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Separation of image-distortion sources and magnetic-field measurement in scanning electron microscope (SEM)
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Micron 40 (2009) 46–50 www.elsevier.com/locate/micron
Separation of image-distortion sources and magnetic-field measurement in scanning electron microscope (SEM) Mariusz Płuska a,b,*, Andrzej Czerwinski a, Jacek Ratajczak a, Jerzy Ka˛tcki a, Łukasz Oskwarek b, Remigiusz Rak b b
a Institute of Electron Technology, Al. Lotnikow 32/46, Warsaw 02-668, Poland Warsaw University of Technology, Faculty of Electrical Engineering, Pl. Politechniki 1, Warsaw 00-661, Poland
Received 31 October 2007; received in revised form 15 January 2008; accepted 17 January 2008
Abstract The electron-microscope image distortion generated by electromagnetic interference (EMI) is an important problem for accurate imaging in scanning electron microscopy (SEM). Available commercial solutions to this problem utilize sophisticated hardware for EMI detection and compensation. Their efficiency depends on the complexity of distortions influence on SEM system. Selection of a proper method for reduction of the distortions is crucial. The current investigations allowed for a separation of the distortions impact on several components of SEM system. A sum of signals from distortion sources causes wavy deformations of specimen shapes in SEM images. The separation of various reasons of the distortion is based on measurements of the periodic deformations of the images for different electron beam energies and working distances between the microscope final aperture and the specimen. Using the SEM images, a direct influence of alternating magnetic field on the electron beam was distinguished. Distortions of electric signals in the scanning block of SEM were also separated. The presented method separates the direct magnetic field influence on the electron beam below the SEM final aperture (in the chamber) from its influence above this aperture (in the electron column). It also allows for the measurement of magnetic field present inside the SEM chamber. The current investigations gave practical guidelines for selecting the most efficient solution for reduction of the distortions. # 2008 Elsevier Ltd. All rights reserved. Keywords: Scanning electron microscopy; Image distortions; Electromagnetic distortions; Electron beam deflection
1. Introduction The image distortions generated by electromagnetic interference (EMI) are the most common problem in SEM. Alternating magnetic field changes the electron beam direction causing characteristic periodic deformations of a specimen edge on the registered images (Fig. 1). The magnitude of these deformations is equal to maximum difference between the obtained and the intended beam position at the specimen surface and can be measured on the images. The geometrical frequency of the deformations depends on a relation between the distortions frequency and used scanning rate. There are several hardware methods for elimination of the distortions as electric and magnetic shielding or active
* Corresponding author at: Institute of Electron Technology, Al. Lotnikow 32/ 46, Warsaw 02-668, Poland. Fax: +48 22 8470631. E-mail address: [email protected] (M. Płuska). 0968-4328/$ – see front matter # 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.micron.2008.01.009
compensation of distorting magnetic field (Vladar, 2003; Isabell, 2004; Peng et al., 2004). The main disadvantages of the hardware solutions are their complexity and costs. It will be shown that the proposed separation of various distortion reasons allows for reduction of these disadvantages. Also digital image processing for SEM-images enhancement can be applied (Homma et al., 1987; Płuska et al., 2006). The combined application of the separation and digital image processing is especially promising for the elimination of the distortion. 2. Method EMI acts on several components of the SEM system, however the geometrical image deformations are mainly generated in two ways: (i) Alternating the magnetic field present in the SEM column and chamber impacts and deflects directly the electron beam.
M. Płuska et al. / Micron 40 (2009) 46–50
47
Fig. 1. Distorted image of reference specimen in small magnification (a) and in high magnification (b). Magnitude of the distortion dx is equal to the half of width of peak-to-peak edge deformation.
(ii) EMI induces the distortions in the electronic circuits of the scanning system, thus the signal applied to the scanning coils is distorted. A peak-to-peak value of the total electron beam deflection can be measured on the SEM image (Fig. 1). Generally, the direct electron beam deflection depends on the magnetic field magnitude and the working distance, i.e. distance between the final aperture of the electron gun and the specimen. Moreover, the shielding efficiency of the SEM housing changes the spatial distribution of distorting magnetic field along the electron beam path through the electron column and microscope chamber. The higher energy means the higher electron velocity. Therefore electrons stay by a shorter period of time under the influence of the magnetic field, thus the beam deflection is lower. Then the beam deflection depends on the electron energy, decreasing with an increase of the energy. However, a different case occurs when the signals applied to the scanning coils are distorted. The magnitudes of the scanning signals are generally coupled in SEM with the electron energy in order to keep the image magnification constant. Therefore, in the case of distortion of the scanning signals (i.e. in the electronic circuits) the beam deflection is independent of the electron energy. Influence of the distortions on the electron beam deflection is illustrated in Fig. 2. A measurement of the magnetic field in SEM is used for the separation of the mentioned influences. A method for the measurement of the magnetic field inside a SEM chamber was proposed by Ishiba and Suzuki (1974), however its limited application only to a case considered there, does not allow to apply this method for a general case of image deformations. In the current investigations the general case is considered of the distortions generated not only in a limited space within the SEM chamber, but along the whole electron beam path through the microscope column and chamber. The currently proposed approach separates the field influence on the electron beam in the SEM chamber from its influence on the electron beam in the SEM column. It can also be identified, which part of distortions generated in the column originates from the scanning block of SEM, and which part of them is generated directly by the magnetic field influence on the
electron beam. Because each source of distortions acts on elements of SEM with a different strength, the separation is crucial for selecting a proper method for reduction of the distortions. The presented method utilizes SEM itself and any additional hardware is unnecessary. The separation also enables to apply a proposed method for the measurement of the alternating magnetic field inside a SEM chamber. Although the distribution of the magnetic field of distortions in SEM generally can be nonuniform, however for some narrow range of working distances it can be assumed as being uniform. The Lorentz force acting on the electron beam is constant for the range of working distances, in which the magnetic field is uniform or can be assumed as approximately uniform. Consequently, an acceleration of electrons in the direction of Lorentz force is constant as well. Therefore, a dependence of electron beam deflection on working distance can be expressed as quadratic equation. Generally, the distortions affect SEM images in two dimensions. Two components dx and dy of electron beam deflection for two orthogonal directions, x and y,
Fig. 2. Simplified diagram of EMI influence on SEM. EMI-generated magnetic field of distortions present in SEM column (Bcol) and chamber (Bch) was marked. Unwanted beam deflection d is caused by the mentioned field and by EMI influence on scanning electronics.
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in the range of working distances, in which Lorentz force is constant, are as follows: eBy vx0 d x ¼ pffiffiffiffiffiffiffiffiffiffiffi w2d þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi wd þ dx0 ; 2 2Eme 2E=me
(1a)
eBx vy0 d y ¼ pffiffiffiffiffiffiffiffiffiffiffi w2d þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi wd þ dy0 ; 2 2Eme 2E=me
(1b)
where Bx and By are two orthogonal components of magnetic field vector B, e is electron charge, E is energy of electrons, me is relativistic electron mass for the specified energy, vx0 and vy0 are orthogonal components of initial electron velocity (initial, i.e. at wd ¼ 0) parallel to Lorentz force direction, dx0 and dy0 are orthogonal components of initial electron beam deflection. When the distribution of the magnetic field inside the SEM chamber is not uniform then its mean value is measured in this way. Application of the method for several narrow ranges of working distance allows also for accurate measurements of the field nonuniformity. Measuring the total deflection for at least three working distances allows to determine all three unknown parameters of the equation, i.e. the magnetic field and the initial velocity and the deflection. The least squares fitting gives the best results. Two components, dxwd and dywd, of this part of the electron beam deflection that is caused only by the magnetic field in the SEM chamber, are as follows: eBy d xwd ¼ pffiffiffiffiffiffiffiffiffiffiffi w2d ; 2 2Eme
(2a)
eBx d ywd ¼ pffiffiffiffiffiffiffiffiffiffiffi w2d ; 2 2Eme
(2b)
3. Results Generally, the presented method is applicable for two orthogonal directions, thus allows for analysis of twodimensional distortions of electron beam. An analysis of two orthogonal directions is possible because the measurements can be performed independently for two perpendicular scanning directions. In the currently described case there was possible such an orientation of the reference specimen toward the magnetic field direction for which the dx component of beam deflection was maximal and the dy component was equal to zero. Therefore, the following analysis is limited to one dimension. Firstly, the correctness of the presented method of the separation was experimentally verified. A reference inductor was used to generate magnetic field. It was placed very closely either to the SEM column or to the microscope chamber (Fig. 2). When magnetic field acted on the SEM column the dependence between the electron beam deflection dx and the working distance wd was linear, as expected (Fig. 3a). It means that there was no interaction of magnetic field with the electron beam in the SEM chamber, thus the parameters which stay by w2d in Eqs. (1a) and (1b) for this case were approximately equal to zero. When magnetic field acted on the electron beam inside the SEM chamber the dependence between the electron beam deflection dx and the working distance wd was squared, as expected (Fig. 3b). It means that there was no interaction of
Although the beam deflection due to the initial velocity – as described in Eqs. (1a) and (1b) – occurs within the chamber, however the initial electron velocity is a result of distortions caused within the column. Therefore, when these components dxwd, dywd of the deflection related to the magnetic field in the chamber are subtracted from the total beam deflection, the rest is related to the part of deflection caused by distortions within the column, as follows: d xl ¼ d x d xwd ;
(3a)
d yl ¼ d y d ywd :
(3b)
Components dxl, dyl are connected to the direct influence of magnetic field on the electron beam in the electron column and to the EMI impact on the electronics in the circuits of the scanning system. It was found that the direct influence of magnetic field on the electron beam is dependent on the electron energy, while the EMI influence on the scanning electronics, as it was described before, is independent of the electron energy. Performing the measurements for various electron energies allows for the separation of the direct influence of magnetic field on the electron beam in the SEM column from the EMI influence on the scanning block of SEM.
Fig. 3. Dependence of electron beam deflection characteristics dx = f(wd ) on electron energy for magnetic field generated by reference inductor placed close to SEM chamber (a) and column (b). The used energies were E1 = 2 keV, E2 = 5 keV and E3 = 10 keV. Strong dependence of the characteristics on electron energy is visible.
M. Płuska et al. / Micron 40 (2009) 46–50
magnetic field with the electron beam in the SEM column, thus the linear components of Eqs. (1a) and (1b) for this case were approximately equal to zero. In both cases when the energy of electrons was changed, it caused a different dependence of the electron beam deflection dx on the working distance wd . It proves that the direct influence of magnetic field on the electron beam in SEM chamber or column is always dependent on the electron energy. It will be shown later that an independence of the electron beam deflection on the electron energy may also be observed and explained by an influence of EMI on the SEM electronics. Secondly, the real, unintended, ‘‘environmental’’ distortions, i.e. distortions that exist in the conditions of everyday SEM work and influence the image (as in Fig. 1) were measured and analyzed. In each case a peak-to-peak value of the electron beam displacement generated by magnetic field of distortions was measured for several electron beam energies and working distances. These measurements allowed for the separation of the distortions related to the peak-to-peak value of the magnetic field present in the SEM chamber and for calculation of its magnitude. Also the distortions related to the electron beam in the column were separated. Fig. 4 shows a peak-to-peak total deflections for four different cases of environmental distortions. For each electron energy the results were approximated with a second order polynomial: dE1 ¼ 0:1801 103 w2d 1:903 106 wd þ 22:00 109 ½m
(4a)
dE1þD1 ¼ 0:1504 103 w2d 1:856 106 wd þ 21:24 109 ½m
(4b)
dE2 ¼ 0:1144 103 w2d 1:448 106 wd þ 18:58 109 ½m
(4c)
dE2þD2 ¼ 0:1084 103 w2d 1:462 106 wd þ 18:36 109 ½m
49
The peak-to-peak values of magnetic field calculated for each case were as follows: BE1 ¼ 89:1 nT;
BE1þD1 ¼ 88:6 nT;
¼ 68:0 nT;
BE2þD2 ¼ 64; 9 nT:
BE2
The environmental distortions usually changes in time, nevertheless two pairs of comparable results were obtained. During the measurements at first two electron energies (E1 = 5 keV and E1+D1 = 7 keV) the distortion source gave stronger magnetic field than for the measurements (performed later) at the consecutive two other energies (E2 = 10 keV and E2+D2 = 13 keV). Fig. 5 shows the beam deflection after subtraction of the squared component, related to the field in the chamber. Although with the changes of the magnetic field magnitude also the slope of the characteristics changed, however for similar magnitudes of magnetic field the results were independent of the electron energy. Lack of dependency of the linear component of the deformation on the electron energy informs that in this case the component was caused by the distortion of the scanning signals in the deflection coils. In the presented case the distortions generated in SEM electronics were in the opposite phase to the ones generated by the direct influence of magnetic field on the electron beam. It led to negative values of the linear components of the distortion in Eqs. (4a)–(4d), while the squared components were positive. For a case when deflections are caused by the direct impact of magnetic field on the electron beam, both components, linear and squared, are phase coherent. However, such opposite phase of the distortion sources is not a general rule for an EMI influence on a SEM electronics. Since in the presented method the electron beam deflection is measured on the SEM-images, the measurement limits are correlated with the image resolution (pixels per nanometer). An application the digital algorithm to the specimen edge detection allows for the measurements of the deformations greater than a few pixels. Due to the discretization error (1 pixel) the deformations with the greater amplitudes are measured more
(4d)
Fig. 4. Deflection characteristics dx = f(wd ) for magnetic field of environmental distortions. Results of measurements of total electron beam deflection dx for two different magnetic field magnitudes: B1 = 65 nT, B2 = 88 nT and four different electron beam energies: E1 = 5 keV, E1+D1 = 7 keV, E2 = 10 keV and E2+D2 = 13 keV.
Fig. 5. Characteristics of electron beam deflection dlx generated in the SEM column by environmental distortions. Two different magnitudes of magnetic field in the chamber: B1 = 65 nT and B2 = 88 nT were revealed. For each field the deflections were independent of the electron energy, although they changed simultaneously with the magnetic field change. Four different electron beam energies were considered: E1 = 5 keV, E1+D1 = 7 keV, E2 = 10 keV and E2+D2 = 13 keV.
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precisely. In order to increase the measurements accuracy, the Discrete Fourier Transform (DFT) analysis of the deformations can be applied. 4. Conclusions A method is presented for a separation of different reasons of SEM image distortions and for a relation of these reasons to particular elements of SEM system. Application of the method allows for selection of optimal solutions for reduction of distortions. Namely, when the total image distortions are mainly independent of the electron energy, their most probable cause is a deformation of the signals in the scanning circuits. Active compensation of magnetic field would not give satisfactory results in this case. An electrical protection of these circuits or digital correction of SEM images is a better solution. A dependence of distortions on the electron energy proves that the direct impact of the magnetic field present in SEM chamber/column on the electron beam is their source. When a magnetic field with stable magnitude and frequency is the main source of distortions then an efficient active compensation of this field is possible, because of predictable influence of the field on the electron beam. A high value of the component of electron beam deflection proportional to squared working distance, together with a low value of other components, means that the distortions affects the electron beam mainly in the SEM chamber, thus an additional shielding of the chamber may reduce the problem. Application of a small shields for the specified parts of SEM would be less expensive than shielding the whole room, in which the microscope is mounted. It is possible when the separation enables to distinguish the elements susceptible to distortions. Furthermore, an isolation of the room by shielding or magnetic field compensation do not consider presence of electric devices
working closely to the electron microscope. It has to be noticed that even the components of SEM system itself, such as pumps, can be important sources of distortions and can generate the periodic magnetic field, which stays unshielded and cannot be easily compensated. When the distortion-detecting coils used in a system of active field compensation in the nearby electron microscope are mounted inside the SEM chamber, they measure only the local value of magnetic field, while as it was shown, image distortions may be generated outside the chamber as well. When there are several sources of distortions, causing nonuniform and nonstationary magnetic field distribution, a proper compensation may be very difficult. Oppositely, the separation of the distortions, and then determination of their importance and sources in SEM system, enable to eliminate these distortions independently and afterwards to check the effectiveness of their elimination. References Homma, K., Komura, F., Furuya, T., 1987. An image correction method for vibrated scan of SEM (scanning electron microscope). In: Proceedings of the International Workshop on Industrial Applications of Machine Vision and Machine Intelligence. pp. 26–30. Isabell, T.C., 2004, Analytical Instrumentation Facility Requirements for Nanotechnology. http://www.nanobuildings.com. Ishiba, T., Suzuki, H., 1974. Measurement of magnetic field of magnetic recording head by a scanning electron microscope. Jpn. J. Appl. Phys. 13 (3), 457–462. Peng, K.C.E., Pradeep, Y.E., Phock, C.T., 2004. Image Compensation Device for a Scanning Electron Microscope. US Patent No. US6791083B2. Płuska, M., Czerwinski, A., Ratajczak, J., Ka˛tcki, J., Rak, R., 2006. Elimination of scanning electron microscopy image periodic distortions with digital signal-processing methods. J. Microsc. 224 (1), 89–92. Vladar, A.E., 2003. Scanning Electron Microscopy in Real World Environment. http://www.nanobuildings.com.
Micron 40 (2009) 46–50 www.elsevier.com/locate/micron
Separation of image-distortion sources and magnetic-field measurement in scanning electron microscope (SEM) Mariusz Płuska a,b,*, Andrzej Czerwinski a, Jacek Ratajczak a, Jerzy Ka˛tcki a, Łukasz Oskwarek b, Remigiusz Rak b b
a Institute of Electron Technology, Al. Lotnikow 32/46, Warsaw 02-668, Poland Warsaw University of Technology, Faculty of Electrical Engineering, Pl. Politechniki 1, Warsaw 00-661, Poland
Received 31 October 2007; received in revised form 15 January 2008; accepted 17 January 2008
Abstract The electron-microscope image distortion generated by electromagnetic interference (EMI) is an important problem for accurate imaging in scanning electron microscopy (SEM). Available commercial solutions to this problem utilize sophisticated hardware for EMI detection and compensation. Their efficiency depends on the complexity of distortions influence on SEM system. Selection of a proper method for reduction of the distortions is crucial. The current investigations allowed for a separation of the distortions impact on several components of SEM system. A sum of signals from distortion sources causes wavy deformations of specimen shapes in SEM images. The separation of various reasons of the distortion is based on measurements of the periodic deformations of the images for different electron beam energies and working distances between the microscope final aperture and the specimen. Using the SEM images, a direct influence of alternating magnetic field on the electron beam was distinguished. Distortions of electric signals in the scanning block of SEM were also separated. The presented method separates the direct magnetic field influence on the electron beam below the SEM final aperture (in the chamber) from its influence above this aperture (in the electron column). It also allows for the measurement of magnetic field present inside the SEM chamber. The current investigations gave practical guidelines for selecting the most efficient solution for reduction of the distortions. # 2008 Elsevier Ltd. All rights reserved. Keywords: Scanning electron microscopy; Image distortions; Electromagnetic distortions; Electron beam deflection
1. Introduction The image distortions generated by electromagnetic interference (EMI) are the most common problem in SEM. Alternating magnetic field changes the electron beam direction causing characteristic periodic deformations of a specimen edge on the registered images (Fig. 1). The magnitude of these deformations is equal to maximum difference between the obtained and the intended beam position at the specimen surface and can be measured on the images. The geometrical frequency of the deformations depends on a relation between the distortions frequency and used scanning rate. There are several hardware methods for elimination of the distortions as electric and magnetic shielding or active
* Corresponding author at: Institute of Electron Technology, Al. Lotnikow 32/ 46, Warsaw 02-668, Poland. Fax: +48 22 8470631. E-mail address: [email protected] (M. Płuska). 0968-4328/$ – see front matter # 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.micron.2008.01.009
compensation of distorting magnetic field (Vladar, 2003; Isabell, 2004; Peng et al., 2004). The main disadvantages of the hardware solutions are their complexity and costs. It will be shown that the proposed separation of various distortion reasons allows for reduction of these disadvantages. Also digital image processing for SEM-images enhancement can be applied (Homma et al., 1987; Płuska et al., 2006). The combined application of the separation and digital image processing is especially promising for the elimination of the distortion. 2. Method EMI acts on several components of the SEM system, however the geometrical image deformations are mainly generated in two ways: (i) Alternating the magnetic field present in the SEM column and chamber impacts and deflects directly the electron beam.
M. Płuska et al. / Micron 40 (2009) 46–50
47
Fig. 1. Distorted image of reference specimen in small magnification (a) and in high magnification (b). Magnitude of the distortion dx is equal to the half of width of peak-to-peak edge deformation.
(ii) EMI induces the distortions in the electronic circuits of the scanning system, thus the signal applied to the scanning coils is distorted. A peak-to-peak value of the total electron beam deflection can be measured on the SEM image (Fig. 1). Generally, the direct electron beam deflection depends on the magnetic field magnitude and the working distance, i.e. distance between the final aperture of the electron gun and the specimen. Moreover, the shielding efficiency of the SEM housing changes the spatial distribution of distorting magnetic field along the electron beam path through the electron column and microscope chamber. The higher energy means the higher electron velocity. Therefore electrons stay by a shorter period of time under the influence of the magnetic field, thus the beam deflection is lower. Then the beam deflection depends on the electron energy, decreasing with an increase of the energy. However, a different case occurs when the signals applied to the scanning coils are distorted. The magnitudes of the scanning signals are generally coupled in SEM with the electron energy in order to keep the image magnification constant. Therefore, in the case of distortion of the scanning signals (i.e. in the electronic circuits) the beam deflection is independent of the electron energy. Influence of the distortions on the electron beam deflection is illustrated in Fig. 2. A measurement of the magnetic field in SEM is used for the separation of the mentioned influences. A method for the measurement of the magnetic field inside a SEM chamber was proposed by Ishiba and Suzuki (1974), however its limited application only to a case considered there, does not allow to apply this method for a general case of image deformations. In the current investigations the general case is considered of the distortions generated not only in a limited space within the SEM chamber, but along the whole electron beam path through the microscope column and chamber. The currently proposed approach separates the field influence on the electron beam in the SEM chamber from its influence on the electron beam in the SEM column. It can also be identified, which part of distortions generated in the column originates from the scanning block of SEM, and which part of them is generated directly by the magnetic field influence on the
electron beam. Because each source of distortions acts on elements of SEM with a different strength, the separation is crucial for selecting a proper method for reduction of the distortions. The presented method utilizes SEM itself and any additional hardware is unnecessary. The separation also enables to apply a proposed method for the measurement of the alternating magnetic field inside a SEM chamber. Although the distribution of the magnetic field of distortions in SEM generally can be nonuniform, however for some narrow range of working distances it can be assumed as being uniform. The Lorentz force acting on the electron beam is constant for the range of working distances, in which the magnetic field is uniform or can be assumed as approximately uniform. Consequently, an acceleration of electrons in the direction of Lorentz force is constant as well. Therefore, a dependence of electron beam deflection on working distance can be expressed as quadratic equation. Generally, the distortions affect SEM images in two dimensions. Two components dx and dy of electron beam deflection for two orthogonal directions, x and y,
Fig. 2. Simplified diagram of EMI influence on SEM. EMI-generated magnetic field of distortions present in SEM column (Bcol) and chamber (Bch) was marked. Unwanted beam deflection d is caused by the mentioned field and by EMI influence on scanning electronics.
48
M. Płuska et al. / Micron 40 (2009) 46–50
in the range of working distances, in which Lorentz force is constant, are as follows: eBy vx0 d x ¼ pffiffiffiffiffiffiffiffiffiffiffi w2d þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi wd þ dx0 ; 2 2Eme 2E=me
(1a)
eBx vy0 d y ¼ pffiffiffiffiffiffiffiffiffiffiffi w2d þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi wd þ dy0 ; 2 2Eme 2E=me
(1b)
where Bx and By are two orthogonal components of magnetic field vector B, e is electron charge, E is energy of electrons, me is relativistic electron mass for the specified energy, vx0 and vy0 are orthogonal components of initial electron velocity (initial, i.e. at wd ¼ 0) parallel to Lorentz force direction, dx0 and dy0 are orthogonal components of initial electron beam deflection. When the distribution of the magnetic field inside the SEM chamber is not uniform then its mean value is measured in this way. Application of the method for several narrow ranges of working distance allows also for accurate measurements of the field nonuniformity. Measuring the total deflection for at least three working distances allows to determine all three unknown parameters of the equation, i.e. the magnetic field and the initial velocity and the deflection. The least squares fitting gives the best results. Two components, dxwd and dywd, of this part of the electron beam deflection that is caused only by the magnetic field in the SEM chamber, are as follows: eBy d xwd ¼ pffiffiffiffiffiffiffiffiffiffiffi w2d ; 2 2Eme
(2a)
eBx d ywd ¼ pffiffiffiffiffiffiffiffiffiffiffi w2d ; 2 2Eme
(2b)
3. Results Generally, the presented method is applicable for two orthogonal directions, thus allows for analysis of twodimensional distortions of electron beam. An analysis of two orthogonal directions is possible because the measurements can be performed independently for two perpendicular scanning directions. In the currently described case there was possible such an orientation of the reference specimen toward the magnetic field direction for which the dx component of beam deflection was maximal and the dy component was equal to zero. Therefore, the following analysis is limited to one dimension. Firstly, the correctness of the presented method of the separation was experimentally verified. A reference inductor was used to generate magnetic field. It was placed very closely either to the SEM column or to the microscope chamber (Fig. 2). When magnetic field acted on the SEM column the dependence between the electron beam deflection dx and the working distance wd was linear, as expected (Fig. 3a). It means that there was no interaction of magnetic field with the electron beam in the SEM chamber, thus the parameters which stay by w2d in Eqs. (1a) and (1b) for this case were approximately equal to zero. When magnetic field acted on the electron beam inside the SEM chamber the dependence between the electron beam deflection dx and the working distance wd was squared, as expected (Fig. 3b). It means that there was no interaction of
Although the beam deflection due to the initial velocity – as described in Eqs. (1a) and (1b) – occurs within the chamber, however the initial electron velocity is a result of distortions caused within the column. Therefore, when these components dxwd, dywd of the deflection related to the magnetic field in the chamber are subtracted from the total beam deflection, the rest is related to the part of deflection caused by distortions within the column, as follows: d xl ¼ d x d xwd ;
(3a)
d yl ¼ d y d ywd :
(3b)
Components dxl, dyl are connected to the direct influence of magnetic field on the electron beam in the electron column and to the EMI impact on the electronics in the circuits of the scanning system. It was found that the direct influence of magnetic field on the electron beam is dependent on the electron energy, while the EMI influence on the scanning electronics, as it was described before, is independent of the electron energy. Performing the measurements for various electron energies allows for the separation of the direct influence of magnetic field on the electron beam in the SEM column from the EMI influence on the scanning block of SEM.
Fig. 3. Dependence of electron beam deflection characteristics dx = f(wd ) on electron energy for magnetic field generated by reference inductor placed close to SEM chamber (a) and column (b). The used energies were E1 = 2 keV, E2 = 5 keV and E3 = 10 keV. Strong dependence of the characteristics on electron energy is visible.
M. Płuska et al. / Micron 40 (2009) 46–50
magnetic field with the electron beam in the SEM column, thus the linear components of Eqs. (1a) and (1b) for this case were approximately equal to zero. In both cases when the energy of electrons was changed, it caused a different dependence of the electron beam deflection dx on the working distance wd . It proves that the direct influence of magnetic field on the electron beam in SEM chamber or column is always dependent on the electron energy. It will be shown later that an independence of the electron beam deflection on the electron energy may also be observed and explained by an influence of EMI on the SEM electronics. Secondly, the real, unintended, ‘‘environmental’’ distortions, i.e. distortions that exist in the conditions of everyday SEM work and influence the image (as in Fig. 1) were measured and analyzed. In each case a peak-to-peak value of the electron beam displacement generated by magnetic field of distortions was measured for several electron beam energies and working distances. These measurements allowed for the separation of the distortions related to the peak-to-peak value of the magnetic field present in the SEM chamber and for calculation of its magnitude. Also the distortions related to the electron beam in the column were separated. Fig. 4 shows a peak-to-peak total deflections for four different cases of environmental distortions. For each electron energy the results were approximated with a second order polynomial: dE1 ¼ 0:1801 103 w2d 1:903 106 wd þ 22:00 109 ½m
(4a)
dE1þD1 ¼ 0:1504 103 w2d 1:856 106 wd þ 21:24 109 ½m
(4b)
dE2 ¼ 0:1144 103 w2d 1:448 106 wd þ 18:58 109 ½m
(4c)
dE2þD2 ¼ 0:1084 103 w2d 1:462 106 wd þ 18:36 109 ½m
49
The peak-to-peak values of magnetic field calculated for each case were as follows: BE1 ¼ 89:1 nT;
BE1þD1 ¼ 88:6 nT;
¼ 68:0 nT;
BE2þD2 ¼ 64; 9 nT:
BE2
The environmental distortions usually changes in time, nevertheless two pairs of comparable results were obtained. During the measurements at first two electron energies (E1 = 5 keV and E1+D1 = 7 keV) the distortion source gave stronger magnetic field than for the measurements (performed later) at the consecutive two other energies (E2 = 10 keV and E2+D2 = 13 keV). Fig. 5 shows the beam deflection after subtraction of the squared component, related to the field in the chamber. Although with the changes of the magnetic field magnitude also the slope of the characteristics changed, however for similar magnitudes of magnetic field the results were independent of the electron energy. Lack of dependency of the linear component of the deformation on the electron energy informs that in this case the component was caused by the distortion of the scanning signals in the deflection coils. In the presented case the distortions generated in SEM electronics were in the opposite phase to the ones generated by the direct influence of magnetic field on the electron beam. It led to negative values of the linear components of the distortion in Eqs. (4a)–(4d), while the squared components were positive. For a case when deflections are caused by the direct impact of magnetic field on the electron beam, both components, linear and squared, are phase coherent. However, such opposite phase of the distortion sources is not a general rule for an EMI influence on a SEM electronics. Since in the presented method the electron beam deflection is measured on the SEM-images, the measurement limits are correlated with the image resolution (pixels per nanometer). An application the digital algorithm to the specimen edge detection allows for the measurements of the deformations greater than a few pixels. Due to the discretization error (1 pixel) the deformations with the greater amplitudes are measured more
(4d)
Fig. 4. Deflection characteristics dx = f(wd ) for magnetic field of environmental distortions. Results of measurements of total electron beam deflection dx for two different magnetic field magnitudes: B1 = 65 nT, B2 = 88 nT and four different electron beam energies: E1 = 5 keV, E1+D1 = 7 keV, E2 = 10 keV and E2+D2 = 13 keV.
Fig. 5. Characteristics of electron beam deflection dlx generated in the SEM column by environmental distortions. Two different magnitudes of magnetic field in the chamber: B1 = 65 nT and B2 = 88 nT were revealed. For each field the deflections were independent of the electron energy, although they changed simultaneously with the magnetic field change. Four different electron beam energies were considered: E1 = 5 keV, E1+D1 = 7 keV, E2 = 10 keV and E2+D2 = 13 keV.
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precisely. In order to increase the measurements accuracy, the Discrete Fourier Transform (DFT) analysis of the deformations can be applied. 4. Conclusions A method is presented for a separation of different reasons of SEM image distortions and for a relation of these reasons to particular elements of SEM system. Application of the method allows for selection of optimal solutions for reduction of distortions. Namely, when the total image distortions are mainly independent of the electron energy, their most probable cause is a deformation of the signals in the scanning circuits. Active compensation of magnetic field would not give satisfactory results in this case. An electrical protection of these circuits or digital correction of SEM images is a better solution. A dependence of distortions on the electron energy proves that the direct impact of the magnetic field present in SEM chamber/column on the electron beam is their source. When a magnetic field with stable magnitude and frequency is the main source of distortions then an efficient active compensation of this field is possible, because of predictable influence of the field on the electron beam. A high value of the component of electron beam deflection proportional to squared working distance, together with a low value of other components, means that the distortions affects the electron beam mainly in the SEM chamber, thus an additional shielding of the chamber may reduce the problem. Application of a small shields for the specified parts of SEM would be less expensive than shielding the whole room, in which the microscope is mounted. It is possible when the separation enables to distinguish the elements susceptible to distortions. Furthermore, an isolation of the room by shielding or magnetic field compensation do not consider presence of electric devices
working closely to the electron microscope. It has to be noticed that even the components of SEM system itself, such as pumps, can be important sources of distortions and can generate the periodic magnetic field, which stays unshielded and cannot be easily compensated. When the distortion-detecting coils used in a system of active field compensation in the nearby electron microscope are mounted inside the SEM chamber, they measure only the local value of magnetic field, while as it was shown, image distortions may be generated outside the chamber as well. When there are several sources of distortions, causing nonuniform and nonstationary magnetic field distribution, a proper compensation may be very difficult. Oppositely, the separation of the distortions, and then determination of their importance and sources in SEM system, enable to eliminate these distortions independently and afterwards to check the effectiveness of their elimination. References Homma, K., Komura, F., Furuya, T., 1987. An image correction method for vibrated scan of SEM (scanning electron microscope). In: Proceedings of the International Workshop on Industrial Applications of Machine Vision and Machine Intelligence. pp. 26–30. Isabell, T.C., 2004, Analytical Instrumentation Facility Requirements for Nanotechnology. http://www.nanobuildings.com. Ishiba, T., Suzuki, H., 1974. Measurement of magnetic field of magnetic recording head by a scanning electron microscope. Jpn. J. Appl. Phys. 13 (3), 457–462. Peng, K.C.E., Pradeep, Y.E., Phock, C.T., 2004. Image Compensation Device for a Scanning Electron Microscope. US Patent No. US6791083B2. Płuska, M., Czerwinski, A., Ratajczak, J., Ka˛tcki, J., Rak, R., 2006. Elimination of scanning electron microscopy image periodic distortions with digital signal-processing methods. J. Microsc. 224 (1), 89–92. Vladar, A.E., 2003. Scanning Electron Microscopy in Real World Environment. http://www.nanobuildings.com.