Electronics Research Laboratory

University of California, Berkeley

1.0 Introduction

This version of SAMPLE-3D is similar to SAMPLE-3Dv1.0 for Lithography, but now has the capability of simulating pattern transfer through the use of NEtch. NEtch is a triangular facet advancement program in which various physical models can be toggled off and on to allow 3D simulation of wet and dry etching and deposition in integrated circuit processing. The lithography simulation capabilities have also been improved. A new version of SPLAT, SPLATv5.0, capable of generating aerial images within thin films is now included as part of the SAMPLE-3D package. The resist dissolution algorithm has been made more robust and CPU efficient by adding an octtree based deloop, thin-triangle regularization and coordinated ray trace/ray advancement. Also, an advection based dissolution simulation has been added (ADVECT) and can be compared with the cell (CRATER) and surface (DEVELOP) models. This new version of SAMPLE comes without the GUI; the user must execute the program by supplying an input deck containing the commands to be executed.

Most of the software may be run as separate stand alone programs. Communication between programs is primarily through files. This is appropriate given the large amounts of data which must be transferred. This form of information transfer also allows intermediate steps to be saved and retrieved for later use.

SAMPLE-3D is designed for use on engineering workstations running under the Unix(TM) operating systems. The plotting programs require the X window system version X11R3 or X11R4. Most of the other programs may be run under different operating systems and do not themselves require X-window support. Memory requirements are fairly large. 16 megabytes of physical memory is a lower limit for practical simulation, although some simulations require less and others are better served by 24 or 32 megabytes. File disk space requirement is typically 5 megabytes for a full 3D lithography simulation. Run times depend on the machine and the problem size but vary from 1-5 minutes for image simulation, from 1-5 minutes for exposure simulation (or 20-45 with PEB), and 10-50 minutes for 3D development on machines such as the DEC3100, DEC5000, Sun 4/280, and IBM RS6000/530.

1.2 Individual Software Components of SAMPLE-3D

SPLAT v5.0 7/7/94: calculates aerial images at the wafer plane in projection optical lithography, including lens defects and phase-shift masks. This new version of SPLAT is capable of modeling thin-film interference effects and aberrations in Zernike Polynomial form.

BLEACH v1.0 11/2/91: generates a dissolution rate matrix from image data and exposure and development models.

DEVELOP v1.0 11/2/91: simulates 3D resist development, using ray-trace. (Has a working implementation of a deloop algorithm.)

CRATER v1.0 11/2/91: is a robust program for cell-removal based on lithography development.

NEtch v1.0 7/7/94: is a new feature that simulates pattern transfer in SAMPLE-3D.

PDRAW v3.2 8/10/91: plots 3D data, with interactive viewpoint selection, back-front sorting for hidden line removal, and simple illumination.

CONTOUR v3.0 5/19/91: generates contour plots of an x-y array of data.

DRAWPLOT v2.2 7/11/91 plots 2D data in f77punch7(SAMPLE 1.8a) format.

DRAWMASK v2.2 11/2/91: accepts a SPLAT command file as input and displays the mask, assigning colors to phase-shifted regions.

CUTAWAY v1.0 11/2/91 takes a PDRAW data file and throws away everything outside of a user-defined rectangular region.

PTOM v1.0 11/2/91 converts a PDRAW data file to a file of polygons for use in Mathematica.

ASC2BIN v1.0 11/2/91 converts ascii rate files to binary format.

1.3 About this manual

1.0 Introduction.

2.0 Installation.

3.0 Running SAMPLE-3D and individual components. This section describes how the important simulation programs may be run either as part of SAMPLE-3D or as separate stand-alone programs. It will be of interest to users who do not have X-window terminals or who wish to create multiple files for batch-mode program execution.

4.0 A Tutorial for doing Lithography Simulation.. A simple example using thin-film SPLAT is traced to provide the user both a tutorial and a quick installation check. Use this example the first time you run SAMPLE-3D to verify that the programs were installed correctly.

4.0 A Tutorial for doing Lithography Simulation.A simple example illustrating isotropic etching into a square contact is provided in order to show the user some of the commands that are used. This example also serves as a check to see that the NEtch module was installed correctly.

6.0 Physical Models and Algorithms in SAMPLE-3D. This section describes the physical models implemented in the various programs contained in SAMPLE - SPLAT, BLEACH, CRATER, DEVELOP and NEtch.

7.0 Examples. Several simulation examples are shown, including g-line, i-line, and deep-UV lithography, with and without PEB and phase-shift, plasma etching, reflection and sputter deposition.

8.0 About the Source Code. This section is meant to give the user a feel for the flow, and some introductory information about the data-structures used to represent the surface state and do various geometric operations in SAMPLE-3D.

9.0 Appendix of Man Pages. Most of the software in the release tape is documented in Unix man page style for convenient reference.This is where the most detailed user information is located.

2.0 Installation

The tested setups are:

DECStation 5000, Ultrix 4.1, DecWindows 4.1

IBM RS6000, AIX 3.1, Motif 1.1

Sun 4, SunOS 4.1.2, MIT X11R4

Sun SparcStation, SunOS 4.1.1, Open Look 3.0

In addition, you need X11R3 or greater for the graphical programs (i.e. Pdraw) to install.

2.2 Organization

SAMPLE3DMake build file

SAMPLE3DClean clean all objects

SAMPLE3D Code.

2.3 Installation

i.e., type mkdir destdir and

cd destdir to change to the newly created directory.

3). Then uncompress the SAMPLE-3D tar file by typing

uncompress SAMPLE3Dv2.0.tar.Z

If done correctly, the .Z suffix that was previously attached to these files should vanish

tar -xvf SAMPLE3Dv2.0.tar

5). You are now ready to start compiling. Make sure you are in the directory where you have installed the SAMPLE-3D code. Now type:

csh SAMPLE3DMake at the Unix prompt.

Since SPLAT is written in FORTRAN, you will also be asked to enter the FORTRAN compiler you have. The two types of compilers for which Makefiles are provided are the XLF (for the IBM XLF compiler) and f77 compilers. If your compiler is different from either of these two, you will need to construct your own Makefile for SPLAT and compile it individually. When compiling begins you should see the following messages about the status of the compilation on the screen:

SAMPLE-3D Release 2.0

=============================

(C) 1994 University of California, Berkeley

compilation and installation

Please enter target (SunOS or AIX or DEC) = AIX

Please enter the Fortran compiler you have (f77 or xlf etc.) xlf

Compiling for OS = AIX

===============================================

Compiling Contour

cc -c -I/usr/include main.c

cc -c -I/usr/include contour.c

cc -c -I/usr/include IOread.c

cc -c -I/usr/include array.c

cc -c -I/usr/include parser.c

cc -c -I/usr/include list.c

cc -c -I/usr/include time.c

cc -c -I/usr/include plotps.c

cc -c -I/usr/include plothp.c

cc -c -I/usr/include plotX11.c

cc -o contour main.o contour.o IOread.o array.o parser.o list.o time.o

plotps.o plothp.o plotX11.o -lm -lX11

===============================================

Compiling Cutaway

cc -O -c main.c

cc -O -c IOread.c

cc -o cutaway main.o IOread.o -lm

===============================================

Compiling Drawmask

....

Check to make sure that the exact configuration, such as the system and machine, matches your current setup.

If the installation is successful, you should see the following message:

Compilation completed successfully

Copy or link needed executables to your bin

Have a nice day!!!

6). After compilation, you may or may not want to remove the object files that were created for each program. To remove ALL the object files that were created, simply type:

csh SAMPLE3DClean at the Unix prompt.

Please consult the SAMPLE-2D manual for instructions on installing it.

2.4 Installation Problems

1. Lack of disk space
   Either provide sufficient space or adjust the ``build.all'' script to build only one module at a time and then delete the installed tar files after the build.
2. Incorrect permission settings
   Make sure you have sufficient permission for the destination directories. Check the status display to see that the destination directories are as desired. If you are installing to a system directory (such as /usr/local/bin), you may have to ``su root.''
   ##The installation script automatically sets the permission level to 0755 for executables and 0644 for libraries. If you need to set different permission levels, you will have to modify each Makefile manually. There are no provisions for customized permission levels at this point. #
3. Missing header or library files
   This occurs normally because of missing or incorrect X libraries. Check to make sure that your X release is complete and current. If the installation still fails, then contact us.
4. Compilation errors
   Make sure standard compilers (like cc and not gcc, ANSI C, or CC) are used.

A full 3D lithography simulation using three modules is performed by running the following:

%splat < splat-inputfile

%bleach -o bleach-inputfile -if 2D or 3D contour-file

%develop -bf rval.3D.binary -et 30.0 -pt 10.0

%netch -if netch-inputfile

The following SAMPLE-3D process flow diagram will serve to explain the dependency of the various modules in a concise manner: In the diagram below, DEVELOP and CRATER serve as development tools for Lithography simulation while NEtch simulates etching and deposition processes. Also note that NEtch can be run without using any information from the SPLAT and BLEACH modules.

Specific information on the various menu options is listed in the man pages at the end of this manual.

3.1 Running SPLAT

The SPLAT program is capable of simulating the effects of lens aberrations, apodization, spatial filtering, focus and magnification effects for high NA, etc. As mentioned before, the latest version of SPLAT (version 5.0) which comes with this release is also capable of modelling thin-film interference effects.

SPLAT accepts a file of trial numbers, with each trial number followed by a list of arguments and delimited by a semicolon (;). A command line beginning with the pound sign (#) is ignored, and a line beginning with an ampersand (&) is considered a continuation of the previous line.

The projection system is specified by defining the illumination wavelength, numerical aperture, defocus, partial coherence, and the mask is specified as a set of rectangles or triangles, each with a given transmittance and phase. Then the image is simulated for a specified region.

The parser does not recognize key words and simply skips over them. The following is a basic SPLAT command file:

# Example SPLAT file

2: wavelength = 0.436 microns;

3: NA = 0.28;

4: defocus = 0.0 microns;

5: partial coherence = 0.7;

6: simulation region is 2 x 2 um at 1 transmittance;

8: cutout (0.0, 0.0) 0.5x0.5 at -1 transmittance 180

& degrees phase;

10: calculate the Fourier coefficients;

11: calculate image intensity (0.0, 0.0)

& xlength = 1.0, ylength = 1.0

& save in file ``image.cnt'';

14: calculate intensity along (0,1) to (1,1) and save

in ``2ddat'';

0: end;

%splat < filename

Triangular mask regions are entered with trial statement 7.

Please consult section 6.1 or the SPLAT user guide for more details on the physical models in SPLAT

3.2 Running BLEACH

Command lines beginning with a pound sign (#) are ignored. Most command lines begin with a key word, are followed by a list of arguments and are concluded by a semicolon (;). For a list of commands recognized by BLEACH please see section 5.2, Dynamic Bleaching, Reaction and Diffusion models in BLEACH.

A typical input file appears as follows:

resmodel (0.4358) (0.5510, 0.058, 0.01)

(1.68, -0.02), (0.7133);

layers (4.73, -0.14) (1.47, 0.0, 0.074);

dose 150;

exposerun;

devrate 2 (0.23 0.0016 5.6 0.25 0.25 0.62 0.08);

BLEACH is run by typing:

%bleach -o bleach-inputfile -if splat-contour-file

3.3 Running DEVELOP

%etch -b binary_ratefile -mdens dens -et etchtime -pt plottime

3.4 Running CRATER

CRATER allows commands to be read from external command files using the -if filename option. Commands are entered in the form of a key word followed by a parameter list and are executed in the order they are received. A semicolon signifies the end of a particular command while the pound sign (#) forces everything until the next semicolon to be ignored. CRATER may also be run interactively. A typical CRATER input file is given in the tutorial in section 3.

Advantages of using a command file include the ability to specify the number of cells in the x, y, and z, directions and to generate plots along x, y, and z planes. A complete list of CRATER commands is given in the man page at the end of this document.

3.5 Running ADVECT

%advect

3.6 Running NEtch

%netch -if netch input file

3.7 Running The Plot Programs.

%setenv DISPLAY host:display

To exit a plot program, simply click the mouse in the window or in the QUIT button if one exists. The plotters will then create a PostScript file named dataplot.ps and prompt to ask if the file should be sent to the default printer. Many of the PostScript plots, especially for 3D, are quite large and may take 20-60 minutes to print on typical laserwriters.

There are also two programs that allow a user to manipulate plot data. CUTAWAY takes a PDRAW data file and four parameters defining a rectangular region and throws away everything outside of that region. PTOM converts a PDRAW data file to a file of polygons for use in Mathematica.

The plot programs all have command line arguments. Some of the programs also support option files for setting line types, axis labels etc. See the man pages at the end of this document for more details.

3.8 Running the Utilities

4.0 A Tutorial for doing Lithography Simulation

4.1 Input Decks for the Simulation

stmt 35: resist layer = RESIST_LAYER 'case1.dat'

The entire SPLAT input file is shown below. For more information on these commands, please look at the explanation given under SPLAT in the Physical Models section of this manual.

# Fast thin-film SPLAT example.

# 0.30 um contact

stmt 1: print = 3

stmt 2: lambda = 0.365 um

stmt 3: na = 0.700

stmt 4: defocus = 0.25 mode = 1 #true defocus

stmt 5: sigma = 0.500

stmt 6: mask = 0.30 x 0.30 trans = 0;

stmt 7: cutout = (0.00, 0.00) 0.200 x 0.20 trans = 1;

stmt 35: resist layer = RESIST_LAYER'case1.dat'

stmt 31: mag = 5 mode = 0;

stmt 32: 10 0;

stmt 10: 0 2;

stmt 11:(-0.30 -0.30) 0.6 0.6'lyr.RESIST_LAYER.ctr';

stmt 14: cutline from (-0.30, 0.0) to (0.30, 0.0)

& with 50 points mode = 1 in'lyr.RESIST_LAYER.plot'

0;

The thin-film SPLAT input file

4.7300 -0.1400 1.00 0.00 0.36500 0.00

1.6800 0.7400 0.200 0.01200 240.0 0.5 30

%run.layers splat.input 1 30

Now, in order to create a 3D intensity file that is accepted by BLEACH, type

%merge.contours lyr.RESIST_LAYER.ctr 1 30 > 3d.dat

The merged contour file can now be sent to BLEACH for exposure simulation. BLEACH contains various process conditions such as the refractive index, A, B, C, and the thickness of the resist which convert the contour file into a binary file containing a matrix of etch rates. The BLEACH input file, bleach.in, is given below:

resmodel ((0.436)

(0.74, 0.2, 0.012)

(1.68, -0.0200)(1.0));

layers (4.73, -0.14);

dose 240;

devrate 2 (0.0620 0.0001 8.5000);

%bleach -o bleach.in -tf -if 3d.dat

etchtime 15;

celldensity 50 50 50;

runcells;

plotcells 3;

quit;

%crater -bf rval.3D.binary -if crater.in

4.2 Output

%pdraw 3D.cells

%contour -cstep 0.08 lyr.1.ctr

5.0 A Tutorial for Using NEtch

The program has several command line options and may not only be run like DEVELOP but may also be run interactively. Generally, however, NEtch interprets and executes commands line by line from a command file or from standard input. The basic command line to run an etching or a deposition simulation is:

%netch -if instruction file

5.1 Generating an Input File

The sim_region command is used to demarcate the simulation region. The following instruction uses a cube of length 2.0 units as the simulation region.

sim_region -1.0 1.0 -1.0 1.0 -1.0 1.0 0.0;

etchlayers first creates one layer, 1.0 microns thick, and defines the etch rate through this layer to be 0.1mm/s. Although only one layer is defined here, the keyword etchlayers can be used to specify the etch rates for several layers. It can only be used with isotropic or directional etching. All other simulations use the keyword etchlayer instead

etchlayers 1 1.0 0.1;

maskpiece 0 -0.5 -0.5 1.0 1.0;

setmask 0;

Next, the nature of the etch is defined. The keyword adv_method defines the surface advancement method. For this simulation, the fixed time step facet motion algorithm was chosen. To simulate an isotropic etch we use the etchmodel command. So, the following lines must now be added to the input file:

adv_method 1;

etchmodel 0;

etchtime 5.0 0.2;

run;

plot3D tutorial_file;

#this line is a comment...

sim_region -1.0 1.0 -1.0 1.0 -1.0 1.0 0.0;

analytic_rate 12;

etchlayers 1 1.0 0.1;

meshaccur 0 0 0 0;

maskpiece 0 -0.5 -0.5 1.0 1.0;

setmask 0;

noclip 1;

adv_method 1;

etchmodel 0;

meshdensity 10;

etchtime 5.0 0.2;

run;

plot3D tutorial_output;

quit;

%netch -if instruction file

A 3D cutaway view of the final 3D result obtained by running NEtch is shown below. The cutaway view is generated by typing

%cutaway xmin xmax ymin ymax pdraw-file

5.2 Structure of the Input file

The user first sets up the structure of the simulation with keywords such as loadrate, sim_region, or etchlayers and is also given some control over the appearance of the simulation, such as the mesh and advancement algorithm with keywords like meshdensity and adv_model.

Then, after executing the simulation with run, the user is able to plot the results that are stored in the program's memory.

The necessary information must be entered in proper order, i.e. initialization commands must be entered before execution commands. The etch model and deposition model commands must be entered before the rates are specified; all other initialization commands may be entered in any order. The advancement method must also be set before specifying the etch or deposition time. It is possible to reset most initialization commands after a simulation has been performed with the exception of the mesh density and simulation region parameters.

NEtch also has a special command called save and load which lets the user save the geometry and certain specific simulation information. This command is useful for saving intermediate states of the surface geometry for loading surface information back into NEtch's data structures at a later time. The user can save the surface information using the save_surface command and load it back in during the time of a simulation by using the load_surface command. This surface will then be used as a non-planar mesh on which a desired simulation may be run. For specific details on save and load, please refer to the man pages at the end of this user guide.

6.0 Physical Models and Algorithms in SAMPLE-3D

6.1 Optical Image Models and Algorithms - SPLAT

The algorithm is based on Hopkin's approach as extended by Michael Yeung to include thin-film effects in the pupil function. SPLAT version 5.0 also allows aberrations to be specified in Zernike polynomials or wave front maps. Modified illuminations in the form of quadrupole, annular or illumination maps can be specified. Phase shift masks and inlens filtering are also included.

The program is capable of simulating the effects of lens aberrations, apodization, spatial filtering, focus and magnification effects for high NA, and modified illumination, and the five primary lens aberrations: coma, astigmatism, distortion, spherical aberration, and curvature or defocus. Apodization schemes, such as the Hitachi spatial filter, can be added to the illumination system. Annular, offaxis and quadrupole illumination sources can be also be simulated. As mentioned before, the latest version of SPLAT (version 5.0) which comes with this release is also capable of modelling thin-film interference effects.

Here are a few of the more commonly used SPLAT commands from the SPLAT user guide:

[STATEMENT] 1 printlevel

STATEMENT 1 sets the level of diagnostic output generated by the program. PRINTLEVEL=1 produces no diagnostic output, while PRINTLEVEL=2 causes the program to echo the input lines to the output. PRINTLEVEL=3, on the other hand, is primarily for interactive/diagnostic use and causes the program to report when statement execution is completed by displaying the input parameters. The default value of PRINTLEVEL is 1.

This statement sets the wavelength, in micrometers, of the light used to illuminate the mask. Currently, the program is set up to accept only a single wavelength. The default is WAVELENGTH = 0.436 mm.

The imaging system is projection-type, with an imaging lens numerical aperture equal to NUMERICAL.APERTURE. Default NUMERICAL.APERTURE is 0.28.

The image can be calculated at a plane other than the plane of best focus. The distance from the plane of best focus, DEFOCUS, is measured in micrometers and defaults to 0.0 Mm. Positive DEFOCUS is defined as being below the gaussian plane, while negative DEFOCUS is above it.MODE is an integer flag used to specify the type of defocus. MODE = 1 specifies that true defocus () will be used and is the default mode. MODE = 0 specifies that approximate defocus () will be used.

STATEMENT 5 sets the partial coherence factor, SIGMA, of the imaging system. Only values of partial coherence that lie between 0.0 (full coherence) and 1.0 (partial coherence) are accepted by the program. SIGMA defaults to 0.7, a value common to most projection printers. SIGMA_IN is used for annular illumination schemes. It indicates the radius of the illumination cone which will be blocked out. The actual illumination occurs only in the annulus from SIGMA_IN to SIGMA. SIGMA_IN defaults to 0.0.

The working area is the size of the mask which is to be imaged and is specified by XLENGTH and YLENGTH in micrometers. This specified area is actually only the first quadrant in Cartesian coordinates. The total/unfolded area is bounded by the coordinates (-XLENGTH,-YLENGTH), (- XLENGTH,YLENGTH), (XLENGTH,YLENGTH), (XLENGTH,-YLENGTH), and a periodic extension in both the X and Y directions is assumed. The optional TRANSMITTANCE is the initial transmittance of the mask (usually either 1 for transparent or 0 for opaque). The image calculation time is approximately proportional to the square of the imaged area, and to avoid long computation times, field sizes with total areas greater than 16 micrometers squared should be avoided. One way to do this is to take advantage of symmetry - see STATEMENT 7 for details. The default for TRANSMITTANCE is 0, while XLENGTH and YLENGTH both default to 2.0 micrometers. SCALE is a positive real number that can be used to scale the mask. This scale factor will also apply to any STATEMENTs 7, 8, 27, and 28 that come after a STATEMENT 6.

This statement is used to add a rectangular feature to the mask. The rectangle specified is mirrored across the x and y axes. Rectangles may overlap other rectangles - it is the user's responsibility to make sure no part of the mask has transmittance greater than 1 or less than 0.

XCOORD = x coordinate of lower left corner of rectangle

YCOORD = y coordinate of lower left corner of rectangle

XLEN = length of rectangle in x direction

YLEN = length of rectangle in y direction

TRANSMITTANCE= transmittance of the rectangle relative to the current transmittance of the mask where it is to be placed.

PHASE = phase angle (normally 0 degrees). This option is used for phase shifted masks.

As an example, to specify a 2 mm x 2 mm transparent square in a 5 mm x 5 mm opaque mask, the following statements could be used:

STATEMENT 6: 5 um x 5 um at 0 transmittance;

STATEMENT 7: (2.0,2.0) 2.0 um x 2.0 um at 1 transmittance;

However, symmetry can and should be utilized to reduce the computation time by locating the center of the rectangle at the origin of the coordinate system in the following manner:

STATEMENT 6: 2 um x 2 um at 0 transmittance;

STATEMENT 7: (0.0,0.0) 1.0 um x 1.0 um at 1 transmittance;

In the last two input statements above, a 1 mm x 1 mm transparent square is defined in a 2 mm x 2 mm opaque mask. Because the program automatically makes even periodic extensions in the x and y directions, the region specified by the user is actually only the first quadrant in the cartesian coordinate system; the other three quadrants are the mirror images of the first, reflected across the x and y-axes respectively. Therefore, the 1 mm x 1 mm square defined above is actually only part of a 2 mm x 2 mm square, with the center of symmetry of that larger square located at the origin. In a similar manner, an opaque square on a transparent mask can be defined using the statements below, where the transmittance is 1 for the background, and -1 for the square.

STATEMENT 6: 2 um x 2 um at 1 transmittance;

STATEMENT 7: (0.0,0.0) 1.0 um x 1.0 um at -1 transmittance;

[STATEMENT] 8 x1 y1 x2 y2 x3 y3 transmittance [phase];

Add a triangular aperture to the mask. The triangle specified is mirrored across the x and y axes. Triangles may overlap other triangles and rectangles - it is the user's responsibility to make sure no part of the mask has transmittance greater than 1 or less than 0. The triangle can be specified in two ways - as a right-angled triangle defined by the corner (right angle) point, base and height or as a general triangle defined by three points. Again, even periodic extensions in the x and y directions are assumed. Please note that if only six arguments are provided, the program assumes that the triangle being defined is a right- angled triangle.

XCOORD = x coordinate of corner of right-angled triangle

YCOORD = y coordinate of corner of right-angled triangle

XLEN = base length of right-angled triangle (may be negative to flip triangle)

YLEN = height of right-angled triangle (may be negative to flip triangle)

X1 = x coordinate of point defining general triangle

Y1 = y coordinate of point defining general triangle

X2 = x coordinate of point defining general triangle

Y2 = y coordinate of point defining general triangle

X3 = x coordinate of point defining general triangle

Y3 = y coordinate of point defining general triangle

TRANSMITTANCE= transmittance of the triangle relative to the current transmittance of the mask where it is to be placed.

PHASE = phase angle (normally 0 degrees). This option is used for phase shifted masks.

Input Statements:

Statement 6: XM x YM @0;

Statement 7: (0,0) (XL,YL) @1;

STATEMENT 9 is used to calculate the transmittance profile of the mask. The transmittance at any point is the sum of the working area(mask) transmittance (see STATEMENT 6) and the transmittances of all rectangles or triangles defined by STATEMENTs 7 and 8 that cover that point. The output file consists of a list of transmittances at points on a grid defined by NX and NY. The default is to calculate for the entire working area, but the user can specify a smaller (or larger) area. MODE defines the type of output obtained from this statement. MODE = 0 produces output to a specified file, MODE = 1 sends a crude contour plot to the terminal, while MODE = 2 does both.

NX = number of divisions along x axis (default = 20)

NY = number of divisions along y axis (default = 20)

MODE = type of output desired

XLLC = x coordinate of lower left corner of rectangle to be plotted

YLLC = y coordinate of lower left corner of rectangle to be plotted

XLEN = length of rectangle in x direction

YLEN = length of rectangle in y direction

DIFFLAG = 1 to limit spatial frequencies (normally not used)

FILENAME= name of file into which to store the calculated intensities.

STATEMENT 10 orders the program to calculate the transmission cross-coefficients (TCCs) as well as the Fourier coefficients of the image intensity profile. This statement can take a long time to execute. MODE = 1 stores the TCCs in binary form in the file FILENAME. FORCE is an integer flag which forces the program to choose which of the 3 integration routines should be used for TCC calculation. FORCE = 0 is the default, FORCE = 1 uses a 1-dimensional integration routine, while FORCE = 2 uses a 2-dimensional integration scheme. When aberrations other than approximate defocus are used or when magnification is set, FORCE = 2 is used automatically.

This statement calculates the image intensity within a rectangle specified by XLLC, YLLC, XLEN, YLEN. The intensities are calculated at each point of a rectilinear NX by NY equally spaced grid within that rectangle. (Note: Maximum NX*NY is 10000) This output file may be used with a 3-dimensional plotting package to provide either a 3- dimensional intensity profile or an intensity contour plot. The parameters are:

XLLC = x coordinate of lower left corner of rectangle to be plotted

YLLC = y coordinate of lower left corner of rectangle to be plotted

XLEN = length of rectangle in x direction

YLEN = length of rectangle in y direction

NX = number of grid-points in the x direction (default is 50)

NY = number of grid-points in the y direction (default is 50)

FILENAME= name of file into which to store the calculated intensities.

Save the Fourier coefficients that describe mask transmittance and image intensity. This input line will produce a relatively large (approx. 30 kbytes) binary output file, which contains the Fourier coefficients as well as the imaging system parameters - numerical aperture, wavelength, coherence factor, mask size. The coefficients can be reloaded with STATEMENT 13 to generate more plot files of the same mask pattern.

STATEMENT 13 is used to load the Fourier mask and image coefficients previously saved with STATEMENT 12. Therefore, for a given set of imaging system parameters (N.A., wavelength, sigma, mask size and pattern), the intensity profile need only be calculated once with STATEMENT 10. STATEMENT 12 saves the data computed by STATEMENT 10 for later use, and STATEMENT 13 reloads this data. Note that the TCCs saved via STATEMENT 10 can be used for any mask pattern, as long as the field size remains constant. On the other hand, STATEMENT 12-13 saves the Fourier coefficients only, so these can be used only for one particular mask pattern.

Calculate the image intensity profile along the line joining points (XI,YI) and (XF,YF). The number of points along that profile and is optionally specified by NPTS, which defaults to 50. The intensity profile is output in the same format as a SAMPLE f77punch7 file. The `x' values in the file represent the distance along the line from the point (XI,YI), while the `y' values represent the light intensity normalized to 1.00. Again, MODE is an integer flag, normally 0, used to specify the format of the intensity profile. MODE = 1 outputs the intensities with 5 decimal spaces (as compared to 3 with MODE = 0). This option is particularly useful for analysis of small patterns such as defects, where the intensity is very low.

XI = x coordinate of initial plot point

YI = y coordinate of initial plot point

XF = x coordinate of final plot point

YF = y coordinate of final plot point

NPTS = number of points (default is 50, maximum is 500)

MODE = accuracy flag (defaults to 0)

STATEMENT 30 allows entry of a single illumination spot. The SPOT_RADIUS is the radius of the illumination spot while (Jx,Jy) indicate its coordinates in the entrance. pupil of the system. The radius of the entrance pupil is normalized to 1. Multiple illumination spots are specified by using up to 10 of these statements. For example, the following commands define a quadrupole illumination scheme for a system with a partial coherence of 0.695. The system partial coherence is computed automatically as the smallest sigma which will overlap all illumination spots.

STATEMENT 30: Spot_radius = 0.2 at (0.35, 0.35);

STATEMENT 30: Spot_radius = 0.2 at (-0.35, 0.35);

STATEMENT 30: Spot_radius = 0.2 at (0.35,-0.35);

STATEMENT 30: Spot_radius = 0.2 at (-0.35,-0.35);

This statement is used to include magnification effects in the calculation of the aerial image. MAGNIFICATION (or more precisely demagnetization) is defined as the object height divided by the image height. MODE = 0, the default mode, specifies that the mask image will be calculated using the mask dimensions at the mask plane. MODE = 1 specifies that the mask image will be calculated using the mask dimensions scaled down by MAGNIFICATION. This statement must be called prior to STATEMENT 6.

This statement turns on the use of the table lookup routines when calculating the TCCs. Instead of recalculating the pupil function every time, the values are stored in a table and subsequently looked up. The main use of this feature is to speed up the thin-film calculations (STATEMENT 35) and it does not provide any speedup for systems with only few aberrations. The number of columns and rows of the lookup table is initialized with dimension grid_pts X grid_pts. A good number of grid points is 50 for the thin film cases--the results differ by less than 1% from those when not using the table. The maximum number of grid points is 400 and the default is 50. The symmetry parameter refers to the use of symmetry in the calculation of the TCCs (STATEMENT 10) which normally reduces the computation time. When symmetry = 0, symmetry in the TCC calculation is turned off. This will speed up the simulation time when the mask area is very small since the determination of the symmetry dominates the simulation time. Explicitly disabling the symmetry is only permitted in conjunction with STATEMENT 35. By default symmetry = 1 which is the state of normal operation.

Statement 35 allows the image to be calculated within the photoresist. The resist is split up into many thin layers as specified in the `thin-film_data_file'. The format of the thin-film input file is given below. The correct number of parameters must be listed on each line and any number of spaces (but no tabs) may be used to separate them.

Thin-film Data File Input Format

substrate_n subsrtate_k medium_n medium_k wavelength

resist_n A B C dose thickness layers

layer1_n layer1_k thickness

layer2_n layer2_k thickness

...

layer12_n layer12_k thickness

The first four parameters are the real and imaginary parts of refractive index of the substrate and medium (Air) respectively. The fifth parameter is the wavelength in the initial medium. The next line specifies the resist properties: the real part of the index of refraction; the resist A, B, C parameters, used to calculate the imaginary part of the index of refraction; dose; thickness; and number of layers. Any lines following the resist parameters specify the real and imaginary parts of the index of refraction of layers under the photoresist and their thicknesses. Up to 12 layers may be specified.

Thin-film Utilities

The following UNIX scripts and or C programs have been created:

run.layers - a unix script to run many thin-film interference simulations using a single input file

Usage: run.layers splat_input_file start_layer end_layer

The script searches for the word `RESIST_LAYER' and replaces it with the current resist layer and then calls SPLAT. At the end of the simulation there will be end_layer 1D intensity files in your current directory. Since this script calls SPLAT, it must be accessible from your current directory.

merge.layers - a unix script used to merge the 1D intensity files created using run.layers into a 2D intensity contour file

Usage: merge.layers filename_RESIST_LAYER.plot start_layer end_layer

merge.contours - a unix script used to merge the 2D intensity contour files created using run.layer into 3D intensity file for input in SAMPLE-3D

Usage: merge.layer filename_RESIST_LAYER.ctr start_layer end_layer

For an illustration of these scripts please refer to the tutorial on Lithography Simulation in section 3.1 of this document.

is used in SAMPLE.

The commands used to run a bleach process are:

resmodel wavelength A B C n k thickness;

The wavelength is in microns. A, B, and C are the Dill exposure parameters.The refractive index follows. The imaginary part is ignored and calculated from the Dill parameters. The thickness is also in microns.

layers n k [(n k thickness)...];

The first (n,k,) pair is the refractive index of the substrate. The next set of parameters is the refractive index and thickness of any material between the substrate and the resist. The layer closest to the substrate is given first. A maximum of 4 layers in addition to the substrate are allowed.

arclayer n k thickness develop_rate

This command specifies that an anti-reflective coating be used directly beneath the photoresist. The parameterss n, k, and thickness (in um) give the refractive index and the thickness of the ARC layer. The isotropic development rate of the ARC layer is set by the parameter develop_rate.

tarlayer n k thickness

A top-anti-reflecting coating will be used over the photoresist when this statement is used. The parameters n, k, and thickness (in um) give the refractive index and the thickness of the TAR layer. The TAR layer material used is assumed to be easily stripped by water, so it is removed very quickly by a development run. For that reason the ratefile will only contain information concerning the resist and possibly an ARC layer.

dose exposure.dose;

The exposure dose is given in millijoules per square micron at the wafer surface.

heatdiffus diff.length;

This statement requests a post exposure bake. The first argument gives the diffusion length in microns.

shipleyahr baketemp baketime;

These are bake parameters for R.A. Ferguson's SNR-248 acid hardening resist model.

devrate model parameters;

The model is either

1. an analytic function with 3 parameters E1, E2, and E3 and the rate = exp(E1 + E2xM + E3xMxM)/10000 um/sec;
2. the Kim model with 3, 6, or 10 parameters R1-R10 and the rate = f(M,z)xR(M) where R(M) = 1.0/((1.0-Mxexp(-R3x(1.0-M)))/R1 + Mxexp(-R3x(1.0-M))/R2) um/sec and f(M,z) = 1-1(R5-(R5-R6)xM))xexp(-z/R4);
3. the Ferguson SNR-248 model with rate = R0x(1-CE/C0)^a, where R0, C0, and a are the argument list.

CRATER is a 3D cell-based volume removal program for simulation of photoresist dissolution. The program reads a dissolution rate file describing the etch rates ina 3D simulation region. A cell removal algorithm with a basic spillover technique is used to simulate resist development. A predetermined time step is used and the simulation is divided into many steps. At each time step, the volume removed from each surface cell is calculated. Any cells which have a volume of less than zero at the end of a step are removed, and the newly exposed underlying cells are added to the list of surface cells. A negative cell volume indicates that the etch front proceeded past the current surface cell into the underlying cells. This extra volume must be deducted from the newly exposed cells to preserve a valid surface representation. To save memory, full information is allocated only for surface cells. Other cells point to a dummy structure indicating whether the cell is full or empty.

If a neighboring cell is devoid of material, the cell face shared with that neighbor is exposed. All exposed faces are moved into the cell, with a distance given by the product of the etch rate at the cell and the time step. The volume removed is thus a product of the face area and the distance traveled.

The volume removal calculation is always performed as if the cell were completely full, until it is removed entirely. This overestimates the amount of material removed from the surface cell. However, the underlying cells do not etch until the surface cell is completely empty. This combination of overetch and underetch yields the correct overall amount of removed material.

The spillover technique is implemented by evenly dividing the excess volume removed from a surface cell among all the unetched cells that share a face with the original cell.

Factors affecting the removal of cells and the rate at which cells are removed are the etch model that is used, the etch rates that are supplied by the user either through a command file or a rate file, and other process conditions. For a list of valid commands, please refer to the Man Pages on Crater in the appendix.

Develop advances the surface using a triangle based scheme while Advect advances the surface by rigorously solving the Hamilton-Jacobie equation. For more information on the models involved in implementing either of these programs, please refer to John Helmsen's Ph.D dissertation which is listed in the References section at the beginning of the user's guide.

6.4 Physical Models for Pattern Transfer - NEtch

Plasma Etching processes in SAMPLE-3D are modeled by formulating a general etch rate based on sputter yield and particle flux distributions at the surface. The current SAMPLE-3D etching model is based on the flux distribution of incident ions and neutral particles. The following four effects must be considered while simulating an etching process:

i) Directly incident ions: In this case v(x), the velocity in the surface normal direction at x is:

where F_i(φ, θ) gives the ion flux distribution over the solid angle of the visible plasma and N_di, the flux integrated over 0<=φ<=π/2 and 0<=φ<=2π, is a normalizing factor. S_i is the normalized yield function equal to S/S_o while R_di, the etch rate for a flat wafer with no shadowing, is described by

ii) Directly Incident Neutral Particles: In this case v(x) is given by:

where the variables represent the same quantities used to describe the velocity due to directly incident ions. For example, R_dn refers to the etch rate on a flat wafer with no shadowing and N_dn is still a normalizing factor.

iii) Indirect Incident Etchant Flux: The velocity function due to this effect is

iv) Isotropic Etching: The velocity function due to isotropic etching is:

The rate parameters R_dn, R_di, R_is, and R_ii and the flux distributions F_i, F_n, and F_ii depend upon substrate materials, etch gasses and other process conditions. The normalizing factors are computed once the flux distributions are obtained. All the individual velocity terms must then be summed up to give the total etch velocity along the surface normal.

Extensions to the basic model:

Sidewall Passivation is required to model the reduction in rate due to the deposition of material on chamber walls and trench slopes. The redeposition rate is:

Damage to the wafer surface may be caused by energetic ions. Reactive neutrals etch damaged areas more vigorously than undamaged areas. This phenomenon of ion-enhanced etching is modeled by adjusting R_dn such that

Computer Implementation of the Etch Model

So far, we have discussed the physics driving the SAMPLE-3D etching model. While trying to implement this model on a computer, however, we must modify it for reasons of speed and computational efficiency. Furthermore, in order to simulate etching on a computer, we must transform the physical etch rates obtained into etch rates along the three Cartesian coordinates. These transformed etch rates can be described by the following equations;

The overall rate along the surface is then given by:

DEPOSITION MODEL

There are two basic Deposition models:

Chemical Vapor Deposition

CVD processes in SAMPLE are modeled by invoking the Isotropic Deposition model. This is done by invoking the Isotropic Etch model discussed above with a negative etch rate as its argument.

Physical Vapor Deposition

In three dimensions, the direction and rate of growth for a point on the surface depend upon flux contributions arriving from several directions. The following formulae describe the components of the growth rate:

where R_d is the redeposition rate on a flat surface perpendicular to the z-axis, F_d is the flux distribution of arriving particles given by

and N_d is a normalizing factor of the flux distribution over the hemisphere. These three velocity relations are used to model Physical Vapor Deposition.

Extensions to the basic model

Basic Surface Migration may be simulated by means of simple two-step model. First the flux arrival for every surface point is calculated using the flux equation used in the previous example. Then the redistribution is calculated by applying an equation of the form:

where s_i is the distance on the surface from node i to the node of interest, σ expresses the surface migration characteristic length, n is the number of surface points and ΔAi is an area element giving a region of influence for v_i.

6.5 Extracting Solid Geometries for Capacitance Analysis

FastCap is a capacitance analysis program from MIT. Currently, the surface to solid routines in SAMPLE-3D outputs a list of triangular panels in the format used by FastCap. This allows FastCap to be run directly on output files and other capacitance or inductance simulators will likely accept this type of format. ((is the only 3D capacitance analyzer for which input topography files are created)). For a complete description on the use of FastCap and obtaining the software, contact:

Prof. Jacob White

Massachusetts Institute of Technology

Department of Electrical Engineering and Computer Science

Room 36-880

Cambridge, MA 02139 U.S.A.

white@rle-vlsi.mit.edu

fastcap@rle-vlsi.mit.edu

createfastcapfile filetype [z_min z_max xy_boundary_offset] fastcap_input_filename;

The first argument, filetype, can have two values, 0 or 1. A filetype of 0 means that all the current surfaces simulated with NEtch will be transferred to a FastCap input file identified by the fastcap_input_filename directly. A filetype of 1 means that the current most advanced surface from NEtch will be transformed into solid geometries using the arguments in brackets, and then the result will be transferred to the fastcap_input_filename.

For a filetype of 0, the arguments in brackets should not be supplied, and the current surfaces within NEtch are transferred to a generic FastCap file format.

For a filetype of 1, the current most advanced surface from NEtch is transformed into solid geometries using the arguments in brackets. Z_min and z_max are the z coordinates of the flat bounding planes that will be used to intersect the etched surface thereby bounding the top and bottom of the solids. Xy_boundary_offset is a positive number used to intersect bounding planes in the X and Y directions of the simulation region. Flat planes offset by the xy_boundary_offset are intersected with the etched surface thereby completing the enclosure of the solid geometries. Because an xy_boundary_offset of zero will not produce an intersection, this argument must be slightly positive.

1). A short description of the process

#SPLAT File Created By SAMPLE-3D GUI for i-line

2 0.3650;

3 0.5000;

4 0.7000;

5 0.5000;

6 4.000000 2.680000 0;

7 Cutout = (0.250000,0.000000) (0.500000x1.440000)at 1.000 0.000;

7 Cutout = (2.250000,0.000000) (0.500000x0.940000)at 1.000 0.000;

7 Cutout = (0.250000,1.440000) (1.500000x0.500000)at 1.000 0.000;

7 Cutout = (1.750000,1.440000) (0.500000x0.500000)at 1.000 90.000;

7 Cutout = (1.250000,0.000000) (0.500000x0.940000)at 1.000 180.000;

7 Cutout = (3.250000,0.000000) (0.500000x1.440000)at 1.000 180.000;

7 Cutout = (2.250000,1.440000) (1.500000x0.500000)at 1.000 180.000;

10;

11 0.000000 0.000000 4.000000 2.680000 `image.cnt';

#Bleach File Created By SAMPLE-3D GUI for Bleach.input

resmodel ((0.3650)

(1.0500, 0.1100, 0.0120)

(1.8200, -0.0330)(1.0000));

layers (6.5220, -2.7050);

dose 240.0000;

exposerun;

heatdiffus 0.0800 1;

devrate 2 (0.0759 0.0001 7.4600);

#Command line for 3D etch simulation;

develop -b rval.3D.binary -mdens 10 -et 60.0;

The picture after 60 seconds of development generated by ETCH, an older version of DEVELOP.

1. The information posted in the following web site: http://tanqueray.eecs.berkeley.edu
2. The web site: http://www.eecs.berkeley.edu/~neureuth

The picture below was generated by DEVELOP. The development time for the simulation was 25 seconds. One can see that the deloop algorithm in DEVELOP was reasonably effective in removing the loop that generated by ETCH.

An attempt to run DEVELOP for a development time beyond 19 seconds resulted in an error as the surface tried to push through the sidewalls of the simulation boundary. We are currently in the process of investigating this particular problem.

#SPLAT File for KrF

2 0.2480;

3 0.4000;

4 0.0000;

5 0.5000;

6 1.930000 1.990000 0;

7 Cutout = (1.560000,0.400000) (0.370000x0.400000) 1;

7 Cutout = (1.160000,0.000000) (0.400000x0.800000) 1;

7 Cutout = (0.360000,1.200000) (1.570000x0.400000) 1;

7 Cutout = (0.360000,0.000000) (0.400000x1.200000) 1;

10;

11 0.000000 0.000000 1.930000 1.990000 `image.cnt';

#Bleach File

resmodel ((0.2480)

(-0.7120, 1.1570, 0.0023)

(1.7900, -0.0088)(1.0000));

layers (1.7000, -3.3800);

dose 25.0000;

shipleyahr 140.0000 60.0000;

exposerun;

heatdiffus 0.0800 1;

devrate 4 (6.4000 0.0350 6.3000);

#Command line for 3D etch simulation;

develop -b rval.3D.binary -mdens 10 -et 60.0;

A tiny rectangular buffer with very slow etch in the x-y direction was put in during development of this mask in order to ensure that the simulation proceeded in a proper manner.

The picture below was generated by running DEVELOP on the same mask with a development time of 19 seconds. An attempt to run DEVELOP for a development time beyond 19 seconds resulted in an error as the surface tried to push through the sidewalls of the simulation boundary. We are currently in the process of investigating this particular problem.

#SPLAT File Created By SAMPLE-3D GUI for i-line;

2 0.3650;

3 0.3200;

4 0.0000;

5 0.5000;

6 2.850000 2.160000 0;

7 Cutout = (0.820000,1.270000) (1.200000x0.890000) 1;

7 Cutout = (0.820000,0.000000) (1.200000x0.870000) 1;

7 Cutout = (1.620000,0.870000) (0.400000x0.400000) 1;

7 Cutout = (0.820000,0.870000) (0.400000x0.400000) 1;

10;

11 0.000000 0.000000 2.850000 2.160000 `image.cnt';

#Bleach File Created By SAMPLE-3D GUI for Bleach.input;

resmodel ((0.3650)

(1.0500, 0.1100, 0.0120)

(1.8200, -0.0330)(1.0000));

layers (6.5220, -2.7050);

dose 180.0000;

exposerun;

heatdiffus 0.0800 1;

devrate 2 (0.0759 0.0001 7.4600);

#Command line for 3D etch simulation;

develop -b rval.3D.binary -mdens 10 -et 120.0;

The picture below was generated by using DEVELOP with a development time of 120 seconds.

#an input deck for a Plasma Etching Simulation

sim_region -1.0 1.0 -1.0 1.0 -1.0 1.0 0.0;

meshdensity 10;

meshaccur 0 0 1 2;

maskpiece 0 -0.21 -0.21 0.42 0.42;

setmask 0;

adv_method 1;

analytic_rate 12;

etchtime 2.0 0.04;

run;

plot3D;

plot2D -1.0 0.0 1.0 0.0 plasmaetch.2D.00s;

clearmask;

#sets advancement method to facet adaptive

adv_method 3;

#invokes the plasma etch model with:

#f=0.0; q=0.0; ion_flux=0.5; s=0.0; m=1.0

etchmodel 2 0.0 0.0 0.5 0.0 1.0;

etchnumlay 2;

etchlayer 1 0.2 0.0 0.0 0.0;

etchlayer 0 0.8 0.0 1.0 0.0;

damage 0 6.0;

etchtime 0.1 0.2;

#run simulation 4 times for intermediate plots

#same as the command ``etchtime 0.4 0.2;''

run;

plot3D plasmaetch.01s;

plot2D -1.0 0.0 1.0 0.0 plasmaetch.2D.01s;

run;

plot3D plasmaetch.02s;

plot2D -1.0 0.0 1.0 0.0 plasmaetch.2D.02s;

run;

plot3D plasmaetch.03s;

plot2D -1.0 0.0 1.0 0.0 plasmaetch.2D.03s;

run;

plot3D plasmaetch.04s;

plot2D -1.0 0.0 1.0 0.0 plasmaetch.2D.04s;

quit;

* These parameters were not used in this simulation

sim_region -1.0 1.0 -0.4 0.4 -1.0 1.0 0.0;

meshdensity 10;

meshaccur 0 0 0 2;

maskpiece 0 0.211052631 -0.21 0.42 0.42;

maskpiece 0 -0.52578947 -0.10473684 0.24 0.24;

setmask 0;

adv_method 1;

analytic_rate 12;

etchtime 2.0 0.04;

run;

plot 3D;

plot 2D -1.0 0.0 1.0 0.0 plasmalag.2D.00s;

clearmask;

adv_method 3;

etchmodel 2 0.0 0.0 0.5 0.0 4.0;

etchnumlay 2;

etchlayer 1 0.2 0.0 0.0 0.0;

etchlayer 0 0.8 0.0 1.0 0.05;

damage 0 5.0;

etchtime 0.1 0.2;

hemisize 45 10;

run;

plot3D plasmalag.01s;

plot2D -1.0 0.0 1.0 0.0 plasmalag.2D.01s;

run;

plot3D plasmalag.02s;

plot2D -1.0 0.0 1.0 0.0 plasmalag.2D.02s;

run;

plot3D plasmalag.03s

plot2D -1.0 0.0 1.0 0.0 plasmalag.2D.03s;

run;

quit;

* These parameters were not used in this simulation

#an input deck to simulate the reflection model used in etching

sim_region -1.0 1.0 -1.0 1.0 -1.0 1.0 0.0;

meshdensity 10;

meshaccur 0 0 1 2;

maskpiece 0 -0.21 -0.21 0.42 0.42;

setmask 0;

adv_method 1;

analytic_rate 12;

etchtime 1.0 0.02;

run;

clearmask;

adv_method 3;

etchmodel 2 0.0 0.0 0.5 0.0 1.0;

etchnumlay 2;

etchlayer 1 0.2 0.0 0.0 0.0;

#the line below sets the rates:

etchlayer 0 0.8 0.0 1.0 0.5;

damage 0 3.0;

etchtime 0.1 0.2;

run;

plot3D plasmarfl.01s;

plot2D -1.0 0.0 1.0 0.0 plasmarfl.2D.01s;

run;

plot3D plasmarfl.02s;

plot2D -1.0 0.0 1.0 0.0 plasmarfl.2D.02s;

run;

plot3D plasmarfl.03s

plot2D -1.0 0.0 1.0 0.0 plasmarfl.2D.03s;

run;

plot3D plasmarfl.04s

plot2D -1.0 0.0 1.0 0.0 plasmarfl.2D.04s;

quit;

* These parameters were not used in this simulation

#an input deck to simulate a dovetail

sim_region -1.0 1.0 -1.0 1.0 -1.0 1.0 0.0;

meshdensity 10;

meshaccur 0 0 1 2;

maskpiece 0 -0.21 -0.21 0.42 0.42;

setmask 0;

adv_method 1;

analytic_rate 12;

etchtime 1.0 0.02;

run;

clearmask;

adv_method 3;

etchmodel 2 0.0 0.0 0.5 0.0 1.0;

etchnumlay 2;

etchlayer 1 0.2 0.0 0.0 0.0;

etchlayer 0 0.8 0.0 1.0 0.5;

etchtime 0.1 0.2;

#notice that no damage term is included

run;

plot3D plasmarfln.01s;

plot2D -1.0 0.0 1.0 0.0 plasmarfln.2D.01s;

run;

plot3D plasmarfln.02s;

plot2D -1.0 0.0 1.0 0.0 plasmarfln.2D.02s;

run;

plot3D plasmarfln.03s;

plot2D -1.0 0.0 1.0 0.0 plasmarfln.2D.03s;

run;

plot3D plasmarfln.04s;

plot2D -1.0 0.0 1.0 0.0 plasmarfln.2D.04s;

quit;

* These parameters were not used in this simulation

The following SAMPLE-3D input deck was used to simulate physical vapor sputter deposition into a square contact hole that was first istropically etched for 5.0 seconds. Notice that the setnewlayer instruction needs to be specified in order to create a layer for deposition. 532 seconds of CPU time were required to run this simulation.

#an input deck to simulate sputter deposition

sim_region -1.0 1.0 -1.0 1.0 -1.0 1.0 0.0;

analytic_rate 12;

etchlayers 1 1.0 0.1;

meshaccur 0 0 0 2;

maskpiece 0 -0.5 -0.5 1.0 1.0;

setmask 0;

noclip 1;

adv_method 1;

#first do an isotropic etch into wafer surface

etchmodel 0;

meshdensity 8;

etchtime 5.0 0.2;

run;

noclip 1;

clearmask;

#then do hemispherical deposition on the mask

depomodel 3 -0.2 2.0 1.2 0.0 0.0 0;

setnewlayer;

adv_method 3;

depotime 1.0 0.2;

run;

plot3D sputter1.10;

plot2D -1.0 0.0.10 0.0 sputter1.2D.10;

run;

plot3D sputter1.20;

plot2D -1.0 0.0 1.0 0.0 sputter1.2D.20;

run;

plot3D sputter1.30;

plot2D -1.0 0.0 1.0 0.0 sputter1.2D.30;

quit;

As usual, an input deck simulating surface migration is given below. The execution of this input file took 1229.8 seconds of CPU time.

#an input deck to simulate surface migration

sim_region -1.0 1.0 -1.0 1.0 -1.0 1.0 0.0;

analytic_rate 12;

etchlayers 1 1.0 0.1;

meshaccur 0 0 0 2;

maskpiece 0 -0.5 -0.5 1.0 1.0;

setmask 0;

noclip 1;

adv_method 1;

etchmodel 0;

etchtime 5.0 0.2;

run;

noclip 1;

clearmask;

#hemispherical deposition where n = 1.0, A = 1.2

depomodel 3 -0.2 1.0 1.2 0.0 0.0 0;

#the following line sets sigma = 0.2

deposurfmigration 0.2 1;

hemisize 45 10;

setnewlayer;

adv_method 3;

depotime 1.0 0.2;

run;

plot3D surfmign.10;

plot2D -1.0 0.0 1.0 0.0 surfmign.2D.10;

run;

plot3D surfmign.20;

plot2D -1.0 0.0 1.0 0.0 surfmign.2D.20;

run;

plot3D surfmign.30;

plot2D -1.0 0.0 1.0 0.0 surfmign.2D.30;

run;

plot3D surfmign.40;

plot2D -1.0 0.0 1.0 0.0 surfmign.2D.40;

quit;

The following SAMPLE-3D input deck can be used to simulate square step deposition. It took 666.4 seconds of CPU time to obtain the resulting 3D profile.

sim_region -1.0 1.0 -1.0 1.0 -1.0 1.0 0.0

analytic_rate 12;

etchlayers 1 1.0 0.1;

meshaccur 0 0 0 2;

maskpiece 0 -0.5 -0.5 1.0 1.0;

#setmask = 1 means that mask features are opaque #and background is open, i.e. etched into

setmask 1;

noclip 1;

adv_method 1;

#first do an isotropic etch into wafer surface

etchmodel 0;

meshdensity 8;

etchtime 5.0 0.2;

run;

noclip 1;

clearmask;

#then do hemispherical deposition

depomodel 3 -0.2 2.0 1.2 0.0 0.0 0;

setnewlayer;

adv_method 3;

depotime 1.0 0.2;

run;

plot3D mesa.10;

plot2D -1.0 0.0.10 0.0 mesa.2D.10;

run;

plot3D mesa.20;

plot2D -1.0 0.0 1.0 0.0 mesa.2D.20;

run;

plot3D mesa.30;

plot2D -1.0 0.0 1.0 0.0 mesa.2D.30;

quit;

7.11 Extracting Solid Elbows for Mutual Capacitance

#simulate & extract polylines to FastCap

loadrate 0 rval.3D.binary.elbow.ibm;

sim_region 0.0 2.0 0.0 2.0 -1.0 1.0 0.0;

celldensity 49 49 101;

meshdensity 4;

meshaccur 0 0 0 0;

meshcheck 1;

adv_method 1;

etchmodel 0;

etchtime 20.0;

noclip 1;

run;

transferpattern 1.0;

plot3D transfer.plot;

adv_method 3;

etchmodel 2 0.0 0.0 0.5 0.0 1.0;

etchnumlay 2;

etchlayer 1 0.85 0.0 0.0 0.0;

etchlayer 0 1.15 0.0 1.0 0.0;

damage 0 3.0;

etchtime 0.1 0.2;

run;

plot3D surf_etch1.plot;

run;

plot3D surf_etch2.plot;

run;

plot3D surf_etch3.plot;

createfastcapfile 1 -0.1 0.0 0.001 elb_cap.inp;

plot3D poly_elbows.plot;

quit;

After issuing the command to createfastcapfile, the surface is intersected with bounding planes in the X,Y, and Z directions. The result is shown below. This figure is a consequence of the second plot3D poly_elbows.plot command.

For the extraction of solids from your etched surface, it may be important to suppress clipping of the etched surface (noclip 1;). Using this command retains at least one node on the etched surface in the corner of an X/Y simulation boundary. The algorithm used to properly identify which parts of an intersected surface can be eliminated uses this node to identify the portion of the surface to be retained.

At this point, a new file called elb_cap.inp has been created. This is an input file generated using the FastCap generic file format. Running FastCap with this input file produces the following capacitance matrix.

INPUT SUMMARY

Expansion order: 2

Number of partitioning levels: 4

Overall permittivity factor: 1

Total number of panels: 1326

Number of conductor panels: 1326

Number of dielectric interface panels: 0

Number of thin conductor on dielectric interface panels: 0

Number of conductors: 2

No expansions at level 4 (lowest)

Percentage of multiplies done by multipole: 82.8%

ITERATION DATA

Starting on column 1 (922_Triangle_Poly%GROUP1)

1 2 3 4 5 6 7 8

Starting on column 2 (404_Triangle_Poly%GROUP1)

1 2 3 4 5 6 7 8

CAPACITANCE MATRIX, attofarads

1 2

922_Triangle_Poly%GROUP1 1 116.3 -50.12

404_Triangle_Poly%GROUP1 2 -50.12 77.77

The fastcapio.[hc] module makes extensive use of two additional modules called intsurf.[hc] and thintria.[hc]. The intsurf.[hc] module contains routines for intersecting surfaces, combining the intersected surfaces, identifying a discontinuous surfaces, and separating a discontinuous surface into multiple surfaces. The thintria.[hc] module contains many query type functions that asks questions about the triangulation of the surface and how triangles can be manipulated so as to remove unwanted triangles without altering the macroscopic features in the surface topography. Of most power in this module is the function called remove_small_thin_triangles_throughout_surface().

All models and utilities in SAMPLE are written either in C or in FORTRAN. Specifically, SPLAT ver5.0 is written in FORTRAN. The rest (BLEACH, NEtch, DEVELOP etc.) are written in C.

This section is meant to give the user a feel for the code organization, simulation as well as flow, some introductory information about the data-structures and various geometric operations in SAMPLE-3D. The information in this section is applicable primarily for the DEVELOP and NEtch modules. For a more comprehensive overview of system and source code organization in SAMPLE-3D please refer to Ed Scheckler's thesis.

SAMPLE-3D can be viewed at three levels of abstraction.

1. At the wafer state level. It maintains a wafer state representation (3D topography description) and alters it according to process models.

2. At the process flow level. It consists of a well-defined program flow for executing operations (unit process steps) on a wafer state representation.

3. At the geometric utility level. It is a collection of surface evolutions, visibility and geometric utilities for coupling process models to the advancement of a topography representation.

The layout of process simulation tools in SAMPLE-3D is shown below.

The process flow view is shown below:

Overall SAMPLE-3D Program Flow:

The basic program flow for all SAMPLE-3D programs mirrors the program flow of NEtch. After initialization, the program parses input commands from an input file. Depending upon these commands, different operations are performed. Many of the operations initialize model parameters or the surface state. Once the models are entered, the program may execute a ``run'' command. Three different run operations are possible:

1). a ray-trace algorithm for lithography development.

2). a facet-motion algorithm for general etching and deposition simulation.

3). a cell-removal algorithm for lithography simulation.

Each of these consists of a loop wherein rates are derived from a process model and applied to a topography deformation algorithm. Modules for updating and refining topography are also included.

The physical models are connected to the algorithms in the step in which the rate for each surface element node is set. Once the rate information is fully specified, facets are advanced and the surface is reconstructed. In general, the full surface motion algorithm must be applied to reconstruct the surface. This process is continued until the simulation time specified by the user is reached. Then the next set of commands entered by the user are deciphered and interpreted.

DATA VIEW

SAMPLE-3D consists of numerous data-files created by running each program. The files are active objects and are passed around from program to program depending upon the process simulation that is desired. The data view in SAMPLE-3D is best explained by the following picture:

SPLAT puts out a 2D or 3D intensity file which can then be sent to bleach for deciphering etch rates. SPLAT can also write a contour file which can be viewed using CONTOUR. BLEACH then outputs an ascii or binary ratefile which can be sent to DEVELOP for resist development simulation. DEVELOP can write the final result in PDRAW and DRAWPLOT formats.

NEtch can also put out the result of running the simulation in PDRAW and DRAWPLOT formats. If a solid extraction step is also desired, an internal transfer of data is carried out so that the current state of the surface can be captured.

9.0 Appendix of Man Pages

NEtch

Last Modified: 06:02pm , July 24, 1998