- Email: [email protected]
Secondary electron detection for distributed axis electron beam systems
Microelectronic Engineering 85 (2008) 1786–1791
Contents lists available at ScienceDirect
Microelectronic Engineering journal homepage: www.elsevier.com/locate/mee
Secondary electron detection for distributed axis electron beam systems S. Tanimoto a,*, D.S. Pickard b, C. Kenney c, R.F.W. Pease d a
Hitachi, Ltd., Central Research Laboratory, Kokubunji, Japan National University of Singapore, Singapore, Singapore Molecular Biology Consortium, Chicago, USA d Stanford University, Stanford, USA b c
a r t i c l e
i n f o
Article history: Received 5 October 2007 Received in revised form 7 April 2008 Accepted 6 May 2008 Available online 16 June 2008 Keywords: Multi-electron-beam system Lithography Inspection DIFA DIVA Secondary electron detection
a b s t r a c t A secondary electron detection scheme for the distributed axis, fixed-aperture system is described. It employs a multi-channel detector array with a through-hole for a primary beamlet on each channel, a field terminator installed between the detector array and sample, and a deflector forming a static transverse electric field between the field terminator and sample. These elements enable detection of the secondary electrons stimulated by the primary beamlet. In order to achieve a high detection rate, small separation of the primary beamlets, and small aberrations, the size and the layout of the through-holes of the field terminator are studied. The equation of motion in an ideal field distribution is analytically solved and the dispersion of the secondary electrons caused by the helical motion in an axial magnetic field and chromatic variation of deflection are calculated. Aberrations are calculated by using numerical simulation. On the basis of these calculations, two types of the field terminator are proposed. One has a single through-hole, which is shared by a primary beamlet and the secondary electrons stimulated by the primary beamlet, per primary beamlet. The other has a through-hole exclusively for a primary beamlet and an extra slot for the secondary electrons, per primary beamlet. Simulations reveal that the former achieves a secondary electron detection rate of 99.7% and aberrations smaller than 4.6 nm, but doesn’t enable the separation of the primary beamlet to be smaller than 1000 lm. In contrast, the latter achieves a secondary electron detection rate of 95.0%, aberrations smaller than 9.7 nm. Furthermore, it also enables the separation of the primary beamlet to be as small as 250 lm, the same as in our detector array at this moment. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction 1.1. System description of DIFA In semiconductor fabrication, electron beam systems have long played important parts in fields such as lithography, inspection and metrology, by virtue of its minute probe size. At the same time, however, by reason of shrinking feature dimensions and growing complexity of semiconductor devices, electron beam systems have always been required to have higher throughput. In any electron beam system, the beam current is one of the major factors to determine the throughput. On the other hand, in conventional single-beam systems, increasing the beam current would enlarge the beam blur due to the Coulomb repulsion force. Furthermore, under the limited brightness of cathodes available at present, increase of the beam current requires an increase in the convergence angle, which is accompanied by growth of aberration and eventual deterioration of the minuteness of the electron beam. * Corresponding author. Tel.: +81 42 323 1111; fax: +81 42 327 7706. E-mail address: [email protected] (S. Tanimoto). 0167-9317/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2008.05.021
A distributed axis, fixed-aperture (DIFA) system has been proposed to overcome this throughput limit [1,2], and the resolution better than 50 nm has already been demonstrated by using a test bed [3]. In this system, primary electron beamlets emitted from a photocathode are distributed in a linear array and focused onto the sample simultaneously by a uniform axial magnetic field, which immerses the whole system. Since the primary beamlets remain separate, a significant increase in total current without the increase in Coulomb blurring is enabled. 1.2. Monolithic multi-channel electron detector As with other multiple electron beam systems, secondary electron detection is one of the key challenges for this method. In order to meet this challenge, a monolithic PIN-diode-based multi-channel detector array, shown in Fig. 1, has been investigated. Techniques developed for the radiation detector in high energy physics [4] were applied to this detector array. The electrodes, in a linear array with a pitch of 250 lm, detect the signals generated by the secondary electrons which collide with the other side of the detector. Each detection area has a through-hole, etched by the
S. Tanimoto et al. / Microelectronic Engineering 85 (2008) 1786–1791
1787
Fig. 1. (a) Micrograph of the PIN-diode-based detector array and (b) enlargement of the through-hole.
Bosch process, to enable transmittance of a primary beamlet. Each through-hole is 150 lm in diameter. We have already demonstrated the capability of parallel detection of secondary electrons stimulated by multiple primary beamlets, as well as a modest internal amplification and fast response time [5].
2. Secondary electron detection scheme using the monolithic multi-channel electron detector 2.1. Configuration of the detection scheme In DIFA, a photocathode illuminates a beam defining aperture plate and forms multiple primary beamlets, which are eventually focused onto the sample at a magnification of unity by a uniform axial magnetic field (Fig. 2). A transverse field formed by a deflector (not shown in Fig. 2) between the beam defining aperture plate
and detector array, deflects all primary beamlets one dimensionally in concert. The sample is scanned making use of the deflection together with the sample stage motion. The length of the deflector is adjusted so that the angle between the primary beamlets and the detector is a right angle and aberrations caused by the deflection are minimized [6]. An upper limit of the scan width to keep aberrations caused by the deflection field along with the fringing field at the through-hole is a remaining issue. A bias VR is applied between the detector array and the field terminator. This bias reduces the landing energy of the primary beamlets in order to decrease the damage to the sample and/or enhance the contrast of the image. At the same time, it increases the detector gain by accelerating the secondary electrons. The region between the field terminator and sample is free of an axial electric field, because the field terminator is electrically connected to the sample to suppress the axial field, i.e., accelerating field for secondary electrons. The deflector, which generates a static transverse
Fig. 2. Secondary electron detection scheme. Note that an axial uniform magnetic field immerses the whole system.
1788
S. Tanimoto et al. / Microelectronic Engineering 85 (2008) 1786–1791
field between the field terminator and sample, deflects the secondary electrons sufficiently before they are accelerated so that they hit the detection area of the detector. In contrast to the secondary electrons, the deflection of the primary beamlets is smaller because of their large energy. 2.2. Behaviour of the primary beamlet In order to minimize unnecessary lens effect for the primary beamlets, the detector array, field terminator and sample should be placed at conjugate image planes with the beam defining aperture plate for the primary beamlets as shown in Fig. 3a. Thus, LII, the axial length of the region II and LI, the axial length of the region I should be equal to the multiple of the distance which a primary beamlet travels during one cyclotron orbit. For the sake of simplicity, we assume that a primary beamlet completes only one cyclotron orbit when it travels through each of the region I, II and III. In region I, the primary beamlet travels with a constant velocity. Then LI is given by
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi LI ¼ p ð8mV 0 =eB2z Þ;
ð1Þ
where eV0 is the kinetic energies of a primary beamlet at the beam defining aperture plate and the detector. In the region II, the primary beamlet is decelerated by the bias VR. The acceleration is given by
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi aII ¼ ð 2eV 1 =m 2eV 0 =mÞ=s;
ð2Þ
where eVI = e(V0 – VR) is the kinetic energies of a primary beamlet at the field ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pterminator. s 2pm=eBz is the cyclotron period. Then LII is given by
LII ¼
1 aII s2 þ 2
rffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffi pffiffiffiffiffiffi 2eV 0 s ¼ p 2m=eB2z ð V 0 þ V 1 Þ: m
ð3Þ
In region III, the primary beamlet travels with a constant velocity again. LIII is given by
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi LIII ¼ p ð8mV 1 =eB2z Þ:
ð4Þ
Throughout this paper we assume that Vo and V1 are 15 kV and 1 kV, respectively and that Bz is 0.2 T, which give LI, LII and LIII of 13.0 mm, 8.16 mm and 3.35 mm, respectively.
2.3. Motion of the secondary electrons Fig. 3b depicts the motion of a secondary electron in an ideal field with perfect uniformity and no fringing at the through-hole. Note that an axial uniform magnetic field immerses the whole system. In the region III, where the electrostatic field has only the xcomponent, the non relativistic equation of motion of a secondary electron is given by [6]
v_ x ¼ eðEx þ vy Bz Þ=m; v_ y ¼ evx Bz =m; v_ z ¼ 0:
ð5Þ
By assuming the initial conditions x(0) = y(0) = z(0) = 0 for position and vx ð0Þ ¼ v0x ,vy ð0Þ ¼ v0y , vz ð0Þ ¼ v0z for velocity, we obtain:
2 2 v0y þ Ex =Bz v0x Ex xþ þ y þ t x x Bz v 2 v þ E =B 2 0x 0y x z ¼ þ
x
x
ð6Þ
and
z ¼ v0z t:
ð7Þ
where x eBz =m ¼ cyclotron frequency. Eq. (6) shows that a secondary electron moves helically. On the other hand, the second part of the left-hand side of Eq. (6) and the Eq. (7) indicates that the center of the helical motion is deflected toward the –y-direction with a velocity of Ex =Bz , as an electron moves toward upward, i.e. to the +z-direction. Hence, the trajectory is interpreted as a convolution of a helical motion and deflection in the y-direction. In the region II, where the electrostatic field has only the z-component, the non relativistic equation of motion of a secondary electron is given by:
v_ x ¼ evy Bz =m; v_ y ¼ evx Bz =m; v_ z ¼ eEz =m:
ð8Þ
This equation means a helical motion around the z-direction. The center of the helical motion is accelerated upward. 2.4. Design study of the field terminator
Beam defining aperture plate Region I E=0 Bz
z y
LI large initial energy
x
small initial energy
Detector array Region II Ez LII Field terminator Region III Ex
VR
LIII
Sample Fig. 3. (a) Trajectory of a primary beamlet. An ideal field with a perfect uniformity and no fringing is assumed. (b) Secondary electron motions. Helical motion and deflection in the y-direction are convoluted. A secondary electron with the large initial energy is less deflected than a secondary electron with low initial energy.
The detection rate of the secondary electron is essential for high throughput. The size and the layout of the through-holes of the field terminator should be designed so that majority of the secondary electrons emitted from the sample surface hit the corresponding detection area of the detector array. Needless to say, a larger through-hole gives a higher detection rate; however, we need to consider the separation of the primary beams, which determines the number of the primary beamlets per unit area. At present, this is designed to be 250 lm. If the diameter of the through-holes is larger than this, a further separation will be needed, and the throughput will be decreased. In Section 3, the necessary size of the through-holes of the field terminator will be estimated from the viewpoint of the secondary electrons broadening. In addition, aberrations of the primary beamlets should also be considered. The field distribution we assumed in Fig. 3 was ideal, i.e., completely uniform without fringing at the through-holes. In practical, however, whenever a voltage is applied to an electrode with a through-hole, the field distribution at the edge of the through-hole and its surrounding region will have a fringing field. In general, a larger through-hole yields a larger fringing field. As a result of the fringing field, trajectories of the primary beamlets will be affected, and aberrations, which degrade the resolution, will
1789
S. Tanimoto et al. / Microelectronic Engineering 85 (2008) 1786–1791
3.2. Chromatic variation of deflection
Ex
From Eqs. (6) and (7), we obtain the deflection of the center of the helical motion d as follows:
Bz
d ¼ Ex LI =Bz v0z :
Dy Deflection
y x
z
Dx
Fig. 4. Helical motions of the secondary electrons emitted toward the +x, +y, x, and y-directions. Meanwhile, each center of the helical motion moves toward the –y-direction, because of the deflection.
occur. In Section 4, the aberrations of the primary beamlets caused by the fringing field will be calculated as a function of the throughhole diameter. Finally, on the basis of these calculations, two types of the field terminator will be proposed in Section 5. 3. Calculation of secondary electrons broadening 3.1. Dispersion caused by the helical motion The right-hand side of the Eq. (6) indicates that the radius of the helical motion depends on the magnetic field strength Bz, electric field strength Ex, and velocity and direction of the secondary electron at the sample surface. Fig. 4 illustrates the helical motions of the secondary electrons emitted toward the +x, +y, x, and y directions. Dx and Dy, the dispersions of the secondary electrons in the x and y-directions, which are defined in Fig. 4, are given by
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi v 2 E =B 2 2 0x x z Dx ¼ þ v20x þ ðEx =Bz Þ2 ; 2¼
x
Dy ¼
x
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 v0y þ Ex =Bz
x
x
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi v0y Ex =Bz 2 v0y þ ð Þ ¼ :
x
ð9Þ
x
For estimation, the secondary electron energy at the sample surface was assumed to be 10 eV at most. This is generally the worst-case value although the energy distribution of secondary electron depends on the sample properties. The secondary electron emission angle was assumed to be 45°. The calculated values of Dx and Dy are shown in Fig. 5. It indicates that the dispersions in both directions are around 150 lm with the secondary electron energy of 10 eV, although Dx is slightly dependent on the transverse field strength.
This means that the deflection is inversely proportional to the vertical velocity at the surface of the sample. In other words, a secondary pffiffiffiffiffiffi electron with the initial energy of 10 eV will be 1= 10times less deflected than a secondary electron with the initial energy of 1 eV. This chromatic variation of deflection causes a dispersion of the secondary electron distribution. We assumed that the secondary electron velocity has only the z-component for the worst-case estimation and calculated the deflection as a function of transverse electric field strength in Fig. 6. We will calculate the necessary through-hole size by using this graph in Section 5. 4. Numerical calculation of aberration of primary beamlets As mentioned in Section 2, each of the through-holes of the field terminator makes a fringing field. The first effect of the fringing field is the lens effect. It is, however, negligible, because the field terminator is placed at a conjugate image plane in our system. The second effect of the fringing field is aberrations caused by the combination of the lens effect itself and an asymmetric field distribution, which comes from the transverse field formed by the deflector. Hence, astigmatism and coma aberrations are to be considered when designing the field terminator. We set the goal of the aberrations to be as small as 10 nm when the primary beam lands on the sample with a half angle of 10 mrad. We calculated the astigmatism and coma aberrations using a simulation program, CO-3D (provided by MEBS). For the sake of simplicity, we assumed only one through-hole on the field terminator. Fig. 7 shows the aberrations as a function of the diameter of the through-hole. The coma aberration is almost constant and always small. On the contrary, the astigmatic aberration grows significantly as the through-hole gets large. In order to keep the aberration as small as 10 nm, the diameter of the through-hole should be smaller than 1250 lm. 5. Proposed designs 5.1. Shared through-hole First, we propose the simplest case, where the field terminator has a single through-hole for one primary beamlet. i.e., a primary beamlet and the secondary electrons stimulated by the primary beamlet share a single through-hole like shown in Fig. 2. In this case, each through-hole should be large enough so that the secondary
175
175 150 125
10 eV
100 75
Dx [μm]
Dx [μm]
150 125
5 eV
50 25 0
ð10Þ
10
20 30 40 E x [V/mm]
100 75
5 eV
50 25
1 eV
0
10 eV
50
0
1 eV
0
10
20 30 E x [V/mm]
40
50
Fig. 5. Dispersions of the secondary electrons in the x and y-direction. The secondary electron emission angle was assumed to be 45°.
1790
S. Tanimoto et al. / Microelectronic Engineering 85 (2008) 1786–1791
700
1 eV
Dx [μm]
600 47 0 μm
500
5 eV
Secondary electrons
400 300
10 eV
200
E0 = 1 eV: Dy = 50 μm E0 = 10 eV : Dy = 150 μm
15 0 μm
470 μm 150 μm
100 0
0
10
20 30 E x [V/mm]
40
Detector through-hole (φ 150 μm)
50
Fig. 6. Deflection in the y-direction as a function of transverse electric field strength. The secondary electron velocity was assumed to have only the zcomponent for the worst-case estimation.
Minimum through-hole for field terminator (φ 990 μm)
Aberrations [nm]
100.000
Fig. 8. Necessary size of the through-hole when a primary beamlet and the secondary electrons stimulated by the primary beamlet share a single through-hole. Deflections of 470 lm and 150 lm are given to the secondary electrons with initial energy (E0) of 1 eV and 10 eV respectively.
astigmatism
10.000 1.000
coma
0.100
600 0.010 0.001
400 0
500
1000
1500
2000
200
Fig. 7. Astigmatic and coma aberrations as a function of the diameter of the through-hole. A transverse field for deflection was assumed to be 20 V/mm. The half angle when the primary beam lands on the sample was assumed to be 10 mrad.
Y [μm]
Through-holediameter [μm]
0 -200
electrons can go through it and be swept to the corresponding detection area of the detector array. We now calculate the necessary through-hole size. Fig. 5 has shown that Dy, the dispersion caused by the helical motion, is 150 lm for secondary electrons with the initial energy of 10 eV. Therefore, deflection of at least 150 lm is needed for secondary electrons with the initial energy of 10 eV, because the diameter of the through-hole of our detector is 150 lm. This indicates that, as shown in Fig. 6, a deflection of 470 lm should be given to the secondary electrons with the initial energy of 1 eV, which has Dy of 50 lm. In total, as shown in Fig 8 the radius of at least 990 lm is necessary for the through-hole of the field terminator. The estimation above might be rough, because an ideal field with perfect uniformity and no fringing at the through-hole is assumed. So we numerically simulated the trajectories of the secondary electrons when the field terminator has a through-hole of 1000 lm in diameter by using CO-3D. Fig. 9 shows the distribution of the secondary electrons at the surface of the detector. The difference of the deflection direction from Fig. 8 stems from the fringing field at the through-hole. Using this result, together with a typical energy spectrum of the secondary electron [7] and Lambertian angular distribution, the detection rate was calculated and found to be 99.7%. The ratio of the secondary electrons which do not pass through the through-hole of the field terminator is 0.3%. The ratio of the secondary electrons which pass through the through-hole of the detector is less than 0.1%. On the other hand, according to Fig. 7, the astigmatism and coma aberrations are 4.6 nm and 0.4 nm, respectively, when the field terminator has a through-hole of 1000 lm in diameter. Overall, by choosing an appropriate diameter, for example, 1000 lm, sufficient detection rate of the secondary electrons and acceptably
-400 -600 -600 -400 -200
0 200 X [μm]
400
600
Fig. 9. A scatter plot of the secondary electrons at the detector surface. The solid and dotted circles indicate the through-hole of the field terminator and detector, respectively.
small aberrations can be obtained; nevertheless, the separation of the primary beamlets should be much larger than 250 lm, the separation of our detector array at this moment. 5.2. Separate through-hole Second, in order to decrease the separation of the primary beamlets and increase the prospects for high throughput, we propose a more complex layout of the through-holes for the field terminator as shown in Fig. 10. In this case, a primary beamlet and the secondary electrons stimulated by the primary beamlet do not share a through-hole anymore. Through-holes for the primary beamlets are lined up one-dimensionally. The slots for the secondary electrons are lined up, for enhancing symmetry, on both side of the line of the through-holes. The diameter of a through-hole is 150 lm, which maintains the small aberrations. A slot is 150 lm wide and 2000 lm long. The separation between a through-hole and slot is 300 lm. With this layout, we simulated the trajectories of the secondary electrons and the aberrations of the primary beamlet. A scatter plot of the secondary electrons at the corresponding detection area of
S. Tanimoto et al. / Microelectronic Engineering 85 (2008) 1786–1791
Holes for primary beamlets
Primary beamlet
Secondary electrons
( Φ 150 μm)
Slots for secondary electrons (150 μm
300 μm
1800 μm)
250 μ m
z
y x
100 μm/div
Fig. 10. A layout of the field terminator which has a through-hole exclusively for a primary beamlet and an extra slot for the secondary electrons, per primary beamlet. A scatter plot of the secondary electrons at the corresponding detection area of the detector array is shown in the right side.
the detector array is shown in the right side of the Fig. 10. The detection rate is 95.0%. On the other hand, the astigmatism aberration is 9.7 nm and the coma aberration is 3.9 nm. Although these values are slightly worse than those in the case of the shared through-hole, they are still acceptable and, what is more, the separation of the primary beamlet of 250 lm can be achieved with this layout. 6. Conclusion A distributed axis, fixed-aperture (DIFA) system, which generates multiple primary beamlets and focuses them simultaneously onto the sample by applying a uniform axial magnetic field, has a desirable property that the total current of the electron beam can be increased without the growth of Coulomb blurring. The secondary electron detection scheme for this system consists of a monolithic PIN-diode-based multi-channel detector array, a field terminator, and an electrostatic deflector. The electrostatic
1791
deflector deflects the electron beams and a bias applied between the field terminator and detector array accelerates them so that they hit the detection area of the corresponding channel of the detector array. The design of the field terminator was studied from the viewpoint of the detection rate, separation of the primary beamlets and aberrations. The dispersion of the secondary electrons in an ideal field distribution was analytically calculated and aberrations are numerically simulated. Two types of the field terminator are proposed on the basis of these calculations. One has a single through-hole, which is shared by a primary beamlet and the secondary electrons stimulated by the primary beamlet, per primary beamlet. Simulations reveal that this type of field terminator achieves a secondary electron detection rate of 99.7% and aberrations smaller than 4.6 nm, but does not enable the separation of the primary beamlet smaller than 1000 lm. The other type has a through-hole exclusively for a primary beamlet and an extra slot for the secondary electrons, per primary beamlet. It will achieve a secondary electron detection rate of 95.0%, aberrations smaller than 9.7 nm. Furthermore, it also enables the separation of the primary beamlet as small as 250 lm, the separation of our detector array at this moment. Acknowledgement This work was partly supported by DARPA Advanced Lithography Program. References [1] T.R. Groves, R.A. Kendall, J. Vac. Sci. Technol. B 16 (1998) 3168. [2] D.S. Pickard, C. Campbell, T. Crane, L.J. Cruz-Rivera, A. Davenport, W.D. Meisburger, R.F.W. Pease, T.R. Groves, J. Vac. Sci. Technol. B 20 (2002) 2662. [3] D.S. Pickard, T.R. Groves, W.D. Meisburger, T. Crane, R.F. Pease, J. Vac. Sci. Technol. B21 (2003) 2834. [4] C. Kenney, S. Parker, IEEE Trans. Nucl. Sci. 46 (4) (1999) 1224. [5] D.S. Pickard, C. Kenney, S. Tanimoto, T. Crane, T. Groves, R.F.W. Pease, J. Vac. Sci. Technol. B25 (2007) 2277. [6] H.P. Kuo, T.R. Grove, J. Vac. Sci. Technol. B 1 (1983) 1316. [7] D.C. Joy, Monte Carlo Modeling for Electron Microscopy and Microanalysis, Oxford University Press, Oxford, UK, 1995.
Contents lists available at ScienceDirect
Microelectronic Engineering journal homepage: www.elsevier.com/locate/mee
Secondary electron detection for distributed axis electron beam systems S. Tanimoto a,*, D.S. Pickard b, C. Kenney c, R.F.W. Pease d a
Hitachi, Ltd., Central Research Laboratory, Kokubunji, Japan National University of Singapore, Singapore, Singapore Molecular Biology Consortium, Chicago, USA d Stanford University, Stanford, USA b c
a r t i c l e
i n f o
Article history: Received 5 October 2007 Received in revised form 7 April 2008 Accepted 6 May 2008 Available online 16 June 2008 Keywords: Multi-electron-beam system Lithography Inspection DIFA DIVA Secondary electron detection
a b s t r a c t A secondary electron detection scheme for the distributed axis, fixed-aperture system is described. It employs a multi-channel detector array with a through-hole for a primary beamlet on each channel, a field terminator installed between the detector array and sample, and a deflector forming a static transverse electric field between the field terminator and sample. These elements enable detection of the secondary electrons stimulated by the primary beamlet. In order to achieve a high detection rate, small separation of the primary beamlets, and small aberrations, the size and the layout of the through-holes of the field terminator are studied. The equation of motion in an ideal field distribution is analytically solved and the dispersion of the secondary electrons caused by the helical motion in an axial magnetic field and chromatic variation of deflection are calculated. Aberrations are calculated by using numerical simulation. On the basis of these calculations, two types of the field terminator are proposed. One has a single through-hole, which is shared by a primary beamlet and the secondary electrons stimulated by the primary beamlet, per primary beamlet. The other has a through-hole exclusively for a primary beamlet and an extra slot for the secondary electrons, per primary beamlet. Simulations reveal that the former achieves a secondary electron detection rate of 99.7% and aberrations smaller than 4.6 nm, but doesn’t enable the separation of the primary beamlet to be smaller than 1000 lm. In contrast, the latter achieves a secondary electron detection rate of 95.0%, aberrations smaller than 9.7 nm. Furthermore, it also enables the separation of the primary beamlet to be as small as 250 lm, the same as in our detector array at this moment. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction 1.1. System description of DIFA In semiconductor fabrication, electron beam systems have long played important parts in fields such as lithography, inspection and metrology, by virtue of its minute probe size. At the same time, however, by reason of shrinking feature dimensions and growing complexity of semiconductor devices, electron beam systems have always been required to have higher throughput. In any electron beam system, the beam current is one of the major factors to determine the throughput. On the other hand, in conventional single-beam systems, increasing the beam current would enlarge the beam blur due to the Coulomb repulsion force. Furthermore, under the limited brightness of cathodes available at present, increase of the beam current requires an increase in the convergence angle, which is accompanied by growth of aberration and eventual deterioration of the minuteness of the electron beam. * Corresponding author. Tel.: +81 42 323 1111; fax: +81 42 327 7706. E-mail address: [email protected] (S. Tanimoto). 0167-9317/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2008.05.021
A distributed axis, fixed-aperture (DIFA) system has been proposed to overcome this throughput limit [1,2], and the resolution better than 50 nm has already been demonstrated by using a test bed [3]. In this system, primary electron beamlets emitted from a photocathode are distributed in a linear array and focused onto the sample simultaneously by a uniform axial magnetic field, which immerses the whole system. Since the primary beamlets remain separate, a significant increase in total current without the increase in Coulomb blurring is enabled. 1.2. Monolithic multi-channel electron detector As with other multiple electron beam systems, secondary electron detection is one of the key challenges for this method. In order to meet this challenge, a monolithic PIN-diode-based multi-channel detector array, shown in Fig. 1, has been investigated. Techniques developed for the radiation detector in high energy physics [4] were applied to this detector array. The electrodes, in a linear array with a pitch of 250 lm, detect the signals generated by the secondary electrons which collide with the other side of the detector. Each detection area has a through-hole, etched by the
S. Tanimoto et al. / Microelectronic Engineering 85 (2008) 1786–1791
1787
Fig. 1. (a) Micrograph of the PIN-diode-based detector array and (b) enlargement of the through-hole.
Bosch process, to enable transmittance of a primary beamlet. Each through-hole is 150 lm in diameter. We have already demonstrated the capability of parallel detection of secondary electrons stimulated by multiple primary beamlets, as well as a modest internal amplification and fast response time [5].
2. Secondary electron detection scheme using the monolithic multi-channel electron detector 2.1. Configuration of the detection scheme In DIFA, a photocathode illuminates a beam defining aperture plate and forms multiple primary beamlets, which are eventually focused onto the sample at a magnification of unity by a uniform axial magnetic field (Fig. 2). A transverse field formed by a deflector (not shown in Fig. 2) between the beam defining aperture plate
and detector array, deflects all primary beamlets one dimensionally in concert. The sample is scanned making use of the deflection together with the sample stage motion. The length of the deflector is adjusted so that the angle between the primary beamlets and the detector is a right angle and aberrations caused by the deflection are minimized [6]. An upper limit of the scan width to keep aberrations caused by the deflection field along with the fringing field at the through-hole is a remaining issue. A bias VR is applied between the detector array and the field terminator. This bias reduces the landing energy of the primary beamlets in order to decrease the damage to the sample and/or enhance the contrast of the image. At the same time, it increases the detector gain by accelerating the secondary electrons. The region between the field terminator and sample is free of an axial electric field, because the field terminator is electrically connected to the sample to suppress the axial field, i.e., accelerating field for secondary electrons. The deflector, which generates a static transverse
Fig. 2. Secondary electron detection scheme. Note that an axial uniform magnetic field immerses the whole system.
1788
S. Tanimoto et al. / Microelectronic Engineering 85 (2008) 1786–1791
field between the field terminator and sample, deflects the secondary electrons sufficiently before they are accelerated so that they hit the detection area of the detector. In contrast to the secondary electrons, the deflection of the primary beamlets is smaller because of their large energy. 2.2. Behaviour of the primary beamlet In order to minimize unnecessary lens effect for the primary beamlets, the detector array, field terminator and sample should be placed at conjugate image planes with the beam defining aperture plate for the primary beamlets as shown in Fig. 3a. Thus, LII, the axial length of the region II and LI, the axial length of the region I should be equal to the multiple of the distance which a primary beamlet travels during one cyclotron orbit. For the sake of simplicity, we assume that a primary beamlet completes only one cyclotron orbit when it travels through each of the region I, II and III. In region I, the primary beamlet travels with a constant velocity. Then LI is given by
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi LI ¼ p ð8mV 0 =eB2z Þ;
ð1Þ
where eV0 is the kinetic energies of a primary beamlet at the beam defining aperture plate and the detector. In the region II, the primary beamlet is decelerated by the bias VR. The acceleration is given by
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi aII ¼ ð 2eV 1 =m 2eV 0 =mÞ=s;
ð2Þ
where eVI = e(V0 – VR) is the kinetic energies of a primary beamlet at the field ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pterminator. s 2pm=eBz is the cyclotron period. Then LII is given by
LII ¼
1 aII s2 þ 2
rffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffi pffiffiffiffiffiffi 2eV 0 s ¼ p 2m=eB2z ð V 0 þ V 1 Þ: m
ð3Þ
In region III, the primary beamlet travels with a constant velocity again. LIII is given by
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi LIII ¼ p ð8mV 1 =eB2z Þ:
ð4Þ
Throughout this paper we assume that Vo and V1 are 15 kV and 1 kV, respectively and that Bz is 0.2 T, which give LI, LII and LIII of 13.0 mm, 8.16 mm and 3.35 mm, respectively.
2.3. Motion of the secondary electrons Fig. 3b depicts the motion of a secondary electron in an ideal field with perfect uniformity and no fringing at the through-hole. Note that an axial uniform magnetic field immerses the whole system. In the region III, where the electrostatic field has only the xcomponent, the non relativistic equation of motion of a secondary electron is given by [6]
v_ x ¼ eðEx þ vy Bz Þ=m; v_ y ¼ evx Bz =m; v_ z ¼ 0:
ð5Þ
By assuming the initial conditions x(0) = y(0) = z(0) = 0 for position and vx ð0Þ ¼ v0x ,vy ð0Þ ¼ v0y , vz ð0Þ ¼ v0z for velocity, we obtain:
2 2 v0y þ Ex =Bz v0x Ex xþ þ y þ t x x Bz v 2 v þ E =B 2 0x 0y x z ¼ þ
x
x
ð6Þ
and
z ¼ v0z t:
ð7Þ
where x eBz =m ¼ cyclotron frequency. Eq. (6) shows that a secondary electron moves helically. On the other hand, the second part of the left-hand side of Eq. (6) and the Eq. (7) indicates that the center of the helical motion is deflected toward the –y-direction with a velocity of Ex =Bz , as an electron moves toward upward, i.e. to the +z-direction. Hence, the trajectory is interpreted as a convolution of a helical motion and deflection in the y-direction. In the region II, where the electrostatic field has only the z-component, the non relativistic equation of motion of a secondary electron is given by:
v_ x ¼ evy Bz =m; v_ y ¼ evx Bz =m; v_ z ¼ eEz =m:
ð8Þ
This equation means a helical motion around the z-direction. The center of the helical motion is accelerated upward. 2.4. Design study of the field terminator
Beam defining aperture plate Region I E=0 Bz
z y
LI large initial energy
x
small initial energy
Detector array Region II Ez LII Field terminator Region III Ex
VR
LIII
Sample Fig. 3. (a) Trajectory of a primary beamlet. An ideal field with a perfect uniformity and no fringing is assumed. (b) Secondary electron motions. Helical motion and deflection in the y-direction are convoluted. A secondary electron with the large initial energy is less deflected than a secondary electron with low initial energy.
The detection rate of the secondary electron is essential for high throughput. The size and the layout of the through-holes of the field terminator should be designed so that majority of the secondary electrons emitted from the sample surface hit the corresponding detection area of the detector array. Needless to say, a larger through-hole gives a higher detection rate; however, we need to consider the separation of the primary beams, which determines the number of the primary beamlets per unit area. At present, this is designed to be 250 lm. If the diameter of the through-holes is larger than this, a further separation will be needed, and the throughput will be decreased. In Section 3, the necessary size of the through-holes of the field terminator will be estimated from the viewpoint of the secondary electrons broadening. In addition, aberrations of the primary beamlets should also be considered. The field distribution we assumed in Fig. 3 was ideal, i.e., completely uniform without fringing at the through-holes. In practical, however, whenever a voltage is applied to an electrode with a through-hole, the field distribution at the edge of the through-hole and its surrounding region will have a fringing field. In general, a larger through-hole yields a larger fringing field. As a result of the fringing field, trajectories of the primary beamlets will be affected, and aberrations, which degrade the resolution, will
1789
S. Tanimoto et al. / Microelectronic Engineering 85 (2008) 1786–1791
3.2. Chromatic variation of deflection
Ex
From Eqs. (6) and (7), we obtain the deflection of the center of the helical motion d as follows:
Bz
d ¼ Ex LI =Bz v0z :
Dy Deflection
y x
z
Dx
Fig. 4. Helical motions of the secondary electrons emitted toward the +x, +y, x, and y-directions. Meanwhile, each center of the helical motion moves toward the –y-direction, because of the deflection.
occur. In Section 4, the aberrations of the primary beamlets caused by the fringing field will be calculated as a function of the throughhole diameter. Finally, on the basis of these calculations, two types of the field terminator will be proposed in Section 5. 3. Calculation of secondary electrons broadening 3.1. Dispersion caused by the helical motion The right-hand side of the Eq. (6) indicates that the radius of the helical motion depends on the magnetic field strength Bz, electric field strength Ex, and velocity and direction of the secondary electron at the sample surface. Fig. 4 illustrates the helical motions of the secondary electrons emitted toward the +x, +y, x, and y directions. Dx and Dy, the dispersions of the secondary electrons in the x and y-directions, which are defined in Fig. 4, are given by
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi v 2 E =B 2 2 0x x z Dx ¼ þ v20x þ ðEx =Bz Þ2 ; 2¼
x
Dy ¼
x
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 v0y þ Ex =Bz
x
x
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi v0y Ex =Bz 2 v0y þ ð Þ ¼ :
x
ð9Þ
x
For estimation, the secondary electron energy at the sample surface was assumed to be 10 eV at most. This is generally the worst-case value although the energy distribution of secondary electron depends on the sample properties. The secondary electron emission angle was assumed to be 45°. The calculated values of Dx and Dy are shown in Fig. 5. It indicates that the dispersions in both directions are around 150 lm with the secondary electron energy of 10 eV, although Dx is slightly dependent on the transverse field strength.
This means that the deflection is inversely proportional to the vertical velocity at the surface of the sample. In other words, a secondary pffiffiffiffiffiffi electron with the initial energy of 10 eV will be 1= 10times less deflected than a secondary electron with the initial energy of 1 eV. This chromatic variation of deflection causes a dispersion of the secondary electron distribution. We assumed that the secondary electron velocity has only the z-component for the worst-case estimation and calculated the deflection as a function of transverse electric field strength in Fig. 6. We will calculate the necessary through-hole size by using this graph in Section 5. 4. Numerical calculation of aberration of primary beamlets As mentioned in Section 2, each of the through-holes of the field terminator makes a fringing field. The first effect of the fringing field is the lens effect. It is, however, negligible, because the field terminator is placed at a conjugate image plane in our system. The second effect of the fringing field is aberrations caused by the combination of the lens effect itself and an asymmetric field distribution, which comes from the transverse field formed by the deflector. Hence, astigmatism and coma aberrations are to be considered when designing the field terminator. We set the goal of the aberrations to be as small as 10 nm when the primary beam lands on the sample with a half angle of 10 mrad. We calculated the astigmatism and coma aberrations using a simulation program, CO-3D (provided by MEBS). For the sake of simplicity, we assumed only one through-hole on the field terminator. Fig. 7 shows the aberrations as a function of the diameter of the through-hole. The coma aberration is almost constant and always small. On the contrary, the astigmatic aberration grows significantly as the through-hole gets large. In order to keep the aberration as small as 10 nm, the diameter of the through-hole should be smaller than 1250 lm. 5. Proposed designs 5.1. Shared through-hole First, we propose the simplest case, where the field terminator has a single through-hole for one primary beamlet. i.e., a primary beamlet and the secondary electrons stimulated by the primary beamlet share a single through-hole like shown in Fig. 2. In this case, each through-hole should be large enough so that the secondary
175
175 150 125
10 eV
100 75
Dx [μm]
Dx [μm]
150 125
5 eV
50 25 0
ð10Þ
10
20 30 40 E x [V/mm]
100 75
5 eV
50 25
1 eV
0
10 eV
50
0
1 eV
0
10
20 30 E x [V/mm]
40
50
Fig. 5. Dispersions of the secondary electrons in the x and y-direction. The secondary electron emission angle was assumed to be 45°.
1790
S. Tanimoto et al. / Microelectronic Engineering 85 (2008) 1786–1791
700
1 eV
Dx [μm]
600 47 0 μm
500
5 eV
Secondary electrons
400 300
10 eV
200
E0 = 1 eV: Dy = 50 μm E0 = 10 eV : Dy = 150 μm
15 0 μm
470 μm 150 μm
100 0
0
10
20 30 E x [V/mm]
40
Detector through-hole (φ 150 μm)
50
Fig. 6. Deflection in the y-direction as a function of transverse electric field strength. The secondary electron velocity was assumed to have only the zcomponent for the worst-case estimation.
Minimum through-hole for field terminator (φ 990 μm)
Aberrations [nm]
100.000
Fig. 8. Necessary size of the through-hole when a primary beamlet and the secondary electrons stimulated by the primary beamlet share a single through-hole. Deflections of 470 lm and 150 lm are given to the secondary electrons with initial energy (E0) of 1 eV and 10 eV respectively.
astigmatism
10.000 1.000
coma
0.100
600 0.010 0.001
400 0
500
1000
1500
2000
200
Fig. 7. Astigmatic and coma aberrations as a function of the diameter of the through-hole. A transverse field for deflection was assumed to be 20 V/mm. The half angle when the primary beam lands on the sample was assumed to be 10 mrad.
Y [μm]
Through-holediameter [μm]
0 -200
electrons can go through it and be swept to the corresponding detection area of the detector array. We now calculate the necessary through-hole size. Fig. 5 has shown that Dy, the dispersion caused by the helical motion, is 150 lm for secondary electrons with the initial energy of 10 eV. Therefore, deflection of at least 150 lm is needed for secondary electrons with the initial energy of 10 eV, because the diameter of the through-hole of our detector is 150 lm. This indicates that, as shown in Fig. 6, a deflection of 470 lm should be given to the secondary electrons with the initial energy of 1 eV, which has Dy of 50 lm. In total, as shown in Fig 8 the radius of at least 990 lm is necessary for the through-hole of the field terminator. The estimation above might be rough, because an ideal field with perfect uniformity and no fringing at the through-hole is assumed. So we numerically simulated the trajectories of the secondary electrons when the field terminator has a through-hole of 1000 lm in diameter by using CO-3D. Fig. 9 shows the distribution of the secondary electrons at the surface of the detector. The difference of the deflection direction from Fig. 8 stems from the fringing field at the through-hole. Using this result, together with a typical energy spectrum of the secondary electron [7] and Lambertian angular distribution, the detection rate was calculated and found to be 99.7%. The ratio of the secondary electrons which do not pass through the through-hole of the field terminator is 0.3%. The ratio of the secondary electrons which pass through the through-hole of the detector is less than 0.1%. On the other hand, according to Fig. 7, the astigmatism and coma aberrations are 4.6 nm and 0.4 nm, respectively, when the field terminator has a through-hole of 1000 lm in diameter. Overall, by choosing an appropriate diameter, for example, 1000 lm, sufficient detection rate of the secondary electrons and acceptably
-400 -600 -600 -400 -200
0 200 X [μm]
400
600
Fig. 9. A scatter plot of the secondary electrons at the detector surface. The solid and dotted circles indicate the through-hole of the field terminator and detector, respectively.
small aberrations can be obtained; nevertheless, the separation of the primary beamlets should be much larger than 250 lm, the separation of our detector array at this moment. 5.2. Separate through-hole Second, in order to decrease the separation of the primary beamlets and increase the prospects for high throughput, we propose a more complex layout of the through-holes for the field terminator as shown in Fig. 10. In this case, a primary beamlet and the secondary electrons stimulated by the primary beamlet do not share a through-hole anymore. Through-holes for the primary beamlets are lined up one-dimensionally. The slots for the secondary electrons are lined up, for enhancing symmetry, on both side of the line of the through-holes. The diameter of a through-hole is 150 lm, which maintains the small aberrations. A slot is 150 lm wide and 2000 lm long. The separation between a through-hole and slot is 300 lm. With this layout, we simulated the trajectories of the secondary electrons and the aberrations of the primary beamlet. A scatter plot of the secondary electrons at the corresponding detection area of
S. Tanimoto et al. / Microelectronic Engineering 85 (2008) 1786–1791
Holes for primary beamlets
Primary beamlet
Secondary electrons
( Φ 150 μm)
Slots for secondary electrons (150 μm
300 μm
1800 μm)
250 μ m
z
y x
100 μm/div
Fig. 10. A layout of the field terminator which has a through-hole exclusively for a primary beamlet and an extra slot for the secondary electrons, per primary beamlet. A scatter plot of the secondary electrons at the corresponding detection area of the detector array is shown in the right side.
the detector array is shown in the right side of the Fig. 10. The detection rate is 95.0%. On the other hand, the astigmatism aberration is 9.7 nm and the coma aberration is 3.9 nm. Although these values are slightly worse than those in the case of the shared through-hole, they are still acceptable and, what is more, the separation of the primary beamlet of 250 lm can be achieved with this layout. 6. Conclusion A distributed axis, fixed-aperture (DIFA) system, which generates multiple primary beamlets and focuses them simultaneously onto the sample by applying a uniform axial magnetic field, has a desirable property that the total current of the electron beam can be increased without the growth of Coulomb blurring. The secondary electron detection scheme for this system consists of a monolithic PIN-diode-based multi-channel detector array, a field terminator, and an electrostatic deflector. The electrostatic
1791
deflector deflects the electron beams and a bias applied between the field terminator and detector array accelerates them so that they hit the detection area of the corresponding channel of the detector array. The design of the field terminator was studied from the viewpoint of the detection rate, separation of the primary beamlets and aberrations. The dispersion of the secondary electrons in an ideal field distribution was analytically calculated and aberrations are numerically simulated. Two types of the field terminator are proposed on the basis of these calculations. One has a single through-hole, which is shared by a primary beamlet and the secondary electrons stimulated by the primary beamlet, per primary beamlet. Simulations reveal that this type of field terminator achieves a secondary electron detection rate of 99.7% and aberrations smaller than 4.6 nm, but does not enable the separation of the primary beamlet smaller than 1000 lm. The other type has a through-hole exclusively for a primary beamlet and an extra slot for the secondary electrons, per primary beamlet. It will achieve a secondary electron detection rate of 95.0%, aberrations smaller than 9.7 nm. Furthermore, it also enables the separation of the primary beamlet as small as 250 lm, the separation of our detector array at this moment. Acknowledgement This work was partly supported by DARPA Advanced Lithography Program. References [1] T.R. Groves, R.A. Kendall, J. Vac. Sci. Technol. B 16 (1998) 3168. [2] D.S. Pickard, C. Campbell, T. Crane, L.J. Cruz-Rivera, A. Davenport, W.D. Meisburger, R.F.W. Pease, T.R. Groves, J. Vac. Sci. Technol. B 20 (2002) 2662. [3] D.S. Pickard, T.R. Groves, W.D. Meisburger, T. Crane, R.F. Pease, J. Vac. Sci. Technol. B21 (2003) 2834. [4] C. Kenney, S. Parker, IEEE Trans. Nucl. Sci. 46 (4) (1999) 1224. [5] D.S. Pickard, C. Kenney, S. Tanimoto, T. Crane, T. Groves, R.F.W. Pease, J. Vac. Sci. Technol. B25 (2007) 2277. [6] H.P. Kuo, T.R. Grove, J. Vac. Sci. Technol. B 1 (1983) 1316. [7] D.C. Joy, Monte Carlo Modeling for Electron Microscopy and Microanalysis, Oxford University Press, Oxford, UK, 1995.