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'''Feedback to this page''': '''[mailto:labadviser@nanolab.dtu.dk?Subject=Feed%20back%20from%20page%20http://labadviser.nanolab.dtu.dk/index.php/Specific_Process_Knowledge/Lithography/EBeamLithography/Dose Testing click here]'''
Content and illustration by Thomas Pedersen, DTU Nanolab unless otherwise noted.
=Introduction=
=Introduction=
In E-beam lithography it is often necesarry to do a dose test in order to get the required result. In a dose test one will expose critical parts of a pattern with various doses and determine the best dose by SEM analysis of the final pattern. There are several ways to set up a dose test array on the JEOL system, in this section we will describe four different setups, each with their own benefits and drawbacks.
In E-beam lithography it is often necesarry to do a dose test in order to get the required result. In a dose test one will expose critical parts of a pattern with various doses and determine the best dose by SEM analysis of the final pattern. There are several ways to set up a dose test array on the JEOL system, in this section we will describe four different setups, each with their own benefits and drawbacks.
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Example frome ChipPlace definine a 10 x 2 element dose matrix with relative doses from 1 to 2, ready for export to V30. Image: Thomas Pedersen.
Example frome ChipPlace definine a 10 x 2 element dose matrix with relative doses from 1 to 2, ready for export to V30.  
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=Scripted expansion of a PEC modulation table=
=Scripted expansion of a PEC modulation table=
The last method is basically the same as the second method above but with support for PEC modulation. Thus in this method we will expand the PEC modulation table into a number of PEC and dose test modulated tables, i.e. we will get one unique table per dose.
The last method is basically the same as the second method above but with support for PEC modulation. This is achieved by expanding the dose modulation table into a set of tables, one for each dose of the dose test. Each modulation table is a scaled version of the initial modulation table, scaled simply by the dose test scaling between each dose. The scaling is done through a Matlab script which can be found below. Since Labadviser does not allow upload of .m files, simply copy the script from below and save as a .m file.
 
Benefits:
*Supports PEC modulation
*Faster execution since it is a single SDF sequence
*Works with large V30 files
 
Drawbacks:
*A bit tricky for first time use
 
 
{| class = "collapsible" width=65% style = "border-radius: 10px; border: 1px solid #CE002D;"
! width=100% | Matlab script for modulation table expansion
|-
|
<pre>
clearvars
%Modulation table modding for dose test of PEC'ed V30's, see Labadviser for further information
%https://labadviser.nanolab.dtu.dk/index.php?title=Specific_Process_Knowledge/Lithography/EBeamLithography/Dose_Testing
%THOPE 2023-11-13
 
%Input variables for modulation table
inputJDI = 'C:\Users\thope\Desktop\thope231113\withcross.jdi';
outputJDI = 'C:\Users\thope\Desktop\thope231113\thope231113.jdi';
m = 9; %number of doses
modulation = 5; %modulation between instances in percent, must be positive
 
%shot time calculation
Base = 220; %Base dose, only for indication, not used for modulation
I = 2e-9; %beam current
pitch = 12; %steps of 0.25 nm
dp = pitch*0.25*1e-9; %beam step in m
 
%Base dose calculation
Doses = (0:1:m-1);
Doses = (Doses*modulation/100+1)*Base;
 
%Read file
fileID=fopen(inputJDI,'r');
A = fscanf(fileID,'%c');
fclose(fileID);
%Find start of modulation table by searching for '('
k1 = strfind(A, '(');
k1 = k1(2:end-1);
%Find end of modulation table by searching for ')'
k2 = strfind(A, ')');
k2 = k2(1:end-2);
n = numel(k1);
%Display input table
disp('Input table:')
disp(A(1:k2(end)+1))
 
%Define zero matrix
class = zeros(n,1);
D = zeros(m,n);
 
%Read base modulation
for i = 1:n
    [class(i),D(1,i)] = readMOD(A,k1(i),k2(i));
end
 
 
%Calculate tables
D(1,:) = 1 + D(1,:)./100 ; %convert from MOD to percent
for i = 2:m
    D(i,:) = D(1,:)*(1+modulation*(i-1)/100);
end
D = round(D,3); %round to 1 decimal
for i = 1:m
    D(i,:) = 100*(D(i,:)-1); %convert to MOD from percent
end
 
 
%Write modulated tables to file
fileID = fopen(outputJDI,'w');
for i = 1:m
    fprintf(fileID,['MOD' num2str(i) ': MODULAT (']);
    for k = 1:size(D,2)
        if k==1
            fprintf(fileID,['( ' num2str(k-1) ', ' num2str(D(i,k)) '  )']);
        else
            if mod(k,3)
                fprintf(fileID,[' , ( ' num2str(k-1) ', ' num2str(D(i,k)) ' )']);
            else
                fprintf(fileID,[' , ( ' num2str(k-1) ', ' num2str(D(i,k)) ' )']);
                fprintf(fileID,['\n' '-    ']);
            end
        end
    end
    fprintf(fileID,')');
    fprintf(fileID,['\n\n']);
end
fclose(fileID);
 
%Modulation table range
range = zeros(m,2);
for i = 1:m
    range(i,1) = D(i,1); %minimum dose
    range(i,2) = D(i,end); %maximum dose
end
range = (range/100+1)*Base;
 
%Frequency range
F = zeros(m,2);
for i = 1:m
    F(i,1) = I./(range(i,1)*dp^2); %minimum dose
    F(i,2) = I./(range(i,2)*dp^2); %maximum dose
end
F = F/1e4;
 
%Display output
disp(newline)
disp('Modulation table | Base dose [µC/cm2] | Modulation range [µC/cm2] | Frequency range [MHz]')
for i = 1:m
    disp(['MOD' num2str(i) ' | ' num2str(Doses(i)) ' | ' num2str(range(i,1),'%.0f')...
        ' - ' num2str(range(i,2),'%.0f') ' | ' num2str(F(i,1),'%.0f') ' - ' num2str(F(i,2),'%.0f')])
end
 
function [a,b] = readMOD(str,k1,k2)
    str = str(k1:k2);
    x = regexp(str,',');
    a = str2double(str(2:x-1));
    b = str2double(str(x+1:end-1));
end
</pre>
 
|-
|}
 
<br clear="all">
 
The number of doses for dose testing is controlled by the parameter '''m''' while the increase in dose between doses is defined by '''modulation''', it is a percentwise change relative to the base dose. For instance, if one wants to do a dose test with 200 µC/cm<sup>2</sup> as base dose in steps of 10 µC/cm<sup>2</sup> one would set '''modulation = 5'''.
 
The output is a single JDI file containing all modulation tables named '''MODx''', where x is a running number from 1 to '''m'''. The array and reference to each modulation table can then be set up in the JDF file as seen below. It is convenient to use the include command '''@''' to reference the JDI file itself rather than copy-paste the tables into the JDF.
 
 
{| class = "collapsible" width=65% style = "border-radius: 10px; border: 1px solid #CE002D;"
! width=100% | Example JDF with a dose test setup defined by the '''ARRAY''' command and reference to individual modulation tables.
|-
|
<pre>
JOB/W  'THOPE',4
PATH DRF5M                                     
ARRAY (-4000,5,2000)/(0,1,0)
ASSIGN P(1) -> ((1,1),MOD1)
ASSIGN P(1) -> ((2,1),MOD2)
ASSIGN P(1) -> ((3,1),MOD3)
ASSIGN P(1) -> ((4,1),MOD4)
ASSIGN P(1) -> ((5,1),MOD5)
AEND
PEND
LAYER  1                                 
P(1)  'mypattern.v30'       
SPPRM 4.0,,,,1.0,1                         
STDCUR  2.0 ;nA                           
@'thopeExpanded.jdi'
       
END                                     
</pre>
|-
|}
 
 
{| class = "collapsible" width=65% style = "border-radius: 10px; border: 1px solid #CE002D;"
! width=100% | Example JDI file as output by the Matlab script.
|-
|
<pre>
MOD1: MODULAT (( 0, -23.6  ) , ( 1, -22.8 ) , ( 2, -22 )
-      , ( 3, -21.2 ) , ( 4, -20.5 ) , ( 5, -19.7 )
-      , ( 6, -18.9 ) , ( 7, -18 ) , ( 8, -17.2 )
-      , ( 9, -16.4 ) , ( 10, -15.6 ) , ( 11, -14.7 )
-      , ( 12, -13.9 ) , ( 13, -13 ) , ( 14, -12.1 )
-      , ( 15, -11.3 ) , ( 16, -10.4 ) , ( 17, -9.5 )
-      , ( 18, -8.6 ) , ( 19, -7.7 ) , ( 20, -6.7 )
-      , ( 21, -5.8 ) , ( 22, -4.8 ) , ( 23, -3.9 )
-      , ( 24, -2.9 ) , ( 25, -2 ) , ( 26, -1 )
-      , ( 27, 0 ) , ( 28, 1 ) , ( 29, 2 )
-      , ( 30, 3 ) , ( 31, 4.1 ) , ( 32, 5.1 )
-      , ( 33, 6.2 ) , ( 34, 7.2 ) , ( 35, 8.3 )
-      , ( 36, 9.4 ) , ( 37, 10.5 ) , ( 38, 11.6 )
-      , ( 39, 12.7 ) , ( 40, 13.8 ) , ( 41, 14.9 )
-      , ( 42, 16.1 ) , ( 43, 17.3 ) , ( 44, 18.4 )
-      , ( 45, 19.6 ) , ( 46, 20.8 ) , ( 47, 22 )
-      , ( 48, 23.2 ) , ( 49, 24.5 ) , ( 50, 25.7 )
-      , ( 51, 27 ) , ( 52, 28.2 ) , ( 53, 29.5 )
-      , ( 54, 30.8 ) , ( 55, 32.1 ) , ( 56, 33.5 )
-      , ( 57, 34.8 ) , ( 58, 36.1 ) , ( 59, 37.5 )
-      , ( 60, 38.9 ) , ( 61, 40.3 ) , ( 62, 41.7 )
-      , ( 63, 43.1 ) , ( 64, 44.5 ) , ( 65, 46 )
-      , ( 66, 47.4 ) , ( 67, 48.9 ) , ( 68, 50.4 )
-    )
 
MOD2: MODULAT (( 0, -16  ) , ( 1, -15.1 ) , ( 2, -14.2 )
-      , ( 3, -13.3 ) , ( 4, -12.5 ) , ( 5, -11.7 )
-      , ( 6, -10.8 ) , ( 7, -9.8 ) , ( 8, -8.9 )
-      , ( 9, -8 ) , ( 10, -7.2 ) , ( 11, -6.2 )
-      , ( 12, -5.3 ) , ( 13, -4.3 ) , ( 14, -3.3 )
-      , ( 15, -2.4 ) , ( 16, -1.4 ) , ( 17, -0.4 )
-      , ( 18, 0.5 ) , ( 19, 1.5 ) , ( 20, 2.6 )
-      , ( 21, 3.6 ) , ( 22, 4.7 ) , ( 23, 5.7 )
-      , ( 24, 6.8 ) , ( 25, 7.8 ) , ( 26, 8.9 )
-      , ( 27, 10 ) , ( 28, 11.1 ) , ( 29, 12.2 )
-      , ( 30, 13.3 ) , ( 31, 14.5 ) , ( 32, 15.6 )
-      , ( 33, 16.8 ) , ( 34, 17.9 ) , ( 35, 19.1 )
-      , ( 36, 20.3 ) , ( 37, 21.6 ) , ( 38, 22.8 )
-      , ( 39, 24 ) , ( 40, 25.2 ) , ( 41, 26.4 )
-      , ( 42, 27.7 ) , ( 43, 29 ) , ( 44, 30.2 )
-      , ( 45, 31.6 ) , ( 46, 32.9 ) , ( 47, 34.2 )
-      , ( 48, 35.5 ) , ( 49, 37 ) , ( 50, 38.3 )
-      , ( 51, 39.7 ) , ( 52, 41 ) , ( 53, 42.5 )
-      , ( 54, 43.9 ) , ( 55, 45.3 ) , ( 56, 46.9 )
-      , ( 57, 48.3 ) , ( 58, 49.7 ) , ( 59, 51.3 )
-      , ( 60, 52.8 ) , ( 61, 54.3 ) , ( 62, 55.9 )
-      , ( 63, 57.4 ) , ( 64, 59 ) , ( 65, 60.6 )
-      , ( 66, 62.1 ) , ( 67, 63.8 ) , ( 68, 65.4 )
-    )
 
MOD3: MODULAT (( 0, -8.3  ) , ( 1, -7.4 ) , ( 2, -6.4 )
-      , ( 3, -5.4 ) , ( 4, -4.6 ) , ( 5, -3.6 )
-      , ( 6, -2.7 ) , ( 7, -1.6 ) , ( 8, -0.6 )
-      , ( 9, 0.3 ) , ( 10, 1.3 ) , ( 11, 2.4 )
-      , ( 12, 3.3 ) , ( 13, 4.4 ) , ( 14, 5.5 )
-      , ( 15, 6.4 ) , ( 16, 7.5 ) , ( 17, 8.6 )
-      , ( 18, 9.7 ) , ( 19, 10.8 ) , ( 20, 12 )
-      , ( 21, 13 ) , ( 22, 14.2 ) , ( 23, 15.3 )
-      , ( 24, 16.5 ) , ( 25, 17.6 ) , ( 26, 18.8 )
-      , ( 27, 20 ) , ( 28, 21.2 ) , ( 29, 22.4 )
-      , ( 30, 23.6 ) , ( 31, 24.9 ) , ( 32, 26.1 )
-      , ( 33, 27.4 ) , ( 34, 28.6 ) , ( 35, 30 )
-      , ( 36, 31.3 ) , ( 37, 32.6 ) , ( 38, 33.9 )
-      , ( 39, 35.2 ) , ( 40, 36.6 ) , ( 41, 37.9 )
-      , ( 42, 39.3 ) , ( 43, 40.8 ) , ( 44, 42.1 )
-      , ( 45, 43.5 ) , ( 46, 45 ) , ( 47, 46.4 )
-      , ( 48, 47.8 ) , ( 49, 49.4 ) , ( 50, 50.8 )
-      , ( 51, 52.4 ) , ( 52, 53.8 ) , ( 53, 55.4 )
-      , ( 54, 57 ) , ( 55, 58.5 ) , ( 56, 60.2 )
-      , ( 57, 61.8 ) , ( 58, 63.3 ) , ( 59, 65 )
-      , ( 60, 66.7 ) , ( 61, 68.4 ) , ( 62, 70 )
-      , ( 63, 71.7 ) , ( 64, 73.4 ) , ( 65, 75.2 )
-      , ( 66, 76.9 ) , ( 67, 78.7 ) , ( 68, 80.5 )
-    )
 
MOD4: MODULAT (( 0, -0.7  ) , ( 1, 0.4 ) , ( 2, 1.4 )
-      , ( 3, 2.4 ) , ( 4, 3.4 ) , ( 5, 4.4 )
-      , ( 6, 5.4 ) , ( 7, 6.6 ) , ( 8, 7.6 )
-      , ( 9, 8.7 ) , ( 10, 9.7 ) , ( 11, 10.9 )
-      , ( 12, 11.9 ) , ( 13, 13.1 ) , ( 14, 14.3 )
-      , ( 15, 15.3 ) , ( 16, 16.5 ) , ( 17, 17.7 )
-      , ( 18, 18.8 ) , ( 19, 20 ) , ( 20, 21.3 )
-      , ( 21, 22.5 ) , ( 22, 23.8 ) , ( 23, 24.9 )
-      , ( 24, 26.2 ) , ( 25, 27.4 ) , ( 26, 28.7 )
-      , ( 27, 30 ) , ( 28, 31.3 ) , ( 29, 32.6 )
-      , ( 30, 33.9 ) , ( 31, 35.3 ) , ( 32, 36.6 )
-      , ( 33, 38.1 ) , ( 34, 39.4 ) , ( 35, 40.8 )
-      , ( 36, 42.2 ) , ( 37, 43.7 ) , ( 38, 45.1 )
-      , ( 39, 46.5 ) , ( 40, 47.9 ) , ( 41, 49.4 )
-      , ( 42, 50.9 ) , ( 43, 52.5 ) , ( 44, 53.9 )
-      , ( 45, 55.5 ) , ( 46, 57 ) , ( 47, 58.6 )
-      , ( 48, 60.2 ) , ( 49, 61.9 ) , ( 50, 63.4 )
-      , ( 51, 65.1 ) , ( 52, 66.7 ) , ( 53, 68.4 )
-      , ( 54, 70 ) , ( 55, 71.7 ) , ( 56, 73.6 )
-      , ( 57, 75.2 ) , ( 58, 76.9 ) , ( 59, 78.8 )
-      , ( 60, 80.6 ) , ( 61, 82.4 ) , ( 62, 84.2 )
-      , ( 63, 86 ) , ( 64, 87.9 ) , ( 65, 89.8 )
-      , ( 66, 91.6 ) , ( 67, 93.6 ) , ( 68, 95.5 )
-    )
 
MOD5: MODULAT (( 0, 7  ) , ( 1, 8.1 ) , ( 2, 9.2 )
-      , ( 3, 10.3 ) , ( 4, 11.3 ) , ( 5, 12.4 )
-      , ( 6, 13.5 ) , ( 7, 14.8 ) , ( 8, 15.9 )
-      , ( 9, 17 ) , ( 10, 18.2 ) , ( 11, 19.4 )
-      , ( 12, 20.5 ) , ( 13, 21.8 ) , ( 14, 23.1 )
-      , ( 15, 24.2 ) , ( 16, 25.4 ) , ( 17, 26.7 )
-      , ( 18, 28 ) , ( 19, 29.2 ) , ( 20, 30.6 )
-      , ( 21, 31.9 ) , ( 22, 33.3 ) , ( 23, 34.5 )
-      , ( 24, 35.9 ) , ( 25, 37.2 ) , ( 26, 38.6 )
-      , ( 27, 40 ) , ( 28, 41.4 ) , ( 29, 42.8 )
-      , ( 30, 44.2 ) , ( 31, 45.7 ) , ( 32, 47.1 )
-      , ( 33, 48.7 ) , ( 34, 50.1 ) , ( 35, 51.6 )
-      , ( 36, 53.2 ) , ( 37, 54.7 ) , ( 38, 56.2 )
-      , ( 39, 57.8 ) , ( 40, 59.3 ) , ( 41, 60.9 )
-      , ( 42, 62.5 ) , ( 43, 64.2 ) , ( 44, 65.8 )
-      , ( 45, 67.4 ) , ( 46, 69.1 ) , ( 47, 70.8 )
-      , ( 48, 72.5 ) , ( 49, 74.3 ) , ( 50, 76 )
-      , ( 51, 77.8 ) , ( 52, 79.5 ) , ( 53, 81.3 )
-      , ( 54, 83.1 ) , ( 55, 84.9 ) , ( 56, 86.9 )
-      , ( 57, 88.7 ) , ( 58, 90.5 ) , ( 59, 92.5 )
-      , ( 60, 94.5 ) , ( 61, 96.4 ) , ( 62, 98.4 )
-      , ( 63, 100.3 ) , ( 64, 102.3 ) , ( 65, 104.4 )
-      , ( 66, 106.4 ) , ( 67, 108.5 ) , ( 68, 110.6 )
-    )
 
</pre>
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