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Sampling depth of total electron and fluorescence measurements in Si L- and K-edge absorption spectroscopy
applied
surface science ELSEVIER
Applied Surface Science 99 (1996) 303-3 12
Sampling depth of total electron and fluorescence measurements in Si L- and K-edge absorption spectroscopy M. Kasrai a,* , W.N. Lennard b, R.W. Brunner a, G.M. Bancroft a, J.A. Bardwell ‘, K.H. Tan d “ Depurtment b Department ’ Institute
of Chemistry,
forMicrostructural
I1 Canadian
The Uniwrsity
of Physics, The UrGersit)
Synchrotron
Sciences. National Radiation
Received
Facility,
ofWestern
Ontario,
of Western Ontario, Research Council Unirersifl
London, London.
Ontario.
Canada N6A 3K7
Ottawa.
Ontario,
of Canada,
of Wisconsin-Madison,
11 August 1995; accepted 29 January
Canada N6A 5B7
Ontario.
Stoughton,
Canudu WI 53589.
KIA
ORI,
USA
1996
Abstract High resolution Si L-edge and K-edge X-ray absorption near edge structure (XANES) spectra for SiO, on Si substrates have been recorded using total electron yield (TEY) and fluorescence yield (FYI techniques. The sampling depths of TEY and FY for Si L-edge and Si K-edge, respectively, have been investigated in the energy range 9% 120 eV and 1830-1900 eV. The maximum sampling depth for TEY is found to be - 5 nm for the Si L-edge and - 70 nm for the K-edge regions. The FY sampling depth at the L-edge is - 70 nm whereas for the K-edge, the sampling depth is several hundred nm. Based on these data, and using a theoretical model, electron escape depths for the TEY measurements in both energy ranges have been deduced.
1. Introduction Total electron yield (TEY) and fluorescence yield (FYI are well established methods for measuring absorption spectra of solid samples [I]. The TEY and FY spectroscopies measure the total number of electrons and fluorescence photons per incident photon, respectively, emitted from the sample as a function of photon energy. It has been shown that since the total electron or fluorescence photon yield emitted from the sample is proportional to the absorption coefficient, both techniques are equivalent to a transmission measurement [l]. However, the main difference between the TEY and FY measurements is the
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effective sampling depths characteristic of the two techniques. The mean free path of electrons created in a solid depends on the kinetic energy (E,) of the electron as well as the nature of the material. Nevertheless, mean free paths are described reasonably well by a universal curve [2] which exhibits several interesting features. The electron mean free path has its highest value when the kinetic energy is very low (E, < 2 eV); for increasing E,, the mean free path decreases and reaches a minimum of - 0.4 nm at E, = 50 eV. For even higher values of l$;., the mean free path again increases monotonically. By measuring low energy electrons, an effective sampling depth of tens of nm can be obtained in the TEY mode. Jones and Woodruff [3] have reported the sampling depth of TEY for the Al,O,/Al system at the Al K-edge. Gudat [4] has also reported the sampling
0 1996 Elsevier Science B.V. All rights reserved
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M. Kasrai et al. /Applied Surface Science 99 (1996) 303-312
depth in the energy range 50-150 eV. Martens et al. [5] have studied the sampling depth of TEY at the Cu K-edge and Tyliszczak and Hitchcock [6] have made measurements at the Cu, MO and Mn K-edges. Erbil et al. [7] have compared the TEY, fluorescence and transmission detection modes for Ge, Ni, Co and As K-edges. Values reported for sampling depths in the above studies vary from 50- 1000 nm depending on the specific edge investigated. SiO, films on silicon play a very important role in semiconductor technology, and X-ray absorption spectroscopy is widely used to investigate the local Si structure [8]. Thus, a good understanding of the sampling depth of these detection schemes is required. To our knowledge, no systematic study has been reported for the sampling depth for TEY and FY measurements for the SiO,/Si system. To achieve this goal, we have used well-characterized SiO, films [9] of varying thicknesses produced on single crystal Si substrates to determine the sampling depth of TEY and FY measurements at the Si L-edge ( N 100 eV) and Si K-edge ( N 1840 eV>.
R cm>. Prior to each experiment, the samples were degreased by successive ultrasonic treatments in acetone, isopropanol and methanol, and rinsed with distilled water followed by a 1% HF etching procedure for 1 min to remove the air-formed SiO, film. Electrical contact to the Si electrodes was accomplished by smearing InGa eutectic on the upper 2 mm of the sample and clipping onto this area with a copper fastener. This contact area was held well above the solution and was cleaved off the sample after the oxide had been grown. The final sample size was 0.8 X 0.8 cm2. The electrolyte was a 1 : 10 v/v aqueous NH,OH solution, or 1 : 1000 v/v aqueous solution with 0.01 M added NaCl. The latter solution was prepared so as to yield an electrolyte with the same conductivity as the former solution. All solutions were prepared from electronic grade chemicals and de-ionized water. The electrochemical cell comprised a conventional 3-electrode configuration with a platinum gauze as a counter electrode and a saturated calomel electrode (SCE) as a reference electrode. The potential was established using an EG and G Model 173 potentiostat. For applied potentials exceeding 8.5 V, a Sorensen DCR-806B power supply was used in a 2-electrode configuration. In both cases, the anodic oxidation time was 5 min at a constant potential. In order to determine SiO, layer thicknesses independently, complementary XPS and ellipsometric
2. Experimental 2. I. Sample preparation Anodic silicon oxides were grown on Si(100) samples cleaved from Si(100) wafers (p-type: 6- 10 Table 1 Thickness Sample No. 1
2 3 4 5 6 J 8 9 10 11 12 13 a 14 ‘I
of SiOz films as measured Voltage (VI 0.4 1.9 3.4 4.9 6.4 8.4 IO 11 13.5 15 17 19 25 35
via ellipsometric
and XPS methods
Ellipsometry (before anneal) (nm) 2.0 2.8 3.9 6.1 9.0 12.5 15.3 17.9 24.2 27.3 37.6 40.6 41.0 82.5
’ Samples 13 and 14 were anodized NH,OH: HzO.
Ellipsometry (after anneal) (nm) 1.4 2.3 3.4 5.1 7.6 10.7 13.3 15.3 21.0 23.7 32. I 34.5 34.7 66.1
in 1 : 1000 NH,OH:H?O
+ 0.01 M NaCl;
XPS (after anneal)
Value used
(nm)
(nm)
1.1 2.0 3.0 4.7 7.0 9.8 12.1 15.6
1.0 1.9 3.0 4.7 7.2 10.3 12.9 14.9 20.6 23.3 31.7 34.1 34.3 65.7
all others
(samples
l-12)
were anodized
in 1: 10
M. Kusrai
er (11. /Applied
Surfurce Science
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ClYY6J
303-312
305
measurements were performed. XPS spectra were acquired on a Perkin Elmer PHI 5500 system equipped with a monochromatic AIK, source. An electron escape depth of 3.18 nm and a ratio 1,-.,/I,,, = 0.70 were used in the calculations, where I,,, and I,,,, are the intensities of the Si 2p peaks originating from an infinitely thick oxide and from a clean (i.e., oxide-free) Si sample, respectively. These parameters were determined for as-grown anodic films [9,10], but were also used for annealed anodic oxides. However, a considerable variation in the attenuation length of thermal oxides has been reported [I 11. The procedure used in this work can be applied to oxides with thicknesses in the range O-150 nm and has a reproducibility better than 1%. Ellipsometry also provided a rapid and convenient method to measure the thickness and was necessarily employed for thicknesses exceeding 150 nm. The measurements were performed with a Rudolph Research AutoEL-II Ellipsometer (A = 632.8 nm). A fixed refractive index of 1.465 was used in the calculations. The thickness of the oxides was measured by ellipsometry, following which the samples were annealed at 700°C for 15 min in N2 gas. The ellipsometric thickness and the XPS thickness of the annealed samples were then measured. The formation conditions and the measured oxide thicknesses are shown in Table 1. The annealed samples had a stoichiometry O/Si = 2.02 as measured by XPS. This compares to O/Si = 2.27 + 0.06 determined for the as-grown oxide [9]. The results in Table 1 show clearly that annealing results in a decrease in the oxide thickness by * 15%. This observation is consistent with a densification of the oxide resulting from the removal of OH groups, which are responsible for the excess oxygen in the as-grown films [ 101. It is also clear that the thicknesses determined by ellipsometry exceed those determined via XPS by a constant value of N 0.4 nm. Thus, for consistency. the thickness of the samples was taken as the ellipsometric thickness after annealing minus 0.4 nm.
University of Wisconsin. Two beam lines were used: For S; L-edge measurements, the Grasshopper soft X-ray beamline, monochromatized by an 1800 grooves/mm grating, was employed. The photon resolution was < 0.1 eV. For Si K-edge measurements, the double crystal monochromator (DCM) beamline was used. Here, the beam was monochromatized using InSb crystals with a photon resolution of - 0.9 eV. The detection system was similar to earlier descriptions [13]. Briefly, for FY measurements. the detector comprised two channel plates (MCP’s) with electrically isolated Cu grids mounted at the front of the channel plates and a copper plate in the back as a collector. The front of the MCP was biased at - 1450 V (to ensure that no electrons impinged on the MCP) and the rear was kept at a potential of - 150 V. The collector itself was at ground potential. The detector was positioned to detect photons emitted at an angle of 50” relative to the surface normal of the sample. The TEY was measured by directly monitoring the sample current. This mode of the TEY measurement was found to yield superior spectra to those obtained using an MCP detector. In order to estimate the energies of the secondary electrons in the current measurements. a Si sample was biased with negative voltage ranging from 1.5 to 10.5 V. It was found that the majority of electrons had energies below 3 eV. Thus Auger electron contribution is small which is consistent with the previous report by Erbil et al. [7]. To ensure a good electrical contact. it was essential to remove the oxide layers from the back of the samples before the measurements. Both TEY and FY were measured for X-rays impinging normally on the sample. All the spectra presented here represent the average of at least 3 scans. For the Si L-edge measurements. the incident flux, I,,. was measured using the current from a 90% transmission gold mesh; for the K-edge an ionization chamber was used. All measurements were then normalized to I,,.
2.2. X-ray ubsorption and data acquisition
3. Results
Photoabsorption spectra were collected at the Canadian Synchrotron Radiation Facility (CSRF) [ 121 situated at the 1 GeV electron storage ring, Aladdin,
3.1. Si L-edge Si L-edge XANES spectra for Si( 100) etched in HF, as received (i.e., covered with a native oxide)
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M. Kasrai et al. /Applied Sqtace Science 99 (I9961 303-312
and SiO, films grown on Si(100) were recorded in TEY and FY modes. Fig. 1 shows the spectra recorded in the TEY mode, after a pre-edge background removal. Comparing spectrum A with spectra B-G in Fig. 1, two regions are easily identified. The absorption features observed from = 99- 104 eV (identified as a) are attributable to Si” (referred to as Si) and those from 104- 110 eV (identified as b and c) are associated with Si4+ (referred to as SiO,). The origin of these features has been discussed elsewhere [ 13,141. As the thickness of the oxide film is increased (spectra B-G), the intensity of peak a decreases and that of peaks b and c increases. For film thicknesses exceeding 4.7 nm, the Si signal can no longer be observed and the spectrum becomes very similar to that for a thick SiO, sample [13]. In order to estimate the maximum sampling depth of the TEY for Si, we need to measure the area under peaks a, b and c. For this purpose, all the
36
J si
.
loo I
104
108
.
112 9
L-edge:
-
Si: I-IF treated
Si: Native oxide
910,: 1.0 Llm
SiO*:l.9 Ilm
siog
3.0 nm
sio,:4.7 nm
sio,:7.0
(G) -,:. 66
i
j ,I.
loo
Photon
104
Energy
nm
i 8,
,
106
112
(eV)
Fig. 1. Si L-edge XANES spectra Si(lOO), measured by TEY technique.
of SiOz
films
grown
on
oI
95
100
.
I
*
105
I
110
.
115
F%otonEnar~(ev)
Fig. 2. A least squares fit of Si L-edge XANES spectrum, resolving Si and SiO, regions: Peaks 1-3 belong to Si and 4-6 belong to SiOz.
spectra were fitted with Gaussian peaks and arctangent background step functions using a least squares program [ 151. As an example, Fig. 2 shows the result of fitting several Gaussian peaks to spectrum C in Fig. 1. Arctangent step functions represent the transition of ejected photoelectrons to the continuum [ 161. For these spectra, two backgrounds have been fitted: one for the Si region and another for the SiOz region. A number of conditions and constraints were introduced to obtain meaningful fits. First, the position of the arctangent step functions for the Si and SiO, regions were aligned just before peak 2 and peak 4, respectively. These positions are rather arbitrary, but these positions gave the best fit to the data [ 171. The positions were kept the same for all samples in order to obtain consistent results. Moreover, as will be seen later, the ratio of SiO, to Si was used for quantitative analysis. Second, the peak widths of peaks 4 and 5 were constrained to be equal. All peak heights and peak positions were allowed to vary. The fitting was not aimed at resolving all the fine structures, but merely to resolve the Si from the SiO, features. It was also found that if the intensity of peaks 2 and 6 after background subtraction is used, a good estimate for the proportion of Si and SiO, can be obtained in the sample. In Fig. 3(A), the peak intensities of Si and SiOz, determined from the fitting procedure, are plotted as a function of the oxide thickness. In TEY measure-
307
M. Kasrai et ul. /Applied Sulfate Science 99 (1996) 303-312 86
ments, the intensities are directly related to the conductivity and surface condition of each sample. This relationship is less significant in the K-edge measurements (see below). Thus, as evident in Fig. 3(A), there are some fluctuations in the data, probably due to different sample thicknesses and slightly different surface conditions. However, the spectral trends are quite clear and show that as the thickness is increased, the Si intensity decreases and the SiO, intensity increases. From these data, we are able to measure the film thickness corresponding to the native oxide. To achieve this goal, the relative intensity ratio, SiO,/Si, is shown in Fig. 3(B). Many of the systematic uncertainties are removed in taking the ratio of intensities; it is evident that the fluctuations in Fig. 3(A) are much reduced in Fig. 3(B). The data in Fig. 3(B) vary smoothly with thickness, yielding a native oxide thickness of 0.7 nm. This value is
a(A)
0.6 ITEY (‘5%L-edge.)1
1LM
pi
L-edge:
104
106
112
’(4
FY
SiO, I t
Si
SO,:
1.0 nm
sio,: 3.0
nm
sioa: 7.0 nm SiO,: 21.0~~1 sioa: 23.onm SiO,: 34.0 nm
SO,: 68.0 wn
Photon
Energy
(ev)
!~~:
09
a
0
0
034
OI. 0
10
I. 20
I. 30
I, 40
I, 50
I. 60
70
ThiCknSSl(nm)
Fig. 3. (A) Si L-edge XANES spectra of SiO, films grown on Si(lOO), measured by the FY technique. (B) Ratio of the Si/SiOz intensity versus the film thickness.
Fig. 3. (A) SiO, and Si signal intensity versus the SiO, film thickness at the L-edge, measured by TEY technique. (B) Ratio of the SiO, /Si intensity versus the film thickness.
somewhat lower than the value reported in the literature [S], but agrees extremely well with recent findings [18]. Si L-edge XANES spectra of samples measured in the FY mode are presented in Fig. 4(A). after a pre-edge background removal. The Si signal intensity diminishes as the SiO, film thickness increases. Since the fluorescence photons have a much larger escape depth than electrons, the sampling depth of the fluorescence measurement is expected to be much larger than that for the TEY data. In order to estimate the sampling depth, the Si/SiO, intensity ratio is shown as a function of the SiOz film thickness in Fig. 4(B). The scatter in the data is more pronounced in these measurements since the fluorescence rate
308
M. Kasrai
ef al. /Applied
Surface Science 95’(IYY61303-312 0.6
(for low-Z elements) is several orders of magnitude smaller than the Auger decay rate. Thus, the counting statistics are not as high as for the TEY data. However, the general pattern is quite clear and indicates that the maximum sampling depth for fluorescence is N 70 nm. No SiO, signal could be detected for native oxide on Si thereby suggesting that the film thickness is < 1 nm (see spectrum 1 in Fig. 4). 3.2. Si K-edge
r
w
Si K-edge XANES spectra were measured in both the TEY and FY modes for all samples. The TEY spectra are illustrated in Fig. 5, after a pre-edge
o.2m Thickness(nm)
t , Si
-,
, .
1
SO.’ ,-
NatWa odds
I..
ISi K-edge:
0
TElY
/:
(0.0 nm)
iz
J
.A0 I 0.0 -
o/o’
0
1
2 Thickneaa
3
4
5
(nm)
Fig. 6. (A) SiO, and Si signal intensity versus the SiO, film thickness measured at the K-edge by the TEY technique. (B) Ratio of the SiO, /Si intensity versus the film thickness.
1880
1880
Photon
Energy
(eV)
Fig. 5. Si K-edge XANES spectra of Si02 Si(100). measured by the TEY technique.
films
grown
on
background removal. It is noted that the SiO, signal can be seen for the native oxide sample. Obviously the sampling depth of the TEY at the K-edge is much larger than that at the L-edge. Indeed, the Si signal can still be observed for an oxide film thickness of 66.1 nm. To determine the maximum sampling depth of the TEY in the Si K-edge range, the same procedure has been followed as for the L-edge case. The data shown in Fig. 6(A) show significantly less scatter than the L-edge data due to a much improved signal-to-background ratio. The signal-tobackground is more than an order of magnitude larger in the K-edge compared to the L-edge. The reasons for the high background in the L-edge have been discussed before [13]. A visual estimate for the maximum sampling depth is _ 70 nm - a value close to that measured for the Si L-edge in the FY
M. Kasrai et al. /Applied SurjaaceScience 99 CI Y96) 303-3 12 I
.
4. Discussion
[Sl K-edge: q SO,
J I I
1840
.
I
1880 Photon
.
.
I
.
l&SO Energy
1
I
(eV)
Fig. 7. Si K-edge XANES spectra of SO, Si(100). measured by the FY technique.
films
309
grown
on
mode. Because of the much higher yield, the quality of the K-edge data is much improved compared to the L-edge data. In the same manner as the L-edge, the SiO,/Si intensity ratio is plotted as a function of the oxide thickness in Fig. 6(B) to determine the thickness of the native oxide. The value of 0.9 nm deduced from this figure is close to that obtained from the L-edge data. Fig. 7 shows the Si K-edge XANES spectra measured in the FY mode, after a pre-edge background removal. As expected, fluorescence photons have a much larger escape depth than secondary electrons and the sampling depth of the Si K-edge measured in FY is indeed quite large. Indeed, the SiO, signal can barely be seen for oxide thicknesses < 21 nm. Suitable samples with thicknesses exceeding 66 nm cannot be grown; thus, the maximum sampling depth of the FY cannot be measured. However, it is clear that the value should be of the order of several hundred nm.
X-ray photoabsorption results in core hole creation which decay through the competing processes of fluorescence radiation and Auger electron emission. Both these processes have been shown to be proportional to the absorption cross section [I ,7]. The relative X-ray and Auger yields depend on the atomic number of the absorbing atom. For light elements (such as Si, P, S), and in particular at the L-edge, the Auger yield exceeds the fluorescence yield by several orders of magnitude. Nevertheless. as has been shown above. the fluorescence yield can be used to measure the absorption spectra [13]. In order to measure Auger electrons, an electron analyser is required. An alternative technique. which is also proportional to the absorption, is total electron yield (TEY) method. This technique encompasses the entire energy range of electrons. However. the electron energy spectrum is dominated by low energy secondary electrons. Henke et al. [ 191 have demonstrated that the majority of electrons for metals have energies below 5 eV with a peak near - I.3 eV. By contrast, the majority of electrons have energies < 2 eV for insulators. Both theoretical calculations and experimental measurements have confirmed that the shape of the low energy electron distribution is independent of the primary photon energy [l]. Since the low energy spectrum for a given material does not change with photon energy, it is reasonable to assume that the escape depth of secondary electrons is independent of the photon energy. Stiihr [I] has treated this problem mathematically and demonstrated that the effective escape depth for secondary electrons in Au is 5 nm and is independent of photon energy in the 300-1500 eV region. However, the number of low energy electrons increases linearly with the photon energy. Based on the above discussion, we expect to find similar escape depths for secondary electrons created in the Si L-edge (N 100 eV region) and Si K-edge (_ 1850 eV region). First, we start with the TEY measurement of the Si K-edge presented in Figs. 5 and 6. The sampling depth of TEY for this region is well above 60 nm. Jones and Woodruff [3] have reported the escape depth of the low energy electrons for the Al,O,/AI system at the Al K-edge ( - 1600 eV) and have concluded that the effective TEY
310
M. Kasrai et al./Applied
Sur$ace Science 99 (1996) 303-312
sampling depth is < 39 nm. Since they were unable to resolve Al signals from Al,O, signals in their spectra, they used a procedure to estimate the contribution of each signal and assumed that the escape depth for the oxide was twice that for the metal. In our case, as was shown in Fig. 5, we have resolved the Si and SiO, contributions, which then makes it possible to obtain separate electron escape depths for each material. We follow the description of Jones and Woodruff [3] for the L- and K-edge TEY yields. Specifically, the differential total electron yield from the oxide, dS,,, is given by sin8dzd8d4,
(1)
where the depth attenuation is described by the same expression as for a no-loss detection method, except that the yield is integrated over the entire azimuth [O, 27r] for 4. I, is the incident photon flux, p,, and A,, are the X-ray absorption coefficient and electron escape depth, respectively, for the oxide. Integrating over the oxide film thickness, d, and for emission into the vacuum for 0 values in the range [O, 7r/2], we obtain S,, =Z,p,,A,,7r[l
-ee-” (1 - u) - UQ,( u)],
where u = d/h,, and E,(u), the exponential of order 1, is given by E,(u)
= I;‘?
f(x)
=eer(l
integral
dr.
We denote the function
(3) f(x)
by
-x)+~‘E,(x).
(4)
For the differential signal from the substrate, we get an expression analogous to Eq. (1)
dSSx =‘ll
PSi
(2)
dS,,,
“P( ,,,,I iexP( ,;,k”,)
Xsin 8dzd+.
0
(5)
Here, the limits for z represent the substrate values [d, x] and the limits on 8 and 4 are the same as before. Thus, integrating to get Ssi
Combining Eqs. (2) and (6) yields the ratio of the oxide and substrate signals, S,,/Ssi
where pO,/ps, = 0.5795 for SiO, over Si using values for psi and po at 1839 eV [20] and calculating puox using conventional density values for SiOZ and Si of 2.27 and 2.326 g/cm3, respectively. In taking the ratio of the measured L- and K-edge signals, systematic uncertainties should be eliminated. There is an implicit assumption that the incident photon beam is not attenuated in the depth of material contributing to the TEY. The experimental data from Fig. 6(A) have been fitted to Eq. (7) using a non-linear least squares analysis. We obtain A,, = 23.4 + 0.5 nm and Asi = 17.0 -t 0.5 nm (assuming +5% uncertainties in the data), yielding A,,/& = 1.4 * 0.1 for the K-edge data, as shown by the smooth curve in Fig. 8(A). The A ratio between oxide and substrate thus deviates from the value 2 assumed by Jones and Woodruff [3] (see below). For the L-edge TEY data, the results are shown in Fig. 8(B). For fitting the L-edge data, we have used p,,/psi = 1.026 for SiO, over Si using psi and p. at 100 eV [20] and calculating pox as above. Again, we obtain an excellent fit and extract best fitted values for the escape depths of A,,, = 1.8 + 0.1 nm and A,, = 0.81 & 0.02 nm (assuming -t 10% uncertainties in the data), yielding &,/A,, = 2.2 which is different from the K-edge but closer to the value 2. The ratio of escape depths of photoelectrons, having kinetic energies = 20-300 eV, have been reported for the SiO,/Si system using XPS 1211. In this energy range, the A,,/A,, ratios change from 1.1 to 2.1. Erbil et al. [7] have shown that the sampling depth of TEY is mainly determined by the escape depth of the original primary Auger electrons. From their work, the ranges for the initial Auger electrons created at the K-edge and L-edge for Si is estimated to be N 400 and - 40 A, respectively. The ratios of AK-edge/AL-edge for Si and SiO, are 21 and 12, respectively which correlate with the ratio of ranges of the primary Auger electrons. We can summarize the above results as follows:
M. Kusrai
et al. /Applied
31
Surjbce Science YY (1 YY6) 303-312
(i) As was stated above, the range of primary Auger electrons is larger at the Si K-edge than the L-edge. The total number of low-energy secondary electrons created at the Si K-edge (N 1840 eV) is also much larger than the corresponding number at the L-edge (N 100 eV). These two factors make the sampling depth of the K-edge much larger than the L-edge. (ii) The background is expected to be much larger at the L-edge due to the higher cross section of valence electrons for low energy photons. Thus we expect to find a much larger signal-to-background ratio for the same number of photons absorbed at the K-edge compared to the L-edge, as confirmed by the above measurements. Thus. the sensitivity of the
30 -
I
Data -Ftt OOQ
Thic!sneas
(Ilm)
Fig. 9. (A) A non-linear least squares fit to SiOl /Si measured by the FY technique at the Si L-edge.
intensity
TEY measurement at the L-edge will be worse than at the K-edge. For the FY data at the L-edge. we can fit the ratio of the oxide to substrate signals, S,,,/S,,, using the expression
S”, 1 - exd - bh,,, > -= = ev( bdF,,x> - 1 (8) exp( - bdp,,, ) SS, T
0
10
20
30
40
Thicknsas 100
.,
.,
50
.,
(
,
[Si L-edge1 St:
60
70
(nm)
,
03)
1
5
6
0.8 pm
910,is_
I’
0
12
.
3
4
where b = 1 + set 19 and 0 = 50”. corresponding to the experimental arrangement. and pC,x is the absorption coefficient for L-edge photons in SiO, to be determined via fitting. Eq. (8). which closely resembles the expression derived for XPS analyses, has been derived to include the attenuation of the incident photon beam (which is tzof negligible, in contrast to the case for detecting emitted electrons for which escape depths are much smaller) in penetrating the sample. Experimental data have been fitted to Eq. (8) and are plotted in Fig. 9. together with the best fitted curve. Although the fit is less than perfect, the best fit is obtained for pm’ = 52 nm. Using estimates for photon attenuation cross sections (at hv = 100 eV) in Si and 0 of 2.66 X 1W ‘* cm’/atom and 1.66 X IO Ix cm’/atom, respectively, we then calculate a photon attenuation distance &’ = 73.5 nm in SiO,, which is in reasonable accord with the value extracted from the best fit to the data.
Thickness(nm)
Fig. 8. (A) A non-linear least squares tit to Si02 /Si intensity measured by the TEY technique at the Si K-edge. (B) A non-linear least squares fit to SiO, /Si intensity measured by the TEY technique at the Si L-edge. The fitted results yield the escape depths for low-energy secondary electrons at the K- and L-edges.
5. Summary
and conclusions
A systematic study has been undertaken to investigate the sampling depth for low-energy secondary
312
M. Kasrai et al/Applied
Surface Science 99 (1996) 303-312
electrons at the Si L- and K-edges for the SiOJSi system using the total electron yield technique. Controlled SiO, films (N l-60 nm> were grown electrochemically on Si(100) substrates. It was found that the sampling depth of the secondary electrons at the L-edge (100 eV) and the K-edge ( 1840 eV) are _ 5 and N 70 nm, respectively. Using the data and developing a theoretical formalism, the escape depths of the low-energy secondary electrons were derived at both edges for Si and SiO,. The escape depths for Si and SiO, at the K-edge were 17 and 23 nm; the corresponding values at the L-edge were 0.8 and 1.8 nm, respectively. Thus, the escape depth for the Si L-edge is much shorter than for the K-edge. Some suggestions have been offered to explain the short range of the low-energy electrons at the L-edge, The sampling depths of the fluorescence photons at the L-edge and K-edge have also been investigated using the fluorescence yield technique. It was found that the sampling depth for fluorescence photons at the L-edge is N 60 nm. Using the data, a mathematical expression was developed to extract the absorption coefficient of fluorescence photons in SiO, at the L-edge and found to be 52 nm. Although it was not feasible to fabricate SiOz films of sufficient thickness to provide for a measure of the corresponding sampling depth of the fluorescence yield at the K-edge, this length is estimated to be several hundred nm.
Acknowledgements This study was financially supported by the Ontario Centre for Materials Research (OCMR) and the Natural Sciences and Engineering Research Council of Canada (NSERC). The authors are grateful to the staff at the Synchrotron Radiation Centre (SRC), University of Wisconsin, for their technical assistance and the National Science Foundation (NSF),
for their support #DMR92 12658.
of the
SRC
under
the
Grant
References [I] J. StGhr,
NEXAFS Spectroscopy, Springer Series in Surface Sciences, Vol. 25 (Springer, Berlin, 1992) ch. 5. [2] I. Lindau and W.E. Spicer, J. Electron Spectrosc. 3 (1974) 409. [3] R.G. Jones and D.P. Woodruff, Surf. Sci. 114 (1982) 38. [4] W. Gudat, PhD Dissertation, University of Hamburg (1974), unpublished. ISI G. Martens, P. Rabe, G. Tolkiehn and A. Werner, Phys. Status Solidi (a) 55 (1979) 105. 161 T. Tyliszczak and A.P. Hitchcock, Physica B 158 (1989) 335. [7] A. Erbil, G.S. Cargill III, R. Frahm and R.F. Boehme, Phys. Rev. B 37 (1988) 2450. [8] G.R. Harp, Z.L. Han and B.P. Tonner, J. Vat. Sci. Technol. A 8 (1990) 2566. [9] D.F. Mitchell, K.B. Clark, J.A. Bardwell, W.N. Lennard, G.R. Massoumi and IV. Mitchell, Surf. Interf. Anal. 21 ( 1994) 44. [lo] K.B. Clark, J.A. Bardwell and J.-M. Baribeau, J. Appl. Phys. 76 (1994) 3114. [I I] S. Tanuma, C.J. Powell and D.R. Penn, Surf. Interf. Anal. 17 (1991) 927. [12] G.M. Bancroft, Can. Chem. News 44 (1992) 15. [13] M. Kasrai, Z. Yin, G.M. Bancroft and K.H. Tan, J. Vat. Sci. Technol. A 11(1993) 2694. [14] D.G.J. Sutherland, M. Kasrai, G.M. Bancroft, Z.F. Liu and K.H. Tan, Phys. Rev. B 48 (1993) 14989; D. Li, G.M. Bancroft, M. Kasrai, M.E. Fleet, R.A. Secco, X.H. Feng, K.H. Tan and B.X. Yang, Am. Miner. 79 (1994) 622. [ 151 T. Tyliszczak, Ban Program, unpublished. 1161 J. Stohr, NEXAFS Spectroscopy, Springer Series in Surface Sciences, Vol. 25 (Springer, Springer. 1992) ch. 7 [17] Z. Yin, M. Kasrai, G.M. Bancroft, K.H. Tan and X. Feng, Phys. Rev. B 51 (1995) 742. [IS] M.L.W. Vanderzwan, J.A. Bardwell, G.I. Sproule and M.J. Graham, Appl. Phys. Lett. 64 (1994) 446. [19] B.L. Henke, J.P. Knauer and K. Premaratne, J. Appl. Phys. 52 (1981) 1509. [201 B.L. Henke, P. Lee, T.J. Tanaka, R.L. Shimabukuro and B.K. Fujikawa, At. Data Nucl. Data Tables 27 (1982) 1, [21] F.J. Himpsel. F.R. McFeely, A. Taleb-Ibrahimi and J.A. Yarmoff, Phys. Rev. B 38 (1988) 6084.
surface science ELSEVIER
Applied Surface Science 99 (1996) 303-3 12
Sampling depth of total electron and fluorescence measurements in Si L- and K-edge absorption spectroscopy M. Kasrai a,* , W.N. Lennard b, R.W. Brunner a, G.M. Bancroft a, J.A. Bardwell ‘, K.H. Tan d “ Depurtment b Department ’ Institute
of Chemistry,
forMicrostructural
I1 Canadian
The Uniwrsity
of Physics, The UrGersit)
Synchrotron
Sciences. National Radiation
Received
Facility,
ofWestern
Ontario,
of Western Ontario, Research Council Unirersifl
London, London.
Ontario.
Canada N6A 3K7
Ottawa.
Ontario,
of Canada,
of Wisconsin-Madison,
11 August 1995; accepted 29 January
Canada N6A 5B7
Ontario.
Stoughton,
Canudu WI 53589.
KIA
ORI,
USA
1996
Abstract High resolution Si L-edge and K-edge X-ray absorption near edge structure (XANES) spectra for SiO, on Si substrates have been recorded using total electron yield (TEY) and fluorescence yield (FYI techniques. The sampling depths of TEY and FY for Si L-edge and Si K-edge, respectively, have been investigated in the energy range 9% 120 eV and 1830-1900 eV. The maximum sampling depth for TEY is found to be - 5 nm for the Si L-edge and - 70 nm for the K-edge regions. The FY sampling depth at the L-edge is - 70 nm whereas for the K-edge, the sampling depth is several hundred nm. Based on these data, and using a theoretical model, electron escape depths for the TEY measurements in both energy ranges have been deduced.
1. Introduction Total electron yield (TEY) and fluorescence yield (FYI are well established methods for measuring absorption spectra of solid samples [I]. The TEY and FY spectroscopies measure the total number of electrons and fluorescence photons per incident photon, respectively, emitted from the sample as a function of photon energy. It has been shown that since the total electron or fluorescence photon yield emitted from the sample is proportional to the absorption coefficient, both techniques are equivalent to a transmission measurement [l]. However, the main difference between the TEY and FY measurements is the
’ Corresponding author. Tel.: + l-519-66121 11 ext. 6332 or 63 18: Fax: + I-519-6613022: e-mail: [email protected]. 0169~3332/96/$15.00 PII
Copyright
SO 169-4332(96)00454-O
effective sampling depths characteristic of the two techniques. The mean free path of electrons created in a solid depends on the kinetic energy (E,) of the electron as well as the nature of the material. Nevertheless, mean free paths are described reasonably well by a universal curve [2] which exhibits several interesting features. The electron mean free path has its highest value when the kinetic energy is very low (E, < 2 eV); for increasing E,, the mean free path decreases and reaches a minimum of - 0.4 nm at E, = 50 eV. For even higher values of l$;., the mean free path again increases monotonically. By measuring low energy electrons, an effective sampling depth of tens of nm can be obtained in the TEY mode. Jones and Woodruff [3] have reported the sampling depth of TEY for the Al,O,/Al system at the Al K-edge. Gudat [4] has also reported the sampling
0 1996 Elsevier Science B.V. All rights reserved
304
M. Kasrai et al. /Applied Surface Science 99 (1996) 303-312
depth in the energy range 50-150 eV. Martens et al. [5] have studied the sampling depth of TEY at the Cu K-edge and Tyliszczak and Hitchcock [6] have made measurements at the Cu, MO and Mn K-edges. Erbil et al. [7] have compared the TEY, fluorescence and transmission detection modes for Ge, Ni, Co and As K-edges. Values reported for sampling depths in the above studies vary from 50- 1000 nm depending on the specific edge investigated. SiO, films on silicon play a very important role in semiconductor technology, and X-ray absorption spectroscopy is widely used to investigate the local Si structure [8]. Thus, a good understanding of the sampling depth of these detection schemes is required. To our knowledge, no systematic study has been reported for the sampling depth for TEY and FY measurements for the SiO,/Si system. To achieve this goal, we have used well-characterized SiO, films [9] of varying thicknesses produced on single crystal Si substrates to determine the sampling depth of TEY and FY measurements at the Si L-edge ( N 100 eV) and Si K-edge ( N 1840 eV>.
R cm>. Prior to each experiment, the samples were degreased by successive ultrasonic treatments in acetone, isopropanol and methanol, and rinsed with distilled water followed by a 1% HF etching procedure for 1 min to remove the air-formed SiO, film. Electrical contact to the Si electrodes was accomplished by smearing InGa eutectic on the upper 2 mm of the sample and clipping onto this area with a copper fastener. This contact area was held well above the solution and was cleaved off the sample after the oxide had been grown. The final sample size was 0.8 X 0.8 cm2. The electrolyte was a 1 : 10 v/v aqueous NH,OH solution, or 1 : 1000 v/v aqueous solution with 0.01 M added NaCl. The latter solution was prepared so as to yield an electrolyte with the same conductivity as the former solution. All solutions were prepared from electronic grade chemicals and de-ionized water. The electrochemical cell comprised a conventional 3-electrode configuration with a platinum gauze as a counter electrode and a saturated calomel electrode (SCE) as a reference electrode. The potential was established using an EG and G Model 173 potentiostat. For applied potentials exceeding 8.5 V, a Sorensen DCR-806B power supply was used in a 2-electrode configuration. In both cases, the anodic oxidation time was 5 min at a constant potential. In order to determine SiO, layer thicknesses independently, complementary XPS and ellipsometric
2. Experimental 2. I. Sample preparation Anodic silicon oxides were grown on Si(100) samples cleaved from Si(100) wafers (p-type: 6- 10 Table 1 Thickness Sample No. 1
2 3 4 5 6 J 8 9 10 11 12 13 a 14 ‘I
of SiOz films as measured Voltage (VI 0.4 1.9 3.4 4.9 6.4 8.4 IO 11 13.5 15 17 19 25 35
via ellipsometric
and XPS methods
Ellipsometry (before anneal) (nm) 2.0 2.8 3.9 6.1 9.0 12.5 15.3 17.9 24.2 27.3 37.6 40.6 41.0 82.5
’ Samples 13 and 14 were anodized NH,OH: HzO.
Ellipsometry (after anneal) (nm) 1.4 2.3 3.4 5.1 7.6 10.7 13.3 15.3 21.0 23.7 32. I 34.5 34.7 66.1
in 1 : 1000 NH,OH:H?O
+ 0.01 M NaCl;
XPS (after anneal)
Value used
(nm)
(nm)
1.1 2.0 3.0 4.7 7.0 9.8 12.1 15.6
1.0 1.9 3.0 4.7 7.2 10.3 12.9 14.9 20.6 23.3 31.7 34.1 34.3 65.7
all others
(samples
l-12)
were anodized
in 1: 10
M. Kusrai
er (11. /Applied
Surfurce Science
YY
ClYY6J
303-312
305
measurements were performed. XPS spectra were acquired on a Perkin Elmer PHI 5500 system equipped with a monochromatic AIK, source. An electron escape depth of 3.18 nm and a ratio 1,-.,/I,,, = 0.70 were used in the calculations, where I,,, and I,,,, are the intensities of the Si 2p peaks originating from an infinitely thick oxide and from a clean (i.e., oxide-free) Si sample, respectively. These parameters were determined for as-grown anodic films [9,10], but were also used for annealed anodic oxides. However, a considerable variation in the attenuation length of thermal oxides has been reported [I 11. The procedure used in this work can be applied to oxides with thicknesses in the range O-150 nm and has a reproducibility better than 1%. Ellipsometry also provided a rapid and convenient method to measure the thickness and was necessarily employed for thicknesses exceeding 150 nm. The measurements were performed with a Rudolph Research AutoEL-II Ellipsometer (A = 632.8 nm). A fixed refractive index of 1.465 was used in the calculations. The thickness of the oxides was measured by ellipsometry, following which the samples were annealed at 700°C for 15 min in N2 gas. The ellipsometric thickness and the XPS thickness of the annealed samples were then measured. The formation conditions and the measured oxide thicknesses are shown in Table 1. The annealed samples had a stoichiometry O/Si = 2.02 as measured by XPS. This compares to O/Si = 2.27 + 0.06 determined for the as-grown oxide [9]. The results in Table 1 show clearly that annealing results in a decrease in the oxide thickness by * 15%. This observation is consistent with a densification of the oxide resulting from the removal of OH groups, which are responsible for the excess oxygen in the as-grown films [ 101. It is also clear that the thicknesses determined by ellipsometry exceed those determined via XPS by a constant value of N 0.4 nm. Thus, for consistency. the thickness of the samples was taken as the ellipsometric thickness after annealing minus 0.4 nm.
University of Wisconsin. Two beam lines were used: For S; L-edge measurements, the Grasshopper soft X-ray beamline, monochromatized by an 1800 grooves/mm grating, was employed. The photon resolution was < 0.1 eV. For Si K-edge measurements, the double crystal monochromator (DCM) beamline was used. Here, the beam was monochromatized using InSb crystals with a photon resolution of - 0.9 eV. The detection system was similar to earlier descriptions [13]. Briefly, for FY measurements. the detector comprised two channel plates (MCP’s) with electrically isolated Cu grids mounted at the front of the channel plates and a copper plate in the back as a collector. The front of the MCP was biased at - 1450 V (to ensure that no electrons impinged on the MCP) and the rear was kept at a potential of - 150 V. The collector itself was at ground potential. The detector was positioned to detect photons emitted at an angle of 50” relative to the surface normal of the sample. The TEY was measured by directly monitoring the sample current. This mode of the TEY measurement was found to yield superior spectra to those obtained using an MCP detector. In order to estimate the energies of the secondary electrons in the current measurements. a Si sample was biased with negative voltage ranging from 1.5 to 10.5 V. It was found that the majority of electrons had energies below 3 eV. Thus Auger electron contribution is small which is consistent with the previous report by Erbil et al. [7]. To ensure a good electrical contact. it was essential to remove the oxide layers from the back of the samples before the measurements. Both TEY and FY were measured for X-rays impinging normally on the sample. All the spectra presented here represent the average of at least 3 scans. For the Si L-edge measurements. the incident flux, I,,. was measured using the current from a 90% transmission gold mesh; for the K-edge an ionization chamber was used. All measurements were then normalized to I,,.
2.2. X-ray ubsorption and data acquisition
3. Results
Photoabsorption spectra were collected at the Canadian Synchrotron Radiation Facility (CSRF) [ 121 situated at the 1 GeV electron storage ring, Aladdin,
3.1. Si L-edge Si L-edge XANES spectra for Si( 100) etched in HF, as received (i.e., covered with a native oxide)
306
M. Kasrai et al. /Applied Sqtace Science 99 (I9961 303-312
and SiO, films grown on Si(100) were recorded in TEY and FY modes. Fig. 1 shows the spectra recorded in the TEY mode, after a pre-edge background removal. Comparing spectrum A with spectra B-G in Fig. 1, two regions are easily identified. The absorption features observed from = 99- 104 eV (identified as a) are attributable to Si” (referred to as Si) and those from 104- 110 eV (identified as b and c) are associated with Si4+ (referred to as SiO,). The origin of these features has been discussed elsewhere [ 13,141. As the thickness of the oxide film is increased (spectra B-G), the intensity of peak a decreases and that of peaks b and c increases. For film thicknesses exceeding 4.7 nm, the Si signal can no longer be observed and the spectrum becomes very similar to that for a thick SiO, sample [13]. In order to estimate the maximum sampling depth of the TEY for Si, we need to measure the area under peaks a, b and c. For this purpose, all the
36
J si
.
loo I
104
108
.
112 9
L-edge:
-
Si: I-IF treated
Si: Native oxide
910,: 1.0 Llm
SiO*:l.9 Ilm
siog
3.0 nm
sio,:4.7 nm
sio,:7.0
(G) -,:. 66
i
j ,I.
loo
Photon
104
Energy
nm
i 8,
,
106
112
(eV)
Fig. 1. Si L-edge XANES spectra Si(lOO), measured by TEY technique.
of SiOz
films
grown
on
oI
95
100
.
I
*
105
I
110
.
115
F%otonEnar~(ev)
Fig. 2. A least squares fit of Si L-edge XANES spectrum, resolving Si and SiO, regions: Peaks 1-3 belong to Si and 4-6 belong to SiOz.
spectra were fitted with Gaussian peaks and arctangent background step functions using a least squares program [ 151. As an example, Fig. 2 shows the result of fitting several Gaussian peaks to spectrum C in Fig. 1. Arctangent step functions represent the transition of ejected photoelectrons to the continuum [ 161. For these spectra, two backgrounds have been fitted: one for the Si region and another for the SiOz region. A number of conditions and constraints were introduced to obtain meaningful fits. First, the position of the arctangent step functions for the Si and SiO, regions were aligned just before peak 2 and peak 4, respectively. These positions are rather arbitrary, but these positions gave the best fit to the data [ 171. The positions were kept the same for all samples in order to obtain consistent results. Moreover, as will be seen later, the ratio of SiO, to Si was used for quantitative analysis. Second, the peak widths of peaks 4 and 5 were constrained to be equal. All peak heights and peak positions were allowed to vary. The fitting was not aimed at resolving all the fine structures, but merely to resolve the Si from the SiO, features. It was also found that if the intensity of peaks 2 and 6 after background subtraction is used, a good estimate for the proportion of Si and SiO, can be obtained in the sample. In Fig. 3(A), the peak intensities of Si and SiOz, determined from the fitting procedure, are plotted as a function of the oxide thickness. In TEY measure-
307
M. Kasrai et ul. /Applied Sulfate Science 99 (1996) 303-312 86
ments, the intensities are directly related to the conductivity and surface condition of each sample. This relationship is less significant in the K-edge measurements (see below). Thus, as evident in Fig. 3(A), there are some fluctuations in the data, probably due to different sample thicknesses and slightly different surface conditions. However, the spectral trends are quite clear and show that as the thickness is increased, the Si intensity decreases and the SiO, intensity increases. From these data, we are able to measure the film thickness corresponding to the native oxide. To achieve this goal, the relative intensity ratio, SiO,/Si, is shown in Fig. 3(B). Many of the systematic uncertainties are removed in taking the ratio of intensities; it is evident that the fluctuations in Fig. 3(A) are much reduced in Fig. 3(B). The data in Fig. 3(B) vary smoothly with thickness, yielding a native oxide thickness of 0.7 nm. This value is
a(A)
0.6 ITEY (‘5%L-edge.)1
1LM
pi
L-edge:
104
106
112
’(4
FY
SiO, I t
Si
SO,:
1.0 nm
sio,: 3.0
nm
sioa: 7.0 nm SiO,: 21.0~~1 sioa: 23.onm SiO,: 34.0 nm
SO,: 68.0 wn
Photon
Energy
(ev)
!~~:
09
a
0
0
034
OI. 0
10
I. 20
I. 30
I, 40
I, 50
I. 60
70
ThiCknSSl(nm)
Fig. 3. (A) Si L-edge XANES spectra of SiO, films grown on Si(lOO), measured by the FY technique. (B) Ratio of the Si/SiOz intensity versus the film thickness.
Fig. 3. (A) SiO, and Si signal intensity versus the SiO, film thickness at the L-edge, measured by TEY technique. (B) Ratio of the SiO, /Si intensity versus the film thickness.
somewhat lower than the value reported in the literature [S], but agrees extremely well with recent findings [18]. Si L-edge XANES spectra of samples measured in the FY mode are presented in Fig. 4(A). after a pre-edge background removal. The Si signal intensity diminishes as the SiO, film thickness increases. Since the fluorescence photons have a much larger escape depth than electrons, the sampling depth of the fluorescence measurement is expected to be much larger than that for the TEY data. In order to estimate the sampling depth, the Si/SiO, intensity ratio is shown as a function of the SiOz film thickness in Fig. 4(B). The scatter in the data is more pronounced in these measurements since the fluorescence rate
308
M. Kasrai
ef al. /Applied
Surface Science 95’(IYY61303-312 0.6
(for low-Z elements) is several orders of magnitude smaller than the Auger decay rate. Thus, the counting statistics are not as high as for the TEY data. However, the general pattern is quite clear and indicates that the maximum sampling depth for fluorescence is N 70 nm. No SiO, signal could be detected for native oxide on Si thereby suggesting that the film thickness is < 1 nm (see spectrum 1 in Fig. 4). 3.2. Si K-edge
r
w
Si K-edge XANES spectra were measured in both the TEY and FY modes for all samples. The TEY spectra are illustrated in Fig. 5, after a pre-edge
o.2m Thickness(nm)
t , Si
-,
, .
1
SO.’ ,-
NatWa odds
I..
ISi K-edge:
0
TElY
/:
(0.0 nm)
iz
J
.A0 I 0.0 -
o/o’
0
1
2 Thickneaa
3
4
5
(nm)
Fig. 6. (A) SiO, and Si signal intensity versus the SiO, film thickness measured at the K-edge by the TEY technique. (B) Ratio of the SiO, /Si intensity versus the film thickness.
1880
1880
Photon
Energy
(eV)
Fig. 5. Si K-edge XANES spectra of Si02 Si(100). measured by the TEY technique.
films
grown
on
background removal. It is noted that the SiO, signal can be seen for the native oxide sample. Obviously the sampling depth of the TEY at the K-edge is much larger than that at the L-edge. Indeed, the Si signal can still be observed for an oxide film thickness of 66.1 nm. To determine the maximum sampling depth of the TEY in the Si K-edge range, the same procedure has been followed as for the L-edge case. The data shown in Fig. 6(A) show significantly less scatter than the L-edge data due to a much improved signal-to-background ratio. The signal-tobackground is more than an order of magnitude larger in the K-edge compared to the L-edge. The reasons for the high background in the L-edge have been discussed before [13]. A visual estimate for the maximum sampling depth is _ 70 nm - a value close to that measured for the Si L-edge in the FY
M. Kasrai et al. /Applied SurjaaceScience 99 CI Y96) 303-3 12 I
.
4. Discussion
[Sl K-edge: q SO,
J I I
1840
.
I
1880 Photon
.
.
I
.
l&SO Energy
1
I
(eV)
Fig. 7. Si K-edge XANES spectra of SO, Si(100). measured by the FY technique.
films
309
grown
on
mode. Because of the much higher yield, the quality of the K-edge data is much improved compared to the L-edge data. In the same manner as the L-edge, the SiO,/Si intensity ratio is plotted as a function of the oxide thickness in Fig. 6(B) to determine the thickness of the native oxide. The value of 0.9 nm deduced from this figure is close to that obtained from the L-edge data. Fig. 7 shows the Si K-edge XANES spectra measured in the FY mode, after a pre-edge background removal. As expected, fluorescence photons have a much larger escape depth than secondary electrons and the sampling depth of the Si K-edge measured in FY is indeed quite large. Indeed, the SiO, signal can barely be seen for oxide thicknesses < 21 nm. Suitable samples with thicknesses exceeding 66 nm cannot be grown; thus, the maximum sampling depth of the FY cannot be measured. However, it is clear that the value should be of the order of several hundred nm.
X-ray photoabsorption results in core hole creation which decay through the competing processes of fluorescence radiation and Auger electron emission. Both these processes have been shown to be proportional to the absorption cross section [I ,7]. The relative X-ray and Auger yields depend on the atomic number of the absorbing atom. For light elements (such as Si, P, S), and in particular at the L-edge, the Auger yield exceeds the fluorescence yield by several orders of magnitude. Nevertheless. as has been shown above. the fluorescence yield can be used to measure the absorption spectra [13]. In order to measure Auger electrons, an electron analyser is required. An alternative technique. which is also proportional to the absorption, is total electron yield (TEY) method. This technique encompasses the entire energy range of electrons. However. the electron energy spectrum is dominated by low energy secondary electrons. Henke et al. [ 191 have demonstrated that the majority of electrons for metals have energies below 5 eV with a peak near - I.3 eV. By contrast, the majority of electrons have energies < 2 eV for insulators. Both theoretical calculations and experimental measurements have confirmed that the shape of the low energy electron distribution is independent of the primary photon energy [l]. Since the low energy spectrum for a given material does not change with photon energy, it is reasonable to assume that the escape depth of secondary electrons is independent of the photon energy. Stiihr [I] has treated this problem mathematically and demonstrated that the effective escape depth for secondary electrons in Au is 5 nm and is independent of photon energy in the 300-1500 eV region. However, the number of low energy electrons increases linearly with the photon energy. Based on the above discussion, we expect to find similar escape depths for secondary electrons created in the Si L-edge (N 100 eV region) and Si K-edge (_ 1850 eV region). First, we start with the TEY measurement of the Si K-edge presented in Figs. 5 and 6. The sampling depth of TEY for this region is well above 60 nm. Jones and Woodruff [3] have reported the escape depth of the low energy electrons for the Al,O,/AI system at the Al K-edge ( - 1600 eV) and have concluded that the effective TEY
310
M. Kasrai et al./Applied
Sur$ace Science 99 (1996) 303-312
sampling depth is < 39 nm. Since they were unable to resolve Al signals from Al,O, signals in their spectra, they used a procedure to estimate the contribution of each signal and assumed that the escape depth for the oxide was twice that for the metal. In our case, as was shown in Fig. 5, we have resolved the Si and SiO, contributions, which then makes it possible to obtain separate electron escape depths for each material. We follow the description of Jones and Woodruff [3] for the L- and K-edge TEY yields. Specifically, the differential total electron yield from the oxide, dS,,, is given by sin8dzd8d4,
(1)
where the depth attenuation is described by the same expression as for a no-loss detection method, except that the yield is integrated over the entire azimuth [O, 27r] for 4. I, is the incident photon flux, p,, and A,, are the X-ray absorption coefficient and electron escape depth, respectively, for the oxide. Integrating over the oxide film thickness, d, and for emission into the vacuum for 0 values in the range [O, 7r/2], we obtain S,, =Z,p,,A,,7r[l
-ee-” (1 - u) - UQ,( u)],
where u = d/h,, and E,(u), the exponential of order 1, is given by E,(u)
= I;‘?
f(x)
=eer(l
integral
dr.
We denote the function
(3) f(x)
by
-x)+~‘E,(x).
(4)
For the differential signal from the substrate, we get an expression analogous to Eq. (1)
dSSx =‘ll
PSi
(2)
dS,,,
“P( ,,,,I iexP( ,;,k”,)
Xsin 8dzd+.
0
(5)
Here, the limits for z represent the substrate values [d, x] and the limits on 8 and 4 are the same as before. Thus, integrating to get Ssi
Combining Eqs. (2) and (6) yields the ratio of the oxide and substrate signals, S,,/Ssi
where pO,/ps, = 0.5795 for SiO, over Si using values for psi and po at 1839 eV [20] and calculating puox using conventional density values for SiOZ and Si of 2.27 and 2.326 g/cm3, respectively. In taking the ratio of the measured L- and K-edge signals, systematic uncertainties should be eliminated. There is an implicit assumption that the incident photon beam is not attenuated in the depth of material contributing to the TEY. The experimental data from Fig. 6(A) have been fitted to Eq. (7) using a non-linear least squares analysis. We obtain A,, = 23.4 + 0.5 nm and Asi = 17.0 -t 0.5 nm (assuming +5% uncertainties in the data), yielding A,,/& = 1.4 * 0.1 for the K-edge data, as shown by the smooth curve in Fig. 8(A). The A ratio between oxide and substrate thus deviates from the value 2 assumed by Jones and Woodruff [3] (see below). For the L-edge TEY data, the results are shown in Fig. 8(B). For fitting the L-edge data, we have used p,,/psi = 1.026 for SiO, over Si using psi and p. at 100 eV [20] and calculating pox as above. Again, we obtain an excellent fit and extract best fitted values for the escape depths of A,,, = 1.8 + 0.1 nm and A,, = 0.81 & 0.02 nm (assuming -t 10% uncertainties in the data), yielding &,/A,, = 2.2 which is different from the K-edge but closer to the value 2. The ratio of escape depths of photoelectrons, having kinetic energies = 20-300 eV, have been reported for the SiO,/Si system using XPS 1211. In this energy range, the A,,/A,, ratios change from 1.1 to 2.1. Erbil et al. [7] have shown that the sampling depth of TEY is mainly determined by the escape depth of the original primary Auger electrons. From their work, the ranges for the initial Auger electrons created at the K-edge and L-edge for Si is estimated to be N 400 and - 40 A, respectively. The ratios of AK-edge/AL-edge for Si and SiO, are 21 and 12, respectively which correlate with the ratio of ranges of the primary Auger electrons. We can summarize the above results as follows:
M. Kusrai
et al. /Applied
31
Surjbce Science YY (1 YY6) 303-312
(i) As was stated above, the range of primary Auger electrons is larger at the Si K-edge than the L-edge. The total number of low-energy secondary electrons created at the Si K-edge (N 1840 eV) is also much larger than the corresponding number at the L-edge (N 100 eV). These two factors make the sampling depth of the K-edge much larger than the L-edge. (ii) The background is expected to be much larger at the L-edge due to the higher cross section of valence electrons for low energy photons. Thus we expect to find a much larger signal-to-background ratio for the same number of photons absorbed at the K-edge compared to the L-edge, as confirmed by the above measurements. Thus. the sensitivity of the
30 -
I
Data -Ftt OOQ
Thic!sneas
(Ilm)
Fig. 9. (A) A non-linear least squares fit to SiOl /Si measured by the FY technique at the Si L-edge.
intensity
TEY measurement at the L-edge will be worse than at the K-edge. For the FY data at the L-edge. we can fit the ratio of the oxide to substrate signals, S,,,/S,,, using the expression
S”, 1 - exd - bh,,, > -= = ev( bdF,,x> - 1 (8) exp( - bdp,,, ) SS, T
0
10
20
30
40
Thicknsas 100
.,
.,
50
.,
(
,
[Si L-edge1 St:
60
70
(nm)
,
03)
1
5
6
0.8 pm
910,is_
I’
0
12
.
3
4
where b = 1 + set 19 and 0 = 50”. corresponding to the experimental arrangement. and pC,x is the absorption coefficient for L-edge photons in SiO, to be determined via fitting. Eq. (8). which closely resembles the expression derived for XPS analyses, has been derived to include the attenuation of the incident photon beam (which is tzof negligible, in contrast to the case for detecting emitted electrons for which escape depths are much smaller) in penetrating the sample. Experimental data have been fitted to Eq. (8) and are plotted in Fig. 9. together with the best fitted curve. Although the fit is less than perfect, the best fit is obtained for pm’ = 52 nm. Using estimates for photon attenuation cross sections (at hv = 100 eV) in Si and 0 of 2.66 X 1W ‘* cm’/atom and 1.66 X IO Ix cm’/atom, respectively, we then calculate a photon attenuation distance &’ = 73.5 nm in SiO,, which is in reasonable accord with the value extracted from the best fit to the data.
Thickness(nm)
Fig. 8. (A) A non-linear least squares tit to Si02 /Si intensity measured by the TEY technique at the Si K-edge. (B) A non-linear least squares fit to SiO, /Si intensity measured by the TEY technique at the Si L-edge. The fitted results yield the escape depths for low-energy secondary electrons at the K- and L-edges.
5. Summary
and conclusions
A systematic study has been undertaken to investigate the sampling depth for low-energy secondary
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M. Kasrai et al/Applied
Surface Science 99 (1996) 303-312
electrons at the Si L- and K-edges for the SiOJSi system using the total electron yield technique. Controlled SiO, films (N l-60 nm> were grown electrochemically on Si(100) substrates. It was found that the sampling depth of the secondary electrons at the L-edge (100 eV) and the K-edge ( 1840 eV) are _ 5 and N 70 nm, respectively. Using the data and developing a theoretical formalism, the escape depths of the low-energy secondary electrons were derived at both edges for Si and SiO,. The escape depths for Si and SiO, at the K-edge were 17 and 23 nm; the corresponding values at the L-edge were 0.8 and 1.8 nm, respectively. Thus, the escape depth for the Si L-edge is much shorter than for the K-edge. Some suggestions have been offered to explain the short range of the low-energy electrons at the L-edge, The sampling depths of the fluorescence photons at the L-edge and K-edge have also been investigated using the fluorescence yield technique. It was found that the sampling depth for fluorescence photons at the L-edge is N 60 nm. Using the data, a mathematical expression was developed to extract the absorption coefficient of fluorescence photons in SiO, at the L-edge and found to be 52 nm. Although it was not feasible to fabricate SiOz films of sufficient thickness to provide for a measure of the corresponding sampling depth of the fluorescence yield at the K-edge, this length is estimated to be several hundred nm.
Acknowledgements This study was financially supported by the Ontario Centre for Materials Research (OCMR) and the Natural Sciences and Engineering Research Council of Canada (NSERC). The authors are grateful to the staff at the Synchrotron Radiation Centre (SRC), University of Wisconsin, for their technical assistance and the National Science Foundation (NSF),
for their support #DMR92 12658.
of the
SRC
under
the
Grant
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