1. Energy-Dispersive X-ray Microanalysis in the TEM Anthony J. Garratt-Reed Neil Rowlands

2. One result of the interaction of an electron beam with matter is the emission of x-rays

3. The energy and wavelength of the X- rays is different for, and characteristic of, each element

4. One result of the interaction of an electron beam with matter is the emission of x-rays The energy and wavelength of the X- rays is different for, and characteristic of, each element Analysis of the X-rays can, therefore, be used as a tool to give information about the composition of the sample

5. In today's talk:

6. i. X-ray emission from materials

7. In today's talk: i. X-ray emission from materials ii. X-ray detectors (brief!)

8. In today's talk: i. X-ray emission from materials ii. X-ray detectors (brief!) iii. Quantitative chemical analysis

9. In today's talk: i. X-ray emission from materials ii. X-ray detectors (brief!) iii. Quantitative chemical analysis iv. Spatial Resolution

10. X-ray emission from materials

11. 2 independent processes

12. X-ray emission from materials 2 independent processes Characteristic X-rays (discrete energies)

13. X-ray emission from materials 2 independent processes Characteristic X-rays (discrete energies) Bremsstrahlung (continuum)

14. Characteristic X-rays 2-step process involving the atomic electrons

15. Characteristic X-rays 2-step process involving the atomic electrons Firstly, the atom is excited by ionization of one of the core-level electrons

17. Characteristic X-rays 2-step process involving the atomic electrons Firstly, the atom is excited by ionization of one of the core-level electrons This is followed by an outer-shell electron losing energy by emission of a photon (the X-ray), and dropping to the core state

19. Bremsstrahlung “Braking radiation”

20. Bremsstrahlung “Braking radiation” All charged particles radiate energy when accelerated

21. Bremsstrahlung

23. X-ray detectors

24. Lithium-drifted Silicon (Si(Li))

25. X-ray detectors Lithium-drifted Silicon (Si(Li)) Used since around 1970 on SEMs

26. X-ray detectors Lithium-drifted Silicon (Si(Li)) Used since around 1970 on SEMs Silicon Drift detector

27. X-ray detectors Lithium-drifted Silicon (Si(Li)) Used since around 1970 on SEMs Silicon Drift detector Over the last 5 years

28. X-ray detectors Lithium-drifted Silicon (Si(Li)) Used since around 1970 on SEMs Silicon Drift detector Over the last 5 years Crystal detectors – Electron Microprobe

29. X-ray detectors Lithium-drifted Silicon (Si(Li)) Used since around 1970 on SEMs Silicon Drift detector Over the last 5 years Crystal detectors – Electron Microprobe Different characteristics

30. Si(Li) crystal

31. Crystal of pure silicon, with lithium diffused in to compensate for any residual carriers

32. Si(Li) crystal Crystal of pure silicon, with lithium diffused in to compensate for any residual carriers About 3mm thick and 3-6 mm diameter

33. Si(Li) crystal Crystal of pure silicon, with lithium diffused in to compensate for any residual carriers About 3mm thick and 3-6 mm diameter Electrodes plated on front and back

34. Si(Li) crystal Crystal of pure silicon, with lithium diffused in to compensate for any residual carriers About 3mm thick and 3-6 mm diameter Electrodes plated on front and back Front electrode is thin to allow X-rays to enter

35. Si(Li) crystal Crystal of pure silicon, with lithium diffused in to compensate for any residual carriers About 3mm thick and 3-6 mm diameter Electrodes plated on front and back Front electrode is thin to allow X-rays to enter Biased by a voltage of 3-500V

36. Si(Li) crystal Crystal of pure silicon, with lithium diffused in to compensate for any residual carriers About 3mm thick and 3-6 mm diameter Electrodes plated on front and back Front electrode is thin to allow X-rays to enter Biased by a voltage of 3-500V Cooled to Liq. N 2

37. Si(Li) crystal Energy of an x-ray generates electron- hole pairs

38. Si(Li) crystal Energy of an x-ray generates electron- hole pairs These are swept from the crystal by the bias voltage, and are detected in the external circuitry as a pulse of charge

39. Si(Li) crystal Energy of an x-ray generates electron- hole pairs These are swept from the crystal by the bias voltage, and are detected in the external circuitry as a pulse of charge Since the average energy required to create an electron-hole pair is constant and predictable (about 3.8eV), the external charge is proportional to the x-ray energy

45. Quantitative Analysis

46. Different techniques for:

47. Quantitative Analysis Different techniques for: SEM

48. Quantitative Analysis Different techniques for: SEM Organic thin sections

49. Quantitative Analysis Different techniques for: SEM Organic thin sections Materials thin sections

50. Quantitative Analysis Different techniques for: SEM Organic thin sections Materials thin sections – Today's talk!

51. Characteristic X-rays 2-step process involving the atomic electrons Firstly, the atom is excited by ionization of one of the core-level electrons This is followed by an outer-shell electron losing energy by emission of a photon (the X-ray), and dropping to the core state

52. Characteristic X-rays 2-step process involving the atomic electrons Firstly, the atom is excited by ionization of one of the core-level electrons This is followed by an outer-shell electron losing energy by emission of a photon (the X-ray), and dropping to the core state - Fluorescence

53. Ionization cross-section

54. The Ionization cross-section is defined as the probability of ionizing a single atom in a region of uniform current density of electrons.

55. Ionization cross-section The Ionization cross-section is defined as the probability of ionizing a single atom in a region of uniform current density of electrons. Usually denoted by “ Q A ” where the “ A ” denotes the particular element of interest

56. Ionization cross-section The Ionization cross-section is defined as the probability of ionizing a single atom in a region of uniform current density of electrons. Usually denoted by “ Q A ” where the “ A ” denotes the particular element of interest It has units of area

57. Ionization cross-section Units are generally Barns, where 1 Barn=10 -24 square centimeters

58. Ionization cross-section Units are generally Barns, where 1 Barn=10 -24 square centimeters Typical values of the cross-section are 100-1000 Barns.

59. Ionization cross-section Units are generally Barns, where 1 Barn=10 -24 square centimeters Typical values of the cross-section are 100-1000 Barns. For practical purposes, the cross-section can be regarded as a function of the electron energy alone, and is independent of the chemical surroundings.

60. Ionization cross-section For practical purposes, the cross-section can be regarded as a function of the electron energy alone, and is independent of the chemical surroundings. Various equations have been proposed to predict the value of the ionization cross- section for all the elements at different beam voltages

61. Characteristic X-rays 2-step process involving the atomic electrons Firstly, the atom is excited by ionization of one of the core-level electrons This is followed by an outer-shell electron losing energy by emission of a photon (the X-ray), and dropping to the core state - Fluorescence

62. Fluorescence Yield

63. Generally given the symbol “  A ” where, again, the subscript “A” denotes the particular element.

64. Fluorescence Yield Generally given the symbol “  A ” where, again, the subscript “A” denotes the particular element. For practical purposes again, the fluorescence yield can be considered to be a constant for a particular transition. (No significant dependence on chemical bonding, for example)

65. Fluorescence Yield For practical purposes again, the fluorescence yield can be considered to be a constant for a particular transition. The fluorescence yield has been measured for a wide range of lines; an equation has been developed to fit these measurements to predict the fluorescence yield in those cases where measurements have not been made.

66. Putting this together --

67. We can write, for a sample of thickness t and density  : where I A is the number of x-rays generated, i p is the probe current in Amps, e is the electron charge, C A is the concentration (weight fraction) of element A in the sample, A A is the atomic weight of element A, s is a partition function to account for the fraction of x-rays in the detected line, and  is the analysis time in seconds.

68. Writing the same equation for element B and dividing:

69. or

70. Since the detector sensitivity  varies for different elements, where the I ’s are now the measured x-ray intensities for the various elements

71. Since the detector sensitivity  varies for different elements, where the I ’s are now the measured x-ray intensities for the various elements The Cliff-Lorimer equation

72. Limitations of Cliff-Lorimer Valid for “thin” samples only

73. Limitations of Cliff-Lorimer Valid for “thin” samples only

74. Limitations of Cliff-Lorimer Valid for “thin” samples only

75. The more common reality!

76. Limitations of Cliff-Lorimer Valid for “thin” samples only Variations of detector parameters (espec. ice)

77. Limitations of Cliff-Lorimer Valid for “thin” samples only Variations of detector parameters (espec. ice) Only works when all elements can be detected

78. Limitations of Cliff-Lorimer Valid for “thin” samples only Variations of detector parameters (espec. ice) Only works when all elements can be detected Spectral Processing

82. Limitations of Cliff-Lorimer

83. Valid for “thin” samples only Variations of detector parameters (espec. ice) Only works when all elements can be detected Spectral Processing Spurious effects -

84. Spurious effects: Fluorescence

85. Spurious effects: Fluorescence Escape peaks

86. Spurious effects: Fluorescence Escape peaks Coherent Bremsstrahlung

87. Spurious effects: Fluorescence Escape peaks Coherent Bremsstrahlung Detector imperfections

88. Spurious effects: Fluorescence Escape peaks Coherent Bremsstrahlung Detector imperfections Etc., etc.

89. Limitations of Cliff-Lorimer

90. Valid for “thin” samples only Variations of detector parameters (espec. ice) Only works when all elements can be detected Spectral Processing Spurious effects Statistics!

91. Statistics Counting of x-rays is a random phenomenon

92. Why do we need counts? 2 sec, low count rate

93. Why do we need counts? 10 secs, low count rate

94. Why do we need counts? 100 secs, low count rate

95. Why do we need counts? 100 secs, high count rate

96. Statistics Counting of x-rays is a random phenomenon In counting N events, there is an uncertainty  (the standard deviation) which is equal to the square root of N

97. Statistics Counting of x-rays is a random phenomenon In counting N events, there is an inherent uncertainty  (the standard deviation) which is equal to the square root of N N has a 95% probability of being within +- 2  of the “Correct” answer

98. Statistics N has a 95% probability of being within +- 2  of the “Correct” answer Hence if 1% precision is required 95% of the time, 40,000 counts must be acquired

99. Statistics N has a 95% probability of being within +- 2  of the “Correct” answer Hence if 1% precision is required 95% of the time, 40,000 counts must be acquired Likewise for 0.1% precision, 4,000,000 counts are required

100. Statistics Likewise for 0.1% precision, 4,000,000 counts are required Approximately half the counts are in the major peak of an element, so 8,000,000 counts must be acquired in the spectrum

101. Statistics Likewise for 0.1% precision, 4,000,000 counts are required Approximately half the counts are in the major peak of an element, so 8,000,000 counts must be acquired in the spectrum Maximum count rate for Si(Li) detector is about 30,000cps, so this will take about 250 seconds (SDD will count at 250,000 cps)

102. Spatial Resolution

104. There is no single definition of “Spatial Resolution”

105. Spatial Resolution There is no single definition of “Spatial Resolution” Analyzing a small particle on a thin support film has very different requirements from analyzing a diffusion gradient in a foil

106. Spatial Resolution There is no single definition of “Spatial Resolution” Analyzing a small particle on a thin support film has very different requirements from analyzing a diffusion gradient in a foil Consider the diffusion example:

107. Spatial Resolution

108. Putting this together -- We can write, for a sample of thickness t and density  : where I A is the number of x-rays generated, i p is the probe current in Amps, e is the electron charge, C A is the concentration (weight fraction) of element A in the sample, A A is the atomic weight of element A, s is a partition function to account for the fraction of x-rays in the detected line, and  is the analysis time in seconds.

109. But … (B is brightness of electron source, C s is spherical aberration coefficient of objective lens)

110. Source Brightness:

111. Inherent function of emitter

112. Source Brightness: Inherent function of emitter Thermionic W:5 V o A/cm 2 /Sr

113. Source Brightness: Inherent function of emitter Thermionic W:5 V o A/cm 2 /Sr Thermionic LaB6:200 V o A/cm 2 /Sr

114. Source Brightness: Inherent function of emitter Thermionic W:5 V o A/cm 2 /Sr Thermionic LaB 6 :200 V o A/cm 2 /Sr Field Emitter:5000 V o A/cm 2 /Sr

115. AND Beam Broadening:

116. Spatial Resolution

117. AND Beam Broadening: Inserting values: Z=26 (Iron),  =8gm/cc, A=56, t=4E -6 cm (40 nm), E o =200KV We find that b= 2.4x10 -7 cm (2.4 nm)

118. Optimizing, We can estimate a spatial resolution of about 2 nm with 1% analytical precision

119. Optimizing, We can estimate a spatial resolution of about 2 nm with 1% analytical precision Or, much better resolution if the required precision is not so high

120. Optimizing, We can estimate a spatial resolution of about 2 nm with 1% analytical precision Or, much better resolution if the required precision is not so high Requires VERY good sample! (e.g. thickness of ~10nm)