CHAPTER 2. ELECTRON INTERACTION OF E-BEAM LITHOGRAPHY
2.4. P ROXIMITY EFFECT CORRECTION METHODS
2.4.4. Top surface image method
The Bethe range of an electron is the total length of path one energized electron can travel before it stopped or reach cut off energy. The Bethe range of polymer material is short for low accelerated voltage electron. For example, the range for PMMA of 5KeV electron is only 0.64 µm [23]. If the thickness of photoresist is larger than half of the electron range, the backscattered electron from substrate will not reach top surface of the photoresist film. The similar phenomena will happen for multi-layer resist structure. For this reason, top surface image technique of high thickness resist or multi-layers resist will be a good solution for low energy E-beam exposure lithography [24, 33]. The major advantage is that no proximity effect correction is necessary. The disadvantage is the increased process complexity. Fig 2-8 shows a typical patterning process of the top surface image technique.
Fig 2-8 A bi-layer process using top surface image of low energy E-beam lithography to alleviate proximity effect [33].
Chapter 3.
Monte Carlo simulation for E-beam lithography
In this chapter, Monte Carlo method will be mentioned. It includes various Monte Carlo models and a simulation program which was developed based on the single scattering model.
The verification of the simulation program was also included. And the proximity effect parameters for the test structures were also obtained by the developed simulation program.
3.1. Monte Carlo Models
There are various models of Monte Carlo simulation for electron interactions, including multiple scattering model, single scattering model, hybrid model, direct simulation model and dielectric function model [25].
3.1.1. Multiple scattering model
Multiple scattering model was initiated by Berger (1963) for practical Monte Carlo calculations of penetrated of charged particles in matter [25]. It was based on the use of Bethe’s stopping power equation describing energy loss and angular distribution for electron scattering from transport equation.
3.1.2. Single scattering model
Single scattering model adopts the screened Rutherford scattering cross section in place of the angular distribution [25]. The energy loss is given by Bethe’s stopping power equation as in the multiple scattering model. It is widely used and suitable for energy dissipation of E-beam lithography.
3.1.3. Hybrid model
Hybrid model initially was proposed by Schneider and Cormack (1959) for the discrete and continuous energy loss processes [25]. It has done much to extend Monte Carlo calculations to alloys and compound materials including secondary electron generation.
3.1.4. Direct simulation model
Direct simulation model is probably the most basic approach leading to a more comprehensive understanding of the various excitations associated with electron penetration [25]. However, it requires exact knowledge of individual inelastic scattering, and this is available for only a few materials.
3.1.5. Dielectric function model
Dielectric function model is based on use of the Mott scattering cross-section and the dielectric function describing elastic and inelastic process, respectively [25]. It is applicable to low energy electron as to high-energy electrons. The disadvantage is that the multiple-variable excitation function requires a large amount of memory for a practical computer simulation.
3.2. Electron interaction with atom
The accelerated electrons impacting on the target surface suffer elastic and inelastic collisions with the atoms of the impacted film via Coulomb forces. Elastic collision deflects the direction of the incident electron and happens when the electron collides with the nuclei of the atoms. On the other way, inelastic collision mainly causes loss of the kinetic energy of the incident electron when the incident electron interacts with the surrounding electrons of the atoms.
3.2.1. Elastic collision
As one electron interacting with the nucleus of an atom, the incident electron will be scattered with direction change and negligible energy loss. The angle of scattering can be calculated by
differential scattering cross section and Monte Carlo simulation. First, the differential scattering cross section should be analyzed. The calculation of differential scattering cross section was based on Born approximation and shielded Coulomb potential method. The shielded Coulomb potential and corrected screened length are given as
2
and Z is the atomic number of the target atom., e is the electric charge of an electron, a0 is the Bohr radius, and d is the corrected length [26]. And the standard form of Born approximation is
2 0
and k is the wave factor of the incident electron, θ is the angle change of the electron after scattering. Substituting the shielded Coulomb potential into the standard Born potential gives
2
The corresponding differential scattering cross section is
2
where σ is the scattering cross section and Ω is the solid angle of the scattering. Substitution of
The kinetic energy of electron is
2 2
2 E k
= h m (3.8)
Using equation (3.8) in (3.7), we get
2 2 2
The total elastic cross section can be obtained by integration as
2 2 2 2 2
and µ represents the effective screening parameter of the electron cloud. The equation becomes
2 2 2 2
To take into account of inelastic scattering, Z2 is replaced by Z(Z+1) [27]. The total scattering cross section becomes
3.2.2. Inelastic collision
Between elastic scattering events with nuclei, the incident electron is assumed to interact with the surrounding electrons of the nearby atoms. And it will lose kinetic energy during the traveling path. This energy loss is usually modeled by the Bethe continuous slowing down approximation [23] as
where N is the atoms number density of the target, γ=1.1658 is a constant, and J represents the mean excitation energy in the solid.
3.3. PC simulation
The simulation program was implemented with VC++ and run in Pentium-4 personal computer.
The random numbers files were downloaded from random organization [28] instead of pseudo random numbers to get adequate randomness. Several thousands random numbers were served for one incident electron of 40 KeV.
3.3.1. Density calculation
The density of the photoresist is necessary for the simulation of electron bombardment. We used electronic balance, AG285, to measure masses of 3 pieces of 6 inches wafers before coating. Then measure the same 3 wafers after spin coating with NEB-A4 photoresist.
The photoresist thickness was measured at n&k tool, NKT-1500. The edge bead removal width of spin coating is 2 mm. The cover area per wafer can be calculated. The density of the coated photoresist can be obtained by following equation as
3
where d is the density of the photoresist film to be calculated, A is the calculated photoresist covered area of one coated wafer, t is the averaged measured thickness of the photoresist film, Mafter and Mbefore are the measured masses of the wafers after and before spin-coating respectively.
3.3.2. Components analysis
It is important to know the composition of the photoresist film before simulation. ESCA (electron spectroscopy for chemical analysis) was used to analyze the photoresist film components. ESCA can’t analyze hydrogen. So we used EA (Elemental Analyzer) for hydrogen ratio analysis. The ESCA result is shown at Fig 3-1 and Table 3-1. The EA result is shown at Table 3-2.
1400 1200 1000 800 600 400 200 0
0
ESCA result of NEB photoresist film
___ O 1s
Counts
Binding Energy (eV)
Counts
Fig 3-1 ESCA spectrum for NEB-A4 photo-resist film. The elements for the analysis are C,O,N and S.
Table 3-1 atomic percentage of NEB-A4 photo-resist film derived from ESCA.
Element AT%
O 11.886 C 1.862 N 85.903 S 0.349
Table 3-2 Atomic weight percentage of elements in photoresist NEB-A4 obtained from EA.
N % C % H %
Exp-1 2.55 71.66 7.03
Exp-2 2.50 71.50 7.22
Average 2.52 71.58 7.17
3.3.3. Mean free path random number R1
The mean free path between collisions could be obtained as [23]
( i i) 1 i
λ=
∑
nσ − (3.16)where σi is the total scattering cross section of ith species and is given at equation (3.17). Using a random number, the distance s an electron travels between the collisions is
ln ,1
s= −λ R (3.18)
where R1 is a random number read from random number file.
3.3.4. Scattering center atom random number R2
The probability of scattering of an atom of the ith species is [23]
( i i)
where ni is the atom number density of ith species and σi is the total scattering cross section of ith species. The scattering center is chosen to be nth species when the following equation is met.
2
3.3.5. Angle of scattering random number R3
The probability of scattering angle is lied between 0 and π. And it can be obtained from
0
where θ is the calculated change of angle of the scattered electron. From (3.22), we can get
3
, and the scattering angle could be obtained from this equation.
3.3.6. Azimuthal angle random number R4
The azimuthal angle Φ is equally spanned between 0 and 2π. It can be easily obtained from
random number as [23]
2 Rπ 4
Φ = (3.24)
3.3.7. Trajectory of scattering
As mean free path, ith species scattering center, θ and Φ are decided, one can calculate the next position and direction of the impinged electron. And the electron will lose kinetic energy during the path. It will repeat and repeat until the electron lost enough energy to reach cut off energy [23]. One step of the electron trajectory is shown at Fig 3-2.
Fig 3-2 One step of electron movement in 2D schematic drawing.
3.4. Verification
To verify correctness of the simulation program, comparison of stopping power, penetration ratio, reflection ratio and energy profile will be done. PMMA (polymethyl methacrylate, C5H8O2) film on silicon substrate was mostly frequently used for simulation, test, and comparison. For energy profile, PMMA film on blank mask plate was used for simulation and comparison.
3.4.1. Stopping power
The incident energized electron will lose power when inelastic interaction occurs during the bombardment process. Continuous slowing down approximation formula is used to calculate the lost power. Stopping power is the lost power per unit length of the incident electron. It depends on the electron energy and the film that the electron traveling.
Stopping power of the films could be verified by the stopping range, Bethe electron range, of the energized electron. Stopping range is the length of path one energized electron could travel before it reached cut off energy. The cut off energy was assumed 500 V during the test [23]. Stopping range depends on the material of the bombarded target and the energy of the incident electron. Higher energized electrons get longer stopping range. Film of low atomic number elements or lower density gets longer stopping range. The result was compared with the reference paper [23], and listed at Table 3-3.
Table 3-3 Verification of stopping range of different accelerated voltage of PMMA and silicon.
material Accelerating
From Table 3-3, the result shows good consistency with the result from the reference paper [23]. The stopping power formula of our program was checked and verified to be correct.
3.4.2. Penetration and reflection ratio
For E-beam lithography, the incident electrons will first traveling at the top resist film. Almost all of them will penetrate to the under layer film or substrate. Some of the penetrating electron will be scattered back to the resist film by elastic collisions with the atoms of the substrate or intermedium film.
400 nm thickness of PMMA film on silicon substrate was used for simulation. 10000 counts of electrons were used for bombardment in the simulation. The penetration ratio is defined as the ratio of the number of electrons, entering under layer film or substrate at least once, to the total number of the incident electrons [23]. And the reflection ratio is defined as the ratio of the number of back-scattered electrons, entering resist film again from under layer film or substrate at least once, to the total number of incident electrons [23]. And the results are listed at Table 3-4 and Table 3-5.
Table 3-4 Comparison of penetration ratio of 400 nm PMMA on silicon substrate of different acceleration voltage 20KV, 10KV, 5KV.
From Table 3-4 and Table 3-5 , the penetration ratios and reflection ratios result shows consistent with the reference. The total elastic cross section formula and random variable of our simulation program are verified to be consistent with the reference.
Table 3-5 Comparison of reflection ratio of 400 nm PMMA on silicon substrate of different acceleration voltage 20KV, 10KV, 5KV.
Energy (KeV)
Reflection Ratio
(%)
Reflection Ratio [23]
(%)
Deviation Percentage
(%)
20 18.3 18.2 0.5 10 23.2 24.2 4.1 5 29.1 30.1 3.3
3.4.3. Energy profile
Finally, constant energy contour was checked for the verification. In this test, 500 nm of PMMA resist film on 0.08 µm Cr film on a thick bulk SiO2 substrate was used for simulation.
500 nm isolated line pattern were used. The incident electron energy for the test is 20 KeV and the dosage is 80 uc/cm2. The patterns are simulated in terms of Gaussian sources at a density of 8 lines/µm (s=0.125 µm) and with a standard deviation σ=0.05 µm. This density was chosen that a 0.5 µm line would contain four beam positions. The constant energy contours of reference paper are dash lines shown at Fig 3-3. Due to symmetry to the line center, only the right half energy profile of the line is shown [30]. Constant energy contours of same energy of our developed program were shown at Fig 3-4.
Fig 3-3 Constant energy density contour of 0.5 µm line for mask case. The source is Gaussian beam with 50nm range, at 20 KeV [30].
Fig 3-4 Simulation energy density contour of 0.5 µm line of our developed program. The source is Gaussian beam of range 50nm at 20KeV.
Three contours of constant energy, 1200, 800 and 325 J/cm3, were compared between the reference paper and our simulation program. In Fig 3-4, the brighter region indicates higher energy density and vice versa. The test condition of the simulation follows the reference.
Similar constant energy profiles were obtained as the reference. Thus we make sure that the deposition of energy of our simulation can successfully indicate the energy deposition for E-beam lithography.
3.5. Simulation result
3.5.1. Electron transverse path
The electron beam accelerating voltage of Leica WePrint-200 is 40KV. For example, when bombarding on a 400nm thickness of NEB photo-resist coating at silicon substrate, the electrons traverse path is simulated and shown as Fig 3-5.
Fig 3-5 simulated electron path for 400 nm NEB film on Silicon substrate with 40KeV electron beam.
3.5.2. Energy parameter fitting
The forward and backward deposited energies were saved separately. The deposition energy of the bottom 50 nm region of photoresist film was used for further calculation [23]. The energy reflection ratio could be calculated as
sum of backward energy of bottom 50 nm sum of forward energy of bottom 50 nm
ηE = (3.25)
The distribution range of forward energy and backward energy can be obtained using curve fitting tool of Matlab. For example, a backward energy fitting result of coating wafer on 1000nm copper with silicon substrate is shown at Fig 3-6.
Fig 3-6 Gaussian fitting of backscattered energy of 40KV E-beam Exposure for 400nm NEB on 1000nm copper with silicon substrate.
3.6. Proximity effect parameters of Monte Carlo method
The proximity effect parameters, the reflection ratios and penetration ratios derived from the
Monte Carlo method are listed at Table 3-6. The forward scattering range is small compared to experiment fitting method. The backscattering ranges of the first 3 films are almost the same due to similar film averaged atoms mass and similar averaged atom number.
For same incident electron energy, from equation (3.13), the total cross section of an atom is nearly proportional to Z4/3, where Z is the atomic number of scattering target. So the total cross section of Ta is the largest and the mean free path is the shortest. The backscattering range for Ta film is the smallest and the energy reflection ratio is the largest due to the largest atom number and the highest weight density.
Table 3-6 Test result of our developed Monte Carlo method for different film structures.
Si-Substrate SiO2_200nm Si3N4_200nm Ta300nm Cu200nm
Average atomic
Chapter 4.
Experiment and discussion
In this chapter, experiment process for 5 types of film structure will be studied. After measurement of the experiment data, proximity effect parameters were extracted with the double Gaussian model. The extracted parameters of proximity effect and GDS (graphic data system) file of designed patterns were inputted to PROXECCO, the proximity effect correction tool which is running at Sun work station, to generate proximity effect corrected file for Leica E-beam exposure system. The corrected exposure results were measured by SEM to check the capability of proximity effect correction.
4.1. Experiment process
4.1.1. Experiment equipments
1. Photo-resist coating and developing: Clean MK-8, TEL.
2. Exposure system：WePrint 200, Leica.
3. CD measurement: S6280, Hitachi.
4. Thickness measurement: n&k analyzer, model: NKT 1500.
5. Electronic balance: model: AG285, Mettler.
6. ESCA: model： Microlab 310F, VG Scientific.
7. EA: model: CHN-O-RAPID, Foss Heraeus.
4.1.2. Experiment process
The wafers were done film processing first. Then coating, exposure and developing processes were done. Measurement and inspection of the wafers followed. Proximity effect parameters were extracted from the measurement data. The procedure is depicted at Fig 4-1. Fig 4-2 shows the procedure for proximity effect correction check.
Fig 4-1 wafer process flow for proximity effect extraction with uncorrected design patterns.
Fig 4-2 wafer process flow for proximity effect correction check with proximity effect correction patterns.
4.1.3. Clean Track coating
The wafers were primed with HMDS vapor to improve photoresist adhesion in AD-unit at TEL (Tokyo electric limited) Clean track first. After HMDS priming, the wafers were cooled by temperature control cool plate. After cooling, they were spin-coated with NEB-A2 photo-resist at coating module by dipping photoresist manually. Soft bake followed to evaporate most solvent at 110oC for 2 minutes.
Film processing
Coating
E-beam exposure with proximity effect corrected file
Developing
CD measurement Film processing
Coating
E-beam exposure with uncorrected design file
Developing
CD measurement
Proximity effect
parameters Extraction
4.1.4. E-beam exposure
The designed patterns were exposed by Leica WePrint-200.The exposure dosage were spanned from 1.1 to 8.0 uC/cm2 with 0.1 uC/cm2 step, 8.2 to 9.0 with 0.2 uC/cm2 step, 9.5 to 15 with 0.5 uC/cm2 step, and 16 to 20 with 1.0 uC/cm2 step.
Leica WePrint-200 is a variable shape beam system. There are two diaphragms in the e-beam path. Each aperture has at least 4 square holes [31]. As the E-beam emit from the e-gun, the first deflection lens system will select one square of the first diaphragm for e-beam to pass.
Then the second deflection lens system will select one square of the second diaphragm to pass and decide how much overlap with the input beam from the first diaphragm. A non-rotated hole could be combined with a rotated one to produce triangular shapes [31].
Fig 4-3 schematic drawing of beam path of Leica WePint 200 [31].
The maximum of the exposed area is 4x4 µm square. The smallest exposed square is 20x20 nm square. The stage use continuous moving method, write-on-the-fly technology.
The scanning mode is vector scanning method. All of the above features improve the throughput of the system.
4.1.5. Clean Track developing
The exposed wafers were processed with PEB (post exposure bake) at 105oC for 2 minutes .Then they were developed with AD-10 developer at develop module. Finally, hard bake process at 110oC for 2 minutes dried the wafers and solidified the photo resist patterns at dehydration hot plate.
4.1.6. CD measurement
All of the wafers were measured and inspected by in-line SEM, Hitachi S6280. The maximum power of the SEM is 150K X. The accelerated voltage for the measurement is 700 V. The current is from 8.0 to 10.0µA. The system uses secondary electrons as signal source. Linear approximation algorithm for CD measurement was used through the experiment.
4.2. Test patterns
For the experiment, we used negative tone E-beam resist. Isolated lines, dense lines and trenches are common semiconductor circuit layout. Isolated dots and dense dots have two dimensional symmetries and thus are usually used for test patterns. So these 5 types of patterns of different sizes were used to evaluate proximity effect. The test patterns were drawn at Fig 4-4.
Fig 4-4 schematic drawing of designed patterns to extract proximity effect parameters and to check proximity effect correction result.
For dense lines, there are 5 duty ratios, 2/3,1/2,1/2.5,1/3 and 1/4. For Isolated-line, Dense line and Dense dot, 22 sizes of dimensions (40nm, 60nm, 80nm, 100nm, 120nm, 140nm, 160nm, 180, 200nm, 220nm, 240nm, 260nm, 280nm, 300nm, 350nm, 400nm, 500nm, 600nm, 800nm, 1µm, 2µm, 4µm) were designed. For Isolated-dot, 128 µm square was added. For trench type, all dimensions were times by 10 except the largest trench patterns. Thus the dimensions are from 400 nm to 20 µm.
The exposure area for all patterns except the largest isolated dots is 30X30 µm 2. The
The exposure area for all patterns except the largest isolated dots is 30X30 µm 2. The