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Estimation of dielectric constant by using mirror effect
Optik - International Journal for Light and Electron Optics 200 (2020) 163383
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.com/locate/ijleo
Original research article
Estimation of dielectric constant by using mirror effect ⁎
Muayyed Jabar Zoory , Saif Mohammed Altimime
T
Department of Physics, College of Science, Mustansiriyah Univ., Baghdad, Iraq
A R T IC LE I N F O
ABS TRA CT
Keywords: Charge effect Trapped charge on dielectric surface Ion beam current Ion mirror phenomenon Insulator charging
An experimental-theoretical investigation has been presented in this paper to study of the ion mirror effect on the Poly Methyl Methacrylate (PMMA) sample, and how to control this effect and use it as an analytical tool for imaging in practical field was presented. This means creating a deeper understanding of the characteristics of ions beam related to the mirror effect. As a result, a mathematical relation for the beam properties of the sample surface has been adopted and realistic physical concepts must be constructed. Where the study of the effect of some parameters on the ion mirror effect was submitted, and these parameters are: the trapped charge quantity on the sample surface and acceleration voltage in the imaging process, a distance of work and irradiation area. The purpose of this study is to achieve a measurement of dielectric constant by using the mirror effect. Where a mathematical relation was derived to estimate the dielectric constant for any of insulating material by using the mirror effect, where it gave good results that correspond to a good extent with the practical results. This was done by knowing the scanning voltage for the disappearance of the mirror effect as well as measuring the Coulomb diameter for each scanning voltage.
1. Introduction Today, the electron optics devices have become indispensable analytical tools in technology fields. The general theory of the movement of electrons and ions appeared in 1926 and was formulated by Hans Busch, who found the theoretical foundations for the charged particle optics using De-Broglie's theory. Hans Busch pointed out that the influence of the axially symmetric magnetic field to a beam of electrons passing through it is the same effect as the glass lens on the light beam passing through it [1]. Where electron optics or ion optics are defined as the branch of physics that deals with the movement of charged particles and its focusing by magnetic and electrical fields, and the generation of images using Electron Beams and Ion Beams [2]. The first and simplest application of electron optics physics is the construction of an electron microscope, As its construction is considered the first use of electronic lenses, which was made in 1931 by Ernst Ruska and Maxknoll for a magnifying glass 1 times. This was followed by major developments in this field. Electronic microscopes have been built with a higher analytical ability, which can be used to visualizing or imaging the lattice of the crystal [1]. This striking development of the electron microscope clearly demonstrated the possibility of generating images of charged particles with wavelengths less than those of visible light. Recently, one of the most important applications of charged particle optics is the focused ion beam (FIB) device [2].
⁎
Corresponding author. E-mail addresses: [email protected] (M.J. Zoory), [email protected] (S.M. Altimime).
https://doi.org/10.1016/j.ijleo.2019.163383 Received 8 June 2019; Accepted 7 September 2019 0030-4026/ © 2019 Published by Elsevier GmbH.
Optik - International Journal for Light and Electron Optics 200 (2020) 163383
M.J. Zoory and S.M. Altimime
1.1. Focused ion beam device (FIB) The focused ion beam device technology has evolved mainly in the period between the late 1970s and early 1980s. Modern systems for this device have become widely available in the researches of semiconductor materials, analysis, environmental treatment and surface modification. A number of authors recently reported using the (FIB) in polymer science applications. FIB applications have reached the field of biology and medical research. Where different samples can be imaged and detected by FIB device, which is a powerful device to complete such a task [3–7]. This technique is used not only for conductive samples. When a sample is irradiated with electrons or ions, the electrons or ions interacts with the sample, leading to a net charge generation on the sample surface. If the sample is conductive, it the charge quickly flows to the bottom of the sample away from the beam point. In the case of a non-conductive sample, the sample will become charged (charge trapped on the sample), which leads to high distortion in the first beam. In certain cases, the stored charge on the sample is capable of reversing incident electrons or ions, which in this case is similar to fixed mirror. 1.2. Mirror effect On the other hand, some of the incoming electrons or ions will be trapped on the sample's surface, and accumulate sharply, which leads to form a layer of charged particles on the surface of the sample, the layer that if not disposed of, will impede the imaging process of the sample. This layer will become like a mirror that has the ability to reverse the initial incident beam regressively. The reflected backward charges will be sent into the wall of the chamber, emitting new secondary electrons. Detecting of those secondary electrons will lead to imaging the area which is inside the chamber space and this phenomenon is called mirror effect [8]. When the initial beam consists of electrons the phenomenon is then called electron mirror effect, while called the ion mirror effect when the ions are the main component of the initial beam. The electron mirror effect has been observed since the 1970s by Clark and Stuart [9] and later it’s observed by Van Veld and Shaffner [10]. As for Ion mirror effect (IME), it was observed by Croccolo and Riccardi [11]. Ion mirror can easily be controlled and used as an analytical tool for imaging and getting information related to the sample characteristics by using (FIB) device [8,12–16]. 2. Theoretical description of trapped charges When studying the insulators in the scanning electron microscope (SEM) and (FIB) devices, the trapped charges on the insulating surface can be calculated in two ways: 2.1. Achieving the mirror effect The vacuum chamber of (SEM) and (FIB) devices is an ideal location to build the charge on the insulating sample. So when the dielectric is bombarded with high-energy electrons or ions, the charges will accumulate regularly on the surface of the sample, i.e. the charge will remain on the surface. In addition, it is simply possible to use an insulating material thick enough, such as a piece of plastic to ensure that the charge remains on the sample surface. Then, when imaging at low energy, the electrons or ions will bounce
Fig. 1. (1.a): Image of the phenomenon of the Ion mirror that occurs inside the FIB device. Figure (1.b): A diagram that reveals the process of charging the insulating surface and the occurrence of the ion mirror. 2
Optik - International Journal for Light and Electron Optics 200 (2020) 163383
M.J. Zoory and S.M. Altimime
back and strike the room walls of (SEM) and (FIB), secondary electrons are formed from the walls and the image will be for the inside walls rather than the surface of the insulating sample. Note the Fig. 1 where this phenomenon is known as the mirror effect. The cause of the mirror phenomenon is the repulsion power between the electrons or ions that are trapped on the surface and the electron or ion beam when imaging at low energy. Fig. 1.a shows the effect of the ion mirror in (FIB) where it is done in two steps: Step 1: trapping charged (Qt) (Red point) through irradiation by a high-energy ion beam, see Fig. 1.b. Step 2: The insulator sample is observed using a low energy ion beam. The ion beam will deviate due to the electric field generated by the trapped charge (a voltage equal to the surface in the dotted red line), see Fig. 1.b. In Fig. 1.b we observe the following:
• Line (1) in Fig. 1.b shows the path of the ion which returns to the coulomb ion region and gives the black disc, see Fig. 1.a. The relationship between the measured diameter of the image of the ion mirror (d) and the real diameter of the aperture of the Coulomb ion is given by the following expression [17]:
4W V d´(2πε° (εr + 1)) ⎤ Qt = ⎡ D sc d ⎣ ⎦
(1) − 12
F / M) and (εr) is the Where (WD) is the distance of work in FIB and (εo) is the permittivity in the vacuum (εo = 8.85 × 10 sample’s electrical insulation constant and (Vsc) represents the surface voltage. By drawing between the (Vsc) and the measured diameter of the ion mirror (d), we can calculate the quantity of trapped charge on the insulating surface.
• The ion path that indicated by line (2) shows the path of the ion that is reflected and bumped into a wall (FIB) and gives a picture of the interior walls (mirror image). • The ion path that indicated by line(3) shows the path of the ion, which deviates from the restricted or trapped charge and gives a distortion to the images of the ionic mirror phenomenon (the disappearance of the mirror phenomenon).
2.2. The disappearance of the mirror phenomenon There is always an electrical voltage associated with the presence of an electrical charge and some of the characteristics of the voltage depend mainly on the quantity of charge. Consequently, the electrical voltage associated with the trapped charge should be determined in order to understand the behavior of the scanning ion beams. We have proposed a model to represent the distribution of the trapped charge or the associated voltage. The simplest model in the current work is the approximation charged disc (see Fig. 2). Thus the sample voltage will be [15]:
ɸs (Z ) =
Qt [ z 2 + Rs2 − z ] 2πRs2 ε°
(2)
The Eq. (2) can be used to find the voltage between two points:
• The voltage at the Coulomb aperture, that is R > > Z where Z = W
D
and Eq. (2) can be rewritten as follows:
Fig. 2. A diagram of the electric field using the approximation of the charged disk. 3
Optik - International Journal for Light and Electron Optics 200 (2020) 163383
M.J. Zoory and S.M. Altimime
ɸgun =
Qt [ (WD )2 + Rs2 − (WD )] 2πRs2 ε°
ɸgun =
2 R2 Qt ⎡ ⎞ ⎛ (WD ) ⎜1 + ⎛⎜ s ⎞⎟ ⎟ 2 ⎢ (WD ) ⎠ 2πRs ε° ⎢ ⎝ ⎠ ⎝ ⎣
1/2
⎤ − (WD ) ⎥ ⎥ ⎦
(3)
To simplify Eq. (3) by using the series of force as follows: 2 1/2
2 ⎛ ⎛ Rs ⎞ ⎞ ⎜1 + ⎜ (W ) ⎟ ⎟ ⎝ D ⎠⎠ ⎝
2
=1+
4
6
6
1 ⎛ Rs2 ⎞ 1 R2 1 ⎛ Rs2 ⎞ 15 ⎛ Rs2 ⎞ − ⎛⎜ s ⎞⎟ + − +… ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ 2 ⎝ (WD ) ⎠ 8 ⎝ (WD ) ⎠ 16 ⎝ (WD ) ⎠ 128 ⎝ (WD ) ⎠
(4)
Since (WD > > R), Eq. (4) can be approximated as follows: 2
2 1/2
⎛ ⎛ Rs ⎞ ⎞ ⎜1 + ⎜ (W ) ⎟ ⎟ ⎝ D ⎠⎠ ⎝
2
=1+
1 ⎛ Rs2 ⎞ ⎜ ⎟ 2 ⎝ (WD ) ⎠
(5)
Now this approximation can be compensated in Eq. (3) and becomes as follows: 2
ɸgun =
⎤ Qt ⎡ 1 R2 ⎞ ⎛ (WD ) ⎜1 + ⎜⎛ s ⎟⎞ ⎟ − (WD ) ⎥ 2 ⎢ 2 ⎝ (WD ) ⎠ 2πRs ε° ⎠ ⎝ ⎣ ⎦
ɸgun =
Qt 4πε° WD
(6)
• When the ion beam voltage increases (Vsc), the ions become closer to the surface of the ion beam (R > > Z) and this causes the
disappearance of the mirror phenomenon, and then the surface's voltage becomes equal to the voltage of the incident ions ΔVsc = −Vscmax . By using the approximation of (Z≈0), Eq. (2) can be written as:
ɸsample =
Qt 2πε° Rs
(7)
When:
ΔVsc = ɸgun − ɸsample
ΔVsc =
1⎞ Qt Qt Qt ⎛ 1 − = − 4πε° WD 2πε° Rs 2πε° ⎝ 2WD Rs ⎠ ⎜
⎟
(8)
Since (WD > > R), then Eq. (8) can be approximated to:
Vscmax =
Qt 2πε° Rs
Qt = 2πε° Rs Vscmax
(9)
3. Result and discussion Poly-methyl-methacrylate (PMMA) was used to achieve the mirror phenomenon. The material was irradiated by the energy of (25 Kv) and the current was (27PA) and the irradiation time was (5 min), while the working distance was (30 mm). The irradiation region's radius was about (0.457 mm) and at room temperature, and under a pressure (inside focused ion beam room) of (2.0 × 10−5 Pa). All of these parameters were constant during work. 3.1. Maximum surface scanning voltage In the current work after the end of the irradiation period, different scanning cards (Vsc) were filmed. Note Fig. 3. The purpose of that is to reach a voltage, which is equal to the surface voltage (Vscmax ), and in which the mirror effect disappears. The results show that the voltage at which the phenomenon of the ion mirror disappears is (18 Kv) (i.e Vscmax = 18Kv ). The results also show that as the scanning voltage increases, the ions become closer to the surface of the insulating sample, which leads to the distortion of the mirror image, thus leading to the disappearance of the mirror phenomenon. It is also observed that the diameter of the Coulomb aperture of the mirror image decreases with increasing scanning voltage. 4
Optik - International Journal for Light and Electron Optics 200 (2020) 163383
M.J. Zoory and S.M. Altimime
Fig. 3. Mirror effect images for different scanning voltage Vsc.
Fig. 4. The relationship between the measured diameter of the Coulomb aperture of the ion mirror's image and different scanning voltage values used for imagining. 5
Optik - International Journal for Light and Electron Optics 200 (2020) 163383
M.J. Zoory and S.M. Altimime
Table 1 Estimation of the electrical dielectric constant for each scanning voltage using the mirror effect. Vsc (Kev)
d (μm)
1/d (μm)−1
εr
6 7 8 9 10 11 12 13 14 15 16 17 18 19
32.91 28.83 24.74 21.94 19.37 17.79 16.19 14.99 13.89 12.87 11.39 10.22 No measurement Disappearing mirror effect
30385.90 34686.09 40420.37 45578.85 50684.24 56211.36 61766.52 66711.14 71994.24 77700.08 87796.31 97847.36 No measurement Disappearing mirror effect
≈2.47 ≈2.45 ≈2.46 ≈2.47 ≈2.54 ≈2.50 ≈2.53 ≈2.52 ≈2.53 ≈2.55 ≈2.76 ≈2.95 No measurement Disappearing mirror effect
By using the mirror effect, it is possible to find the electrical dielectric constant for any insulator by knowing the scanning voltage, as well as measuring the diameter of the Coulomb aperture for each scanning voltage.
3.2. Estimation the quantity of trapped charge By drawing between the measured diameters of mirror images with scanning voltage values as shown in Fig. 4, it is possible by using Eq. (1) to calculate the quantity of trapped charge on a surface of (PMMA). By using Fig. 4 it is possible to find the quantity of trapped charge on the surface of the insulating sample, where it was (Qt≈488 PC). 3.3. Estimation of dielectric constant Now it is possible to find a relationship to calculate the dielectric constant using the mirror phenomenon and by Eqs. (1) and (9) it is found that:
A ⎞ εr = ⎛ −1 V ⎝ sc d ⎠ ⎜
⎟
(10)
max d´ R s Vsc
Where: A = 4WD . Using Eq. (10), the value of the dielectric constant for each scanning voltage will be found, as shown in Table 1. 4. Conclusions The phenomenon of the ion mirror on the PMMA sample and how to control the ionic mirror was studied and used as an analytical tool for imaging samples. The effects of some parameters on the ion mirror phenomenon were studied, such as the quantity of trapped charge on the surface, the accelerated voltage in the imaging process, the distance of work and irradiation area. The relation between these parameters was studied and the electrical dielectric constant was obtained using the mirror phenomenon. References [1] J. Heydenreich, P.J. Goodhew, Electron microscopy and analysis.(The Wykeham Science Series, Herausgegeben von Sir N. Mott und GR Noakes) 191 Seiten, 118 Abbildungen, Preis£ 2, 50 Wykeham Publications Ltd., London/Winchester 1975, Kristall und Technik 11 (1) (1976) K13–K14. [2] MuayyedJabar Zoory, Mirror Effect Investigation for Focused Ion Beams, in University of Al-Mustansiriyah, College of Science, Department of Physics, Baghdad, Iraq, 2011. [3] D.K. Stewart, A.F. Doyle, J.D. Casey, Focused ion beam deposition of new materials: dielectric films for device modification and mask repair, and tantalum films for x-ray mask repair, Electron-Beam, X-Ray, EUV, and Ion-Beam Submicrometer Lithographies for Manufacturing VX, International Society for Optics and Photonics, 1995. [4] S. Reyntjens, D. De Bruyker, R. Puers, Focused ion beam as an inspection tool for microsystem technology, Proc. Microsystem Symp. (1998). [5] B. Ward, et al., Microcircuit Modification Using Focused Ion Beams. In Electron-beam, X-Ray, and Ion Beam Technology: Submicrometer Lithographies VII, International Society for Optics and Photonics, 1988. [6] D.K. Stewart, et al., Focused Ion-beam-induced Tungsten Deposition for Repair of Clear Defects on x-ray Masks. In Electron-beam, X-Ray, and Ion-beam Technology: Submicrometer Lithographies IX, International Society for Optics and Photonics, 1990. [7] J. Glanville, Focused ion beam technology for integrated circuit modification, Solid State Technol. 32 (5) (1989) 270–272. [8] H.N. Al-Obaidi, F.A. Al-Saymary, A.A. Ali, PET Mirror Image Characterization. in Summ. Scho. (2008) Milano, Italy, September 8th–October 8th. [9] D. Clarke, P. Stuart, An anomalous contrast effect in the scanning electron microscope, J. Phys. E: Sci. Instr. 3 (9) (1970) 705. [10] T. Shaffner, R. Van Veld, ’Charging’effects in the scanning electron microscope, J. Phys. E: Sci. Instr. 4 (9) (1971) 633. [11] F. Croccolo, C. Riccardi, Observation of the ion‐mirror effect during microscopy of insulating materials, J. Microsc. 229 (1) (2008) 39–43. [12] M.J. Zoory, Study the properties of polymer PVC using ion mirror effect, Al-Mustansiriya J. Sci. 24 (4) (2013) 34–50. [13] M.J. Zoory, Study a scanning potential influence on probing ion trajectory in sense of the ion mirror effect, J. Univ. Babylon 25 (3) (2017) 1043–1057. [14] M.J. Zoory, M.M. Abid, Study a scanning beam current in focusing ion beam device of overcome mirror effect, Opt. Int. J. Light Electron. Opt. 158 (2018)
6
Optik - International Journal for Light and Electron Optics 200 (2020) 163383
M.J. Zoory and S.M. Altimime
1470–1477. [15] M.J. Zoory, E.H. Ahmed, Influence of sample and ion beam potential on the mirror effect phenomenon at low accelerated voltage, IOP Conference Series: Materials Science and Engineering, IOP Publishing, 2018. [16] S.M.A. Muayyed Jabar Zoory, B.J. Alwan, Estimation the required beam current to eliminate the mirror effect, J. Eng. Appl. Sci. 13 (14) (2018) 10962–10966. [17] B. Vallayer, G. Blaise, D. Treheux, Space charge measurement in a dielectric material after irradiation with a 30 kV electron beam: application to single-crystals oxide trapping properties, Rev. Sci. Instrum. 70 (7) (1999) 3102–3112.
7
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.com/locate/ijleo
Original research article
Estimation of dielectric constant by using mirror effect ⁎
Muayyed Jabar Zoory , Saif Mohammed Altimime
T
Department of Physics, College of Science, Mustansiriyah Univ., Baghdad, Iraq
A R T IC LE I N F O
ABS TRA CT
Keywords: Charge effect Trapped charge on dielectric surface Ion beam current Ion mirror phenomenon Insulator charging
An experimental-theoretical investigation has been presented in this paper to study of the ion mirror effect on the Poly Methyl Methacrylate (PMMA) sample, and how to control this effect and use it as an analytical tool for imaging in practical field was presented. This means creating a deeper understanding of the characteristics of ions beam related to the mirror effect. As a result, a mathematical relation for the beam properties of the sample surface has been adopted and realistic physical concepts must be constructed. Where the study of the effect of some parameters on the ion mirror effect was submitted, and these parameters are: the trapped charge quantity on the sample surface and acceleration voltage in the imaging process, a distance of work and irradiation area. The purpose of this study is to achieve a measurement of dielectric constant by using the mirror effect. Where a mathematical relation was derived to estimate the dielectric constant for any of insulating material by using the mirror effect, where it gave good results that correspond to a good extent with the practical results. This was done by knowing the scanning voltage for the disappearance of the mirror effect as well as measuring the Coulomb diameter for each scanning voltage.
1. Introduction Today, the electron optics devices have become indispensable analytical tools in technology fields. The general theory of the movement of electrons and ions appeared in 1926 and was formulated by Hans Busch, who found the theoretical foundations for the charged particle optics using De-Broglie's theory. Hans Busch pointed out that the influence of the axially symmetric magnetic field to a beam of electrons passing through it is the same effect as the glass lens on the light beam passing through it [1]. Where electron optics or ion optics are defined as the branch of physics that deals with the movement of charged particles and its focusing by magnetic and electrical fields, and the generation of images using Electron Beams and Ion Beams [2]. The first and simplest application of electron optics physics is the construction of an electron microscope, As its construction is considered the first use of electronic lenses, which was made in 1931 by Ernst Ruska and Maxknoll for a magnifying glass 1 times. This was followed by major developments in this field. Electronic microscopes have been built with a higher analytical ability, which can be used to visualizing or imaging the lattice of the crystal [1]. This striking development of the electron microscope clearly demonstrated the possibility of generating images of charged particles with wavelengths less than those of visible light. Recently, one of the most important applications of charged particle optics is the focused ion beam (FIB) device [2].
⁎
Corresponding author. E-mail addresses: [email protected] (M.J. Zoory), [email protected] (S.M. Altimime).
https://doi.org/10.1016/j.ijleo.2019.163383 Received 8 June 2019; Accepted 7 September 2019 0030-4026/ © 2019 Published by Elsevier GmbH.
Optik - International Journal for Light and Electron Optics 200 (2020) 163383
M.J. Zoory and S.M. Altimime
1.1. Focused ion beam device (FIB) The focused ion beam device technology has evolved mainly in the period between the late 1970s and early 1980s. Modern systems for this device have become widely available in the researches of semiconductor materials, analysis, environmental treatment and surface modification. A number of authors recently reported using the (FIB) in polymer science applications. FIB applications have reached the field of biology and medical research. Where different samples can be imaged and detected by FIB device, which is a powerful device to complete such a task [3–7]. This technique is used not only for conductive samples. When a sample is irradiated with electrons or ions, the electrons or ions interacts with the sample, leading to a net charge generation on the sample surface. If the sample is conductive, it the charge quickly flows to the bottom of the sample away from the beam point. In the case of a non-conductive sample, the sample will become charged (charge trapped on the sample), which leads to high distortion in the first beam. In certain cases, the stored charge on the sample is capable of reversing incident electrons or ions, which in this case is similar to fixed mirror. 1.2. Mirror effect On the other hand, some of the incoming electrons or ions will be trapped on the sample's surface, and accumulate sharply, which leads to form a layer of charged particles on the surface of the sample, the layer that if not disposed of, will impede the imaging process of the sample. This layer will become like a mirror that has the ability to reverse the initial incident beam regressively. The reflected backward charges will be sent into the wall of the chamber, emitting new secondary electrons. Detecting of those secondary electrons will lead to imaging the area which is inside the chamber space and this phenomenon is called mirror effect [8]. When the initial beam consists of electrons the phenomenon is then called electron mirror effect, while called the ion mirror effect when the ions are the main component of the initial beam. The electron mirror effect has been observed since the 1970s by Clark and Stuart [9] and later it’s observed by Van Veld and Shaffner [10]. As for Ion mirror effect (IME), it was observed by Croccolo and Riccardi [11]. Ion mirror can easily be controlled and used as an analytical tool for imaging and getting information related to the sample characteristics by using (FIB) device [8,12–16]. 2. Theoretical description of trapped charges When studying the insulators in the scanning electron microscope (SEM) and (FIB) devices, the trapped charges on the insulating surface can be calculated in two ways: 2.1. Achieving the mirror effect The vacuum chamber of (SEM) and (FIB) devices is an ideal location to build the charge on the insulating sample. So when the dielectric is bombarded with high-energy electrons or ions, the charges will accumulate regularly on the surface of the sample, i.e. the charge will remain on the surface. In addition, it is simply possible to use an insulating material thick enough, such as a piece of plastic to ensure that the charge remains on the sample surface. Then, when imaging at low energy, the electrons or ions will bounce
Fig. 1. (1.a): Image of the phenomenon of the Ion mirror that occurs inside the FIB device. Figure (1.b): A diagram that reveals the process of charging the insulating surface and the occurrence of the ion mirror. 2
Optik - International Journal for Light and Electron Optics 200 (2020) 163383
M.J. Zoory and S.M. Altimime
back and strike the room walls of (SEM) and (FIB), secondary electrons are formed from the walls and the image will be for the inside walls rather than the surface of the insulating sample. Note the Fig. 1 where this phenomenon is known as the mirror effect. The cause of the mirror phenomenon is the repulsion power between the electrons or ions that are trapped on the surface and the electron or ion beam when imaging at low energy. Fig. 1.a shows the effect of the ion mirror in (FIB) where it is done in two steps: Step 1: trapping charged (Qt) (Red point) through irradiation by a high-energy ion beam, see Fig. 1.b. Step 2: The insulator sample is observed using a low energy ion beam. The ion beam will deviate due to the electric field generated by the trapped charge (a voltage equal to the surface in the dotted red line), see Fig. 1.b. In Fig. 1.b we observe the following:
• Line (1) in Fig. 1.b shows the path of the ion which returns to the coulomb ion region and gives the black disc, see Fig. 1.a. The relationship between the measured diameter of the image of the ion mirror (d) and the real diameter of the aperture of the Coulomb ion is given by the following expression [17]:
4W V d´(2πε° (εr + 1)) ⎤ Qt = ⎡ D sc d ⎣ ⎦
(1) − 12
F / M) and (εr) is the Where (WD) is the distance of work in FIB and (εo) is the permittivity in the vacuum (εo = 8.85 × 10 sample’s electrical insulation constant and (Vsc) represents the surface voltage. By drawing between the (Vsc) and the measured diameter of the ion mirror (d), we can calculate the quantity of trapped charge on the insulating surface.
• The ion path that indicated by line (2) shows the path of the ion that is reflected and bumped into a wall (FIB) and gives a picture of the interior walls (mirror image). • The ion path that indicated by line(3) shows the path of the ion, which deviates from the restricted or trapped charge and gives a distortion to the images of the ionic mirror phenomenon (the disappearance of the mirror phenomenon).
2.2. The disappearance of the mirror phenomenon There is always an electrical voltage associated with the presence of an electrical charge and some of the characteristics of the voltage depend mainly on the quantity of charge. Consequently, the electrical voltage associated with the trapped charge should be determined in order to understand the behavior of the scanning ion beams. We have proposed a model to represent the distribution of the trapped charge or the associated voltage. The simplest model in the current work is the approximation charged disc (see Fig. 2). Thus the sample voltage will be [15]:
ɸs (Z ) =
Qt [ z 2 + Rs2 − z ] 2πRs2 ε°
(2)
The Eq. (2) can be used to find the voltage between two points:
• The voltage at the Coulomb aperture, that is R > > Z where Z = W
D
and Eq. (2) can be rewritten as follows:
Fig. 2. A diagram of the electric field using the approximation of the charged disk. 3
Optik - International Journal for Light and Electron Optics 200 (2020) 163383
M.J. Zoory and S.M. Altimime
ɸgun =
Qt [ (WD )2 + Rs2 − (WD )] 2πRs2 ε°
ɸgun =
2 R2 Qt ⎡ ⎞ ⎛ (WD ) ⎜1 + ⎛⎜ s ⎞⎟ ⎟ 2 ⎢ (WD ) ⎠ 2πRs ε° ⎢ ⎝ ⎠ ⎝ ⎣
1/2
⎤ − (WD ) ⎥ ⎥ ⎦
(3)
To simplify Eq. (3) by using the series of force as follows: 2 1/2
2 ⎛ ⎛ Rs ⎞ ⎞ ⎜1 + ⎜ (W ) ⎟ ⎟ ⎝ D ⎠⎠ ⎝
2
=1+
4
6
6
1 ⎛ Rs2 ⎞ 1 R2 1 ⎛ Rs2 ⎞ 15 ⎛ Rs2 ⎞ − ⎛⎜ s ⎞⎟ + − +… ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ 2 ⎝ (WD ) ⎠ 8 ⎝ (WD ) ⎠ 16 ⎝ (WD ) ⎠ 128 ⎝ (WD ) ⎠
(4)
Since (WD > > R), Eq. (4) can be approximated as follows: 2
2 1/2
⎛ ⎛ Rs ⎞ ⎞ ⎜1 + ⎜ (W ) ⎟ ⎟ ⎝ D ⎠⎠ ⎝
2
=1+
1 ⎛ Rs2 ⎞ ⎜ ⎟ 2 ⎝ (WD ) ⎠
(5)
Now this approximation can be compensated in Eq. (3) and becomes as follows: 2
ɸgun =
⎤ Qt ⎡ 1 R2 ⎞ ⎛ (WD ) ⎜1 + ⎜⎛ s ⎟⎞ ⎟ − (WD ) ⎥ 2 ⎢ 2 ⎝ (WD ) ⎠ 2πRs ε° ⎠ ⎝ ⎣ ⎦
ɸgun =
Qt 4πε° WD
(6)
• When the ion beam voltage increases (Vsc), the ions become closer to the surface of the ion beam (R > > Z) and this causes the
disappearance of the mirror phenomenon, and then the surface's voltage becomes equal to the voltage of the incident ions ΔVsc = −Vscmax . By using the approximation of (Z≈0), Eq. (2) can be written as:
ɸsample =
Qt 2πε° Rs
(7)
When:
ΔVsc = ɸgun − ɸsample
ΔVsc =
1⎞ Qt Qt Qt ⎛ 1 − = − 4πε° WD 2πε° Rs 2πε° ⎝ 2WD Rs ⎠ ⎜
⎟
(8)
Since (WD > > R), then Eq. (8) can be approximated to:
Vscmax =
Qt 2πε° Rs
Qt = 2πε° Rs Vscmax
(9)
3. Result and discussion Poly-methyl-methacrylate (PMMA) was used to achieve the mirror phenomenon. The material was irradiated by the energy of (25 Kv) and the current was (27PA) and the irradiation time was (5 min), while the working distance was (30 mm). The irradiation region's radius was about (0.457 mm) and at room temperature, and under a pressure (inside focused ion beam room) of (2.0 × 10−5 Pa). All of these parameters were constant during work. 3.1. Maximum surface scanning voltage In the current work after the end of the irradiation period, different scanning cards (Vsc) were filmed. Note Fig. 3. The purpose of that is to reach a voltage, which is equal to the surface voltage (Vscmax ), and in which the mirror effect disappears. The results show that the voltage at which the phenomenon of the ion mirror disappears is (18 Kv) (i.e Vscmax = 18Kv ). The results also show that as the scanning voltage increases, the ions become closer to the surface of the insulating sample, which leads to the distortion of the mirror image, thus leading to the disappearance of the mirror phenomenon. It is also observed that the diameter of the Coulomb aperture of the mirror image decreases with increasing scanning voltage. 4
Optik - International Journal for Light and Electron Optics 200 (2020) 163383
M.J. Zoory and S.M. Altimime
Fig. 3. Mirror effect images for different scanning voltage Vsc.
Fig. 4. The relationship between the measured diameter of the Coulomb aperture of the ion mirror's image and different scanning voltage values used for imagining. 5
Optik - International Journal for Light and Electron Optics 200 (2020) 163383
M.J. Zoory and S.M. Altimime
Table 1 Estimation of the electrical dielectric constant for each scanning voltage using the mirror effect. Vsc (Kev)
d (μm)
1/d (μm)−1
εr
6 7 8 9 10 11 12 13 14 15 16 17 18 19
32.91 28.83 24.74 21.94 19.37 17.79 16.19 14.99 13.89 12.87 11.39 10.22 No measurement Disappearing mirror effect
30385.90 34686.09 40420.37 45578.85 50684.24 56211.36 61766.52 66711.14 71994.24 77700.08 87796.31 97847.36 No measurement Disappearing mirror effect
≈2.47 ≈2.45 ≈2.46 ≈2.47 ≈2.54 ≈2.50 ≈2.53 ≈2.52 ≈2.53 ≈2.55 ≈2.76 ≈2.95 No measurement Disappearing mirror effect
By using the mirror effect, it is possible to find the electrical dielectric constant for any insulator by knowing the scanning voltage, as well as measuring the diameter of the Coulomb aperture for each scanning voltage.
3.2. Estimation the quantity of trapped charge By drawing between the measured diameters of mirror images with scanning voltage values as shown in Fig. 4, it is possible by using Eq. (1) to calculate the quantity of trapped charge on a surface of (PMMA). By using Fig. 4 it is possible to find the quantity of trapped charge on the surface of the insulating sample, where it was (Qt≈488 PC). 3.3. Estimation of dielectric constant Now it is possible to find a relationship to calculate the dielectric constant using the mirror phenomenon and by Eqs. (1) and (9) it is found that:
A ⎞ εr = ⎛ −1 V ⎝ sc d ⎠ ⎜
⎟
(10)
max d´ R s Vsc
Where: A = 4WD . Using Eq. (10), the value of the dielectric constant for each scanning voltage will be found, as shown in Table 1. 4. Conclusions The phenomenon of the ion mirror on the PMMA sample and how to control the ionic mirror was studied and used as an analytical tool for imaging samples. The effects of some parameters on the ion mirror phenomenon were studied, such as the quantity of trapped charge on the surface, the accelerated voltage in the imaging process, the distance of work and irradiation area. The relation between these parameters was studied and the electrical dielectric constant was obtained using the mirror phenomenon. References [1] J. Heydenreich, P.J. Goodhew, Electron microscopy and analysis.(The Wykeham Science Series, Herausgegeben von Sir N. Mott und GR Noakes) 191 Seiten, 118 Abbildungen, Preis£ 2, 50 Wykeham Publications Ltd., London/Winchester 1975, Kristall und Technik 11 (1) (1976) K13–K14. [2] MuayyedJabar Zoory, Mirror Effect Investigation for Focused Ion Beams, in University of Al-Mustansiriyah, College of Science, Department of Physics, Baghdad, Iraq, 2011. [3] D.K. Stewart, A.F. Doyle, J.D. Casey, Focused ion beam deposition of new materials: dielectric films for device modification and mask repair, and tantalum films for x-ray mask repair, Electron-Beam, X-Ray, EUV, and Ion-Beam Submicrometer Lithographies for Manufacturing VX, International Society for Optics and Photonics, 1995. [4] S. Reyntjens, D. De Bruyker, R. Puers, Focused ion beam as an inspection tool for microsystem technology, Proc. Microsystem Symp. (1998). [5] B. Ward, et al., Microcircuit Modification Using Focused Ion Beams. In Electron-beam, X-Ray, and Ion Beam Technology: Submicrometer Lithographies VII, International Society for Optics and Photonics, 1988. [6] D.K. Stewart, et al., Focused Ion-beam-induced Tungsten Deposition for Repair of Clear Defects on x-ray Masks. In Electron-beam, X-Ray, and Ion-beam Technology: Submicrometer Lithographies IX, International Society for Optics and Photonics, 1990. [7] J. Glanville, Focused ion beam technology for integrated circuit modification, Solid State Technol. 32 (5) (1989) 270–272. [8] H.N. Al-Obaidi, F.A. Al-Saymary, A.A. Ali, PET Mirror Image Characterization. in Summ. Scho. (2008) Milano, Italy, September 8th–October 8th. [9] D. Clarke, P. Stuart, An anomalous contrast effect in the scanning electron microscope, J. Phys. E: Sci. Instr. 3 (9) (1970) 705. [10] T. Shaffner, R. Van Veld, ’Charging’effects in the scanning electron microscope, J. Phys. E: Sci. Instr. 4 (9) (1971) 633. [11] F. Croccolo, C. Riccardi, Observation of the ion‐mirror effect during microscopy of insulating materials, J. Microsc. 229 (1) (2008) 39–43. [12] M.J. Zoory, Study the properties of polymer PVC using ion mirror effect, Al-Mustansiriya J. Sci. 24 (4) (2013) 34–50. [13] M.J. Zoory, Study a scanning potential influence on probing ion trajectory in sense of the ion mirror effect, J. Univ. Babylon 25 (3) (2017) 1043–1057. [14] M.J. Zoory, M.M. Abid, Study a scanning beam current in focusing ion beam device of overcome mirror effect, Opt. Int. J. Light Electron. Opt. 158 (2018)
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1470–1477. [15] M.J. Zoory, E.H. Ahmed, Influence of sample and ion beam potential on the mirror effect phenomenon at low accelerated voltage, IOP Conference Series: Materials Science and Engineering, IOP Publishing, 2018. [16] S.M.A. Muayyed Jabar Zoory, B.J. Alwan, Estimation the required beam current to eliminate the mirror effect, J. Eng. Appl. Sci. 13 (14) (2018) 10962–10966. [17] B. Vallayer, G. Blaise, D. Treheux, Space charge measurement in a dielectric material after irradiation with a 30 kV electron beam: application to single-crystals oxide trapping properties, Rev. Sci. Instrum. 70 (7) (1999) 3102–3112.
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