THE INFLUENCE OF CHEMICAL BONDING ON THE LOW-ENERGY Kα SPECTRUM OF SILICON

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THE INFLUENCE OF CHEMICAL BONDING ON THE LOW-ENERGY Kα SPECTRUM OF SILICON

T. Åberg, J. Utriainen

To cite this version:

T. Åberg, J. Utriainen. THE INFLUENCE OF CHEMICAL BONDING ON THE LOW-ENERGY Kα SPECTRUM OF SILICON. Journal de Physique Colloques, 1971, 32 (C4), pp.C4-295-C4-300.

�10.1051/jphyscol:1971454�. �jpa-00214655�

THE INFLUENCE OF CHEMICAL BONDING ON THE LOW-ENERGY Ka SPECTRUM OF SILICON

T. BERG and J. UTRIAINEN

Laboratory of Physics, Helsinki University of Technology, Otaniemi, Finland

Rksumk.

- On montre que la structure d'knergie basse, trouvke rkcemment, de Si

Ka

ligne est sensible aux environs chimiques de l'atome Si. Notre interprktation que la partie la plus remarquable de cette structure d'knergie basse provient des transitions Auger radieuses

K-L2

conduit

B.

une expli- cation des changements les plus kvidents. La formation des excitons rayon

X

est observke au dCbut de la structure

K-L2

et on, donne aussi, des preuves de la structure faible situke entre la ligne

Ka

et le spectre

K-L2

proposC.

Abstract. -

It is shown that the recently found low-energy structure of the Si

Ka

line is sensitive to the chemical environment of the Si atom. Our interpretation that the most prominent part of this low-energy structure is due to

K-L2

radiative Auger transitions leads to an explanation of the most pronounced changes. The formation of x-ray excitons is observed at the onset of ;the

K-Lz

structure and evidence is also presented for a faint structure which is situated between the

Ka

line and the proposed

K-L2

spectrum.

I. Introduction. - Previously we have given evi- dence for radiative K-L' transitions in the elements Mg, Al, Si and S [I]. I n these radiative Auger transitions a photon is emitted and a 2 s or 2 p electron is simul- taneously excited into either a bound or continuum state. The atom is left, as in the radiationless KLL Auger transition, with two vacancies in the L shell.

That part of the

K

spectrum which we interpreted as being due to K-I,2 transitions by comparing known Auger electron energies with measured x-ray energies, is situated on the low-energy side of the Ka line and consists of sharp peaks and several overlapping conti- nua. In order to see how this structure is influenced by the chemical bonding we have studied the Si K spectrum in silicon (Si), carborundum (Sic), quartz (SiO,) and amorphous silicic acid (Si02.nH20).

In section 111 the observed changes are explained in terms of the ionic character of the chemical bonding in S i c and SiO, and are related to known changes in the ordinary K and L spectrum of Si. In section N

the sharp peaks a t the onset of the K-L2 spectrum are proposed to be due to bound exciton levels formed in the field of two final L vacancies. In section V the observation of several faint peaks in the region bet- ween the Kol line and the K-L2 structure is compared with similar observations on Mg, A1 [2] and S [I].

Possible mechanisms that lead to an enhancement of the intensity in this part of the K spectrum are consi- dered.

11. Experiment.

-

The spectra were recorded with

a plane-crystal spectrometer

131. Secondary excitation

was used and the fluorescence radiation was analyzed with an ethylene diamine tartrate crystal (2 d

=

8.808 A). The flowcounter window was cove- red by a polypropylene film. The silicon and quartz specimens were single mosaic crystals. Carborundum and silicic acid specimens were prepared from powders.

The silicic acid specimens were found to be amor- phous by the x-ray diffraction technique.

At least three runs with counting times of 10 or 20 minutes per point were made for pure silicon and each compound. Typical spectra are plotted in figures 1, 2 and 3. The figures do not show the whole spectrum since the low-energy tails extend to about 150 eV from the onset. The spectrum of silicic acid was found to be similar to that of quartz within limits of error except that peak

n :

o 5 was not distinguishable in silicic acid and thus has not been included.

The energy of the observed peak maxima (in a few cases only knicks in the slope were observed) was determined with respect to that of the Ka line. The energy of the Ka line (the weighted mean of a, and a,) was taken from Bearden's table [4] and it was assumed to be the same for Si, S i c and SiO,. From table I1 we notice that this assumption induces only a small error in the results which are collected in table I. For Si the energies of the peaks n

:

o 6 to 11 agree with those previously reported [I]. The shift of the peak n : o 5 and the average shift of the well defined peaks n

:

o 6 and 7 are given in table I1 where all shifts are defined as Eco,,o,,, - E ,,,,,,,.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971454

T. ABERG AND J. UTRIAINEN

FIG. 1. -The low-energy side of the Si Ka line in silicon.

-

^{ENERGY (eV )}

FIG. 2. - The low-energy side of the Si Ka line in carborundum.

111. Chemical shifts.

- We assume that the extend- tely represents the shift of the whole K - L : , ~ part. This

ed structure with its onset at peak

n:

o 6 is due to in turn should be equal to the shift in the excitation

K-L2 double-electron transitions [I]. Consequently energy of an L2,, electron but with opposite sign since

the average shift of the peaks

n :

o 6 and 7 approxima- the K and L,,, shifts of an atom due to the perturba-

FIG.

3.

- The low-energy

side of

the

Si Ka line in

quartz.

Experimental energies (in eV) of peaks found on the low-energy side of the Si Ka line (at 1 740 eV) in silicon and its compounds

(")

Peak

n : o 1 2 3 4 5 6 7 8 9 10 11 12

Substance

Si

1669 1650 1636 1620 1614 1607 1595 1572 1554

Sic

1669 1650 1 632 1617 1612 1598 1 571 1553 ( b )

SiO

2 (e) 1724 1712 1670 1652 1629 1612 1608 1600 1594 1566 1551 1532

SiOz

.

nH2O

(C) 1 724 1 712 1 670 1 653 1613 1608 1600 1 593 1567 1551 1 530 (a)

(.)

The error limits corresponding to statistical uncertainties in the counting rates are

f 1

eV for the peaks

n : o 6

and

7

and

f 2

to

f 3

eV for the other peaks.

( 0 )

Probably disturbed by the

A1 KB

line.

(C)

The peaks

n :

o

1 , 2

(shown as

⁽⁽ knicks ⁾⁾

in the

Kor

slope) and

12

are characteristic for SiO2 and are not discussed in the text.

(a)

Existence very uncertain.

tion of the neighbouring atoms almost cancel

[5].

As is seen from table I1 the absolute values of the Lz,, and K - L ~ , ~ shifts are indeed nearly equal for Si02.

From the observed K-L;,~ shifts given in table I1 the formal charge of the Si ion in S i c and SiO, can be determined within the free-ion model. Calculations of the Hartree-Fock energy of the Auger KL;,~ transi- tion as a function of the charge [6] give the following formal charges of Si

:

+ ^0.3

^f

0.1 in S i c and

+ 0.7 4 0.1 in SiOz. On the other hand, by using the differences between the Hartree-Fock 1 s and 2 p orbital energies for Si, Si' and Si" [7] together

with the Ka shifts we obtain + 1.0 in S i c and

f

1.8 in SiO,. The trend of the formal charges, which is similar in both cases, shows that the Si-C and Si-0 bonds have ionic character, the latter bond being more ionic.

The discrepancy between the two sets of charge values is due to the neglect of the crystal potential which influences the shifts considerably if the initial and final states correspond to a different number of vacan- cies.

The result of other x-ray estimates [8], [9] of the formal Si charge in S i c and SiO, is similar to ours.

In the case of Sic, the infrared spectroscopy data of Spitzer et al. 1101 are also in accordance with our

20

T. ABERG AND J. UTRIAINEN

Various energy shifts (in eV) from Si K, L absorption, emission and Raman spectra

Absorption Emission Raman

Compound

- ^K -

^(") L2,3 ( b )

- ^{K ~ I} - ^a2

^{(? K-L2,3}

- ^(d)

K ~ L 2 , 3

(d)

-

S i c - 0.7 + 0.25 - 2.5 + ^{1 - 4 + 3}

SiO, + ^3.4 + ^5.6 + ^0.2 + ^{0.60 - 7 + 1 - 7 k 3}

(")

Barton and Lindsay [I 11.

( b )

Ershov and Lukirskii [20].

(3 Barinski and Nefedow [8].

(d) This work.

results. Hence the negative K absorption shift observ- ed by Barton and Lindsay [ l l ] for the transition Si-Sic is somewhat unexpected.

According to Ershov et al. [12] who found identical Si L2,, emission and absorption spectra in crystalline and glassy SiO, and lithium silicate glasses, the charac- teristic features of the L2,3 spectra are determined by the short-range order i. e. by the electronic structure of the Si04 tetrahedron. If this is true, there should be no large changes in the shape and position of the K-L2 and related spectra. According to section I1 and table I the difference between the crystalline and amorphous phase does not influence the observed spectrum.

There are, however, changes in the intensity distri- bution of the peaks n

:

o 8 to 11 when going from Si to S i c and SiO,. These peaks are assumed to corres- pond to the 'D and

' S

terms of the final 2 p4 configu- ration and to the 3P and 'P terms of the final 2 s 2 p5 configuration. The excited L electron is in the conti- nuum. However, KL-L3 transitions and K-L, L2,3 excitons may also contribute to this part of the spectrum. No definite conclusions can be drawn from the observed chemical changes.

According to table I1 the peak n

:

o 5 seems to shift in the same direction and with the same amount as the K-L;,~ edge. The corresponding peak in sulfur has been attributed to an internal Raman process where Ka photons are inelastically scattered by L2,3 electrons [I]. The observed shifts are in accordance with this explanation since the maximum energy of the scat- tered photon should be equal to the difference between the Ka energy ho(Ka) and the L2,, binding energy E(L2,,). The calculated maximum energy 1 641 eV based on the recommended fiw(Ka) and E(L,,,) values of Si 141, [13] is slightly larger than the measur- ed peak value shown in table I. A similar tendency exists also between the 'D and 'S K G , ~ Auger energies given by Siegbahn et al. [I41 and our peak values n : o 8 and 9 .

IV. K-L2 excitons. - According to figure 3 the sharp peaks n

:

o 6 and 7 and the Kol line have approxi- mately equal half-widths in SiO,. This indicates that

these peaks correspond to transitions from the K state to bound exciton states where the excited elec- tron is coupled to the Si ion which has two L2,, vacan- cies. The Kossel structure at the onset of the x-ray (or ultraviolet) absorption spectrum in ionic crystals is similar (e. g. [151) with the exception that it is due to an excited electron which is coupled to one vacancy.

Thus, in oxides the first maxima of the L2,3 absorp- tion spectrum of the cation correlate well with the lowest optical transitions from the corresponding free ions 1161. In SiO, the difference between the Ka line and peak n

:

o 6 is 128

$-

1 eV whereas the lowest optical transition from the incomplete L2,3 shell of the Si5+ ion occurs at 123 eV [17]. Hence it may also be possible to associate the peaks

n:

o 6 and 7 with optical free-ion levels.

The exciton peaks seem also to be present in S i c which is a partly ionic crystal and in Si which is, however, a semiconductor with an approximately 1 eV wide energy gap. We note that the peaks n : o 6 and 7 in Si cannot both be due to oxidation of the specimen since they are shifted appreciably when going from Si to SiO,. It is possible to attribute at least a part of the (6,7) structure to the term of the final 2 P4 configuration but this does not explain the appearance of two peaks. The situation is similar in S and perhaps in A1 [I]. Hence two L2,, vacancies and one excited electron may form a localized x-ray exci- ton even in a semiconductor like Si.

V. Additional features of the low-energy Ka spec- trum. - In section I11 peak n : o 5 was attributed to the internal Ka-L2,3 Raman scattering. Table 111 indicates that this scattering also gives rise to a sepa- rate peak in Mg, Si and S. In A1 the two peaks observed correspond to n

:

o 3 and 4 in Si and possibly overlap the Raman scattering peak.

According to a theory by Mizuno and Ohmura [18]

the cross section of the x-ray Raman scattering should

vary from the threshold on as the corresponding absorp-

tion cross section. Hence the Raman profile should

essentially represent the mirror image of the absorption

curve. Their theory is valid provided that the wave-

length of the incoming photon is larger than the orbi-

Energies (in eV) of the forbidden K-L, line, the K-L, M2,, double-electron-transition edge and the Ka-L2,, Raman-band edge

Calculated (7 Experimental

( b )

Element K-L1

K-L1 Mz,3

Koc-L2

, 3

3 4

- - - - - -

^{- 5}

Mg 1 216 1 202 1 202

A1 1 442 1 426 1 414 1 425

1

407

Si 1 690 1 670 1 641 1 669 1 650 1 636

S 2 243 2 219 2 143 2 218 2 200 2 142

(")he K and L, energies are from Bearden and Burr 1131, the Ka energies from Bearden [4] and the M2,3 energies which refer to free atoms in the ( Z - Z + 1) approximation from Moore 1171.

( b )

The peak labelling refers to the Si spectrum. The experimental error is 5 2 eV in all cases.

tal radius of the scattering electron and that the binding energy of the electron is negligible in comparison with the photon energy. These conditions are well satisfied for the internal Ka scattering by L2,, eIectrons in Mg, Al, Si and S. Consequently the Raman struc- ture which starts in the region of peak n : o 5 should have a similar shape as the inverted L2,, absorption curve and should overlap the K-L2 spectrum. In fact we find from recordings of the L2,3 absorption struc- ture in Na, Mg and A1 [19] and Si 1201 that the maxima of the Ka-L,,, and K-L2 spectra approximately agree.

This is a consequence of the fact that the maximum of the L2,, absorption curve which occurs 20 to 30 eV above the threshold happens to be represented in Na, Mg, A1 and Si very well by the formula

ho,,

=

ho(Ka) - E(KL;,~

;

ID)

=

=

E(L$,~

;

'D) - E(L2.3

; 'P)

. (1) The experimental and calculated values agree within

+ 3 eV if Ka values by Bearden [4] and KL;,~ Auger -

energy values by Siegbahn et al. [I41 are used in equa- tion l . It is, however, impossible to explain the whole K-L structure by the Raman scattering mechanism 1 since the Raman peak is too weak at the threshold in comparison with the K-L2 edge and since exciton peaks in that case would occur below the threshold for the continuum. For example in SiO, the expected positions of the Raman excitons are 1 634 2 2 eV and 1 631 t 2 eV from the L,,, absorption spec- trum [20] whereas the K-L2 excitons occur at

1612 + 1 eV and 1 608 + 1 eV (table I).

From the previous discussion it is clear that the peaks n

:

o 3 and 4 cannot be attributed' to the Ka-L,,, or K-L2 structure. According to table IIL the (3,4) structure occurs below the expected position of the

cc

forbidden >> K-L1 line. Hence it is tempting to associate these peaks with K-L, M transitions where M denotes a valence band electron. If we use the free- atom model and simulate the L, vacancy by using the

(2-2

+ 1) approximation we get a good agreement between the calculated position of the K-L, M2,,

transition and that of peak n : o 3 in Al, Si and S (table 111). However, on the basis of the band model of these elements we may expect that K-L1 M transi- tions occur more closely to the K-L, position than the experiments indicate. In any case simple energy argu- ments do not explain the appearance of the second peak n: o 4. Hence a more sophisticated approach which takes into account the perturbation of the valence band by the L1 vacancy is probably needed.

It is interesting to note that we are confronted with the same difficulty as above if we wish to explain the high-energy satellite of the L2,, emission band in Na, Mg, A1 and Si as being due to

~ ; , 3

double-vacancy states [21]. The high-energy edge should correspond to the 'D term of the initial L;,~ state [22] and conse- quently the position of the edge should be given by equation (I), if we assume that no appreciable energy is needed to excite an electron at the Fermi level into the conduction band. However, in Na, Mg and A1 equation (1) gives a value which is approximately 10 eV too large in comparison with experiments [21], [23]. In Si the situation is less clear since the observa- tions by Skinner 1211 and Fomichev and Zimkina [24]

concerning the L2,, high-energy satellite do not agree at all.

VI. Conclusions. -We have shown that the large chemical shifts observed for the most prominent part of the low-energy Si Ka structure can be explained by the K-L2 double-electron transition hypothesis. These shifts could also be explained by assuming that the structure is due to internal Ka-L2,, Raman scattering, but our results indicate that this scattering gives rise only to a very faint peak at the foot of the K-L2 spectrum. K-L;,~ excitons with an electron bound to.

two L2,, vacancies in the final state are shown to be present in the ionic SiO, and in the partly ionic Sic.

It is suggested that these excitons are formed even

in pure Si although the exciton levels would occur far

C4300 T. ABERG AND J. UTRIAINEN

below the (( forbidden energy gap between the unpertur- bed valence and conduction bands. There are some difficulties in the interpretation of the structure bet- ween the

Kor

and K-L2 emission by the K-L,

M

(M=valence band electron) double-electron transition hypothesis and it is shown that the interpretation of the high-energy L,,, satellite as being due to initial double vacancies in the L2,, shell is fraught with simi- lar difficulties.

Acknowledgements. -

One of us

(TA)

wish to thank NORDITA for the award of a fellowship and Prof. P.-0. Lowdin for his generous hospitality a t the Department of Quantum Chemistry of Uppsala University. He would also like t o thank

Dr. R.

Manne and Dr.

M.

R. Hayns for stimulating discussions.

Thanks are also due to Dr.

M.

Linkoaho and

M. E.

Rantavuori for help with the X-ray diffraction measurements.

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