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Q« N BS TECHNICAL NOTE 1 1 06

U.S. DEPARTMENT OF COMMERCE/National Bureau of Standards

FRAME C:

ompact Procedure for

Quantitative Energy-Dispersive

Electron Probe X-ray Analysis

.00

15753

1106

l379
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards' was established by an act ot Congress on March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology

and facilitate their effective application for public benefit. To this end, the Bureau conducts

research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau's technical work is per- formed by the National Measurement Laboratory, the National Engineering Laboratory, and

the Institute for Computer Sciences and Technology.

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research and provides scientific and technical services to aid Federal agencies in the selection, acquisition, application, and use of computer technology to improve effectiveness and

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'Headquarters and Laboratories at Gaithersburg, MD, unless otherwise noted; mailing address Washington, DC 20234. ^Some divisions within the center are located at Boulder, CO 80303.
NOV 3 197^

f -LAC

Frame C: A Compact Procedure for

Quantitative Energy-Dispersive ^^^

Electron Probe X-ray Analysis ID'

R. L Myklebust, C. E. Fiori, and

K. F. J. Heinrich

National Measurement Laboratory

National Bureau of Standards

Washington, DC 20234

K^^^ ''' c,

^^fi£AV O^

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Luther H. Hodges, Jr., Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued September 1 979
National Bureau of Standards Technical Note 1 106

Nat. Bur. Stand. (U.S.), Tech. Note 1 106, 111 pages (Sept. 1979)

CODEN: NBTNAE

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

Stock No. 003-003-021 13-0 Price: $4.00

(Add 25 percent additional for other than U.S. mailing)
Foreword

This publication was written in order to document a data evaluation procedure for quantitative energy-dispersive

electron probe analysis. The procedure is imbedded in a program (FRAME C) written in BASIC, for on-line use with

a small computer. A FORTRAN 4 version is available for use

on a batch mode computer. After a general description of

the procedure, results of analyses of materials of known composition are given, and a detailed example of execution of

FRAME C is presented. In Appendix I, a previously published

communication on Si (Li) detector artifacts is reproduced.

This paper should be useful in acquainting the reader with

some of the problems arising from the use of this detector,

and give the rationale for some of the corrective procedures

in FRAME C. Appendix II contains a list of the symbols used

in the program, with their meaning. Appendix III is a listing of the program.

We hope that the reader will find this documentation to

be complete and clear. Commentaries and criticisms, particularly from potential or actual users of the program, are

welcomed.

R.L.M., C.E.F., and K.F.J.H.

Ill
TABLE OF CONTENTS

I. Introduction 2

II. General Description 6

Ila Background and Line Interference

Corrections 11

lib Description of Subroutines 23

lie Results 35

lid Example 44

III. References 49

IV. Appendices 51

Appendix 1 . 51

Appendix 2 73

Appendix 3 87

IV
LIST OF TABLES

TABLE NO. Page

1. Relative transition probabilities for K3 X-ray

Lines [20] 18

2. Overlap corrections 19

3. Comparative analyses o£ zinc tungstate, ZnWO. . . . 37

4. Mineral analyses 40

5. Analyses o£ NBS low alloy steel 43

LIST OF FIGURES

FIGURE NO. Page

1. Block diagram of the data evaluation system in

¥RMAE C . . 7

2. Block diagram of FRAME C showing all steps in

an analysis 9

3. Schematic representation of two overlapping Gaussian

peaks. Shaded areas are the overlaps of each peak

into the region of interest of the other peak. . 13

4. Spectrum of manganese showing region of interest

(ROI) for FeKa overlapped by MnKg 15

5. Short block diagram of procedures in FRAME C . . .32

6. Spectrum of ZnWO. showing the WLa and ZnKa

overlapping peaks 36

7. Spectrum of anorthoclase (Nunivak) compared to the

synthetic spectrum of the same material generated

by FRAME C 39

V
I
Frame C: A Compact Procedure for Quantitative EnergyDispersive Electron Beam X-ray Analysis

R.L. Myklebust, C.E. Fiori, and K.F.J. Heinrich

Center for Analytical Chemistry

National Bureau of Standards

Washington, D.C. 20234

ABSTRACT

A data evaluation procedure (FRAME C) for carrying out

quantitative electron probe microanalysis with a lithiumdrifted silicon detector was developed for use with a small

computer. The procedure consists of a background correction

calculated from two selected background regions of interest,

a simple method of resolving overlapping peaks, and the

matrix corrections for characteristic radiation (ZAF) . To

save computation time, small groups of adjacent channels

(regions of interest) in the multi-channel analyzer rather

than individual channels are used for the calculations.

The method for computing the overlap factors is described.

Examples of several types of analyses are presented.

Key Words: Computer program; energy dispersive detector;

multichannel analyzer; peak overlap; quantita

tive electron probe microanalysis; x-ray

continuum; x-ray spectrum.
I. Introduction

The program FRAME on which FRAME C is based was written

for use on small computers for routine quantitative electron

probe microanalysis. The main consideration in its development was the need for accurate data reduction in an on-line

operation. Results from the rigorous data reduction program

COR [1]^ were used as a guideline in the adjustment of

simplified expressions, and it was shown that the omission

of the correction for continuum- induced x-ray fluorescence

in FRAME has not introduced significant errors [2] . Earlier experience with MULTI 8 [3] , a data reduction

program requiring extensive manual input, had clearly

indicated the need for internal generation of parameters

such as the x-ray mass absorption coefficients. Such parameters can either be stored in memory or on tapes or discs,

or be generated from fitting algorithms in subroutines. The

FRAME C program was developed in our laboratory for the

Tracor Northern^ TN 1700 multi -channel analyzer (MCA) system

(with 4096 channels) . This system includes a Nova 2 computer

which was expanded to a total memory of 24,000, 16 bit words,

in order to handle FRAME C (which requires approximately

10,000, 16 bit, words). There is a nine-track tape system

available which serves to store spectra for later reference

as standards or evaluation in the MCA. However, no other

external mass storage was available on our computer. For

this reason most parameters used in the presently available

version of FRAME (including the version of FRAME C given in

^Figures in brackets indicate the literature references at

the end of this paper.

^In order to adequately describe materials and experimental

procedures, it was occasionally necessary to identify commercial products by manufacturer's name or label. In no

instance does such identification imply endorsement by the

National Bureau of Standards nor does it imply that the

particular products or equipment is necessarily the best

available for that purpose.
Appendix III) are internally produced from algorithms.

Considerable effort has been spent in ensuring the accuracy

required for the specific purposes in the program. The

reader should be warned, however, against using these algorithms for purposes other than intended, or outside the specified limits of wavelength or energy. We specifically decline

responsibility for any error that may arise from improper

use of these algorithms, as was attempted by some investigators

(e.g., [4]). As external memory devices become available,

some of these parameters (e.g., line and edge energies) will

be stored in tables. The coefficients in the expressions

for computing the energies of x-ray lines and absorption

edges have been fitted in the energy range from 1 keV to

10 keV and should not be used outside of this range.

The new version, FRAME C, extends this on-line analysis

to the evaluation of energy-dispersive spectra from a lithiumdrifted silicon detector (Si (Li)). Some of the parameters

involved (i.e., weights of lines, incomplete charge collection)

are under study and improved values of these parameters will

be incorporated as they become available. The main features

of FRAME, which deal with the evaluation of relative x-ray

intensities, remain unchanged. However, since the resolution

of the Si (Li) detector is lower than that of wavelength

dispersive spectrometers, the steps required to obtain the

relative x-ray intensities from the energy spectra of specimen

and standard are much more elaborate. In essence, what is

required for each spectrum is to subtract the background due

to continuum generation from the characteristic x-ray lines,

and to resolve the line overlaps which occur frequently in

energy spectra [5] . As in wavelength-dispersive spectrometry,

one x-ray line per element is used in the correction scheme.

However, lines which are not used in the correction calculations must also be considered as potential line interferences.
If in FRAME C, an x-ray line below 1 kV is selected,

the program will terminate. Also, for accurate analyses, the

overvoltage range should be 1.5 to 10 (overvoltage is defined

to be the energy of the electrons in the beam divided by the

critical excitation energy of the x-ray line of interest)

.

The dimensions in the program allow for analyses of up to ten

elements, with Ka , La, or Ma x-ray lines. The full-width at

half-maximum (F]\TiM) obtained from a MnKa peak must be known,

and the region of interest for any x-ray peak must be exactly

the same on both the standard and unknown. The output of

results was limited to a simple teletype printout. Within

memory limitations, however, it was possible to include

variants such as the determination of elements by stoichiom.etry or difference.

The slow speed of small computers was an important

consideration in the development of the procedure. Energy

spectra are stored in a pulse-height analyzer, typically 1024

channels for each spectrum. Even simple operations, if they

must be performed at each channel, consume too much time to be

useful in on-line analysis. l\'e therefore decided that only

the channels containing the characteristic x-ray lines would

be used, and that the contents of adjacent channels corresponding to any one peak would be added, to form a "region of

interest" for this peak [6] . The problem to be resolved was

thus to determine the contribution of background and interfering x-ray lines to each region of interest.

The background prediction can be based either on the

use of a reference spectrum (such as that from carbon) with

subsequent calculation of the change in the continuum with

atomic number, as proposed by Smith et al., [7] or on the

reconstruction of the continuous spectrum from the x-ray

emissions of the same target at two or more regions of

interest which are free of lines. Ke chose this second

technique, which is a continuation of the previous work of

Ware and Reed [8] and of Lifshin [9]. The regions of

4
interest for the continuum need not be the same size and can

be selected at will for each spectrum, so that the effects

of line interference and incomplete charge collection can be

minimized. The technique of background correction we have

followed requires the knowledge of the detector efficiency

function. The parameters needed to calculate this efficiency

can be obtained by means of a simple calibration procedure

which is repeated infrequently. The variation of the emitted

continuum at the absorption edges of the target elements is

calculated on the basis of the target composition. Therefore,

this calculation is repeated after each of the iterations

which are part of the matrix (ZAF) correction for characteristic x-ray line intensities [3] included in FRAME C.

The exact form of the absorption correction for the

continuous radiation is still a subject of speculation. We

assume at present in this program that the depth distribution

of the continuum is identical with that of characteristic

radiation [10,11]. The algorithm can be changed as more

evidence is forthcoming. At the present time we have been

unable to obtain experimental proof of systematic error in

applying the algorithm which was proposed for characteristic

radiation in reference [10]

With the use of regions of interest, the problem of line

interferences is reduced to obtaining overlap factors which

determine the fraction of the signal emitted by a line that

falls within the region of interest of another line. The

fact that the shapes of x-ray lines observed in the energy

spectrum are virtually Gaussian is very helpful and once the

apparent width of one line is measured, those of other lines

can be accurately predicted.

The problem of line interference can be resolved if the

count rate produced by the interfering element within the

region of interest of the element to be measured can be

determined. This count rate is obtained as a function of
the count rate in the region of interest of the interfering

element. The calculation is performed in FRAME C by means

of a parameter called the overlap coefficient , which depends

on the line widths and positions and on the choice of regions,

but is independent of specimen composition. Hence, it is

calculated once only for each analytical situation, and

stored for later use. We will define these overlap coefficients more rigorously on page 11.

To establish regions of interest we must know either a priori or from inspection of the spectrum which elements are

present in the specimen. It is possible to check after the

analysis has been performed if all lines were accounted for

correctly. This is done in FRAME C by synthesizing the line

spectrum from the analytical result and comparing it with

the spectrum collected from the unknown specimen. If the

synthesized spectrum is subtracted from the original,

ideally only the continuum should remain. If a line has

been overlooked, it will be visible in the residual spectrum.

II. General Description

Figure 1 shows the configuration of the system used for

analysis and data evaluation. ^ The broken line indicates

connection of the computation sector to a high-speed external

mass storage device (e.g., floppy disc) which will be provided

in future systems but is not presently available in our system.

Therefore, available external memory is slow, and connected to

the MCA rather than the computation sector. This feature

limits the extent to which parameters such as line energy can

be stored for use in the computation sector. In the first

* system used by us, the computations are programmed in BASIC.

If FORTRAN is used, instead, the speed of computation will

increase substantially.

""The computer is used in two discrete sectors. One of these

serves exclusively the MCA functions, and the other is

available for ocmputation in a users language.
CD

Mass

Storag

o

Q

A

"

CD <^

a

PL,

•H

(U

+-> 01>^

trt

o

•H

iH

Cti >

c3

+-> OS T3

0)

+->

<4HO

6

aJ

5hbO

cti •Ht3

U

O

I—

I

•H

PU
A block diagram of the principal steps in a quantitative

analysis by FRAME C is shown in figure 2. The first block

in this figure contains all preliminary calibrations that the

analyst must perform if accurate results are to be obtained.

The first of these concerns the efficiency of the Si (Li)

detector as a function of energy. Photons can escape detection by passing through the detector without being absorbed

or by being absorbed by the beryllium detector window, the

gold coating or the silicon dead layer, before entering the

active region of the detector. By means of an auxiliary

routine included with FR.AME C, we can compute the necessary

parameters from a spectrum of carbon in a calibration procedure separate from the remainder of FRAME C. Neglecting

the effects of x-ray scattering and incomplete charge

collection, we get for the detector efficiency the following

expression

P^ = exp-[ii(Be,E}tg^ + y(Si,E)t^.] [1-exp (-y (Si ,E) t^ - ) ] [1]

D 2 Here, t^. and t^- are the thicknesses fg/cm ] of the silicon ' Si Si ^^ -^ dead layer, and of the active detector region, respectively,

and y(Be,E) and y(Si,E) are the mass absorption coefficients

of beryllium and silicon at the energy E. Another parameter

that must be determined for a particular detector is the

full width at half-maximum (FWHM) of a peak such as the

manganese Ka x-ray peak. This width is necessary to compute

the widths of all other peaks for the computation of peak

interferences. The contribution due to incomplete charge

collection [12] is only significant when an x-ray peak is

measured near the low-energy side of another large x-ray

peak. The approximation to the incomplete charge collection

included in FRAME C will be sufficient to account for this

effect in most detectors. Finally, the energy scale of the

multichannel analyzer (e.g., 10 eV per channel) must be

8
MASS STORAGE PROGRAM MCA TERMINAL

FUNCTIONS

Calibrate

Energy Scale

Accumulate

Spectrum of Standard

Eo, Z, line code,

valence & pure

element intensity

Sets peak ROI, corrects

for background, peak

overlap & applies ZAP

to obtain standard

intensities

NO

Set Background

ROI

-(^Standards complete?^ YES

DISPLAY

Quadrant

2

INPUT: Eo.no.

of elements,

concentration,

Z, line code. & valence for ea. OUTPUT:

Relative

intensities

(^ First unknown point ?^

Accumulate

Spectrum of Unknown

Set Background

ROI

Quadrant

1

No. of elements & Z

for each

YES

NO

Sets Peak ROI

Overlap coef. &

Relative line weights

Computes Overlap coef.

Line code, valence,

pure element intensity & overlap coef.

Corrects for background,

clears peak overlaps & performs ZAF within

iteration loop

Relative line weights

INPUT: No. of elements & Z

for each

I

Synthesizes line spectrum Quadrant

3 OUTPUT: Z,

Concentration

& relative

intensity

All unknown points v^^

finished ? STOP*

Figure 2. Block diagram o£ FRMffi C showing all steps in an

analysis

.
calibrated. All of the above parameters need to be determined

at infrequent intervals; i.e., according to our experience,

every six months to one year.

Two more parameters must be entered before the program

is executed: The electron beam incidence angle and the

x-ray emergence angle. The blocks in Figure 2 are an outline

of a typical analysis. First, x-ray spectra must be collected

from standards for each element to be analyzed in the unknown

specimen. These spectra are processed by the standardization

portion of FRAME C. A multielement standard can serve as

a reference for several elements. In the present version of

FRAME C, all necessary information concerning each element

in the standard is stored in one quadrant of the multichannel

analyzer memory or in a high speed mass storage device such

as a floppy disc. Either method is satisfactory; however,

since we did not have a high speed mass storage device in

our first system, we used the fourth quadrant of the multichannel analyzer as our data file. (See Figure 1).

When all the standard spectra have been processed, the

spectrum from an unknown specimen can be analyzed. Once

regions of interest have been assigned for each element in

the spectrum of the specimen, the overlap factors are computed

for all interferences in the spectrum. Since these depend

only on the widths of the Gaussian peaks, the boundaries of

each region of interest, and the relative x-ray transition

probabilities, they are computed only once. If more than one

unknown is to be analyzed for the same elements, it is not

necessary, to recompute these factors for each unknown.

The background subtraction [11] and the clearing of

x-ray line interferences ]13] require the x-ray absorption

factor, f, for each analytical x-ray line and, in the case of

line interferences, for each interfering x-ray line. In

principle, one v/ould assume that the absorption factor for

continuous radiation would be different from that for

10
characteristic radiation. We find, however, that an expression

such as proposed for characteristic x-radiation in reference

[10] produces a correction for the absorption of the continuum

in the target withoug an identifiable residual error. For

this application the particular energy of interest of the

continuous radiation, E is substituted for the critical

cm

excitation potential, E :

^^^ = [1 + 1.2 X 10"^ • CE ^-^^-E ^•^^)

-x ]"^ [2] cm '- ^ o cm '^ '^ - "- - where x

~ ^ esc i/j , y the appropriate mass absorption coefficient, and ^ the x-ray emergence angle. Since the absorption

factors depend on the specimen composition, they must be

recomputed for each iteration of the matrix correction

[figure 2]

The final step in each analysis is to synthesize an x- ray line spectrum from the analytical results and display it

on the screen of the multichannel analyzer so that it can be

compared with the measured spectrum from the unknown. If the

analysis has been correctly performed, no peaks should be

observed in the measured spectrum that are not in the synthesized spectrum, and vice versa.

Ila. Background and line interference corrections

In energy-dispersive electron probe microanalysis, the

background due to the x-ray continuum is a significant part

of the contents of the region of interest of a characteristic

x-ray peak. We have used a simple but accurate technique

for background correction which is an extension and amplification of schemes proposed by Ware and Reed [8J and by

Lifshin et al. [9]. The technique has been described by

Fieri et al . [11]

The original energy-dispersive version of the FRAME

program, FRAME B, [14] required that all analytical x-ray

peaks be clearly resolved from other x-ray peaks in the

spectrum. This condition is frequently not met in energy11
dispersive analysis. We have developed a simple method

[14] to overcome this limitation which is based on calculating

the overlap of Gaussian peaks of one element into the region

of interest of anothe element. One x-ray line (the analytical line) from each element will have a region of interest

and be used in the ZAF computation to determine the specimen

composition, but all other lines will be considered to

determine if they overlap with the regions of interest of

the analytical lines.

Given an x-ray peak near a region of interest, the

fraction of this peak which falls within the region only

depends on the relative positions of peak and region of

interest and of the standard deviation of the Gaussian peak,

but not on the composition of the specimen. If the interfering peak has its own region of interest, the fraction of

the peak with its own region of interest is equally

independent of composition. Therefore, the ratio between

these two fractions, called the overlap factor, can be

computed once early in the procedure and stored for all

subsequent measurements. Vv'e will develop the argument for

two unresolved peaks, A and B (see figure 3). We will only

describe the computation of the overlap factor due to peak

A on the intensity under peak B. Since peak B contributes

counts to the region of interest for peak A and vice versa,

the correction procedure in practice must be iterative.

Let E. be the center of peak A and E-p the center of

peak B. We can calculate the standard deviations a. and

'B

A

as a function of E. and E^. [15] if the FWHM has been

measured for a peak at any energy (e.g., Mn Ka) . The number

of counts due to peak A at any channel number E. is:

N . = A exp

1 a ^ Vfi

^A

[3]

12
LU

<

z

o

COH

Z

D

o

o

E| Ea E2 E3 Eb E4

CHANNEL NUMBER

Figure 3. Schematic representation of two overlapping

Gaussian peaks. Shaded areas are the overlaps

of each peak into the region of interest of

~ the other peak.

13
where E. is the centroid of the peak of A, and A. the counts

n a channel of narrow width centered around EA

Consequently, the counts N. obtained between the limits

E, and E^ which define the region of interest of element A,

are:

\' h/

exp

1 I^A-^i

2 I aA

dE [4]

while the counts between the limits E^ and E. of the region

of interest of element B are:

\b = ^A/

exp

iK-Ei'

2\ aA

dE [5]

The ^verlap factor is defined as

N

"ab = -M [6]

The number of counts measured in peak A between the limits.

E, and E^ is multiplied by this factor to obtain the number

of counts contributed to the region of interest of peak B

by peak A.

A different type of interference occurs when a peak from

element A which is not used for data reduction (i.e., has no

region of interest) falls within the region of interest

selected for element B (figure 4). In this case, the intensity

of the interfering peak from element A must be obtained from

the count rate within the region of interest of the analytical

peak for element A. If the analytical line and the interfering line are both generated from ionization of the same

shell or subshell, their generated intensities are related

by their respective relative transition probabilities (or

14
GC

LU

CD

UJ

Z

<

X

o

f-1 o

o

(/I

?-l 0)

4->

•Hm

o

O

•H

W)^

C

•Ho •

0)

0) >> ^

o

p.

>

o

p

p

o s

CD i^ CO Mh

•H

13 NNVH3/SlNn03

15
weights of lines) . A transition probability is the intensity

o£ the line of interest divided by the sum of the intensities

of all other lines arising from the same absorption edge. The

emergent and detected intensities are also affected by the

respective absorption factors, and the efficiency of the

detector at the respective energies. For instance:

-^'AKg ^ ^AK6 . f (AKB) . ^E (AKB) ry-, ^'AKa ^Ka ^^^^^^ ^E (AKa)

where ^Aiy-o = I (AKB) /^I (AK) is the transition probability of

the AKB line, f(AKB) is the corresponding absorption correction

factor, and Pp the detector efficiency at the energy E.

The procedure can be extended by a simple adjustment

derived from the generation equation ("atomic number correction") to the relation of lines from different subshells of

the same shell (e.g., La,-LB-i).

When the two lines of interest belong to different

shells (e.g., the analytical line is AuLa-. , and the interfering line is Au Ma), the comparison of generated intensities,

performed in FRAME C, is less accurate than in the previous

case. This situation arises seldom in actual analysis;

research is presently underway to improve the accuracy of

such calculations. The correction for lines from different

edges is made by calculating the relationship of line intensities for element A: From the emitted intensity of the

line of A which has a region of interest, a calculation is

made of the interfering line intensity of element A in

the region of interest of element B. The relative transition

probabilities (weights of lines) are used for this purpose.

For example, if the interfering line is the KB peak of

element A, then to relate the interference of AKB with

another peak BKa to the measured intensity of AKa, the

overlap factor of AKB into the region of interest of BKa is

obtained by:

16
H = ^AKg . ^p(AKa) ^E(AKa) . \b . „

-, AKa *p(AKg) Pg^^^gj ^A

where Iai^o/Iav- is derived from the ratio of generated intensities (weight of line AK3 ) , which is a known parameter

^Iak.

1 of the K3 line and the Ka line; f is the absorption in the

specimen and Pp is the detector efficiency. The weights of

the K3 x-ray lines of elements of atomic number 15 through 30

have been measured by us (see Table 1) as well as by others

[16] and are better known than those of the L or M x-ray

lines. For an extreme peak overlap consider the Cr

K3 line overlapping the Mn Ka line. A two percent error in

the weight of the Cr K3 line will generate an error in the

mass fraction of Mn of 0.0025 in a pure Cr specimen (see

Table 2) . The weights within each of the L and M series of

lines, up to 10 keV, have been estimated by us and are

probably within ±20 percent of their true value.

17
Table 1

Relative Transition Probabilities for KB X-ray Lines [20]

Atomic Number Kg/ (Kg + Kg)

.050

.063

.085

a .097

.104

.113

.114a

.114

.116

.116

.119

.119

.120

.121

.123

.128

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

Interpolated value

18
Table 2. Overlap Corrections

Mass fraction Mass fraction

Specimen

E in

keV

15

Analyzed

for

Overlap

with

MgKB

found before

correction

.0026

found after

correction

MgO Al .0016

AI2O3 15 Mg AlKa .0132 .0058

AI2O3 15 Si A1K3 .0039 .0014

Si02 15 Al SiKa .0072 -.0010

Cr 15 Mn CrK6 .1311 -.0024

Mn 15 Fe MnKB .1045 .0019

Fe 15 Co FeK6 .0653 .0062

Cu 20 Zn CuKB .0206 .0039

Zr 15 Bi ZrL32,

Lyi ,LY3

.0214 -.0113

Bi 15 Zr BiMa,M6,

M?

.0213 -.0009

Zn 20 W ZnKa .1329 .0010

Ta 20 Cu TaLai^ .1968 .0700

The regions of interest for Cu Ka and Ta La overlap. These

lines are too close to be separated well by this method.

The electron beam incidence angle is 90° and the x-ray

emergence angle is 52.5°.

19
To compute overlap factors for all the L x-ray lines,

we relate the intensity of each L line to the La, line (the

measured line). We must, however, take into account that

the ratios of line intensities of the L spectra vary with

excitation potential. This is due to the fact that these

lines arise from three subshells each of which has a different

critical excitation potential. To relate the intensity

of any line to the measured La, line, we compute

an intensity factor which is the intensity of the line "i"

divided by the intensity of the La., line (1. /I. ,).

i

To introduce an energy-dependent term into this factor,

we have integrated the expression:

^nl = ir^ -^^^^ '^ [^J ^^ V [dE/ds]

E

o where s is the mass thickness along the electron path

(g/cm^) , in the same manner as Philibert and Tixier [17] to

obtain the number of ionizations, Y , , in the level nl. nl

^nl = S TT {'Jo-14 lnW[liCU^W)-li(W)]j [10]

M and N/A are constant and can be eliminated since we are calculating the ratios of the x-ray lines for the same element.

U^ is the overvoltage E /E , where E , is the ionization energy

o '^ o nl nl °^ of the edge nl, W is 1166 E , / J where J is the mean ionization

potential, U W is 1166 E /J and li is the logarithmic

integral. We have fitted an expression which approximates

the logarithmic integral [li(x) — 2.905 /x - 3.063] over the

range of interest. The number of electrons in each subshell,

^nl' ^^ determined from basic quantum 'theory , and the pertinent

values for the subshells of interest are as follows:

20
Subshell Numb er of Electrons

K 2 h 2

^2 2

4 4

^1 2

-^2 2

^3 4

M4 4

M. 6

The ratios of lines arising from different absorption edges

are then corrected for differences in overvoltage by multiplying

each line by Y , (Eqn. 10). The total L line intensity factor,

for any L line, thus becomes:

S. = [11]

I Y

The first step in computing the L overlaps is to determine the area of the La, line within its region of interest

by subtracting the areas of all other L lines of the same

element from the region of interest. This is done by

calculating all the overlap factors for these lines and

stripping them out in the same manner as is used for overlaps from other elements. Since the computed overlap factor

for each L line is relative to the La., line alone, this step

is necessary. Overlap factors for the measured lines of

other elements are then computed in the same manner as for

K lines except that the overlapping area of an interfering

peak is multiplied by that peak's intensity factor, S. . In

the case of the ratio La,/Ka, the ratio must be multiplied

by the ratio of fluorescence yields, lo./oOt^, and an atomic

number dependent factor which is at least partly due to the

Coster-Kronig transitions.

21
y^ = 0.095Z - 1.61 [12]

M lines are treated in a similar manner. There are also

provisions for determining the intensity of an M line from an

L line or vice versa. Since we were unable to find an appropriate cross section for the M-series of x-ray lines, we

fitted an empirical expression to the generated Ma/La, ratio

for three elements at five different operating voltages.

^nl>^M = ^^P

54.17 50.05

+ 8.527 [15]

U is the product of the L overvoltage, E /E. , and the M

overvoltage, E /E,, & > o M5 Approximate results can be obtained by

this technique; however, the factors used are not well known

at this time.

In the previous discussion, we have assumed that the

peaks have simple Gaussian shapes. In reality, however, the

peaks are distorted on the low-energy side by the effect of

incomplete charge collection (see Appendix 1) . Consequently,

the x-ray peaks observed by a Si (Li) detector are the convolutions of several contributions. Some peaks consist of

several x-ray lines of the same series (such as Ka^ and

Ka2) • In most cases of multiple peaks (except Ka, y and

KB, 7 r), we compute the peaks separately for each x-ray

line in the same manner as the overlapping peaks from other

elements . For the incomplete charge collection at the lowenergy shoulder of each peak, we have developed an empirical

expression:

I^_ = A^a(E^-E.) exp [-bCE^-E.)] [14]

in which a and b are energy-dependent coefficients fitted

for a particular detector and the other terms are as previously defined. A. was previously obtained as a measure

of line intensity from Eqn. 5.

22
The remaining case of overlap that is computed is the

interference of the escape peak of a characteristic x-ray

line with an analytical line. The expression used to

predict the number of counts in an escape peak based on the

number of counts in the parent peak is that due to Reed and

Ware [18]:

k = 0.038e/(l-0.038e)

esc ^ ^ [15]

where k is the integrated intensity ratio of the escape

peak to the parent peak and

1

^ =

2

, y (Si,Si) . 1 y(Si,E^) 1^ 1 +

y (SijE^y

y (Si, Si) [16]

y(Si,Si) is the mass absorption coefficient for SiKa in

silicon and y(Si,E.) is the mass absorption coefficient for

the parent peak in silicon. An overlap coefficient is then

computed in the same manner as previously described for a peak that has no region of interest. The standard deviation

of the escape peak is that corresponding to its energy rather

than of the parent energy; k is the intensity ratio of

escape peak to parent peak.

lib. Description of Subroutines

A. Main Program for Standards (100-390)

This program is executed for each spectrum of a standard

whether the standard is a pure element or a multi-element

material of known composition. On the spectrum, the operator

must choose two regions of interest for the background determination. These regions must be the first two in the list of

regions contained in the multichannel analyzer (regions

and 1) . The following information must be entered via the

terminal by the operator: 1. the number of elements in the

standard and, for the first standard, the operating potential

(kV) . 2. the mass fraction, atomic number, x-ray line code

23
and valence of each element in the standard. Any elements

that are present in the standard but are not needed for a particular analysis may be excluded by entering a zero for

the x-ray line code. Otherwise, enter 1 for the Ka line, 2 for the La-, line and 3 for the Ma line. The valence for

each element in the unknown must be entered if you wish to

compute the oxygen content of an unknown by stoichiometry

If this is not required, enter a zero for the valence.

The program automatically defines the region of interest

for each peak the signal contents of which are then corrected

for background and any overlap from other peaks . If the

standard contains more than one element, a matrix correction

is performed. The known composition is used to obtain the

calculated intensity ratio (k = I .-./I ). The intensity ^ c std pure-^

of the measured peak is then divided by the calculated intensity ratio to obtain the intensity that w^ould be emitted

under identical conditions from the pure ^ element (I

^ pure

I /k 1 . If the standard is a pure element, the matrix

meas . c^ ^ ' correction is omitted.

The results (see figure 2} are then stored in a random

access data file. In our version of FRAME C, one quadrant

(1024 channels) of the multichannel analyzer was selected to

be used as a data file in the TN 1700. The information

stored in this area is the operating voltage, the number of

elements that have been measured as standards, and, for

each element standard, the atomic number, x-ray line, valence

(if used), and the intensity for the pure element. The only

results printed in the execution of this program are the

calculated intensity ratios for each element in the standard.

B . Main Program for Computing Concentrations in Unknowns

500-900

This program is similar to that for standards. The

same subroutines are called but in slightly different order.

The operator must again select the two background regions of

interes L as before and the number of elements and the atomic

24
number for each o£ them must then be entered via the terminal

All o£ the information stored in the standards file for

each element is retrieved from the file. The region of

interest for each element is assigned and the overlap correction factors are computed and stored in the file with the

standards.

The matrix correction is then performed. The background subtraction and overlap corrections are included

within the main iteration loop of the ZAF corrections and

hence performed in each iteration. At the completion of the

computation, the obtained mass fractions of all elements

are printed, and the x-ray peaks are constructed in one

quadrant of the multichannel analyzer. These peaks may then

be compared with the original spectrum to see if all elements

have been correctly identified and the compositions determined. Additional unknown spectra may then be analyzed for

the same elements without entering any additional information,

The overlap factors previously calculated and stored are

also used in subsequent analyses, thereby saving the time

required for this lengthy computation.

C. Subroutine for retrieval of coefficients and constants

(1000-1495)

The constants and functions needed by the program are

stored in this subroutine as defined in the list of variables,

The detector parameters (P6, P7, Q3) are also retrieved by

this subroutine. These should be redetermined by each user

to match his detector.

25
Line Variable

1440 Qi

1450 Q2

1454 P6

1455 P7

1480 Q3

Definition

X-ray emergence angle in degrees.

Electron beam incidence angle

in degrees

Thickness of Be window on

detector (cm)

Thickness of Si dead layer in

detector (cm)

Full width at half maximum of

MnKa peak (eV)

D . Subroutine for computing all necessary edge and line

energies (1500-1610)

Nine x-ray absorption edge energies and 17 x-ray line

energies are computed for each element. The general expression

used for both edges and lines is:

E = exp [a(lnZ)^ + b(lnZ) - c] [17]

where Z is the atomic number and a, b, and c are coefficients

stored in subroutine C. The x-ray lines are coded by numbers

from 1 to 17 which refer to the Ka, Lai, Ma, KB, La2,

L£, L32, Lgi, Lyi, Ln, LBs, Lys, LBi^, M^i , MB, My, and to the

line from the M -j- -. - N -r-, ^ transition. The edges are in the

order: K, Li, L2, L3, Mi, M2, M3, Mi+, and M5 . If the line

energies are below 1 keV, the calculation is aborted by the

program since the computed energies are of insufficient

accuracy in this region to allow them to be used as the

measured x-ray line for an element. Readers are warned

to refrain from using th 2se eci^uations outs ide the limits

of the regions for ^^-hich they have been developed.

E. Subroutine for compiating mass ab sorption coefficients

(1700-1980)

This subroutine will compute a mass absorption coefficient

for x-rays of any energy above 0.5 keV in any pure element.

26
The absorption coefficients are calculated as proposed by

Heinrich [19] . Least squares fits were made to the logarithm

of the coefficient C and exponent n in the general relation:

y = CX^ [18]

in which A is the wavelength of the x-ray in angstroms. A

comparison of the calculated values with those given by

Heinrich showed agreement within a few percent. To indicate

uncertainties which arise where lines close to absorption

edges are used, a warning is printed if the analytical line

falls within 100 eV of an absorption edge of another element

present in the specimen.

F

.

Subroutine for computing detector efficiency (2000-2095)

The efficiency Pp of the Si (Li) detector, at any photon

energy is determined by the loss of x-ray detection in the

detector due to absorption in the beryllium window, gold

surface layer and the silicon dead layer or by transmission

of the x-rays through the detector without absorption of

the photon:

Pj = axp [-tB,P^,-t^„P^„-tsiu|i] [l-e^vi-t^^^4,n [19]

t is the thickness in cm of each layer ' of material, t, . is

P

' det

the total thickness of the detector, and y- is the linear

absorption coefficient for an x-ray of energy E in the

element i which is obtained in the program by dividing the

mass absorption coefficient by the density.

G

.

Subroutine for computing the primary absorption factor

in a specimen (2100-2140)

The x-ray absorption factor, f , used is that proposed

by Heinrich [10] and modified for oblique beam incidence.

f = [1 + 1.2 X 10"^ Yysin(e) csc(ii^)] [20]

where y is the mass absorption coefficient, il) (deg.) is the

= ( 27X—ray emergence angle, and y = (E ' - E * ) . E is
the operating potential (kV) , E is the critical excitation

potential (kV) and e (deg.) is the electron beam incidence

angle . H. Subroutine for computing the X-ray Continuum Background

(2200-2620)

The method for computing the x-ray continuum is that

proposed by Fiori et al. [11]:

Ie = I

[KiCE„-E) . K^CE^-E)^] p^ f^ [21]

where Ip is the intensity of the continuum at the photon

energy E, E is the operating potential, and Pp and f are

defined in sections F and G respectively. K^ and K2 are

parameters fitted to the background curve, on the basis of

the measurements at the two background regions of interest

selected by the user for measurement. The fit must be

repeated in each iteration because the value of f depends

on the specimen composition.

I . Subroutine to store the information on standards into

quadrant 4 of the TN 1700 multichannel analyzer

(2700-2920)

This subroutine stores in quadrant 4 of the TN 1700, the

atomic number, line code, the background—and overlap—corrected

peak counts for the pure element, and the valence for each

element in the standard that is measured. If a data file

other than a quadrant in the multichannel analyzer is used,

this subroutine must be modified.

J . Subroutine to compute the overlap factors (5000—3450)

This is the main program for computing the overlap

coefficients. In lines 3034-3200, the integrals of the measured

x-ray lines are computed from the assigned energy limits of

each peak together with the energy and width of the peak. The

incomplete charge collection is added to the Gaussian peak

after integration. From line 3205 to 3395, all possible overlaps are computed one by one, beginning with overlap from

28

i
other lines of the same element (Kl = 0) and then each overlap

from other elements in the specimen (Kl = 1). When Kl = 0,

an intensity factor for all observable x-ray lines of an

element relative to the measured x-ray line for the element

is stored in the random access data file for use in reconstructing the x-ray spectrum of the unknown.

K. Subroutine to compute relative peak intensities and

to test for overlaps (5490-5850)

The x-ray generation cross-sections Y , for electron

excitation that are required are computed by equations 10,

12 and 15 in lines 5490-5515 and multiplied by the fluorescence yield w. In lines 5514-5645 the weight of each

x-ray line from an element relative to the measured line

for the element is determined. The overlap coefficients are

calculated for each overlapping line in lines 5750-5850.

It must be emphasized that the values for the weights

of generated lines which appear in lines 5571-5605 are

estimates which will be changed as more information becomes

available.

L . Subroutine to store the overlap coefficients in the

random access data file (5855-5886)

The overlap coefficients are individually stored for

each element together with the atomic number and line of

the interfering x-ray peak. A maximum number of 15 overlaps

per measured line can be stored.

M. Subroutine to compute the relative weights of escape

peaks (5890-5990)

The relative weight of an escape peak [S^ in the program)

to its parent peak is determined by equations 15 and 16.

N. Subroutine to compute the overlapping area of one peak

on another (4000-4150)

The portion of an interfering peak that overlaps the

analytical peak for an element is computed by integrating

the area with the overlapping peak between the energy limits

29
of the analysis peak. Since the area is asymmetrically

placed on the overlapping peak, the integrals from the peak

energy to each energy limit are computed separately and

algebraically summed to obtain the overlapping area. A

correction for incomplete charge collection in the detector

is also added on the low energy side of the peak.

. Subroutine to compute the incomplete charge collection

of the detector (4200-4400)

The expression for incomplete charge collection

(Equation 14) has been integrated to give:

^c = -2 ^A ^i b^ ^

jl - exp [-b(E^-E.)] . [1 + b(E^^-E.)]| [22]

In the program, XI = a and X3 = 1/b. XI and X3 are varied

as a function of the peak energy in lines 4220-4260.

P . Subroutine to integrate the area under a Gaussian

(4500-5090)

This subroutine produces the integral of the error

function:

2 r -t' erf(x) = -t J

e

^ dt [23]

/

Since the integral under a Gaussian is of the form:

ACy) = -^

J

e-( 77=1 dE [24]

v2iT a \ /

the integration may be performed with the error function if

X = t. = A and dt = —— dE . The integration limits are

V 2 not necessarily symmetrical with respect to the peak; therefore,

the integration must be don twice, once for each limit, and

half of each integral is summed to obtain the total for the

area of the peak.

30
Q. Subroutine to correct peaks for overlap, using the

overlap coefficients (5100-5590)

This subroutine must be considered in relation to the

matrix correction. Figure 5 is a flow chart emphasizing the

overlap correction while showing its relation to the rest of

the program. The overlap coefficients for each peak are

recalled from the random access data file. As long as

similar unknowns are being analyzed, these coefficients need

not be recalculated by subroutines J-P.

R. Subroutine to compute the matrix corrections (5500—7150)

The expressions in the matrix correction will not be

defined here since they have been described previously [2]

.

Instead we will list the particular factor being computed

in each region of the subroutine. All factors that are

independent of concentration are computed in the loop from

line 5510 to line 6400. The overvoltage (E /E ) should be & '^ o q

between 1.5 and 10 for each element. The overvoltages are

computed and tested in lines 5530-5580. If the overvoltage

is too low, a message is printed. Absorption coefficients

of pure elements are calculated in lines 5590-5630. The

absorption factors (f ) are determined in lines 5750-5770.

Tests are made for characteristic fluorescence corrections

in lines 5780-6160 and the parameters for the characteristic

fluorescence corrections are defined in lines 6170-6381.

The backscatter losses and stopping powers are computed in

lines 6382-6400. Initial intensity ratios and the first

estimates for concentrations are calculated in lines 6405-

6540.

The main iteration loop begins in line 6550 and the

loop ends in 7050. The atomic-number and absorption corrections are computed in lines 6580 to 6690. The characteristic

fluorescence correction is calculated in lines 6700 to 6810.

The intensity ratios for the assumed concentrations are

determined in line 6820. If the computation is being done

31
Calibrate Spectrometer

&

Multichannel Analyzer

Spectrum of Standard

Displayed in Quadrant 2

I

Set Regions of Interest Correct for Background,

Peak Overlap, ft Apply

ZAP. Data Stored in Quadrant 4

NO

Spectrum of Specimen

Displayed in Quadrant 1

NO

Set Regions of Interest, Overlap Factors Computed

& Stored in Quadrant 4

I

Background Subtracted,

Peak Overlaps Cleared,

& ZAP Performed within

Iteration Loop

I

Output Concentrations,

Synthesize Line Spectrum

& Display in Quadrant 3

NO

STOP

Figure 5. Short block diagram of procedures in FRAME C.

32
for a multielement standard, these intensity ratios are

printed out (lines 6835-6850) and the values are returned to

main program A. If an unknown specimen is being analyzed,

new concentration estimates are obtained from the hyperbolic

equation in lines 6870 and 6872. If the calculations are

complete (line 6874) , the spectrum may be redrawn on the

multichannel analyzer (line 6876). In lines 6900-7040, the

new concentration estimates are used to obtain a new background

correction (line 6980), a new overlap correction (line 6990),

and a new intensity ratio (lines 7000-7040). If the computation is completed, the results are printed in lines 7060-

7140.

S. Subroutine to set the regions of interest (ROI) for

each measured line (8000-8140) . The instructions in this subroutine are specifically

written for a Tracor-Northern TN 1700** multichannel analyzer.

Line 8020 defines the value of Kl which is used to define

the width of any ROI as a function of energy.

Lower limit = E. - Kl a [25]

Upper limit = E^ + Kl a [26]

T. Subroutine to redraw the spectrum in one quadrant of

the multichannel analyzer (8200-8595)

The concentrations obtained by the program together with

the relative peak weights generated in subroutine J are used

to redraw the characteristic line spectrum (without the

continuum) in quadrant 3 of our multichannel analyzer. The

energy limits and intensity of the measured peak are determined in lines 8210-8315. The parameters for all other

"^In order to adequately describe materials and experimental

procedures, it was occasionally necessary to identify commercial products by manufacturer's name or label. In no

instance does such identification imply that the particular

products or equipment is necessarily the best available for

the purpose.

33
peaks are determined in lines 8320-8460. The redrawing of

each peak is done in lines 8500-8595 C^his is really a separate subroutine; however, it is called from line 8310

and 8430 only)

U. Subroutine to compute the concentration of an element

either by stoichiometry or by difference (8600—8740)

One element in an unknown may be determined by difference:

n-1

i = l

or if the unanalyzed element is oxygen, it may be determined

by the stoichiometric relationships to the analyzed elements.

If zeros were entered for the valences of the elements, the

element will be determined by difference (8720-8740). If

non-zero valences were entered for each element (main program

A) , the oxygen content will be determined using the stoichiometric relation of oxygen to each analyzed element (8680-

8690 and 8702)

V. Main program for computing window thickness on a Si (Li)

detector (100-312)

This procedure should be carried out three or four times

a year on each Si (Li) detector to determine the thickness of

the beryllium window and of the silicon dead layer. A

carbon continuum spectrum should be generated at a convenient

operating potential (15 kV) . The operator must select background regions of interest coded and 1 as they are normally

positioned (e.g., 3.5 kV and 7 kV) . Then the operator must

select two more regions of interest: number 2 about half way

up the slope on the low energy side of the silicon K-absorption

edge and number 3 just on the high energy side of the silicon

K-absorption edge. The operator must then enter the atomic

number of the sample (6 for carbon) and the operating potential

The program does 15 iterations and prints out the two thicknesses which can then be entered in lines 1454 for Be and

34
1455 for Si. This program will overlay the main program A.

It, therefore, requires no additional computer memory.

lie. Results

As reported elsewhere [2], the ZAF portion of FRAME C

has been extensively tested and compared with results obtained

with the program COR 2 which includes all available refinements of the quantitation theory. The prediction of the

continuum has also been previously examined and shown to be

adequate for the background corrections [11] . The effectiveness of the interference correction was tested by analyzing

several specimens (pure elements and minerals) for elements

that are not present in the specimens but the lines of which

fall near x-ray lines from elements that are present. For

example, if pure manganese is analyzed for iron, the Mn K3

peak which overlaps with the Fe Ka region of interest contributes a large number of counts to this region. The overlap

correction subtracts the counts due to Mn K3 from the region

of interest of Fe Ka (see figure 4) . Some examples of overlaps that are removed are shown in Table 2. In most cases,

the interference is removed efficiently; however, it must

be noted that the incomplete charge collection is not at

present adequately removed for some elements. Figure 6

shows a mutual overlap of Zn Ka and W La in a spectrum from

zinc tungstate (ZnWO .) , with the results obtained by FRAME C

in Table 3. It must also be noted that the statistical

uncertainty of an overlap corrected peak is greater than the

uncertainty of the same peak if it had no overlap.

3.5
ZnWO

ZnKa

UJ

<

X

o

CO

H

o

o

Figure 6.

CHANNEL NUMBER

Spectrum of ZnWO. showing the KLa and ZnKa

overlapping peaks.

36
o

+->

4->

(/) bOCHU

•H

Klmo

t/i o

r-l <

(1) >

•H

+-) OJ

5h

03P.eO

to

I—I

(ACO

•H

4-> U

03U

PL,

tn

03

T3

(U P

03 t—( u

I—I

03

c/) O

03

5h

t/1 (D

to

0)>

•H

4-" 03 rH

<u

CIh 03

d

rH

O /—\

5h -h

•H (D A-> J > u >—

O CU •H ^

CO x: ^

4->

O

JhD

I—1

+J

03 0)

+-> e

t/) o

>s5h| ^ t-> u u

CDD. too

4-» U

CD

4-» 0) Q

•H

CO

5-. (D

i-H

M

03 0)

4-) e

to o

>.fH|

J-l +-> u u

(Ua

col

•H

U

03>O

d. fil

03

O

1—1

•H

u +J

(D

u > (D o ^

5h o O 2:U| o r^

oo rg

LO (Nl

t-- I—I

oo rsi

oo \o

o^ to ^ (Nl

(Nl LO

to i-n LO CNI

to to

<Z5 o

LO (NJ

p:

(U 0) ^ t/5 4-> •H ^3 u C <D

nJ P o O o

a^ V)

t/5 o

•H rH

P!

<D :3

i-HM t/5 C 0) 03 •H

(U r-i UC a O M

T3

•H (U O ^ n rt H w e (U

OJ p:

<D •H

XI 1—1 C I-H o rt u o p •H o •P

<u

X

iH i-H O OJ

P!

(l> nJ ^H

rH

OJ • • > o «V ^ LO to • cu o (NJ I-H (NJ LO X3

01

!/) c/i P

•H •H P

<D CD p: bOrH 0) 03 bO 3

-M

C cr

I-H 03 (U O t/5 > <U XI U 3

W) c to

Pi 0) •H GO 13

4-> ?H p;

Cti OJ

!h S

(D <D t/1 Ph •H • o X x: t3

03 P <D

(U Si P ^ 1 P! O H x: ^ p: 37
Since the magnitude of the interference from lines that

do not have a region of interest depends on the relative

weights of the lines, these must be known. FRAME C contains

estimates of the weights of lines which will be updated as improved values become available from measurements in our laboratory or elsewhere. In the course of an analysis, a line spectrum of the unknown synthesized by the program is stored for

display in quadrant 3 of the multi-channel analyzer memory.

Gaussian peaks are constructed for each x-ray line from the

weights of lines, the analytical results, the line energies,

and the peak widths. The continuum is not synthesized for the

display since this procedure requires too much time.

The results of an analysis may be evaluated by comparing

the synthesized spectrum with the spectrum obtained experimentally from the specimens. Part of an experimental spectrum

of Nunivak anorthoclase is shown in figure 7 together with

the spectrum synthesized by the program of the same specimen.

The comparison of spectra is particularly useful for detecting

elements which were inadvertently omitted in the analysis.

Results of energy-dispersive analyses of several minerals and

alloys are shown in Tables 4 and 5 together with the results

obtained by chemical analyses and the standards used for

each element. The standards K371, K409, and K412 are glasses

prepared at NBS as microanalyt ical standards. The steels

listed in Table 5 were analyzed by scanning the beam over an

area of 160 x 200 ym; however, this was not always sufficient

to prevent specimen inhomogeneity effects. Also, the large

incomplete charge collection present in the Fe Kg signal is

not adequately removed from the Co Ka region of interest.

We are currently evaluating data collected from several

different Si(Li) detectors to obtain a better estimate of

the contribution of incomplete charge collection. The tests

conducted show that the proposed method for overlap corrections

in energy-dispersive x-ray analysis combined with the FRAME B

program is suitable for general use.

38
^

5

laiMiMVHo/siisinoo

39
Na

Mg

Al

Si

K

Ca

Ti

Mn

Fe

Zn

Ba(La)

Total

Table 4. Mineral Analyj3es

Mai3S Fractions

Anorthoclase (Nunlvak) Rhodonite (Bald Knob)

Chem

FRAME C Chem FRAME C

Set 1^ Set 2 Set 1 Set 2 0611 .0638^ .0639^ - - (.0008)

00012 .0038^ .0020^ .0076 .0096 .0093

1081 .1048^ .1060^ - (.0044)^ (.0005)

3088 .3087^ .3114^ .2194 .2251 .2265

0291 .0291 .0289 - - (-.0006)

0056 .0073^ .0073^ .0567 .0586 .0580

0001 ND^ ND _ _ _

0016

0013

.0013

.0021

.4789^

.9998

.0013

.0020

.4772'

2645 .2735

0131 .0157

0562 .0609

.3893

1.0371

.2730

.0136^

.0606

.3577^

Tephr(3ite Basalt (Juan de Fuca)^

Chem FRAME C

Set 2

Chem FRAME C

Set 1

Na - - .0194 .0256^

Mg - - .0405 .0446^

Al - - .0744 .0723^

Si .1391 .1443 .2375 .2376^

K - - .0016 .0019

Ca - - .0795 .0790^

Ti - - .0111 .0110

Mn .5441 .5410 .0017 .0020

Fe - (.0008) .0919 .0921^

.3139^ .4397^

Total 1^ 1.0058

4Q
Table 4 (Continued)

Composition of Standards (Chem. Analysis)

Element K409 K412 K371 OR-1^ Apatite Tephroite^

.0085

.0983

.2309 .3010 - .1391

.1239

.391

- - - .5441

.0002

.0307 - - ' - .4192 .0073 - .1806

Na .0737 - Mg - .1166

Al .0780 .0491

Si .2538 .2120

K - - Ca .0014 .1090

Ti - - Mn - .0010

Fe .1489 .0774

Zn - - Ba - -

P _ _

41
Table 4 (Continued)

Standards Used

Element Set 1

Na K409

Mg K412

Al K412

Si K412

K OR-1^

Ca K412

Ti Ti02

Mn Tephroite

Fe K412

Zn Pure

Ba K371

Set 2 K409

MgO

AI2O3

SiO^

OR-1

Apatite

Pure

Pure

Pure

Pure

K371

Set 1 and Set 2 refer to the two sets of standards used for these analyses,

Element corrected for overlap.

Oxygen computed by stoichiometry.

Oxygen computed by difference.

ND is "not determined".

Huebner, J. S., U.S.G.S., Reston, Va.

p Jarosewich, E., Smithsonian Institution, Washington, D.C.

L- Synthetic glass, from Geophys. Lab, Washington, D.C.

The operating voltage is 15 kV. The electron beam incidence angle is

90° and the x-ray emergence angle is 52.5°.

42
Table 5. Analyses of NBS Low Alloy Steel

Element

V

Cr

Mn

Fe

Co

Ni

Cu

Pure Fe

.00075

.0009

-.00175

1.000

,0010

-.00089

ND

Mass Fract:ions

SRM 662

Chem. FRAME C

.00041 .00081

.0030 .0039

.0104 .0093

(.953) .953

.0030 .0100

.0059 .0054

.0050 .0058

SRM 663 .

Chem. FRAME C

.0031 .0034

.0131 .0144

.0150 .0134

(.944) .942

.00048 .0069

.0032 .0024

.00098 .0013

Brass Analysis

Chem. FRAME C FRAME^

Cu .7675 .777 .769

Zn .2326 .236 .235

Crystal Spectrometer data.

The operating voltage is 20 kV. The electron beam incidence angle is 90'

and the x-ray emergence angle is 52.5".

43
lid. Example

It is difficult to present an example of an analysis

computed by FR.A,ME C since the data are directly transferred

from spectra stored in the multichannel analyzer into the

program. The contents of each region of interest needed for

a particular spectrum are listed, together with each region's

energy limits, instead of listing the contents of every

channel in the spectrum. ROI(O) and ROI(l) in each spectrum

are the background regions set up by the operator.- All

other regions of interest are defined by the program for

each element to be analyzed.

The example used in what follows is an analysis of an

anorthoclase (Xunivak) mineral obtained from J.S. Huebner of

the U.S.G.S. Five different standards were used for the

eight analyzed elements. The oxygen content of the specimen

was determined s toichiometrically from those of the eight

other elements.

Standard 1: glass K3"l Ba standard

^^^ ^low %igh C°^^^^

3.070 3.290 16462

1 7.139 7.679 13618

2 4.390 4.550 88572

5 Each input typed by the operator is preceded by a question

mark (?) typed by the computer. The region of interest

data that is read from each spectrum is listed before each

computation.

44
100 RUN

ENTER NO. OF ELEMENTS

? 4

ENTER EO

? 5

ENTER CON, ATNO,

? '4192? 56? 2? 2

? -2309? 14? 0?

? -0307? 30? 0?

? '3192? 8? 0?

MELS = -335377

ROI 3-07

ROI 1 7«139

LINE CODE AND VALENCE FOR EACH

29

679

Standard 2

Pure Fe Fe standard

ROI

1

2

low

3.070

8.319

6.320

high

3.290

8.859

6.489

Counts

19890

11529

305924

*100 RUN

ENTER NO. OF ELEMENTS

? 1

ENTER CON, ATNO, LINE CODE AND VALENCE FOR EACH

? 1? 26? 1? 2 MELS = 1

ROI 3-07 3-29

ROI 1 8'319 8-859

Standard 3: gl ass OR-1 K standard

ROI ^low high Counts

2.360 2.580 11212

1 5.710 6.250 9832

2 3.240 3.390 89255

45
*100RUN

ENTER NO

? 6

OF ELEMENTS

ENTER CON, ATNO

,

? -1239? 19? 1? 1

? -0085? 11? 0?

? -0983? 13? 0?

? -301? 14? 0?

? -0073? 56? 0?

? -4601? 8? 0?

LINE CODE AND VALENCE FOR EACH

MELS = ROT

ROI 1

110224

36

71

58

25

Standard 4:

ROI

1

2

3

4

glass K412 Mg, Si, Ca standard

low

700

649

190

670

610

'high

920

189

320

800

770

Counts

10912

5926

79419

194831

. 76100

*100RUN

ENTER NO.

? 6

OF ELEMENTS

ENTER CON, ATNO, LINE CODE AND VALENCE FOR EACH

1166?

212?

109?

0491?

0774?

4349?

MELS = 8

MELS = MELS = ROI

ROI 1

12? 1? 2 14? 1? 4

20? 1? 2 13? 0?

26? 0?

8? 0?

32303E-2

168803

10142

2-7

7-649

92

189

Standard 5

ROI

glass K409

low

2.820

7.649

0.981

1.420

high

3.040

8.189

1.100

1.550

Na and Al standard

Counts

10012

5926

23988

73492

46
*100RUN

ENTER NO. OF ELEMENTS

? 6

ENTER CON, ATNO , LINE CODE AND VALENCE FOR EACH

? -0737? 11? 1? 1

? • 078? 13? 1? 3

? -2538? 14? 0?

? •00136?20? 0?

? -1489? 26? 0?

? '4442? 8? 0?

MELS = 3-84375E-2

MELS = 5-74489E-2

ROI 2-82 3-04

ROI 1 7-649 8»189

Unknown: Anorthoclase (Nunivak)

ROI E, E, . , Counts low high

2.320 2.540 10275

1 8.269 8.809 4124

2 0.981 1.100 25843

3 1.190 1.320 9372

4 1.420 1.550 101766

5 1.670 1.800 286980

6 3.240 3.390 25055

7 3.610 3.770 11031

8 6.320 6.489 2910

9 4.390 4.550 4648

*5 00RUN

ENTER NO. OF ELEMENTS

? 9

ENTER AT. NO -FOR EACH ELEMENT

? 11? 12? 13? 14? 19? 20? 26? 56? 8

NO PLOT ENTER

? IZ C F(X) K

11 6.20325E-2 -571227 3.97415E-2

12 0. .657226 -3.33924E-4

13 -1 .76323 8.23842E-2

14 .307338 .777802 -253665

19 2.89234E-2 -915523 2.55711E-2

20 7.01639E-3 -93084 6.40029E-3

26 1.2845E-3 -986375 1.09671E-3

56 1.64386E-3 .959155 1.18512E-3

8 .469937

TOTAL = -978176

ROI 2-82 3-04

ROI 1 7-649 8-189

47
The synthetic spectrum, drawn by the program, together with

the original spectrum is shown in Figure 7. This comparison

is an important part of the analysis and should not be

neglected when analyzing an unknown material since minor

elements could be missed entirely.

Versions of FRAME C are available in both BASIC and

FORTRAN that do not contain the subroutine to synthesize

the spectrum since they are not written for a computeroriented multichannel analyzer. Users are warned that

without this feature, elements could be overlooked. This

does not mean that the program will always work either.

For example, attempting to measure S Ka and PbMa in the

same specimen will not work since these peaks would occupy

the same region of interest.

48
III. References

[1] Henoc, J., Heinrich, K.F.J. , and Myklebust, R.L.,

A Rigorous Correction Procedure for Quantitative

Electron Probe Microanalysis (COR 2), NBS Tech.

Note 769, August 1973.

[2] Yakowitz, H. , Myklebust, R.L., and Heinrich-, K.F.J. , FRAME: An On-Line Correction Procedure for Quantitative Electron Probe Microanalysis, NBS Tech. Note 796,

October 1973.

[3] Heinrich, K.F.J. , Myklebust, R.L., and Yakowitz, H.

,

A Simple Correction Procedure for Quantitative Electron

Probe Microanalysis, NBS Tech Note 719, May 1972.

[4] Russ, J.C., Scanning Electron Microscopy 1977, Vol. 1,

IITRI, Chicago, 111. 289-296 (1977).

[5] Myklebust, R.L. and Heinrich, K.F.J. , in Energy Dispersion

X-ray Analysis: X-ray and Electron Probe Analysis , ASTM

STP 485, 1971, pp. 232-242.

[6] Reed, S.J.B. and Ware, N.G., X-ray Spectrometry, _2, 2,

1973, pp. 69-74.

[7] Smith, D.G.W., Gold, CM., and Tomlinson, D.A. , X-ray

Spectrometry, 4, 3, 1975, pp. 149-156.

[8] Ware, N.G. and Reed, S.J.B. , J. Phys . E: Sci. Inst.,

6, 1973, pp. 286-288.

[9] . Lifshin, E. , Ciccarelli, M.F., and Bolon, R.B., X-ray

Spectral Measurement and Interpretation, General Electric

Tech. Information Series, Report No. 74CRD159, Sept. 1974.

Heinrich, K.F.J. , Yakowitz, H., Anal. Chem. , 4_7, 14,

1975, pp. 2408-2411.

Fiori, C.E., Myklebust, R.L., Heinrich, K.F.J. , and

Yakowitz, H., Anal Chem. 4_8, 1, 1976, pp. 172-176.

Gedcke, D.A. , X-ray Spectrometry, 1^ 1972, pp. 129-141.

Fiori, C.E., Myklebust, R.L., and Heinrich, K.F.J.

,

Proc. 11th Annual Conf. of Microbeam Analysis Society,

Miami Beach, Florida, Aug. 9-13, 1976, paper 12.

49

[10]

111]

[12]

[13]
[14] Fiori, C.E., Myklebust, R.L., Heinrich, K.F.J. , and

Yakowitz, H., Proc. 10th Annual Conf. of Microbeam Analysis Society, Las Vegas, Nev., Aug. 11-15, 1975, paper 20

[15] Walter, V.J., in Energy Dispersion X-ray Analysis: X-ray

and Electron Probe Analysis , ASTM STP 485, 1971, pp. 82-

111.

[16] Smith, D.G.W., Reed, S.J.B., and Ware, N.G., X-ray Spectrometry 3, 149, 1974.

[17] Philibert, J. and Tixier, R. , in Quantitative Electron

Probe Microanalysis , NBS Special Publ. 298, K.F.J.

Heinrich, ed. 13-33 (1968).

[18] Reed, S.J.B., and Ware, N.G., J. Phys. E: Sci. Inst. _5,

1972, pp. 582-584.

[19] Heinrich, K.F.J. , The Electron Microprobe, McKinley,

Heinrich and Wittry, editors, John Wiley, New York,

296-377 (1966).

[20] Heinrich, K.F.J., Fiori, C.E., and Myklebust, R.L., J^

Appl. Phys. (to be published) (1979).

50
SCAWWIMG ELECTRON MTCROSCOPV / 1 97

S

/Vol. I 5EM Inc., AMF O'Hafie., U 60666, USA

Appendix 1

ARTIFACTS 08SERUEP IM ENERGV-PISPERSI l/E X-RAV SPECTROMETRY IM THE

SCANNING ELECTRON HICROSCOPY

C. E. VioKl and V. E. N^MbuKy

Microanalysis Section, Bldg. 222

National Bureau of Standards

Washington D. C. , 20234

Abstract

X-ray spectra obtained with a lithium-drifted silicon detector attached to

a scanning electron microscope often

contain artifacts which limit the accuracy of qualitative and quantitative

analysis. Three categories of artifacts

are recognized: (1) artifacts which

originate during the physical process of

x-ray detection; (2) artifacts associated with the signal processing chain;

and (3) artifacts which arise from the

environment of the sample and detector.

Artifacts in these categories include:

(1) silicon x-ray escape peaks, peak

broadening, and peak distortions; (2)

dead-time effects, the formation of sum peaks, and anomalous background signals;

and (3) detector micrbphony, excitation

by stray radiation of regions which are remote from the beam impact point, and

effects on x-ray intensities caused by

contamination. Recognition of these

artifacts is required for accurate

qualitative analysis of unknowns,

particularly of low intensity signals.

A procedure is described for qualitative

analysis based on the known properties

of the family of x-ray lines for each

element as well as the artifacts which

can be observed. The implications of

the presence of spectral artifacts on

the accuracy of quantitative analysis

is also discussed.

KEY WORDS : Artifacts, Electron Probe Microanalysis,

Energy Dispersive X-Ray Spectrometry, Microanalysis,

Quantitative Analysis.

Contribution of U.S. Government:

subject to copyright.

not

Introduction

The addition of a silicon (lithium)

energy dispersive x-ray spectrometer to

a scanning electron microscope (SEM)

provides a versatile and powerful instrument for the study of structure on the

micrometer scale. Both the morphology

and the chemical elements (Z >_ 11)

present in micrometer-sized features of

a specimen can be studied. For cursory

work, a qualitative x-ray analysis for

the principal constituents of a specimen

can be obtained in a very short time,

typically minutes. To extract the

maximum amount of information available,

specifically the composition of the

region of interest, considerable effort

must be expended and a careful, logical

approach is required.

An accurate quantitative x-ray

microanalysis is developed in four

distinct but interrelated stages: (1)

The proper choice must be made for

instrument operating parameters, including beam energy and current; and spectrometer parameters, such as amplifier

calibration and pulse processing time.

(2) A systematic qualitative analysis is

performed by identifying all peaks and

recognizing spectral artifacts. (3) The

x-ray intensities for the peaks of

interest are extracted from the spectra

of the unknown and standards after the

continuum radiation is subtracted. (4)

The x-ray intensities are converted into

compositional values through the application of mathematical algorithms which

correct for various matrix effects, such

as electron deceleration, electron backscatter, x-ray absorption in the target,

and production of x-rays by secondary

excitation^ '^ ' ^

. The mathematical

algorithms are dependent on the particular specimen shape and have only been

comprehensively developed and rigorously

tested for one type of specimen: a flat, bulk target which is set normal

to the electron beam. A number of

51
successful computer programs are available which have been developed from

these algorithms '' In addition, a purely empirical approach based on correction factors determined from

standards similar in composition to the

unknown is available''.

\shen energy dispersive x-ray spectrometry (EDS) is employed for x-ray

microanalysis, special considerations

relative to points (1) , (2) , and (3) come into play. Certain operating

conditions must be fulfilled if a satisfactory EDS spectrum is to be obtained.

However, even a spectrum obtained under

optimum conditions may contain numerous

artifacts which can affect the accuracy

of both the qualitative and quantitative

analysis. We shall describe the most

significant artifacts which appear in

the EDS spectrum under typical analytical

conditions for x-ray microanalysis with

a scanning electron microscope or electron probe microanalyzer (EPMA) . A

strategy for qualitative analysis which

is based upon the physics of x-ray

generation and the detection process will

be presented. The steps required to

extract x-ray intensities for quantitative analysis will be described.

The natural x-ray spectrum generated by the incident electron beam in

the sample consists of (1) characteristic x-rays produced during electron

transitions following ionization of an inner electron shell of an atom by the

beam electron and (2) bremsstrahlung

["braking radiation") or continuum x- rays formed during deceleration of the

beam electron in the coulombic field of

the atoms^'^'^. The continuum forms a background extending from zero to the

incident beam energy. The x-ray con- tinuum, while limiting the sensitivity

of the measurement of the characteristic

intensity, is not an artifact, since it

is a product of the electron beamspecimen interaction and does, in fact,

convey information on the -average atomic

number of the specimen. Artifacts are the discrepancies introduced into the

spectrum by the measurement process.

The artifacts observed in EDS spectra

can be broadly classified into three

categories: [1) those which arise

through the nature of the x-ray detection process; [2) those associated

with signal manipulation following the

detector; and (3) those arising from

certain aspects of the detector —

specimen chamber environment. Artifacts

in category (1) include silicon x-ray

escape peaks, peak broadening, and peak

distortions due to incomplete charge

collection. Such artifacts cannot, in

general, be eliminated from the spectrum

through any action on the part of the

analyst. Artifacts in category [2)

include

the spec

the dist

pulse pi

Artifact

tor micr

specimen

stray ra entrance

detector

intensit

contamin

coincidence los

trum due to pul

ortion of the b

le-up and the b

s in category [ ophony, excitat

or parts of th

diation (x-rays

of energetic e

, and effects o ies caused by t ation on the sp

ses , sum peaks in se pile- up, and

ackground due to

ackground shelf.

3) include detecion of the

e instrument by

or electrons)

lectrons into the

n measured x-ray

he build-up of

ecimen.

Artifacts of the Detection Process

The Si(Li) x-ray detector ® ' ^ '' ° '^

operates on the following principle

(Figure 1) . The lithium-doped silicon

has the interesting electrical property

that both negative charges (free electrons in the conduction band) and positive charges (holes in the valence band)

can move easily through the solid when a bias is applied. An energetic photon or particle which enters the detector

causes the formation of such charge car- riers. The incident x-ray photon is

first absorbed by a silicon atom and an energetic electron is emitted (the photoelectric process) . This photoelectron

then creates charge carriers as it

travels in the detector silicon and

scatters inelastically. The silicon

atom is left in an energetic condition,

retaining the energy required to eject

the photoelectron. This energy is subsequently released in the form of either

an Auger electron or a silicon x-ray.

The Auger electron scatters inelastically

and creates charge carriers. The silicon

x-ray can be re-absorbed which initiates

the process again, or it can be scattered

inelastically. Thus, a sequence of

events takes place leading to the deposition of all of the energy of the

original photon in the detector, unless

radiation generated during the sequence,

such as a silicon Ka photon, escapes the

detector. The detector is also sensitive

to energetic electrons which enter; such

electrons can directly form charge

carriers

A bias applied to the detector

serves to collect the charges on the two

surface electrodes. The ideal number of

charges created per incident particle

with energy E (ev) is given by

E/K (1)

where K = 3.8 eV for silicon. For

example, if the detector captures one photon having an energy of 5 keV,

then from equation (1) the total number

of electrons swept from the detector is

approximately 1300 which represents a charge of 2x10'^^ coulombs.' This is an extraordinarily small charge. The

52
X-Rays

1000 V

FWHM/2.3SS

i ( lithium drifted -^1^ region) _

Ol/im p( inactive)

8/im Be

1-

to

Amplifier

Fig (1) Schematic diagram of a typical

lithium-drifted silicon detector.

subsequent circuitry must be capable of

amplifying this signal by about 10^°.

Deviations from the ideal detector

process result in the appearance of

artifacts, principally peak broadening,

peak distortion, silicon x-ray escape

peaks, and silicon and gold absorption

edges

.

Peak broadening

The natural width of an x-ray peak

is of the order of one electron volt,

measured at half the maximum of the peak

intensity (the measured quantity is

designated "full width, half maximum"

(FWHM)). For example for manganese Ka

radiation (5.898 keV) , the FWHM is

approximately 2.3 eV, which makes the

natural width about 0.039 percent of the

peak energy. The measured peak width

from the Si(Li) spectrometer is degraded

to a typical value of 150 eV for MnKa,

or 2.5% of the peak energy. This

degradation in width of the peak occurs because: (1) there''*is a distribution in

the final number of charge carriers

created by capturing photons of a single

energy due to the discrete nature of the

counting process and (2) an uncertainty

is introduced by the thermal noise of

the amplification procfess. The distribution of numbers of charge carriers for

a single photon energy is reasonably

well described by a Gaussian distribution, shown schematically in Figure 2. The FWHM of this distribution can be

calculated from the two sources of noise

by quadrature addition, according to the

equation

FWHM ^^Jc^B^N' (2)

where C is the measure of the uncertainty in the formation of charge carriers

Fig (2) Theoretical Gaussian distribution which describes an EDS peak. a is

the standard deviation of the distribution, A. is the peak amplitude, and y is

the amplitude at any energy

from a photon of energy E and N is the

electronic noise of the amplification

process. The immediate consequence of

the peak broadening is a reduction in

the height of the peak (counts per

energy interval) as compared to the

natural peak and an accompanying de- crease in the peak-to-background ratio.

For practical work, the value of

the FWHM as a function of the peak

energy is conveniently described by the

expression

FWHM^ = 2.5(E-,^-E2]+FWHM2 (3)

where FWHMa is the known full width half

maximum (eV) of a peak of energy E2

(eV) , and FWHMi and Ei refer to those

parameters for any other peak. Thus, if

the FWHM is known for MnKa, the FWHM

appropriate to any other peak can be

calculated.

The value of the FWHM is useful in

estimating the extent of the overlap of

peaks which have similar energies. An

estimate of the extent of overlap is

vital when considering peak interferences in qualitative analysis, where the

identification of a low intensity peak near a high intensity peak may be difficult, and in quantitative analysis,

where the removal of the interference is

necessary for accurate determination of

the composition. An example of the

overlap of peaks is illustrated in the

spectrum of KCl in Figure 5. With a detector of 170 eV resolution (MnKa)

,

the potassium Ka and Kg peaks are nearly

resolved, while the chlorine Ka and Kg

peaks are not.

53
KCl

E„=15l<eV

2KE IkeV) Fig (3) EDS spectrum o£ KCl illustrating

peak overlap: CI Ka,K6 are not resolved

while K Ka,K6 are nearly resolved. The

solid line is a Gaussian fit to the data

points. The shaded area represents the

deviation caused by incomplete charge

collection.

Peak distortion

Two different artifacts cause distortion, i.e., deviation from a Gaussian shape on the low energy side

of a peak: Cl) The collection of

charge carriers created in certain

regions of the detector near the faces

and sides is imperfect due to trapping

and recombination of the electron-hole

pairs, leading to a reduction in the

value of n predicted by equation (1) for

the incident photon. The resulting

distortion of the low energy side of the

peak is known as "incomplete charge

collection"^ ^ ' ^

^ and its effect is

illustrated in Figure 3 for chlorine Ka

and potassium Ka peaks. The deviation

from a Gaussian distribution (shown as a solid line) is a function of energy.

For example, the magnitude of the effect

is significantly different for chlorine

and potassium, which are separated by an atomic number difference of only two.

(2) The background shelf, Figure 4, is a phenomenon in which the presence of a peak increases the background at all

energies below the peak value. Additional counts above the expected background result both from the incomplete

charge collection phenomenon extending

to low energy and from the escape from

the detector of some of the continuum x- rays generated by the photoelectron as

it scatters inelastically in the silicon. Any radiation lost from the detector reduces the number of charge

carriers created. Both the incomplete

charge collection and the loss of

continuum x-radiation lead to a transfer

of counts from the peak to the entire

MnK« ~MnM

310 K

Mn K.(esc)

;:

•

; i

, /

• 'A >^ V MnK^lescI -k,- ^—

^

ElkfVI 55 Fig (4) EDS spectrum derived from Fe

radioactive source. The background shelf

is easily observable at energies below

Mn Ka down to the threshold at 300 eV

The Mn Ka and KB silicon escape peaks are

noted. Extraneous characteristic peaks

from the source holder are observed.

energy region down to zero. Typically,

the background shelf at one-half the

energy of a peak has a relative intensity of about 0.1 percent of the parent

peak. The total number of counts lost

to the full peak due to this effect is

approximately 1 percent.

Silicon x-ray escape peaks

The generation of a photoelectron

leaves the silicon atom in an ionized

state. If the photoelectron is emitted

from the K- shell, the atom can subsequently undergo an electron transition

to fill this K-shell vacancy, with subsequent emission of a silicon K x- ray or an Auger electron. The range of

the Auger electron is only a fraction of

a micrometer, and hence, it is highly

probable that this electron will be re- absorbed in the detector and contribute

its energy to the formation of charge

carriers, yielding the correct value of

energy deposited in the detector. The

SiK x-ray, on the other hand, has a finite probability of escaping the

detector (10 percent of the SiK initial

intensity will remain after 30 ym of

travel through silicon) . When such an x-ray escape occurs from the detector,

it robs the cascade being measured by

the energy carried off in the x-ray,

1.740 keV for SiKa and 1.832 keV for

SiKB. Thus, an artifact peak, the

"escape peak"^"* is formed at an energy

equal to the energy of the parent line

minus the energy of the silicon x-ray.

In principle, both SiKa and SiKg escape

peaks are formed, but the probability

for Kg formation is about 2 percent o£

54
TiKoi 1382K 186 K

SiK Tl K«(esc|

; ; Ti K/»lescl j

Fig (5) Electron-excited EDS spectrum of

titanium. The Ti Ka and KB silicon x-ray

escape peaks and the 2Ka and (Ka+Ke) sum peaks are noted. Extraneous peaks from

the specimen chamber are also observed.

Carbon

E„=10keV

E IkeVI Fig (6) Electron-excited EDS spectrum

from carbon. The silicon and gold absorption edges are illustrated. Solid line

represents a theoretical fit to the con- tinuum.

the Ka, hence only one esc observed per parent peak.

are illustra'ted in Figure

parent peaks are TiKa (4.5

TiKB (4.93 keV) and escape

found at 2.77 keV (TiKa-Si

keV (TiK3-SiKa). The magn

escape peak relative to th

varies from about 1 percen

phorus to 0.01 percent for

rays. Silicon x-ray escap occur for radiation below

energy of the silicon K sh

keV) .

ape peak is

Escape peaks

5, where the

1 keV) and

peaks are

Ka) and 3.19

itude of the

e parent peak

t for phoszinc K Xe peaks cannot

the absorption

ell (1.838

Absorption edges

The typical Si (Li) spectrometer has

a protective window of beryllium (approximately 7.6 ym thick), a front surface

electrode of gold (approximately 20 nm

thick), and an inactive layer of silicon

(20-200 nm thick). X-rays must pass

through each of these layers to reach

the active silicon and be detected. During passage of x-rays through the layers,

absorption occurs. Absorption in the

beryllium window eliminates nearly all.

x-rays below about 600 eV. Above 2 keV,

virtually all x-rays are transmitted

through the window. Between these

limits, the absorption increases with

decreasing energy such that at 1.5 keV

about 70 percent of the x-rays are transmitted while for an energy of 1 keV

the transmission is 45 percent. Absorption by the gold and silicon layers is

much less significant due to the small

mass thickness of these layers. However, a noticeable change in the x-ray

continuum is observed at the absorption

edge of silicon and to a lesser degree

55.

at gold. Figure 6. Just above the energy of the absorption edge, the mass absorption coefficient increases abruptly, resulting in a decrease in the

measured continuum x-radiation. The

height of the resulting step is an indication of the thickness of the

layer. Note that the action of the

broadening effect of the detection process causes the absorption edge, which

in reality is a sharp change of absorption over a range of about 1 eV, to

be smeared over a much broader range,

typically 100 eV for the silicon absorption, edge.

The absorption of x-rays by the

silicon dead layer causes fluorescence

of Si K x-radiation. This results- in the

appearance in the spectrum of a small

silicon peak, the so-called silicon

internal fluorescence peak^**. For most

analysis situations, this fluorescence

peak corresponds to an apparent concen- tration of 0.2 wt . percent or less silicon in the specimen.

The Signal Processing Chain

The signal processing chain which

follows the Si(Li) x-ray detector is

illustrated in Figure 7. Due to the

wide variety of pulse processing systems

available it is necessary here to describe, a genjeralized system. Figure 7,

however, contains the essential features.

In this circuitry, the small charge

developed on the electrodes of the

detector when a single photon is captured is converted into a voltage pulse

of fixed shape and duration which is

suitable for presentation to a multichannel analyzer (MCA) ^ ^ . The nature of

the signals at various points in the
Si (Li) X-RAYS=»

-500

VOLTS

PULSE

REJECTOR

AMPLIFIER BUSY

FAS

AMPLIFIE DISCRIMINATOR

REAL TIME

LIVE TIME

10

CLOCK

GATE

>vOvv\

INHIBIT 11 'CLOCK

5 OUTPUT

-*T0 MCA

^'INHIBIT OUTPUT

8

PILE-UP

INSPECTOR

DEAD-TIME

CONTROL

.12 MCA

BUSY

Fig (7) Schematic diagram of the signal processing chain of a generalized EDS system.

processing chain is shown in Figure 8. The signal produced by the detector at

(1) has the form of a pulse with a rise

time of less than 100 ns and a longer

exponential tail. The passage of a second pulse through the system is shown

in dashed lines. The field effect

transistor (FET) preamplifier has the

function of amplifying the small detector signal with minimum degradation,

to produce a step function (2) , which,

for clarity, is shown without noise.

At this point, the signal is split into

a slow and a fast channel^ ^. The purpose of the slow channel is to amplify

the pulse with the maximum possible

signal-to-noise ratio which is necessary

to yield a high resolution spectrum.

Long time constants are required in

these circuits, hence the designation

"slow." The fast channel operates with

a much poorer signal-to-noise ratio but serves as a monitor on the slow channel

to eliminate pulses which would arrive

too close to one another to be recognized as discrete by the slow channel.

In the slow channel, by a combination of differentiation and integration

circuits in the linear amplifier, the

pulse is shaped and the width is set in

the range. 5-80 ys (3). The choice of

the width strongly affects the achievable

resolution of the system. The time

constants of the resistive-capacitive

networks used in the integrators and

differentiators of the pulse shaping

circuit are commonly grouped into the

parameter labelled "shaping time" on the

amplifier. The magnitude of the shaping

time is typically chosen in the range 2- 20 ys. It must be noted, however, that

the shaping time is not the deadtime.

The deadtime of the amplifier is that

period of time during whicn the voltage

in the slow channel is raised above a

threshold value by the passage of a single pulse and during which time the

slow channel is unavailable for subsequent pulses. The deadtime can be as much as ten times the value of the

shaping time.

The discriminator on the fast

amplifier channel sets a threshold

level, adjustable by the analyst, which

separates real pulses from the spectrum

of noise which is passed and amplified

by the fast amplifier. Note that a high

energy pulse, such as that which results

from a photon of CuKa, is well above

this noise, while a low energy pulse,

such as that from MgKa, is virtually at the same level as the noise and is

therefore difficult to distinguish. The

output of the discriminator is a normalized rectangular pulse of approximately

the same duration as the fast amplifier

pulse. The pile-up inspector examines

the separation of the discriminator

pulses to determine if one or both

pulses in the slow channel must be

rejected at the pulse rejector. If the

first pulse in- the slow channel has

passed its peak before the second pulse

arrives, it is necessary to reject only

the second slow channel pulse. If the

second pulse arrives before the first

has reached its peak, then both pulses

are rejected. The output pulses from

the pile-up rejector are passed to the

multichannel analyzer for sorting.

Deadtime correction functions will

be treated subsequently.

Artifacts of Signal Processing

Pulse pile-up . Artifacts associated

with the processing of the signal originate primarily from pulse coincidence

effects, that is, the nearly simultaneous arrival of x-ray photons in the

56
o

>

1 iima/s**!!*; Wjj^^^^^

2

3

a' '?T'!I.''i""""',^ ''»•'»'' _y\

6 _r

8

9 1 i i I I I I I I 1

I 1I I t

tii 10 U I o

<

11 _r L

12

TIME

L

Fig (8) Schematic illustration o£ signals

found at various points in Figure 7.

detector. If a second photon of energy

Ea enters the detector during that

period of time in which the system is

engaged in processing the pulse developed

from the first photon of energy Ei , then

a combined pulse is developed which has

a value equal to Ei+fE2, where f has a range 0<f<l. The factor f can take on a continuous range of values since the

arriving cascades generated by the

photons can overlap in any proportion.

The coincidence effect is illustrated

schematically in Figure 8. Pulse coincidence or "pulse pile-up"'^ has the

effect of reducing the total count in

57

the peaks Ej and Ea (consider Ei < Ea) , while creating artifact summation

peaks at 2Ei, 2E2 and Ei + E2 as well as

a continuum of intermediate values

between Ej and 2E2. The summation peaks

are readily apparent in the example of

Figure 9(a) and the distortion of the

background by the full range of intermediate summation values is also illustrated. The magnitude of the pulse

pile-up effect is dependent on the rate

of arrival of x-ray pulses at the detector and the value of the system time

constant. The higher the counting rate

and the longer the time constant, the more likely the coincidence of pulses

becomes. Thus, the relative magnitude

of the summation peaks is not a constant

as in the case of escape peaks, but

depends on amplifier parameters. At an input count rate of 10,000 c/s under a peak and a system time constant of 8 \is

,

the double energy peak is typically 0.25

percent of the parent peak.

The action of a pulse pile-up

rejector circuit, which is an integral

part of a modern system, is illustrated

in Figure 9(b), where a significant

reduction in summation peak height as well as the intermediate background with

respect to Fig. 9(a) is obtained. The

summation peaks are not totally supr

pressed by the pile-up rejector because

the time resolution of the rejector has

a limiting value. Pulses which arrive

closer in time than the pulse pair

resolution of the fast channel will be

passed and treated as one pulse. Moreover, the pulse pile-up rejectors can have operational defects and are often

ineffectual for low energy peaks for

which the pulse in the fast channel is

close to the noise. This failure is

also illustrated in Figures 9(a) and (b)

where adequate pulse pile-up rejection

is achieved for silicon, but the rejector circuit fails for magnesitim.

A second technique of coincidence

control is that of Goulding^^. In this

approach, when the pulse monitoring

circuitry detects a photon in the processing system, the SEM electron beam is

blanked off and prevented from reaching

the specimen for the duration of the

pulse processing period, thus preventing

the formation of additional photons

which might cause coincidence. The

Goulding technique has the considerable

advantage that far fewer pulses are discarded, thus increasing the amount of

information which can be obtained in a given time.

Deadtime Correction . The Si(Li) system

detects photons sequentially; it is not

possible to process more than one photon at a time. The period of time

which the system requires to process a
iK- MgKa,/9

61-9 K

2MgK..^

Magnesium

E„= 15 keV

g

••

/v.,:: 3MgK«,^

r v^

Pile-up

1 Spectrum '-^K.::- '^^v^^,^^

,-^''-

i 2 E(keVl

3 L 5

4K71-8 K

•

•

Silicon E,=15keV

J

.1*

.

V.' 2SiK«./J •«..-^;,^^

0- ^ i 2 E (keVi 3 4 5

Fig (9) (a) Electron-excited EDS spectrum

o£ magnesium.

Fig (9) (b) Electron-excited EDS spectrum

of silicon.

pulse and during which it is unavailable

for detecting subsequent photons is

known as the deadtime'^. In order to

compensate for the loss of photons which

arrive during the periods in which the

system is occupied, the internal clock

of the multichannel analyzer (9 in

Figure 8) is gated "off" during the

processing of a pulse by a signal

derived from the slow channel. The

deadtime varies with the energy of the

pulse, and the counting time is automatically compensated for this effect by

control of the clock pulses. If the

system counting period is pre-set to

give a value of T (seconds) , the compensation for deadtime is carried out by

the internal circuitry by effectively

extending the counting period to T+ni*,

where t* (seconds) is the variable

deadtime appropriate to each pulse of any

energy and n is the number of counts in

the whole spectrum. The system deadtime

T is, in general, a function of both the

amplifier deadtime and the time which

the multichannel analyzer requires to

sort the pulse. In Figure 8, the clock

pulses (9) are gated off when the detector pulse first crosses a threshold

value A. Although the pulse to the MCA

is terminated after a time t„, the clock

remains off while the MCA sorts the

pulse, which results in an extended

interruption (10) in the clock. A

modern MCA, operating with an amplifier

set to optimize resolution, will com- plete its sorting function before the

amplifier is ready to accept another

pulse, and thus the system deadtime is

only that of the amplifier. The system

deadtime varies with the choice of amplifier parameters in the range 5 - 80 us. The best resolution is obtained for the

longest shaping time constant, and conse- quently, the longest deadtime. Values ob75 us 144 eV

47 us 147 eV

30 us 152 eV

17 us 169 eV

tained from measurements on a typical system are as follows, where the resolution

is measured as the FWHM at Mn Ka at a count rate of 1000 cps:

Shaping time Pulse width Resolution

8 us

6 us

4 us

2 us The deadtime correction method which

is discussed here is only one of the methods currently in use, but it seems to be

very popular. Other methods are available

but are beyond the scope of the present

discussion. The circuitry of the deadtime correction section of the signal processing system is capable of making a sufficiently accurate correction to satisfy most practical analysis situations.

The analyst must not, however, presume

that he can use any arbitrary high count

rate with the assumption that the deadtime

correction will automatically accommodate

that rate. Indeed, at high count rates,

peak pile-up loss becomes significant.

Every pulse in a double energy peak represents the loss of two pulses from the parent peak. In the generalized schematic

diagram of Figure 7, pulses lost from a peak due to pile-up are not correctly ac- counted by the deadtime circuit. However,

by using a count rate where the sum peaks

are not in evidence in the sr<=>ctrum, this

effect is reduced to an accej. able level.

For those applications where the output count rate of the amplifier is used

directly, such as intensity modulation of

a cathode ray tube for x-ray area mapping

and x-ray line profiling which are applications where a high count rate is especially useful, the analyst should be aware of the following insidious artifact.

58
20 30 , Ml

Input Count Rata IIO^Hzl Fig (10) Relationship of output and input

count rates for the generalized system of

Figure 7 for three different values of the

pulse width.

In Figure 10, the output count rate

measured at point (5) in the system

schematic, Figure 7, is plotted as a function of input count rate at point

(7) . The, output count rate increases

wit^ increasing input count rate only

up to a certain point. The arrival of

pulses eventually becomes so frequent

that the rejection process begins to

dominate, and a point of diminishing

returns is reached. Further increases

in the input count rate actually lead to

a decrease in output count rate. Operation in this high count rate region can

lead to errors in analysis. Due to the

shape of the roll-off, the same output

count rate is observed for two widely

different input count rates, which could

correspond to two different specimen

compositions.. Note that the input count

rate refers to the entire spectrum from

the beam energy down to the pre-set

threshold (typically several hundred eV)

and not to the count rate of a particular

peak or range of energy being viewed in

the MCA. Thus, if a 30 keV beam is used

while the MCA monitors the x-ray range

0-10 keV, x-rays generated in the range

10-30 keV must still be considered as part of the total spectrum count rate.

For a typical system where resolution

is emphasized, the input count rate

should not exceed about 5000 cps.

Through the shaping time parameter, it

is possible to achieve a higher limiting

count rate at the price of system resolution. Curves in Figure 10 show the

count rate response as a function of

pulse width. This figure shows general

trends; the exact curve varies with each

system.

Artifacts of the Detector/Microscope

System

Microphony

The Si(Li) spectrometer contains a detector and electronic circuitry of

extraordinary sensitivity which can respond to radiation of energies other

than x-rays. In particular, stray

electromagnetic and acoustic radiation

can affect the recorded x-ray spectrum.

The coaxial cable through which the

detector/pre-amplif ier communicates with

the main amplifier must be carefully

routed to prevent it from becoming an antenna. The detector must be shielded

against mechanical and acoustic vibration

to which the detector acts as a sensitive

microphone. The analyst can move a poorly routed cable to eliminate electromagnetic interference but is generally

powerless to do anything about the

mechanical isolation of the detector.

Thus, it is important when evaluating a new detector prior to acceptance to

check for microphonic and antenna effects.

In Figure 11(a), a spectrum obtained

under non-microphonic conditions contains

characteristic peaks and a continuum

spectrum with a typical shape showing

cutoff at low energies due to absorption

in the beryllium window. In Figure

11(b), the same spectrum was recorded

with several sources of mechanical and

acoustic vibrations in the vicinity of

the detector — the operation of a wave- length dispersive spectrometer motor,

conversation, etc. The detector res- ponded to these sources, producing an extremely high background in the region

from 2 keV down to keV. The characteristic peaks are broadened due to the

noise in 11(b) as compared to Figure 11

(a) . While virtually every detector has some microphonic response to high intensity noise, the detector should be

isolated well enough to be insensitive

to normal laboratory environment noise

and vibration. The response in Figure

11(b) is quite unacceptable.

The main amplifier should also be

carefully positioned. In general, it

should be kept isolated from

transformers and devices containing

extensive logic circuits such as com- puters or scalers.

Sensitivity to Stray Radiation

Origin . One of the features of the

Si(Lil detector which is normally con- sidered a great advantage is the rela59
CfK«

CrFe Alloy E„=15l<eV

FeK^

FeKP

J. ^^'^'^'^'•''''^i^^^'''''^^^^ V V L^

E (k«VI '0 Fig (11) (a) Electron-excited spectrum of

chromium- iron alloy. (b) Spectrum obtained under same beam conditions as (a) but

with acoustic interference.

tively large solid angle of collection

as compared to the focusing wavelengthdispersive spectrometer. The solid

angle of collection is usually considered from the point of view of the

electron-excited source in the specimen,

with the apex of the cone placed at the

beam impact point, Figure 12. To

appreciate the complete collection

situation, however, we must also consider

the solid angle of collection from the

point of view of the detector, Figure 12.

It is obvious from Figure 12 that the

true solid angle of collection is very

large indeed, including not only the

entire specimen but often a large portion

of the sample stage and chamber walls.

The difference in the collection angle

between the points of view represented

in Figure 12 would be immaterial if the

excitation were really confined to the

volume directly excited by the focused

electron beam. Unfortunately, excitation can occur at a considerable distance from the region of impact of the

focused beam. A schematic diagram of some typical sources of this remote excitation

is shown in Figure 13, Electron- induced

remote sources include scattering from

apertures, backscattering from the

specimen, and re-scattering from the

polepiece. In this regard it should be

noted that a significant fraction of the

backscattered electrons from heavy

elements retain 50% or more of the

incident energy and are thus capable of

exciting x-rays from the specimen'

environment (walls, stage, polepiece).

Interaction with several surfaces is

possible before an electron comes to

rest. X-ray induced remote sources

Noisa

Cr-Fe Alloy E.=15lctV

CrK«

''<. FcKh

>CrK(»ji

" E IkeVI

originate principally from characteristic and continuum x-rays generated by

those electrons which strike the upper

surface of the final beam-defining

aperture. These x-rays can propagate

through the aperture and illuminate

a large portion of the sample chamber as an x-ray fluorescence source. The

significance of this source of remote

excitation depends on (a) the material

of the aperture, (b) its thickness, and

(c) the beam energy. Thin film "selfcleaning" apertures of molybdenum

produce a strong source of remote excitation, since self-absorption of the MoKot (critical excitation energy, 20 keV)

radiation is low and the thin film (12.5

ym) transmits about 78 percent of the

radiation. Considering that this final

aperture may intercept 80 percent of the

total beam, it is obvious that the x-ray

fluorescence effect can be extremely

deleterious to accurate analysis^".

Recognition . It is not always

obvious that a remote source exists, but

its effects can usually be recognized by

employing the following procedure. A

Faraday cup is fabricated from a block

of metal (iron, brass, titanium, etc.)

e.g., by drilling a blind hole of 3 mm

diameter and a few mm in depth and

press fitting a microscope aperture (20

ym to 100 ym diameter) into this hole,

Figure 14. The aperture material should

be different from that of the block.

Spectra are then recorded with the

focussed beam alternately in the hole,

on the aperture material, and on the

block. If no remote sources exist, then

with the beam falling into the aperture

no spectrum should be obtained. If this

so-called "in-hole" spectrum contains

x-ray signals of the Faraday cup materials, then the ratios of the intensities

60
Polepiece

Fig (12)

the point

Solid angle of collection from

of view of the specimen (dense

hatching) and from point of view of EDS

detector (light hatching)

.

)f the characteristic lines to the

'alues obtained from the spectra of the

iperture and block are an indication of

:he magnitude of the problem. For

example, a strong signal for the aper-

:ure material in the in-hole spectrum

.ndicate a source of radiation in the

'icinity of about 1 mm of the beam,

.'hile a high signal for the block

laterial indicates a more distant

Jource, The extraneous radiation has

)een observed to be as high as 20 per-

;ent and is typically between 0.01 and

. percent^°of that obtained with the

>eam directly on the aperture. Exam-

.nation of the peak-to-background ratio

if characteristic peaks observed in the

n-hole spectrum can also indicate the

ype of remote excitation — electron or

;-ray. Excitation by x-rays produces a

luch lower continuum. If the peak-tolackground ratio is higher in the inlole spectrum than in the directly

excited spectrum of the aperture or

ilock containing the element, the remote

xcitation is most likely by x-rays.

Observation of characteristic lines

if the chamber wall or stage materials

^ndicates excitation at great distances

ronv the beam- impact on the specimen,

n this respect, it should be noted that

flat non-tilted specimen and a specimen

if rough surface may behave differently.

L rough specimen is more likely to

catter electrons in all directions to

he surroundings, whereas the backscatered electrons from a flat, specimen

lormal to the beam follow a cosine

distribution peaked about the normal,

'ith little scattering in the horizontal

I lane

.

Objective Lens

\ Beam Forming

\ ^^/^Aperture

/

/ \

Si (Li) Detector

/

/ 2 — I r

1"

I1/ -.-—/

Fig (13) Possible sources of remote x-ray

excitation in an electron beam/EDS system.

Solid lines - electron paths; dashed lines

- x-ray paths.

Correction of Stray-Radiation Problems

Eliminating stray radiation following its recognition is very much dependent on the particular instrumental

configuration. General guidelines only

can be given here.

X-ray fluorescence problems originating in the final aperture can be

minimized by: (1) use of thick apertures

and (2) choosing aperture materials of

higher atomic number, such as platinum

or tantalum. Typical beam energies (30

keV or lower) are insufficient to generate K x-rays, and the L lines of both

materials have energies of less than 10

keV. For apertures of 12.5 ym thickness, the transmission of La x-rays of

the aperture material is less than 3 percent for Pt and 4 percent for Ta.

Transmission of 20 keV continuum is 6 percent for Pt and 15 percent for Ta

.

Electron scattering problems are more difficult to deal with. Apertures

should be kept clean, as debris particles on the circumference can produce

unwanted scattering. Electrons often

scatter in the column and pass around

apertures if passages exist. Aperture,

alignment should be optimized. Double

apertures can be employed with some success, although their alignment is

difficult.

Scattering from the specimen is

difficult to control, especially if the

sample is rough, such as a fracture

surface. Adjacent stage, polepiece, and

chamber wall surfaces can be coated with

carbon-dag or beryllium sheets to prevent generation of characteristic x-rays

61
Pt Aperture

^

100

4

H-m Hole

J

Ti Block

Carbon Backing

Fig C14] Schematic illustration of cross- section through a Faraday cup suitable

for detecting remote sources of radiation,

in the energy region of interest by the

scattered electrons. After all obvious

sources of remote excitation have been

minimized, a remnant "in-hole" spectrum

may still exist. This "in-hole" spectrum can be subtracted from that of an unknown, but the procedure is risky,

since the background spectrum may depend

on scattering from the specimen, and the

surroundings of the specimen and the

standard.

Direct entrance of electrons into

the detector . The Si (Li) detector is

capable of responding to an energetic

electron which enters the active region

of the detector. A pulse is developed

the height of which is a measure of the

energy of the electron. When the beam

electrons strike the sample, a significant fraction, about 30 percent for

copper with a beam normally incident,

are backscattered with a wide energy

range. Many of these backscattered

electrons retain a substantial fraction

of the incident energy. It is inevitable that some of those electrons will

be scattered in the direction of the

detector. The beryllium window with a typical thickness of 7.6 ym (0.3 mil) is

capable of stopping electrons with an energy below about 25 keV. The range of

electrons incident upon a 7.6 ym beryllium film as a function of energy accor- ding to the range equation of Heinrich^^

is shown in Figure 15. Above energies of

25 keV, electrons will begin to penetrate

the window and activate the detector,

although with a loss of e°^rgy due to

inelastic scattering in t beryllium.

When higher energy (>25 k^ beams are employed, the electrons which enter the

detector can have a substantial effect

on the background. An example is shown

in Figure 16 for a 40 keV beam incident

Fig (15) Range of electrons in beryllium

predicted by the equation of Heinrich (21)

7x10

z = '^-^

(E

3 P

p (g/cm ) ,E(keV) ,z (pm)

1-65 1-65

)

In

on arsenic. The background below 20 keV

is greatly distorted by the electron

contribution added to the expected

x-ray continuum as shown by the solid

curve. Above 25 keV, the background is

mostly due to the normal x-ray continuum;

virtually no electrons are able to

penetrate the beryllium window and

retain energies in this range. Note

that the analyst usually examines the

region between 0-10 keV or 0-20 keV.

the example of Figure 16, it may not be

obvious that the background is anomalous

unless the entire spectrum is examined.

Artifacts arising from scattered

electrons entering the detector can be

eliminated with magnetic shielding in

front of the detector snout. In the

windowless variety of Si (Li) spectrometer,

such shielding is an absolute necessity.

The artifact may become more pronounced

for samples with a high atomic number or with surfaces highly tilted relative to the beam. These two conditions will

produce the greatest number of high

energy backscattered electrons. Light

element targets which are flat produce a relatively minor effect. Operation with

an acceleration voltage below 20 keV

will also minimize the effect.

Contamination Effects

Contamination deposited during the

electron beam-specimen interaction may

considerably affect the measured x-ray

intensities. The effects of contamination are observed regardless of the

62
AsL« CuK« AsK« 16-4

K

iKr

Arsenic

E,= 40keV

SI absorption adg* "^/^ .

TIK«

ElktV) Fig (16) Electron-excited spectrum of

arsenic showing background below 25 keV

due to electrons entering the detector.

type of x-ray spectrometer which is

employed, but the capability of the

energy dispersive spectrometer to measure the entire spectrum makes the

recognition of such artifacts easier.

The rate of contamination of a specimen is a complicated function of

many parameters — current density, beam

energy, specimen character, residual

gases in the vacuum system, and extraneous substances which exist on the

surface of the specimen^^. Generally,

the rate of contamination increases with

increasing beam current density. Thus

contamination effects are more noticeable when the electron beam is fixed on

a point of the specimen as compared with

a scanning raster. Contamination from

previous bombardment can often be recognized in images due to differences in

the secondary electron emission in the

contaminated area compared to the rest

of the specimen. In such cases, x-ray

emission will often be affected as well.

The build-up of a contamination

layer on a sample would be intuitively

expected to affect the measured x-ray

intensities through differential absorption effects, i.e., low energy lines

would be more strongly absorbed than

high energy lines. The following experiment, performed on an SEM in which

contamination was very much in evidence

in images, reveals the reverse behavior.

X-ray spectra were recorded on polished

bulk samples with normal beam incidence,

a beam energy of 17.4 keV, and an x-ray

take-off angle at 30° above the surface.

Two cases were measured: (1) beam in a focused, fixed, position and (2) beam

scanned over an area of 100 ym x 100 ym.

Fig (17) Electron-excited spectrum of

carbon from an unsatisfactory detector

showing an extremely thick silicon dead

layer

.

The ratios of intensities of the elements measured in the point mode spectrum- to the scanning mode spectrum are given in Table 1. A consistent decrease

in intensity with increasing x-ray

energy is observed in the point mode as compared to the scanning mode. The

deviation reaches 10 percent at the

highest energy measured. Clearly, this

is not an absorption effect, since the

most energetic lines are the most

strongly affected. A plausible explanation of the effect is that the increased build-up of contamination in the

point mode causes the incoming electrons

to lose a portion of their energy due to

inelastic scattering before reaching the

specimen proper. This energy loss

reduces E , the initial interaction

energy in°the sample. Characteristic x- ray emission, I is strongly dependent

on the difference between E and E , the critical excitation energy:

I «(E -E^)

p

^ c-^ 1.7

The difference (E -E ) decreases as the

critical excitation energy increases for

a fixed value of E . A decrease in E due to contamination will thus have a larger effect on the intensity of the more energetic radiation, since (E -E ) is smaller. This effect is calculated

in Table II. The real behavior observed

in the experiment of Table I is a combination of the absorption effect and

overvoltage effect. Absorption affects

the low energy x-ray lines most strongly

63
Table I Effect of Contamina i.ion on X-ray Signals Observed from NBS Glass K-309

Element

Al

Si

Ca

Ba

Fe

Line

Ka

Ka

Ka

La

Ka

Energy

(keV)

1.49

1.74

3.69

4.47

6.4

Point to Area

Rat io

.98

.97

.93

.93

.90

Table II Calculation of Predicted X-ray Intensities from NBS Glass K-309

^ab (E -E ) ^ C-'

15

1.7

Si

Fe

Cu

1.838

3.607

7.111

8.980

79.955

62.558

33.492

21.150

while the decrease in (E -E ) affects

the high energy lines. ¥he*^experiment

indicates that the overvoltage effect

dominates

Contamination problems can be

significantly reduced with proper attention to the vacuum system and to specimen preparation. For conventional

systems with oil diffusion pumps, the

use of liquid nitrogen cold traps and

chilled surfaces in the specimen chamber

is invaluable. Diffusion pump fluids

which decompose to gases rather than a solid deposit are available^ ^. It is

important to recognize that much of the

contamination routinely observed results

from residual substances on the specimen

(oils, etc.). Careful solvent cleaning

and vacuum baking can frequently remove

such substances and greatly reduce

contamination.

Initial Detector Set Up and Testing

The wide variety of Si(Li) spectrometer — MCA systems precludes a specific description for proper set up

and testing which is applicable to all

instruments. The manufacturer provides

specific instructions on the proper

installation and adjustment of his

instrument. It is usually left to the

analyst in the field to make the actual

E = 14.5

o (E -E ) 1.7

74.86

57.962

29.963

18.251

^P(14.5)/^pC15]

0.936

0.926

0.895

0.863

installation. In this section, we shall

provide some general guidelines and

suggestions to supplement the manufacturers' procedures in order to highlight

the critical areas in the operation of

these systems

(1) Before the Si(Li) detector is

installed on the instrument, it is very

useful to test the system separately by

activating the detector with a radioactive source, preferably Fe^^. The

Fe^^ source emits MnKa and MnKB x-radiation with negligible continuum. The x- ray spectrum of this source should be

recorded with the detector placed on a vibration- free surface such as plastic

foam at least 5 cm from the source. The

amplifier should be electrically isolated

from other electronics. The manufacturer's instructions for setup for

optimum resolution should be followed.

The total spectrum count rate should be

1000 HZ or less, A total of 100,000, or more, counts should be collected. It is

best if this spectrum can be retained in

digital form by storage on magnetic or paper tape. If digital recording is

unavailable, the spectrum should be

written on graph paper in several scale

expansions centered about MnKa. The

merits of this source spectrum are the

following

64
(a) The source spectrum serves as a permanent reference to the as-received

condition of the system. In the event of

a question arising in the future about the

quality of the system, a benchmark is

available

.

(b) The resolution in the as-delivered condition can be measured at the us- ual value, the FWHM for Mn Ka

.

(c) To measure the degree of incomplete charge collection, the peak-to-tail

ratio and the asymmetry of the MnKa peak

should be determined. The peak-to-tail

ratio is typically measured by taking

the ratio of the counts in the peak

channel of MnKa to the counts in a background channel at half the energy of

MnKa. Because of the low background

counts, an average over at least 10

channels should be used. For a typical

detector, this ratio should be about

1000:1. The asymmetry of the MnKa peak

is typically determined by measuring

the full width of the peak at one-tenth

the maximum amplitude (FWTM) . The FWTM

should be no worse than 1.9 FWHM.

(2) After installing the spectrometer on the SEM or EPMA, a spectrum

should be obtained from a manganese

target excited with a 15-20 keV electron

beam at the same count rate and total

MnKa counts as the reference spectrum.

The resolution measured on this spectrum

should not be degraded by more than a few eV over the reference spectrum. If

the resolution has deteriorated significantly and/or large numbers of counts

are observed in the low energy region,

e.g.. Figure 11(b), there are several

possible sources of trouble: microphony,

lack of electrical ground isolation between

circuit components (ground loops) , and

stray radiation from transformers,

computers, etc. Remedies for these

problems depend on the local situation.

Ground loops can usually be eliminated

by connecting all components of the

system" to a single high quality ground

and not interconnecting them.

(3) An eloctron-excited spectrum

should be obtained from spectrographically pure carbon with a scanning beam

to minimize possible contamination.

This specimen should provide a continuum

spectrum which is devoid of characteristic peaks. Such. a spectrum from a typical detector. Figure 6, has the following characteristics:

(a) The intensity o± the lowest

energy channels should nearly reach the

baseline, within about 3 percent of the

intensity maximum in thd continuum hump.

If not, this failure may be indicative

of a poorly set slow channel discriminator, microphony, stray radiation, or ground loops.

(b) A silicon K absorption edge and

a silicon internal fluorescence peak are always observed, as shown in the spectrum

obtained with a normal detector, Figure.

6

In an abnormal detector. Figure 17, the

silicon absorption edge and the silicon

fluorescence peak are much more pronounced, and the magnitude of the absorption

edge will be a function of the bias voltage on the silicon detector.

(4) At this point, the analyst

should examine the entire carbon contin- uum spectrum up to the beam energy for

other artifacts. Specifically, the

presence of any characteristic peaks,

e.g.. Figure 17, is an indication of

stray radiation and a clue to its source.

(5) Spectra should be obtained

from elements which give characteristic

lines throughout the energy range of

interest to check the energy linearity

of the system.

(6) The performance of the pulse

pile-up rejector should be examined as a function of x-ray energy and count rate.

It can be expected that the pile-up

rejector should work well for radiation

as energetic as silicon Ka and greater.

Below silicon Ka, the pile-up rejector

frequently becomes progressively less

satisfactory. Spectra illustrating the

pile-up performance from an optimally

adjusted system (maximum resolution and

maximum allowed count rate). Figure 9(a)

and (b) , show adequate pulse pile-up

rejection for silicon but an almost

total failure for magnesium. A pile-up

continuum below the double energy peak

and even a triple energy peak are observed in the magnesium spectrum. In

the silicon spectrum, only the double

energy peak, which corresponds to coincidence within the time resolution of

the pulse rejector, is observed. As a figure of merit, the area of the silicon

Ka double energy peak should be less

than 1/200 of the parent peak at allowed

system count rates.

(7) For accurate quantitative

analysis, the performance of the deadtime correction circuit should be tested.

The x-ray production in the specimen at

any beam energy is proportional to the

beam current striking the sample. This

fact provides a way to vary the input

count rate to the spectrometer system in

a controlled fashion. A flat, pure

element target such as iron should be

scanned with a beam energy of 15-20 keV.

The current should be set initially to

give a total spectrum count rate of

about 500 HZ. The beam current is

measured in a Faraday cup. The integrated counts across the peak (Peak plus

background) are then plotted as a func65
tion of beam current for a fixed live

time (e.g., 100 s). The plot of counts versus current will be linear over that

count rate range where the deadtime

correction mechanism is functioning

properly.

Qualitative Analysis

Qualitative analysis of energy

dispersive x-ray spectra requires a consideration of basic x-ray physics, a knowledge of the EDS spectrometer system,

intuition, and common sense. From basic

x-ray physics, we require such information as the energies of the family of

lines for each element and the approximate weight of the lines. Knowledge of

the artifacts of the EDS spectrometer

system is needed to identify spurious

peaks in the spectra. Intuition can be

developed as a result of practice.

Finally, the analyst must always be

ready to apply common sense to a problem.

For example, scandium is an exceedingly

rare element, and therefore before

identifying it in the spectrum of an un- known, one should check all possibilities

for other spectral lines.

Typical sources of information on x-ray energies used for qualitative

analysis include "energy slide rules"

available from several manufacturers,

charts, tables^"*, and "KLM" markers

available on sophisticated MCA's. All

of these sources of information are valuable, but each has limitations at

present which can lead to misidentification of peaks. The energy slide rules

are extremely convenient, but frequently

omit lines which are observed in spectra,

such as LI and M-|.^N^„. Since the analyst

has a tendency to identify all lines

from the source of information at hand,

these lines may be misidentif ied.

Tables, such as Bearden's definitive

compilation^"*, are the ultimate reference, but the extraordinary detail of

such tables is overwhelming for practical use. For example, twenty-five L series lines are listed for the heavy

elements, of which nine L lines at most might be seen in analysis under

practical conditions. Existing KLM

markers have the deficiency that certain

lines are not included and usually only

one series CK,L, or M) can be seen at a time. To supplement these sources, a plot of the energies of lines in the

range 1-10 keV observable under practical operating conditions . is given in

Figure 19, The lines are those which

have been observed in the spectra of

pure elements where the full spectrum

integrated count is 5x10^, a condition

considered to be a practical upper limit

(1000 s, live time at 5000 cps) . The

spectra were measured with a 155 eV

resolution detector fitted with a 7 ym

beryllium window. The energies are derived from Bearden's table^"*. This

plot has the advantage that it allows

the analyst to see simultaneously all

lines which might appear at a particular

energy. The plot is useful for assessing situations in which overlap might

exist. At the top of the plot, the

resolution of a typical 155 eV resolution detector is shown as a function of

energy in 1 keV increments.

Guidelines for Qualitative Analysis

The following guidelines have been

developed to give a logical approach to

the problem of qualitative analysis with

the energy dispersive spectrometer. The

problem is sufficiently complicated,

however, that it is difficult to provide

a rote method which cannot fail. The

suggestions are simply guidelines and

not iron-clad rules. The analyst must

use all his resources and be prepared to

deal with unexpected situations. (Note:

We will assume that a 1024 channel MCA

is used with 10 eV/channel, 0-10 keV,

beam energy 20 keV.)

General Guidelines

(1) Always accumulate an adequate

number of counts in the spectrum to give

statistically significant peaks. If it

is difficult to decide whether a peak

exists against the continuum because of

statistical fluctuations in the count in

each channel, then either more counts

should be accumulated to "develop" the

peak or else the analyst should not

identify it.

(2) EDS systems become increasingly

prone to the introduction of spectral

artifacts as the count rate increases.

For a system set up to operate at the

optimum resolution, the total spectrum

input count rate should be kept below

5000 cps.

(3) Try to identify an element by more than one peak. This increases the

confidence with which an identification

is made. In order to excite as many

lines as possible for each element, it

is best to use a high accelerating

potential, 20 kV or more. Specific Guidelines: Major Peaks

(1) Begin with the most intense

peaks and, preferably work downwards in

energy. Reason: The peaks of a given

family, K, L, or M, are generally more separated in energy at the high energy

end of the spectrum and are probably

resolved by the energy dispersive spectrometer.

66
(2) Determine the energy of a large peak. I£ you suspect it is a Ka

peak, look immediately for a KB peak at

about 10 percent of the Ka height. For

K lines of sulfur (2.31 keV) and above,

the Ka-Kg peaks will be resolved with an ordinary 155 eV detector. If peak

ratios are found to be significantly

different than expected, the analyst

should be suspicious of the assigned

identification and consider the possibility of an interference.

(3) If a Ka-KB pair doesn't fit,

try L lines. If an La peak is suspected,

look for the family Lai, 2(1), LBi(.7K

Le2(0.2), Lyi(.08), LY3C.O3), LI (.04)

and Lnt.UlJ. The weignts iistea are only approximate and vary with atomic

number and beam energy. Below 3 keV,

the L family is not well resolved, and

the resultant peak appears asymmetric.

(4) M family lines can be observed

for elements such as cerium and above.

The observed lines are Ma(l) , M3(.6),

M(;(.06), My(.05), and the M..N^ (.01)

transition. Ma and MB are often not

resolved, but since MB is typically 0.6'

Ma a pronounced asymmetry results.

(5) When an element is identified , a ll of its peaks should be marked before

going to the next elemen t. When K lines

are observed at high energies (iron Ka

and greater), look to see if the L lines

for that element can be identified.

Similarly, for L lines of cerium and

above, look to see if the M lines can

also be identified.

When all of the high intensity peaks

have been identified, and the accom- panying families of lines have been

marked, then the remaining low intensity

peaks can be attempted.

Minor Peaks

(1) Sort out the spectral artifacts.

Identify the SiKa escape peaks (E,

.

1.74 keV) which accompany all higft""^"®

intensity peaks with an energy greater

than the absorption energy for silicon K- radiation (1.84 keV)

.

(2) Identify the sum peaks which

result from the coincidence of pulses at

high counting rates. For example, if

there are large peaks with energies E .

,

Eg, and E^, look for sum peaks at 2E.,

2Eg, 2E(.,(E^+Eg), (E^+E^), and (Eg+E^,) . (3) Note that a low level silicon

signal will often be found, caused by

fluorescence of the silicon dead layer at

the surface of the detector at an apparent level of roughly 0.2 percent by

weight in a specimen.

(4) Any peaks remaining after the

above procedure has been carried out have

a reasonable chance of arising from an element rather than an artifact, and

elemental identifications can now be

made. Again, the analyst should start at

high energy and work toward the low

energy end of the scale.

(5) The analyst should always

remember what stray radiation peaks due

to the sample chamber are present in the

spectrum and their approximate magnitude

when assigning elements in the specimen.

If a computer-based MCA is available,

as the final step in a combined qualitative/quantitative analysis, it is invaluable to reconstruct the spectrum and

compare this reconstruction with the

original. In this way, any oversights

can be recognized.

Quantitative Analysis

The subject of quantitative analysis

is covered extensively in other refer- ences and in the present proceedings^^.

For completeness, we shall cover several

major points which are involved in the

first stage of quantitative analysis with

the Si(Li) detector, that is, the extraction of characteristic intensities from

the spectrum.

When we are interested in extracting

accurate values of the x-ray intensities

from the spectrum, close attention must

be paid to the artifacts of the detection

and signal amplification processes.

Particular care must be given to the

count rate limitations of the amplifier.

High counting rates, in excess of 5000

cps, are to be avoided because of potential problems with pulse pile-up-, deadtime correction, peak broadening, and

peak shift.

At the same time, it is important in

quantitative analysis to accumulate an adequate number of counts under the peaks

of interest to reduce statistical fluctuations in the count to an acceptable

level. For example, to reduce the un- certainty due to counting statistics

alone to ±3 percent (99.7 percent con- fidence), at least 10,000 counts integrated under the desired peak are re- quired.

The requirements of a relatively low

counting rate and high values of the

integrated count forces the analyst to use long counting periods, typically in excess of 100 s per spectrum. This

places stringent requirements on the

stability of the electron beam instrument,

and a procedure in which the beam current

is repeatedly monitored to correct for

drift is needed. A principal advantage

of the Si(Li) spectrometer system is its

inherent long-term stability. An analy67
5 6

ENERGY (keV)

Fig (18) Plot of the energies of x-ray lines likely to be observed in EDS spectra

containing about 5,000,000 counts in the full spectrum. The silicon escape peak for

the major line of each series (K,L,M) is also indicated. Solid bars at the top are the

FWHM values produced by a 155 eV (Mn Ka) detector in each 1 keV interval.

tical procedure can be developed in which

stored reference spectra obtained under

standardized conditions are utilized over

long periods of time, e.g., weeks to

months

In the absence of other artifacts,

the two principal modifications which

must be applied to a spectrum to extract

the characteristic intensity are the

subtraction of the background^ ^

' ^ ^ ' ^

under the peak and the subtraction of

peak overlaps^^ '^^ '^' . Both of these

corrections are dependent upon the com- position of the sample which is sought,

and therefore the correction procedures

are usually incorporated into the iteration loop of a matrix correction procedure^ "

.

The analyst who is seeking to carry

out fully quantitative analysis of

unknowns with the Si (Li) spectrometer is

advised to first test his instrument,

spectrometer system, and data reduction

scheme on samples known to be satisfactory for quantitative microanalysis.

Suitable samples which are known to be

microspatially homogeneous and for which

the composition is certified are available from the National Bureau of

Standards, Washington DC, 20234.

Acknowledgements

The authors wish to thank K.F.J.

Heinrich and R.L. Myklebust for their

excellent suggestions and aid in preparing this paper.

68
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2. S.J.B. Reed, Electron Microprobe Analysis , (Cambridge University Press, CamErTTge) 1975.

3. J.I. Goldstein, H, Yakowitz, D.E. Newbury, E. Lifshin, J. Colby, and J. Coleman,

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(Plenum Press, New York) 1975.,

4. J. Henoc, K.F.J. Heinrich, and R.L.

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Washington, D.C, 1973.

5. H. Yakowitz, R.L. Myklebust, and K.F.

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Advances in X-ray Analysis , J.B. Newkirk,

CR. Mallett, and H.C Peiffer, eds . , (Plenum Press, New York)ll, 1968, 287-305.

7. A.E. Bence and A. AlFee, "Empirical

Correction Factors for the Electron Microanalysis of Silicates and Oxides", J. Geol.

76, 1968, 382-403.

8. R. Woldseth, X-ray Energy Spectrometry

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City, CA 94404.

9. D. Gedke, "The Si(Li) X-ray Energy

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Performance", X-ray Spec, !_, 1972, 129 - 141.

10. R. Fitzgerald and P. Ganzel, "X-ray

Energy Spectrometry in the 0.1 to 10 A

Range", Energy Dispersion X-ray Analysis : X-ray and Electron Probe Analysis , ASTM

STP-485, American Society for Testing and

Materials, 1971, 3-35.

11. R.L. Heath, "The Application of HighResolution Solid State Detectors to X-ray

Spectrometry - A Review", Advan. X-ray

Anal. , 15, 1972, 1-35.

12. H.U. Freund, J.S. Hansen, E. Karttunen, and R.W. Fink, "Photon Spectrometry

in the Low Energy Region of 500 eV to 100

keV", Proc. Intern. Conf. on Radioactivity

and Nucl. Spect., 1969, 623-649.

13. E. Elad, C.N. Inskeep, R.A. Sareen,

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Sci. , 20, 1973, 534-544.

14. S7J.B. Reed and N.C Ware, "Escape

Peaks and Internal Fluorescence in X-ray

Spectra Recorded with Lithium Drifted

Silicon Detectors", J. Phys . E: Sci. Instr

5, 1972, 582-584.

69

15. C Williams, "Role of Multichannel

Analyzer in Data Handling", Energy Dispersion X-ray Analysis: X-ray and Electron Probe Analysis , ASTM STP-485, American Society for Testing and Materials,

1971, 125-139.

16. CW. Williams, "Reducing Pulse

Height Spectral Distortion by Means of

DC Restoration and Pile-up Rejection",

IEEE Trans. Nucl, Sci. NS-15(1), 1968,

297-302.

17. S.J.B. Reed, "Pulse Pile-up Rejection in Si(Li) X-ray Systems", J. Phys. E: Sci. Instr., 5, 1972, 1-4.

18. J.M. JakTevic, F.S. Goulding, and

D.A. Landis, "High Rate X-ray Fluores- cence Analysis by Pulsed Excitation",

IEEE Trans. Nucl. Sci., 3, 1972, 392-

400.

19. P.J. Statham, "Pile-up Rejection:

Limitations and Corrections for Residual

Errors in Energy-Dispersive Spectrometers

6, 1977, 94-102.

70. R.B. Bolon and M.D. McConnell, "Evaluation of Electron Beam Tails and X-ray

Spatial Resolution in the SEM", in

SEM/1976, 0. Johari, ed , 1^,1976, 163-170.

21. K.F.J. Heinrich, personal communication. (Details available from authors)

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DISCUSSION WITH REVIETORS

Reviewer I : Could you provide an applicable reference for the numbers given

concerning the natural width of an x-ray

peak, in the first paragraph on "Peak

Broadening"?

Authors : A suitable reference is

L. G. Parratt, Phys . Rev. 44_, 1933, pp.

63-&8. It should be noted that there is some controversy over exact values and

our intention in giving a value for MnKa

was merely to demonstrate how badly a Si (Li) detector will degrade a natural

x-ray spectrum. A MnKa peak of 1000

counts amplitude and natural width of

2.3 eV will be degraded to a peak of

typically 150 eV width and amplitude of

15 counts [assuming 10 eV/channel)

Reviewer I : Please explain what the

"dead layer" (inactive layer] on the

front face of the Si(Li) crystal detector is, and why its presence is unavoidable (which I understand to be the

case) . Can its depth be minimized? How?

Authors : The dead layer is a region in

which the desired electrical properties

of the Si are altered by an excess pre- sence of "dopant" and by the presence of

the gold electrode. The dead layer can

be considered to have two regions. The

first region is a completely inactive

layer of Si which will differentially

absorb incoming radiation. The second

region is a partially active layer in

which an insufficient number of

electron-hole pairs will be collected

for radiation captured in it. This has

the effect of shifting an output pulse

to a low-^r energy. The depth of the

dead layer can be controlled somewhat by

changing the bias applied to the detector. However, other factors determine

the recommended bias. For example, a higher bias will reduce the thickness of

the dead layer and will improve the

charge collection characteristics of the

detector-but the leakage current will

increase and introduce noise which will

degrade resolution.

Reviewer I : It seems to me that in an actual spectrum, it would be difficult

to distinguish among the normal lowenergy tail of a major peak, the asso- ciated absorption edge, and the resulting background shelf. Can this be done

other than by comparison with theoretical fits? How?

Authors: The effect of the background

shelf can be isolated by the use of

monochromatic x-ray lines. For MnKa an

Fe^' radioactive source can be used. For

other x-ray lines it is possible to use x-ray fluorescence. The essense of the

method is as follows. If one wished to determine the peak to tail ratio of

70

CaKa, a thin foil of Ti metal can be

placed above a specimen of, say, CaF in

the SEM. The foil will completely stop

the SEM electron beam, but will transmit

TiKa,K6 and some Bremstrahlung radiation.

Obviously, the thickness of the foil and

the kilovoltage of the electron beam

will have to be correctly chosen. The

detector will then see an essentially

monochromatic source of CaKa x-rays. We

have found that the small deviation

between our theoretical fits and an observed spectrum is mostly explained by

incomplete charge collection.

Reviewers I , III : The authors state in

their introduction that the continuum

"conveys information on the average

atomic number of the specimen". IsTiat are

the features of the continuum which

contain this information and are there

any practical examples of its use?

Authors : For a fixed analysis time and

constant electron beam current and

energy the number of counts in any background channel of the MCA is very nearly

proportional to the average atomic

number of the specimen. Double the

average atomic number of the specimen

and the number of counts in the given

background channel will double. This

fact permits a simple and convenient

estimate of the average atomic number to be made. If the analyst is examining a series of points in an alloy and,

suddenly, all characteristic intensities

seemed too low for one point, he could

use the above property of the continuum

to determine if, for example, an oxide

or carbide phase had been encountered.

On the other hand, the above property

can work against the analyst when "line

profiling" or "x-ray area mapping". If

the background under a peak is a significant fraction of the peak it is possible to encounter situations where the

line profile or x-ray area map is more indicative of the average atomic number

than of the chemical element one is

attemping to analyze for.

Reviewer IV : Many of the commercially

aA'a liable MCA systems offer "data

enhancement" capabilities such as smoothing to reduce statistical noise

and forms of automatic background

subtraction to remove the continuum. Do

the authors have an opinion on the

utility of such features as an aid to

qualitative and/or quantitative analysis

of EDS spectra?

Authors ': At the risk of being labeled

unbelievers in sophisticated statistical

methods we make the following observation: Nothing can beat an unmodified

spectriim with a lot of counts. If a peak stands clearly above the background then it is indeed a peak. How-
ever, smoothing the data with, for

example, a weighted polynomial function,

can alter the statistical variations in

the continuum in such a manner that a novice will very likely see "trace"

peaks where none exist. To explain to a customer the physics of an EDS spectrum

is usually enough. To explain a "smoothed" EDS spectrum is masochism.

For applications where all concerned

understand the underlying statistics

such functions are indeed valuable. In general, we feel that if the analyst is

displeased with the appearance of a spectrum due to statistical noise, he

should gather more counts rather than

push a "smooth" button. In regards to

automatic background correction schemes

a similar argument holds. If the user

trusts and understands the physical or mathematical model he can push the

appropriate buttons and make intelligent

use of the results. But this places a non-trivial problem of documentation on

the manufacturer. The basis of our concern is a fear that the above buttons

are used more often for artistic purposes than physical purposes.

Reviewer IV : The authors have discussed

the excitation of characteristic radiation from the silicon dead-layer of the

detector. Is it possible to obtain

significant secondary radiation from any

of the other components of the detector,

its associated mountings, or its x-ray

collimator?

Authors : For applications of the Si(Li)

detector mounted on a scanning electron

microscope, where the energy of any x- ray will typically be below 30 keV, the

possibility of secondary radiation from

other components in the detector is very

small. Furthermore, the presence of the

continuum tends to mask such signals.

However,, if the counting statistics

permit, it is possible to see the gold

Hjr absorption edge from the gold layer

on the face of tht detector. See figure

6 in the text.

Reviewer I : The experiment described

in the section "Contamination Effects"

indicates that contamination layers

effectively reduce the measured x-ray

intensity for higher-Z elements (Fe) more than for lower-Z elements (Al , Si),

due to predominance of the overvoltage

effect. It has been reported occasionally that an intense stationary beam

has produced a "cratered" contamination

spot with the contamination effectively

removed (or not deposited) in the central, highest-intensity area. Could

not the experim.ental results reported

in Table I have been caused by this

sort of phenomenon? If not, please

indicate why.

Authors : We examined the contamination

spots at high magnification and did not

observe a cratered effect. A cratered

contamination spot would not decelerate

the electrons sufficiently to explain

the effect. It could be that the

brightness of our instrument is

insufficient to cause "cratering".

Reviewer I : In paragraph 2 of "Initial

Set Up and Testing", you recommend that

the Fe^^ test source should be at least

5 cm. from the detector. What is the reason for recommending so great a minimum distance here (Manufacturers'

service people often tape the source to

the collimator.)?

Authors : The degree of distortion to

a peak on its low energy side and the

magnitude and shape of the background

"shelf" extending to zero energy can

be very sensitive to the angle at

which photons arrive at the detector.

Collimation is important. When a test source is taped to the face of the

detector, photons will enter the

detector over a wide range of angles.

If one is merely characterizing the

resolution at FWHM of the detector this

arrangement will more than likely not cause any difficulty. Furthermore, a considerably higher count rate is

available. However, if one is characterizing the peak shape and, or, the

background shelf, it is advisable to move the test source back. We feel

that the shaded area in figure 6 is an example of the above effect. Internal

fluorescence of the silicon dead layer

provides a source of totally uncollimated x-rays since they are generated

exactly at the surface of the active

silicon. The resulting peak is highly

distorted on the low energy side due to

incomplete charge- collection. There is no combination of silicon K absorption

edge and Gaussian peak of the appropriate resolution which will explain the

shape of the continuum below the energy

of silicon in figure 6. Reviewer III : The authors recommend an

Fe ^

' source for initial set up of the

ED system. This is the only source which should be used for the peak-totail check described. However, a Co^^ source has the benefit of producing Fe

K x-rays as well as a 14.4 keV gamma

ray. The presence of two such separated peajcs permits calibration of the

EDS system before installation on the

column. For a beginning analyst who

is not quite sure of the nature of

stray x-rays from his chamber, composition of sample holders or mounts,

contaminant or coating elements in his

"standards", etc., the calibration

capability is more useful than the

71
peak-to-tail measurement. Resolution

can be checked on the Fe Ka line using

equation (3) in 'the text, although this

is not as exact as direct measurement

of the Mn Ka. What comments do the

authors have about the use o£ Co^' as

a calibration source. Authors : We agree the Co^^ is an acceptable calibration source. Our

only objection is that it is a "dirty"

source, emitting several extremely

energetic gamma rays (122 and 136 keV)

in addition to those stated and a significant Bremsstrahlung spectrum. The

higher energy gamma rays could be con- fusing if the amplifier gain settings were initially set low. As observed,

Co^^ should not be used to test the

peak-to-tail ratio.

Fe^^, Co^' and other useful radioactive

standards are available from the

National Bureau of Standards, Office

of Standard Reference Materials. These

are calibrated sources (photons/sec./

steradian) . SRM 4260-B, Fe^% is particularly useful as it is a point

source mounted on a 2.54 cm disk suitable for mounting in the specimen position of a SEM.

Reviewer I : While it is not directly

part of your subject, could you address

a few comments to the question of

whether integrated peak height, or simple peak height (counts in peak

channel) should be used in quantitative

EDS analyses, and why. There still

seems to be considerable confusion

concerning this matter.

Authors : Presumably, the reason for

using only the counts in the peak

channel is to reduce interference from

another, nearby, peak. A better way to

reduce this interference is merely to

integrate half of the peak on the side

opposite from the interfering peak. In another question we note that a natural

x-ray line of 1000 counts amplitude and

width of 2.3 eV is degraded by the

Si(Li) detector into a peak of typically 150 eV width and amplitude of

15 counts. One simply throws away a totally unacceptable amount of information by using the peak channel.

Reviewer I : When peak height or integrated peak height is used in this

paper, does it refer to the usual integration over 1.2 x FWHM?

Authors : In all cases an "integrated"

peak or a "full" peak means the total area of a fitted Gaussian to the data.

"Amplitude" means the number of counts

in a 10 eV wide area centered at the mean energy. This corresponds to one channel of a multichannel analyzer

calibrated with 10 eV/channel.

Reviewer II : The Si (Li) detector has

to be kept at liquid nitrogen temperature. Are there artifacts which would

be caused by accidental failure to maintain that temperature? How would one know if the detector has been damaged

during routine operation?

Authors : Most systems have a circuit

built in, or sold as an option, to

protect the detector in the event of

a warm-up. We strongly recommend such

a circuit. When warm-up occurs the

analyst is alerted by either an alarm

buzzer, or the detector simply stops

working. In the event that a protection

circuit is not available the analyst

might initially see a deterioration in

resolution and an increase in noise at the lower energy end of the spectrum,

such as seen in figure lib. Since the

detector assembly is cryogenically

pumped a temperature is eventually

reached where increasing pressure will

permit a detector bias induced gas discharge to occur. This discharge can destroy the FET of the preamplifier.

With modern day Si (Li) detectors it is

possible to survive a number of warm-ups

without ill effects (if the bias supply

has been turned off). However, this is

not one of the manufactures specifications which we recommend testing.

Reviewer II : What artifacts would be

observed due to a vacuum leak in the

detector? What artifacts would be

observed in a windowless detector due

to ice build-up (from moisture in the

environment) and or contaminants on the

detector surface?

Authors : Again, a vacuum leak sufficient to cause a gas discharge to occur

can cause destruction of the FET in the

preamplifier.

The build up of ice and/or contaminants

causes the following difficulty. One of

the most important characteristics of

the Si(Li) "chip" is its surface resistance. Anything which will degrade

this parameter will degrade the performance. Differential absorption of

low energy x-rays will also occur in

the surface layers of contamination.

RE l/i EWERS I C. W. AndAeiOi

II 0. JohoAi

in W. C. BoAbl

11/ . F. SchambiA

11
Appendix 2

2a. General Variables

Subscripted Variables (Element Number J)

A(I) Atomic weight for atomic number I

B(I) K6/EK ratios for atomic number I

C(J) Mass fractions

D(3,3) Coefficients for computing the constants

in mass absorption coefficient equations.

ECI,J) Energies of absorption edges (edge number I).

G(I,J) Energies of x-ray lines (line number I).

H(I,J) Mass absorption coefficients (absorber I).

K(I,J) Coefficients for computing energies of

absorption edges (edge number I)

.

L(J) Code number for x-ray lines: Ka = 1

,

Lai = 2 , Ma = 3, etc.

0(J,J) Characteristic fluorescence correction

(all terms that are independent of C(J)).

P(J,J) Code numbers for, identifying the characteristic fluorescence correction.

none

1 Ka exciting Ka

2 La exciting Ka

3 Ka exciting La

4 La exciting La

5 Ka exciting Ma

6 La exciting Ma

R(I) Edge jump ratios (edge number I).

T(I,J) Coefficients for computing energies of

x-ray lines (line number I)

.

V(J,J) Overvoltage or, after line 6394, backscatter factors (R)

.

Z ( J) Atomic numbers.

73
2a. General Variables (Continued)

B. Unsubscripted Variables

D2 Detector Efficiency, P^

EO Operating voltage (in kV) , E ,

LI Memory address for a particular channel

number.

L9 Switch for computing line energies

(L9 = 2) or edge energies (L9 = 1)

M3 X-ray emission angle ip

N Number of elements in specimen.

N3 Switch: If N3 = 0, compute standard intensity ratio from known concentrations. If

N3 > 0, compute concentrations in unknown.

N3 + 1 is the number of iterations.

N4 Switch for analyzing more than one similar

unknown point. For first point, N4 = ; for additional points N4 is set to 1 by

the program.

N9 N9/10 is the number of element standards

currently in the standards data file.

P6 Thickness of Be window on detector (cm)

,

*BeP7 Thickness of Si dead layer in detector

(cm), tg^.

Ql CSC ^.

Q2 Initially, the electron beam incidence

angle, 9. After line 1470, sin 9.

Q3 Initially, the full-width at half -maximum,

FWHM, for Mn Ka (eV) . After 1485, Q3 = [(Q3)^ - 14737.5] which is used for computing

peak widths, a , as a function of en^ -'gy.

Variables used as index variables unless otherwise defined:

I, J, Ml, M3, Jl, II, 12, Kl, L2, Bl, Tl, Dl , Nl, K2.

74
2b. Local Variables (for listed subroutines only)

Main Program for Standards (100-390) (For subscripted

variables, the element number is J).

M(J)

Q(J)

W(J)

El

Kl

Background-and overlap-corrected intensities (counts)

.

Valence for each element.

Same as M(J)

.

Operating voltage, E (eV) .

One half of the width integrated for

each peak in units of the standard

deviation, a, for a Gaussian peak.

B. Main Program for Unknown (500-900)

Q(J) Background and overlap corrected intensities for pure elements (counts)

.

C. Subroutine for coefficients and constants (1000-1495)

All variables are global.

List of functions:

FNA(I

FNE(I

FNC(I

FNN(I

FNS(I

FNG(I

FNF(I

FNJ(I

FNL(I

Returns the contents of MCA channel I to the calling routine.

Returns the energy (kV) of MCA channel I.

Returns computer memory address of MCA

channel I

.

Returns the MCA channel number of energy I Returns peak width (standard deviation,

a) , of energy I

.

Returns x-ray line energy of the measured

line of element I.

Returns the atomic number (I) dependence

of the Lai/Ka ratio.

Returns the mean ionization potential for

atomic number I.

Returns the logarithmic integral for I.

75
2b. Local Variables (Continued)

FNM(I) Returns the Ma/Lai ratio.

D. Subroutine for computing x-ray line and edge energies

(1500-1610)

Zl In (Z(J)); natural logarithm of the

atomic number.

E. Subroutine for computing mass absorption coefficients

(1700-1980)

Al Mass absorption coefficient, y = C,X .

C2 Constant in absorption coefficient equation (C^, C^^, C^J.

El Energy at which absorption coefficient

is computed.

Zl In (Z(J))

F. Subroutine for computing detector efficiency (2000-2095)

Al Mass absorption coefficient ij(A,I).

A3 tgg y(X,Be)

A4 t^^ u(A,Au)

G. Subroutine for computing primary absorption in specimen,

f (2100-2140)

P

A2 Absorption coefficient y(X,I)

El Energy of x-ray line (E^).

Fl f , the absorption factor.

Gl Y sin = (E "^'^^ - E,^*^^) sin 9. o 1

X3 X = y ('^ > I) CSC ^ .

H. Subroutine for computing the continuum background

(2200-2620)

F(1,J) Primary absorption factor for specimen,

f . P

76
2b. Local Variables (Continued)

M(I) Integrated counts in the region of

interest I, (ROI(I))

.

U(I) ^^O'^l^^ ^^'^ ROI(I).

W(I) Mean energy (kV) o£ ROI(I)

X(I) (^^0"^1^ ^°^ ROI(I).

Y(I) M(I)/T1.

Al y(X,I) mass absorption coefficient.

N

A2 y = E [C(I) * y(X,I)] average mass

1 = 1

absorption coefficient.

Dl X(0) U(l) - U(0) X(l).

El Same as W(I)

.

Fl f absorption in specimen.

P ^ ^ Gl Tl * (Kl * Xl^ + K2 * XI)

.

G2 Number of MCA channels in a region of

interest

.

Kl Quadratic coefficient in background

equation (Y(l) X(0) - Y(0) X(1))/D1.

K2 Linear coefficient in background equation

(Y(0) U(l) - Y(l) U(0))/D1.

Tl fp * P^/E^.

T5 Contents of a region of interest.

XI Eg-E^

I. Subroutine for storing information on standards in a file (2700-2920)

M(J) Integrated intensity in counts (background

and overlap corrected) for a pure element.

Q(J) Valence of element J if oxygen is to be

computed by stoichiometry

.

77
2b. Local Variables (Continued)

J. Subroutine for computing the overlap factors (3000-3450)

M(J) Total calculated integral of Gaussianshaped peak plus incomplete charge

collection.

S(I,J) Relative weights of x-ray lines (line

number I)

W(J) Same as M(J)

D3 4 standard deviations, 4a, for a peak.

El Calculated integral of lower energyhalf of peak.

E2 Calculated integral of upper energy

half of peak.

E3 Lower energy limit of integral.

E4 Upper energy limit of integral.

E7 Energy of an x-ray line.

E8 Result of integration of Gaussian peak.

G4 Result of integration of incomplete

charge collection function.

02 Computed overlap factor.

S6 Standard deviation, a, for a peak of

energy E7.

T5 (a) Contents of a ROI , or

(b) The energy of an interfering x-ray

line

X2 Value to be integrated by erf(X2)

X2 = ((E3 or E4) - E7)/(S6*/2") or in line

3340, X2 = 1/ln (U^Uj^)

K. Subroutine for computing each type of interference for

subroutine J (3500-3850)

S(I,J) Relative weights of x-ray lines (line

number I)

78
2b. Local Variables (Continued)

Computed x-ray cross-section for edge I.

Computed integral of measured peak.

Fluorescence yields for K, L, or M lines

Relative x-ray cross -sections

.

U(I)/U(K1) where Kl is measured line, I is any other line.

4 a for a peak.

Overvoltage EO/E(I,J).

Part of cross -section equation

1166 ECI,J)/FNJ(Z)

.

Energy of x-ray line.

Integral of overlap fraction.

Overlap factor for one peak on another.

Weight of Kg line, K6/EK.

Standard deviation, a, for energy E7.

Relative weight of escape peak to parent

peak.

X-ray line energy for an analyzed line.

E1*E2

L. Subroutine for storing overlap factors in a data file

(3860-3886)

E9 Index for determining proper memory

address

.

12 Line code of the overlapping line.

02 Computed overlap factor.

X2 Computed overlap factor * 100000.

U(I)

W(J)

X(I)

A1,A2,A3,

A4,A5

D3

El

E2

E7

01

02

Rl

S6

S8

T5

XI

79
2b. Local Variables (Continued)

M. Subroutine for computing overlaps by escape peaks

(3890-3990)

Al

D3

El

E7

S6

S7

S8

T5

Mass absorption coefficient.

4 a for the overlapped peak.

Energy of the parent peak that produces

the escape peak.

Initially the same as El, then the energy

of the escape peak (El-1.74).

Sigma, a, for the escape peak.

Factor in expression for relative weight

of escape peak.

Relative weight of escape peak.

Energy of peak overlapped by escape peak

of energy E7.

N. Subroutines for integrating the overlapping area of any

peak (4000-4130)

E2

E3

E4

E7

E8

G4

01

S6

X2

Integrated area from lower energy limit,

E3, to center of Gaussian peak.

Lower limit of integration.

Upper limit of integration.

Energy of the Gaussian peak.

Integrated area from center of Gaussian

peak to upper limit, E4.

Integrated area of incomplete charge

collection . Total integral of overlap area.

Standard deviation, c, of Gaussian peak

of energy E7.

Function to be integrated bv erf(X2)

X2 = ((E3 or E4) - E7)/(S6*/T).

80
2b. Local Variables (Continued)

0. Subroutine for computing the integrated area of the

incomplete charge collection (4200-4400)

E7 Energy of the x-ray peak.

G4 Calculated integral of the incomplete

charge collection expression

G4 = XI * (S3)2[l - exp(X2)*(l - S2)].

XI, X3 Empirical fitting coefficients for the

incomplete charge expression.

X2 [(E3 or E4) - E7]/X3 where E3 and E4 are

the integration limits.

P. Subroutine for the integration of the areas under

Gaussian peaks by integrating erf(X) (4500-5090)

All variables in this subroutine are used only within

the subroutine.

E8 Area calculated by the integration.

X2 The argument to be integrated.

X2 = [(E3 or E4) - E7]/(S6 * /7) . All other variables in this subroutine are not

individually defined but are listed for information.

They are all temporary variables and their values

are not used in the rest of the program.

A5 F3 81

Bl F4 82

CI Gl Tl

Dl G2 T2

E9 G3 Ul

Fl P2 Wl

F2 P3 Yl

Y2

81
2b. Local Variables (Continued)

Q. Subroutine for correcting overlaps using the overlap

coefficients (5100-5390)

F(3,J) Detector efficiency, Pp , times primary

absorption factor, f , for element J.

M(J) Integrated counts in peak of element J.

W(J) Integrated counts in peak of element J

corrected for overlaps.

Al Mass absorption coefficient y(X,J)

A2 Average mass absorption coefficients

N

y = E C(J) * y(X,J).

J=l

El' Energy of an x-ray line.

Fl Primary absorption factor, f .

Gl Line code of an overlapping peak.

Rl Number of counts in overlapping region.

Yl The computed overlap factor.

R. Subroutine for computing the matrix (ZAP) correction

(5500-7150)

F(I,J) Absorption factor f (1=0 for standard, 1=1 for unknown. ^

M(J) Number of counts in the measured x-ray

peak or the measured intensity ratio (k)

Q(J) Number of counts in a peak from a pure

element

S(I,J) Stopping power (S) (I = other element

number)

U(J) Overvoltage (E /E ) ..

W(J) Number of counts in the measured x-ray

peak corrected for background and overlap

82
2b. Local Variables (Continued)

Al Mass absorption coefficient, yC^>I)-

A2 Average mass absorption coefficient, y.

A3 y" of exciting x-ray line in fluorescence

correction.

Bl Initially, the edge number of a measured

x-ray line. Then one of the factors in

the secondary fluorescence correction.

C1,F3, Factors used for determining if the

L2,P3 secondary fluorescence correction is

needed.

Dl In fluorescence correction, the weight

of the x-ray line. P.-, times the

fluorescence yield, oo-l

El Energy of x-ray line.

Fl Absorption ^ factor, f . ' P

F2 Characteristic fluorescence correction

factor.

F4,X1 Intermediate factors for computing the

secondary fluorescence correction.

G1,G2,P2 Intermediate variables for computing the

backscatter correction R.

G3 Computed intensity ratio, k .

G4 Switch for including or omitting the

drawing of the reconstructed spectrum.

51 Summation of mass fractions.

52 Average stopping power, S = EC-S..

Tl Fluorescence yield of K-lines.

T2 Fluorescence yield of L-lines.

T5 Number of counts in a region of interest

Ul Overvoltage E /E . '' o q

83
2b. Local Variables CContinued)

Wl (R/R) CS/S).

X2 Average of backscatter factors, R = EC.R..

S. Subroutine for assigning regions of interest in a TN 1700

MCA. (8000-8140)

El Lower energy limit of a region of interest

peak 1

E2 Upper energy limit of a region of interest

E , + K.o. peak 1

Kl Width factor (K^) : 2 K.a = width integrated

by the region of interest.

SI Standard deviation, a, for an x-ray peak.

T. Subroutine to draw the x-ray peaks predicted by the

program (8200-8595)

F(3,J) f * P^ ^ ' ^ p E

Q(J) Measured intensity for a pure element.

Al Mass absorption coefficient, y(X,J).

A2 Average mass absorption coefficients, y".

El Energy of x-ray peak.

E2 Amplitude of x-ray peak.

E3, E4 Lower and upper energy limits of region

of interest.

Fl f

P

Gl Computed integral within a region of

interest, ETl.

G3 Computed intensity ratio, k . Jl Energy of channel J.

K2 Energy width of integrated peak (in terms

of standard deviation)

84
2b. Local Variables (Continued)

S1,S2 Standard deviation, a, for energy. El.

S6 Peak overlap factor.

Tl Intensity of spectrum at channel J.

T5 Generated x-ray peak intensity for unknown

U. Subroutine for computing an element, for which a line is

not measured, by stoichiometry (oxygen) or by difference.

F3 Oxygen concentration in an oxide.

G3 Valence of an element.

SI Summation of mass fractions.

V. Main program for computing window thickness on a Si (Li)

detector. (This program will overlay main program A)

(100-312)

M(I) The average number of counts per channel

in ROT (I)

.

S(I) The mean energy (kV) of ROI(I).

U(I) In (K1*X1^ + K2*X1) - ln(M(I)) + ln(Fl/El) - A3

X(I) y(X,Be)pg^

Y(I) y(X,Si)pg.

Al Mass absorption coefficient for element I y(A,i).

A2 Same as Al

.

A3 y(X,Au)p^^t^^

Dl X(0) Y(l) - Y(0) X(l)

.

El Same as W(I)

.

Fl f absorption in specimen.

Gl In (M(I))

.

85
2b. Local Variables (Continued)

P2 Iteration number

Tl In (fp/E^)

XI ^0"^1

86
100

120

130

135

140

141

142

143

144

145

146

147

148

149

150

151

152

154

155

160

170

180

181

185

190

200

210

220

230

240

250

260

270

274

275

276

280

285

290

291

292

293

294

295

296

300

310

312

APPENDIX 3

FRAME C

REM THIS PROGRAM READS STANDARD SPECTRA

G0SU3 1000

PRINT "ENTER NO. OF ELEMENTS"

INPUT N

PRINT

CALL 4, (1)

CALL 4,(3)

IF FNA(2)= GOTO 146

LET E0= FNA(2)/1000

GOTO 151

PRINT "ENTER EO (YOUR TOA IS";M3;'•DEG) " INPUT EO

LET E1=(E0+.00001)*1000

LET Ll= FNC(2)

CALL 3, LI, El

LET Ll= FNC(3)

CALL 3, LI,

CALL 4,(3)

CALL 4,(1)

LET Z[N)=4

LET Z[N+1]=14

LET Z[N+2]=79

PRINT

PRINT "ENTER CON, ATNO, LINE CODE AND VALE!

FOR 1= TO N+2

IF I>N-1 GOTO 230

INPUT C[I] ,ZlI] ,L[Il ,Q[I]

PRINT

LET L9=l

G0SU3 1500

IF L[I1= GOTO 280

LET L9=2

GOSUB 1500

IF FNG(I)>=1 GOTO 280

FROM QUADRANT 2

FOR EACH"

"LINE

380

PRINT OF

GOTO

NEXT I GOSUB 8000

LET N3=

CALL 4,(1)

CALL 4,(3)

LET Ll= FNC(5)

CALL 3,L1,K1*10000

CALL 4, (3)

CALL 4,(1)

GOSUB 3000

GOSUB 2200

CALL 4,(1)

Z[I] BELOW 1 KV"

87
316 CALL 4, (3)

320 GOSUB 5100

330 FOR 1= TO N-1

335 LET M[I1=W[I]

340 NEXT I 352 CALL 4,(3)

356 CALL 4,(1)

360 GOSUB 5500

370 GOSUB 2700

380 STOP

390 END

500 REM THIS PROGRAM READS A SPECIMEN SPECTRUM FROM QUADRANT 1 501 REM THE STANDARDS INFORMATION FROM QUADRANT 4 AND PRINTS

502 REM QUANTITATIVE RESULTS. Al , Bl AND DISPLAY ON.

520 GOSUB 1000

530 CALL 4, ( 0)

550 CALL 4,(3)

570 LET N9= FNA(l)

57 5 LET N4= FNA(3)

576 LET Ll= FNC(3)

577 CALL 3,L1,1

579 IF N4=l GOTO 595

580 PRINT "ENTER NO. OF ELEMENTS"

590 INPUT N

591 LET Ll= FNC(4)

592 CALL 3,L1,N

595 LET E0= FNA(2)/1000

596 LET N= FNA(4)

600 PRINT

610 LET Z[N]=4

620 LET Z[N+1]=14

630 LET Z[N+2]=79

635 IF N4=l GOTO 650

640 PRINT "ENTER AT. NO. FOR EACH ELEMENT"

650 FOR 1= TO N+2

660 IF I>=N GOTO 680

665 IF N4=l GOTO 675

670 INPUT Z[I]

671 LET Ll= FNC(900+I)

672 CALL 3,L1,Z[I]

673 GOTO 680

675 LET Z[I1= FNA(900+I)

680 LET L9=l

690 GOSUB 1500

700 IF I>=N GOTO 800

710 FOR J=10 TO N9 STEP 10

720 IF FNA(J)=Z[I] GOTO 750

730 NEXT J

740 GOTO 800

750 LET L[I]= FNA(J+1)

88
760 LET Q[I]= FNA(J+2)

770 LET L9=2

780 GOSUB 1500

790 GOTO 810

800 LET L[I1=

810 NEXT I 815 PRINT

820 CALL 4, (3)

840 CALL 4,(0)

855 GOSUB 8000

860 LET N3=3

865 IF N4=l GOTO 880

870 GOSUB 3000

880 GOSUB 5500

890 STOP

900 END

1000 REM

1001 REM

1002 REM

1003 REM

1005 DIM

1006 DIM

1007 DIM

1010 DIM

1020 DEF

1025 DEF

1030 DEF

1035 DEF

1036 DEF

1037 DEF

1038 DEF

1039 DEF

1040 FOR

1050 READ R[I]

1060 NEXT I 1070 DATA 1, 1 1080 FOR J=

1090 FOR 1=

1100 READ

1110 NEXT I 1120 NEXT J

1130 DATA -3.9793lE-2,-.033916,-8.653

1140 DATA .834903, .442217, .25141,

1150 DATA 2.423, 2.82526, 3.32315, 4

1160 DATA -4. 14925, -.979241, .931913,

1170 DATA 5.5091, 9.03526, 10.2505,

1180 DATA -3.33802, 3.15348, 8.03561,

1190 FOR J= TO 2

1200 FOR 1= TO 16

1210 READ T[I,J]

THIS SUBROUTINE READS

ENERGIES, ABSORPTION EDGE

KB/K RATIOS, AND ELECTRON

EMISSION ANGLES

C[121 ,Z[121 ,L112] ,Q[12] ,EI8,

M[12] ,W112] ,X[3] ,Y131 ,U[12],

0[12,12] ,H[24,12] ,V[12,121 ,P

K[8,21 ,T[16,21 ,R[91 ,A[921 ,B[

FNA(I)= DTA ((I- LCN (118))

FNE(I)= ECL ((I- LCS (134))

FNC(I)=(I- LCN (118))/ LCN

FNN(I)=1000*(I- FNE( 0))/(

FNL(I)=2.905* SQR (I)-3.063

FNJ (I) =9. 76*1+58. 5*1 "(-.19)

FNF(I)=. 2567*1-6. 8176

FNM(I)= EXP (34.165*1-30.02

1= TO 9

IN COEFFICIENTS FOR COMPUTING

RATIOS, ATOMIC WEIGHTS,

INCIDENCE AND X-RAY

121,G[16,12]

F[3,121 ,S[16,12]

(12,121

501

/ LCN (120))

/ LCS (136))

(120)

FNE(IOOO)- FNE( 0))

7* SQR (I)+8.5268)/1.6

1, 1.17, 1.63, 1, 1.16, 1.4, 1.621, 1.783, 1 TO 2

TO 8

K[I,J1

97E-2,-. 228343, 1.25179

.272951

.31172,-7.838

.688906

12.0025,-11.5803

7.4243

89
1220 NEXT I 1230 NEXT J

1240 DATA -1.99726E-2,-. 123941, -.47555, -.060101

1242 DATA -. 117102 ,-. 192466 ,-. 197431 ,-3 . 22523E-3 , ,035676

1244 DATA 2.88553E-3, 9.57107E-2, .092961, 5.05888E-2

1246 DATA -. 390705 ,-. 386042 ,-. 603132 , .322877

1250 DATA 2.22412, 3.29533, 6.84662, 2.52781

1252 DATA 3.22414, 3.83158, 4.01718, 2.48613, 2.29113

1254 DATA 2.49221, 1.69157, 1.7559, 2.0035

1256 DATA 6.17432, 6.14822, 7.75598, .102358

1260 DATA 5.17774, 9.75836, 20.0833, 5.6437

1262 DATA 9.58711, 10.9293, 11.3323, 8.37742, 8.09392

1264 DATA 8.60965, 6.76302, 6.81839, 7.30182

1266 DATA 19.0119, 18.7034, 21.4878, 5.58269

1270 FOR 1=11 TO 30

1280 READ B[I]

1290 NEXT I 1300 DATA .011, .027, .04, .055, .066, .078, .085, .097

1310 DATA .108, .114, .115, .117, .119, .119, .121

1311 DATA .121, .121, .123, .1235, .125

1320 FOR 1=1 TO 92

1330 READ A[I]

1340 NEXT I 1350 DATA 1.008, 4.003, 6.94, 9.013, 10.82, 12.011

1351 DATA 14.007, 16, 19, 20.18

1360 DATA 22.99, 24.31, 26.98, 28.09, 30.97, 32.06

1361 DATA 35.45, 39.95, 39.1, 40.08

1370 DATA 44.96, 47.9, 50.94, 52, 54.94, 55.85

1371 DATA 58.93, 58.71, 63.54, 65.37

1380 DATA 69.72, 72.59, 74.92, 78.96, 79.91

1381 DATA 83.8, 85.47, 87.62, 88.91, 91.22

1390 DATA 92.91, 95.94, 99, 101.1

1391 DATA 102.9, 106,4, 107.9, 112.4, 114.8, 118.7

1400 DATA 121.8, 127.6, 126.9, 131.3, 132.9, 137.3, 138,9

1401 DATA 140,1, 140,9, 144.2

1410 DATA 145, 150,4, 152, 157, 158.9, 162.5

1411 DATA 164.9, 167.3, 168.9, 173

1420 DATA 175, 178.5, 180.95, 183.85, 186,2

1421 DATA 190,2, 192,2, 195,1, 196,97

1430 DATA 200.6, 204.4, 207.2, 209, 210, 210

1431 DATA 222, 223, 226, 227, 232

1432 DATA 231, 238

1440 LET M3=40

1450 LET Q2=90

1454 LET P6=9.165E-4

1455 LET P7=8.579E-6

1460 LET Ql=l/ SIN {M3/57.2958) i 1470 LET Q2= SIN (Q2/57.2958)

1480 LET Q3=149

1485 LET Q3=Q3"2-14737.5

90
1490 DBF FNS(I)= SQR (2500*I+Q3) *4 . 2466E-4

1492 DEF FNG(I)=G[L[I1-1,I1

1495 RETURN

1500 REM THIS SUBROUTINE COMPUTES ALL OF THE NECESSARY

1501 REM EDGE AND LINE ENERGIES

1520 LET Zl= LOG (Z[Il)

1530 IF L9=2 GOTO 1580

1540 FOR Ml= TO 8

1550 LET ElMl,I]= EXP (K[M1, 0] *Zl*Zl+K [Ml , 1] *Zl-K [Ml ,2]

)

1560 NEXT Ml

1570 IF L9=l GOTO 1610

1580 FOR Ml= TO 16

1590 LET G[M1,I1= EXP (T[Ml, 0] *Zl*Zl+T [Ml ,1] *Z1-T [Ml , 2)

)

1600 NEXT Ml

1610 RETURN

1700 REM THIS SUBROUTINE COMPUTES ALL MASS ABSORPTION

1701 REM COEFFICIENTS REQUIRED

1710 DIM D[3,31

1720 LET D[ 0, 0]=-. 232229

1730 LET D[ 0,1]=-. 254471

1740 LET D[ 0,2]=. 256216

1750 LET D[ 0,3]=1. 35917

1760 LET D[l, 0]=4. 07005

1770 LET D[l,l]=4. 76925

1780 LET D[l,2]=l. 15119

1790 LET D[l,3]=-9. 49212

1800 LET D[2, 0]=-6. 22075

1810 LET D[2,l]=-10.3788

1820 LET D[2,2]=-5. 68485

1830 LET D[2,3]=18.6408

1840 LET D[3,2]=2.6

1850 LET D[3,3]=2.22

1860 LET Zl= LOG (Z[I])

1870 LET D[3, 0]= EXP (-4 . 5522E-3*Zl*Zl-6 . 8535E-3*Z1+1 . 07018)

1880 LET D[3,l]=2.73

1890 IF Z[I]<42 GOTO 1910

1900 LET D[3,l]= EXP (-. 11316*Zl*ZH-. 836883*Z1- . 545969)

1910 FOR Ml= TO 9

1920 LET M3=M1+1

1930 IF Ml=9 GOTO 1945

1940 IF E1<E[M1,I] GOTO 1970

1945 LET L1=M1- INT (M3/3)- INT (M3/4)- INT {M3/7)

1950 LET C2= EXP (D [ , Ll ] *Zl*Zl+D [1 ,L1 ] *Zl+D [2 ,L1 ] ) /R [Ml]

1955 LET A1=C2*(12.398/E1)"D[3,L1]

1960 GOTO 1980

1970 NEXT Ml

1980 RETURN

2000 REM THIS SUBROUTINE COMPUTES THE DETECTOR EFFICIENCY

2010 LET I=N

2020 GOSUB 1700

91
2030 LET A3=A1*1.82*P6

2040 LET I=N+2

2050 GOSUB 1700

2060 LET A4=Al*19.3*8E-7

2070 LET I=N+1

2080 GOSUB 1700

2090 LET D2= EXP (-A3-A4-Al*2 . 33*P7 ) * (1- EXP (-Al*2 . 33* .469)

)

20 95 RETURN

2100 REM THIS SUBROUTINE COMPUTES THE ABSORPTION FACTOR

2101 REM FOR ANY LINE

2110 LET X3=A2*Q1

2120 LET G1=(E0"1.65-E1"1.65)*Q2

2130 LET F1=1/(1+1.2E-6*G1*X3)"2

2140 RETURN

2200 REM THIS SUBROUTINE COMPUTES BACKGROUND UNDER EACH PEAK

2220 FOR 1= TO 1 2230 LET M[I]= ROI (I)/( LCN (158)- LCN (157))

2240 LET W[Il= FNE ( ( LCN (157)+ LCN (158))/2)

2250 NEXT I 2260 FOR J= TO 1

2270 LET A2=

2280 LET E1=W[J]

2290 FOR 1= TO N-1

2300 GOSUB 1700

2310 LET A2=A2+C[I] *A1

2320 NEXT I 2330 GOSUB 2000

2340 GOSUB 2100

2350 LET T1=D2*F1/E1

2360 LET X[J1=E0-E1

2370 LET Y[J]=M[J]/T1

2380 LET U[J]=X[J]*X[J]

2390 NEXT J

2400 LET D1=X[ 0]*U[1]-U[ 0]*X[1]

2410 LET K1=(Y[1]*X[ ] -Y [ 0]*X[1])/Dl

2420 LET K2=(Y[ ] *U [1] -Y [1] *U [ 0])/Dl

2425 IF L[ 01=10 GOTO 2620

2430 FOR J= TO N-1

2440 IF L[J]= GOTO 2610

2450 LET J1=L[J]-1

2460 LET E1=G[J1,J]

2470 LET T5= ROI (J+2)

2480 LET A2=

2490 FOR 1= TO N-1

2500 GOSUB 1700

2510 LET A2=A2+C[I]*A1

2520 NEXT I 2530 GOSUB 2000

2540 GOSUB 2100

2550 LET T1=D2*F1/E1

92
2560 LET X1=E0-E1

2570 LET G1=T1*(K1*X1*X1+K2*X1)

2580 LET G2= LCN (158)- LCN (157)

2590 LET M[J]=T5-G1*G2

2600 LET F[1,J]=F1

2610 NEXT J

2620 RETURN

2700 REM THIS SUBROUTINE WRITES STANDARDS INFORMATION INTO

2701 REM QUADRANT 4.

2710 CALL 4, (1)

2730 CALL 4, (3)

2750 LET N9= FNA(l)

2760 FOR 1= TO N-1

2770 IF L[I1= GOTO 2850

2780 LET N9=N9+10

2790 LET Ll= FNC(N9)

2800 CALL 3,L1,Z [I]

2810 LET Ll= FNC(N9+1)

2820 CALL 3,L1,L[I]

2830 LET Ll= FNC(N9+2)

2840 CALL 3,Ll,M[I]

2842 LET Ll= FNC(N9+3)

2843 CALL 3,L1,Q[I]

2850 NEXT I 2860 LET Ll= FNC(l)

2870 CALL 3,Ll,N9

2880 CALL 4, (3)

2900 CALL 4, (1)

2920 RETURN

3000 REM THIS SUBROUTINE COMPUTES OVERLAP FUNCTION OF ONE

3001 REM PEAK ON ANOTHER.

3010 LET G4=

3015 IF N3> GOTO 3025

3017 CALL 4, (1)

3020 GOTO 3027

3025 CALL 4,(0)

3027 CALL 4, (3)

3029 FOR 1=300 TO 899

3030 LET Ll= FNC(I)

30 31 CALL 3, LI,

3032 NEXT I 3034 FOR 1= TO N-1

3035 IF L[I]= GOTO 3200

3040 LET E7= FNG(I)

3050 LET S6= FNS(E7)

3052 LET T5= ROI (1+2)

3056 LET E3= FNE ( LCN (157))

3060 LET E4= FNE ( LCN (158))

3070 LET X2=(E3-E7)/S6/1.4142

3080 GOSUB 4500

93
3085 G0SU3 4200

3090 LET El= ABS (E8)/2

3100 LET X2=(E4-E7)/S6/1.4142

3110 GOSUB 4500

3120 LET E2= ABS (E8)/2

3130 IF E3<=E7 GOTO 3160

3140 LET W[I1»E2-E1

3150 GOTO 3195

3160 IF E4>=E7 GOTO 3190

3170 LET W[I1=E1-E2+G4

3180 GOTO 3195

3190 LET W[I]=El+E2-!-G4

3195 LET M[I]=W[I1

3200 NEXT I 3205 FOR Kl= TO 1

3230 FOR 11= TO N-1

3240 IF L(I1]= GOTO 3390

3245 LET Jl=

3250 LET T5= FNG(Il)

3260 LET D3=4* FNS(T5)

3270 LET I=N+1

3280 LET S6= ROI (11+2)

3290 LET E3= FNE ( LCN (157))

3300 LET E4= FNE ( LCN (158))

3310 FOR J= TO N-1

3320 IF L[J]= GOTO 3350

3325 IF Kl=l GOTO 3340

3330 IF J=I1 GOTO 3340

3335 GOTO 3350

3340 LET X2=l/ LOG (EO*EO/E [3 , J] /E [8 , J]

3345 GOSUB 3500

3350 NEXT J

3360 IF Kl=l GOTO 3390

3381 FOR J= TO 16

3382 LET Ll= FNC (Il*20+700+J)

3384 LET 02=S [J , II] *100000

3385 IF 02> GOTO 3387

3386 LET 02=

3387 CALL 3,L1,02

3389 NEXT J

3390 NEXT II

3395 NEXT Kl

3400 CALL 4, (3)

3410 IF N3= GOTO 3440

3420 CALL 4,(0)

3430 GOTO 3450

3440 CALL 4, (1)

34 50 RETURN

3490 REM COMPUTE OVERLAPS FOR EACH LINE

3500 LET 02=

94
3501 LET X[l]= EXP (2.373* LOG (Z [J] ) -8 .902)

3502 LET X[2]= EXP (2.946* LOG (Z [Jl ) -13 .94)

3503 LET X[3]=2.27E-5*ZIJ1"2-.001359*Z[J1-. 00657

3504 FOR L2= TO 8

3505 LET M1=L2+1

3506 LET I2=M1- INT (Ml/3)- INT (Ml/4)- INT (Ml/7)

3507 LET M3=2*( INT (Ml/12)- INT (Ml/6)+ INT (Ml/7))

3508 IF E[L2,J]>=E0 GOTO 3513

3509 LET E1=E0/E[L2,J]

3510 LET E2=1166*E[L2,J]/ FNJ(Z[Jl)

3511 LET X1=E1*E2

3512 LET U[M11=M3*(E1-1- LOG (E2)/E2*( FNL(Xl)- FNL (E2) )

) *X [12

3513 NEXT L2

3514 LET A4=l

3515 LET A5=l

3516 LET Al=l

3517 LET A2=l

3518 LET A3=l

3519 IF L[J1=3 GOTO 3530

3520 IF L[J1=2 GOTO 3525

3521 LET A2=U[4]/U[11* FNF(Z[J])

3522 LET A4=U [2] /U [1] * FNF(Z[J])

3523 LET A5=U [3] /U [1] * FNP(Z[J])

3524 GOTO 3533

3525 LET Al=U [1] /U [4] / FNF(Z[J1)

3526 LET A3= FNM(X2)

3527 LET A4=U[2]/U[41

3528 LET A5=U[3]/U[4]

3529 GOTO 3533

3530 LET A2=l/ FNM(X2)

3531 LET A4=U[2]/U[4]/ FNM(X2)

3532 LET A5=U [3] /U [4] / FNM(X2)

3533 LET S[ 0,J]=Al

3534 IF Z[J]>50 GOTO 3540

3535 LET Rl=B[Z[Jl]

3536 IF Z[J]<=30 GOTO 3538

3537 LET Rl=.115*( LOG (Z(Jl)-2.3)

3538 LET S [3 , J] =R1/(1-R1) *A1

3540 LET S[1,J]=A2

3550 LET S[2,J]=A3

3571 LET S[4,J1=.1*A2

3572 LET S [5 , J] = . 044*A2

3573 LET S[6,J]=(.2808-.0016*Z[J])*A2

3574 LET S[7,J]=A5

3575 LET S [8 , J] = . 154*A5

3576 LET S [9 , J] = . 02*A5

3577 LET S [10 , J] = . 166*A4

3578 LET S [11 , J] = .068*A4

3579 LET S [12 , J] = . 104*A4

3602 LET S[13,J]=.06*A3

95
3603 LET S[14,J]=.5*A3*U[8]/U[9}

3604 LET S[15,J1=.05*A3*U[7]/U[91

3605 LET S[16,J]=.01*A3*U[61/U[9]

3625 IF I1=J GOTO 3730

3630 LET E7= FNG(J)

3640 LET S6= FNS(E7)

3642 FOR 12= TO 16

3643 IF S[I2,J]> GOTO 3645

3644 LET S[I2,J]=

3645 NEXT 12

3730 FOR 12= TO 16

3740 LET E7=G[I2,J]

3742 IF T5=E7 GOTO 3840

3744 IF E7<1 GOTO 3840

3746 IF E7>E0 GOTO 3840

3750 LET S6= FNS(E7)

3760 IF E7<T5-D3 GOTO 3840

3770 IF E7>T5+D3 GOTO 3820

3780 GOSUB 4000

3305 IF Kl= GOTO 3815

3810 LET 02=01/W[J]*S[I2,J]

3812 GOSUB 3855

3814 GOTO 3840

3315 IF I2=L[J]-1 GOTO 3840

3816 LET W[J]=W[J]+01*S[I2,J]

3819 GOTO 3840

3820 LET S8=

3825 GOSUB 3900

3830 LET 02=01/W[J1*S8*S[I2,J]

3835 GOSUB 3855

3840 NEXT 12

3850 RETURN

3855 LET 02= INT (02*100000)

3860 IF 02= GOTO 3886

3861 LET E9=

3862 LET X2=J

3864 GOTO 3876

3866 LET E9=l

3868 LET X2=I2

3870 GOTO 3876

3872 LET E9=2

3874 LET X2=02

3876 LET Ll= FNC (Il*40+300+E9+Jl)

3878 CALL 3,Ll,X2

3830 IF E9= GOTO 3866

3882 IF E9=l GOTO 3872

3884 LET Jl=Jl+3

3886 RETURN

3890 REM COMPUTE ESCAPE PEAKS

3900 IF E7<1.838 GOTO 3990

96
3903 LET E1=E7

3905 LET E7=E7-1.74

3910 IF T5<E7-D3 GOTO 3990

3920 IF T5>E7+D3 GOTO 3990

3940 GOSUB 1700

3950 LET S7=.5*(l-327.9/Al* LOG (l+Al/327 .9)

)

3960 LET S8=.038*S7/(1-.038*S7)

3970 LET S6= FNS(E7)

3980 GOSUB 4000

3990 RETURN

4000 REM THIS FUNCTION COMPUTES SPECIFIC OVERLAPS

4010 LET X2={E3-E7)/S6/1.4142

4020 GOSUB 4500

4025 GOSUB 4200

4030 LET E2= ABS (E8)/2

4040 LET X2=(E4-E7)/S6/1.4142

4050 GOSUB 4500

4055 LET E8= ABS (E8)/2

4060 IF E3>=E7 GOTO 4100

4070 IF E4<=E7 GOTO 4120

4080 LET 01=E2+E8+G4

4090 RETURN

4100 LET Ol=E8-E2

4110 RETURN

4120 LET 01=E2-E8+G4

4130 RETURN

4200 REM THIS FUNCTION COMPUTES AN INCOMPLETE CHARGE

4201 REM CORRECTION FOR ALL PEAKS.

4210 LET G4=

4220 LET Xl=6

4230 LET X3=.l

4240 IF E7>=6.4 GOTO 4300

4250 LET X1=.86166*E7*E7-7.4431*E7+18.342

4260 LET X3=-.01683*E7*E7+.14129*E7-. 11489

4270 IF X3<= GOTO 4400

4300 IF E3>=E7 GOTO 4400

4310 LET X2=(E3-E7)/X3

4320 LET G4=X1*X3*X3*(1- EXP (X2)*(l-X2))

4330 IF E4>=E7 GOTO 4400

4340 LET X2=(E4-E7)/X3

4350 LET G4=G4-X1*X3*X3*(1- EXP (X2)*(l-X2))

4400 RETURN

4500 REM THIS FUNCTION INTEGRATES AREA UNDER A GAUSSIAN PEAK

4510 LET Tl=2"(-27)

4520 IF X2= GOTO 5070

4530 LET Yl= ABS (X2)

4540 LET Y2=Y1*Y1

4550 IF Y1<=1 GOTO 4630

4560 LET Cl=2"(3.5)

4570 LET U1=.83*C1

97
4580 LET Sl=2"(Cl*Cl-8)

4590 IF Y1<=U1 GOTO 4770

4600 LET E8=l

4610 LET E9=

4620 GOTO 4730

4630 LET S2=

4640 LET Dl=l

4650 LET T2=l

4660 LET P2=2*Y2

4670 LET Dl=Dl+2

4680 LET T2=P2*T2/D1

4690 LET S2=T2+S2

4700 IF T2>=T1 GOTO 4670

4710 LET E8=(S2+1)*1.12838*Y1* EXP (-Y2)

4720 LET E9=l-E8

4730 IF X2>= GOTO 4760

4740 LET E8=-E8

4750 LET E9=2-E9

4760 RETURN

4770 LET F2=

4780 LET G2=l

4790 LET F1=2*Y1

4800 LET G1=2*Y2+1

4810 LET P3=F1/G1

4820 LET Wl=l

4830 LET Bl=Gl+4

4840 LET A5=-W1*(W1+1)

4850 LET F3=B1*F1+A5*F2

4860 LET G3=B1*G1+A5*G2

4870 LET F4=F3/G3

4880 IF ABS (1-F4/P3)<=T1 GOTO 5040

4890 IF P3>F4 GOTO 5030

4900 IF G3<S1 GOTO 4950

4910 LET F3=F3/S1

4920 LET G3=G3/S1

4930 LET F1=F1/S1

4940 LET G1=G1/S1

4950 LET F2=F1

4960 LET G2=G1

4970 LET F1=F3

4980 LET G1=G3

4990 LET Wl=Wl+2

5000 LET Bl=Bl+4

5010 LET P3=F4

5020 GOTO 4840

5030 LET F4=P3

5040 LET E9=F4* EXP (-Y2) *1 . 12838/2

5050 LET E8=l-E9

5060 GOTO 4730

5070 LET E8=

98
5080 LET E9=l

50 90 RETURN

5100 REM THIS SUBROUTINE CORRECTS PEAKS FOR OVERLAP USING

5101 REM PREVIOUSLY COMPUTED OVERLAP FACTORS.

5110 FOR J= TO N-1

5120 IF L[J]= GOTO 5230

5140 LET A2=

5146 LET El= FNG(J)

5147 GOSUB 2000

5148 FOR 1= TO N-1

5150 GOSUB 1700

5152 LET A2=A2+C[I]*A1

5154 NEXT I 5156 GOSUB 2100

5158 LET F[3,J]=F1*D2

5220 LET W[J]=M[J]

5230 NEXT J

5240 FOR Tl= TO 2

5250 FOR Bl= TO N-1

5255 IF L[B1]= GOTO 5370

5260 LET Rl=

5265 LET J=Bl*40+300

5270 FOR Dl= TO 26 STEP 3

5275 LET L2= FNA(J+Dl)

5285 LET Gl= FNA(J+Dl+1)

5290 LET Yl= FNA (J+Dl+2 ) /lOOOOO

5292 IF Yl= GOTO 5360

5295 LET E1=G[G1,L2]

5300 LET A2=

5305 GOSUB 2000

5310 FOR 1= TO N-1

5315 GOSUB 1700

5320 LET A2=A2+C[I1*A1

5325 NEXT I 5330 GOSUB 2100

5340 LET R1=R1+F1*D2*W[L21*Y1/F[3,L21

5350 NEXT Dl

5360 LET W[B1]=M[B1]-R1

5370 NEXT Bl

5380 NEXT Tl

5390 RETURN

5500 REM THIS SUBROUTINE COMPUTES THE MATRIX CORRECTIONS FOR

5501 FOR J= TO 12

5502 FOR 1= TO 12

5503 LET P[I,J]=

5504 NEXT I 5505 NEXT J

5510 FOR J= TO N-1

5520 IF L[J1= GOTO 6400

5530 LET B1=L[J]''2-1

99
5540 IF BK9 GOTO 5560

5550 LET Bl=

5560 LET U[J]=E0/E[B1,J1

5570 IF U[J1>«1.5 GOTO 5590

5580 PRINT "OVERVOLTAGE TOO LOW"

5590 LET El= PNG (J)

5600 FOR 1= TO N-1

5610 GOSUB 1700

5620 LET H[I,J]=A1

5630 NEXT I 5750 LET A2=H[J,J1

5760 GOSUB 2100

5770 LET F[ 0,J]=Fl

5780 IF L[J1>1 GOTO 5820

5790 LET Cl=5

5800 LET F3=

5810 GOTO 5890

5820 IF L[J]>2 GOTO 5860

5830 LET Cl=3.5

5840 LET F3=l

5850 GOTO 5890

5860 IF L[J1>3 GOTO 5790

5870 LET Cl=3.5

5880 LET F3=2

5890 FOR 11= TO N-1

5900 IF I1=J GOTO 6160

5910 LET P3=

5920 LET L2=(P3+1)"2-1

5930 IF 1.02*ElL2,Il]-E0>= GOTO 6130

5940 IF G[P3,I1]<E[B1,J1 GOTO 6160

5950 IF G[P3,I1]>E[B1,J1+C1 GOTO 6130

5960 LET P[J,I11=P3+1+2*F3

5970 LET 0[J,I1]=EO/E[L2,I11

6030 LET E1=G[P3,I11

6040 FOR 1= TO N-1

6050 GOSUB 1700

6060 LET H[I+13,I1]=A1

6070 NEXT I 6120 GOTO 6160

6130 IF P3=l GOTO 6160

6140 LET P3=l

6150 GOTO 5920

6160 NEXT II

6170 FOR 1= TO N-1

6180 IF P[J,I]= GOTO 6381

6190 LET Y1=A[Z[J11/A[Z[I]]*H[J+13,I]/2*((0[J,I1-1)/(U[J1-1))'^1.6

6200 LET Tl= EXP (2.373* LOG (Z[Il)-8.902)

6210 LET T2= EXP (2.946* LOG (Z [I] ) -13.94)

6220 IF P[J,I1>1 GOTO 6250
6230 LET D1=.88*T1

6240 GOTO 6380

6250 IF P[J,I]>2 GOTO 6280

6260 LET D1=3.696*T2

6270 GOTO 6380

6280 IF P[J,I]>3 GOTO 6310

6290 LET D1=.18*T1

6300 GOTO 6380

6310 IF P[J,I]>4 GOTO 6340

6320 LET D1=.75*T2

6330 GOTO 6380

6340 IF P[J,I]>5 GOTO 6370

6350 LET D1=.01*T1

6360 GOTO 6380

6370 LET Dl=.01*T2

6380 LET 0[J,I1=D1*Y1

6381 NEXT I 6382 LET 01=U[Jl

6383 IF Ul<=10 GOTO 6385

6384 LET Ul=10

6385 LET Gl=. 00873*Ul"3- . 1669*Ul*Ul+.9662*Ul+. 4523

6386 LET G2=.002703*Ul"3- . 05182*Ul*Ul+. 302*U1-. 1836

6387 LET P2=. 887-3 . 44/U1+9 . 33/Ul"2-6 .43/Ul'^3

6392 FOR 1= TO N-1

6394 LET V[I,J]=G1-G2* LOG (P2*Z(I]+25)

6395 LET S [I , J] =2*Z [I] /{ A[Z [I ] ] * (EO+E [Bl , J] )

)

6395 LET S [I , J] =S [I , J] * LOG (583* (EO+E [Bl , J] ) / FNJ(Z[I]))

6398 NEXT I 6400 NEXT J

6405 LET G4=

6410 IF N3= GOTO 6550

6417 PRINT "NO PLOT ENTER 0"

6418 INPUT G4

6420 LET Sl=

6425 PRINT

6430 FOR 1= TO N-1

6440 IF L(I]= GOTO 6480

6450 LET M[I]= ROI (1+2)

6460 LET M[I1=M[I]/Q[I]

6470 LET S1=S1+M[I]

6480 NEXT I 6490 IF L[N-1]> GOTO 6520

6500 LET C[N-1]=1-S1

6510 LET Sl=l

6520 FOR 1= TO N-1

6530 LET C[I]=M[I]/S1

6540 NEXT I 6550 FOR Nl= TO N3

6560 FOR 11= TO N-1

6570 IF L[I1]= GOTO 6880

101
6580 LET S2=

6590 LET X2=

6600 LET A2=

6610 FOR J= TO N-1

6620 LET S2=S2+C(J]*S[J,I11

6630 LET X2=X2+C[J]*VIJ,I11

6640 LET A2=A2+C[J1*H[J,I11

6650 NEXT J

6660 LET El= FNG(Il)

6670 GOSUB 2100

6680 LET W1=(V[I1,I1]*S2)/(S[I1,I11*X2)

6690 LET F[1,I1]=F1

6700 LET F2=

6710 FOR J= TO N-1

6720 IF P[I1,J]= GOTO 6810

6730 LET A3=

6740 FOR 1= TO N-1

6750 LET A3=A3+C[I]*H[I+13,J]

6760 NEXT I 6770 LET X1=Q1*A2/A3

6780 LET B1=(333000/(E0"1.65-E1"1.65))/A3*Q2

6790 LET F4= LOG (1+X1)/X1+ LOG (1+Bl)/Bl

6800 LET F2=F2+C[J]*OlIl,J]/A3*F4

6810 NEXT J

6815 IF C[I1]= GOTO 6880

6820 LET G3=C[I1]/W1*(1+F2)*F[1,I11/F[ 0,11]

6830 IF N3> GOTO 6870

6835 IF L[I1]= GOTO 6880

6840 LET M[I1]=M[I1]/G3

6850 PRINT "MELS =";G3

6860 GOTO 6880

6870 LET G2=M[I1]*C[I1]

6872 LET C [II] =G2* (1-G3) / (G2+G3* (1-M [Il]-C [II] )

)

6874 IF NKN3 GOTO 6880

6875 IF G4= GOTO 6880

6876 GOSUB 8200

6880 NEXT II

6890 IF N3= GOTO 7110

6900 LET Sl=

6910 FOR 1= TO N-1

6915 IF L[I]= GOTO 6930

6916 IF C[I]> GOTO 6920

6917 LET C[I]=

6920 LET S1=S1+C[I]

6930 NEXT I 6940 IF L[N-1]> GOTO 6970

6950 GOSUB 8600

6970 IF N1=N3 GOTO 7050

6980 GOSUB 2200

6982 CALL 4,(0)

102
6986 CALL A, (3)

6990 GOSUB 5100

6992 CALL 4, (3)

6996 CALL 4, ( 0)

7000 FOR 1= TO N-1

7010 IF L[Il= GOTO 7040

7020 LET M[I]=W[Il/QlI]

7030 LET C[I1=C[I1/S1

7040 NEXT I 7050 NEXT Nl

7060 PRINT "Z"/'C",-F(X)","K"

7070 FOR 1= TO N-1

7075 IF L[I]= GOTO 7085

7030 PRINT Z[I1 ,C[I] ,F[1, 1] , Mill

7082 GOTO 7090

7085 PRINT Z[Il ,C[I]

7090 NEXT I 7100 PRINT "TOTAL =";S1

7105 CALL 4, (2)

7110 FOR 1= TO 1

7120 LET T5= ROI (I)

7130 PRINT "ROI";I, FNE ( LCN (157)); FNE ( LCN (158))

7140 NEXT I 7150 RETURN

8000 REM SUBROUTINE TO CREATE A ROI FOR EACH MEASURED LINE

8010 LET Ll=644

8015 LET K2=l

8020 LET Kl=1.1775

8030 FOR 1= TO N-1

8040 IF L[I]= GOTO 8130

8045 LET K2=K2+1

8046 LET I1=L[I1-1

8050 LET Sl= FNS(G[I1,I1)

8060 LET El= FNN (G [II , I] -K1*S1)

8070 LET E2= FNN (G [II ,1] +K1*S1)

8075 CALL 1,101,K2

8030 CALL 1,L1,E1

8090 LET L1=L1+1

8100 CALL 1,L1,E2

8110 LET L1=L1+1

8120 CALL 5

8130 NEXT I 8140 RETURN

8200 REM THIS ROUTINE RECONSTRUCTS PEAKS IN QUADRANT 3

8210 LET T5=G3*Q[I1]/F[3,I11

8230 CALL A, (3)

8240 LET K2= FNA(5)/10000

8250 LET El= FNG(Il)

8250 LET Sl= FNS(El)

8270 LET E3= FNN (El-K2*Sl)

103
8280 LET E4= FNN (E1+K2*S1)

8290 LET Gl=

8300 LET E2=l

8305 LET S2=S1

8310 G0SU3 8500

8315 LET T5=T5/G1*S1

8320 FOR Kl» TO 16

8330 LET E1=G[K1,I11

8340 IF EK.7 GOTO 8450

8345 IF El>10 GOTO 8450

8350 LET S2= FNS(El)

8355 LET E3= FNN(E1-4*S2)

8360 LET E4= FNN{E1+4*S2)

8365 LET S6= FNA (700+20*Il+Kl) /lOOOOO

8370 IF S6= GOTO 8450

8375 LET E2=T5/S2*S6

8380 LET A2=

8385 FOR 1= TO N-1

8390 GOSUB 1700

8395 LET A2=A2+C [I ] *Al

8400 NEXT I 8405 GOSUB 2000

8410 GOSUB 2100

8415 LET E2=E2*D2*F1

8425 CALL 4, (2)

8430 GOSUB 8500

8435 CALL 5 8440 CALL 4, (2)

8445 CALL 4, (3)

8450 NEXT Kl

8460 CALL 4,(0)

8470 RETURN

8500 FOR J=E3 TO E4

8505 IF J>1023 GOTO 8590

8510 LET Jl= FNE(J)

8520 LET T1=E2* EXP (-.5* ABS ( ( Jl-El) /S2) "2)

8530 IF E2>1 GOTO 3560

8540 LET G1=G1+T1

8550 GOTO 8590

8560 LET Ll= FNC(J)

8570 LET T1=T1+ FNA(J)

8580 CALL 3,Li,Tl

8590 NEXT J

8595 RETURN

8600 REM STOICHIOMETRY CALC

3605 LET C[N-1]=

8610 CALL 4,(0)

8620 CALL 4, (3)

8630 FOR 1= TO N-2

8640 FOR J=10 TO N9 STEP 10

104
8650 IF FNA(J)=Z[I] GOTO 8670

8660 NEXT J

8665 PRINT "ELEMENT "?Z[I]?" NOT FOUND"

8667 STOP

8670 LET G3= FNA(J+3)

8675 IF G3= GOTO 8720

8680 LET F3=.5*C[I1*G3*A[Z[N-1]]/A[Z[I]]

8690 LET C[N-1]=C[N-1]+F3

8700 NEXT I 8702 LET S1=S1+C[N-1]

8704 CALL 4, (3)

8705 CALL 4, { 0)

8710 RETURN

8720 LET C[N-1]=1~S1

8730 LET Sl=l

8740 RETURN

105
100 RCM THIS ROUTI^ME COMPUTES THE THICKiMESS OF THE BE WI.nJDQW

102 REM Ai^D THE THICKiNESS OF THE SI DEAD LAYER

130 GOSUB 1000

135 PRINT "ENTER AT. NO. kciD EO

140 INPUT Z[ 0] ,£0

141 PRIivlT

142 LET L [ 0] =10

143 LET .NJ9 = 1

144 LET N=l

145 LET Z [N] =4

146 LET Z [.Nl + 1] =14

147 LET Z[ln1 + 2] =79

148 FOR 1= TO N+2

149 GOSUB 1500

150 NEXT I 151 LET C[ 0] =1

152 FOR P2= TO 14

154 GOSUB 2200

155 FOR 1=2 TO 3

160 LET M[I]= ROI (!)/( LCN (158)- LCN (157))

170 LET W[I]= FlNE(( LCN (157)+ LCN (158) )/2)

180 NEXT I 181 FOR J=2 TO 3

185 LET 1=

190 LET E1=W[J]

200 GOSUB 1700

210 LET A2=A1

220 GOSUB 2100

230 LET Tl= LOG (Fl/El)

240 LET Gl= LOG (M[J1 ) 250 LET X1=E0-E1

260 LET I=N

270 GOSUB 1700

274 LET X[J-2]=A1*1.82

275 LET I=N+1

276 GOSUB 1700

280 LET Y[J-2]=A1*2.33

285 LET I=N+2

290 GOSUB 1700

291 LET A3=Al*19.3*8E-7

292 LET U[J-2]= LOG (Kl*Xl*Xl+K2*Xl) -G1+T1-A3

2 93 NEXT J

294 LET D1 = X[ 0]*Y[1]-Y[ 0]*X[1J

295 LET P6=(U[ 0] *Y [ 1] -U [ 1] * Y [ ] ) /Dl

296 LET P7=(X[ 0] *U [ 1] -X [ 1

] * U [ ] ) /Dl

300 PRINT "T BE=";P6;"T SI=";P7

310 NEXT P2

312 PRINT "INSERT THESE VALUES INTO LINES 1454 AND 1455"

320 STOP

3 90 EiMD

106
NBS-114A (REV. t-Tsi

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1, PUBLICATION OR REPORT NO. NBS TN-1106

S.Ckiv't Acc99sii» Ito. 5. R^cipienf $ Acc«$sioft No.

4. TITLE AND SUBTITLE

FRAME C: A Corpact Procedure for Quantitative Energy-Dispersiv

a

Electron Probe X-r^ Analysis

5. Publication Date jeptember 1979

S. Performing Organization Code

7. AUTHOR(S)

R. L. Myklebust/ C. E. Fiori, and K. F. J. Heinrich

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

10. Project/Task/Work Unit fto.

11. Contract/Grant No.

12. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Sueei. City, si^ie, ziP)

Same as above.

13. Type of Report & Period Covered Final

14. SpMeMTing ^(sncy Code

15. SUPPLEMENTARY NOTES

133 Document describes a computer program; SF-185, FIPS Software Summary, is attached.

IS. ABSTRACT (A 200'Word or Iea3 lactuet summary ot moat aigniticant information. It document includes a significant bibliography or

literature aurvey, mention it here,) A data evaluation procedure (FRAME C) for carrying out quantitative electron probe

microanalysis with a lithium-drifted silicon detector was developed for use with a

small conputer. The procedure consists of a background correction calculated from

two selected background regions of interest, a siirple method of resolving overlapping peaks, and the matrix corrections for characteristic radiation (ZAF) . To

save ccHTputation time, small groins of adjacent channels (regions of interest) in

the multi-channel analyzer rather than individual channels are used for the

calculations. The method for caiputing the overlap factors is describcid. Exanples

of several types of analyses are presented.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the firat letter of the iirat key word utileaa a proper n/jm.'*; aeparaied by aemicoiona) Coitputer progTam; energy dispersive detector; multichannel analyzer;

peak overlap? quantitative electron probe microanalysis; x-ray continuum; x-ray

spectrum

18. AVAILABILITY CE| Unlimited

I I For Official Distribution. Do r4ot Release to NTIS

[\ Order Frorr Sup. of Doc, U.S. Govergnient Printing Office, Washington, DC

20402, SD Stock No. SN003-003- 02113-4

I I Order From National Technical Information Service (NTIS), Springfield, VA. 22H!

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF

PRINTED PAGES

111

2?. Price $4.00

•U.S. GOVERNMENT PRINTING OFFICE : 1979 0-281-067/23''

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