Chapter 2 X-ray fluorescence analysis

Applications of Synchrotron Radiation to Materials Analysis H. Saisho and Y. Gohshi (Editors) 9 1996 Elsevier Science B.V. All rights reserved.

79

CHAPTER 2

X-RAY F L U O R E S C E N C E ANALYSIS Hideo SAISHO and Hideki HASHIMOTO Inorganic Analysis Laboratory, Toray Research Center, Inc. 1-1, Sonoyama 1-Chome, Otsu, Shiga 520, Japan

2.1. I N T R O D U C T I O N Recent trace element analysis requires highly sensitive, simultaneous multi-element methods. Such methods include activation analysis, atomic emission spectrometry, mass spectrometry, and X-ray fluorescence analysis (XRF). XRF facilitates rapid, nondestructive analysis, and has a wide range of applications, including production processes and quality control. Although XRF is not necessarily a high-sensitivity technique (normally, it can only detect ~tg levels), researchers have recently found that synchrotron radiation (SR) greatly improves the sensitivity of XRF, enabling analysis over l.tg-pg ranges [1-3]. Synchrotron radiation is a continuum radiation with a wide wavelength range. Two to three GeV class storage tings currently available supply radiation ranging from microwaves to hard X-rays (20-30 keV). Furthermore, these storage tings provide an X-ray intensity 100-10 000 times greater than conventional X-ray sources. If a wiggler is used, hard X-rays of up to 50 keV can be supplied. In addition, when large scale SR facilities under construction are completed, the available intensity will increase by a few more orders of magnitude. Other advantages of SR include its almost perfect linear polarization and excellent collimation. More sensitive XRF can be attained by increasing the intensity of the signal and reducing the background. Greater signal intensity can be obtained by increasing the intensity of the excitation X-rays. The background is reduced by two characteristics of SR: continuum radiation and polarization. The excellent collimation of SR makes this method suitable for measurements using the total reflection method, which is useful for surface analysis, as well as for microarea analysis using a microbeam. The major characteristics of SR - - high intensity, continuum radiation, polarization, and c o l l i m a t i o n - greatly enhance the capabilities of XRF. Table 2-1 lists the characteristics of synchrotron radiation and the advantages when it is applied to XRF.

80 Table 2-1 Outstanding characteristics of SR for XRF SR characteristics

Advantages

High intensity Linear polarization Continuous spectrum

Signal enhancement Background reduction Selective excitation Total reflection

High collimation

{

Micro-trace analysis

SR-Excited XRF (SRXRF) was first developed in 1972 by Horowitz and Howell [4] for use in microbeam analysis. Working with the Cambridge Electron Accelerator, they used an ellipsoidal condensing mirror and a pinhole to produce a 2 I.tm focused X-ray beam. XRF using this beam attained a detection limit of 10-6 to 10- 9 g cm -2 at a resolution of 2 lxm. Sparks et al. [5, 6] conducted their well-known 1977 experiment at SPEAR of SSRL in order to find primordial superheavy elements using a curved pyrolytic graphite crystal and a Si(Li) detector. They demonstrated that it was possible to detect superheavy elements if at least 5 x 108 atoms were present in the sample. The announcement of this result, as well as the establishment of SR facilities at many locations, led to an increasing number of investigations of XRF analysis in the 1980s. Gilfrich et al.[7], at SSRL in 1983, systematically performed a series of experiments concerning detection limits. Similar research was carded out by Hanson et al. [8] at CHESS of Cornell, Kn6chel et al. [9] at DORIS of HASYLAB, and Bos et al. [10] at the SRS of Daresbury. Iida et al. [ 11] conducted a close investigation into the dependence of the detection limit on the excitation mode at the Photon Factory (PF) of the National Laboratory for High Energy Physics (KEK). Also, Gordon used beam intensity parameters to calculate theoretical values for detection limits at the NSLS of Brookhaven [ 12]. X-Ray total reflection produces a shallow X-ray penetration depth and very little scattering (background), and therefore total reflection XRF (TXRF) is useful for surface analysis and ultratrace analysis [13, 14]. While improvements have been made by Yoneda and Horiuchi [ 15] in the original technique, which used a conventional X-ray tube, the use of SR further enhances the effectiveness of TXRF because of SR's excellent collimation and strongly monochromatic beam [ 16]. Researchers often apply this method to analyze depth profiles [ 17] and layered structures [18]. In these analyses, the reflection curve and fluorescent X-ray profile are measured as changes are made in the incident angle near the critical angle of total reflection. In this chapter, we will discuss equipment used for bulk analysis and surface analysis using SRXRF. These techniques do not include analysis using a microbeam or chemical state analysis for obtaining information on chemical bonding by high energy-resolution measurements. These will be described in the next chapter.

81 2.2. E Q U I P M E N T SRXRF detects X-ray fluorescence caused by a white (non-monochromatic) or monochromatic incident SR beam. The radiation of hard and soft X-rays from the storage ring requires quite different equipment. With hard X-rays, beryllium windows can be used to form a barrier between the ultrahigh vacuum in the storage ring and the low vacuum or air in the sample chamber. Soft X-ray SRXRF requires ultrahigh vacuum through to the sample chamber. This means that completely different equipment is required for the analysis of light elements (atomic number less than 12) and of elements with higher atomic numbers. Hereafter, we will confine our discussion to analytical techniques using hard X-rays. Hard X-ray equipment is built in much the same way as equipment using X-ray tubes or rotating anode Xray generators. The major difference is that in SR equipment, the distance from the light source to the sample is longer (10-30 m). Despite this long distance, high collimation keeps the reduction of SR intensity to very low levels. Equipment known as beamlines introduces the X-rays into the detection system. A beamline is composed of a few beryllium windows, a vacuum system, shutters, and optical elements. Since SR obtained from a bending magnet is linearly polarized in the orbital plane of the accelerated electron, the optical elements usually have an axis of rotation horizontal to the electron's orbital plane. To protect the operator from radiation, the detection system is placed in an iron (or lead) hutch and is remote-controlled. Section 2.2.1. describes the optical elements used in SRXRF. Section 2.2.2. deals with the detectors, and Section 2.2.3. discusses the beamline for X-ray fluorescence incorporating these two components.

2.2.1. Optical elements Total reflection m i r r o r

The X-ray mirror is extensively used in SR experiments as a low pass filter, a high pass filter, or an X-ray focusing device. Since the refractive index for X-rays is very slightly less than unity (a difference of 10-5), an X-ray with a glancing angle smaller than a certain value (critical angle: a few mrad) is totally reflected. The critical angle depends on the kind of substance and the wavelength of the incident X-rays. The complex index of refraction n for an X-ray with a wavelength A is given as follows: (2-1)

n = l - 5 - i fl S = (rJ2~)(Nop/A)(Z

fl = ~/.t/4r~

+ Af' )Z 2

(2-2) (2-3)

82

(a)

(b)

1.0-

1.0ad

~: 1.5/~

0.8-

0.8-

Si " 0 = 4mrad

~,c" 1.6/~

0c " 10.5 mrad

Z,c" 1.7/t~

ov,,~

~0.6-

;>0.6=!,~(

Si

t,,.,)

~0.4-

r

0.4-

ad 0.2-

0.2-

0.0- i 0

i

4

8

'

t

'

12

Glancing angle / mrad

o'o-t'- t ' "

1.2

1.4

i

t

t

t

1.6

1.8

2.0

2.2

Wavelength /

Fig. 2-1. The calculated reflectivities for silicon and platinum: (a) is expressed as a function of glancing angles at a fixed wavelength (1.5 A) of the incident X-rays; (b) as a function of wavelengths at a fixed glancing angle (4 mrad for Si, 12 mrad for Pt).

where re is the classical electron radius, No is Avogadro's number, p is the density, and A is the atomic weight. Thus, (Nop/A) represents the number of atoms found in a unit volume. The quantity (Z+Af) is the real part of the atomic scattering factor, where Z is the number of electrons per atom (atomic number) and zlf' represents the dispersion term. Far away from the absorption edge, Af' is very small, and therefore 6 is proportional to the electron density. The quantity/.t is the linear absorption coefficient. An incidence of an X-ray at a glancing angle less than the critical angle, 0c, which is a grazing angle, will result in total reflection. If we ignore absorption, the critical angle can be given as follows, according to Snelrs law: 0c = ~

(2-4)

Calculated reflection curves for silicon and platinum are shown in Fig. 2-1. Figure 2-1a shows the reflection curves as a function of the angle (glancing angle), and (b) shows them as a function of the incident X-ray wavelength. The critical angle (0c) and critical wavelength (20 can be seen. For a given substance and angle, X-rays of wavelengths less than a certain value (greater energy than a certain value) are not reflected: thus, the mirror works as a low pass filter. As can be seen in Fig. 2-1, for a given wavelength, the more electrons per unit volume, the larger the critical angle. However, as the amount of X-rays absorbed increases, the change in reflectivity near the critical angle is more gradual, which implies a lower

83 efficiency as a low pass filter. Since the critical angle for X-ray wavelengths is a few mrad, the use of an X-ray 2 mm high requires a mirror a few tens of centimeters long. Also, the mirror must be sufficiently smooth if its calculated efficiency is to be attained. Calculated reflection curves for mirrors of different roughnesses are shown in Fig. 2-2. Surface roughness is described as a group of flat planes distributed in a Gaussian manner. Figure 2-2 shows that less than 10/~ roughness is necessary. Surface roughness reduces the reflectivity. When using a mirror and employing a strong SR, it is necessary to ensure thermal stability. Therefore, it is important to place the optical system in a high vacuum or to cool the system. Another way is to position the mirror behind the monochromator, but then the monochromator would have to be protected from the heat. The mirror material is another point for careful consideration. A plane plate of thickness d with a difference in temperature, AT, between the surfaces, bends at a radius of curvature, R, which can be described as follows: R = d/(aAT)

= (kd2)/(otAq)

(2-5)

where k is the thermal conductivity, ct the coefficient of thermal expansion of the material, and Aq the amount of heat transferred through a plate of thickness d. Equation (2-5) indicates that the mirror material should have a high thermal conductivity and a small coefficient of thermal 1.0

t~=0 ~," 1.24 .~

0.8

~06

~

9

a=20

r

~ 0 4-

0.2

0.0 1

2

3

4

5

6

G l a n c i n g angle / m r a d Fig. 2-2. The calculated reflection curves for samples of silicon of roughnesses (t~ = 0, 10 ]~ and 20 ]~).

different surface

84 expansion, i.e., a large k/a. In addition, the mirror material must be able to be ground and polished to a sufficient degree. Fused quartz is widely used since large polishable mirrors can be fabricated. However, despite its small coefficient of thermal expansion, the thermal conductivity of this material is low and therefore it cannot be used where a substantial heat load is expected. Recently, SiC has received attention. It has a high thermal conductivity and a k]o~ value more than 20 times that of quartz. Since it is now possible to make large SiC mirrors, it will be used in most beamlines using an insertion device and in the next generation of large scale rings. The mirror chamber must be kept under ultrahigh vacuum to prevent carbon from adhering to the mirror surface, since this would greatly lower the mirror's efficiency. Total reflection mirrors are generally used for eliminating harmonics. They are also used, in combination with absorbers or transmission mirrors, to emit X-rays with a wide energy band or to focus X-rays. If the absorption characteristics of a very thin mirror are low, the unreflected X-ray comes out of the back of the mirror. Such mirrors are known as transmission mirrors. If a mirror is thin enough (less than 1 lxm thick) and is made of material with a low atomic number, it can be used as a transmission mirror. The calculated transmissivities of thin organic films are shown in Fig. 2-3. Transmission mirrors can be used as highly efficient high pass filters. Soap film is a smooth, stable transmission mirror. It is 300-10 000/~ thick, and very smooth, with a surface roughness less than a few/~. Lairson and Bilderback [19] used a solution of glycerin (35%), Ivory Liquid (2%), and distilled water (63%) to make soap films. They used a 20 Jam wire stretched inside a 10 cm x 30 cm frame to make 8 cm x 20 cm films. The films kept a few days in wet helium.

Figure 2-4 shows the transmitted spectra of the

1.0--

1.0" ~0.8

f

-

thickness: d = 0.5 ilm

9 t,,=q

r thickness: d = 0.1 I.tm

;~0.8 -

~,' 1.24 /~

~, 9 1.24 A

~0.6-

o~ 0 . 6 -

9 v,,,,l

9 t,,,,q

~04-

~0.4-

0.2-

0.2-

0.00

2

I

I

I

I

4

6

8

10

Glancing angle / mrad

0"0-1 0

'

'

2

I

I

I

I

4

6

8

10

Glancing angle / mrad

Fig. 2-3. The calculated glancing angle dependence of transmissivities for polystyrene films using incident X-rays with a wavelength of 1.24/~.

85

10

.--" .._-_ -

jJ

_

.; 9~

-

~

-

"~

-

I

_

0

I

t

0

i

I

i

t

I

12.5 Energy / keV

I

I

25

Fig. 2-4. Transmitted spectra of soap films at a thickness of > 10 000 ]k (broken line) and of 3 200 A (solid line). Both films are set to the same mirror angle (2.4 mrad). From Ref.[19], reprinted by permission of Elsevier Science Publishers B.V., Amsterdam.

films. It indicates the dependence of transmissivity on film thickness. Iida et al. [20] used 0.5 ~tm Mylar film as a transmission mirror. Compared with soap films, the Mylar film is more stable and durable, yet it is less smooth and more difficult to make flat. Mirrors with an ellipsoidal, cylindrical, or hyperboloidal cross section also can be used to condense X-rays. In microprobe analysis, a combination of these mirrors is used to create a micro-sized beam (microbeam). Reflection and transmission mirrors can be combined to select X-rays with appropriate energy bands. This will be discussed later in this section. Crystal monochromator In order to use SR as a monochromatic X-ray excitation beam it must be monochromatized using a monochromator. Crystals are used for this purpose. The diffraction of an X-ray by a crystal is described by Bragg's law 2d sin0 B= nA

(2-6)

where n is the diffraction order, d is the lattice spacing in the crystal lattice, ~, is the X-ray wavelength and 0]3 (the Bragg angle) is the angle which the incident X-ray makes to the

86 reflecting plane. Since sin0 is less than unity, X-rays with wavelengths longer than 2d cannot be reflected. Bragg angles of less than a few degrees or more than 70 degrees cannot be achieved because of the structure of the monochromator. Therefore, the lattice spacing of the crystal lattice plane must match the wavelength used. For example, for Si (111), where d is 3.136/~, the wavelengths that can be obtained range from 0.4 to 6 ]k. Equation (2-6) is differentiated to: AA/A = AE/E = A0 cot0a

(2-7)

From Eq. (2-7) it is evident that energy resolution is determined by the angular width A0 and Bragg angle 0B. The angular width is determined by the angular spread of the incident beam and the reflection width of the crystal monochromator. The angular spread of the incident beam depends on the size and angular divergence of the light source and the geometry of the experiment (distance, slit, etc.). The reflection width is greatly affected by the crystal'sstate of perfection. For a perfect crystal, the reflection width to is given as follows, according to the dynamical theory of diffraction [21 ]: to =

2 9 re ~ 2 .C. [/7111.e -M sin20B uV

(2-8)

where re is the classical electron radius, V the unit-cell volume, Fh the crystal structure factor, e -M the temperature factor, and C the polarization factor. The integral reflecting power, I, for a weakly absorbing crystal is given approximately by 2

I = 1__. 8 .rex .C. [F~ .e -M ~ 3sin20B ~V

(2-9)

where b is a quantity called the asymmetry factor. For a mosaic crystal, kinematical diffraction theory can be applied to rewrite I as follows: \ I=

r2~3

(2-10) .C 2. ~t~2.e-2M

2/aVEsin2 0B The reflection width, energy resolution, and integral reflecting power of perfect crystals which are frequently used are shown in Table 2-2 [22]. The crystal used in a monochromator must not be seriously damaged by a strong SR. Generally speaking, it is impossible to use organic crystals in monochromators. Usually, silicon crystals are used, since large perfect crystals can be made easily and provide the lattice

87 Table 2-2 Parameters of crystal monochromators a Crystal

hkl

als

(second of arc)

b

c

AE/E

(•

5)

I

(xl 0 6 )

Silicon

111 220 311 333

7.395 5.459 3.192 1.989

14.1 6.04 2.90 0.88

39.9 29.7 16.5 9.9

Germanium

111 220

16.338 12.449

32.64 14.46

85.9 67.4

a Bragg reflection width, b Energy resolution, c Integral reflecting power. These parameters are used to determine experimental conditions such as incident X-ray energy and resolution. From Ref. [22], reprinted by permission of Elsevier Science Publishers B. V., Amsterdam.

spacing required in the hard X-ray region. Since SR is polarized in the horizontal direction, a non-horizontal monochromator rotational axis will jeopardize the efficiency. When the monochromator with a horizontal rotational axis is used, the diffracted beam goes up or down: therefore, changing the Bragg angle to change the wavelength varies the direction of the diffracted beam. This means that all units positioned behind the monochromator (slit, sample, detector, etc.) must be moved every time the Bragg angle is changed. A monochromator with a parallel double-crystal (or a channel-cut crystal) always reflects the beam in the same direction. In this case, the above units can simply be moved up and down, en bloc. It is also possible to keep the height of the outgoing beam constant by attaching a mechanism to translate the crystal while rotating the doub!e-crystal monochromator [23]. This makes the equipment even easier to use. Special care must be taken to eliminate harmonics when using a monochromator. It is clear from Bragg's law that for any X-ray, with a wavelength A, there will be an X-ray with a wavelength 2/n which will be reflected at the same angle. The relative intensity of harmonics depends on the spectn~m of the light source, the integral reflecting power of the crystal, etc. If absorption is ignored, the integral reflecting power is proportional to (2/n)2lF~e-M, a quantity that monotonically decreases with increasing order n. Considering the SR spectrum, therefore, the second and third harmonics are the problems in the X-ray region. In some cases, the second harmonics disappear due to the symmetry of the crystal. One such example is Si(111). In this case, harmonics pose very little problems if the storage ring can supply a relatively high incident energy (more than 15 keV for a 2 GeV class storage ring). Basically there are two methods of eliminating harmonics. One uses a total reflection mirror. As

88 discussed previously in this section, the mirror totally reflects X-rays of wavelengths longer than a certain value (the critical wavelength) and does not reflect those with shorter wavelengths. The other method employs a beamline without a mirror. Harmonics can be eliminated by slightly detuning two crystals used in a double-crystal monochromator. As shown in Table 2-2, the reflection width for Si(333) is much smaller than that for Si(111). This makes it possible to reduce the intensity of harmonics by detuning. Also used is an optical system that increases the intensity of the beam by focusing the incident X-ray using a curved second crystal (sagittal focusing) [24-26]. SR has a high degree of collimation in the vertical direction (angular spread: approx. 0.1 mrad), but it is also spread in the horizontal direction. An ordinary beamline can take in a few mrad of a beam in the horizontal direction, but given the long distance (10-30 m) from the light source to the hutch, the beam will be spread more than a few cm on the sample. Therefore, if the incident beam is not focused, a fiat-crystal monochromator can only supply less than 1 mrad of the beam. A focusing optical system collects much of the beam and improves the detection limit by producing more than 10 times the intensity. Another focusing optical system employs a fiat-crystal monochromator and a curved mirror. When using this system, however, the position of the mirror should be carefully considered. If the mirror is positioned in front of the monochromator its adjustment can be made at the beginning, and no further adjustment is needed when tuning the monochromator to change the energy. However, in this position SR could damage the mirror surface. When the mirror is positioned behind the monochromator damage is negligible, but then it requires more complicated adjustment. Protecting the monochromator from the heat of SR must also be considered when using an insertion device or a larger scale ring. Resolution may be sacrificed if higher intensity is desired. The properties of a mosaic crystal monochromator are between the wide band-pass (see the following section) and perfect crystal monochromators [ 11]. As shown in Eqs. (2-9) and (2-10) the mosaic crystal monochromator provides greater reflection intensity. The pyrolytic graphite mosaic crystal produces greater reflection intensity, but the band width is spread to about 170 eV, yielding an X-ray of 8 keV. Silicon with a rough ground surface also displays mosaic crystal properties. It is important to choose a monochromator that best matches the size and composition of the sample.

Wide band-pass monochromator In some cases, greater intensity is required and the high resolution of a crystal monochromator is not. A wide band-pass monochromator is defined as a monochromator with an energy resolution, AE/E, of more than 0.1. There are two types of such monochromators. One combines a total reflection mirror with an absorber or a transmission mirror. The other type uses a synthetic multilayer as a monochromator element. Iida et al. [20] studied monochromators that combined a total reflection mirror and an aluminum absorber (or a transmission mirror such as a soap film or Mylar film). Their calculations are shown in Figs. 2-5 and 2-6, and the results of their experiments in Figs. 2-7

89

1.0

_

P~ ~

%.I

p,.

~

0.5 //

-

-

/

e/

//

/ /

-

0.0

_/

200_/'-'11~\ // ~'k~ / 409.. "'.'~k,.x~

/

j"-

-.-'r"~-"l

m

5

'

m

,

m

n

~

~

m

10 Energy / keV

_

m

i

-

T - -

15

Fig. 2-5. Calculated fused quartz reflection mirror responses in combination with A1 absorbers (broken lines) and without an absorber (solid line). The glancing angle of the reflection mirror is 2.5 mrad. The absorber thicknesses are shown in the figure in ~tm. The cutoff on the low energy side is not sharp. From Ref. [20], reprinted by permission of Elsevier Science Publishers B. V., Amsterdam.

I

1.0 p~ p,.

-

~

. l

l

.I

3//

/

-

~~ 0.5

I

i

a

i

i

i

/ / i

/

_

I

I

_1 I

/

/

/,

2")[ ~ / 2.3 I / I I I I 2

I

I

t

I

I

I i

I I

I I

I m

0.0 5

a

t

m

n

10 Energy / keV

n

m

15

Fig. 2-6. Calculated fused quartz reflection mirror responses in combination with (broken lines) and without (solid line) a soap film transmission mirror. The glancing angles of the transmission mirror are shown in the figure in mrad. The soap film thickness is 1 000 A. The cutoff on the low energy side is sharp compared with the cutoff of the reflection mirror / absorber combination. The glancing angle of the reflection mirror is 2.5 mrad. From Ref. [20], reprinted by permission of Elsevier Science Publishers B. V., Amsterdam.

90 ,=

1.0

(a)

~

aW~tshO%ter -

1.0

(b)

-

. ~ 4 - - - . . without f ,I,IiN absorbeq / ~ ~ 70/.tm

o N

70 m ~0.5

140 m

0.0:

0.0 I

4

0.5

i

i

I

6

8

.1

i_

10

i

i

12

i

i

i_

i

14 16

!

i

6

4

i

8

!

i

10

i

i

12

I

I

I

]

14 16

Energy / keV

Energy / keV

Fig. 2-7. Measured responses of the Pt coated (a), and non-coated (b), fused quartz mirror in conjunction with the A1 absorbers. A wide energy band-pass greater than 20% was achieved. From Ref. [20], reprinted by permission of Elsevier Science Publishers B. V., Amsterdam.

1.0-

1.0~ '(1))' ' ' A ~ - ~ [with p m '~,~

9

i

ttrans

No.o

,,, 4

6

8

'withou; ~ tr.ans. ]

l

o.o 10 12 14 16 18 20 Energy / keV

4

6

8 10 12 14 16 Energy / keV

18

Fig. 2-8. Measured responses of the fused quartz reflection mirror using soap film (a) and Mylar (b) transmission mirrors. For the use of the transmission mirror, each curve shows the response of a different glancing angle to the transmission mirror. A sharper cutoff at the low energy tail is achieved than with the reflection / absorber combination. From Ref. [20], reprinted by permission of Elsevier Science Publishers B. V., Amsterdam.

91 and 2-8. They obtained a wide band pass of more than 0.2. That using a transmission mirror has a sharper cutoff in the low energy region (see Fig.2-8a). Figure 2-9 shows the spectrum of X-ray fluorescence measured by the energy dispersive method, using chelated metal-resin beads as a sample. When using an absorber, the signal-to-background (S/B) ratio is large in the low energy region, but the X-ray fluorescence of Zn overlaps the scattered X-ray. On the other hand, the combination of a total reflection mirror and a transmission mirror provides an excellent S/B ratio for the X-ray fluorescence emitted by Zn. Synthetic multilayers have recently been receiving attention as excellent wide band-pass monochromators. These synthetic lattices stack two substances, with different atomic numbers (e.g., silicon and tungsten), one on the other at intervals between a few and a few tens of A. Early in their development there were problems resulting from the two substances diffusing at the interface. Recently, however, it has been possible to produce excellent multilayers in the desired combinations and intervals [27]. Because of their controllable lattice spacing they are useful not only as wide band-pass monochromators but also as monochromators for the soft X-ray region m a region that has lacked an appropriate monochromator. 2.2.2.

Detectors

It is often pointed out that a stable SR permits a correct calculation of its intensity, wavelength distribution, and angular distribution. In fact, however, the incident X-ray has to be monitored to ensure accurate measurements and experiments. This is because, even if the electron or positron beam put out by the storage ring is very stable, it cannot prevent the SR intensity from fluctuating because of the thermal instability of the optical elements. Fluctuations in position and direction of the electron or positron beam also contribute to fluctuations in the intensity of the X-rays. This is why the current in the storage ring beam cannot be used to monitor the incident X-ray. Monitoring part of the X-ray flux is not desirable either, since the flux does not necessarily have a uniform wavelength and intensity distribution. The ionization chamber is generally used as a detector for monitoring in the Xray region. When an X-ray irradiates a gas, the gas absorbs the radiation and is ionized. In the ionization chamber method, the electric charge caused by this ionization is measured to obtain the intensity of the incident X-ray. The height of the emitted pulse signals is too small to be measured. Therefore, normally the direct current is measured instead. The current produced in the ionization chamber is linearly related to the number of the incident photons: I = neEe/W

(2-11)

where I is the output current of the chamber (A), n the number of the incident photons (s-l), e the detector efficiency, E the energy of an incident photon (eV), e the electronic charge (1.6 x 10 -19 C) and W the energy to produce an electron-ion pair (eV). Despite the complicated process of gas ionization, W is known to be characteristic of a gas molecule, regardless of the

92

(a) |

1.0

l

(b) !

l

i

i

"2.5 GeV 92.3 mA

!

.0 2.5 GeV 75.9 mA

Zn MAX. CTS. 3628.5

Mn

Zn MAX. CTS. 4764.8

Ar

.

~05

Scattered

'.5

Mn

o~,,4

Ar Ca


.0

0.0 I

i

2

i

i

4

i

i

i

i

a

i

I

I

6 8 l 0 12 Energy / keV

i

.

I

14 16

2

4

6

8

10 12 14

16

Energy / keV

Fig. 2-9. Fluorescence spectra from a Ca, Mn and Zn adsorbed chelate resin with 20 ppm concentrations of each element, using the reflection mirror and A1 absorber combination (a), and the reflection / transmission mirror combination (b). Counting time, 100 s; MAX. CTS., maximum counts. From Ref. [20], reprinted by permission of Elsevier Science Publishers B. V., Amsterdam. kind of ionizing particle and the operating conditions of the ionization chamber. When n = 109 photons s-1, e = 0.2, E = 8 000 eV, and W = 30 eV, I will be 8.5 x 10-9 A. There are many kinds of ionization chambers. The structure of the one used at the Photon Factory is shown in Fig. 2-10. The parallel-plate type is employed because (1)the electric field between the

H.V I'1' Electrode

X-Rays Electrode

Amplifier

Fig. 2-10. Schematic diagram of a typical ionization chamber (parallel-plate type) used at the Photon Factory.

93 electrodes is uniform, (2) it is easy to set up, and (3) it is easy to use. A voltage is applied across the electrodes to keep ions and electrons apart. The ionization chamber has a wide dynamic range of more than 5 decades, high linearity, and is free of dead-time losses. The Xray absorption can be controlled by changing the pressure and kind of the gas contained in the ionization chamber, or the electrode length therein. The X-ray absorption by nitrogen and argon contained in a chamber with a 17 cm electrode is shown in Fig. 2-11. It is desirable to use 5-20% of the incident X-ray for intensity measurements, transmitting the rest to the sample. Another method of monitoring incident X-rays uses a scintillation counter to measure the radiation scattered by a foil made of a low atomic weight element such as aluminum. The method of detecting X-ray fluorescence is basically the same as that of laboratory X-ray devices. When using SR, the energy dispersive method is often employed because it is capable of rapid, simultaneous multi-element analysis. A solid state detector is saturated at a few thousand counts s-1. When XRF is used for trace element analysis, scattered radiation makes up the greatest percentage of X-rays reaching the detector. Fortunately, however, since SR is linearly polarized, scattered radiation can be dramatically reduced by positioning the detector perpendicular to the beam. The calculations for this are discussed in Section 2.3.2. A high counting rate system is also considered. Furthermore, multi-element detectors have been developed. They incorporate up to a few tens of detectors. Reduction of X-rays to individual detectors eliminates dead-time losses due to saturation, and the large solid angle which can be covered by the multiple detectors increases the overall detection efficiency. A large solid angle is of great importance when measuring by the wavelength dispersive method. 2.2.3.

Beamlines

The first thing to do when fabricating a beamline for XRF is to determine the energy region for measurement. Different beamlines are required for analysis or measurement of different energy regions: i.e., the analysis of light elements in the soft X-ray region of less than 1-2 keV, the measurement of X-rays in the region of 2-30 keV, or of the K-series X-rays of heavy elements. For measurement of heavy elements, the beamline must be fashioned in such a manner that it can accommodate a large scale SR facility or a wiggler. Strict shielding of radiation is also required. When using soft X-rays, the beamline must be made under high vacuum, since beryllium windows cannot be used in this case. The absorption of X-rays by beryllium is shown in Fig. 2-12. In a beamline for measuring the X-ray fluorescence in a 230 keV region, 2 to 4 beryllium windows are normally used. The total thickness is 300 ~tm1 mm. The design of the optical system depends on whether a microbeam is used or not. It must also be decided whether a crystal or a wide band-pass monochromator should be used. If desired, the optical system can be designed to be compatible with both types of monochromator. Different equipment in the same beamline should be substituted in the hutch for the energy dispersive and the wavelength dispersive methods. As an example, Beamline 4A installed at the Photon Factory is shown in Fig. 2-13. (In this chapter we will not discuss the focusing optical mirror system which is inserted between the

94

100-

1.080-

N2

6

0.8-

owit

'~

60-

.-,06-

o

9 1,,,~

~4oo

~0.4-

< 20

0.2-

0

' 0

I 10

'

I 20

'

I 30

Incident X-ray energy /keV Fig. 2-11. Absorption curves of X-rays passing through 17 cm lengths

0.0-

,

0

I

4

'

I

8

'

I

'

12

Incident X-ray energy /keV Fig. 2-12. The calculated transmissivities of X-rays through a 300 ~tm

of gases (N2 and air).

thick beryllium window.

monochromator and the hutch for analysis using a microbeam.) It is about 9 m from the source of light to the outer wall of the ring. A double-crystal monochromator is positioned about 1 m from the wall. Three beryllium windows are used, with a total thickness of 650 ~tm. To maintain the outgoing beam at a constant height, regardless of its energy, this monochromator is equipped with a mechanism to translate the first crystal parallel to the incoming beam whilst allowing it to be rotated [28]. It also can put out a strong beam by focusing rays in the horizontal direction using a curved second crystal. When Si(111) is used Double-crystal monochromator

Branch beam shutter

Slit

R I1

P,

i

Crystal

Fig. 2-13. Schematic drawing of Beamline 4A at the Photon Factory.

Hutch

95 as the monochromator crystal, the energy width for an 8 keV X-ray is 3.3 eV. The photon flux in this energy band is of the order of 108 photons s-1 for a beam 1 mm square. The equipment in the hutch must be remote-controlled, since it is impossible to enter during use of the X-ray beam. The equipment used for the energy dispersive method and built into a hutch includes a slit, a sample chamber, an incident X-ray monitor, and a solid state detector. A small TV camera is very useful for monitoring the position of the sample. A laser beam is sometimes used to help in positioning the equipment and the sample. The sample chamber should be able to hold a vacuum and be equipped with a remote control device for inserting several samples. The solid state detector must be positioned perpendicular to the beam. This minimizes scattering, since the SR is linearly polarized in the orbital plane of the storage ring [29]. Figure 2-14 shows the vertical divergence distribution of the SR (11 keV) from one electron [ 11]. The abscissa shows the angle from the electron orbit, and the vertical distance is measured at a position 14 m from the light source. The vertical polarization component vanishes on the orbital plane of the electron beam. This means that most X-rays are horizontally polarized when the beamline is horizontal to the orbital plane of the electron. Therefore, if the sample and the detector are positioned within 1 mm of the beam center, the

1.0

el

0.5

% 0.0

0

\

.1 .2 Angle / mrad

Displacement / mm Fig. 2-14. Calculated vertical divergence distribution of the SR from one electron at E = 11 keV. Parallel and perpendicular polarization components and their sums are shown by the solid, broken and dotted lines, respectively. The abscissa indicates the angle from the electron orbit and also the vertical displacement at 14 m from the source point. From Ref. [11], reprinted by permission of Elsevier Science Publishers B. V., Amsterdam.

96 vertical polarization component is very small. Iida et al. [11] measured the intensity distribution, in the vertical direction, of incident and scattered X-rays and X-ray fluorescence, as well as the distribution of the ratio of the intensity, in this direction, of the X-ray fluorescence and the scattered X-ray. The results are shown in Fig. 2-15. The monochromator has a single Si crystal, lapped with #600 SiC. The solid state detector is positioned perpendicular to the beam. While the intensity of X-ray fluorescence is proportional to the intensity of the incident X-ray, that of the scattered radiation is at a minimum at the beam center. Non-monochromatic excitation has the best detection limit in absolute (weight) amount because such excitation uses a very strong incident X-ray. However, when the scattering is strong or when the sample contains matrix elements with high atomic numbers, the emitted Xray fluorescence saturates the detector, resulting in a high detection limit in relative concentration. Monochromatic excitation coupled with a crystal monochromator allows the incident X-ray energy to be adjusted to the most efficient value for the element to be measured. For this reason, this method provides a lower detection limit in relative concentration. However, it yields a higher detection limit in absolute amount than excitation by a nonmonochromatic beam, because the total X-ray intensity for excitation is lower. The wide

[

I

I

I

I

I

I

I

-1.0

.-.mr ,d

30 I--

"~,

\

-0.5~

20

e,

10-

I '

0 1 2 Vertical d i s p l a c e m e n t / m m

,.$

0

Fig. 2-15. The variation of the incident ( 9 ), and scattered ( i ) , Zn K(t fluorescence (A) radiations, and the ratio of the Zn signal to the scattered radiation (o) as a function of the vertical displacement. The sample is a 20 ppm Zn adsorbed chelate resin. The monochromator used is silicon lapped with SiC. The excitation energy was 11 keV. Null vertical displacement indicates the center of the beam. The vertical resolution was 250gm. l~rom Ref. [11], reprinted by permission of Elsevier Science Publishers B. V., Amsterdam.

97 band-pass monochromator has features which lie somewhere between these two. The most efficient method should be chosen according to the composition of the sample and the elements to be measured. SR has a very small angular divergence in the vertical direction (approx. 0.1 mrad). Therefore, the maximum size of the beam's vertical component arriving at the sample is limited to a few millimeters. When a large beam is required, and it is necessary to enlarge it, the asymmetric reflection (asymmetric Bragg magnifier) of a crystal can be used (see Chapter 8, Section 8.3.5). Use of the asymmetric reflection easily permits the diffracted beam to have a cross section about 10 times larger than that of the original beam. From Liouville's theorem, a geometry which increases the cross section of a beam also improves its collimation. On the other hand, the beam's cross section can be reduced by using this method in the opposite way. Unlike the method using a slit, it maintains the intensity of the beam. Other components of a beamline include a vacuum system (vacuum pumps, vacuum indicators, valves), shutters, and an interlock system. In addition, a beam position monitor is useful for experiments using a microbeam. The control system for X-ray fluorescence detection is basically the same as the one used in the laboratory. 2.3. XRF USING M O N O C H R O M A T I C EXCITATION 2.3.1.

Characteristics

Despite its rapid, nondestructive analysis, XRF is not quite sensitive enough. To improve detection limits, the incident intensity must be increased to increase the intensity of X-ray fluorescence, and the background must be reduced. SR meets these requirements with its wide continuous spectrum and high intensity. The intensity of SR is 100-10 000 times that of conventional X-ray sources. It also is linearly polarized. This property can be Used to 'reduce the background: a detector positioned perpendicular to the incident X-ray beam reduces scattering. A monochromatic X-ray of a specified energy can also be separated from SR using a monochromator. The characteristics of monochromatic excitation are as follows: (1) The excitation energy can be designated to be slightly above the absorption edge of a specified element. This increases the sensitivity of measurement for that element. The absence of the unnecessary spectrum reduces the background and improves the S/B ratio. (2) Overlapping peaks can be experimentally separated. Choosing an excitation energy to be between the absorption edges of the elements involved can eliminate the effect of an extraneous element. (3) The strong signals emitted by predominant matrix elements quickly saturates the solid state detector, affecting the detection of trace elements. Setting the excitation energy below the absorption edge of the predominant matrix elements reduces the strong signals. (4) The known spectral characteristics of the exciting X-ray facilitate fundamental calculations and thus help improve the precision.

98 The difference between continuum- and monochromatic excitation is indicated in Fig. 2-16 [ 11]. Twenty ppm of calcium, manganese, and zinc each adsorbed in a chelated resin are used as the sample. Continuum SR, with and without an A1 absorber, and SR monochromatized by a crystal monochromator, are used as the excitation sources. The surface of the silicon crystal used in the monochromator is lapped using SiC. The results clearly show that the use of SR greatly improves the S/B ratio. Of particular note is that much less scattering occurs in the case of monochromatic excitation compared with other methods. Figure 2-17 shows the changes in the spectrum of X-ray fluorescence in relation to changes in the excitation energy using a NIST SRM 612 Glass Wafer (major constituents: SiO2 (72%), CaO (12%), Na20 (14%), and A1203 (2%), plus about 50 lxg g-1 of many other elements) [30]. Figure 2-17a is for excitation by a 19.5 keV X-ray, and Fig.2-17b for a 10.5 keV X-ray. It shows that the latter improves the (a) . . . . . .

":'. 1.0

.1,,,4

=

2.5GeV 105.0mA MAX.CTS_ Ar 1437 ,,.,) C ~ I'Mn ~ Z n

.0

0.5

).5

Ar

0.0 2

4 ' 6 ' 8;' 1'0"1~2' 14 Energy / keV

1.0

05

- MAX.CTS. "_ 2436.0 - ir

4

6

8

10

12

14

Energy / keV

l ZB fi il

~ "~ il Nil ]

0.0 2

4

6

8

10

12

Energy / keV Fig. 2-16. Comparison of fluorescence spectra from a 20 ppm metal adsorbed chelate resin excited using: (a) continuum SR; (b) continuum SR with a 280 ~tm thick A1 absorber; and (c) monochromatized SR. Counting time is 100 s for (a) and (b), and 200 s for (c). From Ref. [11], reprinted by permission of Elsevier Science Publishers B. V., Amsterdam.

99 (a) .

1.0

.

-

.

t

.

Ca

.

.

.

E~," 19.5 keV t: 500s

I[

SRM (Glass612fer) Max.CTS.: 6323

scatl

d

0.5

![ -

Sr Zr Nb

l] [[

Si

Rare earth and transition

~Y~ Rbl[ /1 I] l[

Al[I

]l]ll

! "11

0 0

5

10 Energy/keV

15

20

(b) 1.0 Ca

-

_ _

E~," 10.5 keV t" 500 s

SRM 612 (Glass Wafer) Max.CTS.: 31251

m

0.5

Scat.

-

m

[" [--

.

Rare earth and 11 transition /I" [Vi elements I!

o 0

5

10 Energy/keV

15

20

Fig. 2-17. The change in SRXRF spectra from a NIST Standard Reference Material 612 caused by the excitation energy [E?'is 19.5 keV for (a), 10.5 keV for (b)]: t = counting time; Scat. = scattered radiation. From Ref. [30], reprinted by permission of Kodansha, Tokyo.

S/B ratio significantly for elements with absorption edges in the 5-10 keV range, such as rare earth and transition elements. This is because the excitation efficiencies of these elements are increased, and because unnecessary spectrum components which contribute to the background are eliminated.

100 ooo

(a)

3000 -

E r " 16.00 keV t :200s

800

(b)

As + Pb

Scat.

d

Ey" 12.50 keV

2500 -

t

9 200 s

AsKs

Scat.

2000 -

600

1500-

. v,.=l r~

400-t

AI

A1

II / PbL~I 1000500 -

0

i

i

i

i

I

0

5

10

15

20

E n e r g y / keV

.it...

O0

"~ 5

_

i

i

10

15

i 20

Energy / keV

Fig. 2-18. Advantage of selective excitation. SRXRF spectra of a sample containing Pb and As caused by excitation energy above the Pb Lin and As K edges (a), and between them (b). Max. counts: 1 296 (a) and 2 330 (b). From Ref. [31], reprinted by permission of Elsevier Science Publishers B. V., Amsterdam.

Now we will discuss the effect of selective excitation. Figure 2-18 shows the spectra of an A1203 sample containing a 0.1% mixture of As and Pb in a 1:1 molar ratio [31]. The excitation energy is 16.0 keV for Fig. 2-18a, and 12.5 keV for Fig. 2-18b. The K absorption edge of As is at 11.862 keV and the LIII absorption edge of Pb is at 13.038 keV: therefore, if conditions (a) are used the peaks of As Ka (10.53 keV) and Pb La (10.55 keV) overlap. If conditions (b) are used, the excitation energy is set between As K and Pb LIII: hence, no peak appears for Pb La, and the peak of As makes its quantitative analysis possible. The detection limit and accurate quantitative analysis are the most important factors of XRF used for elemental composition analysis (percent) and trace element analysis (ppm, ppb). We will consider these factors below. 2.3.2. Detection limit

Determinants of the detection limit (a) Excitation efficiency and fluorescence yield. When an X-ray irradiates a substance, the X-ray photons excite the atoms of the substance, emitting inner-shell electrons as photoelectrons and creating orbital vacancies. This process of excitation is due to the photoelectric effect. Therefore, the probability of photoelectric absorption (photoelectric effect) is linearly related to the excitation efficiency. This depends on the element and the energy of the incident X-ray. The contribution of photoelectric absorption to total absorption for incident X-ray energies of 10, 30, and 100 keV is shown in Fig. 2-19, which is plotted

101 100

..-

...

80

J ~-60/I /I

I

/I'

:""

/

x : photoelectric absorption. Oc:Comptonscatte ng.

/

f

./" ......

OT:Th~176 scatte~ng" ~: : electron-pair creation.

20

0~

I

20

I

I

40 60 Atomic n u m b e r

I

80

Fig. 2-19. Ratio of total absorption (~t) to photoelectric absorption (x) [32].

using the tables reported by McMaster et al. [32]. This shows that, except for the 100 keV radiation, the total absorption coefficient can be regarded as the excitation efficiency, since most of the absorption coefficient is due to photoelectric absorption. The absorption coefficient's dependence on incident X-ray energy is shown in Fig. 2-20, based on Sasaki's table [33]. The absorption coefficient (excitation efficiency) is highest when the energy is slightly above the absorption edge. The vacancies caused by this excitation are filled by electrons from the outer shells. As shown in Fig. 2-21, the process of filling the vacancies is accompanied by a release of energy, which occurs by one of the following two processes. In the first case, an electron in an outer shell drops to the energy level of a vacancy, emitting an X-ray photon with energy equal to the difference between the two energy levels involved. In the other process, the released energy is transferred to another electron to eject an Auger electron. The ratio of the number of emitted X-ray photons to the number of primary vacancies created is called the fluorescence yield, which depends on the element and the absorption edge. Figure 2-22, plotted using the values tabulated by Bambynek et al. [34], shows the fluorescence yield for the K-series X-ray fluorescence. Elements with small atomic numbers have a low probability of releasing X-ray fluorescence, most of them emitting Auger electrons. In the detection of X-ray fluorescence using the K absorption edge, Ka and K~ lines are emitted. As shown in Table 2-3, the intensity ratios of the Ka to KI~ lines are also element dependent.

102 500 -

7 I " absorption edge

r

~400O C

o300-

9 1=,,4

O

0

o200

ZrK

0

~lO0r~

d~

<

0-

Fe K

Pt LIII

I_

~

I

I

I

I

I

I

0

5

10

15

20

25

Energy / keV Fig. 2-20. Energy dependence of absorption coefficients for Fe, Pt and Zr, plotted as a function of incident X-ray energy [33].

X-Ray fluorescence emission

Auger electron emission (the Auger effect) ctron

2P3/2 2Pl/2 ..... [ O-'---~

2S Ko~1 X-r

ls

i

--O

Fig. 2-21. Energy release mechanism after the X-ray absorption process.

103 1.00.8

Table 2-3 Relative Ko~ line intensities in the K-series

""

Atomic number

9

o0.6-

20 24 28 32 36 40 44 48 52 56

~

0

.

4

-

02

0.0I 0

'

I 40

'

I 80

Relative intensity (Kct)

'

0.887 0.883 0.881 0.871 0.856 0.844 0.833 0.824 0.816 0.809

Atomic number Fig. 2-22. Fluorescence yields for K absorption edges [34].

The product of the excitation efficiency, the fluorescence yield, and the ratios of the Ka line represents the intensity of the Ka X-ray fluorescence detected. Calculated values for this product (the fluorescence intensity) are indicated in Fig. 2-23. Since the most suitable excitation energy for the desired measurement can be selected, SRXRF using monochromatic excitation improves the detection limit.

lOO~ 6"

4: . 2-

0 0 0 0r ~ @

_= 1~ ........ 15

I

I

I

I

I

20

25

30

35

40

Atomic number Fig. 2-23. Variation in fluorescence intensity (mass absorption coefficient x fluorescence yield x relative intensity of Kt~ line) with atomic number at 15 keV of the incident X-ray energy. The 15 keV incident X-ray energy is smaller than the binding energies of the electrons in the K shells for atomic numbers above 37.

104

(b) Scattered X-ray and bremsstrahlung. The detection limit is affected to a great extent by the background. The X-ray scattered by the sample contributes greatly to the background. Environmental and biological samples, both the subjects of trace element analysis, are composed mainly of light elements such as carbon and oxygen, and contain very small amount of metals. Much of the radiation intensity from these samples, measured by the energy dispersive method, is the result of scattering caused by light elements. Baryshev et al. [2] and Hanson [35] made thorough studies of scattering by polarized X-rays. In the following we will describe the theory explaining why polarized X-rays reduce the background. There are two classifications of X-ray scattering: coherent scattering and incoherent scattering. The differential cross section of coherent scattering (Thomson scattering) for a free electron is as follows: dtYT = dO

rg.le. ol =

(2-12)

where e 0 is the polarization vector (in the direction of the electric field) of the incident X-ray, e* is the conjugate complex polarization vector of the scattered radiation, and r0 is the classical electron radius. For linear polarization: (d~)

= rZ.sin2O

(2-13)

pol

where ~ is the angle between the direction of polarization of the incident X-rays and the direction of observation. Therefore, the differential cross section of Thomson scattering becomes zero when the direction of observation coincides with the direction of polarization of the incident X-rays. Since the SR obtained using a bending magnet is polarized in the horizontal direction, Thomson scattering can be minimized by positioning the detector perpendicular to the SR beam. On the other hand, for a fully unpolarized X-ray: (d-~o)

= 1 .r~.(l+cos20) unpol 2

(2-14)

where 0 is the angle between the direction of propagation and the direction of observation. Therefore, observation from the perpendicular direction minimizes Thomson scattering also. However, in this case most of the scattering results from electrons bound to atoms rather than from free electrons. This form of Thomson scattering is called Rayleigh scattering. The differential cross section of this scattering in a plane horizontal to a detector is as follows:

105

= r~-{f(q, Z)}2.(1 - sin20)

dO'R)

(2-15)

-d-~/pol wherefis the atomic scattering factor, q = sin (0/2)/~ is the momentum transfer, and Z is the atomic number. Observation from the perpendicular direction minimizes the scattering. Incoherent scattering is called Compton scattering. The differential cross section of Compton scattering for a polarized X-ray is expressed by Klein-Nishina's formula: dO'c)

= ur 2 .(KK0)2 " (__~+ K

4cos2~ - 2)

(2-16)

where ~ is the angle between incident and scattered photons; K0 = 2rr/2o and K = 2n/~, are the wave numbers of the incident and scattered X-rays, respectively. Using the Compton formula,

K/Ko =

[1 +

a .(1 -

cos0 )]-1

(2-17)

a = Eo/mc 2

(2-18)

where E0 is the incident photon energy. When 0 = ~ = 90 ~ the intensity of the scattered radiation is minimized. For an unpolarized X-ray,

_

d--~/unpol - -~-

~-0 -- sin20 )

(2-19)

The dependence of the intensity of Compton scattering upon the polarization is indicated in Fig. 2-24 [ 10]. We have previously confirmed that the linear polarization of SR greatly reduces the scattering. However, even though SR is perfectly linearly polarized on an electron's or positron's orbital plane, it contains another polarization component away from the orbital plane. The beam and the window of the detector both have finite size : therefore, Compton scattering cannot be completely eliminated (see Fig. 2-15), although scattering can be minimized by positioning the detector perpendicular to the beam. Compton scattering can be reduced by increasing the distance between the sample and the detector: however, this reduces the solid angle and weakens the signals reaching the detector. Another cause of a background is bremsstrahlung. In the energy region normally used for XRF the sample absorbs most X-rays through the photoelectric effect. The photoelectrons created in this process decay in the sample while emitting continuous X-rays, which also contribute to the background. The energy of a photoelectron ejected from the K shell of an atom by the photoelectric effect is as follows:

106

1.0xl0

-3

/ 0~~89"

-3

/

J

// /

0.5•

/

/

/

0=~=90"

5 10 15 E n e r g y / keV

20

Fig. 2-24. Ratio of theoretical difference cross sections for Compton scattering of polarized to unpolarized radiation under scattering angles 0 = ~ = 90 ~ and 0 = ~ = 89 ~ From Ref. [10], reprinted by permission of Amsterdam.

Elsevier Science Publishers

Ex = E I - EK(Z)

B.V.,

(2-20)

where EI is the energy of the incident X-ray and EK(Z) is the energy (work function) required to excite an electron from the K shell up to the continuous energy level. For a sample with a matrix of an element of atomic number Z, if Nx photons with energy between Ex and Ex + dEx are emitted [36], Nx = 2.5•

10-6.Z.Ni.cYip.t ~ X "(Ez9

Ex)

(2-21)

where NI is the number of incident photons, t is the thickness of the sample (g cm-2), and crw is the photoelectric absorption cross section of the incident X-ray. The distribution of the bremsstrahlung for a 10 keV X-ray with a carbon matrix is shown in Fig. 2-25, which is calculated from Eq. (2-21).

107 1.0 0.8 .~..~ r,r

I=

"

~

"~0.4 r~

o.2 0.0 0

2

4

6

8

10

Energy / keV Fig. 2-25. Calculated bremsstrahlung intensity versus its energy in a carbon matrix using a 10 keV incident X-ray energy [36].

Calculated values of the detection limit It is important in SRXRF to estimate the detection limit correctly. The detection limit is commonly defined as the minimum concentration or absolute amount, of an element in a sample, which can be detected with a confidence level of above 90%. Gordon [12] calculated this theoretically. His calculations are based on the parameters of the NSLS, a 2.5 GeV ring. He considered two kinds of samples. One contained a carbon matrix, as an example of a bioorganic substance, and the other a mineral sample containing nine kinds of elements. Both samples were assumed to be attached to a carbon-matrix substrate of 1 mg cm -2 (e.g., a Kapton film). Both the energy dispersive and wavelength dispersive methods were considered. In the energy dispersive method a Si(Li) detector with a 30 mm 2 crystal area was assumed to be used, and in the wavelength dispersive method a multi-channel crystal spectrometer system. To calculate the detection limit, Gordon used the following formula: CD(ppb) = N x 109 / (I (7 T G A)

(2-22)

where: N is the detectable signal, I is the integrated beam intensity, cr is the cross section in cm 2 g-l, T is the sample thickness in g c m -2, G is the fraction of the solid angle subtended by the detector, and A is the self-absorption correction.

108 From the criteria of Currie [37], N is equal to 3.29(nNbg)a/2 (Nbg is the background beneath the signal; 1 -< n --<2). In this calculation, Gordon took the size of the detector and the distance from the sample into consideration. He also calculated the detection limit for the photon fluxes, further increased at higher energies by using a 6-pole wiggler. Figure 2-26 shows Gordon's calculations of the determination (quantitation) limits for the carbon matrix sample measured by the energy dispersive method. The determination limit (CQ) was obtained from the detection limit (CD) using CQ/CD=I0f/3.29, wherefis a correction coefficient for the amount of background. The distance from the sample to the detector is 10 cm. The value (CQ) is for a one-minute measurement. The detection limit (Co) is from a third to a fifth of this value. 3

10

i

i

i

i

Ktx

9

l

i

LO~

~- ld 30 keV

t\

0 eV,

"~ 101

,

15 keV v

~o 10 0 .~ "~

0keV

!~~,~~3 keV \ -11 10 10

N \20keV

10keY 15 keY

1

I

I

I

I

20

30

40

50

t

60

t

70

80

Atomic number Fig. 2-26. Determination limits for 2 mg cm -2 carbon matrix sample using a Si (Li) detector and a one-minute measurement. Sensitivity curves are shown for five excitation energies ranging from 5 to 30 keV. The sensitivity expressed is a determination limit (concentration measurements) with a 10% standard deviation attributed to counting statistical errors. The detection limits are a factor of 3 to 5 lower than the determination limits shown here. From Ref. [12], reprinted by permission of Elsevier Science Publishers B. V., Amsterdam.

109 Experimental values of the detection limit

Starting in the 1980s, XRF experiments were conducted at various SR facilities, and the detection limit studied experimentally. Gilfrich et al. [7] made their experiments at SPEAR of SSRL. The beamline they used was not equipped with a mirror or a monochromator. It produced a non-monochromatic beam with 1 mrad divergence in the horizontal direction. The X-ray energy ranged from 2 to 60 keV. The experiments were carried out using the energy dispersive method and the wavelength dispersive method employing a fiat crystal. A vacuum deposit of metal on a Mylar film, and a solution dropped on a Millipore filter were used as samples. The X-rays were obtained using a 3 GeV ring with a storage ring beam current of 40-80 mA. The energy dispersive method allowed a 100-s measurement using a 2.4 • 10-4cm 2 incident beam size. The wavelength dispersive method employed a 0.4 cm 2 beam (100-s measurements). It used LiF and PET as analyzer crystals and a proportional counter as the detector. All the samples measured were very thin. The detection limit was assumed to be three times the standard deviation of the background (Fig. 2-27). The energy dispersive method gave a detection limit of the order of 10-12 g in absolute amount.

::i. ..

100

!

|

!

(a) Energy -1 dispersion 10

o ,~ o o

-2 10

m

10.3

i

/ /)/

K-lines I

20

I

I

40

i

i

l

_

10~ (b) . . . . Wavelength/ 10 -1 - d i s p e r s i i ~

_

10 -2

- - - - On filter On Mylar

-

L-lines I

I

60

Atomic number

I

I

80

10-3

~K .i

20

--~'--O'n filter On Mylar j ~ A 1

lines ~ n e s n

n

40

n

i

60

.

,

80

Atomic number

Fig. 2-27. Detection limits as a function of atomic number as measured by (a) energy dispersion and (b) wavelength dispersion. From Ref. [7], reprinted by permission of the American Chemical Society, Washington, D. C.

110 Also at SPEAR, Giauque et al. [38] studied the dependence of the detection limit on the excitation energy, taking advantage of the fact that monochromatic excitation can be set to any level. They reported that, under optimum conditions, they obtained a detection limit of 20 ppb for many elements. Bos et al. [ 10] compared SRXRF detection limits with those of conventional XRF and an analytical technique using proton excitation (proton induced X-ray emission spectrometry: PIXE). The conventional X-ray source used a Mo anode and Zr, Mo, and Ti filters. This source produced a 17.5 keV X-ray at 26 kV and 12 mA. For proton excitation, they used 3 MeV protons produced using a cyclotron. In the SR experiment, they used X-rays of 16.5 keV and 9.1 keV in beamline 7 at the SRS of Daresbury incorporating a pyrolytic graphite crystal monochromator. Measurements were conducted using NIST Orchard Leaves (SRM 1571) and Human Hair (IAEA-HH1). The detection limits obtained for each sample are shown in Fig. 2-28. The calculation was based on the criteria of Currie [37]. Measurements were made for 1 000 s at 2 GeV with a beam current of 200 mA. Compared with conventional XRF, SRXRF substantially improved the detection limits. It was found that SRXRF is nearly equivalent to PIXE up to Z = 30, and has an advantage for heavier elements. Specifically, the detection limit can be improved further because this method allows the user to set the excitation energy to any desired value (see the results using 9.1 keV in Fig. 2-28). They also studied how the V K~ X-ray arising from the 9.1 keV X-ray changed, depending on the sample thickness (Fig. 2-29). The results indicated that the detection limit is very sensitive to sample thickness when the sample is thin. Hanson et al. [8] performed their experiments at CHESS. This ring has an electron energy of 5 GeV and generates strong SR in the hard X-ray region. They used a channel-cut silicon monochromator, and chose the same sample that Bos et al. [10] used (SRM 1571). X-Rays of 13.0, 16.25 and 24.9 keV were used as incident beams. The detection limits were calculated using the criteria of Currie [37] (Fig. 2-30). The present authors performed a similar experiment at the Photon Factory. Using a 2.5 GeV ring with a storage ring beam current of about 200 mA, we measured several types of NIST standard reference materials. Powder samples were applied thinly to adhesive tape. The measured spectra of Bituminous Coal (SRM 1632a), Oyster Tissue (SRM 1566), Orchard Leaves (SRM 1571), Citrus Leaves (SRM 1572), and Aluminum-Silicon Alloy (SRM 87a) are shown in Fig. 2-31. A Si (111) double-crystal monochromator was used, with a 15 keV exciting X-ray. The X-ray fluorescence measuring device was developed by Iida et al., and the measurement time was 500 s. The sample and the Si(Li) detector were 45 mm apart. The size of the beam's cross section is shown in the figure. The cross section was changed so that the detector would not be saturated under the same geometrical conditions. The measurement was made under vacuum. The detection limits calculated based on the criteria of Currie [37] are given in Table 2-4 and in Fig. 2-32. Organic and alloy samples were found to have quite different detection limits. This is due to the different matrices of the samples. Even among organic samples, different compositions give different detection limits. Measurements of Citrus Leaves and of Aluminum-Silicon Alloy using an X-ray tube are shown in Fig. 2-33.

111 3-

10

7 e~o

(a)

102

o 1

10

l

o

10

0

i

SRXRF (E?= 9.1

10

e~

3

-

I

20

10

10

7

I

-1

[IET = 16.5 keV)

,[

30

40

(b)

102 -SRXRF

(ET = 16.5

O

o~

O o

~

10

10

0 -

-1

10

PIXE

-

SE,RXRF1 k ,V " ~ ~ ( T = 9.1 keV) ~

.,

, -. _~

I

!I

i

I

I ~"~-

20

30

,

40

A t o m i c number Fig. 2-28. Detection limits of several elements in, (a) NIST Orchard Leaves, and (b) IAEA Human Hair, for different excitation modes. From Ref. [10], reprinted by permission of Elsevier Science Publishers B. V., Amsterdam.

112

A

-

3000

0.04 X

~

/

~

2 GeV, 130 mA

/

o 2000

X

-0.03

1000 s

/

E~,= 9.1 keV -

1000 I - d

~:It:x_____

1,7 1,1

0

Z

.

.

.

.

.

.

b) I

I

10

i

20

-

30

i

40

Thickness (mg c m

I

0.02 k~ 0.01

"~

50

-2)

Fig. 2-29. Number of V K~ counts of samples with well defined thickness. Curve b shows the root of the number in the background beneath the peak normalized to the .peak content (proportional to the detection limit). From Ref. [10], reprinted by permission of Elsevier Science Publishers B. V., Amsterdam.

3

I0

I

I

I

I

+ 13.0 keV x 16.25 k e V -

It

§

~.~

1

' 24.9 keV

§

9~ lO -

s9

It e

N

§247

0

m NIlI

9

++

~

x

Ig Ig

...b

lo -~-2

10

I

10

16

I

I

22

28

I

34

40

Atomic number

Fig. 2-30. Detection limits of several elements in NIST Orchard Leaves when fluoresced with 13.0, 16.25 and 24.9 keV X-rays [8]. (Reprinted with permission from A.L. Hanson, H.W. Kraner, K.W. Jones, B.M. Gordon, R.E. Mills and J.R. Chen, "Trace Element Measurements with Synchrotron Radiation", IEEE Trans. Nucl. Sci., NS-30, 1339 (1983). 9 IEEE.)

113 5

10 t 04

(a) SRM 1632a (Bituminous Coal) Fe " Ti+V ^ ,,. K+Ca I /~Fe

1

~"

o~

"

o'

~~.'s ls

EL~

[(vkI

1

I

/~h"

Scat. /~

Br

.JVi

~

1

1

AY

Zn

.CTS..

10

,,,I,I /I

o

10

B.S.: 2.2 x 3.0 mm .dJ._

I 0

I 5

I 10

_ll ......

I 15

I

20

Energy / keV 5

10 10 r~

(b) SRM 1566 (Oyster Tissue) Zn

4 -

K p , SCI ~ ~Ca

1 03 -

Scat. As+Pb

Fe

~ L

Br

0

10 2 I ..I]

1

10 o

MAX.CTS:7337 B.S.: 2.2x 3.0 mm2

10 -

I 5

0

I 10

I 15

LLL_JtU,"ll=l...

I

20

Energy / keV 5

10 -

(c)

SRM 1571 (Orchard Leaves)

4

K A Ca

10 r~

1 0z -

pS

Scat.

fV~Ca

Fe

~MA

Mn

Pb+As Fe

Zn

Br

1 02 1

10 o

10 -i 0

I~ll

X. B.S.: 1.5X2.9 mm2

/l_d.I 1 ~

I

I

I

I

5

10

15

20

Energy / keV Fig. 2-31. SRXRF spectra from NIST Standard Reference Materials under vacuum. Excitation energy, 15 keV; counting time, 500 s; MAX. CTS, maximum counts; B.S., beam size; Scat., scattered radiation. Except for SRM 87a, thin samples were attached to adhesive tape: SRM 87a was used as it was.

114 5

10

-

(d)

SRM 1572 (Citrus Leaves)

4

10 :"4. r.~

1

Ca

-

03

B.S.: 0.7 X 0.4 mm

p~ICa

-

As+Pb

S

2

10

MAX.CTS" 4108

-

Mn

Fe

Cu

t~

2

Scat.

13r

Zn

Pb

1

10 0

10

0

I

I

10

15

..........

t

|

I

20

Energy / keV 5

10 "] 1 04 9i...i r,r

3

(e) SRM 87a (A1-Si Alloy)

1

10"]

Zn Fe Ni Cu Zn Ga/1 Mn,~e ~ \ ~ ~ 77APb

A1,Si

02

Pb

Scat. ~

9

101 10

o

I"

I

0

I

I

I

5

10

15

.....

~

I

20

Energy / keV Fig. 2-31. SRXRF spectra from NIST Standard Reference Materials under vacuum. continued Table 2-4 Detection limits in ppm (l.tg g - l ) obtained by the measurements of NIST SRMs at the Photon Factory on Beamline 4A Element Ti Cr Mn Fe Co Ni Cu Zn

SRM 1632a SRM 1566 SRM 1571 SRM 1572 SRM 87a (Bituminous Coal) (Oyster Tissue) (Orchard Leaves) (Citrus Leaves) (Al-Si Alloy) 60 m ~ 30 . 9 5 4

m -10 5 .

m 4 5 3 .

~ 4 3

.

m ~ 7 6

800 350 260 140

3 3 2

70 60 60

.

2 1 1

Measuring conditions are described in Fig. 2-31. Detection limits are calculated on the basis of the Currie criteria [37].

115

[] zx 9 O x

1000 _ ~......,~ o

~

~

9 Bituminous Coal 9 Oyster Tissue "Orchard Leaves "Citrus Leaves 9 AI-Si Alloy

~:~ 1 0 0 ..r

@

10-

0.1

I

I

I

!

I

I

I

20

22

24

26

28

30

32

Atomic number Fig. 2-32. Detection limits for NIST SRMs, derived from the spectra shown in Fig. 2-31 on the basis of Currie's criteria [37].

The measurements were made under vacuum, using a Mo anode of 40 kV and 20 mA, and a Mo secondary target. Measurement times were 1 000 s for Citrus Leaves and 500 s for the Alloy. Compared with measurements employing SRXRF, there is a clear difference in the background level. The detection limits of Orchard Leaves obtained from the experiments of Hanson et al. [8], Bos et al. [10] and ourselves are listed in Table 2-5. Each used a different ring, optical system, excitation energy, and sample thickness; yet the results all agree within 1 ppm. Iida et al. [ 11, 20], at the Photon Factory, studied the variation in the detection limits with the excitation mode. The samples used were 0-100 ppm of Zn, Mn, and Ca, adsorbed in a chelate resin, attached to adhesive tape. X-Ray fluorescence was measured by the energy dispersive method to allow calculation of the detection limits, using a white (nonmonochromatic) beam; an aluminum absorber only; a single-crystal monochromator using a silicon crystal surface lapped with SiC; a wide band-pass monochromator using a total reflection mirror and an aluminum absorber; and a wide band-pass monochromator using a total reflection mirror and a transmission mirror. The results are shown in Table 2-6. The strong intensity of white (non-monochromatic) excitation gives a low detection limit, in absolute amount. Using an absorber improves the detection limit for Zn, in relative

116 concentration. This is because scattering in the high energy region is reduced. The crystal monochromator gives the best detection limit in relative concentration since it reduces the background caused by scattering. The wide band-pass monochromator exhibits excellent performance in both relative concentration and absolute amount.

sRM1572

U' [ ~,

, t

(Citrus Leaves)

] 103~-

I , Scat. I A I

t~a Ca

10

'1

TM

.

1

.

.

I

5

. . . .

I

. . . .

10

I

.

.

.

.

15

1

sRMZTa

04

_/ 103~102

I

(Al-Si Alloy)

, Scat. I /~ 'l

Ni b tb

l,Si TiCr~

10

ii 20

1

5

10

15

20

Energy / keV

Energy / keV

Fig. 2-33. Spectra of NIST SRMs by XRF using a conventional secondary target (Mo) energy dispersive system, measured with a Mo tube, 40 kV, 20 mA, 1 000 s. The samples are those used in Fig. 2-32.

Table 2-5 Comparison of detection limits (ppm) of four elements in NIST Orchard Leaves (SRM 1571) by three different workers Element Mn Fe Cu Zn

Hanson et al. [8] a 4 2 0.6 0.5

a CHESS: 5.144 GeV, b SRS" 2 GeV, c PF: 2.5 GeV,

Bos et al. [10] b 2 2 0.6 0.5

16.25 keV, 16.5 keV, 15 keV,

300 s. 1000 s. 500 s.

Authors c 5 3 1 1

117 Table 2-6 Comparison of detection limitsa(DLs) for different excitation modes [11, 20] Excitation mode

DL in relative concentration

Irradiation area/ mm 2

DL in absolute amount Zn/pg

Zn(ppb) Mn(ppb) Ca(ppb) Continuum

550

410

440

3.5 x 10-3

0.13

Continuum 170 with absorber b Crystal 60 monochromator Mirror/absorber b 430

240

750

2.8 x 10- 2

0.34

70

200

1.1

4.7

180

410

1.1 x 10-2

0.33

Reflection/ 100 transmission(soap)

140

470

4.2 x 10-3

0.03

a The definition of the DL was a signal at least three times the square root of the background criterion. The counting time was 100 s. b A1 of 280 mm in thickness was used.

2.3.3.

Calibration

Calibration is performed in basically the same way as when calibrating conventional XRF. However, monochromatic excitation and collimation further facilitate calibration calculations. The results of an experiment on thin samples of several elements, performed by Kntchel et al. [39] using DORIS at HASYLAB are shown in Fig. 2-34. The results show excellent linearity. When using monochromatic excitation, the quantity of an element can be determined from the quantitative analysis value of another element using an X-ray fluorescence cross section.

Table 2-7 Calculated contents of several analyte elements in NIST Orchard Leaves (SRM 1571) using the known content of Fe (300 ppm) from the data shown in Fig. 2-23 Element K Ca Cr Mn Ni Cu Zn

Calculated values

Certified values

0.5% 0.9% 2.6 ppm 46 ppm 0.8 ppm 12 ppm 24 ppm

1.47% 2.1% 2.6 ppm 91 ppm 1.3 ppm 12 ppm 25 ppm

118

An example of determining the concentration of elements, based on the quantitative analysis value for iron, is shown in Table 2-7. SRXRF is also useful when using the fundamental parameters method, since it produces monochromatic incident X-rays and high collimation.

lO3 102

G 101

n

m

10~ 10-1 ,.,

10~ ~

..... 10I ~

1(~2

1~)3

Concentration (Bg g-1) Fig. 2-34. Calibration plots : (A) chromium; (m) arsenic (• 1.50); (0) yttrium; ( , ) molybdenum (• 0.75); (O) cesium (x 0.50): Co is the ratio of the counting rate to the standard. From Ref. [39], reprinted by permission of Elsevier Science Publishers B. V., Amsterdam.

2.3.4. A d v a n t a g e s

and d r a w b a c k s

We would add two more to the many advantages of SRXRF we have already described. First, because of its high sensitivity, this method can be used in the analysis of lower concentrations, using smaller samples, than conventional XRF. The X-ray fluorescence spectrum of a strand of hair is shown in Fig. 2-35. Even a small amount of sample can provide a spectrum with a satisfactory S/B ratio. This suggests that SRXRF is suitable for microbeam analysis. Another advantage is that SRXRF causes far less radiation damage to samples than methods such as PIXE which use charged particles as the excitation source. It is reported that the beam does more than 102 of the damage to blood cells caused by photon excitation [40]. We will now discuss the drawbacks of the present SRXRF technique. The SRXRF analysis of two kinds of aluminum alloys was compared with chemical analysis and glow discharge mass spectrometry of the same samples. We attempted to determine sample B, based on the quantitative analysis value (chemical analysis value) of sample A. The results are shown in Table 2-8 [31]. The detection limits for trace element analysis of metals show that SRXRF has no advantage over the other methods. Even with SR excitation, it is difficult to reduce the

119 spectral background below the lag g-1 level for many industrial materials containing elements with high atomic numbers. Attention should be paid to the effect of diffraction caused by the sample. Sutton et al. [41] discussed the effect of diffraction in continuum radiation. We will describe this same problem due to diffraction that we experienced when using monochromatic excitation [31]. We used the highly pure aluminum employed in VLSIs as a sample. The sample was cut from a block of material, using a superhard steel cutter, while dripping alcohol, and degreased. It is known that this sample contained about 80 ppb of U and Th. A preliminary XRF

(a) 1000

MAX.CTS: 2379 Cu

Scat.

.s..

~o 100

N

A /~

lO i .

1 -! o

I

I

I

5

10

15

.1..... I__ I

20

Energy / keV ,=

(b) ,=

ooo

s

-

MAX.CTS: 1068

,=

Zn

.

.I==4 r~

Scat.

Br

~

100-!..

N

-

Ar Ca

Fe

Br

Cu Zn Pb

lO. ,=

1

-

0

I

I

I

I

5

10

15

20

Energy / keV Fig. 2-35. SRXRF spectra of a strand of human hair (male)" (a), white part; (b), black part. Excitation energy, 16 keV; counting time, 1 000 s.

120 Table 2-8 Analytical results for two aluminum alloys obtained by three different methods Element

Cr Cu Fe Mn Zn Th(ppm) U(ppm)

Chemical analysis a (%)

GDMS b (%)

Sample A

Sample B

Sample A

Sample B

0.059 0.0073 0.11 0.060 0.018

0.0005 0.0009 0.11 0.0030 0.0050

0.062 0.007 0.12 0.068 0.018

<0.001 0.001 0.14 0.003 0.005

0.06 0.38

0.06 0.18

0.07 0.33

0.07 0.15

SRXRF (%) Sample B c

0.01 0.001 0.10 0.002 0.004 Not detected Not detected

a U was analyzed by fluorophotometry, Th by colorimetry and other elements by inductively coupled plasma atomic emission spectrometry. b GDMS is glow discharge mass spectrometry. c SRXRF analysis values of sample B are calculated on the basis of the chemical analysis values of sample A and the SRXRF measurement values of both samples. From Ref. [31], reprinted by permission of Elsevier Science Publishers B. V., Amsterdam.

measurement gave the amounts of U and Th shown in Fig. 2-36a. However, neither element was detected in the final measurement (Fig. 2-36b). Since we thought that the peaks that appeared in the preliminary test were caused by X-rays diffracted by the sample, we changed the incident angle slightly. This changed the spectrum in the 12-15 keV region, confirming that the results obtained in the preliminary test were incorrect. When we measured silicon containing a small amount of U, a diffraction peak appeared near the U Lo~ peak, as shown in Fig. 2-36c. Transition metals were also detected in this sample. These could have contaminated the sample when it was being prepared. After washing the sample with acid, only a small amount of iron was detected, as shown in Fig. 2-36d. Special attention must be paid to these problems, since the peaks from diffraction and contaminants on the sample surface might overlap the data used for analysis. Another problem with SRXRF is the increase in background due to resonant Raman scattering, as pointed out by Jaklevic et al. [42]. We have repeatedly maintained that when monochromatic excitation is employed, the energy of the incident X-ray can be set to any appropriate value to maximize efficiency. In addition, for an element with a large atomic number, the background can be reduced by setting the energy of incident radiation just below the absorption edge of that element. However, Jaklevic et al. [42] suggested that this was not always true. They suggested that setting the excitation energy just below the absorption edge of a matrix material caused resonant Raman scattering, and increased the background. Raman

121

scattering is a continuous spectrum with a cutoff in the high energy region. At SSRL, they studied Cu in GaAs. The X-ray fluorescence was measured with incidences of 9.2, 9.8, 10.0 keV. The absorption edge of Ga is at 10.37 keV. The intensity of resonant Raman scattering, which changes with the sum of Rayleigh and Compton scattering, was found to increase as the

1.0,

9

,

I

"~ ~" (a) ,~d [

'

I

L

"1

,

I

11

(b)

?"~

9

9

(?)

i,,

OI

|

,

Th Ltx ET. 20.50 keV (9) U L o ~ t:2000s

,

I

,

13 15 Energy / keV . . . . ET: 19.60 keV t : 2000s Fe

17

t:2,00s 0

,

5

~

,

'i~| "1

,

25

1.(l

~(d

E7:. 19.60 keY t: 1000 s

Th La

I k T Cr/! Fe

[ /

10 15 20 Energy / keV

~ !f,~#

Fe

.,./v

Ey. 22.70 keV

~

=

,, ]~,,.[

1~,! It

Th Ltx I J IU Lo~.f"-

~k%...TiCr~Fe ^ / ] , Ni

, E~ 22.70keV

/J t: 200 s

I U L a t'1 ~ 0

Fe

,

~ ,~ "~

Ey. 19.60 keV 3

5

t'2000s 7 9

0 11

13

15

2

4

6

8 10 12 14 16 18 20 Energy / keV

Energy / keV Fig. 2-36. SRXRF spectra of high-purity aluminum (a, b and d) and silicon (c). (a) Preliminary; (b) at two different tilt angles using the same sample as in (a); (c) at two different tilt angles of silicon containing a trace amount of U; and (d) after surface cleaning of the sample, following the measurement of (b). From Ref. [31 ], reprinted by permission of Elsevier Science Publishers B. V., Amsterdam.

122 incident energy gets closer to the absorption edge. The ratio of the peak areas of resonant Raman scattering and Rayleigh-Compton scattering was found to be 2.3 at an incidence of 10 keV, and 0.64 at an incidence of 9.2 keV. The detection limit for Cu was 1 ppm at an incidence of 10 keV, and 0.6 ppm at an incidence of 9.2 keV. The same workers compared this GaAs sample with a cellulose matrix sample and found that the background for Cu was 12.9 times larger than for cellulose at 10 keV, and 4 times larger at 9.2 keV. 2.4. E L E M E N T A L ANALYSIS BY TOTAL R E F L E C T I O N XRF 2.4.1. Total reflection method

The detection limit in XRF is improved by a greater signal intensity and lower background. To reduce the background in the energy dispersive method, it is necessary to reduce the scattering caused by the sample and the sample holder, and to keep down bremsstrahlung. We saw in Section 2.3.2. that polarized SR greatly reduces the background. In ordinary XRF, the sample supports should be as thin as possible. Various micrometer-thick materials, such as Mylar films and Kapton films, are used depending on the purpose of the analysis. To further reduce the background, XRF can use the total reflection of X-rays. As will be described in Section 2.4.2. if an X-ray is totally reflected by a surface, it hardly penetrates the substance. Therefore, attaching the sample to an optically fiat surface (reflector) keeps the scattering caused by the sample holder to a minimum, thereby improving the detection limit. Yoneda and Horiuchi [ 15] were the first to demonstrate the effectiveness of this method, using an X-ray tube (W target, 35 kV, 15 mA) and the energy dispersive method. A glancing angle was adjusted to be much lower than the critical angle, to achieve nearly 100% reflectivity. Detection limits of the order of ng were achieved for Cr, Fe, Ni and Zn. They also reported that this method eliminates the matrix effect and facilitates calibration. Experiments employing the total reflection method were made later using an X-ray tube or a rotating anode, and have become very popular, particularly in recent years [ 13, 14]. Analysis in the pg range is now performed routinely. Today, total reflection XRF spectrometers for silicon wafers take advantage of the nondestructive, highly sensitive, simultaneous multielement analysis method. These spectrometers, equipped with an automatic measurement device, are used to measure trace quantities of metal contaminants on the surface of silicon wafers, and make it possible to map them with a detection limit of 108-1010 atoms cm -a. An advantage of these units is that they can be installed "in-line" at semiconductor plants. In the laboratory, total reflection X-ray fluorescence (TXRF) spectrometry is mainly used for highly sensitive detection of impurities in solution, which may be dropped on a reflector and dried, or for the analysis of contaminants on silicon surfaces. However, most problems concerning calibration have yet to be solved. Iida et al. [16] thoroughly investigated the SR method at the Photon Factory. The advantages of using SR for TXRF are as follows: (1) Monochromatic excitation can be used to improve the S/B ratio.

123 (2) The excellent collimation of SR is suitable for total reflection experiments using grazing incident beams applied at small glancing angles. (3) The linearly-polarized beam further reduces the background. (4) Selective excitation improves the detection limit. Thus, SR is the most suitable excitation source for TXRF. 2.4.2. The principles of the total reflection method

As discussed in Section 2.2.1., the refractive index of X-rays is very slightly smaller than unity. Therefore, a highly collimated X-ray beam applied to a fiat surface at an angle smaller than the critical angle is totally reflected. Such a beam penetrates the sample only slightly, and the reflectivity of the X-ray is independent of its polarization. Under these grazing incidence conditions, the reflectivity R can be expressed as follows, using Fresnel's formula [43]: Ar ]2=

R=lAi

01- 02 '12 01+02

(2-23)

I

where Ai and Ar are the electric field amplitudes of the incident and reflected X-rays, respectively, and 01 and 02 are the respective glancing angles, as shown in Fig. 2-37. Generally, 02 is a complex number, described as follows using the complex index of refraction. 02 = ( 0 7 -

2~-

(2-24)

i 2fl2) 1/2 = P2 + i q2

p2 = 1 {[(01 - 262) 2 + 4/~] 1/2 + ( 0 2 _ 262)}

(2-25)

q22 = 1 {[(01 -- 2 ~ ) 2 + 4]322]1/2 - (0 2 - 2~)}

(2-26)

The values $2 and t2 are those indicated in Eqs.(2-2) and (2-3) for the reflector. The amplitude of the transmitted (refracted) X-ray is attenuated in the z direction. The depth at which the X-ray intensity attenuates to 1/e is given by Zp(O1) = 1

2k l.q2

=

~,

.[{ (0 2 _ 262)2+ 4132} 1/2 _ (0 2 _ 262)1-

1/2

(2-27)

2"~

where ~ is the wavelength of the incident X-ray, and kl=2n/A. The results of the calculation of the reflectivity and penetration depth (Zp) for silicon near the critical angle are given in Fig. 2-38. The wavelength of the X-ray is 1.24 A. For glancing angles smaller than the critical angle, the penetration depth of the X-ray is very small (a few tens of A). There is a standing wave on the surface of the sample due to the interference of the incident and reflected X-rays. The intensity of the X-ray on the surface of the sample is given by

124 Medium 1 (n l )

Medium 2 (n 2 ) Z

Fig. 2-37. Schematic drawing of X-rays when incident X-rays from air or vacuum (n1-1) irradiate the surface of a material having refractive index n2.

1.0-

.:-10

0.8-

-10

5

4

"~-06.~ 9

l,io

-10 ~0.4-

3

O

=

-lO

0.2-

2

>o

=,

0.0

I

0

2

I

I

I

4

6

8

lO

1

10

Glancing angle / mrad Fig. 2-38. The calculated glancing angle dependence of reflectivity and penetration depth for a silicon wafer using an incident X-ray with a 1.24/~ wavelength.

125 M(O1) = 4 O ? / { ( O1 +p2)2 + q2}

(2-28)

Calculation of this value for silicon gives the results shown in Fig. 2-399 The product of the intensity on the surface and the depth of penetration of the X-ray gives the intensity distribution of the X-ray fluorescence emitted by the substrate shown in Fig. 2-40. At a glancing angle smaller than the critical angle the intensity of X-ray fluorescence is very close to zero. The scattered X-rays are caused by X-rays that go into the substrate without being reflected. Therefore, the closer the reflectivity is to unity, the less is the scattering9 The condition of the surface of the substrate affects its reflectivity. A rough surface reduces the reflectivity, and thus increases the intensity of the emitted scattering and X-ray fluorescence. Surface roughness can be described using a group of fiat planes distributed in a Gaussian manner. Taking the standard deviation of the Gaussian distribution as tr, the reflectivity is given by R = Ro-exp[ - (4 11;010"/~)2]

(2-29)

where Ro is the reflectivity for a surface with no roughness. The reflection curve for a (r = 10 /~ is shown in Fig. 2-41 a. The corresponding X-ray fluorescence intensity is shown in Fig. 24lb. The angular dependence of the intensity of X-ray fluorescence when a sample is spread very thinly on a substrate was calculated by Iida et al. [16] and is shown in Fig. 2-42a (tr is hereafter assumed to be zero, unless otherwise noted). The intensity is about twice as large above the critical angle as below it. The intensity of the X-ray fluorescence emitted from the 4 m

1.0--"

=0.8"~0.6-

~2-

9 ~,.,.,,I

r~

r~ = 0.4-

~_~ 0.2-

00

I

I

I

I

I

2

4

6

8

10

G l a n c i n g angle / m r a d Fig. 2-39. The calculated X-ray intensities on the silicon surface (perfect surface; tr= 0) as a function of glancing angles, using a 10 keV incident X-ray.

0.0-

0

I

I

I

I

I

2

4

6

8

10

G l a n c i n g angle / m r a d Fig. 2-40. The calculated X-ray fluorescence intensities from a silicon substrate ( a = 0) as a function of glancing angles, using a 10 keV incident X-ray.

126

"-:'.1.0-

(b)

, - , 0 8. -

0.8-

.1,.=1

t~

"-06-

9- 0 . 6 0 0

O

0 L)

00.4-

~0.4O

0.2-

r

0.2-

c~

0.0-

I

I

0

2

~I~ 4

~0.0

I

I

I

6

8

10

Glancing angle / mrad

J

!

I

I

I

I

I

0

2

4

6

8

10

Glancing angle / mrad

Fig. 2-41. The glancing angle dependence of reflection from a silicon surface (a); and the X-ray fluorescence intensities from a silicon substrate (b). Surface roughness, 10/~; incident X-ray energy, 10 keV.

(a)

(b) f

.1,.-I

-

Sample

/

.

/ f J

9 i,..,.I

O

f

/

-

/

/

/

o .

,

/ O

-

!

-

I Reflector )I

-

-

0

I. . . .

~'I

I

1

B

I

!

I I

2

Normalized glancing angle (0/0c)

s

1

~

I

2

3

=

I

4

=

I

,

5

Glancing angle / mrad

Fig. 2-42. (a) Calculated intensities of the signals from the sample (solid line) and from the reflector (broken line) as a function of glancing angles. (b) Angular dependence of the Zn ( 9 ) and Si (o) fluorescence signals, which are from the sample and the reflector, respectively. From Ref. [16], reprinted by permission of the American Chemical Society, Washington, D. C.

127

(a) 1.0

(b)

-2"5MGeA~lgr

:lA50

2.5 GeV 133.9 mA | MAX. CTS. :651 ~Zn

1.0

I Zn

0.5

!i Sca'"

0.5 si

II

i 0.0

0.0 I

2

I

I

4

I

I

6

I

I

I

8

I

10

Energy / keV

I

I

12

2

4

6

8

10

12

Energy / keV

Fig. 2-43. Spectra (a) and (b) obtained at different glancing angles, corresponding to A and B in Fig. 2-42, respectively. From Ref. [16], reprinted by permission of the American Chemical Society, Washington, D. C.

substrate shows an S/B ratio which greatly improves below the critical angle. The results of the experiment by Iida et al. [16] are shown in Fig. 2-42b. A sample of 2 lal of a Zn solution was used, dried on an optically flat reflector. The intensity of X-ray fluorescence for Zn and Si is indicated in Fig. 2-42b. The measured values agree well with the calculated values. When the spectrum was measured near the critical angle shown in Fig. 2-43 [ 16], there was very little scattering below the critical angle. The beam width was a few tens of ILtm.

2.4.3. Liquid sample analysis Figure 2-44a [31 ] shows the spectrum of a solution containing 1 ~tg m1-1 each of V, Fe, Ni, Zn, and Pb dried on a fused quartz reflector, measured by the total reflection method at the Photon Factory. The XRF spectrum of the same solution dried on filter paper is shown in Fig. 2-44b [31 ]. The experiment was conducted using Beamline 4A and equipment developed by Iida et al. The horizontal axis of rotation of the sample holder makes this device suitable for SR experiments. Measurements are made in the air using a 14 keV monochromatic X-ray obtained from a Si(ll 1) double-crystal monochromator. It is evident that using the total reflection method produces very little scattering and improves the S/B ratio. Similar experiments on Ti, Mn, Cu, and Ge were carded out. The detection limits obtained are indicated in Table 2-9 [30]. In the total reflection method, any absorption and secondary excitation in the sample is negligible because the sample is very thin. We applied TXRF to a synthetic sample from 100 ~tl of a solution containing 50 ng g-1 of V, Cr, Mn, Fe, Ni, Cu and Zn, dried on a silicon

128 wafer (Fig. 2-45). The intensity corrected for air absorption, excitation efficiency, relative Ko~ line intensity and fluorescence yield is shown in Fig. 2-46. This shows that a fixed amount of sample gives a constant X-ray fluorescence intensity, within the experimental error. Therefore, we can ignore the matrix effect and secondary excitation.

1.0

_a) Total Reflection Zn

~=s" tET' "20014. : lilLl 0s it

~, ~ /,,' ~,."

keVFe

~U.3" k

,!1, il ,

i!t

I 0

"

0

Scat,

i,~!t ~'-" '

2

4

6

"

8

I .~~

Analysis

tE"T'5~'0keY

Scat!

I ,i

i~t! " "

(b)

o

i,/ :

Ni '

10 12 14

0

.*~~.

1

3

~"~"'.-"'~

5

7

9

.

11

'

13 15

Energy / keV

Energy / keV

Fig. 2-44. Comparison of SRXRF spectra: (a) 100 ng of each element on the fused quartz, by total reflection; and (b) 100 ng of each element on the filter paper, by ordinary bulk analysis. From Ref. [31], reprinted by permission of Elsevier Science Publishers B. V., Amsterdam. Table 2-9 Comparison of the detection limitsa between two different methods by SR excitation Element V Fe Ni Zn Pb Ti Mn Cu Ge

Total reflection (ng) 0.03 0.02 0.01 0.01 0.02 0.04 0.02 0.01 0.005

Bulk analysis (ng) 0.07 0.07 0.05 0.04 0.04 0.07 0.06 0.06 0.03

a The detection limit is defined as the quantity which gives a signal equal to three times the square root of the background. From Ref. [30], reprinted by permission of Kodansha, Tokyo.

129

Zn

1 400-

12 0 0 -

Cu Ni

"-:"

=. I O 0 0 ;~

800

-

9~

~o

E~" 12 keV t 9 1000 s MAX.CTS 9 1361

Fe

600

Mn Cr

-

Scat.

400200 0

I

I

i

I

I

0

5

10

15

20

Energy / keV Fig. 2-45. SR-Excited TXRF spectrum from the sample prepared by drying 100 lxl of a solution containing 50 ng of each element (V, Cr, Mn, Fe, Ni, Cu, and Zn) on a silicon wafer.

10,,-:,. ::::186-

v

..

--

^

v . X

.

.

.

v

X

4-

~20 i

I 22

I 24

I 26

I 28

I 30

I 32

Atomic number Fig. 2-46. The X-ray fluorescence intensity values of each element, corrected for excitation efficiencies, fluorescence yields, relative Ktx line intensities, and air absorption between the detector and the sample shown in Fig. 2-45.

This method, however, has many problems when it comes to quantitative analysis. One of these involves sample preparation. It is virtually impossible to make a quantitative estimate because of questions concerning where the sample solution is dropped on the reflector, how large an area it covers, and whether it is spread uniformly. It is also difficult to determine where on the sample the X-ray falls. One solution to this problem is to use an internal

130 standard. Pella and Dobbyn [44] used this method to measure the ppb concentration level of Se in human blood serum, using germanium as an internal standard. For trace analysis in the total reflection geometry, using the internal standard, monochromatic excitation with SR allows us to quantify elements reliably and easily, and to improve detection limits compared to X-ray tube excitation. As an example, we will describe an experiment on a NIST reference material (Trace Elements in Water, SRM 1643b). The spectrum of the total reflection X-ray fluorescence for this sample is shown in Fig. 2-47a. A 15 keV X-ray obtained using a Si(111) double-crystal monochromator was used for excitiation. Next, Ge, which was absent from the original sample, was added to bring the concentration up to 70 ng g-1. Then, 100 l.tl of this solution was dried on the reflector. Its spectrum is shown in Fig. 2-47b. The values for the other elements, determined from the amount of Ge, after corrections for excitation efficiency, fluorescence yield, relative Ko~ line intensity and air absorption between the sample and the detector, are indicated in Table 2-10. The detector efficiency is assumed to be constant for the given energy region and the values are in good agreement with the NIST certified values. However, this method has limited applications, since an element not originally present in the sample has to be added. The following procedure can deal with any detectable element as an additional element and is expected to be applied to trace element analysis in liquid samples [45]. For measurements employing the energy dispersive method using monochromatic excitation, the following relationship holds between the concentration of element i contained in the sample and the intensity of X-ray fluorescence [46]: Tabel 2-10 Quantitative determination of several elements in NIST SRM 1643b (Trace Elements in Water) by SR-excited TXRF using Ge a as an internal standard Element

Determined (ppb)

Certified (ppb)

V Cr Mn

49 23 27

45.2+0.4 18.6+0.4 28 +2

Fe Co

120 42

99 +8 26 +1

Ni

49

49 +3

Cu

30

21.9+0.4

Zn

71

66 +2

a Ge was added to SRM 1643b so as to contain 70 ng g-1 in the aqueous solution for measurement.

131 Ci_

li4xR 2(]2s, o +/Zs,isin ~/sin ~)[Ps PoOi[(lIK/P)oOJKfK]i(1 - exp{-[(/Zs,o +/2s,isin tF/sin ~)/ps]psT/sin tF} )

(2-30)

where: C i is the concentration of analyte element i. li is the fluorescence intensity for the analyte line of element i. Po is the intensity of the exciting X-ray beam. Di is the detector efficiency. R is the distance from the sample to the detector. l,ts,o is the linear absorption coefficient of the sample for the exciting X-ray beam energy. l.ts,i is the linear absorption coefficient of the sample for the fluorescence energy of element i. is the incident angle of the exciting X-ray beam. is the angle between the sample surface and the detector, the takeoff angle.

Ps is the density of the sample. T is the thickness of the sample. (,UK/P)o is the mass absorption coefficient of analyte element i for the exciting X-ray beam. tOKis the fluorescence yield of the K-series line.

fK is the intensity ratio of Ks to the total K-series lines. When the sample is very thin, this can be approximated by Ci =

li 4 x ' R 2

(2-31)

PoDi[(l.tK/P)oCOKfK]iPsT / sin tp The term [(l.tK/P)otOKfK]i is a quantity peculiar to an element, that is the constant of its element parameters; the remaining terms, excluding li, 4r~R2/(PoDiPsT/sin tF), are a constant parameter determined by experiment (assuming the detector's efficiency to be independent of X-ray energy). If the term [(PK/P)oOJKfK]i denotes ei and the remaining terms, excluding li, are represented by K, the above equation will be reduced to

Ci =

li K

(2-32)

9 ei

which is validated by the data shown in Fig. 2-46. However, when a solution with a high salt concentration is used, the salt will remain on the reflector after drying, and affect the measurement by absorbing some X-rays. Using a first approximation, to correct this absorption by the matrix we add the correcting term exp(tz~i3). This is based on the assumption that the absorption coefficient of an X-ray is approximately proportional to the cube of its wavelength: 2~"is the wavelength of the fluorescent X-ray of the analyte element i, and a is a quantity which depends on the absorption, and will be determined experimentally.

132 5

10

-

/

\

(a)

Ca Ca

4

10

Fe

Ni

4"

"]

E r" 15keV t 9 500 s

MnCO Cu Cu

-

tCr+lCo! +As ~ +Fe JIN~//I/Z l ~ S e

10 3-

i rMn~ I

n

Scat.

]As

0

1 02 -

1

10

-

MAX.CTS 9 18468 B.S. 9 0.11 x 2.8 mm 2

10 ~ 0

i

!

i

i

5

10

15

20

Energy / keV 10 10 "

.1-,~

5

4

10

1

(b)

-

-

Cu Mn Ni ,7+ + [, ~n -Fe F e l N i l

F_7 9 15 keV t 9 200 s

+

iv

-

o~

Co

Ca ~Ca

As ~ ~ Ge

Scat. /~

C

-

1

10 10

:0.15 x 3.0 mm

B.S.

0

0

~[

I

I

I

I

5

10

15

20

Energy / keV Fig. 2-47. SR-Excited TXRF spectra from the samples obtained by drying 100 ~tl of NIST SRM 1643b, (a); and the solution prepared so as to contain 70 ng g-1 of Ge in SRM1643b, (b).

Let us consider the case of three elements in unknown amounts contained in a sample. The intensity of the X-ray from each element is related to its concentration as follows:

C1 -

ll.exp(aZ13)

K.el

(2-33)

133

C2 =

12.exp(aA 3)

(2-34)

K.e2 13.exp(aA 3) C3 =

(2-35)

K.e3 If two of these elements are added at specific concentrations (Ci', i = 2, 3), then

C1 =

ll'.exp(aA13)

(2-36)

K'.el C2+ C2' =

12'.exp(a~,23)

(2-37)

K'.e2 C3+ C3' =

13'.exp(o~A33)

(2-38)

K'.e3 In these six equations, (2-33) to (2-38), li and li' are measured values and ,~,i and ei are peculiar to these elements - - v a l u e s that can be determined using constants. Thus, there remain six unknown quantities, K, K', Ci (i = 1, 2, 3), and a, which can be determined by solving simultaneous equations. Quantitative analysis will be possible for elements other than these three, using the values of K and a determined using the equation

Ci = li . exp(aA/3) / K.ei

(i>4 )

We made measurements on two kinds of samples. One was the synthetic standard used in the experiment shown in Fig. 2-46, and the other the NIST standard reference material used for the experiment shown in Fig. 2-47. For the calculation of quantitative values, the synthetic sample and NIST SRM were each divided into subsamples, A and B. Vanadium and nickel were added to subsamples A until the concentration of each element reached 50 ng g-1. Likewise, manganese and zinc were added to subsamples B until the same concentrations of each element were reached. Then, 100 lxl of each sample was dropped onto and dried on a silicon wafer in the same manner as the experiments shown in Figs. 2-45 and 2-47. These preparations were performed in a Class 1 000 clean booth. A 12 keV monochromatic X-ray created using a Si (111) double-crystal monochromator, was applied to each sample at a glancing angle of about 2 mrad. The counting time was 1 000 s. The results of the quantitative analyses listed in Tables 2-11 and 2-12 suggest that this is a very satisfactory method for trace element analysis. It requires no consideration of the spot size or the area irradiated, and provides rapid, simultaneous multi-element analysis of ppb concentration levels using a simple sample treatment. It has a wide range of applications since unknown amounts of the elements to be added can be selected. However, the expedient correction used above for absorption by the matrix may be further improved by a more precise approximation.

134 Table 2-11 Results for the synthetic sample Found, ng g-1 Element

Added a, ng g-1

V Cr Mn Fe Ni Cu Zn

50 50 50 50 50 50 50

Addition of V and Ni for calculation b

Addition of Mn and Zn for calculation c

42 48 49 49 55 49 56

42 47 47 47 51 46 52

a Added values are given for comparison. b For the calculation of K and ct, the fluorescence intensities of V, Ni and Cr were used. c For the calculation of K and o~, the fluorescence intensities of Mn, Zn and Ni were used. From Ref. [45], reprinted by permission of the Japan Society for Analytical Chemistry, Tokyo. Table 2-12 Results for NIST SRM 1643b Found, ng g-1 Element

Certified a, ng g-1

V Cr Mn

45.2+0.4 18.6+0.4 28 +2

Fe

99

Co Ni Cu Zn

Addition of V and Ni for calculation b

Addition of Mn and Zn for calculation c

38 14 22

43 15 21

+8

120

114

26 +1 49 +3

28 53

24 47

21.9+0.4

23

20

66

99

86

+2

a Certified values are given for comparison. b For the calculation of K and ct, the fluorescence intensities of V, Ni and Mn were used. c For the calculation of K and ct, the fluorescence intensities of Mn, Zn and Ni were used. From Ref. [45], reprinted by permission of the Japan Society for Analytical Chemistry, Tokyo.

135

2.4.4. Near surface analysis When the incident X-ray is totally reflected it penetrates only a few tens of A into the sample. This property of the TXRF method makes it possible to carry out the elemental analysis of the area near the sample surface. Conventional XRF only performs bulk analysis, and cannot be used to analyze the sample surface. A significant feature of TXRF is that while it maintains the rapid, nondestructive, and simultaneous multi-element analysis of conventional XRF, it can also be applied to surface analysis. This method has been extensively used in the laboratory for surface analysis of silicon wafers. However, there have not been many cases where SR has been used for surface analysis where the samples must be handled carefully. It is very difficult not to contaminate samples from the time they are prepared in the laboratory, through transportation, until they are measured at a SR facility. In this section, we will discuss precautions for using SR-excited TXRF for surface analysis. Any element on the surface will cause X-ray fluorescence. However, the intensity of the fluorescence varies, depending on whether the elements are on the sample surface or slightly below it. This difference is illustrated in Fig. 2-48, which shows the calculated dependence of the X-ray fluorescence intensity on the glancing angle, for the same quantity (1012 atoms cm -2) of iron distributed inside silicon in the following ways: (1) close to the surface, (2) homogeneously from the surface to a depth of 10 A, (3) homogeneously from the surface to a depth of 100 A, and (4) homogeneously from the surface to a depth of 1 000 A. It should be noted for quantitative analysis that the X-ray fluorescence intensity caused by the same amount

,--:,.4A

: top surface ..... : surface to 10 A - - -: surface to 100 A

~39~ 2 o o r,o

1s,

0-

s"

........ ...I

I

I

I

I

2

4

6

8

10

G l a n c i n g angle / m r a d Fig. 2-48. The calculated glancing angle dependence of Fe Ko~ intensities on the following distributions of Fe (1012 atoms cm -2) in the silicon substrate: (1) only on the top surface; (2) on the homogeneous distribution from the surface to 10 A in depth; (3) on the homogeneous distribution from the surface to 100 A in depth; (4) on the homogeneous distribution from the surface to 1 000 A in depth.

136 of element varies greatly depending on the distribution and the glancing angle. At the Photon Factory, Iida et al. [47] measured the dependence of X-ray fluorescence on the glancing angle, using a 3.5-l.tm-thick Gal_xAlxAs thin film (x - 0.298) epitaxially grown on GaAs. In comparison with GaAs, there were fewer As atoms near the surface of this thin film. This is mostly due to sublimation that occurs during sample preparation. To estimate the depth of the reduced As concentration they calculated the exhausted length (the distance from the surface to where the concentration is 1/2 of the bulk concentration value) to be about 100 /~, on the assumption that the As concentration increases from the surface value of zero to the bulk value in the manner of a complementary error function. Changes in the chemical composition of compound semiconductors can also be measured by destructive methods, such as ion channeling and SIMS; however, the present method does not destroy the sample. Bloch et al. [48] performed an experiment at SSRL on the interface between a polymer solution and the air. The method they employed allows measurements in any atmosphere, and therefore is suitable for analyzing the surface of liquids. They positioned an optically flat reflector in front of the sample, to control the glancing angle of the incident X-ray. The sample was a slightly sulfonated polystyrene dissolved in dimethyl sulfoxide. The polymer had a molecular weight of 115 000, with a chain containing about 10 mole% manganese sulfonate. By measuring the dependence of the S Ka from the solvent and the Mn Ka from the polystyrene on the glancing angle, they found that the polymer concentrations increased on the interface, since the Mn intensity was higher at smaller angles. With uniformly soluble MnC12, the intensity ratio was found to be constant. They also compared this method with the optical method. The minimum penetration depth is a few tens of A for X-rays and hundreds of A for the optical method. Also, in the optical method, polymer solutions are generally transparent to a depth of a few thousand/~, allowing penetration to infinite depths at angles above the critical angle. This means that the X-ray method provides a far more sensitive surface analysis for this kind of sample.

2.4.5. Depth profile analysis As shown in Fig. 2-38, the penetration depth increases from a few tens of/~ to a few l.tm as the glancing angle of the incident X-ray increases beyond the critical angle. This means that the depth profile of the element being studied can be analyzed by changing the glancing angle in small increments. Iida et al. [17] used a silicon wafer ion-implanted with As to measure the dependence of the intensity of As K a X-ray fluorescence on the glancing angle (1-5 mrad). They also made the same measurements on a sample heat-treated at 1 000~ for 20 min. As shown in Fig. 2-49, the increase in As concentration on the sample surface brought about by the heat treatment gives a greater intensity of X-ray fluorescence below the critical angle. The decrease in the intensity at glancing angles above the critical angle corresponds to a reduction of the total amount of As. The demonstrated intensity of X-ray fluorescence has been found to agree well with the value calculated using the profile analyzed by the SIMS method.

137 _1

'

I/.~

/ -

/

'

I

'

I_

\

/

\

/

'

A

-

/ o~==l

tD - / / o1-,~

\

I

1

""

B

/

-

2

\

i

I

-!

i

3

4

Glancing angle / mrad Fig. 2-49. Reflected X-ray intensity (broken line) and As K intensifies (solid lines) for Si wafers, before (A), and after (B), annealing, as a function of glancing angles. From Ref. [17], reprinted by permission of Elsevier Science Publishers B. V., Amsterdam.

Figure 2-50 (dotted line) shows a depth profile analysis of a silicon sample ion-implanted with iron (40 kV, 1 x 1015 atoms cm -2) [31]. Iron ion-implanted in this manner shows a Gaussian distribution, with a 123 A standard deviation around the peak ion concentration at a depth of 302 ,~. The dependence of the X-ray fluorescence on the glancing angle, calculated from this profile, is shown by the solid line in the figure. The slight difference from the measured values is probably due to the spread in energy and angle of the beam. We made the following calculations to ascertain how sensitive the curve of the X-ray fluorescence plotted against the glancing angle is to the depth profile. Using Fresnel's formula [43], the amplitude, At, of the transmitted X-ray is given by

A t _ 201 Ai 01+02

(2-39)

where Ai, 01 and 02 have the values indicated in Eq. (2-23). The intensity of the transmitted X-ray just beneath the surface is given by

~_~ 2

=

4 012 (01 +p2) 2 + q22

(2-40)

138 [In the actual calculation, the values of 01, P2 and q2 are used9 See Eqs. (2-24)-(2-26).] The transmitted X-ray, expressed by Eq. (2-40), is transmitted in the medium while being absorbed. The X-ray fluorescence intensity for an element distributed at a given depth in the medium is calculated from the transmitted X-ray intensity and the concentration of the element at that depth. Figure 2-51 shows the calculations for the ion-implanted iron described in Fig. 2-50, with different standard deviations for their Gaussian functions9 The calculated Fe Ka intensity vs. the glancing angles, at different depths of peak concentration, are shown in Fig. 2-52. The X-ray fluorescence profile is found to be quite sensitive to these parameters. Application of this characteristic to thin film samples will be discussed in detail in the following section. Measuring the depth profile of impurities at the surface during the analysis solves the problems mentioned in the preceding section, i.e., the difficulty in making a quantitative determination of an element caused by the dependence of the X-ray fluorescence intensity on the elemental concentration profile. Various applications of the above method are expected because of the nondestructive depth profile analysis in air that it provides.

1E22

_ _ _ Calc. 302.~

"

Exp.

d

"IE16 0

O

Depth (/~)

1000

O

0

1

2

3

I

I

4

5

6

Glancing angle / mrad Fig. 2-50. Depth profile analysis of implanted Fe in a silicon wafer. From Ref. [31 ], reprinted by permission of Elsevier Science Publishers B. V., Amsterdam.

139 2.5-

.

,~

:300A

i

:c=100

~~ .2~ . 0 -

.......

5 0 ko

: o =

~15-

~

~

9 v.,,l

~l.Or~

os-

0

"

0.0 . . . .

I

0

2

I

I

4 6 Glancing angle / mrad

I

I

8

10

Fig. 2-51. The glancing angle variation in Fe Kcz intensifies with different Fe concentration distributions in a silicon wafer, changing standard deviations (cr) at a fixed peak depth (Zp) of 300 ,~ below the surface in a Gaussian distribution. (o" is the halfwidth at half of the maximum concentration)

3 . 0 - -

c~" 100 .,~

:

,.~,,~2 . 5 -

9

'i ~~,,,

~t=2 0 - "

zp = 3oo A

....... : Zp = 200 .A Zp 400 A

o

"-" 1 . 5 o i

o10-.

=._.

. . . . . . . . . .

=_.

r~

o0.5-

se

#

0.0-

0

2

4

6

8

10

Glancing angle / mrad Fig. 2-52. The glancing angle variation in Fe Ko~ intensifies with different Fe concentration distributions in a silicon wafer, changing peak concentration depth (Zp) below the surface at a fixed standard deviation (o') of 100 A in a Gaussian distribution.

140 2.4.6.

Application

to thin film s a m p l e s

TXRF is effective not only for the elemental analysis of a sample surface, but is also useful for the analysis of thin films. As explained above, the depth of penetration of the incident Xray can be controlled by changing its glancing angle to the sample. This makes it possible to match the measurement conditions to the sample thickness. We will discuss an experiment using a 1.2-gm-thick photoresist polymer coated on a silicon wafer [ 18]. Small amounts of impurities in photoresist polymers are normally measured by chemical analysis. In this case, TXRF was chosen because the impurities were in a thin film spread on a wafer. The experiment was conducted using Beamline 4A at the Photon Factory. A 9.6 keV monochromatic X-ray with a Si(111) double-crystal monochromator was utilized. The intensities of the incident and reflected X-rays were measured using an ionization chamber, and the intensity of the X-ray fluorescence measured using a Si(Li) detector. The sample and the detector were 5 mm apart. The measured reflection curve is shown in Fig. 2-53. The curve shows two critical angles. That in the low glancing angle region is the critical angle for the resist polymer, and the other, in the high glancing angle region, the critical angle for the silicon wafer. This means that, if the incident angle is gradually increased from a low value, the behavior of the incident X-ray will be changed in the following manner. First, it is totally reflected on the resist surface. Then, as the glancing angle becomes greater than the critical angle of the resist (2.15 mrad),

1.0 0.8 ~. 0 0

0.6 0.4

0

0.2 I 2

I

I 3

I

i--r------4

Glancing angle / m r a d Fig. 2-53. The observed angular dependence of reflectivities from a silicon wafer covered with a resist polymer. The critical angle of the resist is around 2 mrad, and that of silicon around 3 mrad [ 18].

141 the X-ray penetrates the polymer, and is totally reflected on the silicon-resist interface until the glancing angle reaches the critical angle of the silicon wafer (3.20 mrad). The reflection curve rises until the glancing angle reaches the critical angle, because of the change in the effective cross section of the incident X-ray. We measured the X-ray fluorescence using glancing angles of 2 and 3 mrad. The measurements were made in air and lasted for 2 000 s. At 2 mrad, the maximum penetration of the X-ray into the resist is only 100 J., and most X-ray fluorescence is emitted from the surface. At 3 mrad, the measured X-ray fluorescence comes from all parts of the resist film. The spectra of the X-ray fluorescence for these two cases are shown in Fig. 2-54. Both show X-ray fluorescence from the silicon substrate, argon in the

0=2 mrad

0 =3 mrad

~ ~

es'st

~, ~

t

Silicon (a)" Schematic drawing of total reflection with changing glancing angles (2 mrad and 3 mrad).

10

105 /L

0= 2 mrad

0= 3 mrad

/

4|

~~

10[ Ar 10 3

8

Scat.

Scat.

l~

]

/

,o31 - tt

Si

102

0

5

Energy / keV

10

0

5

10

Energy / keV

(b): SR-Excited TRXF spectra obtained. On the left side (2 mrad) total reflection occurs on the resist surface; on the right side (3 mrad) on the interface between the resist and silicon wafer. Counting time is 2000 s. Fig. 2-54. Impurity (Fe) analysis in a thin resist film on a silicon wafer [18].

142 air, and iron which is regarded as an impurity in the sample. The problem with measuring the quantity or distribution of the profile of iron is the dependence of the X-ray fluorescence intensity on the depth profile, as described in the previous discussion on surface analysis. Assuming the total quantity of iron to be constant, we calculated the intensity using the two glancing angles (2 mrad, 3 mrad) for the following four kinds of distributions: (1) homogeneous from the surface to 10 A, (2) homogeneous from the surface to 100 A, (3) homogeneous from the surface to the interface, (4) decreasing linearly from the surface to the interface. The calculated values for 2 mrad are: (1) 0.74, (2) 0.49, (3) 0.007, and (4) 0.014; and for 3 mrad: (1) 0.31, (2) 0.28, (3) 0.24, and (4) 0.25. Note that the unit for these values is arbitrary. The peak area of the X-ray fluorescence of iron measured in this experiment has been found to be four times as large at 3 mrad as at 2 mrad. We attempted a quantitative analysis, based on the assumption that the iron concentration was homogeneously distributed on the thin resist film and that it also contaminated the surface of the film. Comparing the measured and calculated values of the X-ray fluorescence intensity using 2 and 3 mrad we found that 92% of the iron detected was homogeneously distributed in the film, with 8% contaminating the surface. Our estimate of the amount of iron showed that 1.7 x 1012 a t o m s cm -2 were contained inside the film with 1.5 x 1011 atoms cm -2 attached on the surface. The amount of iron contained inside is converted to approx. 1.3 ppm in relative weight concentration- a value in good agreement with that obtained by chemical analysis (1.0 ppm). However, the depth concentration profile must be measured if one needs a more precise quantitative determination. 2.5. C H A R A C T E R I Z A T I O N OF LAYERED STRUCTURES BY GRAZING INCIDENCE

2.5.1. X-Ray spectroscopy using grazing incidence As discussed in the preceding section, the penetration depth changes as the incident angle of X-rays changes around the critical angle of total reflection. Also, under these conditions the incident X-rays interfere with reflected X-rays. Interference occurs inside the film in a sample with a layered structure, which affects the reflection curve and the X-ray fluorescence intensity profile for the constituent elements. The interference effects depend on factors which include the number and thickness of layers, the concentration profile, the roughness of the surface or interfaces, and the existence of transition layers on interfaces. This makes it possible to determine important parameters of the film structure, by analyzing the reflection curve and the X-ray fluorescence intensity profile measured as functions of the glancing angles. For multilayered materials, the following parameters can be determined by this method: (1) The thickness and density of individual layers. (2) The concentration profile of constituent elements. (3) The roughness of the surface or interfaces. (4) The existence of transition layers between the surface and the thin film, and between a

143 thin layer and the substrate, as well as the thickness, density and composition of the transition layers. (5) The depth profile of impurities. Interference shows up as oscillations on the reflection curve. Back in the 1930s, Kiessig [49] analyzed oscillations in the curve exhibited by reflection from a monolayer thin film, and described a method of determining film thickness. He regarded the oscillations as fringes of equal inclination, and determined the film thickness from a relationship between it and the optical path difference. Parratt [50] formulated a rigorous method for calculating the reflection curve for multilayered materials, and attempted to analyze these materials from the changes in the reflection curve, especially around the critical angle. He made systematic calculations on oxidized layers of copper, and compared them with experimental results. N6vot and Croce [51] gave a more rigorous definition for the conventional method of incorporating interface roughness as a Debye-Waller factor [a scalar treatment, see Eq. (2-29)] and obtained an equation that enabled a vectorial analysis. They used this equation in a detailed analysis of surface layers of polished glass. They measured the reflectivity at glancing angles varying from the critical angle to much larger values. This is important in determining very sensitive roughness values, since roughness has a great effect on the reflection curve, particularly when the glancing angle is large. Generally speaking, reflectivity is very small at large glancing angles. Therefore, careful experimentation is required to determine oscillations in reflectivity with high precision. Vidal and Vincent [52] developed a matrix calculation method to systematically determine reflectivity for multilayered materials using a computer. The roughness term is also incorporated in the matrix elements. They used this method to evaluate layered synthetic materials. Kr61 et al. [53] established a method of calculating the angular dependence of X-ray fluorescence intensity. Using the matrix treatment of Vidal and Vincent, this method enabled a rigorous determination of X-ray fluorescence emitted from individual layers. The experiments were carded out on the thin layers of semiconductor wafers. In the above experiments, only Kr61 has used SR. This is not necessary for measuring reflection curves; careful measurement using specially designed equipment produces satisfactory results. In fact, as well as N6vot and Croce, Huang and Parrish [54] performed precise experiments using equipment they had developed incorporating a channel-cut monochromator. However, monochromatized X-rays obtained from SR are useful for the measurement and analysis of X-ray fluorescence intensity profiles. The high intensity, tunability, and high collimation of SR are indispensable for measurements of minute compositions and applications to very thin films and transition layers. Sakurai and Iida [55] have proposed a method for determining each layer thickness of mutilayered thin films by a Fourier transformation of oscillations known as the Kiessig structure [49]. Other research using the grazing incidence method includes a laboratory study, in combination with ellipsometry [56], of a thin film on a compound semiconductor, and an effort to examine heterojunction roughness using soft X-rays (SR) [57, 58]. Heald et al. [59] used the grazing incidence method to measure both reflection curves and EXAFS, in order to analyze metallic multilayers.

144

2.5.2. Determination of the thickness of monolayer thin films (Kiessig's method [49]) Kiessig established a simple method for determining the thickness of monolayer thin films. He assumed the oscillations that appear in the reflection curve to be fringes of equal inclination. When the X-rays are incident at an angle slightly larger than the critical angle of the sample, part of the X-ray beam goes into the thin film. As shown in Fig. 2-55, X-rays reflected by the surface and by the interface interfere with one other. The reflectivity from the interface is so small that X-rays emitted after repeated reflection within the film can be neglected. The X-rays can be assumed to be parallel beams (coming from a light source infinitely far away), and the two beams (AB and A'B') which interfere are parallel and come from the same incident X-rays. We write N for the foot of a perpendicular line, A'N, dropped from A' to AB. Since there is no optical path difference between the two beams beyond A'N, the difference in the optical paths is expressed by A = n2.(AC + CA' ) - nl.AN

(2-41)

where nl is the refractive index of air or a vacuum (=1), and n2 is the refractive index of the film, which takes a complex number if there is any absorption. Let the film thickness be dE, then, since 01, 02<<1, the optical path difference is expressed by

Air (vacuum): n = n 1 = 1

B ~ / B

N

d2

~

~monolayer:

Substrate: n = n 3 Fig. 2-55. Schematic representation of fringes of equal inclination.

n =n

145

A

=

2d2 02 = 2d2( 0 7 -

02 ]1/2

(2-42)

lc/

See Eqs. (2-4) and (2-23) for the meanings of 01, 02 and 01c. The intensity of reflected Xrays is a maximum or minimum value when the optical path difference is an integer (m) or a (m + 1/2) multiple of the wavelength. Therefore, changes in the intensity of reflected X-rays depend on 01. Let the wavelength of the incident (reflected) X-rays be ~; then the intensity becomes a maximum value when:

mA = 2 d2(O2 - 021e!]1/2

for&<&,

(m + 1/2) A, = 2 d2(07 - 02) 1,2

for & > &

and (2-43)

The term (m + 1/2) is required because a phase shift occurs during reflection when d;2 > 63, i.e., the electron density is higher in the film than the substrate. See Eq. (2-2) for definitions of 62 and t~3. From Eq. (2-43), the values of 01 corresponding to the m-th maximum is related to m as follows:

021(m) = 02 + $2m2

for $2 < 63,

4d~ and

O2(m) = 02c + A 2(m + 1/2) 2

for ~ > ~

(2-44)

44 Therefore, 012(m) plotted against m 2 or (m + 1/2) 2 forms a straight line, and d2 can be determined from the slope. Therefore, highly accurate determinations of the film thickness can be obtained without contact with or destruction of the sample. Further, since 01c [= (262) 1/2] can be determined from the intercept of the line, the density of the thin film can also be obtained. We carded out an experiment on a Ni thin film deposited on a silicon wafer using a sputtering method. Measurements were made using 1.2 A monochromatized X-rays at Beamline 4A of the Photon Factory. The reflection curve measured is shown in Fig. 2-56. Oscillations can be seen in the curve. Since nickel has a larger t~than silicon (62 > 53), 012(m) corresponding to the maximum oscillation was plotted against (m + 1/2)2 (Fig. 2-57). The result is a straight line. From the slope of the line, the thickness of the Ni thin film was determined to be 454 + 3/~. The critical angle (01c) was found to be 5.6 + 0.2 mrad. As described above, it is easy to determine the film thickness and the critical angle, i.e., the sample density and composition of a monolayer thin film. However, this method cannot be applied to samples having more than one layer or having transition layers.

146

10

;~' 10-

o

1

-

-

;;> 2

lo-~

1

-

10

-4

-m 0.0

I

I

I

I

I

I

0.2

0.4

0.6

0.8

1.0

1.2

Glancing angle / degree Fig. 2-56. The reflection curve of a Ni thin film deposited by sputtering. The incident X-ray wavelength is 1.2 A. 1.0 0.8 ~~

0.6

~

0.4 0.2 0.0

I

I

I

I

o

20

4o

60

I

a0 (m+l/2) 2

I

I

I

loo

12o

14o

Fig. 2-57. A plot of maximum oscillation values for the Ni thin film on a silicon substrate shown in Fig. 2-56. The straight line was obtained by least-squares.

2.5.3.

Calculation

of reflection

curves-1

(Parratt's

method

[50])

Kiessig's method uses only the period of the oscillations that appear in the reflection curve. More information would be available if it were possible to analyze the entire reflection curve, including the amplitude of the oscillations. It is also important to have a method for analyzing multilayered thin films. One way to analyze the reflection curve is to determine the parameters such as the film thickness and composition, and to construct a theoretical curve; the parameters are then adjusted to make an experimental curve fit the theoretical curve. It is therefore necessary to have a theoretical method for calculating the reflection curve. Parratt formulated a method for determining the

147 reflectivity of grazing incident X-rays for multilayered samples, using the electromagnetic theory (continuity of the tangential components of electric and magnetic fields on interfaces) and Fresners optics formulae. When monochromatized X-rays irradiate a sample, (without multilayers), the electric field vectors of the incident [El(Zl)], reflected [E~(zl)], and refracted [E2(z2)] X-rays are expressed as follows:

El(z1) - El(0)exp{i[(.ot -(kl,xX1 + kl,zZl)]) E~(z1) = E[(0)exp{i[~ot -(kl,xXl - kl,zZl)]} E2(z2) = E2(0)exp{i[~ot -(k2.~x2 + k2.zZ2)]}

(2-45) (2-46) (2-47)

where z denotes the perpendicular distance from the surface (which has a positive value in the sample), and k i (= 2~/Ai, i=1, 2) is the propagation vector of X-rays. Suffix 1 represents the outside of the surface, and suffix 2 the inside. The plane of incidence is an xz plane. The continuity of the tangential component of the electric field vector on the interface requires that, if there is a grazing incidence, the following holds true: k2.x = kl, x = kl, and k2.z = k102 = kl (012- 2 6 2 - 2ifl2) 1/2. From Fresners formulae, the reflectivity can be expressed as a function of the glancing angle by

(2-48)

01 + 02

(01 + p2)2+ q2

where P2, q2, 01, and 02 are defined in the same way as in Section 2.4.2.: see Eqs. (2-24)-(226). Now consider a sample having N layers (air, 1; layers, 2 to N - l ; substrate, N). Assume also that the interfaces are perfectly smooth. Denote the thicknesses of individual layers as dn. The thickness of the air, dl (vacuum), will not be considered. From the boundary condition of the continuity of the electric vectors on the interface, there is the following relationship between layers n-1 and n (n = 2, 3,..., N):

an-lEn-1 + an-l_l Er_l = a-nllEn_ (an-lE,-1-an-l_l E r _ l ) f , - l k l = (

+ an E~

a~lxE.-a. Er)Lkl

fn = Pn - iqn an = exp( - iktfndn / 2 )

(2-49) (2-50) (2-51) (2-52)

[En is the value on the n-th interface of the electric field that propagates downward (to the substrate) through the interface; En r is the value on the n-th interface of the electric field

reflected upward from the interface (to the surface)]. From these equations, the reflection

148 coefficients of the electric fields' amplitudes are expressed by the following recursion formulae:

rn-l,n =

a4_l( rn,n+l + Fn-l,n)

rn,n+lFn-l,n + 1

(2-53)

rn,n+1 = a2n (E r / En)

(2-54)

fn-1 - f n Fn-l,n =fn-1 + fn

(2-55)

The calculation starts with n = N, and proceeds until the reflectivity R = I rl,212 is determined. Note that rN,N+I = 0, since there is no upward electric field, EN r, in the substrate. The parameters required for these calculations are dn (film thickness), Sn (composition and density), and fin (composition and density). A comparison of the calculated results with the experimental values makes it possible to establish an optimum model of the multilayered structure. Parratt measured the reflection curve of a copper film (thickness approx. 2 000 A) deposited on glass, and compared the results with the values calculated by the above method. First he used a two-layered structure of copper and glass. The reflection curves did not agree very well, and the value of ~, which is proportional to density, was found to be about 10 percent smaller than the value for bulk copper. Then he considered a three-layered model with an additional oxide (Cu20) layer, and searched for an optimum model by changing the thickness of each layer. He went as far as a five-layered structure: Cu20 (90% density of the bulk value) + Cu20 + Cu (90% density of the bulk value) + Cu + glass. Although the calculated results did not coincide perfectly with the experimental values, they provided quite a good approximation. These results suggest that, in order to examine the structure of thin films, even monolayer materials must be regarded as multilayered. This means a satisfactory analysis cannot be based only on the period of the oscillations; the entire reflection curve must be considered. This is why it is very important for thin film analysis to have a method, such as the one shown in this section, for calculating the reflectivity of multilayered structures. Unfortunately, the calculations are tedious when the sample has many layers.

2.5.4. Incorporation of roughness and transition layers Real samples have rough surfaces and interfaces. They can also contain transition layers. Omitting these factors from the reflectivity calculation prevents precise comparisons with experimental results. A rough interface and transition layers reduce reflectivity, which can be observed in the reflection curve. We will describe the method for incorporating these factors which was established by N6vot and Croce [51 ].

149 Consider an interface where homogeneous substances meet. The refractive indices can be represented by n l (upper layer) and n2 (lower layer). The roughness of the interface, as shown in Fig. 2-58, is expressed as the root-mean-square of deviations of the depth coordinate ZD.

0.2 = ( z 2 )

(2-56)

If the roughness value is not very large, it will be smaller than kln -1, k2n-1 (kin is the normal component of wave vectors for each layer, i). A real rough interface can be considered as many smooth planes distributed in a Gaussian manner. The peak of the Gaussian distribution is the average plane (P0) of the deviations of the rough interface. Therefore, using this assumption, if the reflection coefficient of a perfect interface is represented by ri, that for a rough interface, re, can be described by rR = rlexp(

-

81r,2klnk2n0.2)

(2-57)

The reflectivity is given by the square of the absolute value of the refection coefficient (R = I rR 12). The above equation also gives the reflectivity of a transition layer whose refractive index changes in the manner of an error function. If we assume that

9

m

n(z)= nl + (n2- nl).F(z)

(2-58)

F(z)=l~fZ___ooex[~ -v2x0-2

(2-59)

20.2 ,u2]du

,

+++

+++P0

/I +

++ I

Fig. 2-58. Schematic representation of a rough interface: Po is the average plane surface (perfect interface); P is the actual interface.

150 when nl is unity (the refractive index of air or a vacuum), we obtain the same reflectivity in a similar manner to the method for the rough interface above. Namely, consideration is made by substituting a transition layer for a rough interface, and the refractive index for the parameter representing the roughness. Conversely, a transition layer as shown in Eqs. (2-58) and (2-59) can be used to analyze interface roughness. Now consider a multilayered material, as shown in Fig. 2-59. The amplitudes of the electric fields are represented by a, b, a, and ft. Since only transmitted X-rays exist in the substrate, if aj_ 1 is known, Eq. (2-57) can be used to determine bj-1 o n the Oj-1 interface. The following relations hold on the Dj_ 2 interface.

OtJ-1 + rR'j-2~J-I 1 + rR, j_ 2

(2-60)

bj_2 = otj_l + flj-1- aj-2

(2-61)

aj-2 -

where rR, j-2 is the refection coefficient on the Dj_2 interface, defined by taking into consideration its roughness and transition layer. Consecutive calculations to the first layer, D1, determine the reflectivity of the multilayered material, I bl[al I2. N6vot and Croce [51 ] used the above method to analyze a thin layer formed on a surface by polishing, oxidation, or contamination. We will describe their analysis in the following. The a M

bl

1

D1

M

M i-2

~

~

b1_2

DF2

M j-1

r

DF1 u.

i

aj Substrate

Fig. 2-59. Sketch of electric fields for a multilayered material.

Z

151 surface layer in question is assumed to be sufficiently thin (less than a few tens of A). Its refractive index and thickness are also assumed to be sufficiently uniform. If the refractive index and the average thickness of the surface layer are denoted by no and 1:o, respectively, the refractive index for a given depth (z) between the surface layer and the substrate (refractive index = n2) is expressed by n2(z) = n 2 + (n 2 - n2)F(z-'ro, or)

fz

(2-62)

0u

F ( z - v o , o') = V2xcr2 J-oo

(2-63)

And, when the layer composition and density continuously change from the surface to depth z2, the refractive index is expressed by n2(z) = n~ + (n~ - n~)[ 1 - exp( - z/z2)]

(2-64)

Using Eqs. (2-58) and (2-59), the surface roughness can also be included in n(z). Ntvot and Croce measured the reflectivity of grazing incident X-rays to examine how various methods of polishing change the surfaces of various kinds of glass. An X-ray tube was used in their experiments. Reflection curves were observed using glancing angles between 0 and 3 ~ For pure silica glass, polished with pine resin mixed with cerium oxide, the refractive index had a maximum value at 51 A, below the surface. This value is obtained by adding Eqs. (2-58), (2-62), and (2-64) and by comparing the reflectivity determined from the experimental results with that from the calculated ones. This means a high-density layer was formed at that depth. It was also found that it could be eliminated by heat treatment. The value for z2 obtained in this case is 225 A, and the refractive index decreases continuously according to Eq. (2-64). It was also found that the surface was not dense, having a roughness of 7.75 A. They also discovered that when aluminosilicate glass (density, 2.63; SiO2, 60%; A1203, 20%; CaO, 20%) was polished using pine resin mixed with iron oxide, a very thin low-density layer (density, 2.04; Zo, 21 A) was formed, with a high-density layer below (maximum density, 2.71 at 48 A; z2, 200 A). The surface roughness was found to be 9 A.

2.5.5. Calculation of reflection curves-2 (Matrix treatment) The methods for calculating reflectivity indicated in Sections 2.5.3 and 2.5.4 require complicated data handling when there are many layers. Vidal and Vincent [52] reported a very convenient method for calculating the reflectivity of multilayered samples incorporating roughnesses. In this method, one matrix corresponds to each layer. TO handle a multilayered film, the matrices representing the layers can simply be multiplied.

152 First, we will discuss the case where roughness is omitted, as shown in Fig. 2-60. The electric fields above and below the interface (y > Yo, Y < Yo) can be expressed by

e(x,y) = [E2exp( - i(2y) + e~exp(+i(2y)] exp(itrx)

(for y > yo )

E(x,y) = [El'exp( - i(ly) + El'rexp(+i(ly)] exp(iax) (for y < yo )

(2-65a) (2-65b)

ko=2~/~,

(2-66)

o[ = kocos01

(2-67)

(i = {(koni) 2 - a2} 1/2 (i=1, 2)

(2-68)

where ko is the wave number of the incident X-rays, 01 their glancing angle and ni (i = 1, 2) the refractive index. In the case of S polarization (the electric field vector is perpendicular to the incident plane), the electric fields can be expressed as follows, using the boundary condition of the continuity of electric field on the interface.

/p11

E~

P21

P22

, 69,

E1 'r

Pll -- alext~-i((1 - (2)Y]

(2-70)

P12 = a2ex~+ i ( ( l + (2~]

(2-71)

P21 = a2ext~-i((1 -!- (2)Y]

(2-72)

P22 = a l e x ' + i ( ( 1 - ~2~]

(2-73)

where al = 1+~1/~'2, a2 = 1-~1/(2.

The reflectivity, R, is given by

Medium 2 ( = n 2 ) E2

yo !

E1 r

E 1'

Medium 1 ( = n 1 ) r

x

Fig. 2-60. Sketch of electric fields of a perfect interface between two media of refractive indices n l and n2.

153

R = [P21/Pll

I2

(2-74)

The case of P polarization (where the electric field vector is parallel to the incident plane) can also be handled if the above (1/~2 is replaced by (~l/ff2} X (E2/E1)

(2-75)

where ei = ni 2 is the dielectric constant. In the case of a multilayered material, the product of the matrix corresponding to each interface can be simply calculated. This method is very useful because it permits the use of the same procedure to calculate the reflectivity for samples having any number of layers. If cr is the roughness, then for S polarization the matrix will become

(E2) = (p 11exp[4 ~"1-~'2)20"2/2] E:~ p2lexp[4 r + ~'2}20-'2/2]

(2-76) P22ex~4 ~1_~2)2o-2/2]

E1 'r

The roughness of each interface can be determined by comparing the experimental results with the calculations. Vidal and Vincent [52] used the reflection curves for grazing incident X-rays to evaluate a multilayered X-ray mirror. We will employ this method to compare the effects of the surface roughness and interface roughness of a sample with a monolayer. Figure 2-61 shows the reflection curve of a nickel thin film (300 A) on a silicon substrate. It indicates that surface roughness mainly reduces the reflectivity, and interface roughness decreases the contrast of oscillations.

2.5.6. Calculation of X-ray fluorescence intensity The discussions above deal with the angular dependence of reflectivity, which is used for analyzing the structure of thin films. This structure can also be elucidated using the dependence on the glancing angle of the X-ray fuorescence emitted from constituent elements. Since this can be observed for each constituent element, it provides more information than the reflection curve alone. However, X-ray fluorescence from thin films is so weak at grazing incident angles that it was rarely used experimentally until SR became available. In this section, we will describe a method of calculating the intensity of X-ray fluorescence. The structure of a film can then be analyzed by comparing the experimental profile with the calculated results. Kr61 et al. [53] developed a method for calculating the intensity of X-ray fluorescence from multilayered samples, using Vidal and Vincent's treatment of matrices for calculating the reflectivity. Consider a multilayered material shown in Fig. 2-62. Layer j is located above the

154

10

0

......

~ , .

-1

10 ;>.

"'":

-

on a

Ni surface

( ~ = 0 on an interface between Ni and Si )

-2

9 v,,,4 .v-,I

o"= 20/~

10

-

9

10-3

;,.

\

_

,,"_'~ :'',

,..

-4 10

-

-5 10

-

0

I

I

I

5

10

15

I 20

Glancing angle / mrad 0 10

. . . . . .

_

. . . . . .

_

_

_

_

-

~ = 20]k on an interface between Ni and Si -1 10

;>

-

-2 10

-

r O O

10-3

_

" "J

-4 10

~i

-

-5

m,

I 5

10

0

i 10

I 15

I 20

Glancing angle / mrad Fig. 2-61. The calculated reflection curves of a Ni thin film (thickness = 300 A) on a silicon substrate. Dotted lines indicate the case of neither interface nor surface roughness. Solid lines indicate the case of either surface or interface roughness: the upper figure shows values for a Ni surface where (r = 20 ~, and the lower figure shows values for an interface between Ni and Si where o" = 20/~.

j-th interface. If S polarization is assumed, then transmitted X-rays

Ej § and reflected X-rays

Ej- are expressed by

Ef (x,z) = Aj exp(ipjz) exp(ikoxx) E](x,z) = Bj exp(-ipjz)exp(ikoxx)

(2-77) (2-78)

155

kjx = kj cosOj = kj+lCOSOj+1 = kj+l, x = kox pj = kj sinOj + iaj = (kZn 2 - gn2cos20)l/2

(2-79) (2-80)

where Aj, Bj, and pj are complex quantities, and kj and aj are the magnitudes of the real and imaginary parts, respectively, of the complex wave vector. Refer to Fig. 2-62 for Oj. The complex wave vector for layer j is expressed by k02n~, using the complex refractive index, where k0 is the wave number (2~/~) of the incident X-rays and 0 their glancing angle. If the matrix connecting the electric fields above and below the j-th interface is lj, then

l e;(zj) l(1

~j rj l

ei( j)

Ej++l(ZJ)t Ej++l(Zj)=lj t Ei+l(Zj) E;+l(Zj)

where rj and tj are the Fresnel coefficients of reflection and refraction, respectively.

9Air or vacuum

E-~ (Zo)

E+ (Zo)

nj

"

o.

o.

Ej+I(Zj ) -

j-th interface nj+l

+ j) Ej+I(Z

E+ (ZN)

EN (ZN)

nN ns

Substrate

z Fig. 2-629 Schematic representation of electric fields of a multilayered material.

(2-81)

156

zj,

The matrix, Tj+I(Z-Zj) , that connects the z coordinate, at the j-th interface with a point z inside the layer, (/+1) Zj+l), is determined as follows:

(zj
Ej++I(ZJ)~exp[-ipj+,(z-zj)] 0 exp[ipj+ l(Z-Zj)] Ej+1(zj)

I

E j+ 1(Z)

Tj+,(z-zj) E;+I(Z)

I

(2-82)

E;+l(Z)

Matrix Sj corresponds to the roughness of the j-th interface:

e;-r}e; rj(e;-e;)) SJ = l-~r~ rj(ef-ef ) ef-r~ef e+=exp[-(Pj+l+pj)24[2] ef =ext~-(Pj+l-pj)24]2 ]

(2-83) (2-84) (2-85)

where crj denotes the roughness parameter of the j-th interface. From Eqs. (2-81)-(2-83), the following relation is obtained:

( Ei(zj~ )=

Ei+,(z)

(2-86)

If the matrix that connects the electric field at the substrate with the electric field at the interface between the surface and the air or vacuum is PON,then

pl~

PoN=( pl0N p201N P22 ON

(2-87)

If this matrix is calculated, we can obtain

E~(zo)) Eo(zo)

= PON

where

Es+(ZN)is

leo(Zo)/e~(zo~

E+(ZN) 0

(2-88)

the value of the electric field inside the substrate.

can be obtained by calculating [p2~ ' / pl~

I~

The reflectivity

157 The electric field at below. If

z,

(Zj_1 < Z < Zj), Can be determined using matrix PiN, defined as shown

PjN = IjSj

T j + I ( Z j + I - Z j ) - " 9 INSN

(2-89)

ET(z) =Tj(zTz)Pju(e+s(ZU)o) E;(z)

(2-90)

then

Es+(ZN) can be expressed as follows using the electric field of the incident X-rays, Ei. E+(zN) = E~(zo____.._~)= E__i_i p l ON

(2-91)

p l ON

Equations (2-89)-(2-91) make it possible to determine the electric fields in individual layers and in the substrate. Also, using Maxwell's equations, and taking the permeability/lj - 1, the magnetic field can be expressed by

-

Hjy(Z)

-

/ko

-

(2-92) (2-93)

=0 +

(2-94)

In order to calculate the X-ray fluorescence intensity, the time average of the density of the energy flow, i.e., the Poynting vector P(z), must be determined. P(z) = C(Re(ExH*) )

(2-95)

where Re is the real part; (), the time average; H*, the complex conjugate of H; and C, the multiplicative constant. Substituting the electric and magnetic fields for the corresponding variables provides the components of the Poynting vector. We now describe the calculation of the intensity of X-ray fluorescence from a given layer. The excitation efficiency, fluorescence yield, and absorption of X-ray fluorescence are ignored. With this simplification, all we have to know is the intensity of the incident X-rays required to excite X-ray fluorescence in layer j. It is necessary also to subtract the X-rays that penetrate the sample without being reflected by the surface, those absorbed by layers up to j - l , as well as those going into layer j+ 1. The Xray fluorescence intensity, for z from zero to zj_l, is given by

158

Yj=C

[

1-R-I=I k

tan ~j = Pjz/Pjx

(2-96) sin [~z/c)]Pi0(z) J (2-97)

where Pi0 represents the incident X-ray flux, R the reflectivity, ~j the direction of Poynting vector Pj(z), and Pjx and Pjz the x and z coordinate components, respectively, of Pj(z). The quantity ~)j is different from Oj representing the direction of propagation of the electric field [see Eq. (2-80) and Fig. 2-62]. Then, the X-ray fluorescence intensity from layer j can be expressed by

Yj+I- Yj (2-98) In the next section, we will discuss examples of thin film analysis using both the angular dependence of reflectivity and of X-ray fluorescence intensity. The analysis was performed by comparing the results of a SR experiment with the reflection curve and X-ray fluorescence profile obtained by the method of Kr61 et al [53]. 2.5.7. Characterization of titanium wafers

and

carbon-titanium thin films on

silicon

The angular dependence of reflectivity and X-ray fluorescence intensity, measured and analyzed using the grazing incidence method, is described in the following [60, 61 ]. The two samples used were a titanium thin film deposited on a silicon wafer by a sputtering method, and a carbon-titanium thin film also sputtered on a silicon wafer. Parts of these samples were cut off and heated in argon. The experiment was conducted using Beamline 4A at the Photon Factory. A Si (111) double-crystal monochromator was used to monochromatize 10 keV X-rays, which were shaped into a beam of less than 0.1 mm in height and 2 mm in width by passing them through a slit. The intensity of the incident and reflected X-rays was measured with an ionization chamber, and the intensity of X-ray fluorescence with a Si(Li) detector. Figure 2-63 shows the reflection curve measured for the titanium thin film. It reveals that the period of the oscillations is reduced after heat treatment. This suggests that high temperatures thicken titanium layers. However, since the amount of titanium remains the same, this effect is believed to be caused by titanium silicide formation during heat treatment. The observed X-ray fluorescence profiles are shown in Fig. 2-64. An attempt was made to create an optimum model by comparing the results with the calculations done by Kr61 et al. [53]. Curves calculated for a metallic titanium thin film, which was not heat-treated, shown in Fig. 2-65, did not agree with the experimental results. Therefore, the model was modified to fit the reflection curve and X-ray fluorescence profile, with the assumption that additional layers were formed on the surface and interface. Figure 2

159

Heat treatment temperature

/'/

\

"1-x

50~

V

"

'

"

"r.

8 Without heat treatment f

f

f

4

5

6

Glancing angle / mrad Fig. 2-63. Experimental reflection curves for Ti on Si wafer samples (with and without heat treatment). Heat treatment temperatures 9250~ 500~ and 750~ From Ref. [60], reprinted by permission of Plenum Publishing Corp., New York.

I

(d)

~i

(c)

*w~

8

3

4 5 6 Glancing angle / mrad

7

Fig. 2-64. Ti Ktx fluorescence intensity profiles for Ti on Si wafers. Without heat treatment (a); and with heat treatment at 250~ (b), at 500~ (c), and at 750~ (d). From Ref. [60], reprinted by permission of Plenum Publishing Corp., New York.

160

9 I,,,,,I

j~176

f

9 ~,,,I

o..,. "

t

9 1,,,,,I

i

ov,,~

~

i

e~

3

4

5

6

""

7

I

4

G l a n c i n g angle / m r a d

I

5

6

7

Glancing angle / m r a d

Fig. 2-65. Comparison of the calculated curves (broken lines), based on the model, with the experimental reflection curve and Ti Ktx fluorescence profile.

......

-...... Calc.

.=.

9 ~,,,I

. . . j

2

4

5

6

Glancing angle / m r a d

7

3

Exp.

I

I

I

4

5

6

7

Glancing angle / m r a d

Fig. 2-66. Comparison between the experimental results for the sample without heat treatment and the calculations based on the model for a Ti0.42Oo.58 (11 n m ) / T i (43 nm)/ TiSi2 (6 nm)/ silicon substrate. For the oxide layer tS= 9.16x10 -6, fl = 3.55x10-7; for the titanium t~ = 8.56x10 -6, fl = 4.84x10-7; for the silicide t~= 8.08x10 -6, fl = 2.67x10-7; and for the silicon substrate d; - 4.75xl 0 -6, fl = 7.42xl 0-8. From Ref. [60], reprinted by permission of Plenum Publishing Corp., New York.

161 -66 shows that the calculated curves based on this modified model are in good agreement with the experimental ones. The thickness, concentration, and density of each layer were determined. From these results, the total amount of titanium was calculated to be 24 l.tg cm -2, a value that agrees well with that determined by chemical analysis. Analysis of heat-treated samples revealed that transition layers on the surface and interface had been eliminated; a thick, homogeneous silicide layer had been formed instead. The experimental results for the thin film sputtered with carbon-titanium, before heat treatment, are shown in Fig. 2-67. The reflection curve shows two critical angles. The small one is that of carbon and the large one that of titanium. The X-ray fluorescence profile detected the Ka line of iron. Although iron is an impurity, analysis must take its existence into consideration. Assuming a carbon-titanium two layered structure, it was found that the sample had a surface roughness of 50/~, a carbon layer density of 1.7 g cm -3, and a titanium silicide (65% Ti and 35% Si) layer with a density of 4.4 g cm-3. The density of the carbon layer was considerably smaller than that of graphite (2.26 g cm-3). However, as shown in Fig. 2-68, there is a significant difference between the experimental and calculated reflection curves in the vicinity of the critical angles. Therefore, it was necessary to once again incorporate transition layers into the model. The curve from the experimental results and the curve which resulted when the transition layers were incorporated in the model are shown in Fig. 2-69. This modification suggests that there are two high-density transition layers (carbon, p = 2.0; carbon, p = 1.7) near the surface. The total concentration of iron contained in each of the three

~,

TiKtx

FeK~ m~ = (t.24

= .

;> !

O

I

I

I

2

I

I

3

4

5

6

Glancing angle / mrad

7

2

I

I

I

I

3

4

5

6

I

7

Glancing angle / mrad

Fig. 2-67. Experimental results for the carbon and titanium sputtered sample without heat treatment. From Ref. [60], reprinted by permission of Plenum Publishing Corp., New York.

162 1.0

.~n-I

0.5

1

2

3

4

5

6

Glancing angle / m r a d Fig. 2-68. Comparison of the experimental reflection curve (bold line) with the calculated curve; the sample is assumed to be carbon ( 2 8 0 n m ) / Ti0.65Si0.35/ silicon substrate [61 ]. The carbon layer contains iron as an impurity. The values of t~and fl of the carbon layer are affected by iron. For the carbon layer t5= 3.45x10 -6, fl = 2.57x10 -8 and for the silicide layer t~= 8.46x10 -6, t = 3.57x10-7.

carbon layers was 2%, which is in good agreement with the value determined from the X-ray fluorescence intensity. The results of the 250~ heat treatment sample, shown in Fig. 2-70, indicate much steeper curves near the critical angles, in the reflection curve and in the Fe Ks fluorescence profile. This suggests that the two high-density transition layers previously mentioned have been eliminated during heat treatment. In the 750~ heat treatment sample shown in Fig. 2-71, the titanium fluorescence profile is similar in pattern to the iron fluorescence profile. These similar patterns point to the formation of a homogeneous monolayer on the silicon substrate surface. We have shown that measurements of the reflection curve and X-ray fluorescence profile at grazing incident angles provide an excellent method for analyzing thin films. The benefits of this method are that it is nondestructive, and that sample composition, thickness, density and elemental concentration can be determined. Although still used in very few studies of this kind, SR is expected to be widely employed in the near future.

163 Carbon

20nm

S = 4 . 1 4 x 10 ~ , f l = 4 . 1 0 x 10 -8 , p - 2 . 0 Carbon S = 3 . 4 7 x 1 0 -4, f l = 3 . 4 4 x l O 4, 0 = 1 . 7

20 nm

Carbon 260 nm

S = 3.13 x 10-6 , f l = 2 . 5 7 x 10 4 , p = 1.5

Titanium silicide t5 = 8.46 x 10 -6, fl = 3.57 x 10-7,/9 - 4.35

23 nm

Silicon substrate

1.0

o~,~

0.5

1

2

3

4

5

6

Glancing angle / mrad

Fig. 2-69. Comparison of the experimental reflection curve (bold line) with the calculated curve [61].

164

Ti Ko~ fluorescence profile ]

~ v...~

Reflection curve

I

"7.

I

I

Fe Ko~ fluorescence profile m

2

I

I

3

4

5

2

Glancing angle /mrad

3 4 6 7 Glancing angle / mrad

Fig. 2-70. Experimental results for the samples without heat treatment (bold line) and with heat treatment at 250~ From Ref. [60], reprinted by permission of Plenum Publishing Corp., New York.

~

TiKo~

.~,,I

e~

r~

O

I

3

I

4

I

I

5

i

i

I

6

Glancing angle / mrad Fig. 2-71. Comparison of the Ti Kcx fluorescence profile with the Fe Ko~ fluorescence profile using the 750~ heat-treated C / Ti / Si substrate sample. From Ref. [60], reprinted by permission of Plenum Publishing Corp., New York.

165

2.6. PROSPECTS FOR FUTURE DEVELOPMENT With the advent of a third generation high-brilliance synchrotron source, and further extensive use of insertion devices, we can expect further advances in X-ray fluorescence analysis. We will discuss two such prospects: bulk analysis and surface analysis. The former mainly uses monochromatic excitation XRF, and the latter is based on the total reflection of Xrays.

2.6.1. Bulk analysis

Heavy element analysis Since conventional X-ray methods using ordinary tube excitation cannot provide sufficiently high excitation energy, researchers have been forced to use L- or M-series X-rays to analyze lanthanoids and actinoids. Compared with K-series X-rays, these characteristic X-rays have an intensity at least one order of magnitude lower and suffer from considerable interference because of closely arranged spectral lines, which result because the X-rays have small energy level differences. Furthermore, the energy region where these spectral lines are observed includes the characteristic X-rays of common, smaller atomic number elements (the third and fourth period elements). This results in a complex spectrum and makes accurate analysis even more difficult. Generally speaking, higher energy analyte lines reduce interference because their excellent penetrating powers decrease absorption by a matrix. Also, since no naturally occurring elements emit L-series lines of more than 20 keV, use of K-series lines has great advantages for the analysis of elements heavier than rhodium, both in precision and in sensitivity. Uranium is a good example. The K absorption edge of this element is approximately 115.6 keV. Therefore, if it were possible to excite uranium using an X-ray source with a higher energy level than 115.6 keV, analysis of uranium with very little interference would be possible. Consider another example. The K absorption edge of neodymium, used in materials such as laser glass, is at about 43.6 keV. If it were possible to excite it with X-rays of more than 50 keV, sufficient excitation efficiency would be achieved to conduct analysis of its trace quantities. In fact, an analysis of rare earth elements with K-lines, using VEPP-4 at Novosibirsk, equipped with a high-energy ring (5 GeV), detected amounts lower than ppm [62].

XRF using soft X-ray excitation X-ray fluorescence of second period elements (superlight elements) causes the release of a very small number of photons, compared with the number of photoelectrons and Auger

166 electrons observed. Also, the energy required for them to fluoresce is very low. These characteristics pose difficult problems for fluorescence measurement which uses an ordinary X-ray optical system. However, if the optical system is improved, and radiation from a large scale ring and an undulator combination is used as an excitation source, it will make the system sensitive enough for bulk analysis of these elements. This was tried at the Photon Factory, where an experiment has been reported using the undulator as the excitation source and a synthetic multilayer as the optical element [63]. Absolute (standardless) method The energy tunability and excellent collimation of SR are indispensable for accurate elucidation of the excitation and emission mechanisms of X-ray fluorescence, and for clarifying the interactions between analyte lines and any spectral lines emitted by elements other than analytes. Development of these analysis techniques will open up the possibility of an absolute method: i.e., a quantitative technique that requires no reference standard. When it is freed from reference standards, XRF will not be affected by the precision and accuracy of reference samples which have to be standardized by other methods such as chemical analysis. This will permit not only highly reliable ultratrace analysis, but also highly accurate measurements of the stoichiometric relationships of unknown substances. An example of analysis without standard references, based on the characteristics of SR, is a study by Bowen et al. [64]. They determined the concentration of As contained in a silicon sample ion-implanted with As, simply by measuring As and Si X-ray fluorescence intensities of the sample. They assumed a Gaussian distribution for the As concentration, and based the quantitative analysis on fluorescence yields and absorption coefficients available in the literature.

2.6.2. Surface analysis Excitation sources with higher brilliance, and improved measuring equipment and optical systems, will certainly combine to yield determination limits in the order of ppt (10-12 g g-l) and femtogram quantities (10 --15 g) using TXRF. As the use of SR increases, the structural analysis of thin films as described in Section 2.5 will also be employed to evaluate the surfaces and interfaces of various advanced materials. Recently, the X-ray standing wave method has received considerable attention as a total reflection surface analysis technique. It has been found to be useful for determining the structures of ultrathin organic films [65] and diffuse layers on liquid-solid interfaces [66]. This method is based on the phenomenon of diffraction and the accompanying oscillations in X-ray fluorescence intensity. In experiments, the angular dependence of the fluorescence intensity is measured and analyzed. Thus, depth profile analysis using X-ray standing waves has provided an experimental means of researching interfaces, an area that was previously only investigated theoretically.

167 As discussed above, the use of SR as an excitation source is creating a new range of possibilities. XRF, even itself, has made analysis more sensitive and has helped in the development of structural analysis techniques. In the future, SRXRF will provide more useful information for the characterization of a wide range of advanced materials.

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