Inspection device and inspection method

Abstract

To provide an inspection device and an inspection method that can accurately reconstruct a processed shape of a cross section.SOLUTION: According to one embodiment, an inspection device having a measuring unit and a controller is provided. The measuring unit measures a physical quantity of a sample formed with a predetermined pattern according to the predetermined pattern. The measuring unit generates a first spectrum pattern according to a result of measurement. The controller applies a parameter to a shape function to predict a processed cross-sectional shape. The shape function indicates an amount of ion flux according to an etching depth in processing the predetermined pattern in dry etching processing. The controller determines a second spectrum pattern according to the predicted processed cross-sectional shape. The controller adjusts the parameter while comparing the first spectrum pattern and the second spectrum pattern with each other. The controller reconstructs the processed cross-sectional shape of the sample according to a result of adjustment.SELECTED DRAWING: Figure 7

Description

[Technical Field]

[0001] The present embodiment relates to an inspection device and an inspection method. [Background technology]

[0002] Inspection devices may measure physical quantities corresponding to a predetermined pattern formed on a sample, and reconstruct a cross-sectional processed shape from a spectral pattern corresponding to the measurement results. In inspection devices, it is desirable to reconstruct the cross-sectional processed shape with high accuracy. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] U.S. Patent Application Publication No. 2021 / 0150116 [Patent Document 2] U.S. Patent No. 10,692,693 [Patent Document 3] US Patent Application Publication No. 2020 / 0261034 [Non-patent literature]

[0004] [Non-Patent Document 1] Junling Li: “Topography Simulation of Intermetal Dielectric Deposition and Interconnecting Metal Deposition Processes”, Ph. D. Dissertation, Stanford University Ph. D. Dissertation, Stanford University, 1996. Summary of the Invention [Problem to be solved by the invention]

[0005] An object of one embodiment is to provide an inspection device and an inspection method that can reconstruct a cross-sectional processed shape with high accuracy. [Means for solving the problem]

[0006] According to one embodiment, there is provided an inspection apparatus having a measurement unit and a controller. The measurement unit measures a predetermined pattern on a sample. When irradiated, the sample According to a given pattern Radiation diffracted by The measuring unit generates a first spectral pattern according to the measurement result. The controller predicts the processed cross-sectional shape by applying parameters to the shape function. The shape function indicates the amount of ion flux according to the etching depth when processing a predetermined pattern in a dry etching process. The controller obtains a second spectral pattern according to the predicted processed cross-sectional shape. The controller compares the first spectral pattern with the second spectral pattern. The degree of match between the first spectral pattern and the second spectral pattern is equal to or greater than a threshold. The parameters are adjusted, and the controller reconstructs the processed cross-sectional shape of the sample according to the adjustment results. [Brief explanation of the drawings]

[0007] [Figure 1] FIG. 1 is a diagram showing the configuration of an inspection apparatus according to an embodiment. [Figure 2] 5A to 5C are diagrams showing the operation of a measurement unit in the embodiment. [Figure 3] FIG. 4 is a diagram showing the operation of a controller in the embodiment. [Figure 4] 4 is a flowchart showing the operation of the inspection device according to the embodiment. [Figure 5] 5A to 5C are diagrams illustrating a dry etching process according to an embodiment. [Figure 6] 5A to 5C are diagrams showing the linearity of ions and the processed cross-sectional shape in the embodiment. [Figure 7] FIG. 4 is a diagram showing a shape function according to the embodiment. [Figure 8] 10A and 10B are diagrams showing changes in shape functions in the depth direction according to an embodiment. [Figure 9]10A and 10B are diagrams showing prediction results of a machining cross-sectional shape based on convolution of a plurality of shape functions in an embodiment. [Figure 10] 5A and 5B are diagrams showing correspondence between a processed cross-sectional shape and a plurality of shape functions in the embodiment. [Figure 11] FIG. 4 is a diagram showing an algebraic equation having a shape function as a solution in the embodiment. [Figure 12] FIG. 6 is a diagram showing temporal changes in coefficients in the embodiment. [Figure 13] 10A and 10B are diagrams showing a time trace of a processed cross-sectional shape in the embodiment. [Figure 14] 10A and 10B are diagrams showing temporal changes in the depth positions of the frontage portion, the upper bowing portion, and the lower bowing portion in the embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0008] An inspection device according to an embodiment will be described in detail below with reference to the accompanying drawings, but the present invention is not limited to the embodiment.

[0009] (Embodiment) The inspection device according to the embodiment is a device for obtaining a cross-sectional processed shape of a predetermined pattern non-destructively, for example, a T-SAXS (Transmission Small Angle X-ray Scattering) device. The inspection device measures physical quantities corresponding to the predetermined pattern for a sample on which the predetermined pattern is formed, and reconstructs the cross-sectional processed shape according to a spectral pattern corresponding to the measurement results and a calculated spectral pattern. The inspection device 1 can be configured as shown in FIG. 1. FIG. 1 is a diagram showing the configuration of the inspection device 1.

[0010] The inspection device 1 has a measurement unit 10 and a controller 20. The measurement unit 10 measures physical quantities corresponding to a predetermined pattern formed on a sample SP. The predetermined pattern is, for example, a fine hole pattern (e.g., at the nanometer level). A fine hole pattern has a high aspect ratio structure, making it difficult for light to penetrate to the bottom, making optical measurement difficult. Therefore, the measurement unit 10 measures radiation diffracted by the sample SP when radiation (e.g., X-rays) is irradiated onto the sample SP. The measurement unit 10 generates a spectral pattern PT1 according to the measurement results.

[0011] The measurement unit 10 has a radiation irradiation unit 11 and a spectrum acquisition unit 12. The radiation irradiation unit 11 irradiates radiation onto a sample SP. As shown in Fig. 2, the radiation irradiation unit 11 has a radiation source 11a and a radiation optical system 11b, and the spectrum acquisition unit 12 has a radiation detector 12a and a positioning mechanism 12b. Fig. 2 is a diagram showing the operation of the measurement unit 10.

[0012] The radiation source 11a generates radiation and emits a radiation beam. The radiation source 11a is, for example, an X-ray source. Examples of the X-ray source that can be used include a particle accelerator source, a liquid anode source, a rotating anode source, a stationary solid anode source, a microfocus source, a microfocus rotating anode source, and an inverse Compton source.

[0013] The radiation optical system 11b shapes the radiation beam emitted from the radiation source 11a and guides it to the sample SP. The radiation optical system 11b is, for example, an X-ray optical system. The radiation optical system 11b may collimate the radiation beam or may focus the radiation beam near the sample SP.

[0014] The positioning mechanism 12b rotatably supports the sample SP. The sample SP is, for example, a substrate on which a predetermined pattern is formed. The radiation beam incident on the sample SP is diffracted according to the predetermined pattern (for example, a fine hole pattern) in the sample SP.

[0015] The radiation detector 12a collects radiation scattered from the sample SP. The radiation detector 12a is, for example, an X-ray detector. The radiation detector 12a has a plurality of pixels arranged two-dimensionally and can acquire a two-dimensional intensity distribution of radiation.

[0016] For example, a fine hole pattern is periodically arranged at a predetermined spatial period on the sample SP. The spectrum acquisition unit 12 measures the radiation diffracted by the sample SP and acquires a spectrum pattern PT1 according to the measurement results. The spectrum pattern PT1 includes information on the periodicity of the arrangement of the fine hole pattern as well as information on the three-dimensional structure of the hole pattern. If the three-dimensional structure of the hole pattern differs, the spectrum pattern PT1 also differs accordingly. The spectrum pattern PT1 is, for example, an X-ray scattering pattern.

[0017] The spectrum acquisition unit 12 can acquire an image showing angle-resolved scattered X-ray intensity as a spectrum pattern PT1 by using the positioning mechanism 12b to determine the position and direction of the sample SP while collecting scattered radiation with the radiation detector 12a. For example, in the example of Fig. 2, images IM1, IM2, and IM3 are acquired as the spectrum pattern PT1 when the tilt angles of the radiation of the sample SP with respect to the optical axis are +1.0°, 0.0°, and -1.0°, respectively.

[0018] The measurement unit 10 supplies the spectrum pattern PT1 acquired by the spectrum acquisition unit 12 to the controller 20.

[0019] The controller 20 reconstructs a processing cross-sectional shape from the spectral pattern PT1 (for example, an X-ray scattering pattern) on a library basis. The processing cross-sectional shape will also be referred to as a processing cross-sectional profile. The library includes a shape function.

[0020] A shape function is a function that expresses a processed cross-sectional shape (processed cross-sectional profile) based on a physical model. This allows for a more faithful expression of the processed cross-sectional shape, closer to the actual shape, than when using an ordinary polynomial. The shape function indicates the amount of ion flux corresponding to the etching depth when processing a predetermined pattern (e.g., a fine hole pattern) in a dry etching process. If the hole pattern is axially symmetric, the shape function indicates the cross-sectional shape of one side of the hole pattern axis. If the predetermined pattern (e.g., a fine hole pattern) can be considered to have an approximately axially symmetric shape, the three-dimensional shape of the predetermined pattern (e.g., a fine hole pattern) can be obtained by rotating the curve represented by the shape function around the depth axis.

[0021] The shape function is a function obtained by integrating the ion flux incident on the sidewall of the hole pattern in the depth direction according to the etching depth. The ion flux includes the incident angle distribution of ions based on the velocity distribution function. When the spread angle of ions emitted from the ion generation location is θ and the parameter indicating the degree of ion spread is n, the ion flux is expressed as cos n+2 The shape function is the solution of an algebraic equation whose order includes a parameter that indicates the degree of spreading of the ion.

[0022] The shape function further indicates the change in shape depending on the etching time. The shape function also includes a coefficient that depends on the etching time. The coefficient includes the quantity obtained by multiplying the etching rate by time. In other words, the shape function is a shape expression based on the mechanism of the dry etching process, making it possible to express the shape including time evolution. Because the relationship between parameter fluctuations and the state during processing is clear, when process conditions are changed, it is possible to estimate which parameters should be changed and by how much, making it easy to determine the parameters. Furthermore, from the change in parameter values ​​after fitting, it may be possible to detect changes in process conditions, mainly related to ion straightness.

[0023] This makes it possible to non-destructively trace the cross-sectional shape over time, which is a very time-consuming process in process development, and to confirm the change in the cross-sectional shape over time while reusing the same or similar parameters. This significantly improves the development TAT (Turn Around Time) for tracing the cross-sectional shape over time.

[0024] The controller 20 has a prediction unit 21, a calculation unit 22, an adjustment unit 23, a reconstruction unit 24, and a library 25. The prediction unit 21 acquires a shape function by referring to the library 25. As shown in FIG. 3, the prediction unit 21 predicts a machined cross-sectional shape by applying parameters to the shape function. FIG. 3 is a diagram showing the operation of the controller 20. The calculation unit 22 obtains a spectral pattern PT2 according to the predicted machined cross-sectional shape. The calculation unit 22 calculates and obtains a scattering pattern when the predicted machined cross-sectional shape is diffracted by radiation (e.g., X-rays) through simulation.

[0025] The adjustment unit 23 acquires the spectral pattern PT1 from the spectrum acquisition unit 12 and acquires the spectral pattern PT2 from the calculation unit 22. The spectral pattern PT1 is a pattern (measured pattern) actually measured by the measurement unit 10. The spectral pattern PT2 is a pattern (calculation result) calculated by the calculation unit 22. The adjustment unit 23 adjusts (matches) the parameters while comparing the spectral pattern PT1 with the spectral pattern PT2. The adjustment unit 23 compares the spectral pattern PT1 with the spectral pattern PT2, and if the degree of match between them is lower than a threshold, changes the parameters and supplies them to the prediction unit 21.

[0026] The prediction unit 21 predicts the machining cross-sectional shape by applying the changed parameters to the shape function. The calculation unit 22 calculates a spectrum pattern PT2 according to the predicted machining cross-sectional shape. The adjustment unit 23 compares the spectrum pattern PT1 with the spectrum pattern PT2, and if the degree of match between the two is equal to or greater than a threshold, notifies the reconstruction unit 24 that the two match.

[0027] The reconstruction unit 24 reconstructs the processed cross-sectional shape of the sample in accordance with the adjustment result of the adjustment unit 23. That is, the reconstruction unit 24 acquires the processed cross-sectional shape from the prediction unit 21 in response to notification from the adjustment unit 23 that the spectrum pattern PT1 and the spectrum pattern PT2 match. The reconstruction unit 24 determines (shape determination) the acquired processed cross-sectional shape as the processed cross-sectional shape of the sample.

[0028] That is, the processing cross-sectional shape is reconstructed using a shape function that more faithfully expresses the processing cross-sectional shape closer to the actual shape while matching the spectrum pattern PT1 and the spectrum pattern PT2, thereby improving the robustness of inspection by the inspection device 1.

[0029] Next, the operation of the inspection device 1 will be described with reference to Fig. 4. Fig. 4 is a flowchart showing the operation of the inspection device.

[0030] The inspection device 1 acquires a spectral pattern PT1 by measurement (S1). The inspection device 1 irradiates radiation (e.g., X-rays) onto a sample SP on which a predetermined pattern (e.g., a fine hole pattern) is formed, and detects the radiation diffracted by the predetermined pattern. The inspection device 1 generates a spectral pattern PT1 (e.g., an actual SAXS image) according to the detected radiation. The inspection device 1 also identifies the measurement conditions used for the measurement (S2). The measurement conditions include the tilt angle of the sample SP during the measurement.

[0031] In parallel with this, the inspection device 1 acquires a shape function by referring to the library 25 (S3). The shape function indicates the amount of ion flux corresponding to the etching depth when processing a predetermined pattern (for example, a fine hole pattern) in the dry etching process.

[0032] The inspection device 1 adjusts the parameters by performing the loop process of S4 to S7 using the spectrum pattern SP1 measured in S1, the measurement conditions acquired in S2, and the shape function obtained in S3.

[0033] For example, the inspection device 1 determines parameters according to the spectrum pattern SP1 and measurement conditions (S4), and applies the parameters to a shape function to predict the cross-sectional processed shape. The inspection device 1 calculates a spectrum pattern PT2 according to the predicted cross-sectional processed shape (S5). The inspection device 1 compares the spectrum pattern PT1 measured in S1 with the spectrum pattern PT2 calculated in S5, evaluates the error (S6), and determines whether the evaluation result satisfies the convergence condition for the loop processing from S4 to S7 (S7).

[0034] If the degree of match between the spectral pattern PT1 and the spectral pattern PT2 is lower than the threshold value (No in S7), the inspection device 1 changes the parameters (S4) and predicts the processed cross-sectional shape by applying the changed parameters to the shape function. The inspection device 1 recalculates the spectral pattern PT2 according to the predicted processed cross-sectional shape (S5). The inspection device 1 compares the spectral pattern PT1 measured in S1 with the spectral pattern PT2 calculated in S5, evaluates the error (S6), and determines whether the evaluation result satisfies the convergence condition for the loop processing from S4 to S7 (S7). That is, the inspection device 1 repeats the loop processing from S4 to S7 until the degree of match between the spectral pattern PT1 and the spectral pattern PT2 is equal to or greater than the threshold value (Yes in S7).

[0035] When the degree of match between the spectrum pattern PT1 and the spectrum pattern PT2 is equal to or greater than a threshold (Yes in S7), the inspection device 1 determines that the cross-sectional processed shape predicted in S4 is the cross-sectional processed shape corresponding to the actually measured spectrum pattern PT1, and ends the process. This allows the processed cross-sectional shape of the sample SP to be reconstructed. The reconstructed processed cross-sectional shape can be used, for example, to evaluate the appropriateness of process conditions.

[0036] Next, the shape function will be described. The shape function indicates the amount of ion flux corresponding to the etching depth when processing a predetermined pattern in a dry etching process.

[0037] The dry etching process is performed in a plasma processing apparatus 100 as shown in Fig. 5. Fig. 5 is a diagram showing the dry etching process. In Fig. 5, the direction perpendicular to the surface of the sample SP is defined as the Z direction, and two directions perpendicular to the Z direction in a plane perpendicular to the Z direction are defined as the X direction and the Y direction.

[0038] A sample SP is placed on the lower electrode 104b in the processing chamber CH. A resist pattern RP having a fine hole pattern RPa is formed on the surface of the sample SP. The controller 101 includes a CPU 101a and a memory unit 101b. The memory unit 101b stores process condition information 101b1. The controller 101 controls the gas supply system 102 and the exhaust system 103 to adjust the amount of processing gas in the processing chamber CH according to the process condition information 101b1. The controller 101 controls the power supply 104 according to the process condition information 101b1 to form an electric field between the upper electrode 104a and the lower electrode 104b in the processing chamber CH. This generates a plasma PL of the processing gas in a space CHa separated from the lower electrode 104b on the +Z side in the processing chamber CH, ionizing the processing gas. Furthermore, as indicated by the dotted arrow, the electric field in the -Z direction accelerates ions (reactive ions) of the processing gas toward the film FM to be processed on the sample SP (e.g., a substrate). The sample SP is irradiated with ions using the resist pattern RP as an etching mask, and the film to be processed FM is etched to form, for example, a hole pattern 200 corresponding to the hole pattern RPa.

[0039] The shape function is a shape expression based on the mechanism of the dry etching process. In the dry etching process, as shown in Fig. 6, ions 300 are accelerated from their generation location (space CHa) to the film FM to be processed on the sample SP with a certain divergence angle in the -Z direction. Fig. 6 is a YZ cross-sectional view showing the linearity of the ions and the processed cross-sectional shape.

[0040] For example, when the process gas is in an ideal thermal equilibrium state, the distribution of the velocity vectors of the ions 300 traveling from the generation location to the sample SP can be approximated by Maxwell's velocity distribution function. As a result, if the divergence angle is θ, the flux of the ions 300 traveling from the generation location to the sample SP is an amount that depends on the angular distribution function f(θ). The angular distribution function f(θ) indicates the angular distribution of the velocity vectors of the ions according to Maxwell's velocity distribution function.

[0041] When a parameter indicating the degree of spreading of the ions 300 (i.e., straightness) is n, the ion flux from the generation location (space CHa) toward the sample SP is expressed by the angular distribution function f(θ)=cos n It is a quantity that depends on θ. Parameter n indicates the directionality of the angular distribution of ions. Parameter n takes a larger value as the electric field acting on the ions becomes stronger (i.e., the greater the anisotropy of etching). The larger parameter n is, the more rectilinear the ions tend to travel.

[0042] Ion irradiation forms a hole pattern 200 in the film FM to be processed, as shown in FIG. 6 . For simplicity, FIG. 6 illustrates the cross-sectional shape of one hole pattern 200. The cross-sectional shape of the hole pattern 200 is approximated by an axisymmetric cross-sectional shape. The axis AX of the hole pattern 200 is approximately parallel to the direction of the electric field, as indicated by the dashed-dotted line in FIG. 6 . The hole pattern 200 is formed by etching the film FM to be processed using the hole pattern RPa of the resist pattern RP as an etching mask. The film FM to be processed is formed by stacking films FM2 and FM1, and the hole pattern 200 penetrates film FM1 and reaches partway through film FM2. The hole pattern 200 may penetrate film FM1 and further penetrate film FM2 to reach film FM3. The film FM1 is, for example, an insulating film and may be formed of a material primarily composed of an oxide, such as silicon oxide. The film FM2 is, for example, an insulating film and may be formed of a material primarily composed of a nitride, such as silicon nitride. The film FM3 is, for example, a conductive film, and can be formed from a material containing a metal such as tungsten, copper, or aluminum as a main component.

[0043] The hole pattern 200 may extend in the Z direction in a YZ cross-sectional view including the axis AX, and may have a bowing shape in which the diameter increases at a predetermined Z position between the +Z end and the -Z end. The hole pattern 200 has a bottom 201, a bowing portion 202, and an opening 203. The bottom 201 is located at the -Z end of the hole pattern 200 and closes the hole pattern 200. The opening 203 is located at the +Z end of the hole pattern 200 and opens the hole pattern 200 to the +Z side. The bowing portion 202 is located between the bottom 201 and the opening 203 in the Z direction and has a relatively large width in the XY plane. The bowing portion 202 is a portion of the hole pattern 200 in which the maximum XY spacing of the sidewalls 204 is relatively large.

[0044] If the width of the front portion 203 in the XY plane is the front diameter w, the width of the bowing portion 202 in the XY plane is the bow width b, and the width of the bottom portion 201 in the XY plane is the bottom width w', these satisfy the relationship in the following mathematical expressions 1 and 2. b>w Formula 1 b>w'···Equation 2

[0045] Ion irradiation forms, for example, a hole pattern 200 in the film to be processed FM, and the flux of ions that contribute to etching is called ion flux. In formulating the ion flux, as shown in Figure 7, it is considered to be divided into an ion flux that forms a bottom 201 and an ion flux that forms a sidewall 204. The amount of ion flux that forms the bottom 201 normalized by the total ion flux irradiated from the ion generation location is called the bottom ion flux amount, and Γ ion,BTM The amount of ion flux that forms the side wall 204 is normalized by the total ion flux irradiated from the ion generation location and is called the amount of ion flux on the side wall, and Γ ion,SIDEThe volume of the ion is found by convolving the product of the component cosθ of the ion velocity vector parallel to the axis AX and the component sinθ perpendicular to the axis AX with the divergence angle θ and the angle φ around the axis AX, and the number of ions in that volume is found by multiplying this by the angular distribution function f(θ). If the number of ions is normalized by the number when the divergence angle is 90° (=π / 2), the ion flux amount Γ at the bottom 201 is ion,BTM can be expressed by the following Equation 3.

number

[0046] The aspect ratio AR is defined as a parameter representing the depth position from the frontage 203 within the hole pattern 200. When the depth from the frontage 203 at a depth position of interest is D and the opening diameter is w, the aspect ratio AR can be calculated as shown in Equation 4. AR=D / w Equation 4

[0047] Ion flux amount Γ at the bottom 201 ion,BTM is calculated as the proportion of ions that reach the bottom 201 without spreading from the opening 203 to the sidewall 204. The angle θ of the bottom 201 viewed from the opening 203 is given by the following equation 5.

number

[0048] The proportion of ions that spread from the frontage 203 to the sidewall 204 is given by the angular distribution function of Equation 6 below. f(θ)=cos n θ···Equation 6

[0049] Substituting Equations 4 to 6 into Equation 3 and performing convolution, the ion flux amount Γ at the bottom 201 is obtained. ion,BTM is expressed as cos n+2 It is a quantity that depends on θ.

number

[0050] Ion flux amount Γ of the side wall 204 ion,SIDE is calculated as the proportion of ions that spread from the opening 203 to the side wall 204 and reach the side wall 204. This is related to the amount of ions that reach the bottom 201 depending on the depth position, so the ion flux amount Γ at the bottom 201 can be calculated as follows, as expressed by the following formula 8: ion,BTM is a quantity that depends on the derivative of the aspect ratio AR.

number

[0051] In Equation 8, C(t) is a coefficient that depends on the etching time t. To simplify the equation, in Equation 7, AR=x Tokki,

number

number

number

number

[0052] Substituting this formula 9 into formula 8 and differentiating it, the ion flux amount Γ of the side wall 204 is obtained. ion,SIDE is expressed as the following Equation 10 using x.

number

[0053] For example, when ions are incident with a certain degree of spread, n=n1 and t=t1 are substituted into Equation 10, and the ion flux amount Γ is calculated by taking x=AR as the vertical axis. ion,SIDE When plotted on a graph with the horizontal axis as the ion flux, the result is shown by the dotted line in Figure 8. If the ion flux directly represents the etching amount, the shape shown by the dotted line in Figure 8 will approximately represent the processed cross-sectional shape at etching time t1 when the ion linearity is n1. In other words, Figure 8 shows the predicted processed cross-sectional shape.

[0054] In addition, when ions are incident with a certain degree of directionality, n = n2 (> n1) and t = t1 are substituted into Equation 10, and the ion flux amount Γ is calculated with x = AR as the vertical axis. ion,SIDE When plotted on a graph with the horizontal axis as the abscissa, it is shown by the solid line in Figure 8. If the ion flux directly represents the etching amount, the shape shown by the solid line in Figure 8 will approximately represent the processed cross-sectional shape at etching time t1 when the ion linearity is n2.

[0055] Compared to the dotted line processed cross-sectional shape, the solid line processed cross-sectional shape corresponds to a larger value of n. As shown in FIG. 8, the bowing portion 202 of the solid line processed cross-sectional shape has a broader shape in the x direction than the bowing portion 202 of the dotted line processed cross-sectional shape. The x position (aspect ratio AR2) of the bowing portion 202 of the solid line processed cross-sectional shape is deeper than the x position (aspect ratio AR1) of the bowing portion 202 of the dotted line processed cross-sectional shape. The peak value (peak ion flux amount Γ2) of the bowing portion 202 of the solid line processed cross-sectional shape is smaller than the peak value (peak ion flux amount Γ1) of the bowing portion 202 of the dotted line processed cross-sectional shape.

[0056] That is, the larger n is and the greater the ion directivity is, the broader the bowing portion 202 in the hole pattern 200 tends to be and the deeper it tends to be located. This is thought to be consistent with the spreading behavior of ions.

[0057] In dry etching, the processed cross-sectional shape may be formed to include two bowing sections 202-1, 202-2 in the depth direction, as shown by the solid line in FIG. 9. This is thought to be due to the contribution of multiple ions with different directivities to the etching. In this case, the etching amount by dry etching is thought to include an ion incident angle distribution based on the convolution of multiple different velocity distribution functions. In other words, the processed cross-sectional shape can be expressed as a shape based on the convolution of multiple shape functions, as shown in FIG. 9. FIG. 9 is a diagram showing the predicted results of the processed cross-sectional shape based on the convolution of multiple shape functions.

[0058] For example, if the first ions are injected with a relatively low directivity, n=n 11 , t=t 11 Substituting this into Equation 10, the ion flux amount Γ is calculated with x=AR as the vertical axis. ion,SIDE When the horizontal axis is used to plot the ion flux, it is shown by the dashed line in Figure 9. If the ion flux directly represents the etching amount, the shape function shown by the dashed line in Figure 9 is 11 The etching time of the first ion is t 11 This approximately represents the amount of ion flux at

[0059] Furthermore, when the second ions are injected with a relatively high directivity, n=n 12 (>n 11 ), t=t 11 Substituting this into Equation 10, the ion flux amount Γ is calculated with x=AR as the vertical axis. ion,SIDE When the horizontal axis is used to plot the ion flux, it is shown by the two-dot chain line in Figure 9. If the ion flux directly represents the etching amount, the shape function shown by the two-dot chain line in Figure 9 is 12 The etching time of the second ion is t 11 This approximately represents the amount of ion flux at

[0060] 9 is superimposed on the shape function shown by the dashed line in FIG. 9 and the shape function shown by the two-dot chain line in FIG. 9, the processed cross-sectional shape shown by the dotted line in FIG. 9 is approximately obtained. The processed cross-sectional shape shown by the dotted line is obtained by approximately superimposing the shape function shown by the dashed line in FIG. 9 on the shape function shown by the two-dot chain line in FIG. 9. 203 ) in a deeper region, the actual processed cross section shown by the solid line in FIG. 9 is well fitted to the results of cross-sectional SEM observation. In FIG. 9, the depth position of the upper bowing portion 202-1 is 11 The depth position of the lower bowing part 202-2 is indicated by the aspect ratio AR 12 The depth position (aspect ratio AR) of the upper bowing part 202-1 is 11 ) corresponds to the depth position where the ion flux amount in the shape function of the dashed line reaches a peak. 12 ) corresponds to the depth position where the ion flux amount in the shape function of the two-dot chain line reaches its peak. That is, it is confirmed that of the two-stage bowing portions 202-1, 202-1, the upper bowing portion 202-1 is formed mainly by etching with the first ions, and the lower bowing portion 202-2 is formed mainly by etching with the second ions.

[0061] The processed cross-sectional shape based on the convolution of a plurality of shape functions is obtained as the sum of the plurality of shape functions, as shown in Fig. 10. Fig. 10 is a diagram showing the correspondence between the processed cross-sectional shape and a plurality of shape functions. Ion flux amount Γ of the side wall 204 ion,SIDE As shown in FIG. 10, is expressed by the following Equation 11. Gamma ion,SIDE =S0+S1(x)+S2(x)-S3(x)+ε i Formula 11

[0062] Equation 11 is a shape function based on the convolution of multiple shape functions and can be called a convolution shape function. A convolution shape function is obtained as the sum of multiple shape functions. In Equation 11, the shape functions S0 + S1(x) in the first and second terms are shape functions for the first ion, and correspond to the dashed-dotted line graph in the right diagram of Figure 10, which corresponds to the bowing section 202-1 in the upper part. The shape function S0 in the first term is a constant value regardless of the depth parameter x. The shape function S1(x) in the second term is a function of the depth parameter x and is obtained as the solution to the algebraic equation AE1 shown in Figure 11(a), where the parameter n1 indicating the directivity of the first ion is the order EX1 and EX2. The order is EX1 = 2n1 + 2, and EX2 = n1 + 4. The algebraic equation AE1 corresponds to the establishment of a thermal equilibrium state.

[0063] In Equation 11, the three-term shape function S2(x) is the shape function of the second ion, and corresponds to the two-dot chain line graph in the right diagram of FIG. 10, and corresponds to the bowing section 202-2 in the lower part. The two-term shape function S2(x) is a function of the depth parameter x, and is obtained as a solution to the algebraic equation AE2 shown in FIG. 11(b), in which the parameter n2 indicating the directivity of the second ion is set to orders EX3 and EX4. The orders are EX3 = 2n2 + 2 and EX4 = n2 + 4. The algebraic equation AE2 corresponds to the establishment of a thermal equilibrium state.

[0064] The four-term shape function S3(x) is the shape function due to ions reaching the bottom surface, and corresponds to the dotted line with a narrow pitch in the right diagram of Figure 10. The four-term shape function S3(x) is a function of the depth parameter x, and is obtained as the solution of the algebraic equation AE3 shown in Figure 11(c).

[0065] Next, the tracing of the processed cross-sectional shape with time by the shape function will be described with reference to Fig. 10 and Figs. 12 to 14. Fig. 12 is a diagram showing the change in coefficient C(t) with time. Fig. 13 is a diagram showing the tracing of the processed cross-sectional shape with time. Fig. 14 is a diagram showing the change in depth position of the frontage portion 203, the upper bowing portion 202-1, and the lower bowing portion 202-2 with time.

[0066] The shape function includes a coefficient that depends on the etching time, and can indicate the change in shape depending on the etching time.

[0067] For example, in the case of FIG. 10, the shape function S1(x) corresponding to the upper bowing portion 202-1 includes a coefficient C1(t) that depends on the etching time. When this coefficient C1(t) is plotted on a graph with time t on the horizontal axis and the coefficient value on the vertical axis, it changes approximately along a straight line, as shown in FIG. 12. FIG. 12 is a diagram showing changes in the coefficient over time. The slope of the graph of coefficient C1(t) indicates the etching rate by the first ions. In other words, when the etching rate by the first ions is ER1 and the etching time is t, coefficient C1(t) is expressed by the following equation 12. The etching rate ER1 is a constant that does not depend on time t. C1(t)=ER1×t...Formula 12

[0068] The shape function S2(x) corresponding to the lower bowing portion 202-2 includes a coefficient C2(t) that depends on the etching time. When this coefficient C2(t) is plotted on a graph with time t on the horizontal axis and the coefficient value on the vertical axis, it changes approximately along a straight line, as shown in FIG. 12. The slope of the graph of coefficient C2(t) indicates the etching rate by the second ions. In other words, when the etching rate by the second ions is ER2 and the etching time is t, coefficient C2(t) is expressed by the following equation 13. The etching rate ER2 is a constant that does not depend on time t. C2(t) = ER2 × t Equation 13

[0069] Substituting formulas 12 and 13 into the formula shown in Figure 10, t = t 21 Substituting into the formula, x=AR is the vertical axis, and the ion flux amount Γ ion,SIDE The graph, with the horizontal axis being t, is shown by the dotted line in Figure 13(a). The processed cross-sectional shape predicted by the convolution shape function is 21 This fits well with the results of SEM observation of the processed cross section.

[0070] Substituting formulas 12 and 13 into the formula shown in Figure 10, t = t 22 (>t 21 ) into the formula, and the ion flux amount Γ is calculated with x=AR as the vertical axis. ion,SIDE The graph, plotted with the horizontal axis as the dotted line in Fig. 13(b), shows the processed cross-sectional shape predicted by the convolution shape function. 22 This fits well with the results of SEM observation of the processed cross section.

[0071] Substituting formulas 12 and 13 into the formula shown in Figure 10, t = t 23 (>t 22 ) into the formula, and the ion flux amount Γ is calculated with x=AR as the vertical axis. ion,SIDE When graphed with the horizontal axis as the axis of rotation, it is shown by the dotted line in Figure 13(c). The processed cross-sectional shape predicted by the convolution shape function is plotted against the actual time t 23 This fits well with the results of SEM observation of the processed cross section.

[0072] Substituting formulas 12 and 13 into the formula shown in Figure 10, t = t 24 (>t 23 ) into the formula, and the ion flux amount Γ is calculated with x=AR as the vertical axis. ion,SIDE When graphed with the horizontal axis as the axis of rotation, it is shown by the dotted line in Figure 13(d). The processed cross-sectional shape predicted by the convolution shape function is 24 This fits well with the results of SEM observation of the processed cross section.

[0073] By examining the processed cross-sectional shape indicated by the dotted line in Figure 13(a) → Figure 13(b) → Figure 13(c) → Figure 13(d), it is possible to trace the change in the processed cross-sectional shape over time using the convolution shape function. This makes it possible to non-destructively trace the processed cross-sectional shape over time, which is an extremely time-consuming process in process development.

[0074] For example, as shown in Fig. 14, it is possible to confirm the change over time of a predetermined portion in the cross-sectional processed shape. Fig. 14 is a diagram showing the change over time in the depth position of the frontage portion 203, the upper bowing portion 202-1, and the lower bowing portion 202-2. The depth position of the frontage portion 203 (aspect ratio AR 203 ), plotted on a graph with time t on the horizontal axis and depth position on the vertical axis, they change approximately along a straight line, as shown in FIG. 14. Similarly, the depth position (aspect ratio AR 11 ), plotted on a graph with time t on the horizontal axis and depth position on the vertical axis, they change approximately along a straight line, as shown in FIG. 14. 12 ) are plotted on a graph with time t on the horizontal axis and depth position on the vertical axis, they change approximately along a straight line, as shown in FIG.

[0075] In other words, by tracing the temporal changes of the same or similar parameters, it is possible to confirm the temporal changes in the cross-sectional processing shape, thereby reducing the number of parameters used to trace the processing cross-sectional shape over time and making the processing of the temporal tracing of the processing cross-sectional shape more efficient.

[0076] As described above, in the embodiment, the inspection apparatus 1 reconstructs the processed cross-sectional shape using a shape function adjusted so that the degree of match between the measured spectral pattern PT1 and the spectral pattern PT2 calculated from the shape function is equal to or greater than a threshold. The shape function used is a function that indicates the ion flux amount corresponding to the etching depth when processing a predetermined pattern (e.g., hole pattern 200) in a dry etching process and includes an ion incident angle distribution based on a velocity distribution function. The shape function may include an ion incident angle distribution based on the convolution of multiple different velocity distribution functions. This allows the processed cross-sectional shape to be reconstructed using a shape function that represents the processed cross-sectional shape based on a physical model, thereby enabling flexible response to changes in the cross-sectional processed shape due to changes in process conditions, etc., and easily improving the robustness of inspections performed by the inspection apparatus 1.

[0077] For example, consider the case where a machined cross-sectional shape is approximated by a general polynomial. A general polynomial is obtained by raising a variable to a predetermined power and multiplying it by a predetermined coefficient, and then adding together multiple results. In a general polynomial, the power and coefficient are both constant. In this case, initial parameters are set for the general polynomial, a spectral pattern PT2' is calculated from the shape represented by the general polynomial, and the parameters applied to the general polynomial are adjusted so that the measured spectral pattern PT1' matches the spectral pattern PT2', thereby reconstructing the machined cross-sectional shape. When the measured spectral pattern PT1' matches the spectral pattern PT2' corresponding to the general polynomial, the shape represented by the general polynomial may deviate from the actual machined cross-sectional shape due to inappropriate initial parameters. In other words, the prediction accuracy of the machined cross-sectional shape represented by the general polynomial is likely to vary depending on whether the initial parameters to be applied are appropriate or inappropriate.

[0078] In contrast, in the embodiment, a function is used as the shape function, which indicates the amount of ion flux according to the etching depth when processing a predetermined pattern (e.g., hole pattern 200) in a dry etching process, and includes an ion incident angle distribution based on a velocity distribution function. This makes it possible to reconstruct the processed cross-sectional shape using a shape function that expresses the processed cross-sectional shape based on a physical model, thereby making it possible to flexibly respond to changes in the cross-sectional processed shape due to changes in process conditions, etc., and easily improve the robustness of inspection by the inspection device 1.

[0079] For example, when approximating the machined cross-sectional shape with a generalized polynomial and tracing the temporal change in the machined cross-sectional shape, m time steps (m is an integer greater than 3) are set to be traced. For example, in the first step, 10 parameters are applied to the generalized polynomial to predict the machined cross-sectional shape and fit it to the actual machined cross-sectional shape observed with a cross-sectional SEM. In the second step, another 10 parameters are applied to the generalized polynomial to predict the machined cross-sectional shape and fit it to the actual machined cross-sectional shape observed with a cross-sectional SEM. In the mth step, yet another 10 parameters are applied to the generalized polynomial to predict the machined cross-sectional shape and fit it to the actual machined cross-sectional shape observed with a cross-sectional SEM. The total number of parameters used to trace the temporal change in the machined cross-sectional shape is 10 × m. In other words, the processing load may increase as the number of time steps to be traced increases.

[0080] In contrast, in the embodiment, the temporal change in the cross-sectional processed shape can be confirmed by tracing the temporal change in the same or similar parameters. For example, m time steps to be traced are provided, and common parameters are used in each step. If two parameters are used for the origin position of the function, one for the exponent, and one for the bow width, which are doubled for two steps, and three parameters are used for the bottom position and the slope, the total number of parameters used to trace the temporal change in the processed cross-sectional shape is (2 + 1 + 1) × 2 + 3 = 11. In other words, the number of parameters used to trace the temporal change in the processed cross-sectional shape can be reduced, and the processing of the temporal tracing of the processed cross-sectional shape can be made more efficient.

[0081] 9 and 10 illustrate an example in which the shape function is based on the convolution of multiple Maxwell's velocity distribution functions. However, the shape function may include other velocity distribution functions in addition to or instead of the Maxwell's velocity distribution function. For example, velocity distribution functions applicable to the shape function include normal distribution, exponential distribution, distributions according to trigonometric functions such as sin, cos, and tan, power distribution, uniform distribution, and distribution functions obtained by performing arithmetic operations and convolution on these distributions. That is, the shape function may include an ion incidence angle distribution based on the convolution of Maxwell's velocity distribution function with another velocity distribution function. Alternatively, the shape function may include an ion incidence angle distribution based on the convolution of a first velocity distribution function different from Maxwell's velocity distribution function with a second velocity distribution function different from Maxwell's velocity distribution function.

[0082] Although several embodiments of the present invention have been described, these embodiments are presented as examples and are not intended to limit the scope of the invention. These novel embodiments can be embodied in various other forms, and various omissions, substitutions, and modifications can be made without departing from the spirit of the invention. These embodiments and their modifications are included within the scope and spirit of the invention, and are also included in the scope of the invention and its equivalents as defined in the claims. [Explanation of symbols]

[0083] 1 inspection device, 10 measurement units, 20 controllers.

Claims

1. a measurement unit that measures radiation diffracted by a sample in a predetermined pattern when the sample is irradiated with radiation and generates a first spectral pattern in accordance with the measurement result; a controller that predicts a processed cross-sectional shape by applying parameters to a shape function that indicates an ion flux amount corresponding to an etching depth when processing the predetermined pattern in a dry etching process, obtains a second spectral pattern according to the predicted processed cross-sectional shape, adjusts the parameters while comparing the first spectral pattern with the second spectral pattern so that the degree of coincidence between the first spectral pattern and the second spectral pattern is equal to or greater than a threshold, and reconstructs the processed cross-sectional shape of the sample according to the adjustment result; An inspection device equipped with:

2. the predetermined pattern includes a hole pattern, The shape function is a function obtained by integrating the amount of ion flux incident on the sidewall of the hole pattern in the depth direction according to the etching depth. The inspection device according to claim 1 .

3. The shape function includes an incident angle distribution of ions based on a velocity distribution function. The inspection device according to claim 1 .

4. The shape function includes an ion incidence angle distribution based on a convolution of a plurality of different velocity distribution functions. The inspection device according to claim 1 .

5. When the ion spreading angle is θ and the parameter indicating the degree of spreading of the ion is n, the shape function is expressed as cos ｎ＋２ Including θ 5. The inspection device according to claim 3 or 4.

6. The shape function is a solution of an algebraic equation whose order includes a parameter that indicates the degree of spreading of the ion. The inspection device according to claim 1 .

7. The shape function further shows the change in shape as a function of etching time. The inspection device according to claim 1 .

8. The shape function further includes a coefficient that depends on the etching time. The inspection device according to claim 7.

9. The coefficient includes the etching rate multiplied by time. The inspection device according to claim 8.

10. measuring radiation diffracted by a sample in a predetermined pattern when the sample is irradiated with radiation; generating a first spectral pattern in response to the measured results; predicting a processed cross-sectional shape by applying parameters to a shape function that indicates an ion flux amount corresponding to an etching depth when processing the predetermined pattern in a dry etching process; determining a second spectral pattern according to the predicted processed cross-sectional shape; adjusting the parameters while comparing the first spectral pattern with the second spectral pattern so that a degree of match between the first spectral pattern and the second spectral pattern is equal to or greater than a threshold; Reconstructing a processed cross-sectional shape of the sample according to the adjusted result; An inspection method comprising:

11. the predetermined pattern includes a hole pattern, The shape function is a function obtained by integrating the amount of ion flux incident on the sidewall of the hole pattern in the depth direction according to the etching depth. The inspection method according to claim 10.

12. The shape function includes an incident angle distribution of ions based on a velocity distribution function. The inspection method according to claim 10.

13. The shape function includes an ion incidence angle distribution based on a convolution of a plurality of different velocity distribution functions. The inspection method according to claim 10.

14. When the ion spreading angle is θ and the parameter indicating the degree of ion spreading is n, the ion flux amount is cos ｎ＋２ Including θ The inspection method according to claim 12 or 13.

15. The shape function is a solution of an algebraic equation whose order includes a parameter that indicates the degree of spreading of the ion. The inspection method according to claim 10.

16. The shape function further shows the change in shape as a function of etching time. The inspection method according to claim 10.

17. The shape function further includes a coefficient that depends on the etching time. The inspection method according to claim 16.

18. The coefficient includes the etching rate multiplied by time. The inspection method according to claim 17.

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