eBeam Lithography simulation and Proximity Effect Correction

pecebl

Simulation for eBeam Lithography using Casino3, Python, CUDA and FFT.

This package requires a Nvidia's CUDA GPU capable

A third party software is needed for generating the psf data (i.e.Casino3).

pecebl gives some basic pattern designer like : dot, line, rectangle, ring, circle, move, replace, append.

pecebl should make it easy:

• to simulate a pattern exposure by using the FFT convolution (pecebl.fft_ops.fft_exposure).
• to find the corrected dose distribution by using FFT deconvolution (pecebl.fft_ops.fft_pec).

Installation

This package requires Anaconda distribution for Python

Create a python's virtual environment

with my yml file:

The easiest way to create your virtual environment is using my environment.yml file:

conda env create -f environment.yml -n youreblenv

or if you want to create it by yourself:

conda create -n youreblenv python=3.7 cudatoolkit pyqt pywin32

install pecebl

Activate your virtual environment: activate youreblenv

Now you can install pecebl in local mode by cd to your local pecebl directory then enter: python setup.py install

or using pip : pip install pecebl

check installation

check your installation with : pecebl --show if everything is fine you will see an exposure example's plot.

Getting started

I) Building the PSF data

We will get at the end of this section a 2D matrix data with the psf at the center. Here are the steps to do:

1. Decide the hardware parameters you want to use: the beam energy, the beam current. And the physical properties of your sample.
2. Get the interaction between the electron beam and your sample. You can do it by experiment or by monte-carlo simulation like Casino3. We call it the psf function.
3. Map the psf function to a 2D matrix of size equals to the writefield you want to simulate. We call it the PSF data.

I-1) Setup the electron beamer

We use a Zeiss Supra40 SEM with 30 kV and the 7.5 µm aperture

from pecebl.sem import supra40 as beamer

meb = beamer.Supra40(30)

meb.change_aperture(7.5)

meb.info()

I-2) Import data from Casino3 simulation

We use the psf file from Casino3 simulation in examples/data folder: ZEP520_1e7_30kV_100mrad_1pt

from pecebl.psf_import.Casino import Casino3 as cs3

sim=cs3('ZEP520_1e7_30kV_100mrad_1pt')

The number of electron paths simulated in Casino3 was 1e7. The beam writer Raith Elphy Plus has 6 MHz of electronic speed. i_y for locating at the peak of the psf and i_z for placing at the middle depth of the ebeam resist. In this example, I use Casino3 in a grid size of (x=8000, y=0.6, z=310) in nm divided by (nx=8000, ny=6, nz=6) dots, hence i_y=3 and i_z=3. Now we can get the psf_fct:

psf_fct=get_psf_fct(1e7, sim, 6, meb.beam_current, i_y=3, i_z=3)

I-3) Building the PSF data

NP is the number of pixels, WF is the writefield (nm). We can calculate the pixel_size then map the two columns data psf_fct to a 2D matrix z_psf of size (WF, WF) $(nm^2)$ (or (NP, NP) $(pixel^2)$):

NP = 2048; WF = 5000

pixel_size=np.float32(WF/NP)

from pecebl.ebl_kernels import kernels as ker

z_psf=ker.build_psf(psf_fct, NP, WF, pixel_size, pg.dot(0,0)[0])

II) Pattern designer

II-1) Create a pattern

Get photonic crystal example1 centered at (0,0), hole radius 48 nm, pitch 170 nm and stepsize 4 nm

from pecebl.designer import PatternDesigner as pg

final_pattern=pg.example1(a=170, r=48, ss=4)

from pecebl.utils import *

plt.plot(final_pattern[:,0], final_pattern[:,1], 'o', ms=1)

plt.axis('equal');plt.show()

Building the dose distribution

We need to 'cut' data in blocks and grid for parallel calculation on GPU.

from sympy.ntheory import primefactors

primefactors(final_pattern.shape[0])

So we cut the final_pattern into grid of blocks size: (11*61, 3*137)

Now we can get dose distribution data: dose_dis is the initial dose distribution for our pattern. Default dose factor is 1 at each dot of the pattern.

dose_dis = ker.build_dose_distribution(final_pattern, NP, WF, pixel_size, blockdim=(671,1), griddim=(411,1))

We can change the exposure dose for $30\mu C/cm^2$ (ss = 4, speed = 6) by multiply a dwelltime factor:

dose_dis *= dtfactor(30,4,meb.beam_current,6)

III) Exposure process

Before applying the FFT transformations, we need to transform the z_psf data (Victor Podlozhnyuk white paper)

ppsf=np.empty((NP,NP),np.float64)

ppsf[:NP//2-1,NP//2+1:]=z_psf[NP//2+1:,:NP//2-1]

ppsf[:NP//2-1,:NP//2+1]=z_psf[NP//2+1:,NP//2-1:]

ppsf[NP//2-1:,:NP//2+1]=z_psf[:NP//2+1,NP//2-1:]

ppsf[NP//2-1:,NP//2+1:]=z_psf[:NP//2+1,:NP//2-1]

del z_psf

III-2) Exposure

We have the PSF and the dose distribution, we can do a FFT convolution to expose our pattern:

from pecebl.fft_ops import fft_ops as fft

z = fft.fft_exposure(ppsf, dose_dis)

print(np.min(z.real),np.min(z.imag),np.max(z.real),np.max(z.imag))

plt.imshow(z.real,origin='lower', extent=[-WF/2, WF/2, -WF/2, WF/2],interpolation="nearest", cmap=plt.cm.jet)

plt.show()

IV) Develop

The development process is simplified by a threshold operation. We use a threshold of 3 eV for ZEP520A ebeam resist.

th_resist = 3

z_dev = (z.real> th_resist) * z.real

z_dev[z_dev > 0] = 1

plot the development result:

plt.imshow(z_dev,origin='lower', extent=[-WF/2, WF/2, -WF/2, WF/2])

plt.show()

PEC

In this section, we want to find the dose distribution matrix and we know the target exposure. The way to get this target exposure will be discussed later. We start from previous section I) to get the z_psf and also its padded ppsf

I) Import target exposure

The example is in the filename target_ebl_for_pec.npy

import zipfile

zfile = zipfile.ZipFile("target_ebl_for_pec.zip","r")

with zfile as zip_ref: zip_ref.extractall()

z_target=np.load(zfile.namelist()[-1])

plt.imshow(z_target,origin='upper', extent=[-WF/2, WF/2, -WF/2, WF/2],interpolation="nearest", cmap=plt.cm.jet)

plt.show()

II) Get PEC by deconvolution

pec = fft.fft_pec(ppsf,z_target)

plotting:

plt.imshow(pec.real,origin='upper', extent=[-WF/2, WF/2, -WF/2, WF/2],interpolation="nearest", cmap=plt.cm.jet)

plt.show()

The pec found by FFT deconvolution may contain negative values, with a simple operation we can avoid it. Depend on your hardware constraint you could make some adjustment then implement the resulting dose distribution to your hardware to obtain the desired exposure.

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