穿透式電子顯微鏡

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穿透式電子顯微鏡

穿透式電子顯微鏡 TEM TEM

張銀祐張銀祐 2006/12 2006/12

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定義定義

電子顯微鏡電子顯微鏡,,一般是指利用電磁場偏折、聚一般是指利用電磁場偏折、聚焦電子及電子與物質作用所產生散射之原焦電子及電子與物質作用所產生散射之原

理來研究物質構造及微細結構的精密儀理來研究物質構造及微細結構的精密儀器。器。

利用電子與物質作用所產生之訊號來鑑定利用電子與物質作用所產生之訊號來鑑定微區域晶體結構、微細組織、化學成份、

微區域晶體結構、微細組織、化學成份、

化學鍵結和電子分佈情況的電子光學裝化學鍵結和電子分佈情況的電子光學裝置。置。

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Transmission Electron Microscopy Transmission Electron Microscopy

(TEM) (TEM)

^TEM ^TEM ^- ^- experimental analysis of material and electronic experimental analysis of material and electronic devices.

devices.

Material morphology Material morphology

Material defects Material defects

Chemical composition Chemical composition

Crystallographic structure Crystallographic structure

Extremely high resolution images Extremely high resolution images

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Transmission Electron Microscope Assembly Transmission Electron Microscope Assembly

Electrons emitted form e-Electrons emitted form e-gun hot gun hot filament/field emission.

filament/field emission.

Electrons are accelerated (100-Electrons are accelerated (100- 300 kV) down the column.

300 kV) down the column.

^E-^E-s are collimated and converged s are collimated and converged by apertures and

by apertures and emgemg lenses.lenses.

^E-^E-beam size: 1mm beam size: 1mm -- < 20 nm.< 20 nm.

Specimen in a special holder is Specimen in a special holder is located below the condenser lens.

located below the condenser lens.

Emerging electrons are focused Emerging electrons are focused by the condenser lens.

by the condenser lens.

Diffraction pattern (DF) -Diffraction pattern (DF) - in the in the lower focal plane of objective.

lower focal plane of objective.

Inverted image (II)-Inverted image (II)- below the below the lower focal plane.

lower focal plane.

Magnified (10Magnified (10²² -- 1010⁶⁶) DF or II ) DF or II obtained on fluorescent screen.

obtained on fluorescent screen.

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TEM TEM 主要發展方向主要發展方向

高電壓：增加電子穿透試片的能力，可觀察較厚、較具代表性的試片臨場觀高電壓：增加電子穿透試片的能力，可觀察較厚、較具代表性的試片臨場觀察察(in(in--situ situ observalionobservalion) ) 輻射損傷輻射損傷; 減少波長散怖像差; 減少波長散怖像差(chromatic aberration) ; (chromatic aberration) ; 增加分辨率等，目前已有數部

增加分辨率等，目前已有數部22一一3 3 MeVMeV 的TEM的TEM在使用中。在使用中。

高分辨率：已增進到廠家保證最佳解像能為點與點間高分辨率：已增進到廠家保證最佳解像能為點與點間0.18 nm0.18 nm、線與線間、線與線間 0.14nm

0.14nm。美國於。美國於1983年成立國家電子顯微鏡中心，其中1983年成立國家電子顯微鏡中心，其中l000 keVl000 keV之原子分辨之原子分辨電子顯微鏡

電子顯微鏡 (atomic resolution electron microscope，(atomic resolution electron microscope，AREM) AREM) 其點與點間之其點與點間之分辨率達0. 17nm分辨率達0. 17nm，可直接觀察晶體中的原子。，可直接觀察晶體中的原子。

分析裝置：如附加電子能量分析儀分析裝置：如附加電子能量分析儀 (electron analyzer，(electron analyzer，EA) EA) 可鑑定微區域的可鑑定微區域的化學組成。

化學組成。

場發射電子光源: 場發射電子光源: 具高亮度及契合性，電子束可小至具高亮度及契合性，電子束可小至1 nm1 nm。除適用於微區域。除適用於微區域成份分析外，更有潛力發展三度空間全像術

成份分析外，更有潛力發展三度空間全像術(holography)(holography)。。

近年來將TEM近年來將TEM與與SEMSEM結合為一，取二者之長所製成的結合為一，取二者之長所製成的掃描穿透式電子顯微鏡掃描穿透式電子顯微鏡 (scanning transmission electron microscope

(scanning transmission electron microscope，，STEM)STEM) 亦漸普及亦漸普及。。STEM 附STEM 附加各種分析儀器，如

加各種分析儀器，如XPMA、XPMA、EA 等，亦稱為EA 等，亦稱為分析電子顯微鏡分析電子顯微鏡 (analytical (analytical

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Specimen Preparation for (S)TEM Specimen Preparation for (S)TEM

For Si 100 kV - < 200 nm,

1MV - ~ 1 μm Plan-view

Mounting by a face down on a polishing block using bees wax.

Lapping by 15 μm diamond paste or 400-grit paper to ~ 100 μm.

Ultrasonic boring to extract 3 mm discs.

Remelting wax and cleaning discs in acetone or trichloroethane.

Jet thinning (for Si) using 4 parts 50% HF:6 parts 65 % HNO₃until a hole appears (~ 10 μm).

Ion milling.

If buried features:

Top layer of a sample must be removed

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TEM: Preparation of Cross

TEM: Preparation of Cross - - sectional (Vertical sectional (Vertical Section) Specimens

Section) Specimens

3 mm

30mμ

Ar+

α = 10o μ

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電子顯微鏡在材料科學上的應用電子顯微鏡在材料科學上的應用

差排理論

(dislocation theory)

：由於晶體中缺陷

：由於晶體中缺陷交互作用的複雜性，藉

交互作用的複雜性，藉TEM直接觀察，不僅解

TEM

直接觀察，不僅解

決了許多困難，而且引導了差排理論的進一步發

展。差排的交互作用、結構以及分佈都可由

展。差排的交互作用、結構以及分佈都可由 TEM觀察到

TEM

觀察到

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機械性質機械性質 by TEM by TEM

TEM不僅可觀察晶體中及其經加工、熱處理後的

TEM

不僅可觀察晶體中及其經加工、熱處理後的

差排結構，而且能直接觀測到次晶形成、角隅

化、再結晶、潛變、多相晶體中差排與析出物交

互作用等與物質機械性質有密切關係的許多現象

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離子佈植離子佈植 (ion implantation) (ion implantation)

離子佈植

(ion implantation) : 半導體中供給帶電子

(ion implantation) :

半導體中供給帶電子

之雜質元素常由離子佈植方式摻入。由高能量離

子引致之位移損傷、不規則區之形成、非晶化以

及退火後磊晶成長、缺陷之形成與聚合、相互作

用等，均可由

用等，均可由TEM

TEM

觀察

Nb⁺/CrN

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界面結構界面結構

磊晶磊晶//基底界面差排之形式、特性、基底界面差排之形式、特性、BurgersBurgers 向量、排列及間隔均可由

向量、排列及間隔均可由TEMTEM鑑定，高分鑑定，高分辨影像更可觀測界面原子排列情形

辨影像更可觀測界面原子排列情形

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TEM TEM 繞射與成像繞射與成像

電子束與試片作用，在物鏡之後聚焦平面電子束與試片作用，在物鏡之後聚焦平面 (back focal plane)

(back focal plane)形成繞射圖形形成繞射圖形(diffraction (diffraction pattern)

pattern) ，而在成像平面，而在成像平面 ( image plane ) ( image plane ) 生生成放大像成放大像。。

在操作電子顯微鏡時，常以改變中間鏡電在操作電子顯微鏡時，常以改變中間鏡電流方式使中間鏡聚焦於物鏡之後聚焦平面流方式使中間鏡聚焦於物鏡之後聚焦平面或成像平面，再分別觀察繞射圖形或放大或成像平面，再分別觀察繞射圖形或放大像。像。

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TEM TEM 繞射與成像繞射與成像

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對比對比

與試片作用之電子束形成的影像以兩極方與試片作用之電子束形成的影像以兩極方式呈現對比，即

式呈現對比，即

(1)(1)相對比相對比(phase contrast)(phase contrast)

(2)(2)繞射對比繞射對比 (diffraction contrast) (diffraction contrast)

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相對比相對比

由直射與繞射電子束經透鏡系統重合，相由直射與繞射電子束經透鏡系統重合，相互干互干涉而生成，如涉而生成，如圖圖2.142.14所示。對鑑別率所示。對鑑別率

較佳之電子顯微鏡而言，由直射與繞射電較佳之電子顯微鏡而言，由直射與繞射電

子束干涉所生成之干涉

子束干涉所生成之干涉條紋常與繞射電子條紋常與繞射電子束對應晶格平面投影有一定關係，稱為晶束對應晶格平面投影有一定關係，稱為晶格像格像 ( lattice image )( lattice image )。而在適當條件下，。而在適當條件下，

由多電子束干涉甚至可觀察到原子之結構由多電子束干涉甚至可觀察到原子之結構像像 ( structure image) ( structure image) 。。

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繞射對比繞射對比

由電子束照射試片各部份之繞射條件不同由電子束照射試片各部份之繞射條件不同而生成的兩種成像力式，即：

而生成的兩種成像力式，即： (l) (l) 明視野成明視野成像像 ( bright field image)( bright field image)；； (2) (2) 暗視野成像暗視野成像

(dark field image)

(dark field image) 。。可參考圖可參考圖2.182.18 及及圖圖

2.192.19 。。 (1) (1) 明視野成像明視野成像 : : 由物鏡孔徑擋住繞由物鏡孔徑擋住繞射電子束，僅讓直射電子束

射電子束，僅讓直射電子束通過成像。通過成像。 (2) (2) 暗視野成像：

暗視野成像：由物鏡孔徑擋住直射電子由物鏡孔徑擋住直射電子束，僅讓繞射電子束

束，僅讓繞射電子束通過成像。通過成像。

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繞射對比繞射對比

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Dark Dark - - Field Image in TEM Field Image in TEM

Insertion of a small aperture into Insertion of a small aperture into the back focal plane of objective.

the back focal plane of objective.

Aperture is laterally dislocated Aperture is laterally dislocated from the optical axis.

from the optical axis.

Undeviated electrons are stopped. Undeviated electrons are stopped.

Only scattered electrons can pass Only scattered electrons can pass through it.

through it.

Image contrast is formed by the Image contrast is formed by the local variation of intensity of

local variation of intensity of scattered electrons.

scattered electrons.

Image is constructed from Image is constructed from

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Bright and Dark Field Images Bright and Dark Field Images

TEM of Molybdenum

TEM of Molybdenum - - oxide crystal oxide crystal

Advantage of the DF image is the much higher contrast: feature that are only visible with difficulty in BF image often stand out in the dark-field image.

More pronounce advantage of DF image is the possibility to bring out some features selectively.

BF DF

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Selective Enhancement of Features in DF Selective Enhancement of Features in DF

Image Image

a

b

BFI of particles in Al-Cu alloy:

DFI: dark-field conditions selected to show the particles seen on their side.

DFI showing the conspicuous,

close to vertical particles.

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選區繞射選區繞射 (selected area diffraction) (selected area diffraction)

選區繞射選區繞射 (selected area diffraction)(selected area diffraction)乃以中乃以中間鏡孔徑選取試片中特定區域而獲得此微間鏡孔徑選取試片中特定區域而獲得此微小區域小區域之繞射資料。由選區繞射可得到微之繞射資料。由選區繞射可得到微

小區域顯微像與繞射圖形之相互關係。在小區域顯微像與繞射圖形之相互關係。在觀察多晶或多相試片時特別有用。另外還觀察多晶或多相試片時特別有用。另外還可利用選區繞射確定微結構分析繞射及對可利用選區繞射確定微結構分析繞射及對比條件。比條件。

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Conventional TED Patterns:

SAD from Different Structures SAD from Different Structures

Conventional TED pattern Conventional TED pattern

Amorphous: Series of Amorphous: Series of diffused concentric rings.

diffused concentric rings.

Polycrystalline: Sharp Polycrystalline: Sharp concentric rings

concentric rings. .

Single crystal: Regular spot Single crystal: Regular spot TED pattern.

TED pattern.

Monocrystalline.

Then structural analysis can Then structural analysis can be carried out.

be carried out.

In amorphous matrix, the

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Cross

Cross - - sectional TEM micrograph of sectional TEM micrograph of

a Cr a Cr - - C:H/N film C:H/N film

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Silicon Nanowires Grown by Two Different Silicon Nanowires Grown by Two Different

Methods Methods

200 nm

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High Resolution Image of a Silicon Nanowire High Resolution Image of a Silicon Nanowire

SiO

₂

2 nm

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Bright Field TEM Image: Plan

Bright Field TEM Image: Plan - - View View

Polycrystalline Si

Grey level of contrast arises Grey level of contrast arises from individual grains.

from individual grains.

Various crystallines ^Various crystallines have have different crystallographic different crystallographic orientation.

orientation.

Such images for Such images for

determination of grain size determination of grain size from from

d = 1.5l/nM d = 1.5l/nM

l l - - length of the line, length of the line,

n n - - number of crossed grain, number of crossed grain,

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HIGH HIGH - - RESOLUTION MICROGRAPHS RESOLUTION MICROGRAPHS

Cross

Cross-

-

sectional HREM

sectional HREM micrographs of Si/SiO

micrographs of Si/SiO₂₂/PolySi

/PolySi REQUIREMENTS

REQUIREMENTS

Specimen must be thin 10 nm Specimen must be thin 10 nm at 200 kV for

at 200 kV for Si Si. .

The incident e- The incident e -beam oriented: beam oriented:

coincides with one of the simple coincides with one of the simple crystallographic direction.

crystallographic direction.

Micrograph taken near Micrograph taken near

‘optimum defocus ‘ optimum defocus’ ’ - - Scherzer Scherzer defocus.

defocus.

Using this method thickness of Using this method thickness of layer can also be found.

layer can also be found.

2 nm cBN

Au

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DIFFRACTION PATTERNS IN TEM DIFFRACTION PATTERNS IN TEM

Material present in specimen give rise a transmitted electron Material present in specimen give rise a transmitted electron diffraction (TED) pattern in back focal plane of the objective.

diffraction (TED) pattern in back focal plane of the objective.

Pattern of TED can be analyzed as that of X- Pattern of TED can be analyzed as that of X - ray diffraction. ray diffraction.

High lateral resolution 10 nm because of very thin specimen (~10 nm) High lateral resolution 10 nm because of very thin specimen (~1 0 nm) allows to study individual precipitates.

allows to study individual precipitates.

Two methods for forming diffraction patterns Two methods for forming diffraction patterns

1. Conventional TED:

Selected Area diffraction (SAD): requires the Selected Area diffraction (SAD): requires the insertion of an aperture in the image plane of objective

insertion of an aperture in the image plane of objective - - area to be area to be analyzed is selected by the aperture.

analyzed is selected by the aperture.

TED pattern from selected area - TED pattern from selected area -on the TEM screen transferring the on the TEM screen transferring the TEM into diffraction mode

TEM into diffraction mode - - by changing the current in objective lens by changing the current in objective lens focal plane changes.

focal plane changes.

2.Convergent Beam Diffraction:

Formation of a convergent incident e- Formation of a convergent incident e - beam.

beam.

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Simple Crystal Structures

2 2

2 k l

h d

_hkl

a

+

= +

Simple cubic Body –centered cubic Face centered cubic (e.g. P) (e.g. W) (e.g. Au, Al)

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Miller Indices

2 2

2 k l

h d

_hkl

a

+

= +

A convenient method of defining the various planes in a crystal is to use Miller indices, which are determined by first finding the intercepts of the plane with three basis axes in terms of the lattice constants, and then taking the reciprocals of these numbers and

Miller indices of important planes in a cubic crystal.

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Some Other Conventions

(h k l)

(h k l) : for plane that : for plane that intersepts intersepts the x axis on the negative the x axis on the negative side of

side of the origin. the origin.

{h k l}

{h k l} : for planes of equivalent symmetry such as {100} for : for planes of equivalent symmetry such as {100} for (100), (010), (001), (100), (010), and (001) in cubic (100), (010), (001), (100), (010), and (001) in cubic

symmetry.

[ [ hkl hkl ] ] : for the direction of a crystal such as [100] for x axis. : for the direction of a crystal such as [100] for x axis.

< < hkl hkl > > : for a full set of equivalent directions. : for a full set of equivalent directions.

[a [a

₁₁

a a

₂₂

a a

₃₃

c] c] : for hexagonal lattice. Here it is customary to use : for hexagonal lattice. Here it is customary to use four

four axes with the c axis as the [0001] direction. axes with the c axis as the [0001] direction.

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Interplanar Spacing in a Simple Cubic

Lattice

1 cos

cos

²

α +

²

β +

²

γ =

(

² ² ²

) ¹

2 2

= +

+ k l h

a d

_hkl

(

d_hkl cosα

) (

² + d_hkl cosβ

) (

² + d_hkl cosγ

)

² = d_hkl²

γ β

α cos

cos / cos /

/ = = =

l a d k

a d h

a

d_hkl _hkl _hkl

( / ) ( / ) ( ) /

²

¹

2 2

2

= +

+

l a

d k

a d h

a

d_hkl _hkl _hkl

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Diffraction in TEM

Reinforced conditionsReinforced conditions nλnλ = 2d sin θ= 2d sin θ

Miller index notation is used for Miller index notation is used for defining

defining crystalographiccrystalographic planes and planes and directions, e.g., for simple cubic directions, e.g., for simple cubic crystal

crystal

By convention for e-By convention for e-diffraction usediffraction use

¹¹^st^st order n=1 and, e.g., 2order n=1 and, e.g., 2^nd^nd order order use multiple Miller indices.

use multiple Miller indices.

²²^nd^nd order (n = 2) from a plane (131) order (n = 2) from a plane (131) can be called the 1

can be called the 1^st^st order order diffraction from a plane (262).

diffraction from a plane (262).

Bragg

Bragg’’s law can be then s law can be then λλ = 2d sin θ= 2d sin θ

Significance of

Significance of θθ angle at eangle at e-diffraction-diffraction

For 100 keV^{For 100}keV, , λλ = 0.0037 nm; for Al = 0.0037 nm; for Al crystal d = 0.4nm

crystal d = 0.4nm…… sinsinθθ = = 0.0046

0.0046……θθ= 0.26.5= 0.26.5^o^o. Hence λ. Hence λ = 2d θ= 2d θ or λor λ/d = 2 /d = 2 θθ

2 2

2 k l

h d

_hkl

a

+

= +

E-beam strongly diffract only from planes of atoms almost being parallel to e-beam.

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Diffraction Planes in TEM

Back focal plane of objective Objective

Back focal plane of post specimen lens

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Formation of Diffraction Patterns in TEM

For small diffraction angle For small diffraction angle

Combining with eq. Combining with eq. λ λ / / d = 2 d = 2 θ θ

^L

λ

λ - - camera constant camera constant

^L

^L ^– ^– camera length is not physical distance camera length is not physical distance but notional adjusted by operator.

but notional adjusted by operator.

^Distance ^Distance g g of diffraction spot is inversely of diffraction spot

is inversely

proportional

to to d d spacing spacing

θ

= 2 L g

λ λ

L d

g d or

L

g = =

Crystal

with spacing d

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Diffraction Pattern and Reciprocal Lattice Diffraction Pattern and Reciprocal Lattice

g = g ∝

α

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Ewald

Ewald Sphere Construction

Sphere Construction

Formal demonstration

Formal demonstration between between the reciprocal lattice and

the reciprocal lattice and diffraction pattern

diffraction pattern

a) a)

Diffraction crystal

–

presented

presented by its reciprocal lattice

by its reciprocal lattice

b) b)

E

-

beam is presented by a

beam is presented by a vector

vector 1/λ

1/

λ, parallel to the beam

, parallel to the beam direction, and terminating at the

direction, and terminating at the

origin of the reciprocal lattice

c) c) Sphere of radius 1/ Sphere of radius 1/ λ is drawn λ is drawn about A.

about A.

Ewald

Ewald sphere passes through a sphere passes through a reciprocal lattice point, a

reciprocal lattice point, a distance 1/d from the origin.

distance 1/d from the origin.

From geometry From geometry

θ λ λ

θ λ 2 sin

2 /

sin 1 or d

d

d = =

=

Diffraction occurs when the Ewald sphere touches a

reciprocal lattice point

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Material structure can be inferred from analyzing numerous specimen tilts.

A SAD Pattern from a single crystal consists of a regular array of diffraction spots.

Miller indices can be found by a ratio technique. For a cubic crystal

^{Ratio of}

g

squares gives a ratio of the

Σ

of the squares of the plane’s indices.

Spacing of the plane producing diffraction spots can be found from

g

_hkl

=λL/d

_hkl

Angle between any two diffracting vectors is identical to the angle between corresponding planes.

Single Crystal: SAD Pattern Single Crystal: SAD Pattern

( ) ( )

g h k l

for two difraction vectors g

g

h k l

m n o

hkl

hkl mno

2 2 2 2

2 2

2 2 2

∝ + +

= + +

+ +

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Conventional TED Patterns:

SAD from Different Structures SAD from Different Structures

Conventional TED pattern

Amorphous: Series of diffused concentric rings.

Polycrystalline: Sharp concentric rings.

Single crystal: Regular spot TED pattern.

Monocrystalline.

Then structural analysis can be carried out.

In amorphous matrix, the

positions of atoms are not

normally required.

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Experimental Conditions for TED Patterns Experimental Conditions for TED Patterns

Specimen area must be flat and horizontal in the

microscope.

This area must be at the unique height at which tilting the sample will not cause

moving the image - minimizes any distortion in diffraction pattern produced by e-optics.

TED pattern should contain as many complete rings as

possible - for accurate measurement - large SAD aperture.

At least 6 innermost rings.

Ring diameter should be

measured along one diameter.

(43)

43 43

Analysis: Polycrystalline Diffraction Pattern

Measure radii of the rings g

₁

, g

₂

, g

₃

, etc.

Calculate the d spacing d

₁

, d

₂

, d

₃

, etc of planes, give rise to rings g

₁

, g

₂

, g

₃

, etc. from eq. d = Lλ/g

d spacing obtained identify with cross-referring data to those tabulate in X-ray diffraction files, which list the spacing of thousands of

materials.

Not all plane diffract – depends on the structure factor, which must be calculated If it is 0 – plane does not diffract. For some crystals the

structure factor rules are simple.

For face-centered cubic crystal diffract only when Miller indices are unmixed, i.e., odd or even.

For body centered diffraction - only h+k+l is even.

(44)

Analysis: Polycrystalline Diffraction Pattern

g measured from the pattern, we need to match the crystal planes to the rings (index the rings)

Since g is inversely proportional to d, the innermost ring has largest d spacing.

^(*)

Considering all possible values of h,k, and l a possible series of increasing g values would be the sequence 100, 110, 111, 200, 210, 211, 220, 311, etc

The structure factor rules tell us that for Au, face centered cubic material h, k, l must be unmixed and therefore rings 100 110, 210 and 211 will not appear and sequence of the ring must be 111, 200, 220, 311, etc

Even without knowing the camera constant we can check this by measuring the ratios of the radii g₂/g₁, g₃/g₁etc and comparing them with ratios calculated from equation (*)

) ( h

²

k

²

l

²

a

L d

g = L λ = λ + +

(45)

45 45

Energy Dispersive X

Energy Dispersive X - - ray Spectroscopy in TEM ray Spectroscopy in TEM

EDS for compositional analysis.

X-ray produced specific to chemical element.

Number of photons per increment path dt: I_Adt = n_AZ_A dt.

For two components A and B of specimen (< 10 nm)

I_A/I_B = n_AZ_A/n_BZ_B

Z_A,B - atomic correction number standard or standardless

Intensity measured with a solid state detector.

Sensitivity 0.2 atomic %.

Spatial resolution ~10 nm

(46)

Energy Dispersive X

Energy Dispersive X - - ray Spectroscopy in TEM ray Spectroscopy in TEM

Cross-sectional bright field image - an electronic device

EDS analysis of ~ 150 nm nanometers thick TiSi₂

metalization layer shows stoichiometric composition.

High spatial resolution (<10 nm) - interaction volume is limited by the specimen thickness

Peaks are resolved well from the background.

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47 47

Electron Energy Loss Spectroscopy in TEM Electron Energy Loss Spectroscopy in TEM

Some electrons undergo energy loss in specimen.

Magnetic prisms deflects electrons entering the spectrometer.

Electrons suffering the greatest losses are deflected through the greatest angle than those unaltered.

The electrons that did not suffer the energy loss: zero-loss electrons.

Spectrum is created by detecting the position and intensity of energy loss electrons relative to zero-loss

electrons.

(48)

Three Regions in the EEL Spectra Three Regions in the EEL Spectra

First: Dominated by zero-loss peak.

^Second: Up to 50 eV loss:

Interaction to form plasmon oscillations.

^Third: Losses above 100 eV:

Energy required to ionize the atoms.

Quantification

Ionization losses appears like steps on a continuous

background.

Background empirically fitted and Subtracted from the spectrum.

Concentration is proportional to the intensity of edges.

For two elements n_A/n_B= I_AQ_B/I_BQ_A

Q_A and Q_B - ionization cross- sections for A and B.

Quantification difficult because

Edges decay over large energy range

overlap and

Some suffer multiple scattering

(49)

49 49

Epitaxial growth of cBN on diamond Epitaxial growth of cBN on diamond

HRTEM cross-sectional image

(50)

Epitaxial growth

Epitaxial growth Si Si - - D D - - cBN cBN

cBND structure

prepared at 950

^o

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