
1\	Electron Beam—Specimen Interactions: Interaction Volume						1
1.1\	What		Happens When the Beam Electrons Encounter Specimen Atoms?				2
1.2\	Inelastic				Scattering (Energy Loss) Limits Beam Electron
	Travel in the Specimen\ ...........................						2
1.3\	Elastic			Scattering: Beam Electrons Change Direction of Flight\			4
1.3.1\	How	Frequently Does Elastic Scattering Occur?\					4
1.4\	Simulating					the Effects of Elastic Scattering: Monte Carlo Calculations	5
1.4.1\	What		Do Individual Monte Carlo Trajectories Look Like?\				6
1.4.2\	Monte			Carlo Simulation To Visualize the Electron Interaction Volume\			6
1.4.3\	Using		the Monte Carlo Electron Trajectory Simulation to Study
	the Interaction Volume\ ............................						8
1.5\	A Range Equation To Estimate the Size of the Interaction Volume\						12
\	References ..................................................						14
2\	Backscattered Electrons ..						15

2.1Origin\ ............................................................ 16

2.1.1\ The Numerical Measure of Backscattered Electrons 16 2.2\ Critical Properties of Backscattered Electrons\ 16 2.2.1\ BSE Response to Specimen Composition (η vs. Atomic Number, Z)\ 16 2.2.2\ BSE Response to Specimen Inclination (η vs. Surface Tilt, θ)\ 20 2.2.3\ Angular Distribution of Backscattering\ 22 2.2.4\ Spatial Distribution of Backscattering . 23 2.2.5\ Energy Distribution of Backscattered Electrons\ 27

2.3Summary ...................................................... 27

\References .................................................... 28

3\	Secondary Electrons\ ......... 29

3.1Origin\ ............................................................ 30

3.2Energy Distribution\ ................................. 30

3.3\	Escape Depth of Secondary Electrons	30
3.4\	Secondary Electron Yield Versus Atomic Number\	30
3.5	Secondary Electron Yield Versus Specimen Tilt\	34
3.6\	Angular Distribution of Secondary Electrons	34
3.7\	Secondary Electron Yield Versus Beam Energy	35
3.8\	Spatial Characteristics of Secondary Electrons	35

\References .................................................... 37

4\	X-Rays ......................................	39
4.1	Overview ......................................................	40

4.2Characteristic X-Rays ............................... 40

4.2.1Origin\............................................................. 40

4.2.2Fluorescence Yield\..................................... 41

4.2.3 X-Ray Families\ 42

4.2.4X-Ray Nomenclature\ ................................. 43

4.2.5X-Ray Weights ofLines\ ............................. 44 4.2.6\ Characteristic X-Ray Intensity\ ................ 44


4.3	X-Ray Continuum (bremsstrahlung) ... 47
4.3.1\	X-Ray Continuum Intensity ..................... 49
4.3.2\	The	Electron-Excited X-Ray Spectrum, As-Generated		49
4.3.3\	Range		of X-ray Production\...................... 50
4.3.4\	Monte		Carlo Simulation of X-Ray Generation	51
4.3.5\	X-ray Depth Distribution Function, ϕ(ρz)			53

XVI\ Contents

4.4 X-Ray Absorption 54

4.5X-Ray Fluorescence\.................................. 59

\References .................................................... 63

Scanning Electron Microscope (SEM) Instrumentation

5.1Electron Beam Parameters .................... 66

5.2Electron Optical Parameters ................. 66

5.2.1Beam Energy\ ............................................... 66


5.2.2	Beam Diameter			67
5.2.3	Beam Current\			67
5.2.4\	Beam	Current Density\ .............................. 68
5.2.5\	Beam	Convergence Angle, α\ .................. 68
5.2.6\	Beam	Solid Angle		69
5.2.7\	Electron		Optical Brightness, β ................ 70

5.2.8Focus .............................................................. 71

5.3 SEM Imaging Modes\................................ 75 5.3.1\ High Depth-of-Field Mode ...................... 75

5.3.2High-Current Mode\................................... 78

5.3.3 Resolution Mode 80

5.3.4Low-Voltage Mode\ .................................... 81

5.4Electron Detectors\ ................................... 83

5.4.1\ Important Properties of BSE and SE for Detector Design and Operation 83

5.4.2Detector Characteristics\ .......................... 83


5.4.3\	Common	Types of Electron Detectors\			85
5.4.4\	Secondary			Electron Detectors\ ............... 86
5.4.5\	Specimen		Current: The Specimen as Its Own Detector\		88
5.4.6\ A Useful, Practical Measure of a Detector: Detective
	Quantum Efficiency ................................... 89

\References .................................................... 91

6\	Image Formation\	93
6.1\	Image Construction by Scanning Action	94
6.2	Magnification\	95
6.2.1\	Magnification, Image Dimensions, and Scale Bars	95

6.3Making Dimensional Measurements WiththeSEM:

How Big Is That Feature? ........................ 95

6.3.1Calibrating theImage ............................... 95


6.4	Image Defects\			98
6.4.1\	Projection		Distortion (Foreshortening)\	98
6.4.2\	Image	Defocusing (Blurring)\................ 100

6.5Making Measurements onSurfaces WithArbitrary Topography: Stereomicroscopy ................................... 102

6.5.1Qualitative Stereomicroscopy\ ............. 103

6.5.2Quantitative Stereomicroscopy\ .......... 107

\References .................................................. 110

SEM Image Interpretation\

111

7.1Information inSEM Images \ ................ 112


7.2\	Interpretation of SEM Images of Compositional Microstructure			112
7.2.1\	Atomic Number Contrast With Backscattered Electrons			112
7.2.2\	Calculating Atomic Number Contrast\			113
7.2.3\	BSE Atomic Number Contrast With the Everhart–Thornley Detector\			113
7.3\	Interpretation of SEM Images of Specimen Topography\			114
7.3.1\	Imaging		Specimen Topography With the Everhart–Thornley Detector\	115
7.3.2\	The	Light-Optical Analogy to the SEM/E–T (Positive Bias) Image\		116
7.3.3\	Imaging		Specimen Topography With a Semiconductor BSE Detector\	119
\	References .................................................. 121

XVII

Contents

8\	The Visibility of Features in SEM Images\	123
8.1\	Signal Quality: Threshold Contrast and Threshold Current\	124

\References .................................................. 131


9\	Image Defects\.................... 133
9.1	Charging\ .................................................... 134
9.1.1\	What	Is Specimen Charging?\ ............... 134
9.1.2\	Recognizing			Charging Phenomena in SEM Images	135
9.1.3\	Techniques		to Control Charging Artifacts (High Vacuum Instruments)\		139

9.2Radiation Damage\ ................................. 142

9.3	Contamination	143
9.4\	Moiré Effects: Imaging What Isn’t Actually There	144

\References .................................................. 146

10\	High Resolution Imaging	147
10.1\ What Is “High Resolution SEM Imaging”?		148

10.2Instrumentation Considerations\ ...... 148


10.3\	Pixel			Size, Beam Footprint, and Delocalized Signals\							148
10.4\	Secondary								Electron Contrast at High Spatial Resolution		150
10.4.1\	SE	range Effects Produce Bright Edges (Isolated Edges)\									151
10.4.2\	Even			More Localized Signal: Edges Which Are Thin Relative							152
	to the Beam Range\
10.4.3\	Too		Much of a Good Thing: The Bright Edge Effect Can Hinder
	Distinguishing Shape\ ............................. 153
10.4.4\	Too		Much of a Good Thing: The Bright Edge Effect Hinders								154
	Locating the True Position of an Edge for Critical Dimension Metrology
10.5\	Achieving							High Resolution with Secondary Electrons			156
10.5.1\	Beam				Energy Strategies\......................... 156
10.5.2	Improving theSE 1 Signal\....................... 158
10.5.3\	Eliminate						the Use of SEs Altogether: “Low Loss BSEs“				161
10.6\	Factors					That Hinder Achieving High Resolution					163
10.6.1	Achieving Visibility: TheThreshold Contrast										163
10.6.2\	Pathological									Specimen Behavior\ ........ 163
10.6.3\	Pathological									Specimen and Instrumentation Behavior	164

\References .................................................. 164


11\	Low Beam Energy SEM ... 165
11.1\	What		Constitutes “Low” Beam Energy SEM Imaging?\			166
11.2\	Secondary				Electron and Backscattered Electron Signal Characteristics
	in the Low Beam Energy Range\ ........ 166
11.3\	Selecting			the Beam Energy to Control the Spatial Sampling
	of Imaging Signals\ ................................. 169
11.3.1\	Low	Beam Energy for High Lateral Resolution SEM				169
11.3.2\	Low	Beam Energy for High Depth Resolution SEM				169
11.3.3\	Extremely			Low Beam Energy Imaging\		171

\References .................................................. 172


12\	Variable Pressure Scanning Electron Microscopy (VPSEM)				173
12.1\	Review:			The Conventional SEM High Vacuum Environment	174
12.1.1\	Stable		Electron Source Operation\ ...... 174
12.1.2	Maintaining Beam Integrity .................. 174
12.1.3\	Stable		Operation of the Everhart–Thornley Secondary Electron Detector\		174
12.1.4	Minimizing Contamination ................... 174
12.2\	How	Does VPSEM Differ From the Conventional SEM
	Vacuum Environment?\ ......................... 174

\XVIII Contents


12.3\	Benefits	of Scanning Electron Microscopy at Elevated Pressures		175
12.3.1	Control ofSpecimen Charging\ ............ 175
12.3.2\	Controlling		the Water Environment of a Specimen\	176
12.4\	Gas Scattering Modification of the Focused Electron Beam			177

12.5VPSEM Image Resolution\ .................... 181


12.6\	Detectors for Elevated Pressure Microscopy\			182
12.6.1\	Backscattered		Electrons—Passive Scintillator Detector	182
12.6.2\	Secondary	Electrons–Gas Amplification Detector\		182

12.7Contrast inVPSEM\.................................. 184

\References .................................................. 185

13\

ImageJ and Fiji\

187

13.1The ImageJ Universe\ ............................. 188

13.2Fiji\ ................................................................. 188

13.3Plugins\ ........................................................ 190

13.4Where toLearn More ............................. 191

\References .................................................. 193

14\	SEM Imaging Checklist\ .. 195
14.1\	Specimen Considerations (High Vacuum SEM; Specimen Chamber Pressure < 10−3 Pa)\		197
14.1.1\	Conducting	or Semiconducting Specimens\	197
14.1.2	Insulating Specimens\ ............................. 197

14.2Electron Signals Available ................... 197

14.2.1Beam Electron Range\ ............................. 197

14.2.2Backscattered Electrons ........................ 197

14.2.3Secondary Electrons \ .............................. 197

14.3Selecting theElectron Detector ........ 198

14.3.1\ Everhart–Thornley Detector (“Secondary Electron” Detector)\ 198

14.3.2Backscattered Electron Detectors\ ...... 198

14.3.3“Through-the-Lens” Detectors ............. 198


14.4\	Selecting the Beam Energy for SEM Imaging\		198
14.4.1	Compositional Contrast WithBackscattered Electrons\		198
14.4.2	Topographic Contrast WithBackscattered Electrons\		198
14.4.3	Topographic Contrast WithSecondary Electrons		198
14.4.4\	High	Resolution SEM Imaging\ ............. 198

14.5Selecting theBeam Current \ ............... 199

14.5.1	High Resolution Imaging\ ...................... 199
14.5.2\	Low	Contrast Features Require High Beam Current and/or Long Frame Time to Establish Visibility\	199

14.6Image Presentation\ ............................... 199

14.6.1“Live” Display Adjustments\ ................... 199

14.6.2Post-Collection Processing\ ................... 199

14.7Image Interpretation ............................. 199

14.7.1Observer’s Point ofView\........................ 199

14.7.2Direction ofIllumination\ ....................... 199

14.7.3Contrast Encoding\................................... 200

14.7.4\ Imaging Topography With the Everhart–Thornley Detector\ 200 14.7.5\ Annular BSE Detector (Semiconductor Sum Mode A + B and Passive Scintillator)\ 200 14.7.6\ Semiconductor BSE Detector Difference Mode, A−B\ 200 14.7.7\ Everhart–Thornley Detector, Negatively Biased to Reject SE\ 200 14.8\ Variable Pressure Scanning Electron Microscopy (VPSEM) 200

14.8.1VPSEM Advantages\ ................................. 200

14.8.2VPSEM Disadvantages ............................ 200

15\	SEM Case Studies\ ............. 201
15.1\	Case Study: How High Is That Feature Relative to Another?	202
15.2\	Revealing Shallow Surface Relief\ ..... 204
15.3\	Case Study: Detecting Ink-Jet Printer Deposits\	206

XIX

Contents


16\	Energy Dispersive X-ray Spectrometry: Physical Principles and User-Selected
	Parameters\.......................... 209
16.1\	The	Energy Dispersive Spectrometry (EDS) Process\			210
16.1.1\	The	Principal EDS Artifact: Peak Broadening (EDS Resolution Function)\			210
16.1.2	Minor Artifacts: TheSi-Escape Peak\ ... 213
16.1.3\	Minor		Artifacts: Coincidence Peaks .... 213
16.1.4\	Minor		Artifacts: Si Absorption Edge and Si Internal Fluorescence Peak\		215
16.2\	“Best		Practices” for Electron-Excited EDS Operation\		216
16.2.1	Operation oftheEDS System ...............				216
16.3\	Practical			Aspects of Ensuring EDS Performance for a Quality
	Measurement Environment ................ 219
16.3.1	Detector Geometry\ ................................. 219
16.3.2	Process Time\				222

16.3.3Optimal Working Distance .................... 222

16.3.4Detector Orientation\ .............................. 223

16.3.5Count Rate Linearity\ ............................... 225

16.3.6Energy Calibration Linearity ................. 226

16.3.7Other Items\................................................ 227

16.3.8\	Setting	Up a Quality Control Program\	228
16.3.9	Purchasing anSDD\.................................. 230

\References .................................................. 234

17\ DTSA-II EDS Software\ ..... 235

17.1Getting Started WithNIST DTSA-II\ ... 236

17.1.1Motivation .................................................. 236

17.1.2Platform\ ...................................................... 236

17.1.3Overview\ .................................................... 236

17.1.4Design\ ......................................................... 237

17.1.5\ The Three -Leg Stool: Simulation, Quantification and Experiment Design\ 237 17.1.6 Introduction toFundamental Concepts 238

17.2Simulation inDTSA-II\ ............................ 245

17.2.1Introduction\ .............................................. 245

17.2.2Monte Carlo Simulation ......................... 245

17.2.3	Using theGUI ToPerform aSimulation\	247
17.2.4	Optional Tables	262

\References .................................................. 264


18\	Qualitative Elemental Analysis by Energy Dispersive X-Ray Spectrometry\							265
18.1\	Quality			Assurance Issues for Qualitative Analysis: EDS Calibration				266
18.2\	Principles					of Qualitative EDS Analysis\		266
18.2.1\	Critical		Concepts From the Physics of Characteristic X-ray Generation					266
	and Propagation\
18.2.2\	X-Ray Energy Database: Families of X-Rays\							269
18.2.3\	Artifacts				of the EDS Detection Process\			269
18.3\	Performing						Manual Qualitative Analysis	275
18.3.1\	Why	are Skills in Manual Qualitative Analysis Important?						275
18.3.2\	Performing						Manual Qualitative Analysis: Choosing the Instrument
	Operating Conditions ............................. 277

18.4Identifying thePeaks\ ............................ 278


18.4.1	Employ theAvailable Software Tools\			278
18.4.2\	Identifying		the Peaks: Major Constituents	280
18.4.3\	Lower	Photon Energy Region\ .............. 281
18.4.4\	Identifying		the Peaks: Minor and Trace Constituents	281
18.4.5	Checking Your Work\................................ 281
18.5\	A Worked Example of Manual Peak Identification			281
\	References .................................................. 287

XX\ Contents

19\	Quantitative Analysis: From k-ratio to Composition	289
19.1	What Is ak-ratio?\	290

19.2Uncertainties ink-ratios ....................... 291

19.3 Sets ofk-ratios\ 291 19.4\ Converting Sets of k-ratios Into Composition\ 292

19.5The Analytical Total ................................ 292


19.6	Normalization\		292
19.7	Other Ways toEstimate C Z		293
19.7.1\	Oxygen	by Assumed Stoichiometry\ .. 293

19.7.2Waters ofCrystallization\........................ 293

19.7.3Element by Difference\............................ 293

19.8Ways ofReporting Composition\....... 294

19.8.1	Mass Fraction\ ............................................ 294
19.8.2	Atomic Fraction\		294
19.8.3	Stoichiometry\ ........................................... 294
19.8.4	Oxide Fractions		294
19.9\	The	Accuracy of Quantitative Electron-Excited X-ray Microanalysis\	295

19.9.1Standards-Based k-ratio Protocol\ ....... 295

19.9.2“Standardless Analysis”\ .......................... 296 19.10\ Appendix\ ................................................... 298

19.10.1\The	Need for Matrix Corrections To Achieve Quantitative Analysis\	298
19.10.2\The	Physical Origin of Matrix Effects\ . 299

19.10.3 ZAF Factors inMicroanalysis\ ................ 299

\References .................................................. 307

20\ Quantitative Analysis: The SEM/EDS Elemental Microanalysis k-ratio

Procedure for Bulk Specimens, Step-by-Step 309 20.1\ Requirements Imposed on the Specimen and Standards\ 311

20.2Instrumentation Requirements\ ........ 311

20.2.1Choosing theEDS Parameters\ ............. 311

20.2.2Choosing theBeam Energy, E0\ ............ 313

20.2.3Measuring theBeam Current ............... 313

20.2.4Choosing theBeam Current\................. 314

20.3\	Examples of the k-ratio/Matrix Correction Protocol with DTSA II		316
20.3.1\	Analysis	of Major Constituents (C > 0.1 Mass Fraction)
	with Well-Resolved Peaks\...................... 316
20.3.2\	Analysis	of Major Constituents (C > 0.1 Mass Fraction)
	with Severely Overlapping Peaks\ ....... 318
20.3.3\	Analysis	of a Minor Constituent with Peak Overlap From

aMajor Constituent\ ................................ 319

20.3.4Ba-Ti Interference inBaTiSi 3O9\ ............. 319 20.3.5\ Ba-Ti Interference: Major/Minor Constituent Interference in K2496

Microanalysis Glass\ ................................. 319 20.4\ The Need for an Iterative Qualitative and Quantitative

Analysis Strategy\ .................................... 319


20.4.1\	Analysis	of a Complex Metal Alloy, IN100\		320
20.4.2	Analysis ofaStainless Steel\ ..................			323
20.4.3\	Progressive		Discovery: Repeated Qualitative–Quantitative Analysis
	Sequences\..................................................			324

20.5Is theSpecimen Homogeneous?\ ...... 326

20.6Beam-Sensitive Specimens ................. 331

20.6.1	Alkali Element Migration\....................... 331
20.6.2\	Materials	Subject to Mass Loss During Electron Bombardment—
	the Marshall-Hall Method\ ..................... 334
\	References .................................................. 339

XXI

Contents

21\

Trace Analysis by SEM/EDS\

341

21.1\ Limits of Detection for SEM/EDS Microanalysis 342 21.2\ Estimating the Concentration Limit of Detection, CDL\ 343

21.2.1Estimating CDL from a Trace or Minor Constituent from Measuring

a Known Standard\ ................................... 343

21.2.2Estimating CDL After Determination of a Minor or Trace Constituent

343with Severe Peak Interference from a Major Constituent\

21.2.3Estimating CDL When a Reference Value for Trace or

Minor Element Is Not Available\........... 343


21.3\	Measurements			of Trace Constituents by Electron-Excited Energy
	Dispersive X-ray Spectrometry\ ......... 345
21.3.1\	Is a Given Trace Level Measurement Actually Valid?				345
21.4\	Pathological		Electron Scattering Can Produce “Trace” Contributions
	to EDS Spectra\				350
21.4.1\	Instrumental		Sources of Trace Analysis Artifacts\		350
21.4.2\	Assessing	Remote Excitation Sources in an SEM-EDS System			353

21.5Summary .................................................... 357

\References .................................................. 357


22\	Low Beam Energy X-Ray Microanalysis\								359
22.1\	What			Constitutes “Low” Beam Energy X-Ray Microanalysis?					360
22.1.1\	Characteristic							X-ray Peak Selection Strategy for Analysis\	364
22.1.2\	Low		Beam Energy Analysis Range\...... 364
22.2\	Advantage of Low Beam Energy X-Ray Microanalysis\								365
22.2.1	Improved Spatial Resolution ................ 365
22.2.2\	Reduced					Matrix Absorption Correction			366
22.2.3\	Accurate					Analysis of Low Atomic Number Elements at Low Beam Energy			366
22.3\	Challenges						and Limitations of Low Beam Energy X-Ray Microanalysis\		369
22.3.1	Reduced Access toElements ................ 369
22.3.2\	Relative				Depth of X-Ray Generation: Susceptibility to Vertical Heterogeneity				372
22.3.3\	At	Low Beam Energy, Almost Everything Is Found To Be Layered\							373

\References\................................................. 380


23\	Analysis of Specimens with Special Geometry: Irregular Bulk
	Objects and Particles									381
23.1\	The	Origins of “Geometric Effects”: Bulk Specimens								382
23.2\	What			Degree of Surface Finish Is Required for Electron-Excited X-ray
	Microanalysis To Minimize Geometric Effects?\									384
23.2.1	No Chemical Etching\ .............................. 384
23.3\	Consequences								of Attempting Analysis of Bulk Materials
	With Rough Surfaces\............................. 385
23.4\	Useful				Indicators of Geometric Factors Impact on Analysis					386
23.4.1	The Raw Analytical Total\........................ 386
23.4.2\	The	Shape of the EDS Spectrum\ ......... 389
23.5\	Best		Practices for Analysis of Rough Bulk Samples\							391
23.6	Particle Analysis\									394
23.6.1\	How		Do X-ray Measurements of Particles Differ
	From Bulk Measurements? .................... 394
23.6.2\	Collecting						Optimum Spectra From Particles			395
23.6.3\	X-ray Spectrum Imaging: Understanding Heterogeneous Materials									400
23.6.4\	Particle					Geometry Factors Influencing Quantitative Analysis of Particles				403
23.6.5\	Uncertainty							in Quantitative Analysis of Particles\		405
23.6.6	Peak-to-Background (P/B) Method\ .... 408

23.7Summary .................................................... 410

\	References .................................................. 411

\XXII Contents

24\

Compositional Mapping\

413

24.1\ Total Intensity Region-of-Interest Mapping 414 24.1.1\ Limitations of Total Intensity Mapping\ 415

24.2X-Ray Spectrum Imaging\..................... 417

24.2.1	Utilizing XSI Datacubes .......................... 419
24.2.2	Derived Spectra	419
24.3	Quantitative Compositional Mapping	424
24.4\	Strategy for XSI Elemental Mapping Data Collection	430

24.4.1Choosing theEDS Dead-Time .............. 430

24.4.2Choosing thePixel Density ................... 432

24.4.3Choosing thePixel Dwell Time\ ............ 434

\References .................................................. 439


25\	Attempting Electron-Excited X-Ray Microanalysis in the Variable Pressure
	Scanning Electron Microscope (VPSEM)\			441
25.1\	Gas Scattering Effects in the VPSEM			442
25.1.1\	Why	Doesn’t the EDS Collimator Exclude the Remote Skirt X-Rays?		446
25.1.2\	Other		Artifacts Observed in VPSEM X-Ray Spectrometry\	448
25.2\	What Can Be Done To Minimize gas Scattering in VPSEM?\			450
25.2.1	Workarounds ToSolve Practical Problems			451

25.2.2Favorable Sample Characteristics ....... 451

25.2.3Unfavorable Sample Characteristics .. 456

\References .................................................. 459

26\	Energy Dispersive X-Ray Microanalysis Checklist\	461
26.1	Instrumentation\	462

26.1.1SEM ............................................................... 462

26.1.2EDS Detector\ ............................................. 462 26.1.3\ Probe Current Measurement Device\ . 462

26.1.4 Conductive Coating\ ................................ 463

26.2Sample Preparation\............................... 463

26.2.1Standard Materials\ .................................. 464

26.2.2Peak Reference Materials\ ...................... 464

26.3Initial Set-Up ............................................. 464

26.3.1	Calibrating theEDS Detector\...............		464
26.4	Collecting Data\		466

26.4.1Exploratory Spectrum\ ............................ 466

26.4.2Experiment Optimization ...................... 467

26.4.3Selecting Standards\ ................................ 467

26.4.4 Reference Spectra 467

26.4.5Collecting Standards\ .............................. 467

26.4.6Collecting Peak-Fitting References\ .... 467

26.4.7	Collecting Spectra FromtheUnknown\		467
26.5	Data Analysis		468
26.5.1	Organizing theData ................................ 468
26.5.2	Quantification\		468
26.6	Quality Check\		468
26.6.1\	Check	the Residual Spectrum After Peak Fitting\	468

26.6.2Check theAnalytic Total\ ........................ 469

26.6.3Intercompare theMeasurements\ ....... 469

\Reference .................................................... 470

27\	X-Ray Microanalysis Case Studies	471
27.1\	Case Study: Characterization of a Hard-Facing Alloy Bearing Surface\	472
27.2\	Case Study: Aluminum Wire Failures in Residential Wiring	474
27.3\	Case Study: Characterizing the Microstructure of a Manganese Nodule\	476
\	References .................................................. 479

XXIII

Contents

28\	Cathodoluminescence\ ... 481

28.1Origin\ .......................................................... 482

28.2Measuring Cathodoluminescence\ ... 483

28.2.1	Collection ofCL\	483
28.2.2	Detection ofCL	483
28.3	Applications ofCL\	485
28.3.1	Geology ....................................................... 485
28.3.2	Materials Science\	485
28.3.3	Organic Compounds ............................... 489

\References .................................................. 489

29\	Characterizing Crystalline Materials in the SEM\	491
29.1\ Imaging Crystalline Materials with Electron Channeling Contrast\		492

29.1.1Single Crystals ........................................... 492

29.1.2Polycrystalline Materials\........................ 494


29.1.3\	Conditions				for Detecting Electron Channeling Contrast\	496
29.2\	Electron			Backscatter Diffraction in the Scanning Electron
	Microscope ................................................ 496
29.2.1	Origin ofEBSD Patterns\ ......................... 498
29.2.2\	Cameras			for EBSD Pattern Detection . 499
29.2.3	EBSD Spatial Resolution ......................... 499
29.2.4\	How	Does a Modern EBSD System Index Patterns				501
29.2.5\	Steps		in Typical EBSD Measurements			502

29.2.6Display oftheAcquired Data\ ............... 505

29.2.7Other Map Components ........................ 508

29.2.8\ Dangers and Practice of “Cleaning” EBSD Data\ 508 29.2.9\ Transmission Kikuchi Diffraction in the SEM 509

29.2.10Application Example ............................... 510

29.2.11Summary\ .................................................... 513

29.2.12\Electron Backscatter Diffraction Checklist\ 513

\References .................................................. 514


30\	Focused Ion Beam Applications in the SEM Laboratory\		517
30.1	Introduction\		518
30.2	Ion–Solid Interactions\ .......................... 518
30.3\	Focused	Ion Beam Systems ................. 519
30.4	Imaging withIons		520

30.5Preparation ofSamples forSEM\ ....... 521

30.5.1	Cross-Section Preparation\ .................... 522
30.5.2\	FIB	Sample Preparation for 3D Techniques and Imaging	524

30.6Summary .................................................... 526

\References .................................................. 528

31\ Ion Beam Microscopy\ ..... 529 31.1\ What Is So Useful About Ions?\........... 530

31.2Generating Ion Beams\ .......................... 533

31.3Signal Generation intheHIM ............. 534

31.4\ Current Generation and Data Collection in the HIM\ 536

31.5Patterning withIon Beams\ ................. 537

31.6Operating theHIM\ ................................. 538

31.7\	Chemical	Microanalysis with Ion Beams	538
\	References .................................................. 539
\	Supplementary Information\		541
	Appendix\ .................................................... 542
\	Index\.......................................................... 547

1		1

Electron Beam—Specimen

Interactions: Interaction

Volume

1.1\ What Happens When the Beam Electrons Encounter Specimen Atoms? – 2

1.2\ Inelastic Scattering (Energy Loss) Limits Beam

Electron Travel in the Specimen – 2

1.3\ Elastic Scattering: Beam Electrons Change

Direction of Flight – 4

1.3.1\ How Frequently Does Elastic Scattering Occur? – 4

1.4\ Simulating the Effects of Elastic Scattering: Monte Carlo Calculations – 5

1.4.1\ What Do Individual Monte Carlo Trajectories Look Like? – 6 1.4.2\ Monte Carlo Simulation To Visualize the Electron

Interaction Volume – 6

1.4.3\ Using the Monte Carlo Electron Trajectory Simulation to Study the Interaction Volume – 8

1.5\ A Range Equation To Estimate the Size of the Interaction Volume – 12

\References – 14

J. Goldstein et al., Scanning Electron Microscopy and X-Ray Microanalysis, https://doi.org/10.1007/978-1-4939-6676-9_1

\2 Chapter 1 · Electron Beam—Specimen Interactions: Interaction Volume

1	1.1\ What Happens When the Beam
	Electrons Encounter Specimen Atoms?

By selecting the operating parameters of the SEM electron gun, lenses, and apertures, the microscopist controls the characteristics of the focused beam that reaches the specimen surface: energy (typically selected in the range 0.1– 30 keV), diameter (0.5 nm to 1 μm or larger), beam current (1 pA to 1 μA), and convergence angle (semi-cone angle 0.001–0.05 rad). In a conventional high vacuum SEM (typically with the column and specimen chamber pressures reduced below 10−3 Pa), the residual atom density is so low that the beam electrons are statistically unlikely to encounter any atoms of the residual gas along the flight path from the electron source to the specimen, a distance of approximately 25 cm.

kThe initial dimensional scale

With a cold or thermal field emission gun on a highperformance SEM, the incident beam can be focused to 1 nm in diameter, which means that for a target such as gold (atom diameter ~ 288 pm), there are approximately 12 gold atoms in the first atomic layer of the solid within the area of the beam footprint at the surface.

At the specimen surface the atom density changes abruptly to the very high density of the solid. The beam electrons interact with the specimen atoms through a variety of physical processes collectively referred to as “scattering events.” The overall effects of these scattering events are to transfer energy to the specimen atoms from the beam electrons, thus setting a limit on their travel within the solid, and to alter the direction of travel of the beam electrons away from the well-defined incident beam trajectory. These beam electron–specimen interactions produce the backscattered electrons (BSE), secondary electrons (SE), and X-rays that convey information about the specimen, such as coarseand fine-scale topographic features, composition, crystal structure, and local electrical and magnetic fields. At the level needed to interpret SEM images and to perform electronexcited X-ray microanalysis, the complex variety of scattering processes will be broadly classified into “inelastic” and “elastic” scattering.

1.2\ Inelastic Scattering (Energy Loss)

Limits Beam Electron Travel

in the Specimen

“Inelastic” scattering refers to a variety of physical processes that act to progressively reduce the energy of the beam electron by transferring that energy to the specimen atoms through interactions with tightly bound inner-shell atomic electrons and loosely bound valence electrons. These energy loss processes include ejection of weakly bound outer-shell

atomic electrons (binding energy of a few eV) to form secondary electrons; ejection of tightly bound inner shell atomic electrons (binding energy of hundreds to thousands of eV) which subsequently results in emission of characteristic X-rays; deceleration of the beam electron in the electrical field of the atoms producing an X-ray continuum over all energies from a few eV up to the beam’s landing energy (E0) (bremsstrahlung or “braking radiation”); generation of waves in the free electron gas that permeates conducting metallic solids (plasmons); and heating of the specimen (phonon production). While energy is lost in these inelastic scattering events, the beam electrons only deviate slightly from their current path. The energy loss due to inelastic scattering sets an eventual limit on how far the beam electron can travel in the specimen before it loses all of its energy and is absorbed by the specimen.

To understand the specific limitations on the distance traveled in the specimen imposed by inelastic scattering, a mathematical description is needed of the rate of energy loss (incremental dE, measured in eV) with distance (incremental ds, measured in nm) traveled in the specimen. Although the various inelastic scattering energy loss processes are discrete and independent, Bethe (1930) was able to summarize their collective effects into a “continuous energy loss approximation”:

dE / ds (eV / nm) = − 7.85(Z r / AE)ln (1.166 E / J ) \ (1.1a)

where E is the beam energy (keV), Z is the atomic number, ρ is the density (g/cm3), A is the atomic weight (g/mol), and J is the “mean ionization potential” (keV) given by

J (keV)= (9.76 Z + 58.5 Z −0.19 )x10−3	\	(1.1b)
	\

The Bethe expression is plotted for several elements (C, Al, Cu, Ag, Au) over the range of “conventional” SEM operating energies, 5–30 keV in . Fig. 1.1. This figure reveals that the rate of energy loss dE/ds increases as the electron energy decreases and increases with the atomic number of the target. An electron with a beam energy of 20 keV loses energy at approximately 10 eV/nm in Au, so that if this rate was constant, the total path traveled in the specimen would be approximately 20,000 eV/(10 eV/nm) = 2000 nm = 2 μm. A better estimate of this electron “Bethe range” can be made by explicitly considering the energy dependence of dE/ds through integration of the Bethe expression, Eq. 1.1a, from the incident energy down to a lower cut-off energy (typically ~ 2 keV due to limitations on the range of applicability of the Bethe expression; see further discussion below). Based on this calculation, the Bethe range for the selection of elements is shown in . Fig. 1.2. At a particular incident beam energy, the Bethe range decreases as the atomic number of the target increases, while for a particular target, the Bethe range increases as the incident beam energy increases.

1.2 · Inelastic Scattering (Energy Loss) Limits Beam Electron Travel in the Specimen
. Fig. 1.1 Bethe continuous
energy loss model calculations for			Bethe continuous energy loss model
dE/ds in C, Al, Cu, Ag, and Au as a			Bethe continuous energy loss model
dE/ds in C, Al, Cu, Ag, and Au as a	25
function of electron energy	25
function of electron energy
		Au
(eV/nm)	20
(eV/nm)	15	Ag
		Ag
rate		Cu
loss		Cu
loss	10
Energy	10
Energy		Al
		Al
	5
		C
	0
	5	10	15	20

Incident beam energy (keV)

. Fig. 1.2 Bethe range calcula-
tion from the continuous energy					Bethe range
loss model by integrating over the		14000
range of energy from E0 down to a
cut-off energy of 2 keV		12000
		12000
		10000
	(nm)	8000
	range	8000
	range
	Bethe	6000
		6000
		4000
		2000
		0
		5	10	15	20

Incident beam energy (keV)

3		1

Cu, Ag

25 30

kNote the change of scale

The Bethe range for Au with an incident beam energy of 20 keV is approximately 1200 nm, a linear change in scale of a factor of 1200 over an incident beam diameter of 1 nm. If the beam–specimen interactions were restricted to a cylindrical column with the circular beam entrance footprint as its

cross section and the Bethe range as its altitude, the volume of a cylinder 1 nm in diameter and 1200 nm deep would be approximately 940 nm3, and the number of gold atoms it contained would be approximately 7.5 × 104, which can be compared to the incident beam footprint surface atom count of approximately 12.

\4 Chapter 1 · Electron Beam—Specimen Interactions: Interaction Volume

	1.3\ Elastic Scattering: Beam Electrons
1	1.3\ Elastic Scattering: Beam Electrons
1			Change Direction of Flight

	Simultaneously with inelastic scattering, “elastic scattering”
	events occur when the beam electron is deflected by the elec-
	trical field of an atom (the positive nuclear charge as partially
	shielded by the negative charge of the atom’s orbital elec-
	trons), causing the beam electron to deviate from its previous
	path onto a new trajectory, as illustrated schematically in
	. Fig.		1.3a. The probability of elastic scattering depends
	strongly on the nuclear charge (atomic number Z) and the
	energy of the electron, E (keV) and is expressed mathemati-
	cally as a cross section, Q:
		Qelastic(>φ 0 ) =1.62×10−20 (Z2 / E2 )cot2 (φ0 / 2)
				2			(1.2)
			[events > φ0 / electron (atom / cm		)	\	(1.2)
						\

where ϕ0 is a threshold elastic scattering angle, for example, 2°. Despite the angular deviation, the beam electron energy is effectively unchanged in energy. While the average elastic scattering event causes an angular change of only a few degrees, deviations up to 180o are possible in a single elastic scattering event. Elastic scattering causes beam electrons to deviate out of the narrow angular range of incident trajectories defined by the convergence of the incident beam as controlled by the electron optics.

1.3.1\ How Frequently Does Elastic

Scattering Occur?

The elastic scattering cross section, Eq. 1.2, can be used to estimate how far the beam electron must travel on average to experience an elastic scattering event, a distance called the “mean free path,” λ:

. Fig. 1.3 a Schematic illustration of elastic scattering. An energetic electron is deflected by the electrical field of an atom at location P1

through an angle ϕelastic. b Schematic illustration of the elastic scattering cone. The energetic electron scatters elastically at point P1 and can

land at any location on the circumference of the base of the cone with equal probability. c Schematic illustration of a second scattering step, carrying the energetic electron from point P2 to point P3

where A is the atomic weight (g/mol), N0 is Avogadro’s number (atoms/mol), and ρ is the density (g/cm3). . Figure 1.4

shows a plot of λelastic for various elements as a function of electron energy, where it can be seen that the mean free path

is of the order of nm. Elastic scattering is thus likely to occur hundreds to thousands of times along a Bethe range of several hundred to several thousand nanometers.

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λelastic (cm)= A /

N0 ρQelastic(>φ 0 )

λelastic (nm)=10

ρQelastic(>φ 0 )