ISSN 10637397, Russian Microelectronics, 2015, Vol. 44, No. 4, pp. 269–282. © Pleiades Publishing, Ltd., 2015. Original Russian Text © Yu.A. Novikov, 2015, published in Mikroelektronika, 2015, Vol. 44, No. 4, pp. 306–320.
Virtual Scanning Electron Microscope. 5. Application in Nanotechnology and in Micro and Nanoelectronics Yu. A. Novikov A.M. Prokhorov General Physics Institute, Russian Academy of Sciences, Vavilova str., 38, Moscow, 119991 Russia email:
[email protected] Received January 13, 2014
Abstract—The provided examples demonstrate the application of a simulatorbased virtual scanning elec tron microscope (SEM) in certification of test object sizes on a lowvoltage SEM and in calibration of a high voltage SEM operating in the slow secondary electron detection mode. Using the virtual SEM, the problem of comparing different SEM calibration techniques is solved. DOI: 10.1134/S1063739715030075
1. INTRODUCTION The development of modern micro and nanoelec tronics [1] requires measuring the characteristics of microcircuits and controlling their fabrication tech nology. The main characteristics of microcircuits are the linear dimensions of their elements [1–5], which currently lie within a wide range from 20 nm [1] to hundreds of micrometers. In the micrometer range, optical methods for measuring the linear dimensions yield good results. However, optics work badly on a scale of less than 1 µm. Here, the best existing tech nique is scanning electron microscopy [3–12], which overlaps almost the entire important range for micro and nanoelectronics. However, scanning electron microscopes (SEMs) have certain drawbacks. The main one is that extracting information from SEM images requires solving the inverse problem, which is incorrect (although this is a common drawback of most measuring devices [13]). In such problems, minor deviations in the input data can lead to signifi cant deviations in the output data. The incorrect measuring problems are solved using different techniques [13]. Currently, the most promis ing technique is the application of virtual measuring devices. According to [13], a virtual measuring device (VMD) is a computer program, which, using the input data that reproduce the characteristics of an object investigated on a real measuring device, generates the output data analogous to those obtained on the real device. The VMD can be based on an imitator or a simulator; however, as was shown in [14], the virtual SEM (VSEM) cannot be created using an imitator. Studies [15, 16] described the VSEM that is based on a simulator of information analogous to the infor mation obtained using a real SEM during investiga tions of real objects analogous to virtual ones. Such a VSEM is intended for application in nanoelectronics where the surface relief of micro and nanostructures
has a trapezoidal profile. Therefore, structures with the trapezoidal profile are used in the VSEM as virtual objects. This work is the fifth (final) part of the VSEM description, which provides examples of the VSEM application in nanotechnology and in micro and nanoelectronics. 2. SEM CALIBRATION AND CERTIFICATION OF THE TEST OBJECT’S DIMENSIONS The main function of the VSEM as a virtual mea suring device [13] is to prove the correctness of solving an inverse problem, i.e., extracting information from images obtained on real SEMs upon scanning real objects. Let us consider a few examples of solving such problems using the VSEM described in studies [15, 16]. All the VSEM data reported here were obtained using a PC with a Pentium Dual dualcore processor operating in the singlecore mode with a processor speed of 2.2 GHz and a motherboard bus speed of 800 MHz. These parameters are typical of modern PCs used both in everyday life and for the automation of measuring devices. As a real object, we will use an MShPS2.0Si test object [7, 8, 17, 18] (Fig. 1) consisting of five groups (Fig. 1a), each containing three pitch structure (Figs. 1a and 1b). Each pitch structure (Figs. 1b, 1c) comprises 11 grooves (10 protrusions) on the single crystal Si(100) surface formed by liquid anisotropic etching. The protrusions and grooves have a trapezoi dal profile (Figs. 2a, 2b) with the side walls inclined at angle ϕ relative to the test object’s surface normal. The side walls of the elements of such an object coincide with the Si {111} crystallographic planes and the top of the protrusions and the bottom of the grooves coincide with the Si {100} crystallographic planes (Fig. 2c). Thus, the inclination angle ϕ of the side wall is deter
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1 μm (b) 500 μm (b)
500 nm (c) {111} 50 μm (c)
{100} Fig. 2. (a) SEM images of a cleavage, (b) AFM image of a relief, and (c) schematic of the arrangement of the crystal lographic planes in the MShPS2.0Si test object’s pitch structure.
The test object was described in more detail in studies [7–11, 17, 18]. The MShPS2.0Si test objects are used for determining the main parameters of the SEMs used for visualizing and measuring the linear dimen sions of microcircuits in micro and nanoelectronics [7–12, 17–23]. These test objects correspond to the Russian National Standards (GOST R) [24, 25], which ensure transferring the size from the prototype meter to the nanoscale and regulating SEM operation on this scale.
10 μm Fig. 1. SSE images of the MShPS2.0Si test object and its separate parts obtained on an S 4800 SEM at different magnifications. (a) General view of the test object, (b) its central module, and (c) pitch structure 2 in the area of hor izontal guide lines.
mined as the angle between the (111) and (100) crys tallographic planes:
ϕ = arccot 2 ≈ 35.26 ° .
2.1. Certification of Test Object Dimensions on a LowVoltage SEM Certification of the nanometer element size of a test object is one of the main problems to be solved in
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Fig. 3. (a) Real and (b) generated images of a protrusion with a trapezoidal profile and large side wall inclination angles and (c) shapes of the signals comprising these images (signals 1 and 2, respectively). The size of the mark in the images is 500 nm.
the measurements of linear dimensions of microcir cuit elements. In global practice, it is considered that certification of test objects and measurements of criti cal (minimum) microcircuit dimensions should be performed on lowvoltage SEMs [17, 18]. For this purpose, special lowvoltage SEMs (CDSEMs) are produced that are intended for measuring the critical dimension of microcircuit elements. Let us consider how the VSEM can help in certifying the linear dimensions of a test object on a lowvoltage SEM. For this purpose, an image of one of the protrusions in the MShPS2.0Si test object was detected on an S 4800 SEM operating in the lowvoltage mode (the probe electron energy is E = 1 keV) [7, 8]. The real image (2560 × 1920 pix in size) of such a protrusion is shown in Fig. 3a. In study [19], this image was used for RUSSIAN MICROELECTRONICS
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determining the electron density distribution in a low voltage SEM probe. The pixelsize m in the image, according to the SEM manufacturing company data, was 0.8268229 nm/pix. Figure 3c shows the shape of one of the signals (signal 1) comprising the real image. Figure 4 shows the schematics of a protrusion (Fig. 4a) of the trapezoidal shape with large inclination angles ϕ of the side walls relative to the perpendicular to the base of the structure and parameters of protrusion ele ments and the SEM lowvoltage signal (Fig. 4b) with control sizes measured on the signals. The angles sat isfying the condition [26, 27] s = h tan ϕ Ⰷ d,
are considered large. Here, d is the effective SEM probe diameter [20, 21] (hereinafter, diameter), h is the relief height (depth), and s is the projection of an inclined side wall onto the base of the structure. When conditions
b, u, s Ⰷ d,
(1)
are met, the protrusion parameters (b, u, and s), con trol signal sizes (B, U, and S), and SEM characteristics (m and d) are related to each other as
u = mU ,
d = mD,
(2)
s = mS,
(3) b = mB.
(4)
In study [19], the SEM electron probe diameter d = 28 nm and protrusion parameters given in Table 1 (test object) were obtained by using formulas (2)–(4), the determined control sizes on the signals (Fig. 4), 2015
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Table 1. Parameters of protrusions in the MShPS2.0Si test object determined on a lowvoltage SEM, specified model ob ject parameters, and model protrusion parameters obtained by processing the simulated image Protrusion parameters Top, nm Bottom, nm Side wall projection, nm
Test object
Model
591.8 ± 0.4 1412.5 ± 0.6 410.5 ± 0.2
592 1412 410
and the pixelsize provided by the SEM manufacturing company. Note that in this experiment, the pixelsize provided by the SEM manufacturing company was used. How ever, in the certification of test objects on special microscopes [17, 18], the pixelsize is determined using a laser interference, which makes it possible to certify test object elements accurately. Here, we demonstrate the SEM application in certification rather than the certification by itself. Therefore, a highly accurate pix elsize is not the necessary condition here. The accu racy provided by the SEM manufacturing company is sufficient. To check the correctness of solving inverse problem [13] on the VSEM described in studies [15, 16], we (a) 0.03
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Fig. 5. Amplitude spectra of (a) SEM and (b) VSEM low voltage images presented in Figs. 3a and 3b, respectively.
Processing 591.95 ± 0.07 1412.02 ± 0.03 410.03 ± 0.04
generated an image of the model analog of the test object’s protrusion with the parameters given in Table 1 (model) and the VSEM parameters identical to those of the real SEM [19]. The generated image was 2560 × 1920 pix in size. The generation time was 13.8 min. The image is presented in Fig. 3b and the signals com prising the image are shown in Fig. 3c (signal 2). The real and virtual images were compared by comparing the signals comprising the images (Fig. 3c) and using the amplitude spectra of the images [16] shown in Fig. 5. It can be clearly seen that the signals and amplitude spectra of the real (Fig. 5a) and gener ated (Fig. 5b) images coincide. Therefore, the virtual image can be used for checking the correctness of solv ing the inverse problem for the real image. Solution of the inverse problem for the virtual image yielded the protrusion parameters given in Table 1 (processing) and the probe diameter d = 29.5 ± 0.1 nm. Although the probe diameter was somewhat overstated compared to the one used in the simulation, the parameters of the model protrusion elements were determined rather well. This indicates that the param eters of the real protrusion were determined correctly. Large errors in the size of the elements of the real pro trusion are indicative of a larger spread of its dimen sions compared to the real test object. 2.2. Calibration of a HighVoltage SEM Each scanning electron microscope requires cali bration, i.e., determination of its main parameters, including pixelsize m and electron probe diameter d. At present, there exist several techniques [7–10] for calibrating a SEM that operates in the highvoltage mode at the slow secondary electron (SSE) detection. Let us consider application of the VSEM in one such technique. Calibration of an S 4800 SEM operating in the SSE accumulation mode was performed at the probe elec tron energy E = 20 keV using the MShPS2.0Si test object [7, 8], the images of which are shown in Fig. 1 at different magnifications. In the calibration, the image with a size of 2560 × 1920 pix consisting of pro trusions 5 and 6 of the pitch structure (Fig. 1c) of the central module (Fig. 1a) was used, which is shown in Fig. 6a. Figure 6c presents the shape of one of the sig nals (signal 1) comprising the image in Fig. 6a. The calibration with the use of the certified pitch value t = 2001 ± 1 nm [22] yielded the pixelsize
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Fig. 6. (a) Real and (b) generated highvoltage SSE images of a pitch (two protrusions and a groove in between) of the MShPS2.0Si test object and its virtual analog and (c) shapes of the signals comprising these images (signals 1 and 2, respectively). The size of the mark in the images is 2 µm.
m = 2.250 ± 0.002 nm/pix (the manufacturing company value for the image in Fig. 6a is m = 2.254972 nm/pix) and the SEM electron probe diameter d = 15 ± 2 nm. In addition, the parameters of protrusions 5 and 6 and the groove between them were determined (Table 2, test object). To create a virtual (model) object, we use the sizes given in Table 2 (model). As a result, using the SEM [15, 16], a model image shown in Fig. 6b was gener ated. The image size is 2560 × 1920 pix. The genera tion time is 39.3 min. During generation, the VSEM’s effective probe [15] consisted of two components
FEF ( x, t ) = A1F ( x, t ) − A2FBSE ( x, t ) , RUSSIAN MICROELECTRONICS
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where t is the scanning coordinate; F(x, t) is the narrow component of the Gaussian shape, which simulates the electron distribution density in the SEM electron probe [15] with the diameter d = 15 nm [20, 21]; and FBSE(x, t) is the broad component described by the Gaussian distribution, which simulates the backscat tered electron distribution density [15] with the diam eter d = 5 µm. The contributions of components A1 and A2 to the effective probe were the same. Note that diameter d of the effective probe [20, 21] with the Gaussian shape
F ( x, t ) =
2 1 exp ⎛ − (t − x ) ⎞ , ⎜ 2 ⎟ 2πσ ⎝ 2σ ⎠
is related to parameter σ of the Gaussian as [19] d = σ 2π ≈ 2.5σ.
The real and virtual images were compared by comparing the signals comprising the images (Fig. 6c) and using the amplitude spectra of the images [16] shown in Fig. 7. It can be clearly seen that both the sig nals and amplitude spectra of the real (Fig. 7a) and generated (Fig. 7b) images coincide. Therefore, the virtual image can be used for checking the correctness of solving the inverse problem for the real image. 2015
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Table 2. Parameters of elements of the MShPS2.0Si test object determined of a highvoltage SEM (standard deviations of the corresponding size are in the parenthesis), specified model object parameters, and results obtained by processing the simulated image Relief
Parameter
Model
Processing
587(4)
586
586.4 ± 0.3
Bottom, nm
1375(4)
1376
1376.6 ± 0.7
Top, nm
1415(4)
1414
1414.5 ± 0.7
Bottom, nm
623(7)
624
624.5 ± 0.3
Top, nm
585(4)
586
586.4 ± 0.3
1377(4)
1376
1376.6 ± 0.7
Side wall projection, nm
395.3(1.6)
395
395.1 ± 0.2
Pitch, nm
2001 ± 1
2001
2001 ± 1
Protrusion 5
Test object
Top, nm
Groove
Protrusion 6
Bottom, nm
Solution of the inverse problem [13] for the model structure yielded the VSEM parameters (the pixelsize m = 2.2501 ± 0.0011 nm/pix and the probe diameter d = 16.1 ± 0.7 nm) and the sizes of the elements of the model structure given in Table 2 (processing). All the results of the SEM calibration (m and d) and certifica tion of the sizes of the test object elements coincide within the experimental error with the data at the VSEM input (Table 2 (model)) and the results obtained using the real test object (Table 2 (test object)). This proves the correctness of the highvolt age SEM calibration and the certification of the sizes of the test object’s elements. 3. DEMONSTRATION OF VSEM CAPABILITIES To demonstrate wide capabilities of the VSEM described in studies [15, 16], we will solve the problem that can be solved in no other way. This problem is to choose the best method for SEM calibration and cer tification of the size of the test object.
3 U 4
2 B 1
Fig. 8. Image of a real signal obtained on a highvoltage SEM in the SSE detection mode upon scanning a step with a large side wall inclination angle and approximation of separate signal parts by straight lines and determination of control points 1–4.
3.1. Two Methods for SEM Calibration In studies [7, 8] two SEM calibration techniques with the use of test objects with the trapezoidal profile and large angles of side wall inclination were described, which are simultaneously the techniques for certification of the parameters of relief elements in such test objects. Both techniques are based on the approximation of separate parts of the SSE signal of the SEM by straight lines. Figure 8 shows the form of a real signal obtained on a highvoltage SEM in the SSE detection mode upon scanning the steps with a large angle of side wall inclination by the electron probe. Separate parts of the signal are approximated by the straight lines (the dashed lines in Fig. 8). It can be seen that such an approximation can be rather good. The intersection points of the straight lines called the control points (points 1–4 in Fig. 8) are used in both techniques as the input data for determining the SEM parameters during calibration and measurements of the size of trapezoidal structure elements during their certification. Note that the control points obtained in this manner do not lie on the SEM signal. 3.1.1. The first SEM calibration technique. This technique [7] was the first SEM calibration technique with the use of test objects with the trapezoidal relief profile and large angles of inclination of protrusion and groove side walls. This technique was created by modifying [28] the method for measuring the size of structure elements with the trapezoidal profile and the small angles of the side wall inclination in order to use this method in structures with large angles of side wall inclination. Technique 1 consists in the following. Figure 9 shows a schematic of the pitch structure profile (Fig. 9a) with the parameters that characterize the structure and a schematic of an SSE signal of the highvoltage SEM (Fig. 9b) with control points 1–16 determining the measured parameters of the signal from Fig. 9b. When conditions
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SL 2
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T Fig. 9. Schematics of (a) a pitch structure profile with the parameters of the structure and (b) the highvoltage SSE signal obtained on a SEM with the parameters measured on the signal.
b p,t , u p,t , s L,R Ⰷ d
(6)
are met, in technique 1, the relation between the signal parameters, structure, and SEM have the form
s L = mS L,
t = mT ,
(7)
d = mD,
(8)
s R = mS R,
(9)
u p = mLp − d,
b p = mG p − d,
(10)
ut = mLt + d,
bt = mGt + d,
(11)
where m is the pixelsize [7] in the image and d is the diameter of the SEM electron probe. The rest param eters of the structure and signal are presented in Fig. 9. Using expressions (7)–(9), one can calibrate the SEM, i.e., determine pixelsize m and probe diameter d, from the known structure pitch t or projections sL or sR of the inclined side walls. In addition, one can certify the dimensions of the structural elements, i.e., the sizes of the upper and lower bases of the protrusions (expressions (10)) and grooves (expressions (11)) and the projections of the inclined side walls (expressions (9)) using the known pixelsize m and SEM probe diameter d. RUSSIAN MICROELECTRONICS
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Note the following feature of the technique: the electron probe diameter enters expressions (10) and (11) as a systematic correction. Therefore, to certify a test object, one should know the probe diameter, which can however be measured on the signal itself (see expression (8) and Fig. 9b). The presence of the systematic correction does not allow considering tech nique 1 to be a direct method for measuring the linear dimensions of the upper and lower bases of the trape zoidal protrusions and grooves in the test object. How ever, the direct measuring method is used in the mea surements of the structure’s pitch and the projections of the inclined side walls of the elements of structure 1. This technique is also the direct method for SEM cal ibration with the use of the structure’s pitch and pro jections of the inclined side walls as the certified dimensions. 3.1.2. The second SEM calibration technique. Instead of control points 1–16 from Fig. 9b, technique 2 uses points 1–8 shown in the schematic of the signal (Fig. 10b), which are related to the boundary points of the pitch structure elements (Fig. 10a) [8]. This rela tion is shown in Fig. 10 by the dashed lines. Points 1– 8 in Fig. 10b are the midpoints between the corre sponding control points 1–16 in Fig. 9b. These new
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Fig. 10. Schematics of (a) a pitch structure with the trapezoidal profile and large side wall inclination angles and (b) the high voltage SSE signal obtained on a SEM upon scanning the structure. The dashed lines indicate the couplings between profile boundary points and signal control points 1–6.
points determine the new signal parameters shown in Fig. 10b. In technique 2, on the fulfillment of conditions (6), the relations between the new signal parameters, struc ture element sizes, and SEM characteristics [8] are (12) t = mT ,
d = mD,
(13)
s L = mS L,
s R = mS R,
(14)
u p = mU p,
b p = mB p,
(15)
(16) ut = mU t , bt = mBt . Using expressions (12)–(16), one can calibrate the SEM, i.e., determine pixelsize m and probe diameter d
when any of the sizes of the structural elements are known (expressions (12) and (14)–(16)) or certify the sizes of structural elements (structure pitch (expres sion (12)) and the upper and lower bases of protrusions (expressions (15)) and grooves (expressions (16)), as well as the projections of the inclined side walls (expressions (14)), when the pixelsize m is known. Note the following feature distinguishing formu las (15) and (16) from expressions (10) and (11). For mulas (15) and (16) do not contain probe diameter d, which makes technique 2 a direct method for measur ing any sizes of elements of the test object. In addition, technique 2 is the direct method for SEM calibration with the use of the sizes of any test object elements as certified sizes.
Table 3. Certification of dimensions of model test object elements using two techniques Parameter
Model
Pitch, nm
2000
1999.97 ± 0.15
2000.0 ± 0.3
500
500.1 ± 1.8
500.07 ± 0.08
500
497.4 ± 1.8
499.3 ± 0.2
Bottom, nm
1500
1501.1 ± 1.8
1499.4 ± 0.4
Top, nm
1500
1502.4 ± 1.8
1500.7 ± 0.4
Bottom, nm
500
498.8 ± 1.8
500.6 ± 0.2
Top, nm
500
497.8 ± 1.8
499.2 ± 0.2
1500
1501.0 ± 1.8
1499.4 ± 0.4
Side wall projection, nm Left protrusion
Groove
Right protrusion
Top, nm
Bottom, nm
Technique 1
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Fig. 11. (a) Generated SSE image of the model pitch structure with large side wall inclination angles, (b) signal shape, and (c) amplitude spectrum of this image. The size of the mark in the images is 2 µm.
3.2. Comparison of the SEM Calibration Techniques Although formulas (12)–(16) can be obtained from formulas (7)–(11) and vice versa and the initial data (control points 1–16 in Fig. 9b) are identical for both techniques, techniques 1 and 2 yield different results of the SEM calibration and measurements of the sizes of the structural elements of the test object. Only the VSEM with the known parameters of a structure at the input can decide which technique yields a correct (or the best) result. To solve this problem, we used a model test object consisting of 11 grooves with the trapezoidal profile RUSSIAN MICROELECTRONICS
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and large angles of inclination of the side wall, which is a virtual analog of the MShPS2.0Si test object. We generated a highvoltage SSE image of protrusions 5 and 6 and the groove between them for such a model object. The virtual image size was 2560 × 1920 pix. The pixelsize was m = 2.250879 nm/pix (specified). The generation time was 39.1 min. The sizes of elements of the virtual object are given in Table 3 (model). The element height (depth) was h = 707 nm. The standard deviation of the coordinates determining the structural elements was 1 nm. The effective probe [15] used in the generation comprised two components (see expression (5)). The narrow 2015
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Fig. 12. Results of determination of pitch t of the virtual structure using (a) the first and (b) second techniques obtained by pro cessing the generated highvoltage SSE image presented in Fig. 11a.
component of the Gaussian shape, which simulates the SEM electron probe, was 30 nm in diameter at a standard diameter deviation of 1 nm. The broad com ponent, also having a Gaussian shape, which simu lates the contribution of backscattered electrons [15], was 5 µm in diameter at a standard diameter deviation of 0.1 µm. The contributions of the components to the effective probe (expression (5)) were identical. Figure 11 shows the generated SSE image of the highvoltage SEM (Fig. 11a), signal shape (Fig. 11b), and the amplitude spectrum [16] (Fig. 11c) of the image. According to the schematic of the signal (Fig. 9b), the control points were obtained on the signals that were used for determining the sizes of the structural ele ments by the two techniques. The results obtained are illustrated in Figs. 12 and 13 and given in Table 3. Figure 12 shows the determination of the struc ture’s pitch t using the first (Fig. 12a) and second (Fig. 12b) techniques. Since in the pitch image (two protrusions) the two techniques can yield different numbers of pitches by different control points (see Fig. 9b), Figs. 12a and 12b contain different numbers of results marked as the measurement number. The average pitches calculated from these data are given in Table 3
and shown in Fig. 12 by the solid lines. The dashed lines in these figures bound the error interval. It can be seen that both techniques yield good results. Figure 13 illustrates the determination of projec tion s of the inclined side wall of the structure using the first (Fig. 13a) and second (Fig. 13b) techniques. Since in the image of the two protrusions the two tech niques can yield different numbers of projections of the inclined side walls (analogously to the structure pitch), Figs. 13a and 13b contain different numbers of results. The average values of the inclined side wall projections calculated from these data are given in Table 3 and shown in Fig. 13 by the solid lines. The dashed lines in these figures bound the error interval. Note the difference between technique 1 for mea suring the inclined side wall projection and technique 2. The spread of the measured results in technique 1 sig nificantly exceeds the errors of the measurements of each separate result. All the measurement results are grouped in two regions. This indicates that in tech nique 1 at a given measurement accuracy the problem of determination of the inclined side wall projection is somewhat incorrect [13], which results in the rather large total measurement error. This spread of the
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Fig. 13. Results of determination of projection s of the inclined side wall of a virtual structure using (a) the first and (b) second techniques obtained by processing the generated highvoltage SSE image presented in Fig. 11a.
results can significantly affect the conclusions drawn from such measurements. Meanwhile, despite the aforesaid, technique 1 yields good results: the total error of determination of the inclined side wall projection is only 0.4%. Note that in the micro and nanoelectronics the errors inserted by a measuring technique should not exceed 1%. The error of technique 1 is smaller by a factor of 2.5. Therefore, this technique is applicable for SEM calibration and linear size measurements in micro and nanoelectron ics, if the total measurement error is calculated cor rectly. The second technique for determination of the inclined side wall projection yields much better results. It exhibits no anomalies in the behavior of the measurement results and their errors. In addition, the error of the determination of the inclined side wall projection in the second technique is smaller than the total error of the first technique by a factor of 20. Note that the inclined side wall projection is most widely used in different SEM calibration methods [7, 9, 23]. The upper and lower bases of the protrusions and grooves measured using techniques 1 and 2 are given in RUSSIAN MICROELECTRONICS
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Table 3. It can be seen that, within the acceptable error range, the results of technique 1 are fairly good. How ever, technique 2 yields much better results on the parameters of a virtual test object. Therefore, tech nique 2 is recommended for SEM calibration and, especially, for the certification of the dimensions of the relief elements in the test objects. Note that the certi fication of the dimensions of the test object’s elements in a lowvoltage SEM and the calibration of a high voltage SEM described above were performed using technique 2. 3.3. The Origin of the Difference between the Results Obtained Using Techniques 1 and 2 To clarify the origin of the difference between the results obtained using techniques 1 and 2, we built his tograms of the coordinates of control points 2 and 3 and midpoint B (Fig. 14) obtained from the coordi nates of points 2 and 3 (Fig. 8) for forming an image of the left part of the left protrusion of a virtual object shown in Fig. 11a. The histograms are described well by the Gaussian curves 2015
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3
50
40
30
20
10
0 980
990
1000 X, nm
1010
1020
1030
Fig. 14. Histograms of coordinates of control points 2 and 3 and midpoint B (Fig. 8) for the image presented in Fig. 11a and their approximation by the Gaussian curves. Vertical lines indicate the histogram centers (mean values of the corresponding quanti ties).
g ( X , M , σ) =
2 I exp ⎛ − ( M − X ) ⎞ ⎜ ⎟ 2 2πσ 2σ ⎝ ⎠
(17)
with the parameters given in Table 4. It can be seen that the distributions of points 2 and 3 are much broader than the distribution of midpoint B. This is explained as follows. Figure 15a shows straight lines AA’, CC ', and ABC (solid lines) that approximate the SSE signal of a SEM from a step. The intersections of these straight lines form the control points A and C and midpoint B. Due to the noise on another signal, the straight lines will be arranged differently. For example, there will be a straight line A'B'C' instead of the straight line ABC (dashed line in Fig. 15a); consequently, there will be new control points A' and C ' and a new midpoint B'. Displacement of the straight line ABC to the posi tion A'B'C' can be decomposed into two displace ments: parallel (Fig. 15b) and oblique (Fig. 15c). For the parallel displacement, conditions
Δ A = A − A ' ≠ 0 and Δ C = C − C ' ≠ 0
(18)
ΔB = B − B' ≠ 0,
(19)
yield while for the oblique displacement, conditions (18) yield Δ B = B − B ' = 0.
(20)
Therefore, the oblique displacement contributes to the spread of the positions of control points A and C, but does not contribute to the spread of the positions of midpoint B. This manifests itself in the difference between the σ values given in Table 4 for different con trol points. Thus, the errors of determination of the midpoint positions used in the second technique are much smaller than the errors of determination of the control points used in the first technique. These differences make the second technique more accurate than the first one.
Table 4. Parameters of Gaussians describing the histograms of coordinates of points 2, 3, and B Point
I
M, nm
σ, nm
2
325
983.84 ± 0.11
1.95 ± 0.07
3
325
1016.65 ± 0.18
3.28 ± 0.13
B
325
1000.24 ± 0.05
0.98 ± 0.04
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VIRTUAL SCANNING ELECTRON MICROSCOPE
(a)
C
A'
backscattered and slow secondary electrons. The gen eration time is comparable to the time required for obtaining an image on a real SEM. The results obtained using the VSEM and real SEM operating in analogous modes with analogous test objects appear consistent. The simulatorbased virtual SEM can be used for —SEM calibration; —certification of test object element sizes; —measuring linear dimensions of microcircuit elements in nanoelectronics; —planning SEM experiments; —theoretical investigations on the SEM; —SEM operation training; —distant (internet) SEM operation training; —teaching students (lab practice).
C' B
B'
A
(b) C
C'
281
B
B'
A'
ACKNOWLEDGMENTS This study was supported in part by the Russian Foundation for Basic Research, project no. 1108 01217.
A
REFERENCES (c) C'
C B
B'
A'
A
Fig. 15. Schematic of the formation of positions of control points (A and C) and midpoint (B) with regard to the sta tistical spread at the formation of straight lines approxi mating the signal. For more details, see the text.
The above example shows that there are absolutely correct problems do not exist. Upon variation in the problem parameters, e.g., with an increase in the mea surement accuracy, the correct problem can become incorrect. Therefore, virtual measuring devices [13] should be permanently used. Otherwise, incorrect results can be obtained and unjustified conclusions can be drawn even for a problem that is correct at first sight. 4. CONCLUSIONS A simulatorbased virtual scanning electron micro scope allows generating images of virtual structures with a trapezoidal profile in modes analogous to the lowvoltage and highvoltage mode at the detection of RUSSIAN MICROELECTRONICS
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1. International Technology Roadmap for Semiconductors, 2013 Edition, Metrology, 2013. 42 p. //public.itrs.net 2. Postek, M.T., Nanometerscale metrology, Proc. SPIE, 2002, vol. 4608, pp. 84–96. 3. Postek, M.T. and Vladar, A.E., Critical Dimension Metrology and the Scanning Electron Microscope. Hand book of Silicon Semiconductor Metrology, Diebold, A.C., Ed., New York–Basel: Marcel Dekker Inc., 2001. pp. 295–333. 4. Novikov, Yu.A. and Rakov, A.V., Measurements of sub micron pattern features on solid surfaces with a scan ning electron microscope. 1. Instruments and methods (Review), Russ. Microelectron., 1996, vol. 25, no. 6, pp. 368–374. 5. Novikov, Yu.A. and Rakov, A.V., Measurements of sub micron pattern features on solid surfaces with a scan ning electron microscope. 2. New concept of scanning electron microscopebased metrology (Review), Russ. Microelectron., 1996, vol. 25, no. 6, pp. 375–383. 6. Hatsuzawa, T., Toyoda, K., and Tanimura, Y., Metro logical electron microscope system for microfeature of very large scale integrated circuits, Rev. Sci. Instrum., 1990, vol. 61, no. 3, pp. 975–979. 7. Volk, Ch.P., Gornev, E.S., Novikov, Yu.A., Ozerin, Yu.V., Plotnikov, Yu.I., Prokhorov, A.M., and Rakov, A.V., Linear standard for SEMAFM microelectronics dimensional metrology in the range 0.01–100 µm, Russ. Microelectron., 2002, vol. 31, no. 4, pp. 207–223. 8. Novikov, Yu.A., Gavrilenko, V.P., Ozerin, Yu.V., Rakov, A.V., and Todua, P.A., Silicon test object of the linewidth of the nanometer range for SEM and AFM, Proc. SPIE, 2007, vol. 6648, pp. 66480R1–66480R11. 9. Volk, Ch.P., Gornev, E.S., Novikov, Yu.A., Ozerin, Yu.V., Plotnikov, Yu.I., and Rakov, A.V., Linear measurement 2015
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19. Novikov, Yu.A., Electron distribution density in a low voltage SEM probe, Mikroelectronika, 2014, vol. 43, no. 5, pp. 361–370. 20. Volk, Ch.P., Gornev, E.S., Novikov, Yu.A., Plotnikov, Yu.I., Rakov, A.V., and Todua, P.A.,, Problems of measure ment of geometric characteristics of electron probe of scanning electron microscope, Linear measurements in micrometer and nanometer ranges for microelectronics and nanotechnology, Moscow: Nauka, 2006, P. 77–120. (Proc. IOFAN, Vol. 62). 21. Gavrilenko, V.P., Novikov, Yu.A., Rakov, A.V., and Todua, P.A., Measurement of the parameters of the electron beam of a scanning electron microscope, Proc. SPIE, 2008, vol. 7042, pp. 70420C1–12. 22. Novikov, Yu.A., Imaging of a test object with a trapezoi dal profile and large side wall inclinations in a scanning electron microscope in the backscattered electron mode, J. Surf. Investig. Xray Synchrotron Neutron Tech., 2011, vol. 5, no. 5, pp. 917–923. 23. Volk, Ch.P., Novikov, Yu.A., Rakov, A.V., and Todua, P.A., Calibrating a scanning electron microscope in two coordinates by the use of one certified dimension, Measur. Tech., 2008, vol. 51, no. 6, pp. 605–608. 24. Gavrilenko, V.P., Lesnovskii, E.N., Novikov, Yu.A., Rakov, A.V., Todua, P.A., and Filippov, M.N., First Russian standards in nanotechnology, Bull. Russ. Acad. Sci., Physics, 2009, vol. 73, no. 4, pp. 433–440. 25. Gavrilenko, V.P., Filippov, M.N., Novikov, Yu.A., Rakov, A.V., and Todua, P.A., Russian standards for dimensional measurements for nanotechnologies, Proc. SPIE, 2009, vol. 7378, pp. 7378121–7378128. 26. Novikov, Yu.A., Rakov, A.V., and Todua, P.A., Classifi cation of test objects for use in calibration of scanning electron microscopes in the nanometric range, Measur. Tech., 2009, vol. 52, no. 2, pp. 142–147. 27. Novikov, Yu.A., Gavrilenko, V.P., Rakov, A.V., and Todua, P.A., Test objects with rightangled and trape zoidal profiles of the relief elements, Proc. SPIE, 2008, vol. 7042, pp. 7042081–70420812. 28. Novikov, Yu.A., Rakov, A.V., and Stekolin, I.Yu., SEM measurements of VLSI submicron topography, Russ. Microelectron., 1995, vol. 24, no. 5, pp. 321–323.
Translated by E. Bondareva
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