Spatial stochastic scattering.
Lithographic projection system.
See paper 58 in the list of publication: The contributions of stochastic coulomb interactions and collective space-charge field aberrations to spatial spreading in charged particle projection systems, by F H Read and N J Bowring, Microelectronic Engineering 73-74, 97-105 (2004). See also paper 54.
Combination of thin lens action with stochastic scattering, using sct3clln.cpp.
A doublet projection system.
2 ideal thin lenses, at z = 160 and 360, with f = 160 and 40.
Object radius 0.5mm, magnification 1/4.
The currents used in the published study are 5,10,15,20,25 microAmp.
The pencil angles alpha are 0.1,0.25,0.5,1.5,2.5,5,7.5,10,12.5 mrad.
In the present example file the current is 20 microAmp, alpha is 2.5 mrad.
Control data in sct3clln.dat:
tempout.dat
2
160.
160.
0.
0.
1.
360.
40.
0.
0.
1.
2003
1
4
0. 0.16 0.0005 0.0009 0. 0.975E-9
0.16 0.32 0.0009 0.0004 0.973E-9 2.009E-9
0.32 0.36 0.0004 0.00065 2.007E-9 2.252E-9
0.36 0.40 0.00065 0.00025 2.250E-9 2.556E-9
Explanation of the parameters:
tempout.dat =output data file name.
2 = number of thin lenses, followed by 2 sets that gives:
z of lens plane, focal length, cs, cc, reference energy for cc
2003 = seed (for randomisation, same each time for same seed value).
1 = number of scattering subdivisions for each trajectory step
(usually 1, unless the trajectory integration steps are long
and the other conditions are such that one or more complete
collisions can occur inside a step, in which case the step
should be subdivided here to give not more than one collision
per subdivision).
4 = number of 'regions', maximum 100 (see below).
0. 0.16 0.0005 0.0009 0. 0.975E-9
= zi,zf,Bi,Bf,ti,tf for region 1, etc
where i = initial, f = final,
z = coordinates of end of region (in metres),
B = maximum impact parameter (in metres),
t = time limits for scattering events (in seconds),
Reasons for choice of radii for density and charge tubes in present file
and in sct3clln.dat:
Mask: Spacing of points = 0.07.
Spacing = average spacing = sqrt(pi*r**2/N), where N is total
number of points, including symmetry reflections.
In practice there would be a very large number of points,
each carrying a small current.
To simulate this, use r_density = 0.07, so that density for each
ray is the current of the point divided by the area occupied by
the point, which is correct.
Near mask: Rays start to overlap when z*alpha = 0.035,
ie z =14 forr alpha = 2.5 mrad
The radius of the beam is then 0.6, spacing is 0.017.
Lens 1: Radius = 0.5 + 160*alpha = 0.9, spacing = 0.025.
Cross-over: At z = 320. Radius = 160*alpha = 0.4.
Spacing of these rays is 0.011.
Lens 2: Radius = r_cross-over + 0.125 = 0.525, spacing = 0.015.
Wafer: Radius 0.125. Spacing = 0.018.
Use r_density = 0.018, same reason given for mask.
Summary for beam radius:
alpha mask lens1 cross-over lens2 wafer
z= 0 160 320 360 400
2.5 0.5 0.9 0.4 0.525 0.125
Summary for spacing of points or rays:
-which is minimum for r_density
alpha mask lens1 cross-over lens2 wafer
z= 0 160 320 360 400
2.5 0.07 0.025 0.011 0.015 0.018
Summary for r_density:
-which has maximum 0.1*beam_radius
alpha mask lens1 cross-over lens2 wafer
z= 0 160 320 360 400
2.5 0.07 0.025 0.04 0.053 0.018
Compromise and simplify for r_density:
-can only have 2 changes
alpha mask lens1 cross-over lens2 wafer z ranges
z= 0 160 320 360 400
2.5 0.07 0.07 0.025 0.025 0.018 0-280-390-405
Put r_tube = 0.5*r_density.
Conditions for other values of alpha are given in the private file coulres.dat
The present data file is for combined stochastic and collective effects.
The external file is scatter3.dll, derived from sct3clln.cpp.
For stochastic scattering only, use large mesh spacings (50 50 50),
which causes the system to be effectively field-free
(ie no space-charge fields).
For collective scattering only add a line 'activate_stochastic = 0'
in scatter3.cpp (saved in sct3cllu.cpp).
The output of the present file is analysed by this program (in Fortran):
For the rest of the information, please see the data file itself