electron, e0 = 8.8543 x 10 -]2 F m -] is the dielectric con- stant, E is the electron energy, Zeri is the effective atomic number of the ith layer of the target, and.
ELSEVIER
Thin Solid Films, 251 (1994) 67-71
Monte Carlo simulation of electron-beam exposure distributions in the resist on structures with high-To superconducting thin films J. Georgiev, G. Mladenov, D. Ivanov Institute of Electronics, Bulgarian Academy of Sciences, Tzarigradsko shousse 72, 1784 Sofia, Bulgaria Received 17 January 1994; accepted 5 May 1994
Keywords: Electron scattering; Electronic devices; Superconductivity
Abstract
The spatial distributions of absorbed electron energy density in PMMA on structures incorporating YBa2Cu307 high-Tc superconducting thin films deposited on different substrates were determined using a Monte Carlo simulation (MCS), which takes into account the exact boundary conditions on interfaces between different layers of the target. The ability of our Monte Carlo program to accurately simulate the radial exposure distributions was demonstrated. The effects of substrate material (SrTiO 3 and MgO), beam energy (40 and 80 x 10-16 J) and high-temperature superconducting (HTS) film thickness (100 and 300 nm) on these distributions were investigated. The distributions obtained in this work can further be employed in a proximity effect correction algorithm as well as in a proper development model.
1. Introduction
In 1986 Bednorz and Muller [1] reported on a hightemperature superconducting (HTS) system B a - L a C u - O and some months later another HTS material was discovered, namely Y - B a - C u - O [2]. The transition temperature Tc of the latter material is about 90 K, which supports a superconductor action at liquidnitrogen temperatures (77 K). Since that time the field of deposition and application of high-To thin films has been the object of intensive investigation. Improvements to the capabilities of high-T¢ superconductor electronics depend on the development of versatile lithographic and patterning processes, which allow delineation of submicron and even nanogeometries with proper dimensional control and at the same time do not degrade the characteristics of the HTS film. Electron beam lithography (EBL) is commonly applied for creating patterns of such small dimensions. It is, however, associated with some drawbacks which affect its accuracy and applicability. The main of them is the so-called 'proximity effect' [3]. This name is usually used to describe effects caused by the non0040-6090/94•$7.00 © 1994 - - Elsevier Science S.A. All rights reserved SSDI 0040-6090(94)06189-R
uniform electron exposure received in the resist due to distributions of forward-scattered and backscattered electrons initiated by incident electrons. Thus, the effect of a finely focused electron beam is not just in the exposure of the resist within the regions that are to be exposed, but also in the undesirable exposure in adjacent regions. The proximity effect is quantitatively described by the spatial distribution of absorbed electron energy density in the resist. Exact data for this distribution are needed for the proper correction for proximity effect and successful application of EBL. Many experiments have been performed and various theoretical models, both analytical and computational (Monte Carlo simulations), have been utilized in order to evaluate the spatial distribution of energy deposition by an electron beam in solid targets. Nevertheless, the Monte Carlo technique is most widely used for this purpose [4-12]. The aim of this work is to study the spatial distribution o f the absorbed electron energy density in the resist on targets incorporating YBa2Cu30 7 HTS thin film deposited on different substrates such as SrTiO 3 and MgO (Fig. 1) using Monte Carlo simulation.
J. Georgiev et al. / Thin Solid Films, 251 (1994) 67-71
68 El ect ron
10 2`
Beam 125nm
f"E
PMt,4A
-x
HTS
10 EXPERIMENT/16/ •,.'-'_.'.." MONTE CARLO SIMULATION Eo = 8 0 x 1 0 - ' " d
thin film 10 -1
Substrote
0-
SrTiO3iMgO
I0-'" N
-'i
Fig. I. Geometry o f the investigated systems.
I0 -L Z 1 0 -4
2.
Monte
Carlo
simulation
In order to analyse our multilayer systems, an MCS program was developed. It is based on both a single scattering theory and a continuous slowing-down approximation. The screened Rutherford formula is used for the total elastic scattering cross-section: e4Zeri(Zefi + 1)
(1)
at = 4nsoZE2,8(# + I)
where e = 1.602 × 10 -19 C is the electric charge of an electron, e0 = 8.8543 x 10 -]2 F m -] is the dielectric constant, E is the electron energy, Zeri is the effective atomic number of the ith layer of the target, and / 1 12/~Z 1/3\2
# = 0 . 2 5 1 ~") " eli
(2)
is the screening parameter of Nigam et al. [13], where h = h/2n = 1.054 43 x 10 -34 J s is Planck's constant, p is the momentum of an electron, and a 0 = 0.530 x 10-]° m is the radius of the hydrogen atom. For the energy loss between single elastic scattering events the Bethe law is assumed [14]: (27~e4piZefil, {1.166E'~
-dE
dx
-
t
-
-
-
In
A.,i ) t
-
-
)
(3)
where p~, A~F~and Jer~ are the mass density, the effective atomic weight, and the effective mean ionization potential of the ith layer of the target respectively. As is evident from Eq. (3), the logarithmic term becomes negative below E = Jots/1.166. To prevent this failure we use the parabolic extrapolation of ( d E / d x ) -] derived by Rao-Sahib and Wittry [ 15] for E < 6.338Jerk:
--dE -
-
dx
-
2ne4NA z e f i p i/Aef i 1.26(EJen) 112
(5)
where N A is Avogadro's number. Hence, using this extrapolation, the trajectory of each electron can be followed until its energy slows down to 80 x 10 - ] 9 J instead of the value of 800 x l 0 - ] 9 J which is commonly used as cut-off energy. In the cases when the electron leaves the target as a backscattered or a
1 0 -B
0
. . . . . . . .
5' .........
1'o.........
LATERAL DISTANCE
l's . . . .
R(jarn)
Fig. 2. Comparison of the radial distributions of absorbed energy density on Si substrate obtained from MCS, and experimentally by Rishton and Kern [16], E 0 = 80 x 10 -16 J.
transmitted particle or its residual range in the substrate is not sufficient to reach the resist layer again, the calculation is terminated. To take into account the differences in both the scattering and the stopping properties at the interfaces between different layers of the target, a procedure for recalculation of the free path length [9] and of the energy loss is included. In order to evaluate the accuracy of our MCS program, the simulated radial distribution of the absorbed energy density was compared directly with the normalized point exposure distribution obtained experimentally by Rishton and Kern [16]. As is seen in Fig. 2 the agreement is rather good except in the region between 0.1 and 0.8 pm range. The disagreement in this region may be due to one or more of the following reasons. (1) Simulation was performed for a zero-width 6 function, while in the experiment a real electron beam with a certain current density distribution has been used. This distribution can be taken into account by convolving a certain mathematical function (e.g. Gaussian function) representing it with the spatial distribution of absorbed energy density obtained for a zero-width 6 function. (2) Low-level, long-range tails in the beam distribution, which may cause an additional exposure of the resist, as mentioned by Rishton and Kern [16], but cannot be measured and taken into account. (3) Fast secondary electrons (E > 1.6 x 10 -16 J). The effect of these electrons on spatial distribution of absorbed energy density can be evaluated and taken into account theoretically by involving a model of generation of such electrons, e.g. the so-called knock-on model [8], and this is one of the directions for further
J. Georgiev et al. / Thin Solid Films, 251 (1994) 67-71
development of our program. However, the disagreement between the experimental and the simulated distributions of absorbed energy density discussed above is only in the region attributed to the forward-scattered electrons. Since the aim of this work is to study the effect of YBa2Cu307 HTS thin film as well as of SrTiO3 and MgO substrates on the spatial distribution of the absorbed energy density in the resist, we are interested mainly in the exposure caused by the backscattered electrons, where the agreement is very good. Thus the distributions obtained from MCS may be used as a reliable basis for the evaluation of actual distributions.
69
10 m ] -e..'-'.- 125mn -__
125nm
~"~ lO ' l E
F.~ == 40x10 -tl J
II, 1 ,
N
..:10 O
,2 10 10
3. Results and discussion
\
1
(a) The variables that were investigated in this work are the substrate material (SrTiO3 and MgO), the electron beam energy (40 and 80 x 10 -16 J) and the HTS film thickness (100 and 300nm). Calculations were performed on an IBM 4381 machine with 30 000 electron trajectories for each simulation. All distributions were obtained for a zero-width (5 function. For the generation of random numbers the IBM uniform random number generator RNDM2 of the CERN Computer Centre Program Library was used. It is a combined multiplicative congruential generator and shift register generator with a period of about 5 x 1018 numbers.
i
i
i
i
i
i
o
i
i
i
|
i
i
i
~
,,.~
1
|
i
I
i
i
i
I
I
2 4 LATERAL DISTANCE R(.um)
10 =1 10 ~
~...,~,, 12Snm 125nm • -'-'..,-, 125nm - - _ 125nm
10
PMMA~IOOnm YBa~Cu~O~/$rTiOs PMMA/3OOnrn YBa~u~)~/SrTiO= PMMA/.IOOnm YSa#Cu~).,/MgO PMMA~C3OOnmYBo=Cu~D.n;/MgO ~
.E
=
80x10 -II J
¢-~
¢o
3. I. Effect of substrate material Fig. 3 shows a comparison between radial distributions of the absorbed energy density in a 125 nm PMMA resist film on 100 and 300 nm HTS layers of YBA2Cu307 deposited on different substrates, namely SrTiO3 and MgO at two beam energies: 40 x 10-]6 J (a) and 80 x 10-16J (b). In this figure three regions are well seen with respect to the substrate material. The first one is in the peaks of the distributions and is usually attributed to the forward-scattered electrons. In this region there is almost no difference between the compared radial distributions. The second region is from the peaks to the crosspoints of the distributions. Here the energy deposited in the resist by the electrons, backscattered from the substrate of higher values of the effective atomic number Zer and the mass density p, i.e. from the SrTiO3 substrate, is greater than that deposited by the electrons backscattered from the MgO substrate. The third region is from the cross-points to the flanks of the distributions. Here the situation changes: the energy deposited in the resist on the MgO substrate is greater than in that on the SrTiO 3 one due to the longer trajectories of the electrons in the MgO substrate.
10 ' ;
~.~-,~,~~
I
0 (b)
I
I
I
I
I
..
i
i
i
I
I
I
i
I
I
I
I
I
I
I
I
I
5 10 LATERAL DISTANCE R ~ m )
Fig. 3. Radial distributions of the absorbed energy density in 125 n m P M M A resist film deposited on mentioned target systems: (a) Eo = 40 x 10-16 J and (b) E o = 80 x 10-16 J.
3.2. Effect of beam energy Fig. 4 compares the radial distributions of absorbed energy density for the two structures: 125 nm PMMA/ 100 nm YBazCU3OT/SrTiO3 (a), and 125 nm PMMA/ 300 nm YBazCu307/MgO (b) at two beam energies, 40 and 80 x 10-]6 J respectively. Again, three regions can be identified. In the first one--from the incident point to about 100nm--the peaks of distributions for 40 x 10 -16 J are higher than those for 80 × 10 - 1 6 J. This fact results from both the more efficient forward scattering and the higher energy loss in the resist at lower energies.
70
J. Georgiev et al. / Thin Solid Films, 251 (1994) 67-71
,o.]
The distributions in Fig. 4 show that the increase in the beam energy reduces the undesirable exposure by the backscattered electrons only to a certain distance from the incident point. Therefore, if the dimensions of the whole pattern to be created are greater than this distance, and the number, of the exposed pixels is large enough (depending on the dimensions of the pattern) it may appear that the proximity effect at a higher accelerating voltage is greater than at a lower one.
I0~ :::::
-- 4o.lo-I',
J
80x10-
J
10 s
lo lOS,
3.3. Effect of H T S thin film thickness
o ~..10 =" 10 1 i
O
(a)
i
,
i
i
i
i
i
i
I
i
i
i
i
i
5 LATERAL DISTANCE R(jJm)
i
i
I
10
I0'" 10
= 40xlO-l~
:::::
8oxlo-
J
. . ~ 1 0 e.
E •~ ' i 0
4.
10 o ~ . 1 0 =10
o
(b)
5
lo
LATERALDISTANCEROJrn)
From the comparison between the radial distributions of the absorbed energy density for different HTS thin film thicknesses, i.e. 100 and 300 nm, on the same substrate (either SrTiO3 or MgO) in Fig. 3, it is well seen that in the regions close to the incident point of the electron beam the distributions for the thicker HTS film are 'higher' due to the greater number of electrons backscattered from this film to the resist. In distant regions the values of the absorbed energy density for thinner HTS films are higher. A simple explanation for this effect is as follows. The electrons backscattered from the substrate at great distances from the point of incidence have already undergone multiple scattering at small angles and have lost a significant portion of their energy in the substrate. Thus a large number of these electrons are absorbed in the HTS thin film and the number is as greater as the film is thicker. There is another feature which is worth pointing out. The dependence of the spatial distributions of the absorbed energy density on the thickness of HTS film is stronger for the substrate of lower effective atomic number Z~r and mass density p (MgO) as well as for the lower beam energy (40 x 10-]6 J).
Fig. 4. Radial distributions of the absorbed energy density at 40 and 80x 10-t6J in: (a) 125nm PMMA/100nm YBa2Cu307/SrTiO3; (b) 125 nm PMMA/300 nm YBa2Cu307/MgO.
4. Conclusions
In the second r e g i o n - - f r o m 100nm to about 1.8 pm for SrTiO3 and to about 2.8 pm for M g O - - t h e value of the absorbed energy density is higher for E 0 ---40 × 1 0 - 1 6 J due to the greater number of electrons backscattered from the substrate to the resist, the more pronounced loss of their energy in the resist, and the shorter spread of the electrons in the substrate at lower energies. In the third r e g i o n - - f r o m the cross-points to the flanks of the distributions--the value of the absorbed energy density is higher for E0 = 80 × 10 -16 J due to the wider spread of electrons in the substrate at higher accelerating voltages. This wider spread leads to a much greater number of electrons backscattered from the substrate to the resist at large distances from the incident point.
The spatial distributions of energy density deposited by an electron beam in the resist on SrTiO3 and MgO substrates with YBa2Cu307 thin films on them were obtained by means of Monte Carlo simulation. The results show that the HTS thin film causes an additional backscattering of penetrating electrons in the regions close to the incident point of the electron beam. This effect is as greater as the film is thicker, as lighter as the substrate, as lower as the beam energy, and must be taken into account in order to create patterns of intended dimensions. The increase in the beam energy from 40 to 8 0 × 1 0 - 1 6 J reduces undesirable exposure by backscattered electrons only to a certain distance from the incident point, but causes a fogging exposure beyond this distance up to 8 - 9 pm for SrTiO3 substrate and to 12 gm for MgO substrate.
J. Georgiev et al. [ Thin Solid Films, 251 (1994) 67-71
The influence o f H T S film thickness u p o n the spatial distribution o f a b s o r b e d energy density is stronger for the substrate o f lower effective a t o m i c n u m b e r and mass density ( M g O ) as well as for the lower accelerating voltage (25 kV). The distributions obtained in this w o r k can be used to correct for the proximity effect or to simulate the profile development in the resist. Further studies are necessary to investigate the influence o f the resist thickness o n the energy density distributions, to determine the b e a m energy and the high-To superconducting film thickness at which this film no longer affects the scattering and the energy loss o f the penetrating electrons and to choose the analytical approximation o f radial distributions o f the absorbed energy density. A m o r e detailed study is n o w in progress.
Acknowledgements The authors would like to express their thanks to R. C h a k a l o v o f the Institute o f Electronics at the BAS for helpful discussion concerning the technology o f deposition o f H T S thin films, their properties and application.
71
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