Dependence of PMMA electron beam resist
sidewall shape on exposure dose and resist
thickness
Cite as: AIP Conference Proceedings 2411, 040001 (2021); https://doi.org/10.1063/5.0067068
Published Online: 02 November 2021
Robert Andok, Katia Vutova, Elena Koleva, et al.
AIP Conference Proceedings 2411, 040001 (2021); https://doi.org/10.1063/5.0067068
© 2021 Author(s).
2411, 040001
Dependence of PMMA Electron Beam Resist Sidewall Shape
on Exposure Dose and Resist Thickness
Robert Andok1, Katia Vutova2, b), Elena Koleva2, 3,
Anna Bencurova1 and Ivan Kostic1, a)
1
2
Institute of Informatics, Slovak Academy of Sciences, Dubravska cesta 9, 845 07 Bratislava, Slovak Republic
Institute of Electronics, Bulgarian Academy of Sciences, 72 Tzarigradsko chaussee blvd., Sofia 1784, Bulgaria
3
University of Chemical Technology and Metallurgy, 8 Kliment Ohridski blvd., Sofia 1756, Bulgaria
a)
Corresponding author: ivan.kostic@savba.sk
b)
katia@van-computers.com
Abstract. The influence of electron beam lithography parameters (such as electron energy, resist thickness, the exposure
dose) on the resist sidewall shape (profile) was studied for the PMMA (polymethyl-methacrylate) positive resist. The
profile of the positive tone resist PMMA was investigated depending on varying exposure doses for the resist thicknesses
600 and 1300 nm, and electron energy 30 keV. Simulation results based on measurements along the resist profile depth
are presented and discussed. The results obtained contribute to the knowledge on electron scattering in resist/substrate in
electron beam lithography for the case of field emission cathode and Gaussian intensity distribution, and to the
development and approval of models for the prediction and precise control of resist profiles in thick PMMA layers for 3D
proximity effect simulation, the bilayer resist system, and the lift-off method.
INTRODUCTION
Electron beam lithography (EBL) is widely used in many research areas and very high resolution patterns in thin
high resolution electron beam resists can be fabricated down to a few nanometers [1, 2].
Besides, there are applications where thick electron beam resist is required, i.e. photonic elements, gray scale
lithography [3], etc. EBL in thick resist layer suffers from broadening of the energy deposition profile of the electron
beam inside the resist caused by electron scattering in the resist and the substrate, and the resolution becomes a
problem. Therefore, precise process control and proximity effect correction are important for achieving the desired
structures [4, 5]. Various methods are applied for the patterning using thick resist, e.g. bilayer/multilayer methods
[6], lift-off method [7], electroplating [8], etc. The calculation of the spatial distribution of electron energy
deposition density in the thick resist requires measurements of the sidewall shape (profile) variation with exposure
dose and the understanding 3D proximity effects in the thick electron beam resist.
The majority of works on proximity effect in EBL are based on a two-dimensional (2D) model, where the energy
deposition along the resist depth dimension is not considered, and the point spread function (PSF) or energy
deposition profile is assumed to be 2D [9, 10]. Generally, there is a lack of systematic experimental data on profile
measurements for 3D proximity effect simulation, although there are some works on that subject [11, 12].
In this paper, we present a study of profile dependence on the exposure dose in the thick positive electron beam
resist PMMA for the resist thicknesses 600 and 1300 nm, and electron energy 30 keV. Based on measurements
along the resist profile depth, profile simulation is performed and results are discussed.
Applied Physics of Condensed Matter (APCOM 2021)
AIP Conf. Proc. 2411, 040001-1–040001-7; https://doi.org/10.1063/5.0067068
Published by AIP Publishing. 978-0-7354-4138-5/$30.00
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EXPERIMENTAL
Experiments on a 600 and 1300 nm thick layer of polymethyl-methacrylate (PMMA) [13] electron beam resist
were carried out using EBL control system Elphy Quantum (Raith) installed on a scanning electron microscope
Inspect F50 (FEI) with a field-emission cathode and Gaussian intensity distribution [14]. The exposures were
performed at an electron energy of 30 keV. PMMA was coated on silicon (Si) substrate. All exposure tests were
immersed in the developer MIBK:IPA (1:3) for 60 seconds. A high-resolution scanning electron microscope Quanta
3D (FEI) was used for dimension measurements of PMMA resist profiles at the magnification of 100 000× and
200 000×. More detailed description of experiments was published in [14].
RESULTS
The influence of various exposure doses on the profile for 600 nm thick PMMA resist is demonstrated in Fig. 1,
and for 1300 nm thick PMMA resist in Fig. 2, respectively. The energy of electrons was in both cases 30 keV. In
both figures, the exposure dose is increased from left to right. Because of a single pixel line mode, the exposure line
dose unit is expressed in nC/cm.
(a)
b)
c)
FIGURE 1. Developed resist profiles at various exposure line doses for 600 nm thick PMMA resist and 30 keV electron energy:
a) D =1.78 nC/cm, b) D = 17.70 nC/cm, and c) D = 28.69 nC/cm.
(a)
b)
c)
FIGURE 2. Developed resist profiles at various exposure line doses D for 1300 nm thick PMMA resist and 30 keV
electron energy: a) D = 4.07 nC/cm, b) D = 8.13 nC/cm, and c) D = 32.54 nC/cm.
In case of 600 nm PMMA resist thickness, the linewidth at the top of PMMA resist is increased by a small value
from 37.23 through 69.15 up to 85.11 nm for exposure doses 1.78, 17.70 and 28.69n C/cm, respectively. However,
the linewidth at the bottom of PMMA resist is increased on remarkable value from nearly zero through 287.23 up to
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437.10 nm, respectively. The dose of 1.78 nC/cm is minimal value where the resist is developed down to the
substrate. However, the sidewall shape is not linear but rounded. At higher dose, the sidewall shape becomes nearly
linear in the main middle part of the resist thickness but the angle of side wall slope is increased with the exposure
dose. In case of 1300 nm PMMA resist thickness, the higher exposure dose is required to develop resist down to the
substrate, and the minimal value is 4.07 nC/cm. The side wall shape is nearly similar to that one for 600 nm PMMA
resist thickness.
Figure 3 represents solubility rate curves calculated on the base of experimental contrast curves for (1) a 600 nm
thick PMMA resist on Si substrate for 30 keV electron energy, and (2) a 1300 nm thick PMMA resist on Si substrate
for 30 keV electron energy.
Dissolution rate, nm/sec
30
25
20
2
15
10
1
5
0
0
20
40
60
80 100 120 140 160 180 200
Exposure dose Q, PC/cm2
FIGURE 3. Solubility rates at various exposure doses for MIBK:IPA 1:3 developer, development time 60 s.
As can be seen, the PMMA resist shows a nonlinear development behaviour. Based on the residual resist
thickness as a function of the development time, we calculated the solubility rates for MIBK:IPA 1:3 developer
at different resist thicknesses (600 and 1300 nm) when the exposure dose varied from 38.9 to 194.6 μC/cm2 for 30
keV energy (Fig. 3). A low dissolution rate at low exposure doses and a sharp increase of the PMMA resist removal
at higher doses of exposure has been observed.
In EBL, the problem of the electron scattering (called “proximity effect”, PE) in the resist and substrate is crucial
and therefore accurate knowledge of the 3D energy deposition function (EDF) in the resist used is needed for
achieving a high e-beam lithography resolution [15]. The PE was studied for exposures by equipment with a
Gaussian electron beam at 30 keV electron energy for the cases of 600 and 1300 nm thick PMMA resist layers on Si
substrate, respectively.
Figure 4 is a comparison between EDF at the resist surface (near the resist surface) (curve 1) and at the resist
bottom (curve 2) for 600 nm PMMA/Si at electron energy of 30keV. The analytical approximation for EDF was
performed by a sum of two Gaussians. The values of the proximity effect parameters (βf, βb, ηE) at the resist bottom
and near the resist surface (at a depth of 20 nm) are the following: (0.0426 μm, 2.642 μm, 0.212) and (0.0631 μm,
2.833 μm, 0.497) for point source. The values of the PE parameters were calculated applying our Monte Carlo tool
for modeling EBL exposure process [15]. Based on these simulation results, nearly vertical side walls of the image
in the resist should not be expected that is also confirmed by the obtained calculated data for the sidewall slope
angle of the developed resist profiles (Fig. 6), calculated contour plots of the developed half linewidths (Fig. 7) and
experimental data (Fig. 1).
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FIGURE 4. EDF (r) near the resist surface (curve 1) and at the resist bottom (curve 2) for 600 nm PMMA at 30 keV.
The EBL experiments were performed for both PMMA resist thicknesses 600 and 1300 nm for various doses
at electron energy of 30 keV, development time of 60 sec in MIBK:IPA 1:3 developer. The experimental exposure
conditions of the investigated EBL parameters are presented in Tab. 1.
TABLE 1. EBL experimental conditions.
Resist thickness (nm)
600
1300
Line dose (nC/cm)
Minimum
35.53
4.067
Maximum
118.44
81.34
FIGURE 5. Measurement details about developed profiles in PMMA resist at single pixel lines exposure.
EBL series of test line structures formed in the layers of PMMA resist with different thicknesses (600 and 1300
nm) for the case of 30 keV electron energy aiming to study the influence of the exposure dose and of the resist
thickness on the profile geometry and to finding the conditions of obtaining vertical image sidewall, were
conducted. The values of the linewidth of the PMMA profiles after development were measured at 5 levels along the
resist depth as shown in Fig. 5 – at the top of the resist layer (LT), at 100 nm below the top of the resist (LT1), at the
middle level of the resist depth (LM), at 100 nm above the resist/substrate interface (LB2) and at the resist/substrate
interface (LB - bottom), respectively.
Based on the performed experiments and data for 1800 nm resist thickness [14], the resist profile sidewall angles
were calculated using the measured developed resist linewidths at two levels along the resist depth – LB2 and LM
(Fig. 5).
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A regression model for the sidewall slope angle YA of the developed PMMA resist profiles as a function of the
exposure line dose (x1) and the resist thickness (x2) is estimated for coded values of the parameters in the region
[–1 y 1]:
YA = 56.45–13.50 x1+8.68 x2+15.28 x12+7.70 x22
(1)
The corresponding experimental variation intervals of the investigated parameters exposure line dose (z1) and resist
thickness (z2) are presented in Tab. 2.
TABLE 2. Parameters and their variation intervals for the sidewall slope angle mode and the overall half line width model.
Parameter
Line dose – z1 (nC/cm)
Resist thickness – z2 (nm)
Resist depth –z3 (nm)
Coded
zmin, i
zmax, i
x1
x2
x3
4.067
600
0
284.69
1800
1800
FIGURE 6. Contour plot of the sidewall slope angle of the developed resist profiles as a function of the exposure line dose and
the PMMA resist thickness at 30 keV electron energy.
The coded values xi of the process parameters can be found using their maximal (zmax) and minimal (zmin) values
by the equation:
xi = (2zi – zmax,i–zmin,i)/(zmax,i – zmin,i)
(2)
The accuracy of the model is estimated by the multiple correlation coefficient R = 0.914 which defines that the
model is good enough for prediction and optimization of the sidewall slope angle. The calculated values of the
sidewall slope angles of the developed PMMA resist images in the range of 65–90 degrees are presented in Fig. 6.
The measured linewidth data were used to assess an overall model describing the dependence of the developed
resist half line width (YHLW) on the exposure dose (x1) and the resist depth (x3). The experimental variation ranges of
the investigated parameters exposure line dose (z1), resist thickness (z2) and resist depth (z3) are shown in Tab. 2.
The assessed regression model relating the developed resist half linewidth (YHLW) to the varying line dose (x1),
resist thickness (x2) and resist depth (x3) (Tab. 2) in the region [–1 y 1] is:
YHLW = 484.53+271.80 x1+134.81 x2–459.38 x3–134.21 x12–269.45 x22–237.46 x1x3+156.30 x2x3+138.94 x12x3
(3)
The value of the corresponding multiple correlation coefficient is R = 0.951, which defines a good prediction
accuracy of using the estimated model and its usability for optimization of the developed resist image geometry
(nearly vertical side-wall shape).
The proposed models are useful for predicting and controlling the shape (geometry) of the developed resist
profiles in PMMA layers with different thicknesses in the interval 600–1800 nm. The half linewidths can be
calculated by Eq. (3) for a chosen resist thickness in the range of 600–1800 nm. Then using Eq. (1) or contour plots
of the sidewall slope angle of the developed profiles (Fig. 6), a variation interval of suitable exposure line doses for
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obtaining optimal (nearly vertical) image sidewall shapes, can be evaluated. For example, the line dose interval can
be determined in correspondence to the sidewall slope angle range of 65–90 degrees. For the chosen line dose region
and using Eq. (3), the developed half linewidths, depending on the resist depth can be determined. Fig. 7 shows
calculated contour plots of the developed half linewidths vs. the exposure line dose and the PMMA resist depth in
the cases of: 600 nm thick layer of PMMA on Si substrate (Fig. 7a) and 1300nm thick PMMA layer on Si (Fig. 7b)
at 30 keV electron energy and MIBK:IPA 1:3 developer for 60 s.
a) 600 nm
b) 1300 nm
FIGURE 7. Contour plots of the developed resist half linewidths as a function of the exposure line dose and the PMMA resist
depth at 30 keV electron energy.
FIGURE 8. Contour plots of the half linewidths for 900 nm resist thicknessas a function of the line dose and the PMMA resist
depth and the corresponding profile for the dose of 80 nC/cm.
Contour plots of the half linewidths for 900 nm PMMA resist thickness depending on the line dose (for dose
regions, where the expected slope angles are in the range of 69–90 degrees) are shown in Fig. 8. Predicted
developed profile in PMMA for the line doses of 80 nC/cm (Fig. 8), is also presented and the linewidth at the
resist/substrate interface (bottom) is 1192.2 nm while at the top being 393.6 nm (Fig. 8).
CONCLUSION
The influences of exposure dose and resist thickness on the profile of the developed lines in thick PMMA resist
layers were studied experimentally and theoretically. The profile comparison was done for PMMA resist thicknesses
600 and 1300 nm, respectively. The profile broadening increases significantly with the electron beam exposure dose
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for both thicknesses, however the sidewall shape is nearly similar. Experimental results contribute to the resist
profile database, and are useful for 3D proximity effect simulation. Solubility rate curves calculated on the base of
experimental contrast curves for the case of 30 keV electron energy shows a nonlinear development behaviour. The
calculated spatial energy deposition distribution in the resist and the proximity effect parameters for 600 nm PMMA
thick PMMA on Si substrate exposed by 30 keV showed that nearly vertical side walls of the image in the thick
resist should not be expected.
For predicting and optimizing the shape of the developed resist image in the PMMA resist, a model for the
sidewall slope angle and an overall model for the developed resist half linewidth as a function of the exposure dose
are assessed. The models are based on the experimental data obtained. Simulations for different lithography process
conditions (resist thicknesses and exposure doses) are performed. For different PMMA thicknesses, contour plots of
the developed resist half linewidths depending on the exposure line dose along the resist depth at 30 keV electron
energy were given. The models are useful for predicting the shape (geometry) of the developed resist profiles in
PMMA layers with thicknesses in the range 600–1800 nm and for choosing appropriate lithography conditions.
The results presented here contribute to the knowledge of electron scattering in resist/substrate in e-beam
lithography for the case of field emission cathode and Gaussian intensity distribution and to development and
approval of simulation tools for prediction and precise control of obtained resist profiles in PMMA.
ACKNOWLEDGMENTS
This work was supported by the SAS - BAS joint research project “Semiconducting metal oxide - new materials
for environmental sensors”, by the Bulgarian National Science Fund under thecontract KP-06-N27/18, and by the
Ministry of Education of the Slovak Republic and the Slovak Academy of Sciences under the Contract No. VEGA
2/0119/18. SEM facilities at the Institute of Electrical Engineering SAS are gratefully acknowledged.
REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
M. A. McCord and M. J. Rooks, “Electron Beam Lithography” in Handbook of Microlithography,
Micromachining and Microfabrication I, edited by P. Rai-Choudhury, (SPIE Optical Engineering, Bellingham,
WA,1997), pp. 139-249.
S. Yasin, D. G. Hasko and H. Ahmed, Applied Physics Letters 78, 2760 (2001).
F. Hu and S.-Y. Lee, J. Vac. Sci. Technol. B 21, 2672-2679 (2003).
I. Kostic, K. Vutova, R. Andok, V. Barak, A. Bencurova, A. Ritomsky and T. Tanaka, Journal of Physics:
Conference Series 992, 012057 (2018).
E. Koleva, K. Vutova and I. Kostic, Journal of Physics: Conference Series 1089, 012015 (2018).
K. Indykiewicz, B. Paszkiewicz, T. Szymanski and R. Paszkiewicz, Journal of Electrical Engineering 65, 381385 (2014).
F. J. Yaghmaie, A. Gusman and R. Prohaska, Microelectronic Engineering 87, 2629 (2010).
S. Gorelick,V. A. Guzenko, J. Vila-Comamala and C. David, Nanotechnology 21, 295303 (2010).
S. J. Wind, P. D. Gerber and H. Rothuizen, J. Vac. Sci. Technol. B 16, 3262-3268 (1998).
M. Peckerar, R. Bass and K, Rhee, J. Vac. Sci. Technol. B 18, 3143-3149 (2000).
V. V. Aristov, S. V. Dubonos, R. Ya. Dyachenko, B. N. Gaifullin, V. N. Matveev, H. Raith, A. A. Svintsov and
S. I. Zaitsev, J. Vac. Sci. Technol. B 13, 2526-2528 (1995).
S.-Y. Lee and K. Anbumony, Microelectronic Engineering 83, 336-344 (2006).
I. Kostic, K. Vutova, E. Koleva, R. Andok, A. Bencurova, A. Konecnikova and G. Mladenov,“Study on
polymers with implementation in electron beam lithography,” in Polymer Science Research advances, practical
applications and educational aspects, edited, by A. Méndez-Vilas and A. Solano-Martín (Formatex Research
Center, Badajoz, Spain, 2016), pp. 488-497.
I. Kostic, K. Vutova, E. Koleva, R. Andok, A. Bencurova, J. of Physics: Conf. Series 1492, 012015 (2020).
K. Vutova and G. Mladenov, “Computer simulation of processes at electron and ion beam lithography - part 1”,
in Lithography, edited by M. Wang (Intech, Vukovar, Croatia, 2010), pp. 319-350.
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