JP2014020917A - Sample evaluation method and sample evaluation program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To calculate sample characteristics in a short time concerning a sample evaluation method and a sample evaluation program.SOLUTION: A sample evaluation method comprises: a step of expressing a microscopic image f(x,y) by a finite sum of products of bases and coefficients Zin a function space; a step of acquiring a computation image g(x,y) of electric characteristics of a computation model 20 by theoretical calculation with physical property information of the computation model 20 as an input value; a step of expressing a computation image g(x,y) by a finite sum of products of bases and coefficients Zin a function space; a step of determining whether or not a microscopic image f(x,y) is similar to a computation image g(x,y) with the use of coefficients Zand coefficients Z; a step of changing physical property information when dissimilarity is determined; a step of re-acquiring a computation image g(x,y) of electric characteristics of the computation model 20 by theoretical calculation with changed physical property information as an input value; and a step of determining that a sample A has changed physical property information when similarity is determined in a step of determining whether the images are similar or not.

Description

  The present invention relates to a sample evaluation method and a sample evaluation program.

  In the development stage and mass production stage of semiconductor elements such as MOS transistors, various tests are performed to evaluate the electrical characteristics of the semiconductor elements. There is a scanning probe microscope (Scanning Probe Microscopy: SPM) as an apparatus used in the test.

  The scanning probe microscope can visualize electrical characteristics such as a current value, a dielectric constant, and impedance between the probe and the sample by scanning the surface of the sample with the probe. Depending on which of these electrical properties are visualized, scanning probe microscopes are classified into various types.

  For example, when current is visualized, it is called a scanning spreading resistance microscope (SSRM), and when impedance is visualized, it is called a scanning microwave microscope (SMM). When the dielectric constant is visualized, it is called a scanning capacitance microscope (Scanning Capacitance Microscopy: SCM) or a scanning nonlinear dielectric microscope (Scanning Nonlinear Dielectric Microscopy: SNDM).

  Here, the electrical characteristics of the sample visualized by the scanning probe microscope depend not only on the physical property value of the sample itself but also on the distortion in the sample and the observation environment. For example, the electrical characteristics of the impurity diffusion region of the semiconductor substrate have different values depending on the strain caused by the stress from the periphery. In addition, when the electrical characteristics such as resistance value are not uniform on the surface of the sample, the electric field distribution between the surface of the sample and the probe becomes anisotropic, and the electrical characteristics of the sample are accurately visualized. I can't.

  The image obtained by the scanning probe microscope is affected by the distortion and the observation environment as described above, and does not accurately reflect the electrical characteristics of the sample without distortion.

  Several methods for acquiring an accurate image of a sample with a scanning probe microscope by eliminating the influence of distortion have been proposed, but all have room for improvement.

  For example, a method for obtaining an accurate image representing the electrical characteristics of a sample by a finite element method has been proposed. In this method, a calculation model of a sample is constructed, and the electric characteristics of the sample when there is no distortion and the distortion that can occur in the sample are used as input values of the finite element method. Then, the calculated image of the electrical characteristics of the sample assumed to be obtained from these input values is compared with the microscopic image of the sample obtained with the scanning probe microscope. After that, the difference between the electrical characteristics of the calculated image and the microscopic image is obtained for each pixel, and the electrical characteristics and distortion, which are input values of the finite element method, are changed so that the difference is minimized for all pixels. The electrical characteristics assumed when there is no distortion are obtained.

  However, in this method, since the comparison is performed for each pixel, a long time is required for the calculation. Therefore, it is difficult to select a representative point from all the pixels and obtain a difference in electrical characteristics between the calculated image and the microscope image at the representative point, and to perform a high-precision analysis.

  The purpose of the sample evaluation method and sample evaluation program is to calculate the characteristics of a sample in a short time.

  According to the following disclosure, using a scanning probe microscope, obtaining a microscopic image of a sample, representing the microscopic image as a finite sum of products of a plurality of bases and coefficients in a function space, and Creating a calculation model of a sample; and obtaining a calculation image of electrical characteristics of the calculation model by using physical property information of the calculation model as an input value in theoretical calculation using the calculation model; Using the step of representing the calculated image by a finite sum of products of a plurality of the bases and coefficients in the function space, the coefficient representing the microscope image, and the coefficient representing the calculated image, the microscope image And the step of determining whether or not the calculation image is similar and the step of determining whether or not they are similar in the step of determining whether or not they are similar A step of changing the physical property information to be used; a step of acquiring a calculated image of electrical characteristics of the calculation model by the theoretical calculation using the changed physical property information as the input value; and acquiring the calculated image. After the step of re-doing, the step of determining whether or not they are similar is performed again, and when it is determined that the steps are similar in the step, the sample has the physical property information after the change And a step of judging that the sample evaluation method is provided.

  In the disclosed sample evaluation method, a calculated image and a microscopic image of a sample are represented by a finite sum of products of bases and coefficients in a function space, and by using coefficients of these images in the function space, It is determined whether the microscopic images are similar. Since the number of these coefficients used for similarity determination is smaller than the number of pixels in the calculation image and the microscope image, the time required for calculation can be shortened compared with the case where each image is compared pixel by pixel. .

FIG. 1 is a configuration diagram of a sample evaluation system according to the first embodiment. FIG. 2 is a perspective view for explaining a method of acquiring image data by SSRM in the first embodiment. FIG. 3 is a diagram illustrating an example of a microscopic image represented by image data in the first embodiment. FIG. 4 is a flowchart showing the sample evaluation method according to the first embodiment. FIG. 5 is a perspective view showing an example of a calculation model used in the first embodiment. FIG. 6 is an example of an STEM image that can be used to determine the shape of the sample in the first embodiment. FIG. 7 is a diagram illustrating an example of an EDX image used in the first embodiment. FIG. 8 is a diagram illustrating an example of a distortion distribution used in the first embodiment. FIG. 9 is a diagram illustrating a microscopic image in the first embodiment and a calculation result of a Zernike moment obtained from the microscopic image. FIGS. 10A to 10C are diagrams showing a calculation image in the first embodiment and a calculation result of the Zernike moment obtained from the microscope image. FIGS. 11A to 11C are diagrams for explaining the binning process in the second embodiment. FIG. 12 is a diagram schematically illustrating a method for determining the similarity between a calculation image and a microscope image in the second embodiment. FIG. 13 is a flowchart showing the processing contents in the third embodiment. FIG. 14 is a diagram (part 1) schematically showing the processing contents in the third embodiment. FIG. 15 is a diagram (part 2) schematically illustrating processing contents in the third embodiment.

(First embodiment)
FIG. 1 is a configuration diagram of a sample evaluation system according to the present embodiment.

  The sample evaluation system 1 includes a calculation unit 2 and a scanning probe microscope 3. Among these, the calculation unit 2 is a personal computer, for example, and operates according to a sample evaluation program P described later.

  The sample evaluation program P is executed by the calculation unit 2 reading from an arbitrary recording medium. Examples of such a recording medium include a CD-ROM (Compact Disc-Read Only Memory), a DVD (Digital Versatile Disc), a USB (Universal Serial Bus) memory, a flash memory, and a hard disk drive.

  On the other hand, the scanning probe microscope 3 is SSRM, SMM, SCM, or SNDM, and outputs image data D of a microscope image representing the electrical characteristics of the sample to the calculation unit 2 via the network 4. The output electrical characteristics are determined by the type of scanning probe microscope 3. For example, in SSRM, the current of the sample is output as an electrical characteristic, and in SMM, the impedance between the probe and the sample is output as an electrical characteristic. In SCM and SNDM, the dielectric constant between the probe and the sample is output as an electrical characteristic.

  Hereinafter, a case where SSRM is used as the scanning probe microscope 3 will be described as an example.

  FIG. 2 is a perspective view for explaining a method of acquiring image data D by SSRM.

  In SSRM, the surface of the sample A is scanned by the conductive probe 18 maintained at the ground potential while applying a predetermined bias voltage of about −1 V to the back surface of the sample A by the power source 15. The current flowing between the sample A and the probe 18 is amplified by the amplifier 19, and the current is associated with the position of the probe 18 and output as image data D.

  The position of the probe 18 can be specified by irradiating the probe 18 with the laser light L from the laser light source 17 and detecting the reflected light by the photodetector 16.

  In this example, as the sample A, the silicon substrate 10 on which the transistor TR is formed is used. The transistor TR has a source / drain region 11 and a gate electrode 12 and is covered with an interlayer insulating film 13.

  FIG. 3 is a diagram showing an example of the microscope image 8 represented by the image data D. As shown in FIG.

  In this example, the microscope image 8 by SSRM is superimposed on the STEM image represented by the dotted line. As shown in FIG. 3, the source / drain region 11 and the gate electrode 12 are visualized in the microscope image 8 due to the difference in the current value flowing through the sample A.

  When SMM is used instead of SSRM, the impedance appears in the microscope image 8, and when SCM and SNDM are used, the dielectric constant appears in the microscope image 8.

  Here, the microscopic image 8 is a visualization of the current distribution flowing through the sample A, but since the current is proportional to the resistance of the sample A, the microscopic image 8 can be regarded as a visualization of the resistance distribution of the sample A.

  However, the electrical characteristics of the sample A such as the resistance distribution vary depending on the strain in the sample A. The above-described microscopic image 8 shows the resistance distribution of the sample A in a state where the strain exists, and the resistance distribution when the sample A is not strained cannot be understood from the microscopic image 8 alone.

  Therefore, in the present embodiment, the resistance distribution of the sample A when there is no distortion is acquired as follows, and the strain distribution generated in the sample A is grasped.

  FIG. 4 is a flowchart showing a sample evaluation method according to this embodiment.

  As shown in FIG. 4, this sample evaluation method includes steps S1 to S9. Among these steps, what the computer 2 executes is performed by the computer 2 reading the sample evaluation program P (see FIG. 1).

  In the first step S 1, the calculation unit 2 obtains the image data D from the scanning probe microscope 3 via the network 4, thereby obtaining a microscope image 8 of the sample A created by the scanning probe microscope 3.

  The microscope image 8 is formed by associating a current value with each of a plurality of pixels, and is represented by a function f (x, y). The point (x, y) is a coordinate point in an orthogonal coordinate system arbitrarily set in the microscope image 8.

Next, the process proceeds to step S2, and the calculation unit 2 develops the microscope image f (x, y) in a predetermined function space. The method of expansion is not particularly limited, but in the present embodiment, the function f (x, y) is finite as shown in the following equation (1) in the function space based on the Zernike polynomial V _{n, m} (x, y). Expressed as a sum, the coefficient Z _{n, m} of each base is obtained.

In equation (1), the coefficient Z _{n, m} of each basis V _{n, m} (x, y) is called a Zernike moment and is calculated from the following equation (2).

  However,

It is.

The Zernike polynomial V _{n, m} (x, y) forms a complete orthogonal system within a unit circle centered at the origin of the xy space. The Zernike moment Z _{n, m} is a rotation invariant whose value remains unchanged even when the microscope image f (x, y) is rotated around the origin, and is also called a rotation invariant feature. Thus, obtaining the Zernike moment Z _{n, m} of the microscope image f (x, y) as shown in the equation (1) corresponds to extracting the rotation object property of the microscope image f (x, y). .

In the Zernike moment Z _{n, m} , the subscript n is called the order, and the subscript m is called the iteration number. Among the subscripts n, the maximum value N in the expression (1) is hereinafter referred to as the maximum order. The maximum order N can be arbitrarily set by the user according to the calculation accuracy, and is set to 10 in the present embodiment.

  Note that the order n and the iteration number m are

It has the regularity.

Due to this regularity, when the maximum order N is set as described above _, the number of Zernike moments Zn _{, m} in equation (1) is 36.

Further, there is no particular limitation as to which of the plurality of Zernike moments Z _{n, m} is included in the sum of the right side of Expression (1). For example, if the microscopic image f (x, y) does not have a predetermined rotation target property and the absolute value of the Zernike moment Z _{n, m} corresponding to the rotation target property is small, the Zernike moment Z _{n, m} is _expressed by the equation The calculation speed may be increased by excluding from (1).

  Furthermore, the function space is not limited to the above, and the function f (x, y) may be subjected to Fourier expansion in a function space based on an exponential function as in the following equation (6).

In the finite sum of the right side of Equation (6), the coefficient Fu _{, v} of the base exp [-2πi (ux + vy) / N] is the Fourier coefficient of the microscopic image f (x, y).

  Next, the process moves to step S3, and the user creates a calculation model of sample A.

  FIG. 5 is a perspective view showing an example of the calculation model.

  In FIG. 5, the same elements as those described in FIG. 2 are denoted by the same reference numerals as those in FIG. 2, and description thereof is omitted.

  The calculation model 20 is used when calculating the electrical characteristics of the sample A in the theoretical calculation such as the finite element method, and is created using the shape of the sample A and the physical property information of the sample A.

  Among these, the shape of the sample A can be obtained from CAD data used for the design of the sample A and a STEM (Scanning Transmission Electron Microscope) image of the sample A.

  FIG. 6 is an example of an STEM image that can be used to determine the shape of the sample A in this way.

  On the other hand, the physical property information of the sample A includes a strain distribution S (x, y) in the sample A and a resistance distribution R (x, y) of the sample A when there is no strain. In the resistance distribution R (x, y) and the strain distribution S (x, y), the point (x, y) is a coordinate point in the same orthogonal coordinate system as in the microscopic image f (x, y). .

  The resistance distribution R (x, y) is roughly estimated from the element distribution in the sample A. Therefore, in this embodiment, an EDX (Energy Dispersive X-ray spectroscopy) image of the sample A is obtained in order to grasp the element distribution, and the resistance distribution R (x, y) of the sample A is estimated from the EDX image.

  FIG. 7 is a diagram showing an example of the EDX image. In this example, the distribution of each of oxygen element (O), nitrogen element (N), silicon element (Si), phosphorus element (P), arsenic element (As), and cobalt element (Co) is illustrated.

  The method of estimating the resistance distribution R (x, y) is not particularly limited, and the resistance distribution R (x, y) may be estimated by tracing the element distribution in each EDX image of FIG.

  Further, the resistance distribution R (x, y) may be estimated using a SIMS (Secondary Ion Mass Spectrometry) image instead of the EDX image.

  The strain distribution S (x, y) is created using the technique developed by the inventors of the present invention in Japanese Patent Application Laid-Open No. 2006-242914 and Japanese Patent Application Laid-Open No. 2007-093344.

  FIG. 8 is a diagram showing an example of a strain distribution created using these methods.

  Next, the process proceeds to step S4, and in the theoretical calculation using the calculation model 20 described above, the shape and physical property information of the calculation model 20 are used as input values, whereby the calculation image g (x , y). An example of the theoretical calculation is a finite element method.

  The physical property information that is the input value of the finite element method is, as described above, the resistance distribution R (x, y) of the calculation model 20 when there is no distortion and the strain distribution S (x, y) of the calculation model 20. is there. The calculation image g (x, y) to be obtained is a current distribution assumed in the calculation model 20 when it has a strain distribution S (x, y).

  In the calculation, it is assumed that a voltage is applied to the calculation model 20 under the same conditions as the actual SSRM in FIG. For example, a current flowing between the probe 18 and the calculation model 20 is applied to the surface of the calculation model 20 in a state where a predetermined bias voltage of about −1 V is applied to the back surface of the calculation model 20 and the probe 18 is grounded. A calculation image g (x, y) is obtained by obtaining each point and imaging the current value.

  Next, the process proceeds to step S5, where the calculation unit 2 expands the calculation image g (x, y) into a finite sum as in the following equation (7) in the same function space as in step S2.

Similar to equation (1), the function V _{n, m} (x, y) in equation (7) is a Zernike polynomial that is the basis of the function space, and the coefficient Z ^′ _{n of the} basis V _{n, m} (x, y) _{, m} is the Zernike moment.

Further, the maximum order N of the Zernike moment Z ^′ _{n, m} in equation (7) is the same as in equation (1), and the number of terms in equation (7) is also the same as in equation (1).

Further, the formula (1) as well as microscopic image g (x, y) in no predetermined rotational symmetry, Zernike moments Z _^'n corresponding to the rotational _symmetry, when the absolute value of _m is small, the The Zernike moment Z ^′ _{n, m} may be excluded from the equation (7) to increase the calculation speed.

  If the microscope image f (x, y) is Fourier expanded as shown in equation (6) in step S2, the calculated image g (x, y) is calculated as shown in equation (8) in step S5. Fourier expansion.

In the finite sum of the right side of Expression (8), the coefficient Gu _{, v} of the base exp [-2πi (ux + vy) / N] is the Fourier coefficient of the calculation image g (x, y).

Next, the process proceeds to step S6, where the Zernike moment Z _{n, m} (see equation (1)) representing the microscopic image f (x, y) and the Zernike moment Z ^′ _{n, m} representing the calculated image g (x, y) are obtained. (See equation (7)), it is determined whether or not the microscopic image f (x, y) and the calculated image g (x, y) are similar.

  For this determination, first, the calculation unit 2 calculates the square sum Δ of the following equation (9).

Then, determining that the sum of squares delta is, when smaller than the threshold delta _th set by the user, calculating unit 2 is micrograph f (x, y) and calculate image g (x, y) and are similar To do. On the other hand, when the square sum delta is not less than the threshold delta _th, the calculation section 2, the microscope image f (x, y) and calculate image g (x, y) and is determined not to be similar.

When the functions f (x, y) and g (x, y) are subjected to Fourier expansion in step S1 and step S5, the following equation (10) is used by using the Fourier coefficients _{Fu, v} , _{Gu, v.} The sum of squares Δ may be calculated as follows.

  Here, if it is determined that the microscopic image f (x, y) and the calculated image g (x, y) are not similar, it is used to calculate the calculated image g (x, y) in step S4. There is a possibility that the strain distribution S (x, y) and the resistance distribution R (x, y) are different from these actual distributions in the sample A.

Therefore, in this case, the process proceeds to step S7, and the physical property information used in the finite element method is changed. The physical property information is the above-mentioned resistance distribution R (x, y) and strain distribution S (x, y) .In this step, these distributions are converted into a new resistance distribution R ^′ (x, y) and a new strain distribution S ^′ ( x, y).

The method of the change is not particularly limited, and the calculation unit 3 may automatically change the resistance distribution R (x, y) and the strain distribution S (x, y) by an arbitrary algorithm. There is a Simplex method as an algorithm that can be used in this step. In Simplex method, and the square sum of the equation (9) and the objective function, Zernike moments to minimize the value of the objective function Z _^'n, so that _m is obtained new resistance distribution ^R' (x, y) and the new Find the strain distribution S ^′ (x, y).

  Note that since the strain has the same value in the same material, the strain in the same material is collectively changed rather than individually changing the strain value at all points (x, y) of the calculation model 20. It is efficient to change.

Next, the process proceeds to step S8, and a calculation image g () of the electrical characteristics of the calculation model 20 is obtained by the finite element method using the changed physical property information R ^′ (x, y) and S ^′ (x, y) as input values. Get x, y) again.

  Thereafter, by performing Step S6 again, it is determined whether or not the microscopic image f (x, y) and the calculated image g (x, y) are similar.

Here, if it is determined that the microscopic image f (x, y) and the calculated image g (x, y) are similar, the process proceeds to step S9, where the sample A has a new resistance distribution R ^′ ( The calculation unit 2 determines that x, y) and the new strain distribution S ^′ (x, y) are included.

  The basic steps of the sample evaluation method according to the present embodiment are thus completed.

  9 to 10 are diagrams showing how the sum of squares Δ is reduced by repeating step S6 as described above.

Among these, FIG. 9 is a diagram showing a microscopic image f (x, y) and a calculation result of the Zernike moments Zn _{, m} obtained therefrom.

On the other hand, FIG. 10 (a) ~ (c) is a calculated image _{g (x, y),,} Zernike moments Z _^'n obtained from this is a diagram showing the calculation results of the _m. Further, these figures, each of the Zernike moment Z _^'n, Zernike moments Z _n of _m and _9, also square sum Δ obtained from _m are also shown.

  In this example, the number of executions of step S6 increases in the order of FIG. 10 (a), FIG. 10 (b), and FIG. 10 (c). The image g (x, y) becomes similar to the microscopic image f (x, y).

  According to the present embodiment described above, the resistance distribution R (x, y), which is the input value of the finite element method, and the distortion are set so that the calculated image g (x, y) is similar to the microscopic image f (x, y). The distribution S (x, y) is updated, and the updated resistance distribution R (x, y) can be identified as the resistance distribution of the sample A when there is no distortion. Also, from this result, the sample S has an updated strain distribution S (x, y), and the finally obtained calculation image g (x, y) shows the electrical characteristics of the sample S. It can be understood that the image is an accurate representation.

  Furthermore, in this embodiment, in determining the similarity between the calculated image g (x, y) and the microscopic image f (x, y), these images are not compared for each pixel, but the calculated image g ( Since x, y) and the microscopic image f (x, y) are expanded into a finite sum in the function space and the base coefficients are compared with each other, the calculation can be performed in a short time.

  For example, when the calculated image g (x, y) and the microscopic image f (x, y) each have 256 × 256 pixels, the image similarity is calculated for each pixel. The similarity must be calculated as many times as. If the calculation image g (x, y) is similar to the microscopic image f (x, y) and the calculation of 10 seconds per pixel has to be performed 10 times, finally, 76 days (= 10 × 10 ×) 256 × 256 seconds).

On the other hand, in the present embodiment, a microscopic image f (x, y) and a calculated image g are obtained by using Zernike moments Z _{n, m} and Z ^′ _{n, m} whose maximum order is N at most as shown in Expression (9). Judge the similarity with (x, y). When the maximum order N is 10, the number of terms in Equation (9) is 36, and the number of calculations can be greatly reduced as compared with the case of calculating for each pixel as described above.

  In addition, calculation accuracy and calculation time are in a trade-off relationship, but these can be controlled by the maximum order N. Therefore, the user can set the maximum order N appropriately so that the calculation accuracy and calculation are convenient for the user. Time can be easily controlled.

(Second Embodiment)
In the present embodiment, the calculation unit 2 performs binning processing on each of the calculation image g (x, y) and the microscope image f (x, y) of the first embodiment as described below. Also reduce calculation time.

  11A to 11C are diagrams for explaining the binning process.

  FIG. 11A is a microscopic image f (x, y) that has not been subjected to binning processing.

  On the other hand, FIG. 11B is a microscopic image f (x, y) that has been subjected to a binning process that groups adjacent 4 × 4 pixels into one.

  FIG. 11C shows a microscopic image f (x, y) that has been subjected to a binning process for grouping adjacent 8 × 8 pixels into one.

  Using such binning processing, in the present embodiment, it is determined whether the calculated image g (x, y) and the microscope image f (x, y) are similar as follows.

  FIG. 12 is a diagram schematically showing the similarity determination method, and is a diagram for explaining the contents of step S6 in the present embodiment.

First, in the first similarity determination, a binning process in which the calculation unit 2 combines 8 × 8 pixels into one for each of the calculation image g (x, y) and the microscope image f (x, y). Then, Zernike moments Z _{n, m} and Z ^′ _{n, m} representing these images are calculated in the same manner as in the first embodiment.

When the calculation unit 2 determines that the square sum Δ in Expression (9) is greater than or equal to the threshold Δ _th , the calculation unit 2 calculates the square sum Δ again according to the first embodiment. The threshold _Δth is not particularly limited, but in this example, the threshold _{Δth is set} to 0.5.

On the other hand, the calculation unit 2 performs a second round of similarity judgment in the case of square sum delta is determined to be smaller than the threshold delta _th.

In the second time, the resolution by the binning process is increased more than in the first time, and the calculation unit 2 adds 4 × 4 pixels to each of the calculation image g (x, y) and the microscope image f (x, y). After the binning process is performed, the Zernike moments Z _{n, m} and Z ^′ _{n, m} representing these images are calculated as in the first embodiment.

At the same time, the calculation unit 2 changes the threshold value _Δth to a value smaller than the first time by a predetermined value. In this example, the threshold _Δth is changed to 0.2, which is smaller by 0.3 than the first value (0.5).

When the calculation unit 2 determines that the square sum Δ in Expression (9) is equal to or greater than the threshold value Δ _th , the square sum Δ is calculated again according to the first embodiment.

On the other hand, when the square sum delta is determined to be smaller than the threshold delta _th, the calculation unit 2 performs a third time similarity judgment.

In the third time, the calculation unit 2 changes the threshold _Δth to a value smaller than the second time by a predetermined value without performing binning processing on the calculated image g (x, y) and the microscopic image f (x, y). To do. In this example, the threshold value _Δth is changed to 0.1, which is 0.1 smaller than the second value (0.2).

When the sum of the squares of Equation (9) delta is less than a threshold delta _th after the change is calculated image g (x, y) and the calculation section microscopy image f (x, y) and are similar 2 judges. Therefore, in this case, the process proceeds to step S9 described in the first embodiment, and it is determined that the sample A has the resistance distribution R ^′ (x, y) and the strain distribution S ^′ (x, y). To do.

  The basic steps of the sample evaluation method according to the present embodiment are thus completed.

According to the present embodiment described above, as shown in FIG. 12, since the binning process is used in the first and second similarity determination, the calculated image g (x, y) and the microscopic image f (x, y) This reduces the number of pixels of each and reduces the calculation time for calculating the Zernike moments Z _{n, m} and Z ^′ _{n, m} from these images.

In addition, since the threshold value _Δth is reduced every time it is repeated, the calculation accuracy can be ensured while reducing the calculation time as described above.

(Third embodiment)
The microscopic image acquired by the scanning probe microscope depends on the observation environment in addition to the physical property information of the sample.

  For example, in SSRM, a bias voltage is applied between the sample and the probe, and the current flowing between them is measured. However, when the thickness of the sample decreases, the current flows through the low-resistance region in the sample. Therefore, the current path is not perpendicular to the sample surface, and the current path may spread.

  In this case, the resistance of the sample directly under the probe cannot be measured accurately, and the microscopic image acquired by SSRM becomes inaccurate.

The resistance distribution R ^′ (x, y) and strain distribution S ^′ (x, y) of the sample finally obtained in the first embodiment are calculated on the microscope image that has become inaccurate in this way depending on the observation environment. Since they are intended to be similar, the resistance distribution R ^′ (x, y) and the strain distribution S ^′ (x, y) also include the influence of the observation environment.

Therefore, in this embodiment, the influence of the observation environment is excluded from the resistance distribution R ^′ (x, y) and the strain distribution S ^′ (x, y) as follows.

  FIG. 13 is a flowchart showing the processing content of step S4 in the present embodiment. As described in the first embodiment, step S4 is a step of obtaining a calculation image g (x, y) of the electrical characteristics of the calculation model 20, but in this embodiment, step S4 is the following sub-step S20. ~ S24.

  FIG. 14 is a diagram schematically showing the processing content of the first sub-step S20.

  In sub-step S20, as shown in FIG. 14, the calculation model 20 is divided into a plurality of calculation areas 20a. This process is also called a sectioning process, and FIG. 14 illustrates a case where the calculation model 20 is divided into 64 × 64 calculation areas 20a by the sectioning process.

  Next, the process proceeds to substep S21.

  FIG. 15 is a diagram schematically showing the processing content of sub-step S21.

  In sub-step S21, a finite number of representative areas 20b are selected from the calculation areas 20a. In FIG. 15, the representative area 20b is shown in black, and the calculation area 20a other than the representative area 20b is shown in white.

  The representative region 20b is a region where the current value of the calculation model 20 is calculated later. However, if the representative regions 20b are close to each other, a current path is generated so as to span a plurality of representative regions 20b depending on the calculation result. In SSRM, the situation is the same as the current path expanding. Therefore, in this substep, it is preferable to select the representative region 20b as randomly as possible.

Next, the process proceeds to sub-step S22, where the electrical characteristics of the calculation model 20 are obtained for each representative region 20b by the finite element method, and a first image g ₁ (x, y) representing the electrical characteristics of the calculation model 20 is obtained. get. The electrical characteristics are the same as those in the finally calculated image g (x, y). In this embodiment, the current distribution of the calculation model 20 is determined as the electrical characteristics.

  The input values of the finite element method are the same as when calculating the calculation image g (x, y) in the first embodiment, the shape of the calculation model 20, the resistance distribution R (x, y), and the strain distribution. This is physical property information of the calculation model 20 such as S (x, y).

The current distribution of the calculation model 20 shown in the first image g ₁ (x, y) is obtained by performing the calculation only in the representative region 20b in FIG. 15, so that the current path is widened. It is not a correct calculation result.

Next, the process proceeds to sub-step S23, where the electric characteristics of the calculation model 20 are obtained for each calculation area 20a other than the representative area 20b by the finite element method, and the second image g ₂ (x , y). The electrical characteristics calculated in this step are the current distribution of the calculation model 20 as in the sub-step S22.

  Similarly to the substep S22, the input values of the finite element method also include the shape of the calculation model 20 and physical property information of the calculation model 20 such as the resistance distribution R (x, y) and the strain distribution S (x, y). It is.

The current distribution of the calculation model 20 shown in the second image g ₂ (x, y) is obtained by performing calculation while limiting to the calculation region 20a other than the representative region 20b in FIG. Therefore, as in the first image g ₁ (x, y), the current path does not spread in the calculation result of the second image g ₂ (x, y).

Next, the process proceeds to sub-step S24, where the first image g ₁ (x, y) and the second image g ₂ (x, y) are added to obtain a calculated image g (x, y).

As described above, in the calculation result of the first image g ₁ (x, y) and the second image g ₂ (x, y), since the spread of the current path is suppressed, the calculation obtained by adding them together The spread of the current path is also suppressed in the image g (x, y).

Thereafter, the resistance distribution R ^′ (x, y) and the strain distribution S ^′ (x, y) of the sample A are obtained by performing Steps S5 to S9 described in the first embodiment.

According to the present embodiment described above, the spread of the current path is suppressed in the calculation image g (x, y) as described above. Therefore, the resistance distribution R ^′ (x, y) and the strain distribution S ^′ (x, y) obtained so that the calculated image g (x, y) is similar to the microscopic image f (x, y) This is a case where there is no spread of the current path in the sample by eliminating the influence of the observation environment. Thereby, in the present embodiment, it is possible to obtain an accurate resistance distribution R ^′ (x, y) and distortion distribution S ^′ (x, y) from which the influence of the observation environment is eliminated.

Further, when this embodiment is combined with each of the first embodiment and the second embodiment, the calculation time can be further increased. For example, if the maximum order of the Zernike moments Z _{n, m} used in the first embodiment is 10 _, the number of Zernike moments Z _{n, m} is 36 as described in the first embodiment. In this case, the number of pixels of the original microscope image f (x, y) is 256 × 256, the number of divisions by the sectioning process of this embodiment is 5 × 5, and the number of binning processes of the second embodiment is three times. Then, the calculation speed is 121 (= 256 × 256 / (36 × 5 × 3)) times.

  Such speeding-up is particularly beneficial when the number of pixels of the microscope image f (x, y) is large. For example, when the number of pixels is 4096 × 4096, the calculation speed is about 30,000 times when the same calculation as described above is performed. To be faster.

(Other embodiments)
In the first embodiment, in step S2, the microscopic image f (x, y) is developed with the Zernike polynomial V _{n, m} (x, y) as shown in Equation (1).

In step S2, the microscopic image f (x, y) is not directly developed by the Zernike polynomial V _{n, m} (x, y) as described above, but is temporarily given by the following formula (11). y) may be subjected to Fourier transform.

In this case, the Fourier coefficient _{Fu, v} in the equation (11) is expanded by the Zernike polynomial V _{n, m} (x, y) as in the following equation (12).

Similarly, in step S5, the calculated image g (x, y) is not directly expanded by the Zernike polynomial V _{n, m} (x, y), but is temporarily expressed as the following expression (13). (x, y) may be Fourier expanded.

After that, the Fourier coefficient _{Gu, v} of the equation (13) is expanded by the Zernike polynomial V _{n, m} (x, y) as in the following equation (14).

Then, the square sum Δ of Equation (9) may be calculated using Zernike coefficients Z _{n, m} and Z ^′ _{n, m} of Equation (12) and Equation (14).

  The following additional notes are disclosed for each embodiment described above.

(Supplementary Note 1) By using a scanning probe microscope, obtaining a microscope image of the sample;
Representing the microscopic image as a finite sum of products of a plurality of bases and coefficients in a function space;
Creating a calculation model of the sample;
In the theoretical calculation using the calculation model, by obtaining physical property information of the calculation model as an input value, obtaining a calculation image of the electrical characteristics of the calculation model;
Representing the computed image as a finite sum of products of a plurality of the bases and coefficients in the function space;
Using the coefficient representing the microscopic image and the coefficient representing the calculated image to determine whether the microscopic image and the calculated image are similar;
Changing the physical property information used in the theoretical calculation when it is determined that they are not similar in the step of determining whether or not they are similar; and
Re-acquiring a calculation image of electrical characteristics of the calculation model by the theoretical calculation using the physical property information after the change as the input value;
After the step of re-acquiring the calculated image, the step of determining whether or not they are similar is performed again, and when it is determined that the samples are similar in the step, the physical property information after the change of the sample is obtained. Determining that it has,
A sample evaluation method characterized by comprising:

  (Supplementary Note 2) In the step of determining whether or not they are similar, it is determined that they are similar when the sum of squares of the absolute values of the coefficients of the calculation image and the microscope image is smaller than a threshold value. The sample evaluation method according to appendix 1, wherein it is determined that the sum of squares is not similar when the sum of squares is equal to or greater than the threshold value.

(Supplementary Note 3) In the step of determining whether or not they are similar,
It is determined whether or not the coefficients of the calculated image and the microscopic image subjected to the binning process are similar to each other,
If it is determined that they are similar, the threshold value is changed to a threshold value that is smaller by a predetermined value, the resolution by the binning process is increased, and the calculated image and the microscopic image subjected to the binning process are increased. The sample evaluation method according to appendix 2, wherein it is determined whether or not each of the coefficients is similar.

  (Supplementary note 4) The sample evaluation method according to any one of supplementary notes 1 to 3, wherein a Zernike polynomial is used as the base and a Zernike moment is used as the coefficient.

  (Supplementary note 5) The sample evaluation method according to any one of supplementary notes 1 to 3, wherein an exponential function is used as the base and a Fourier coefficient is used as the coefficient.

(Supplementary Note 6) In the step of representing the microscopic image by the finite sum, Fourier transform of the microscopic image is represented by a finite sum of products of a Zernike polynomial and a Zernike moment, and the Zernike moment is the coefficient.
In the step of representing the calculation image by the finite sum, Fourier transform of the calculation image is expressed by a finite sum of products of a Zernike polynomial and a Zernike moment, and the Zernike moment is used as the coefficient. The sample evaluation method according to any one of 1 to Appendix 3.

(Supplementary Note 7) The step of acquiring the calculation image includes:
Dividing the calculation model into a plurality of calculation regions;
Selecting a representative area from among the calculation areas;
Obtaining the electrical characteristics of the calculation model for each representative region and obtaining a first image representing the electrical characteristics of the calculation model;
Obtaining the electrical characteristics of the calculation model for each of the calculation areas other than the representative area, and obtaining a second image representing the electrical characteristics of the calculation model;
The sample evaluation method according to any one of supplementary notes 1 to 6, further comprising a step of adding the first image and the second image to form the calculated image.

(Supplementary Note 8) The physical property information of the calculation model is a resistance distribution and a strain distribution of the calculation model,
The sample evaluation method according to any one of appendix 1 to appendix 7, wherein the electrical characteristic of the calculation model is a current distribution of the calculation model.

(Appendix 9) Obtaining a microscope image representing the electrical characteristics of a sample obtained using a scanning probe microscope,
The microscope image is represented by a finite sum of products of a plurality of bases and coefficients in the function space,
In the theoretical calculation using the calculation model of the test sample, by obtaining physical property information of the calculation model as an input value, a calculation image of the electrical characteristics of the calculation model is obtained,
The calculation image is represented by a finite sum of products of a plurality of the bases and coefficients in the function space,
Using the coefficient representing the microscopic image and the coefficient representing the calculated image, it is determined whether the microscopic image and the calculated image are similar,
When it is determined that the similarity is not similar in the determination, the physical property information used in the theoretical calculation is changed,
By the theoretical calculation using the physical property information after the change as the input value, a calculation image of the electrical characteristics of the calculation model is obtained again,
After re-acquisition of the calculated image, the determination as to whether or not they are similar is performed again, and when it is determined that the images are similar in the determination, the sample has the physical property information after the change. Judge that
A sample evaluation program for causing a computer to execute processing.

DESCRIPTION OF SYMBOLS 1 ... Sample evaluation system, 2 ... Calculation part, 3 ... Scanning probe microscope, 4 ... Network, 10 ... Silicon substrate, 11 ... Source drain region, 12 ... Gate electrode, 13 ... Interlayer insulation film, 15 ... Power supply, 16 ... Light Detector: 17 ... Laser light source, 18 ... Probe, 19 ... Amplifier, 20 ... Calculation model, 20a ... Calculation area, 20b ... Representative area, A ... Sample, D ... Image data, TR ... MOS transistor.

Claims (5)

Using a scanning probe microscope to obtain a microscopic image of the sample;
Representing the microscopic image as a finite sum of products of a plurality of bases and coefficients in a function space;
Creating a calculation model of the sample;
In the theoretical calculation using the calculation model, by obtaining physical property information of the calculation model as an input value, obtaining a calculation image of the electrical characteristics of the calculation model;
Representing the computed image as a finite sum of products of a plurality of the bases and coefficients in the function space;
Using the coefficient representing the microscopic image and the coefficient representing the calculated image to determine whether the microscopic image and the calculated image are similar;
Changing the physical property information used in the theoretical calculation when it is determined that they are not similar in the step of determining whether or not they are similar; and
Re-acquiring a calculation image of electrical characteristics of the calculation model by the theoretical calculation using the physical property information after the change as the input value;
After the step of re-acquiring the calculated image, the step of determining whether or not they are similar is performed again, and when it is determined that the samples are similar in the step, the physical property information after the change of the sample is obtained. Determining that it has,
A sample evaluation method characterized by comprising:   In the step of determining whether or not they are similar, it is determined that they are similar when the sum of squares of the absolute values of the coefficients of the calculated image and the microscope image is smaller than a threshold, and the sum of squares The sample evaluation method according to claim 1, wherein it is determined that the similarity is not similar when the value is equal to or greater than the threshold value. In the step of determining whether or not they are similar,
It is determined whether or not the coefficients of the calculated image and the microscopic image subjected to the binning process are similar to each other,
If it is determined that they are similar, the threshold value is changed to a threshold value that is smaller by a predetermined value, the resolution by the binning process is increased, and the calculated image and the microscopic image subjected to the binning process are increased. The sample evaluation method according to claim 2, wherein it is determined whether or not the coefficients are similar to each other. The step of obtaining the calculated image includes
Dividing the calculation model into a plurality of calculation regions;
Selecting a representative area from among the calculation areas;
Obtaining the electrical characteristics of the calculation model for each representative region and obtaining a first image representing the electrical characteristics of the calculation model;
Obtaining the electrical characteristics of the calculation model for each of the calculation areas other than the representative area, and obtaining a second image representing the electrical characteristics of the calculation model;
The sample evaluation method according to claim 1, further comprising a step of adding the first image and the second image to form the calculated image. Obtain a microscope image representing the electrical characteristics of the sample obtained using a scanning probe microscope,
The microscope image is represented by a finite sum of products of a plurality of bases and coefficients in the function space,
In the theoretical calculation using the calculation model of the test sample, by obtaining physical property information of the calculation model as an input value, a calculation image of the electrical characteristics of the calculation model is obtained,
The calculation image is represented by a finite sum of products of a plurality of the bases and coefficients in the function space,
Using the coefficient representing the microscopic image and the coefficient representing the calculated image, it is determined whether the microscopic image and the calculated image are similar,
When it is determined that the similarity is not similar in the determination, the physical property information used in the theoretical calculation is changed,
By the theoretical calculation using the physical property information after the change as the input value, a calculation image of the electrical characteristics of the calculation model is obtained again,
After re-acquisition of the calculated image, the determination as to whether or not they are similar is performed again, and when it is determined that the images are similar in the determination, the sample has the physical property information after the change. Judge that
A sample evaluation program for causing a computer to execute processing.

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