CASINO Scanning

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SCANNING VOL. 29, 92–101 (2007)

© Wiley Periodicals, Inc.

CASINO V2.42—A Fast and Easy-to-use Modeling Tool for ScanningElectron Microscopy and Microanalysis Users

DOMINIQUE DROUIN1, ALEXANDRE RÉAL COUTURE1, DANY JOLY1, XAVIER TASTET1, VINCENT AIMEZ1,

RAYNALD GAUVIN2

1Electrical Engineering Department, Universite de Sherbrooke, Sherbrooke, Québec, J1K 2R1, Canada2Department Mining, Metals and Materials Engineering, McGill University, Montreal, H3A 2B2 , Canada

Summary: Monte Carlo simulations have been widelyused by microscopists for the last few decades. In thebeginning it was a tedious and slow process, requiringa high level of computer skills from users and longcomputational times. Recent progress in the microelec-tronics industry now provides researchers with afford-able desktop computers with clock rates greater than3 GHz. With this type of computing power routinelyavailable, Monte Carlo simulation is no longer anexclusive or long (overnight) process. The aim of thispaper is to present a new user-friendly simulation pro-gram based on the earlier CASINO Monte Carlo pro-gram. The intent of this software is to assist scanningelectron microscope users in interpretation of imag-ing and microanalysis and also with more advancedprocedures including electron-beam lithography. Thisversion uses a new architecture that provides resultstwice as quickly. This program is freely available to thescientific community and can be downloaded from thewebsite: www.gel.usherb.ca/casino. SCANNING 29:92– 101, 2007. © 2007 Wiley Periodicals, Inc.

Key words: Monte Carlo simulation software, scanningelectron microscopy, BE line scan, X-ray line scan, E-beam lithography

PACS: 02.70.Uu; 05.10.Lm; 07.05.Tp; 68.37.Hk;85.40.Hp

Introduction

The motivation of this work was to provide an easy-to-use and accurate simulation program of electron

Address for reprints: Dominique Drouin, Département degénie électrique et génie informatique, Université de Sherbrooke,Sherbrooke (Québec), J1K 2R1, Canada,E-mail: [email protected]

Received 8 December 2006; Accepted with revision25 January 2007

beam–sample interactions in a scanning electron micro-scope (SEM). It can be used to assist scanning electronmicroscopy users in planning and interpreting their rou-tine SEM-based imaging and analysis and also in moreadvanced topics such as electron-beam lithography. Onthe basis of a single-scattering algorithm, this softwareis specially designed for modeling low-energy beaminteractions in bulk and thin foil samples. The initialversion of CASINO (Hovington et al . 1997) was devel-oped for expert users and presented some limitationsin data handling capabilities. These aspects have beenaddressed in the present version by the developmentof a new user interface. This paper presents the simu-lation models used, the main features of the program,and some example applications.

CASINO v2.42 Structure and Principles

This software has been developed using C++ objectoriented programming language. It therefore takes fulladvantage of the native PC operating environment. Thegraphical interface used was the MFC library. The fol-lowing section describes the details of program opera-tion: sample modeling, electron trajectory calculations,output and other special features.

Sample Modeling

Two basic geometries for sample representation arehandled by CASINO v2.42: vertical planes and hor-izontal planes. These simple models can be used toreproduce a large number of real samples such as mul-tilayers, heterostructures and grains boundaries. Usingthe Simulation/Modify Sample dialog box, the appropri-ate type of geometries for the desired sample modeling,the total number of regions with different chemicalcomposition, and the thickness or width of each regionare set. The substrate option extends the thickness of the bottom region in the case of horizontal planes, or


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D. Drouin et al.: CASINO 2.42 93

the width of both first and last regions in the case of vertical planes, to a value much larger than the electronpenetration depth in the sample.

Each of the added layers then needs to be matched toa chemical composition. This operation is easily doneby “double-clicking” on the layer and then enteringdirectly the chemical formula (SiO2 for SiO2) or theatomic or weight fraction of each element present. The

software will calculate an average density based on theweight fraction of each element, but it is recommendedto use known density values in g/cm3, if available.A library function allows the user to store specialcompositions, for uncommon alloys and compounds.

Electron Trajectory Calculation

The main part of a Monte Carlo program is the sim-ulation of a complete electron trajectory. This sectiondescribes the different steps and physical models usedby CASINO to calculate electron trajectories.

Different physical models are preprogrammed, soexpert users can set them using the Simulation/ChangePhysical Models according to their different prefer-ences. The present work uses the default values.

The tool is intended to represent, as accurately aspossible, the actual interaction conditions in SEMs.Modern electron optics and advanced electron sourcessuch as field emission can achieve subnanometerimage resolution on the sample. CASINO assumes aGaussian-shaped electron beam, where the user canspecify the electron-beam diameter of their instrument,d , representing 99.9% of the total distribution of elec-trons. The actual landing position of the electron on the

sample is thus calculated using eq(1):

X 0 =d

log( R1)

2 × 1.65× cos(2π R2)

Y 0 =d

log( R1)

2 × 1.65× cos(2π R3) (1)

where R x are random numbers uniformly distributedbetween 0 and 1.

The initial penetration angle is fixed by the user, andno scattering angle is initially calculated. The distancebetween two successive collisions is evaluated using

the equations:

L = −λel log( R4)[nm] (2)

1

λel= ρ N 0

ni=1

C i σ i

el

Ai(3)

where C i , Ai are the weight fraction and atomic weightof element i , respectively, ρ is the density of theregion (g/cm3) and N 0 the Avogadro’s constant. Thevalue of the total cross-section (Mott and Massey

1949, Czyzewski et al . 1990), σ i (nm2), for each

chemical element of the region is determined using theprecalculated and tabulated value (Drouin et al ., 1997).

This program neglects the effect of inelastic scatter-ing on electron deviation and groups all the electronenergy loss events in a continuous energy loss function(Joy and Luo, 1989). With this assumption, the energy,in keV, between collisions can be calculated using the

following equations:

E i+1 = E i +dE

dS L (4)

dE

dS =−7.85× 10−3ρ

E i

×

n j=1

C j Z j

F jln

1.116

E i

J j+ k j

[keV/nm] (5)

where Z j and J j are atomic number and mean ionizationpotential of element j , respectively. K j is a variable only

dependant of Z j (Gauvin and L’Espérance 1992).The elastic collision angle is determined using pre-

calculated values of partial elastic cross-section and arandom number (Drouin et al ., 1997). For regions con-taining multiple chemical elements, the atom responsi-ble for the electron deviation is determined using thetotal cross-section ratio (Hovington et al . 1997).

These steps are repeated until the electron energyis less than 50 eV or the electron escapes the surfaceof the sample and is recorded as a backscatteredelectron (BE). The default minimum energy can beadjusted using Simulation/Options; however, it is notrecommended to use a value lower than 50 eV. Most

of the default physical models used are not accuratebelow 50 eV, but higher values can be set by the userin order to speed up the calculation.

As the electron travels within the sample, the pro-gram will correct the trajectories while crossing theinterface between two regions. In this case, no angu-lar deviation is calculated and a new random number isgenerated to calculate the distance, L, in the new region.Using the same random number to calculate L when theelectron trajectory is crossing an interface will intro-duce an artifact within the electron trajectory comparedto the green line, where a new random number was usedwhen an electron trajectory was crossing an interface.

This method produces a more reliable distribution of the maximum depth of electrons in homogeneous andmultilayer samples of the same chemical compositioncompared to using the same random number to calcu-late L in each new region.

Representation of Collected Data

Once the electron trajectories are simulated in thematerial, a large amount of information can be derived


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Fig 2. Top-down view of absorbed energy in InGaAsP sample showing contour energy lines (Accelerating voltage 7 kV, Number of electron trajectories simulated = 20, 000).

1.3ln Ga

LIIILIII

2.2

1.7

1.3

0.87

0.44

0

1.8

1.5

1.1

0.73

0.36

0

1

0.78

0.52

X R a y I n t e n s i t y



X

R a y I n t e n s i t y

0.26

0

2.1

1.7

1.2

0.83

0.41

0

0 44 89 1.3E+002

Depth (nm)

As

LIII

1.8E+002 2.2E+002

0 44 89 1.3E+002

Depth (nm)

1.8E+002 2.2E+002 0 44 89 1.3E+002

Depth (nm)

1.8E+002 2.2E+00

0 44 89 1.3E+002

Depth (nm)

P

K

1.8E+002 2.2E+00

Fig 3. (ρ Z ) curve of InGaAsP sample simulated at 5 keV, 20,000 electrons trajectories.


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96 SCANNING Vol. 29, 3 (2007)

may be exported to scientific graphing software for fur-ther analysis. Specific settings, such as the precision of each distribution, can be adjusted through the Distribu-tions/Select distribution dialog box.

The Energy by Position distribution is a very inter-esting tool to investigate absorbed energy in the sampleand has application in the areas of electron-beamlithography, cathodoluminescence, and electron-beam-

induced current (EBIC), for example. This featurerecords, in a three-dimensional matrix of cubic ele-ments, the amount of energy lost by all the simulatedelectron trajectories. The user needs to set the num-ber of elements in each dimension and the programadjusts automatically the maximum range of electronsaccording to the settings of the Max Range Parameter found in Distributions/Select distribution dialog box.The user can inspect modeled interactions in all the dif-ferent layers of the matrix in the XY or XZ planes usingthe Distributions/Energy by Position Display Options orsum all the information and display either a top-downview of the surface or a cross-sectional view of the

energy absorbed in the sample. Also, an option allowsthe display of energy contour lines calculated from thecenter of the landing point and shows the percentage

of energy not contained within the line. For example,a 10% line is the frontier between an area containing90% of the absorbed energy and the rest of the sam-ple (Figure 2). A gray shading overlay of the densityof absorbed energy is also shown in Figure 2. The grayshade ranges from light to dark as the density increases.Specific applications may require more detailed anal-ysis of the location and amount of energy absorbed

in the sample; in those cases the Distributions/Export Data options will give access to the raw data in keVfor each volumetric element.

One other feature, also calculable from the electronenergy lost in the sample, is the generation of charac-teristic X-rays. Complete details of the physical modelsused to generate X-rays can be found in Hovingtonet al . (1997). If the Generate x-ray option is set in

Distribution/Select Distribution dialog box, the soft-ware will generate characteristic X-rays and compilethe results in either classical (ρ z )) curves or as radialdistributions. The slices or ring number of the distri-bution can be set by the user by adjusting the value

next to the Generate X-ray check box. This value thendetermines the Z or R thickness by dividing thetotal electron range by the number of slices or ring. The

0 44

ln2.6E+002

2.1E+002

1.6E+002


1E+002

52

0

3.9E+003

3.1E+003

2.3E+003

X R a y I

n t e n s i t y

1.6E+003

7.8E+002

0

1.5E+003

1.2E+003

8.9E+002


6E+002

3E+002

0

5.3E+003

4.3E+003

3.2E+003


2.1E+003

1.1E+003

0

LIII

Ga

LIII

89 1.3E+002

Distance (nm)

As

LIII

1.8E+002 2.2E+002 0 44 89 1.3E+002

Distance (nm)

P

K

1.8E+002 2.2E+00

0 44 89 1.3E+002

Distance (nm)

1.8E+002 2.2E+000 44 89 1.3E+002

Distance (nm)

1.8E+002 2.2E+002

Fig 4. X-Ray intensities as a function of radial distance (nm) from electron-beam center, simulated at 5 keV, 20,000 electronstrajectories.


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(ρ z )) curves (Figure 3) give information about the X-ray generation depth of each chemical element in thesample. X-ray intensities are normalized with respectto (0) as a function of depth, in nanometres. (0) iscalculated from the X-ray intensity generated in a filmof thickness Z and of the same chemical composition.This information may then be useful in choosing appro-priate SEM conditions for the quantitative or qualitative

analysis of thin films, for example. The radial distri-bution function collects generated X-rays in concentriccylinders centered on the primary electron-beam impactpoint. Figure 4 shows an example of this distribution.This type of distribution provides information on thelateral spreading of electrons and the associated X-raygeneration volumes.

Special Software Features

Many features have been added in this version of CASINO to improve the general use of Monte Carlo

simulations. The graphical interface allows the userto view results while the simulation is in progress toprevent wasting time modeling with improperly set sim-ulation conditions. A step-by-step wizard walks usersthrough the different dialog boxes to define the sample,set the SEM parameters, and select the distributionsto be generated. All the simulation data are stored ina single file to simplify the handling of the results.

Fig 5. Energy (keV/nm2) absorbed in 500 nm of PMMA resistdeposit on quartz plate as a function of radial distance frombeam center. (Accelerating voltage 50 kV, Number of electrontrajectories simulated = 1, 000, 000).

Once the simulation is completed, the results can bedirectly printed, exported in BMP format, or transferredto spreadsheet software for further analysis or format-ting. A backup file is automatically created every 5 min(or as user customized in the Simulation/Options dialogbox), to minimize the risk of data loss and also toallow the resumption of an uncompleted simulation.

5.0%10.0%25.0%50.0%

75.0%90.0%

-761.0 nm -380.5 nm 0.0 nm 380.5 nm 761.0 nm

1200.6 nm

900.4 nm

600.3 nm

300.1 nm

0.0 nm

Fig 6. Cross-section view of absorbed energy in tree layers PMMA resists on GaAs substrate simulated with 30 kV acceleratingvoltage.


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98 SCANNING Vol. 29, 3 (2007)

Also, linescans of signals arising from the electronbeam doing single scans across a nonhomogenous sam-ple (vertical planes) can be generated through theSimulation/Setup microscope dialog box. In such condi-tions, a vector of the electron-beam landing position iscreated and sequentially simulated. The data associatedwith each position can either be saved for later study

or discarded to prevent memory overflow.

Application Examples

The following examples illustrate the applicationof the simulation tool in relation to electron-beam

lithography, X-ray linescan, and BE linescan modeling.

Electron-beam Lithography

Electron-beam lithography is a widely used toolfor the manufacture of semiconductor devices eitherthrough photomask fabrication or by a direct writingprocess. In both cases, proximity correction is crucialfor effective high-density patterning. This techniqueallows better correlation between the pattern written

on the photomask or substrate and the pattern design.Correction of the pattern for proximity effects dur-ing electron-beam writing requires knowledge of BEenergy and spatial distribution. Figure 5 presents theenergy absorbed in 500 nm of PMMA as a functionof position, in nanometers, simulated at 50 keV on aglass substrate. This plot has been obtained using the

Energy by position distribution function and sums theenergy in the first 500-nm layers of resist. This plot is

(a)

(b)

Fig 7. Fabrication of T-gate for HEMT. (a) PMMA resist profile after electron-beam exposure and chemical development.(b) Cross-sectional view of the T-gate after the resist lift-off process.


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then used to calculate total energy absorbed in the resist

layer when the beam is scanning the pattern. Appropri-

ate modification of the pattern prior to exposition is

performed in regions where the energy level reaches

the resist threshold dose outside the desired area.

Direct writing of devices using electron-beam lithog-

raphy is frequently used for microwave chips fabri-

cation, because of its very high spatial resolution litho-

graphic capability, and in some cases for 3D model-

ing of electron resist requirements. Indeed, high elec-

tron mobility transistor (HEMT) gates exhibit a very

narrow footprint and a large cross-section requiring

complex fabrication steps. Those characteristics can

be achieved using multiple resist layers and multiple

(a)

(b)

Fig 8. Comparison of simulated (a) and measured (b) X-ray linescan obtain on a cross-section of InGaAs/InP heterostructure.(Accelerating voltage, 5 keV, Number of electron trajectories simulated = 5000).


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100 SCANNING Vol. 29, 3 (2007)

exposures. Absorbed energy cross-section modeling,such as shown in Figure 6, can assist the user in thedetermination of the exposure parameters and resistthickness. Once the resist exposure parameters suchas accelerating voltage and dose are properly fixed,the transistor T-gate can be successfully fabricated(Figure 7).

X-ray Linescans

X-ray linescan modeling is a useful technique toinvestigate the spatial variation of chemical composi-tion. For example, grain boundary interfaces in met-allurgical domains or semiconductor heterostructurecross-sections can be characterized using such tech-niques to determine the level of inter-diffusion occur-ring at the interface of two different materials. Toevaluate correctly the chemical intermixing at the inter-face, the effect of the electron-beam interaction volumewithin the sample must be considered. One approach

to consider this effect is by simulating the X-ray lines-can across a perfect interface (showing no diffusion)to determine the lateral spreading of electrons and thencomparing this data with experimental measurements.If a discrepancy between the two curves is observed,then variation can be associated with inter-diffusion.Evaluation of the inter-diffusion level can be also esti-mated by comparing simulations performed on lessabrupt interfaces, by adding vertical planes with a gra-dient in chemical composition, and experimental mea-surements. Figure 8 shows a comparison between sim-ulated and measured linescans obtained from a cross-section of InGaAs/InP heterostructure. This sample was

fabricated by chemical beam epitaxy and no postde-position treatment has been performed. The interfacebetween InGaAs and InP layers is extremely sharp withno inter-diffused materials.

Backscattered Electron Profiles

In the same manner as described in the previous sec-tion, a BE profile can be simulated from samples featur-ing phase interfaces. Figure 9 presents the BE profilesimulated and measured on the same heterostructureconsidered in the section “Electron trajectory calcula-

tion”. Generally there is good agreement between thetwo curves but some differences are present near thesample edge and on large layers (>75 nm) of InGaAswhere asymmetries of interface contrast are present. Allthese discrepancies can be explained by the BE detec-tor modeling in CASINO. As an example, BE escapingat the edge of the sample do not contribute to the over-all BE signal owing to their very low or even negativeescape angle relative to sample surface. In such cases,the solid angle of collection and positioning of mostcommercials BE detectors prevent collection of these

Measured

Simulated

Fig 9. Comparison of measured and simulated BE profile as afunction of beam position in nanometers obtained on InGaAs/InPheterostructure cross-section. (Accelerating voltage 3.75 keV,

Number of simulated electrons, 500,000 per points).

BEs. Improved BE detector modeling is presently underinvestigation.

Summary

An improved simulation tool for modeling elec-tron–sample interactions in a scanning electron micro-scope, based on a Monte Carlo method, has been devel-oped. It can be used for modeling BEs, X-ray emissions

and absorbed energy in the sample. This has applica-tions in many different areas including electron-beamlithography and thin film X-ray microanalysis. A copyof the program can be downloaded from the follow-ing website: www.gel.usherb.ca/casino. Despite the factthat this software was designed for SEM application, itcan be used for STEM or TEM analysis. But the usermust be aware of the energy limitation. No relativis-tic effect has been included within the models and thiseffect will start to be more important at higher energy(>50 keV). Further work to increase the number of sample geometries handled by the program and also toadd secondary electron emission modeling capability is

in progress.

Acknowledgments

The authors would like to greatly thank all thecontributors to this version of CASINO who havebeta-tested it and also provided useful recommenda-tions (Hovington et al . 1997). Also, thanks are dueto Bruce Faure and Jacques Beauvais for the electron


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micrographs of the T-gate transistor. This work wasfunded by NSERC. Brendan J. Griffin is also acknowl-edged for many useful discussions in the course of preparing this paper.

References

Czyzewski Z, MacCallum DO, Romig A, Joy DC: Calculationsof Mott scattering cross section. J Appl Phys 68(7),3066–3072 (1990).

Drouin D, Hovington P, Gauvin R: CASINO: a new era of Monte Carlo code in C language for the electron beaminteraction - Part II: tabulated values of Mott cross section.

Scanning 19, 20–28 (1997).Gauvin R, L’Espérance G: A Monte Carlo Code to Simulate the

Effect of Fast Secondary Electron on kAB Factors and Spa-tial Resolution in the TEM. J Microsc 168, 152–167 (1992).

Hovington P, Drouin D, Gauvin R: CASINO: a new era of Monte Carlo code in C language for the electron beaminteraction - Part I: description of the program. Scanning19, 1–14 (1997).

Joy DC, Luo S: An empirical stopping power relationship forlow-energy electrons. Scanning 11, 176–180 (1989).

Mott NF, Massey HSW:. The Theory of Atomic Collisions,Clarendon Press, Oxford (1949).

Press WH, Flannery BP, Teckolsky SA, Vetterling WT: Numer-ical Recipes, 2nd ed., Cambridge University Press, Cam-bridge (1992).

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