sensor position based on the second sample position. In some other embodiments (e.g., as shown in the diagram), the incident angle is adjusted to a second incident angle. Figures 18 to 20 As shown in the diagram, the incident angle is adjusted to a second incident angle by rotating the sample 108 to a second sample position using actuator 702 about axis 704, rotating the beam expander 202 and reflector 802 to a second source position using actuator 804 about axis 704, and rotating the reflector 802 to a second reflector position using actuator 806 about axis 809. In some other embodiments (e.g., as shown in the diagram), the incident angle is adjusted to a second incident angle. Figures 21 to 23As shown in the diagram, the incident angle is adjusted to a second incident angle by rotating the beam expander 202 and the reflector 802 to a second source position using actuator 804 about axis 704 and by rotating the reflector 802 to a second reflector position using actuator 806 about axis 809. The analyzer 112 and the light sensor 116 are rotated to a second sensor position based on the second source position by actuator 708 about axis 704.

[0082] When the actuator position has been set, the heterodyne light source 102 generates a second source beam 130-2 directed toward the sample 108.

[0083] Beam splitter 104 reflects a first portion of the second source beam 130-2, thereby forming a second beam splitter reflected beam 134-2. First analyzer 110 polarizes the second beam splitter reflected beam 134-2, thereby forming a second reference beam 140-2. First optical sensor 114 measures the intensity signal of the second reference beam 140-2. First phase measurement circuit 602 determines the phase of the intensity signal of the second reference beam 140-2.

[0084] Beam splitter 104 transmits a second portion of the second source beam 130-2, thereby forming a second incident beam 132-2. Beam expander 202 expands and collimates the second incident beam 132-2, thereby forming a second expanded incident beam 220-2. In some embodiments (e.g., as...) Figures 18 to 20 and Figures 21 to 23 As shown in the diagram, the reflector 802 reflects the second extended incident beam 220-2 toward the beam expander 202 and the sample 108.

[0085] The second extended incident beam 220-2 is incident on the sample 108 at a second incident angle different from the first incident angle. A portion of the second extended incident beam 220-2 is reflected by the sample 108, thereby forming the second sample reflected beam 136-2.

[0086] The second analyzer 112 polarizes the second sample reflected beam 136-2, thereby forming a second test beam 138-2. The pixels of the second optical sensor 116 measure the intensity of the second test beam 138-2. The second phase measurement circuit 604 determines the phase of the intensity signal of the second test beam 138-2.

[0087] The phase difference circuit 606 determines the phase difference (e.g., the second phase difference) between the phase of the intensity signal of the second test beam 138-2 and the phase of the intensity signal of the second reference beam 140-2.

[0088] Next, a third measurement is performed using the third source beam 130-3 of the heterodyne light and the third incident angle. In some embodiments (e.g., as...) Figures 15 to 17As shown in the diagram, the sample 108 is rotated to a third sample position around axis 704 using actuator 702, and the incident angle is adjusted to a third incident angle. Analyzer 112 and optical sensor 116 are rotated to a third sensor position based on the third sample position via actuator 708 around axis 704. In some other embodiments (e.g., as shown in the diagram), the incident angle is adjusted to a third incident angle. Figures 18 to 20 As shown in the diagram, the incident angle is adjusted to a third incident angle by rotating the sample 108 about axis 704 to a third sample position using actuator 702, rotating the beam expander 202 and reflector 802 to a third source position using actuator 804 about axis 704, and rotating the reflector 802 to a third reflector position using actuator 806 about axis 809. In some other embodiments (e.g., as shown in the diagram), the incident angle is adjusted to a third incident angle. Figures 21 to 23 As shown in the diagram, the incident angle is adjusted to a third incident angle by rotating the beam expander 202 and the reflector 802 to the third light source position by using actuator 804 to rotate the reflector 802 to the third reflector position by using actuator 806 to rotate the reflector 802 to the third reflector position. The analyzer 112 and the light sensor 116 are rotated to a third sensor position based on the third light source position by actuator 708 to rotate the beam expander 202 and the reflector 802 to the third reflector position by using actuator 806 to rotate the reflector 802 to the third reflector position by using actuator 708 to rotate the beam expander 202 and the reflector 802 to the third reflector position.

[0089] When the actuator position has been set, the heterodyne light source 102 generates a third source beam 130-3 directed toward the sample 108.

[0090] Beam splitter 104 reflects a first portion of the third source beam 130-3, thereby forming the third beam splitter reflected beam 134-3. First analyzer 110 polarizes the third beam splitter reflected beam 134-3, thereby forming the third reference beam 140-3. First optical sensor 114 measures the intensity signal of the third reference beam 140-3. First phase measurement circuit 602 determines the phase of the intensity signal of the third reference beam 140-3.

[0091] Beam splitter 104 transmits a second portion of the third source beam 130-3, thereby forming a third incident beam 132-3. Beam expander 202 expands and collimates the third incident beam 132-3, thereby forming a third expanded incident beam 220-3. In some embodiments (e.g., as...) Figures 18 to 20 and Figures 21 to 23 As shown in the diagram, the reflector 802 reflects the third extended incident beam 220-3 toward the beam expander 202 and the sample 108.

[0092] The third extended incident beam 220-2 is incident on the sample 108 at a third incident angle different from the first and second incident angles. A portion of the third extended incident beam 220-3 is reflected by the sample 108, thereby forming the third sample reflected beam 136-3.

[0093] The second analyzer 112 polarizes the reflected beam 136-3 from the third sample, thereby forming a third test beam 138-3. The pixels of the second optical sensor 116 measure the intensity of the third test beam 138-3. The second phase measurement circuit 604 determines the phase of the intensity signal of the third test beam 138-3.

[0094] The phase difference circuit 606 determines the phase difference (e.g., the third phase difference) between the phase of the intensity signal of the third test beam 138-3 and the phase of the intensity signal of the third reference beam 140-3.

[0095] The calculation circuit 608 determines the refractive index, extinction coefficient, and thickness of the sample 108 based on a first phase difference (corresponding to a first incident angle), a second phase difference (corresponding to a second incident angle), and a third phase difference (corresponding to a third incident angle). For example, the calculation circuit 608 determines the refractive index, extinction coefficient, and thickness of the layer of the sample 108 along a first region of the sample based on the phase difference between the phase of the first intensity signal of the first test beam 138-1 (corresponding to the test photodetector 206) and the phase of the intensity signal of the first reference beam 140-1, the phase difference between the phase of the first intensity signal of the second test beam 138-2 (corresponding to the test photodetector 206) and the phase of the intensity signal of the second reference beam 140-2, and the phase difference between the phase of the first intensity signal of the third test beam 138-3 (corresponding to the test photodetector 206) and the phase of the intensity signal of the third reference beam 140-3. Similarly, the calculation circuit 608 determines the refractive index, extinction coefficient, and thickness of the layer of sample 108 along the second region of the sample based on the phase difference between the phase of the second intensity signal of the first test beam 138-1 (corresponding to the test photodetector 208) and the phase of the intensity signal of the first reference beam 140-1, the phase difference between the phase of the second intensity signal of the second test beam 138-2 (corresponding to the test photodetector 208) and the phase of the intensity signal of the second reference beam 140-2, and the phase difference between the phase of the second intensity signal of the third test beam 138-3 (corresponding to the test photodetector 208) and the phase of the intensity signal of the third reference beam 140-3.

[0096] In some embodiments, to determine the distribution of refractive index, extinction coefficient, and thickness of a sample having N layers, 3×N phase difference measurements are performed at 3×N different incident angles. For example, to determine the distribution of refractive index, extinction coefficient, and thickness of a sample having three layers, phase difference measurements are performed at nine different incident angles. Furthermore, all nine different phase difference measurements for the three-layer sample are used to determine the refractive index, extinction coefficient, and thickness of each layer of the sample. For example, the refractive index, extinction coefficient, and thickness of the first layer of the sample are determined based on all nine different phase difference measurements; the refractive index, extinction coefficient, and thickness of the second layer of the sample are determined based on all nine different phase difference measurements; and the refractive index, extinction coefficient, and thickness of the third layer of the sample are determined based on all nine different phase difference measurements. In some embodiments, the incident angle is in the range between 0 degrees and 90 degrees, between 10 degrees and 80 degrees, or some other suitable range.

[0097] Figure 24 Flowcharts of some embodiments of method 2400 for determining the distribution of refractive index, extinction coefficient, and thickness of layers across the surface of a sample are shown. While method 2400 is shown and described below as a series of steps or events, it should be understood that the order in which such steps or events are shown should not be construed as limiting. For example, some steps may occur in a different order and / or simultaneously with other steps or events in addition to those shown and / or described herein. Furthermore, not all steps shown are necessary to implement one or more aspects or embodiments described herein. Moreover, one or more of the steps depicted herein may be performed in one or more separate steps and / or stages.

[0098] In frame 2402, a first source beam of heterodyne light is generated by a heterodyne light source and directed toward the sample, such that the first source beam is incident on the sample at a first incident angle.

[0099] In block 2404, a first analyzer is used to polarize a first source beam to form a first reference beam, and a second analyzer is used to polarize the portion of the first source beam reflected by the sample to form a first test beam.

[0100] In block 2406, the intensity signal of the first reference beam is measured using a reference photodetector, and the intensity signal of the first test beam is measured using a test photodetector.

[0101] In block 2408, the phase difference between the phase of the first test intensity signal and the phase of the first reference intensity signal is determined. Figure 15 , Figure 18 , Figure 21 Block diagrams 1500, 1800, and 2100 are shown for some embodiments corresponding to blocks 2402, 2404, 2406, and 2408.

[0102] In box 2410, a second source beam of heterodyne light is generated by a heterodyne light source and directed toward the sample, such that the second source beam is incident on the sample at a second incident angle.

[0103] In box 2412, a first analyzer is used to polarize the second source beam to form a second reference beam, and a second analyzer is used to polarize the portion of the second source beam reflected by the sample to form a second test beam.

[0104] In block 2414, the intensity signal of the second reference beam is measured using a reference photodetector, and the intensity signal of the second test beam is measured using a test photodetector.

[0105] In box 2416, the phase difference between the phase of the second test intensity signal and the phase of the second reference intensity signal is determined. Figure 16 , Figure 19 , Figure 22 Block diagrams 1600, 1900, and 2200 are shown for some embodiments corresponding to blocks 2410, 2412, 2414, and 2416.

[0106] In box 2418, phase difference measurements are repeated for additional incident angles based on the number of layers in the sample. Figure 17 , Figure 20 , Figure 23 Block diagrams 1700, 2000, and 2300 are shown corresponding to some embodiments of block 2418.

[0107] In box 2420, the distribution of the refractive index, extinction coefficient, and thickness of the sample layers across the sample surface is determined based on the phase difference. Figure 5 , Figure 14 Figures 500 and 1400 show some embodiments of the distribution of refractive index, extinction coefficient, and thickness of layers across the surface of the sample.

[0108] Therefore, in some embodiments, this disclosure relates to a method including: generating a first source beam of heterodyne light directed toward a first test layer, such that the first source beam is incident on the first test layer at a first incident angle. The method includes: polarizing the first source beam to form a first reference beam, and polarizing a portion of the first source beam reflected by the first test layer to form a first test beam. The method includes: measuring an intensity signal of the first reference beam and measuring an intensity signal of the first test beam. The method includes: determining a difference between the phase of the intensity signal of the first test beam and the phase of the intensity signal of the first reference beam. The method includes: determining the refractive index, extinction coefficient, and thickness of the first test layer based on the difference between the phase of the intensity signal of the first test beam and the phase of the intensity signal of the first reference beam. In some embodiments, the method further includes: generating a second source beam of heterodyne light directed toward the first test layer, such that the second source beam is incident on the first test layer at a second incident angle different from the first incident angle; polarizing the second source beam to form a second reference beam, and polarizing a portion of the second source beam reflected by the first test layer to form a second test beam; measuring an intensity signal of the second reference beam and measuring an intensity signal of the second test beam; determining the phase difference between the phase of the intensity signal of the second test beam and the phase difference between the phase of the intensity signal of the second reference beam; and further determining the refractive index, extinction coefficient, and thickness of the first test layer based on the phase difference between the phase of the intensity signal of the second test beam and the phase difference between the intensity signal of the second reference beam. In some embodiments, the method further includes: generating a third source beam of heterodyne light directed toward the first test layer, such that the third source beam is incident on the first test layer at a third incident angle different from the first and second incident angles; polarizing the third source beam to form a third reference beam, and polarizing a portion of the third source beam reflected by the first test layer to form a third test beam; measuring an intensity signal of the third reference beam and measuring an intensity signal of the third test beam; determining the difference between the phase of the intensity signal of the third test beam and the phase of the intensity signal of the third reference beam; and further determining the refractive index, extinction coefficient, and thickness of the first test layer based on the difference between the phase of the intensity signal of the third test beam and the phase of the intensity signal of the third reference beam. In some embodiments, the method further includes: setting the incident angle of the first source beam to a first incident angle; setting the incident angle of the second source beam to a second incident angle; and setting the incident angle of the third source beam to a third incident angle. In some embodiments, measuring the intensity signal of the first test beam includes measuring the intensity signal of a first ray of the first test beam and measuring the intensity signal of a second ray of the first test beam.In some embodiments, determining the difference between the phase of the intensity signal of the first test beam and the phase of the intensity signal of the first reference beam includes: determining the difference between the phase of the intensity signal of a first ray of the first test beam and the phase of the intensity signal of the first reference beam; and determining the difference between the phase of the intensity signal of a second ray of the first test beam and the phase of the intensity signal of the first reference beam. In some embodiments, determining the refractive index, extinction coefficient, and thickness of the first test layer based on the difference between the phase of the intensity signal of the first test beam and the phase of the intensity signal of the first reference beam includes: determining the refractive index, extinction coefficient, and thickness of the first test layer along a first region of the first test layer based on the difference between the phase of the intensity signal of the first ray of the first test beam and the phase of the intensity signal of the first reference beam; and determining the refractive index, extinction coefficient, and thickness of the first test layer along a second region of the first test layer that is different from the first region based on the difference between the phase of the intensity signal of the second ray of the first test beam and the phase of the intensity signal of the first reference beam. In some embodiments, the method further includes: determining the refractive index, extinction coefficient, and thickness of a second test layer located below the first test layer based on the difference between the phase of the intensity signal of the first test beam and the phase of the intensity signal of the first reference beam.

[0109] In other embodiments, this disclosure relates to a method comprising: generating a first source beam of heterodyne light toward a sample including a first test layer using a heterodyne light source. The method includes: polarizing a first portion of the first source beam using a first analyzer to form a first reference beam. The method includes: measuring an intensity signal of the first reference beam using a first optical sensor. The method includes: expanding a second portion of the first source beam using a beam expander to form an expanded beam. The expanded beam is incident on the first test layer at a first incident angle, and a portion of the expanded beam is reflected by the first test layer to form a first reflected beam. The method includes: polarizing the first reflected beam using a second analyzer to form a first test beam. The method includes: measuring a first intensity signal of the first test beam using a first pixel of a second optical sensor, and measuring a second intensity signal of the first test beam using a second pixel of the second optical sensor; the method includes: determining a difference between the phase of the first intensity signal of the first test beam and the phase of the intensity signal of the first reference beam. The method includes: determining a difference between the phase of the second intensity signal of the first test beam and the phase of the intensity signal of the first reference beam. The method includes: determining the refractive index, extinction coefficient, and thickness of a first test layer at a first region along the first test layer based on the difference between the phase of a first intensity signal of a first test beam and the phase of an intensity signal of a first reference beam. The method also includes: determining the refractive index, extinction coefficient, and thickness of the first test layer at a second region along the first test layer, spaced from the first region, based on the difference between the phase of a second intensity signal of the first test beam and the phase of an intensity signal of the first reference beam. In some embodiments, a second portion of the first source beam is expanded and collimated by a beam expander, such that the surface of the first test layer is covered by the expanded beam. In some embodiments, the method further includes: adjusting a first incident angle by rotating the first test layer about an axis; and rotating a second analyzer and a second optical sensor about an axis in response to rotating the first test layer about the axis. In some embodiments, the method further includes: reflecting the second portion of the first source beam toward the beam expander and the first test layer using a mirror; and adjusting the first incident angle by rotating the first test layer, the mirror, and the beam expander about an axis. In some embodiments, the method further includes: reflecting a second portion of the first source beam toward the beam expander and the first test layer using a mirror; adjusting a first incident angle by rotating the mirror and the beam expander about an axis; and rotating a second analyzer and a second optical sensor about an axis in response to rotating the mirror and the beam expander about an axis. In some embodiments, the method further includes: reflecting the first portion of the first source beam with a beam splitter before polarizing the first portion of the first source beam; and transmitting the second portion of the first source beam with a beam splitter before expanding the second portion of the first source beam.In some embodiments, the first source beam of the heterodyne light is generated by generating a precursor beam having S-polarized and P-polarized light and modulating the phase difference between the S-polarized and P-polarized light of the precursor beam according to a modulation frequency.

[0110] In some other embodiments, this disclosure relates to an apparatus including a heterodyne light source, a beam splitter, a first analyzer, a first optical sensor, a beam expander, a second analyzer, a second optical sensor, and characterization circuitry. The heterodyne light source is configured to generate a first source beam of heterodyne light directed toward a first test layer. The beam splitter is located between the heterodyne light source and the first test layer and is configured to reflect a first portion of the first source beam and transmit a second portion of the first source beam. The first analyzer is configured to polarize the first portion of the first source beam to form a first reference beam. The first optical sensor is configured to measure the intensity of the first reference beam. The first analyzer is located between the beam splitter and the first optical sensor. The beam expander is located between the beam splitter and the first test layer. The beam expander is configured to expand and collimate a second portion of the first source beam to form an expanded beam. The second analyzer is configured to polarize a portion of the expanded beam reflected by the first test layer to form a first test beam. The second optical sensor includes a first pixel and a second pixel configured to measure the intensity of the first test beam. The second analyzer is located between the first test layer and the second optical sensor. Characterization circuitry is coupled to the first and second optical sensors. The characterization circuit is configured to determine the difference between the phase of the intensity of a first test beam and the phase of the intensity of a first reference beam. The characterization circuit is also configured to determine the refractive index, extinction coefficient, and thickness of a first test layer based on the phase difference between the phase of the intensity of the first test beam and the phase of the intensity of the first reference beam. In some embodiments, the apparatus further includes: a first actuator configured to rotate the first test layer about an axis to adjust the incident angle of the extended beam incident on the first test layer; and a second actuator configured to rotate a second analyzer and a second optical sensor about an axis. In some embodiments, the apparatus further includes: a mirror located between a beam splitter and a beam expander, and configured to reflect a second portion of the first source beam toward the beam expander and the first test layer; a first actuator configured to rotate the first test layer about an axis; and a second actuator configured to rotate the mirror and the beam expander about an axis to adjust the incident angle of the extended beam incident on the first test layer. In some embodiments, the apparatus further includes: a mirror located between a beam splitter and a beam expander, configured to reflect a second portion of the first source beam toward the beam expander and the first test layer; a first actuator configured to rotate the mirror and the beam expander about an axis to adjust the incident angle of the expanded beam onto the first test layer; and a second actuator configured to rotate a second analyzer and a second optical sensor about an axis. In some embodiments, the heterodyne source includes a laser source configured to generate a laser beam comprising S-polarized light and P-polarized light, wherein the heterodyne source further includes a modulator configured to modulate the phase difference between the S-polarized light and the P-polarized light of the laser beam.

[0111] Some embodiments of this application provide a method for characterizing a film, comprising: generating a first source beam of heterodyne light directed toward a first test layer, such that the first source beam is incident on the first test layer at a first incident angle; polarizing the first source beam to form a first reference beam, and polarizing a portion of the first source beam reflected by the first test layer to form a first test beam; measuring an intensity signal of the first reference beam and measuring an intensity signal of the first test beam; determining a difference between the phase of the intensity signal of the first test beam and the phase of the intensity signal of the first reference beam; and determining the refractive index, extinction coefficient, and thickness of the first test layer based on the difference between the phase of the intensity signal of the first test beam and the phase of the intensity signal of the first reference beam.

[0112] In some embodiments, the method further includes: generating a second source beam of heterodyne light directed toward the first test layer, such that the second source beam is incident on the first test layer at a second incident angle different from the first incident angle; polarizing the second source beam to form a second reference beam, and polarizing a portion of the second source beam reflected by the first test layer to form a second test beam; measuring an intensity signal of the second reference beam and measuring an intensity signal of the second test beam; determining a difference between the phase of the intensity signal of the second test beam and the phase of the intensity signal of the second reference beam; and further determining the refractive index, the extinction coefficient, and the thickness of the first test layer based on the difference between the phase of the intensity signal of the second test beam and the phase of the intensity signal of the second reference beam.

[0113] In some embodiments, the method further includes: generating a third source beam of heterodyne light directed toward the first test layer, such that the third source beam is incident on the first test layer at a third incident angle different from the first incident angle and the second incident angle; polarizing the third source beam to form a third reference beam, and polarizing a portion of the third source beam reflected by the first test layer to form a third test beam; measuring an intensity signal of the third reference beam and measuring an intensity signal of the third test beam; determining a difference between the phase of the intensity signal of the third test beam and the phase of the intensity signal of the third reference beam; and further determining the refractive index, the extinction coefficient, and the thickness of the first test layer based on the difference between the phase of the intensity signal of the third test beam and the phase of the intensity signal of the third reference beam. In some embodiments, the method further includes: setting the incident angle of the first source beam to the first incident angle; setting the incident angle of the second source beam to the second incident angle; and setting the incident angle of the third source beam to the third incident angle. In some embodiments, measuring the intensity signal of the first test beam includes measuring the intensity signal of a first ray of the first test beam and measuring the intensity signal of a second ray of the first test beam. In some embodiments, determining the difference between the phase of the intensity signal of the first test beam and the phase of the intensity signal of the first reference beam includes: determining the difference between the phase of the intensity signal of the first ray of the first test beam and the phase of the intensity signal of the first reference beam; and determining the difference between the phase of the intensity signal of the second ray of the first test beam and the phase of the intensity signal of the first reference beam. In some embodiments, determining the refractive index, extinction coefficient, and thickness of the first test layer based on the difference between the phase of the intensity signal of the first test beam and the phase of the intensity signal of the first reference beam includes: determining the refractive index, extinction coefficient, and thickness of the first test layer along a first region of the first test layer based on the difference between the phase of the intensity signal of the first ray of the first test beam and the phase of the intensity signal of the first reference beam; and determining the refractive index, extinction coefficient, and thickness of the first test layer along a second region of the first test layer that is different from the first region based on the difference between the phase of the intensity signal of the second ray of the first test beam and the phase of the intensity signal of the first reference beam.In some embodiments, the method further includes determining the refractive index, extinction coefficient, and thickness of a second test layer located below the first test layer based on the difference between the phase of the intensity signal of the first test beam and the phase of the intensity signal of the first reference beam.

[0114] Other embodiments of this application provide a method for characterizing a film, comprising: generating a first source beam of heterodyne light toward a sample including a first test layer using a heterodyne light source; polarizing a first portion of the first source beam using a first analyzer to form a first reference beam; measuring an intensity signal of the first reference beam using a first optical sensor; expanding a second portion of the first source beam using a beam expander to form an expanded beam, wherein the expanded beam is incident on the first test layer at a first incident angle, and a portion of the expanded beam is reflected by the first test layer to form a first reflected beam; polarizing the first reflected beam using a second analyzer to form a first test beam; measuring a first intensity signal of the first test beam using a first pixel of a second optical sensor, and measuring a second intensity signal of the first test beam using a second pixel of the second optical sensor. The method involves determining the difference between the phase of the first intensity signal of the first test beam and the phase of the intensity signal of the first reference beam, and determining the difference between the phase of the second intensity signal of the first test beam and the phase of the intensity signal of the first reference beam; determining the refractive index, extinction coefficient, and thickness of the first test layer in a first region along the first test layer based on the difference between the phase of the first intensity signal of the first test beam and the phase of the intensity signal of the first reference beam, and determining the refractive index, extinction coefficient, and thickness of the first test layer in a second region along the first test layer spaced from the first region based on the difference between the phase of the second intensity signal of the first test beam and the phase of the intensity signal of the first reference beam.

[0115] In some embodiments, the second portion of the first source beam is expanded and collimated by the beam expander, such that the surface of the first test layer is covered by the expanded beam. In some embodiments, the method further includes: adjusting the first incident angle by rotating the first test layer about an axis; and rotating the second analyzer and the second photosensor about the axis in response to rotating the first test layer about the axis. In some embodiments, the method further includes: reflecting the second portion of the first source beam toward the beam expander and the first test layer using a mirror; and adjusting the first incident angle by rotating the first test layer, the mirror, and the beam expander about an axis. In some embodiments, the method further includes: reflecting the second portion of the first source beam toward the beam expander and the first test layer using a mirror; adjusting the first incident angle by rotating the mirror and the beam expander about an axis; and rotating the second analyzer and the second photosensor about the axis in response to rotating the mirror and the beam expander about the axis. In some embodiments, the method further includes: reflecting the first portion of the first source beam with a beam splitter before polarizing the first portion of the first source beam; and transmitting the second portion of the first source beam with the beam splitter before extending the second portion of the first source beam. In some embodiments, the first source beam of the heterodyne light is generated by generating a precursor beam having S-polarized light and P-polarized light and modulating the phase difference between the S-polarized light and the P-polarized light of the precursor beam according to a modulation frequency.

[0116] Some embodiments of this application provide an apparatus for characterizing a film, comprising: a heterodyne light source configured to generate a first source beam of heterodyne light directed toward a first test layer; a beam splitter located between the heterodyne light source and the first test layer, configured to reflect a first portion of the first source beam and transmit a second portion of the first source beam; a first analyzer configured to polarize the first portion of the first source beam to form a first reference beam; a first photodetector configured to measure the intensity of the first reference beam, wherein the first analyzer is located between the beam splitter and the first photodetector; and a beam expander located between the beam splitter and the first test layer, configured to expand and collimate the second portion of the first source beam from... The extended beam is formed; a second analyzer is configured to partially polarize the extended beam reflected by the first test layer to form a first test beam; a second photosensitive sensor includes a first pixel and a second pixel configured to measure the intensity of the first test beam, wherein the second analyzer is located between the first test layer and the second photosensitive sensor; and a characterization circuit is coupled to the first photosensitive sensor and the second photosensitive sensor and configured to determine the difference between the phase of the intensity of the first test beam and the phase of the intensity of the first reference beam, and to determine the refractive index, extinction coefficient and thickness of the first test layer based on the difference between the phase of the intensity of the first test beam and the phase of the intensity of the first reference beam.

[0117] In some embodiments, the apparatus further includes: a first actuator configured to rotate the first test layer about an axis to adjust the incident angle of the extended beam incident on the first test layer; and a second actuator configured to rotate the second analyzer and the second photosensor about the axis. In some embodiments, the apparatus further includes: a mirror located between the beam splitter and the beam expander, configured to reflect a second portion of the first source beam toward the beam expander and the first test layer; a first actuator configured to rotate the first test layer about an axis; and a second actuator configured to rotate the mirror and the beam expander about the axis to adjust the incident angle of the extended beam incident on the first test layer. In some embodiments, the apparatus further includes: a mirror located between the beam splitter and the beam expander, configured to reflect a second portion of the first source beam toward the beam expander and the first test layer; a first actuator configured to rotate the mirror and the beam expander about an axis to adjust the incident angle of the extended beam incident on the first test layer; and a second actuator configured to rotate the second analyzer and the second photosensor about the axis. In some embodiments, the heterodyne light source includes a laser light source configured to generate a laser beam comprising S-polarized light and P-polarized light, and wherein the heterodyne light source further includes a modulator configured to modulate the phase difference between the S-polarized light and the P-polarized light of the laser beam.

[0118] The foregoing outlines features of several embodiments to enable those skilled in the art to better understand various aspects of the embodiments of this disclosure. Those skilled in the art should understand that they can readily use the embodiments of this disclosure as a basis to design or modify other processes and structures for performing the same purposes and / or achieving the same advantages as the embodiments described herein. Those skilled in the art should also recognize that such equivalent constructions do not depart from the spirit and scope of the embodiments of this disclosure, and that various changes, substitutions, and alterations can be made herein without departing from the spirit and scope of the embodiments of this disclosure.

Claims

1. A method for characterizing a film, comprising: generating a first source beam of heterodyne light toward a first test layer such that the first source beam is incident on the first test layer at a first angle of incidence; polarizing the first source beam to form a first reference beam and polarizing a portion of the first source beam reflected by the first test layer to form a first test beam; measuring an intensity signal of the first reference beam and measuring an intensity signal of the first test beam; determining a difference between a phase of the intensity signal of the first test beam and a phase of the intensity signal of the first reference beam; and determining a refractive index, an extinction coefficient, and a thickness of the first test layer based on the difference between the phase of the intensity signal of the first test beam and the phase of the intensity signal of the first reference beam.

2. The method of claim 1, further comprising: generating a second source beam of heterodyne light toward the first test layer such that the second source beam is incident on the first test layer at a second angle of incidence different from the first angle of incidence; polarizing the second source beam to form a second reference beam and polarizing a portion of the second source beam reflected by the first test layer to form a second test beam; measuring an intensity signal of the second reference beam and measuring an intensity signal of the second test beam; determining a difference between a phase of the intensity signal of the second test beam and a phase of the intensity signal of the second reference beam; and further determining the refractive index, the extinction coefficient, and the thickness of the first test layer based on the difference between the phase of the intensity signal of the second test beam and the phase of the intensity signal of the second reference beam.

3. The method of claim 2, further comprising: generating a third source beam of heterodyne light toward the first test layer such that the third source beam is incident on the first test layer at a third angle of incidence different from the first angle of incidence and the second angle of incidence; polarizing the third source beam to form a third reference beam and polarizing a portion of the third source beam reflected by the first test layer to form a third test beam; measuring an intensity signal of the third reference beam and measuring an intensity signal of the third test beam; determining a difference between a phase of the intensity signal of the third test beam and a phase of the intensity signal of the third reference beam; and further determining the refractive index, the extinction coefficient, and the thickness of the first test layer based on the difference between the phase of the intensity signal of the third test beam and the phase of the intensity signal of the third reference beam.

4. The method of claim 3, further comprising: setting the angle of incidence of the first source beam to the first angle of incidence; setting the angle of incidence of the second source beam to the second angle of incidence; and setting the angle of incidence of the third source beam to the third angle of incidence.

5. The method of claim 1, wherein, Measuring the intensity signal of the first test beam includes measuring an intensity signal of a first ray of the first test beam and measuring an intensity signal of a second ray of the first test beam.

6. The method of claim 5, wherein, Determining the difference between the phase of the intensity signal of the first test beam and the phase of the intensity signal of the first reference beam includes: Determining a difference between a phase of the intensity signal of the first ray of the first test beam and the phase of the intensity signal of the first reference beam; and Determining a difference between a phase of the intensity signal of the second ray of the first test beam and the phase of the intensity signal of the first reference beam.

7. The method of claim 6, wherein, Determining the refractive index, the extinction coefficient, and the thickness of the first test layer based on the difference between the phase of the intensity signal of the first test beam and the phase of the intensity signal of the first reference beam includes: Determining the refractive index, the extinction coefficient, and the thickness of the first test layer at a first region along the first test layer based on a difference between the phase of the intensity signal of the first ray of the first test beam and the phase of the intensity signal of the first reference beam; and Determining the refractive index, the extinction coefficient, and the thickness of the first test layer at a second region along the first test layer different from the first region based on the difference between the phase of the intensity signal of the second ray of the first test beam and the phase of the intensity signal of the first reference beam.

8. The method of claim 1, further comprising: Determining a refractive index, an extinction coefficient, and a thickness of a second test layer located below the first test layer based on the difference between the phase of the intensity signal of the first test beam and the phase of the intensity signal of the first reference beam.

9. A method for characterizing a film, comprising: generating, with a heterodyne light source, a first source beam of heterodyne light toward a sample comprising a first test layer; polarizing, with a first analyzer, a first portion of the first source beam, thereby forming a first reference beam; measuring, with a first light sensor, an intensity signal of the first reference beam; expanding, with a beam expander, a second portion of the first source beam, thereby forming an expanded beam, wherein the expanded beam is incident on the first test layer at a first angle of incidence and a portion of the expanded beam is reflected by the first test layer, thereby forming a first reflected beam; polarizing, with a second analyzer, the first reflected beam, thereby forming a first test beam; measuring, with a first pixel of a second light sensor, a first intensity signal of the first test beam and measuring, with a second pixel of the second light sensor, a second intensity signal of the first test beam; determining a difference between a phase of the first intensity signal of the first test beam and a phase of the intensity signal of the first reference beam and determining a difference between a phase of the second intensity signal of the first test beam and the phase of the intensity signal of the first reference beam; and determining a refractive index, an extinction coefficient, and a thickness of the first test layer at a first region along the first test layer based on the difference between the phase of the first intensity signal of the first test beam and the phase of the intensity signal of the first reference beam, and determining the refractive index, the extinction coefficient, and the thickness of the first test layer at a second region along the first test layer spaced apart from the first region based on the difference between the phase of the second intensity signal of the first test beam and the phase of the intensity signal of the first reference beam.

10. An apparatus for characterizing a film, comprising: a heterodyne light source configured to generate a first source beam of heterodyne light toward a first test layer; a beam splitter located between the heterodyne light source and the first test layer and configured to reflect a first portion of the first source beam and to transmit a second portion of the first source beam; a first analyzer configured to polarize the first portion of the first source beam, thereby forming a first reference beam; a first light sensor configured to measure an intensity of the first reference beam, wherein the first analyzer is located between the beam splitter and the first light sensor; a beam expander located between the beam splitter and the first test layer and configured to expand and collimate the second portion of the first source beam, thereby forming an expanded beam; a second analyzer configured to polarize a portion of the expanded beam reflected by the first test layer, thereby forming a first test beam; a second light sensor comprising a first pixel and a second pixel configured to measure an intensity of the first test beam, wherein the second analyzer is located between the first test layer and the second light sensor; and a characterization circuit coupled to the first light sensor and the second light sensor and configured to determine a difference between a phase of the intensity of the first test beam and a phase of the intensity of the first reference beam, and to determine a refractive index, an extinction coefficient, and a thickness of the first test layer based on the difference between the phase of the intensity of the first test beam and the phase of the intensity of the first reference beam.

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