ISSN 1063-7842, Technical Physics, 2015, Vol. 60, No. 10, pp. 1515–1518. © Pleiades Publishing, Ltd., 2015. Original Russian Text © S.Yu. Kupreenko, N.A. Orlikovskii, E.I. Rau, A.M. Tagachenkov, A.A. Tatarintsev, 2015, published in Zhurnal Tekhnicheskoi Fiziki, 2015, Vol. 85, No. 10, pp. 101–104.
PHYSICS OF NANOSTRUCTURES
Determination of Thickness of Ultrathin Surface Films in Nanostructures from the Energy Spectra of Reflected Electrons S. Yu. Kupreenkoa, N. A. Orlikovskiib, E. I. Rau*a, A. M. Tagachenkovc, and A. A. Tatarintsevb a Moscow
State University, Moscow, 119991 Russia Physicotechnological Institute, Russian Academy of Sciences, Nakhimovskii pr. 36/1, Moscow, 117218 Russia c Institute of Nanotechnologies in Microelectronics, Russian Academy of Sciences, Nagatinskaya ul. 18, Moscow, 115487 Russia *e-mail:
[email protected] b
Received February 19, 2015
Abstract—A new method for determining the thickness of opaque films on bulk substrates is considered in the nanometer size range. The method is based on analysis and measurements of the energy spectra of back-scattered electrons. The thicknesses of local film nanostructures are determined from the amplitude values of the spectra and from their shift on the energy axis. DOI: 10.1134/S1063784215100205
INTRODUCTION The number of various 3D structures produced for micro- and nanoelectronics, which have a multilayer thin-film structure with the fragment sizes on the order of 1–10 nm in a lateral direction and along the depth, has increased due to rapid development of nanotechnologies. Accordingly, the problem of nondestructive diagnostics of such 3D sandwich structures and their metrology in all three coordinates arises. The nanometrology apparatus for measuring linear lateral sizes has been developed, while the problem of measuring the depth of nano-objects (i.e., quantitative nondestructive probing of 3D structures over their depth) is still at the stage of finding the optimal solution. The available most widespread optical methods of measurements of thicknesses of thin-film coatings (ellipsometry and interference method) do not possess lateral resolution necessary for nanostructures and require optical transparency of films, which substantially limits the domain of their application. X-ray diffraction analysis used for determining the film thickness, as well as the method based on Rutherford back scattering of ions, does not possess the required lateral resolution either. The most admissible way for this purpose is the scanning probe profiler [1], but it requires the presence of a step at the film–substrate interface. The method for measuring thicknesses of free films and films on substrates, which is based on the dependence of the coefficient of reflected electrons (REs) on the film thickness and on the energy of incident electrons, has become very popular [2, 3]. Sometimes, the thicknesses of film coatings are determined from
the amplitude of the RE energy spectra [4] or from the shift of the peaks of these spectra [5–7]. However, these electron-probe methods require as a rule preliminary calibration of experimental setup using a set of test control samples consisting of various materials and films of various thicknesses. The obtaining of such a large number of gauge samples with different combinations of the composition of the material and substrate and different film thicknesses is an almost unsolvable problem. In connection with these limitations, we propose here a more accurate and universal method for measuring the local thicknesses of film coatings, which is almost free of the above drawbacks and does not require standard gauge test samples. 1. EXPERIMENTAL Figure 1 shows schematically two conditional structures that demonstrate the uniqueness of the proposed method. If a fragment of a nanostructure consisting of a material with atomic number Z2 and thickness d is hidden at depth t under the planar surface of a material with atomic number Z1, only a scanning electron microscope (SEM) with a nanometer electron probe makes it possible to visualize this structure with nanometer lateral size x, as well as t and d, which is on the massive (thick) substrate (Fig. 1a). This study aims at determining the depth t of the nanostructure. At present, such measurements can be taken only using the transverse cut of the structure (e.g., by an ion scalpel) followed by its observation from the side of the cut in a modern high-resolution SEM. However, this method is destructive, which is
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(b)
I0
I0
D
D
IBSE
IBSE
Z1
Z2
d
Z1
θ
t
Z2
t
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X
Fig. 1. Schematic representation of nanostructures “film on substrate” for which film thickness t is determined.
6000
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Au on Si t1 = 5.7 mm t2 = 10.7 mm t3 = 17.6 mm t4 = 23 mm t5 = 29 mm
6000 N(E)
5000 4000
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Au 5 4 3 2
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Au
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1000
1000 0
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5000 N(E)
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15 Ep
0
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Fig. 2. (a) Experimental N(E) spectra of electrons reflected from the bulk Si and Au samples and Au films of thickness t on the Si substrate; (b) spectra of bulk Au and Al samples and compositions of a three-layer sample consisting of Al films of thickness 30, 60, 100, 150, and 220 nm on the Au film of thickness 30 nm deposited onto the Si substrate.
inadmissible or undesirable in many cases. Analogous difficulties arise in the case of the structure shown in Fig. 1b, where film Z2 of thickness t is in the depth of a narrow (of nanometer size) dip in the matrix with atomic number Z1. In this situation, the only limitation is imposed on the exit angle θ of the reflected electron flux IRE. In Fig. 1, I0 denotes the incident electron flux in the SEM and D is the position of the RE detector (in the given case, in entrance diaphragm of the toroidal electron spectrometer installed in the SEM [8]). For control experiments, we prepared several “film-on-substrate” test structures with preset and accurately measured thickness of thin-film layers with different thicknesses and chemical compositions of
the materials. The samples were obtained by thermal sputtering of metal layers on the substrate in a vacuum chamber with a tungsten evaporator and the system for controlling the thicknesses of the deposited films based on a quartz resonance detector ensuring an error in determining the thickness not exceeding 10%. After each stage of depositing the next layer, more precise control measurement of thickness was performed from the height of the step at the interface between the film and the substrate using a Talystep probe contact profiler or an atomic force microscope (for ultrathin films). Both methods are characterized by an error in determining thickness up to 5%. The experimental spectroscopy of the samples in reflected electrons was performed on an LEO 1455 VP SEM (Zeiss) equipped TECHNICAL PHYSICS
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DETERMINATION OF THICKNESS
Isf, arb. units Au on Si 130 t = 27.8 nm t = 22.8 nm 120 1 t = 17.6 nm 110 100 2 t = 10.7 nm 90 80 t = 5.7 nm 70 60 3 50 Si 40 30 20 0 10 20 30 40 50 X, μm Fig. 3. Profiles of the signals from the spectrometer, recorded across Au strips of thickness t deposited on the bulk Si substrate, recorded for E0 = 5 (1) and 15 keV (2, 3) for relative energy Ep/E0 of spectrometer adjustment equal to 0.94 (1, 3) and 0.96 (2).
with a laboratory model of a toroidal sector electrostatic spectrometer [8]. Figure 2a shows typical RE energy distribution spectra for a film made of a material with a larger atomic number Zf than atomic number Zs of the substrate (i.e., Zf > Zs); Fig. 2b shows such spectra for a film made of a light material on the substrate made of a heavy material (i.e., Zf < Zs). The spectra from massive targets made of materials appearing in the film– substrate system are also shown on the same figure. One of the control samples was a silicon crystal on which thin strips of gold layers 10 μm in width and thickness t = 5.7, 10.7, 17.6, 23, and 29 nm were deposited. The profile of the spectrometer signal obtained by scanning with the electron probe across these strips are shown in Fig. 3 and indicate a high sensitivity and selectivity of the experimental setup to the difference in the film thicknesses. Profile diagrams of the signal also show that more accurate results of calculations are obtained for a higher energy Ep/E0 of adjustment of the spectrometer. The shape of the spectra in Fig. 2 lead to the conclusion that the changes in the spectral shifts on the energy axis are smaller than the variations of the corresponding spectral amplitudes for a fixed energy Ep/E0 of the spectrometer depending on the thickness of film coatings. This leads to the conclusion that the film thicknesses should be preferably measured from the change in signal amplitudes and not from the energy shift of the spectra, which was precisely done in this work. TECHNICAL PHYSICS
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2. CALCULATION OF THICKNESS OF NANOFILM COATINGS For bulk samples, exact expressions have been obtained for differential coefficients of REs, which determine the energy spectra (see, e.g., [9]), while the results obtained for layered structures are either too cumbersome for practical estimates [7] or require simulations based on the Monte Carlo method [10]. For this reason, we will use here the approach for calculating the signal from layered samples used for integral RE coefficients [3], but taking into account the fact that the values of differential coefficients are taken for the measured RE spectra. Then, the general form of signal Isf for a fixed energy Ep/E0 of REs for a sample consisting of the substrate material with atomic number Z0 and a film of thickness t made of a material with atomic number Zf is given by
I sf = I S 0 + (I f 0 − I S 0 )
If , I f0
(1)
where I S 0 and I f 0 are the values of signals from bulk samples with materials Z0 and Zf, respectively, measured by a spectrometer; If is the calculated value of the signal from free film Zf of thickness t [9],
(
)
⎤, (2) I f = I 0 ⎡1 − exp − 2 A t ⎣⎢ R cos θ ⎦⎥ where θ is the angle of detection of REs with the help of the spectrometer (in our case, θ = 25°). Decay parameter A depends on the film material and the energy of primary electrons, which determine their penetration depth Rf. It follows from relations (1) and (2) that in the absence of the film on the surface (t = 0), we obtain a signal only from the bulk target (substrate), Isf = I S 0 , while for film thickness t > R/A, we obtain a signal for the bulk target consisting of the film material with Zf (i.e., Isf = I f 0 ). Naturally, these boundary conditions depend on the atomic number of the target material, on the film thickness, on energy E0 of incident electrons, and, hence, on penetration depth R for these electrons in the target material [11],
R [nm] =
27.6 AE 01.67 [keV]
(3) , ρ Z 0.89 where ρ (g/cm3) is the density and A is the atomic mass. Parameter A = 2R/xc appearing in expression (2) depends on depth xc of the diffusion center of primary electrons, which is successfully expressed by the relation [11]
⎛ 1.21γ 2 ⎞ (4) x c = R ⎜1 − ⎟, 2 ⎝ (1 + γ 2 ) ⎠ where γ = 0.187Z0.667, which gives, for example, xc/R = 0.137 for Au and xc/R = 0.344 for Al. Ultimately, we obtain the following computational relations for the samples under investigation:
Isf, arb. units
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5000 4500 4000 3500 3000 2500 2000 1500 1000 500 0
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0
t, nm (Al films) 400 600
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in Fig. 2b, the calculations become more complicated. The problem of determining the thicknesses of such submerged films is at the stage of solution at present.
Au on Si (5 keV)
Au on Si (15 keV)
Al on Si (15 keV)
5
10 15 20 t, nm (Au films)
25
30
Fig. 4. Calculated and experimental RE signals for filmon-substrate samples as functions of film thickness t. Experiments were carried out for the Au film on the Si substrate for E0 = 5 and 15 keV and for E0 = 15 keV for the Al film on the Cu substrate.
I sf (Au −Si) = I Si 0 + (I Au 0 − I Si 0 ) ⎡ ⎛ t Au ⎞⎤ × ⎢1 − exp ⎜ − 14.6 , RAu cos θ ⎟⎠⎦⎥ ⎣ ⎝ I sf (Al −Cu) = I Cu 0 + (I Al 0 − I Cu 0 ) ⎡ ⎛ t Al ⎞⎤ × ⎢1 − exp ⎜ − 5.814 ⎟⎥ , R ⎣ ⎝ Al cos θ ⎠⎦ where the experimental values are I Si 0 = 400, I Au 0 = 6300 for I0 = 1 nA in the first relation and I Cu 0 = 3660 and I Al 0 = 1180 for I0 = 4 nA in the second relation; the values of RAu and RAl are determined by formula (3); cosθ = cos25° = 0.906. The results of calculations are shown in Fig. 4. It can be seen from Figs. 3 and 4 that better linearity of dependences Isf = f(t) is observed for measurements with higher values of E0 and Ep/E0 (i.e., for high energies and in spectral regions corresponding to higher energies). The calculated relations Isf = f(t) depend on the choice of the fixed energy Ep of the spectrometer to the right or left of the peaks in the spectra for which calculations are performed, i.e., depend on the most probable reflection depth xηp = (xc)p as compared to thickness t: xηp < t or xηp > t. Parameter p can be determined from the relation p = η–0.333, where η is the RE coefficient [9]. Generally, more accurate results of measurements are obtained by choosing the spectrometer adjustment energy Ep/E0 > Emax for Zf > Zs, and for Ep/E0 < Emax for Zf < Zs, where Emax is the position of the energy spectrum peak from the heavier bulk material of the sample. For complex multilayer structures analogous to those represented
CONCLUSIONS The measurement of the thicknesses of ultrathin film coatings and the depth of occurrence of structural elements with nanometer lateral sizes is carried out with a high degree of accuracy with the help of energy spectra of reflected electrons in a scanning electron microscope. The amplitudes of the signals being detected from bulk samples forming the film-on-substrate system and from the samples under investigation are determined from the analytic expressions for differential coefficients of reflected electrons taken at fixed adjustment energy of the spectrometer. The values of experimental signals in the spectra are used in computational relations for determining the sought film thicknesses. The absolute error of measurements amounts to fractions of a nanometer for thin films and several nanometers for relatively thick films; i.e., the errors in determining the thicknesses of film coatings generally do not exceed 5%. ACKNOWLEDGMENTS This study was supported financially by the Russian Foundation for Basic Research (project no. 15-0201557). REFERENCES 1. V. L. Mironov, Fundamentals of Scanning Probe Microscopy (Tekhnosfera, Moscow, 2004). 2. H. Niedrig, J. Appl. Phys. 53, R15 (1982). 3. P. B. DeNee, in Scanning Electron Microscopy, Ed. by O’Hare (SEM, Chicago, 1978), Vol. 1, pp. 741–745. 4. F. Schlichting, D. Berger, and H. Niedrig, Scanning 21, 197 (1999). 5. E. Rau, H. Hoffmeister, R. Sennov, and H. Kohl, J. Phys. D: Appl. Phys. 35, 1433 (2002). 6. M. Dapor, E. Rau, and R. Sennov, J. Appl. Phys. 102, 063705 (2007). 7. V. P. Afanas’ev, A. V. Lubenchenko, A. B. Povolotskii, and S. D. Fedorovich, Tech. Phys. 47, 1444 (2002). 8. A. V. Gostev, N. A. Orlikovskii, A. I. Rau, and A. A. Trubitsin, Tech. Phys. 58, 447 (2013). 9. E. I. Rau, S. A. Ditsman, S. V. Zaitsev, N. V. Lermontov, A. E. Luk’yanov, and S. Yu. Kupreenko, Izv. Ross. Akad. Nauk, Ser. Fiz. 77, 1050 (2013). 10. L. Reimer, M. Bongeler, M. Kassens, F. Liebscher, and R. Senkel, Scanning 13, 381 (1991). 11. K. Kanaya and S. Okayama, J. Phys. D: Appl. Phys. 5, 43 (1972).
Translated by N. Wadhwa TECHNICAL PHYSICS
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