ISSN 10274510, Journal of Surface Investigation. Xray, Synchrotron and Neutron Techniques, 2014, Vol. 8, No. 6, pp. 1252–1257. © Pleiades Publishing, Ltd., 2014.

Dependence between the Defocusing of the LowVoltage SEM Probe and Its ElectronDensity Distribution Yu. A. Novikov A.M. Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow, 119991 Russia email: [email protected] Received May 16, 2014

Abstract—The influence of the defocusing of a lowvoltage scanning electron microscope (SEM) probe on its electrondensity distribution is analyzed. It is demonstrated that a focused probe has a Gaussian shape. A defo cused probe can be represented as the sum of several Gaussian probes different in intensity shifted relative to each other. The proposed method can be efficiently used by both consumers preferring SEM applications for scientific and technological purposes and SEM designers who want to improve their operating capabilities. DOI: 10.1134/S1027451014060135

INTRODUCTION Scanning electron microscopes (SEM) are widely employed in various fields of science and technology. In the last few years, they have found increasing appli cation in nanotechnology in the visualization of the surface relief of solid states and in measuring linear sizes in the range of 1–1000 nm [1–4]. For modern commercial SEMs, the electronprobe diameters are usually greater than 10 nm [5, 6], falling within the ranges 10–30 (new microscopes) and 30–100 nm (after 3yr operation). Thus, SEM probe diameters are comparable or exceed nanostructurecomponent sizes in the entire nanotechnology size range (1–100 nm). In this case, to solve the problems concerning relief visualization and linear size measurements, a SEM probe must have the known electrondensity distribu tion (EDD) shape. However, the EDD of modern SEMs is often unknown and even probe diameters are not indicated in SEM registration certificates. This is explained by the fact that there are no internationally recognized techniques for measuring SEM electron probe parameters. According to the primaryelectron energy [7, 8], all SEMs can be divided into three groups: high (probe electron energy E ≥ 10 keV), low (E ≤ 2 keV), and moderatevoltage (2 keV < E < 10 keV) instruments. In this case, lowvoltage SEMs are regarded as belonging to a peculiar group for which specialized instruments (socalled criticaldimension SEMs produced to mea sure the critical (minimum) sizes of microcircuits) are created. For two groups, namely, high and moderatevolt age SEMs, methods for measuring the SEM electron probe diameters [5, 6], which rely on test objects with trapezoidal profiles and large inclination angles of the lateralwall of relief components [7–12], have been developed. These methods were developed so as

to create Russian national standards for test objects [13, 14] and are now employed in scanning electron microscopy. As a result, it became possible to start studying the more complex characteristics of elec tron probes with the help of analogous techniques and test objects. The main characteristic is the SEM probe EDD. The method for measuring the electrondensity dis tribution in the probe of a lowvoltage SEM was for the first time described in [15]. It was demonstrated that a SEM probe operating in the lowvoltage mode has a Gaussian EDD at the focus. Knowing such a distribu tion is necessary for SEM application to nanotechnol ogy, in which this instrument is used to measure the lin ear sizes of microcircuit components (their sizes [1] are comparable with the electronprobe diameter). More over, knowing this is of importance in the development and application of a virtual SEM [16]. Recently, the probe defocusing method started to be used to measure ultrasmall sizes in scanning elec tron microscopy [17, 18]. It is obvious that the defo cusing process varies the EDD in the probe. Hence, in substantiating this method, it is necessary to compre hend its influence on nanostructuresize measure ments. For this purpose, the true electrondensity dis tribution of the probe must be known at any focus. This work presents the results obtained by investi gating the dependence between the lowvoltage SEM probe defocusing and variations in the EDD of the probe. THEORY OF THE METHOD Let us consider the case where a lowvoltage SEM probe scans a step that is infinite along the Y axis and has a trapezoidal profile with a large angle ϕ of lateral

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wall inclination (Fig. 1). The large lateralwall inclina tion angle [11, 12] implies that the condition s = X2 – X1 = htanϕ Ⰷ d (1) is valid. Here, s is the inclinedsidewall projection onto the structure base, h is the step height, X1 and X2 are the coordinates of the lateralwall boundaries, and d is the effective diameter [5, 6] of the electron probe (below, the electronprobe diameter). The escape depth of secondary electrons (SEs) restricts the substance region from which these elec trons are liberated in vacuum and lie in the range of 1– 10 nm [19]. Its boundary is designated by a dashed line in Fig. 1. In [20], the SE escape depth zS is defined as zS = 1.9AZ

–0.6

/ρ.

(2)

If the substance density ρ is specified in grams per cubic centimeter, zS is expressed in nm. In the case of silicon, formula (2) provides zS(Si) = 4.7 nm. According to [5, 6], the SE emission signal can be written using the expression +∞

V(T) ∼

∫ I ( X )n ( X, T ) dX.

(3)

–∞

Here, n(X, T = 0) is the EDD in the probe, T is the probecenter position at a given instant (scanning coordinate), and I(X) is a function describing the emission properties of the step surface. This function is characterized by the surface relief: ⎧ I 1, X ≤ X 1 ⎪ I ( X ) = ⎨ I 2, X 1 < X < X 2 , ⎪ ⎩ I 3, X ≥ X 2

(4)

where I1, I2, and I3 are constants that are independent of X and satisfy the condition I1 ≈ I3, I2 > I1, I3. (5) Differentiating expression (3) with respect to the scanning coordinate and allowing for (4), we obtain n(–T) ~ ∂V(T)∂T (6) and n(T) ~ –∂V(T)∂T (7) in the vicinity of coordinates X1 and X2. The X1 and X2 positions relative to the structure are shown in Fig. 1. Thus, the lowvoltage SEM EDD along the scan ning axis can be found by differentiating the lowvolt age SEM signal. The proposed method was experimentally verified in [15] with the help of an S4800 SEM at a probe electron energy of E = 200 eV and a working distance of 2 mm. The image size was 1280 × 960 pixels. It was demonstrated that a focused probe can be defined by a Gaussian EDD.

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n(X, Y, T) S(X, Y) V(T) SE

SE

zS ϕ

X=T

X1

h

X2

Fig. 1. Scanning diagram whereby a step is scanned by means of the electron probe of a lowvoltage SEM (see details in the text).

EXPERIMENTAL Let us investigate how defocusing affects the shape of the electron probe of a lowvoltage SEM by means of the same S4800 microscope. In this case the probe electron energy is E = 1 keV, the working distance is 7.9 mm, and image size is 2560 × 1920 pixels. The probeelectron energy (1 keV) was chosen to be close to the upper boundary of the lowvoltage energy range (2 keV) [7, 8] because SEM defocusing reduces the probeelectron density and, consequently, the SEM signal, thereby increasing the noise contribu tion that strongly affects its differentiation. The pri maryelectron energy was taken greater than that used in [15]. Hence, the signal increased and, accordingly, the noise contribution decreased. The SEM focal distance was increased to obtain a higher focal depth and a lower influence of structure height on the investigation results [15]. The image size was magnified because the probe diameter increased substantially upon defocusing. Experiments were carried out without SEM cali bration. This is due to the fact that this process is not required to determine probe shape. The structural parameters of a test object and a SEM probe (more exactly, their absolute numerical values) were deter mined using the pixel size specified by the SEM man ufacturer (m = 0.8268229 nm/pixel). In accordance with previous studies performed with the use of the given SEM, the pixel size coincides with the SEM cal ibration to within 1–2% (the latter was implemented on the basis of Russian national standards [13, 14]). In this work, the object under study was the ridge of an MShPS2.0Si test object [8, 9], which is a silicon structure with a trapezoidal profile and large lateral wall inclination angles of ridges and grooves thereof. The images of the general view of the structure men tioned above at different magnifications are presented in Fig. 2. The test object includes five groups, each having three pitch structures. The pitch structures are 11 grooves (ten ridges) in silicon. A more detailed

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NOVIKOV

(а)

500 μm

(b)

50 μm

description of the MShPS2.0Si test object can be found in [8, 9]. The choice of the given test object is associated with the fact that the probe diameter increases during the defocusing process and can lead to the violation of condition (1). The ridges of the MShPS2.0Si test object are greater than those of the test object used in [15] (Table 1). Hence, the probe can be defocused to a larger extent with the use of the MShPS2.0Si test object. The probe was defocused by rotating the SEM focusing handle. Focused and increasingly defocused images of the ridges of the test objects are depicted in Figs. 3a and 3b–3d, respectively. It is seen that their blurring increases strongly with defocusing. The ridge component sizes were obtained by processing the focused image shown in Fig. 3a via the technique described in [7–10]. These sizes presented in Table 1.

10 μm

(c)

Fig. 2. SEM image of the general view of the MShPS2.0Si test object at different magnifications.

EXPERIMENTAL RESULTS AND DISCUSSION As in [15], the experimental signal images were summed to reduce the influence of noise. The total signals 1–4 near coordinate X1, which were deter mined, respectively, from the images shown in Figs. 3a–3d, are depicted in Fig. 4. In analogy with [5, 6], these signals were employed to calculated the probe diameters at different defocusing levels, which are given in Table 2. As can be seen, defocusing is accom panied by an 11fold increase in the probe diameter. Differentiating the signals shown in Fig. 4, we obtained the EDDs (Fig. 5) corresponding to different

(а)

500 nm

(b)

500 nm

(c)

500 nm

(d)

500 nm

Fig. 3. Ridge images obtained with the help of the S4800 SEM: (a) focused and (b–d) increasingly defocused states. JOURNAL OF SURFACE INVESTIGATION. XRAY, SYNCHROTRON AND NEUTRON TECHNIQUES

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levels of probe defocusing. The determined distribu tions were approximated by several Gaussians having different intensities and shifts relative to each other:

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2 1 3 4

⎛ ( X – A i ) 2⎞ Ii n(X) = Ii gi ( X ) = ⎟ , (8)   exp ⎜ –  2 ⎝ ⎠ σ 2π 2σ i i i=1 i=1 N

N

∑

∑

where N is the number of Gaussians and Ii is the con tribution of each Gaussian. The approximation parameters are given in Table 2. It is evident that an electron probe is described well by a Gaussian shape at the focus. This outcome is con firmed by data reported in [15], i.e., a focused probe has a Gaussian shape. Its profile is altered due to defo cusing so that the probe cannot be described by a sin gle Gaussian curve. However, it can be described by Table 1. Ridge parameters of the test object used in [15] and the MShPS2.0Si test object Ridge parameters

In [15]

MShPS2.0K

Top, nm

297.9 ± 0.5

591.8 ± 0.4

Bottom, nm

634.2 ± 0.6

1412.5 ± 0.6

Inclined wall projec tion, nm

168.1 ± 0.3

410.5 ± 0.2

100

200

300

400 500 X, pixel

600

700

800

Fig. 4. S4800 SEM signal shapes obtained when the elec tron probe moved toward the left wall of the ridge: (1) focused and (2–4) increasingly defocused states.

several Gaussians that have different intensities and are shifted relative to each other (see Fig. 5, Table 2). Such behavior of a defocused electron beam can be explained by the fact that a SEM cathode has several electron emission centers and, consequently, can exhibit a number of “independent” probes with Gaus sian shapes. When a SEM is well designed and prop erly adjusted, these probes can be brought to a single center. The defocusing process violates probe conver gence. Hence, the used defocusing methods [19, 20] for measuring nanostructurecomponent sizes must be thoroughly analyzed and data correctness must be proved.

Table 2. Approximating Gaussian parameters and probe diameters Signal

Gaussian

1

Position, nm

σ, nm

Contribution, %

d, nm

0.000 ± 0.002

12.15l ± 0.002

100

28 86

1

–26.31 ± 0.04

20.99 ± 0.02

49.27 ± 0.10

2

26.3l ± 0.04

20.94 ± 0.02

50.73 ± 0.11

2

1

–68.4 ± 1.0

22.8 ± 0.2

17.0 ± l.7

2

–32.2 ± 1.3

26.1 ± 1.1

22 ± 2

3

25.9 ± 0.7

36.05 ± 0.17

52.5 ± 0.7

4

73.12 ± 0.06

14.98 ± 0.07

8.61 ± 0.10

1

–144.94 ± 0.17

31.3 ± 0.4

9.5 ± 0.4

2

–55.3 ± 0.6

63.8 ± 1.1

45.3 ± l.l

3

78.5 ± 0.8

59.1 ± 0.5

39.7 ± 0.7

4

150.78 ± 0.10

19.3 ± 0.14

5.49 ± 0.10

160

3

320

4

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(b)

1

2

(c)

(d)

3 2

3

2 1 4

1

4

Fig. 5. (points) Shapes of the derived SEM signals shown in Fig. 4, (curves 1–4) their expansion in terms of Gaussian functions, and the sums of these expansions.

CONCLUSIONS A method for measuring the electrondensity dis tribution of a lowvoltage scanning electron micro scope probe has been created. This technique makes it possible to determine such a density at probe diame ters of 30–300 nm. The dependence between defocus ing and the SEMprobe shape is investigated. A low voltage SEM probe involves several Gaussiantype probes shifted relative to each other. These probes can be combined into a single probe with a Gaussian shape. The proposed method can be useful for both con sumers performing scientific and technological studies based on SEMs and SEM designers who want to improve their operating capabilities. ACKNOWLEDGMENTS I thank V.B. Mityukhlyaev and A.V. Rakov for par ticipation in experiments and helpful discussions.

This work was supported in part by the Russian Foundation for Basic Research, project no. 1108 01217. REFERENCES 1. International Technology Roadmap for Semiconductors, 2013 Edition. Metrology. 2013. 42 p. // public.itrs.net 2. M. T. Postek and A. E. Vladar, in Handbook of Silicon Semiconductor Metrology, Ed. by A. C. Diebold (Marcel Dekker, New York, Basel, 2001), p. 295. 3. M. T. Postek, Proc. SPIE 4608, 84 (2002). 4. V. P. Gavrilenko, Yu. A. Novikov, A. V. Rakov, and P. A. Todua, Proc. SPIE 7405, 7405041 (2009). 5. Ch. P. Volk, E. S. Gornev, Yu. A. Novikov, Yu. I. Plotni kov, A. V. Rakov, P. A. Todua, in Linear Measurements in Micrometer and Nanometer Ranges for Microelectronics and Nanotechnology, Moscow: Nauka, 2006, P. 77. (Proc. IOFAN, Vol. 62) [in Russian]. 6. V. P. Gavrilenko, Yu. A. Novikov, A. V. Rakov, and P. A. Todua, Proc. SPIE 7042, 70420C1 (2008).

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DEPENDENCE BETWEEN THE DEFOCUSING OF THE LOWVOLTAGE SEM PROBE 7. Ch. P. Volk, V. B. Mityukhlyaev, Yu. A. Novikov, A. V. Rakov, and P. A. Todua, Meas. Tech. 52, 713 (2009). 8. Yu. A. Novikov, V. P. Gavrilenko, Yu. V. Ozerin, A. V. Rakov, and P. A. Todua, Proc. SPIE 6648, 66480R1 (2007). 9. Ch. P. Volk, E. S. Gornev, Yu. A. Novikov, Yu. V. Ozerin, Yu. I. Plotnikov, A. M. Prokhorov, and A. V. Rakov, Russ. Microelectron. 31, 207 (2002). 10. V. P. Gavrilenko, V. B. Mityukhlyaev, Yu. A. Novikov, Yu. V. Ozerin, A. V. Rakov, and P. A. Todua, Meas. Sci. Technol. 20, 0840221 (2009). 11. Yu. A. Novikov, A. V. Rakov, and P. A. Todua, Meas. Tech. 52, 142 (2009). 12. V. P. Gavrilenko, Yu. A. Novikov, A. V. Rakov, and P. A. Todua, Proc. SPIE 7718, 77180Y1 (2010). 13. V. P. Gavrilenko, E. N. Lesnovsky, Yu. A. Novikov, A. V. Rakov, P. A. Todua, M. N. Filippov, Bull. Russ. Acad. Sci.: Phys. 73, 433 (2009). 14. V. P. Gavrilenko, M. N. Filippov, Yu. A. Novikov, A. V. Rakov, and P. A. Todua, Proc. SPIE 7378, 7378121 (2009).

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15. Yu. A. Novikov, J. Surf. Invest.: Xray, Synchrotron Neutron Tech. 7, 1277 (2013). 16. Yu. V. Larionov and Yu. A. Novikov, Proc. SPIE 7800, 78000X1 (2012). 17. V. P. Gavrilenko, V. A. Kalnov, Yu. A. Novikov, A. A. Orlikovsky, A. V. Rakov, P. A. Todua, K. A. Valiev, and E. N. Zhikharev, Proc. SPIE 7272, 7272271 (2009). 18. M. N. Filippov, Yu. A. Novikov, A. V. Rakov, and P. A. Todua, Proc. SPIE 7521, 7521161 (2010). 19. Practical Scanning Electron Microscopy, Ed. by J. I. Goldstein and H. Yakowitz (Plenum Press, New York, London, 1975). 20. Yu. A. Novikov and A. V. Rakov, in Mechanisms of Sec ondary Electron Emission from a Relief Surface of Solids, Moscow: Nauka. Fizmatlit, 1998, P. 3. (Proc. IOFAN, Vol. 55) [in Russian].

Translated by S. Rodikov

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