ISSN 10637826, Semiconductors, 2014, Vol. 48, No. 8, pp. 1109–1117. © Pleiades Publishing, Ltd., 2014. Original Russian Text © M.N. Drozdov, Yu.N. Drozdov, A.V. Novikov, P.A. Yunin, D.V. Yurasov, 2014, published in Fizika i Tekhnika Poluprovodnikov, 2014, Vol. 48, No. 8, pp. 1138–1146.
FABRICATION, TREATMENT, AND TESTING OF MATERIALS AND STRUCTURES
Quantitative Calibration and Germanium SIMS Depth Profiling in GexSi1 – x/Si Heterostructures M. N. Drozdov^, Yu. N. Drozdov, A. V. Novikov, P. A. Yunin, and D. V. Yurasov Institute for Physics of Microstructures, Russian Academy of Sciences, ul. Ul’yanova 46, Nizhni Novgorod, 603950 Russia ^email:
[email protected]nnov.ru Submitted November 28, 2013; accepted for publication December 19, 2013
Abstract—Methods for minimizing nonlinear matrix effects in the quantitative determination of germanium concentrations in GexSi1 – x layers by secondary ion mass spectrometry are discussed. The analysis conditions with positive SiCs+, GeCs+ and negative Ge–, Si– secondary ions produced during sputtering by cesium ions are used in the TOF.SIMS5 setup with a timeofflight mass analyzer. In contrast to published works for TOF.SIMS setups, the linear dependence of the ionconcentration ratio Ge–/Si– on x/(1 – x) is shown. Two –
new linear calibrations for the germanium concentration as a function of the cluster Ge 2 secondary ion yield are proposed. The calibration factors are determined for all linear calibrations at various energies of sputtered +
cesium ions and Bi+ and Bi 3 probe ions. It is shown for the first time that the best depth resolution among the possible conditions of quantitative germanium depth profiling in GexSi1 – x/Si multilayer heterostructures is provided by the calibration mode using elemental Ge– and Si– negative secondary ions. DOI: 10.1134/S1063782614080090
1. INTRODUCTION The quantitative analysis of the elemental compo sition of semiconductor heterostructures by secondary ion mass spectrometry (SIMS) differs significantly for impurity and matrix elements. For lowconcentration impurity elements, the relative sensitivityfactor method has long been developed and entered into SIMS practical guidances (see, e.g., [1]). This method is based on the linear dependence of the intensity of secondaryion emission for impurity elements on their concentration, which makes use of a small set of test structures to calibrate sensitivity in practical studies. For matrix elements, the dependence of the intensity of the secondaryion beam on the element concentra tion appears nonlinear and also often nonmonotonic, e.g., for GexSi1 – x structures. This is due to the mani festation of socalled matrix effects, i.e., the depen dences of the ionization coefficient of sputtered atoms on the atomic environment in solids. Therefore, the quantitative analysis of such elements requires a large set of test structures in a wide concentration range. However, even in this case, the results of analysis will be ambiguous at a nonmonotonic concentration dependence of the intensity. Several approaches were proposed to compensate for matrix effects in the quan titative analysis of semiconductor heterostructures. The most commonly used is the MCs+ approach with sputtering by cesium ions, and the element M is deter + mined by measuring MCs+ or MCs 2 positive cluster
secondary ions. This approach was first proposed in [2] for the III–V semiconductor compounds InxGa1 – xAs and AlxGa1 – xAs for which the CsIn+ and CsAl+ sec ondaryion emission intensity depends linearly on the In or Al concentration and matrix effects are absent. Later this approach was tested in the analysis of GexSi1 – x structures [3]. In contrast to III–V struc tures, in GexSi1 – x, compensation for matrix effects does not mean their absence, the GeCs+ secondary ion emission intensity depends nonlinearly on the ger manium concentration x. The dependence of the ratio GeCs+/SiCs+ on the quantity x/(1 – x) appears linear, (1) GeCs+/SiCs+ = K1[x/(1 – x)]. This should be kept in mind, since the MCs+ approach is often associated (see, e.g., [4]) with the linear dependence of the emission intensity of such secondary ions on the element concentration, and there exist theoretical models justifying this depen dence. Nevertheless, the use of linear dependence (1) is very convenient for the quantitative determination of germanium in GexSi1 – x structures. In addition to dependence (1), a similar depen dence was also detected in [3] for other secondary ions, 70Ge+ and 30Si+ during sputtering with oxygen ions, 70Ge+/30Si+ = K [x/(1 – x)]. (2) 2 Studies of the GexSi1 – x structures were continued in [5–11] for various analysis conditions and germa
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nium concentrations. In [7], one more method for compensating matrix effects was found, in which 70 Ge– and 30Si– negative secondary ions during sput tering with cesium ions were used. For the ratio of their intensities, a linear dependence similar to (1) and (2) is also satisfied, 70
Ge–/30Si– = K3[x/(1 – x)].
(3)
In [8], it was shown that, along with GeCs+ and + + SiCs+ secondary ions, GeCs 2 and SiCs 2 secondary ions also satisfy linear relation (1). In this case, the + Ge(Si)Cs 2 ion emission intensity appears several times larger than that of Ge(Si)Cs+, which makes them more convenient for analyzing GexSi1 – x struc +
tures. In [8], the absence of matrix effects for GeCs 2 +
secondary ions was also shown, i.e., the GeCs 2 ion sig nal is proportional to x; however, this result was not reproduced in other studies. The obtained expres sions (1)–(3) became the basis of quantitative determi nation of the germanium concentration in GexSi1 – x lay ers; in [11], good agreement with the results of x mea surements by other methods for multilayer structures was found as well. The listed variants of linear calibration of the ger manium concentration were obtained for SIMS sys tems with magneticsector and quadrupole mass ana lyzers. The number of studies of the calibration of SIMS systems with timeofflight mass analyzers is much smaller, which is quite explainable, since this type of system started to be used for analyzing semi conductor heterostructures relatively recently. It is clear that simple extension of the results obtained for SIMS systems with magneticsector and quadrupole mass analyzers to systems with timeofflight mass analyzers is unjustified: in systems of the former type, the same ion beam plays the role of both the sputtering and probe beam. Therefore, the sputtered material is analyzed. For SIMS systems with timeofflight mass analyzers, the functions of probing and sputtering are divided between two different ion beams. Here, by analogy with Auger electron spectroscopy, the mate rial remaining on the surface in the modified layer is analyzed. Certainly, the probe ion beam also sputters the surface; however, its sputtering rate is very low, and the steadystate SIMS mode condition is satisfied for it. In [12], the MCs+ approach to GexSi1 – x structures was compared for different SIMS systems: CAMECA IMS5F with a magneticsector mass analyzer and TOF.SIMS5 with a timeofflight analyzer. It was shown that expression (1) is valid for both system types, although the linear approximation error for the TOF.SIMS5 was larger: the correlation coefficient RL was 0.9997 for the magneticsector mass analyzer and 0.9974 for the timeofflight analyzer. In [13], it was shown for the TOF.SIMS5 system that the linear
Table 1. Germanium concentration and degree of relaxation in structure no. A Layer number from the Si sub strate
Ge concentra tion, %
Degree of layer relaxation
1 2 3
9.2 ± 0.5 29.2 ± 0.5 47.2 ± 1
0.08 0.75 0.76
Table 2. Germanium concentration and degree of relaxation in structure no. B Layer number from the Si sub strate
Ge concentra tion, %
Degree of layer relaxation
1 2 3
21.5 ± 0.5 40.8 ± 0.5 58.3 ± 0.5
0.8 0.9 0.8
dependence (3) is valid only to x ≈ 0.33 for 70Ge– and 30 – Si secondary ions during sputtering with cesium ions; at higher germanium concentrations, significant deviation from the linear dependence is observed. As an alternative variant of compensation for matrix effects in the analysis of GexSi1 – x structures, a new approach to analysis of the full secondaryion spectrum during sputtering with cesium ions was proposed for timeofflighttype SIMS systems [14, 15]. In [13, 16], this approach was updated for the simultaneous deter mination of impurity and matrix elements. The full spectrum approach is based on the summation of all elemental and cluster secondary ions containing Ge and Si atoms up to the six order, Ge6Si6. It was shown [13–16] that this approach allows compensation for matrix effects in the whole range of germanium con centrations x from 0 to 1. As a possible explanation, it is assumed [13, 15, 16] that the summation of all emit ted secondary ions is equivalent to analysis of the sput tered neutral atom flux for which matrix effects are absent. However, such calculation appears very labori ous and practically inconvenient for layerbylayer analysis, since it requires the summation of current values of no less than 40 lines in the mass spectrum. Furthermore, the depth resolution of this method is worse than that of other methods for compensating matrix effects [16]. In this work, the applicability of the MCs+ (expres sion (1)) and Ge– and Si– (expression (3)) approaches to the quantitative determination of germanium in GexSi1 – x structures (0 < x < 0.6) by timeofflight sec ondaryion mass spectrometry using a TOF.SIMS5 system is studied. This work continues the study [17], where the germanium concentration was restricted to a value of x = 0.38. The applicability of linear approx SEMICONDUCTORS
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QUANTITATIVE CALIBRATION AND GERMANIUM SIMS DEPTH PROFILING (a) x = 47.2%
Intensity, cps
104
x = 29.2%
x = 9.2%
Si substrate
1111
Intensity, cps 4000 2 3000
103
1 10
2000
2
1 2 3 4
101 100
0
1000
200
400
600
800
1000 Time, s
(b)
104
0
0
10
20
30
40 50 60 Ge concentration, %
Fig. 2. Dependences of the emission intensity of (1) GeCs+
Intensity, cps
+
and (2) GeCs 2 positive secondary ions on the germanium concentration.
103 102 101 100
1 2 3 0
200
400
600
800 Time, s
Fig. 1. Time distribution profiles of the intensity of second aryion emission in structure no. A, measured upon sput tering with cesium ions with an energy of 2 keV; (a) positive +
+
ions: (1) SiCs+, (2) GeCs+, (3) SiCs 2 , (4) GeCs 2 ; (b) neg –
ative ions: (1) 30Si–, (2) 74Ge–, (3) Ge 2 .
imation (1), (3) to two sputtering cesium ion energies of 1 and 2 keV most commonly used in the layerby layer analysis in a TOF.SIMS5 system and to Bi+ and + Bi 3 probe beams is shown. A new nonlinear calibra – tion mode using Ge 2 cluster secondary ions for mea surements is proposed. This mode was discussed in [6]; however, it was not developed. Furthermore, the results of the quantitative layerbylayer analysis of GexSi1 – x/Si structures, obtained in different mea surement modes were compared. In contrast to impu rity elements, where the massspectrum lines of an element with maximum intensity are used, for matrix elements, in particular Ge, several highintensity lines can be used; in this case, matrix effects are compen sated to the same extent. It is clear that the mode with the best depth resolution should be used when choos ing the quantitative depthprofiling conditions. How SEMICONDUCTORS
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ever, to our knowledge, the depth resolutions for vari ous quantitative calibration modes have not yet been compared (with the exception of previously men tioned study [16] for the full spectrum approach). We note that we restricted this study to the mode of sput tering with cesium ions; sputtering with oxygen ions is not considered. In [18], we found that, at incidence angles of 45° for sputtering oxygen ions used in a TOF.SIMS5 system, the crater bottom roughness rapidly develops in GexSi1 – x structures; the root meansquare roughness Sq is 3–5 nm at a depth of 1 μm. This reduces the resulting depth resolution. At the same time, in the case of sputtering with cesium ions, the roughness Sq increased only slightly, from 0.8 to 1.2 nm, at a depth of ~1 μm. Therefore, the mode of sputtering with cesium ions is more preferable for the quantitative depth profiling of GexSi1 – x/Si hetero structures with thin layers and abrupt junctions using the TOF.SIMS5 system. 2. EXPERIMENTAL To calibrate the sensitivity with respect to Ge, two GexSi1 – x/Si structures no. A and no. B were grown, Table 3. Calibration coefficient K1 and correlation coeffi cient for expression (1) Measured ions GeCs+, SiCs+ +
+
GeCs 2 , SiCs 2
Cs ion energy, keV
K1
RL
1 2 1 2
0.63 0.63 0.69 0.74
0.999 0.9984 0.9995 0.999
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Normalized intensity (a) 1.0
2
0.8
1
Normalized Ge intensity 1.4 Bi+ 1.2 Bi+3 1.0
0.6
0.8 0.6
0.4
0.4 0.2 0.2 0
0
0.4
0.2
0.6
0.8
1.0
Normalized intensity
1.2 1.4 x/(1 − x)
(b)
0.5
0.3
0.4
0.5
0.6
Fig. 3. Calibration curves for secondary ions (1) GeCs+ +
and (2) GeCs 2 , based on expressions (1) (a) and (4) (b).
each consisting of three alloy layers 200 nm thick with a step x profile. The structures were grown on Si (001) substrates by molecularbeam epitaxy using a Riber SIVA21 system. The germanium concentration x in individual layers was determined by Xray diffraction using a Bruker Discover D8 installation, taking into account the deviation of the alloy lattice parameter from Vegard’s law, which made it possible to improve the measurement accuracy. The germanium concen Table 4. Calibration coefficient K4 and correlation coeffi cient for expression (4)
GeCs+, SiCs+ +
+
GeCs 2 , SiCs 2
40 50 60 Ge concentration, %
+
x
Measured ions
30
Bi+ and Bi 3 probe ions.
0.1
0.2
20
1
0.2
0.1
10
Fig. 4. Dependences of the emission intensity of 74Ge neg ative secondary ions on the germanium concentration for
0.3
0
0
2
0.4
0
0
Cs ion energy, keV
K1
RL
1 2 1 2
0.77 0.77 0.83 0.86
0.9993 0.9994 0.9993 0.9997
tration and degree of relaxation of elastic stresses of the individual layers for structures no. A and no. B are given in Tables 1 and 2. The depth profiling modes with different calibrations were compared using two multilayer structures with “thick” (no. C) and “thin” (no. D) layers. Structure no. C consisted of ten Ge0.37Si0.63 layers 12.3 nm thick, separated by Si layers 34 nm thick. Structure no. D consisted of three Ge δ layers two monolayers thick each, separated by Si layers; the structure period was 40.3 nm. SIMS measurements were performed using a TOF.SIMS5 system with a timeofflight mass ana lyzer and two ion guns with different functions, i.e., probing or sputtering. The latter was performed by cesium Cs+ ions with energies of 1 and 2 keV and a beam current of ~100 nA. Probing was performed by + bismuth, elemental Bi+ or cluster Bi 3 ions with an energy of 25 keV and a beam current of 1 pA. The etch crater size was from 200 × 200 to 400 × 400 μm; the central crater region from 40 × 40 to 80 × 80 μm in size was probed, respectively. Either positive (for the MCs+ – mode) or negative (Ge–, Si–, and Ge 2 ) secondary ions were measured. Depth profiling using the TOF.SIMS5 system is described in more detail in [18]. The crater depth required to calibrate the sputter ing rate was determined using a Talysurf CCI 2000 optical profilometer. 3. EXPERIMENTAL RESULTS 3.1. Calibration of the Germanium Concentration Scale in the MCs+ Approach Figure 1a shows the profiles of the distribution of positive secondary ions GeCs, SiCs, GeCs2, and SiCs2 SEMICONDUCTORS
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for structure no. A, measured during sputtering with + Cs+ ions with an energy of 2 keV. Cluster Bi 3 probe ions were used, since this increases the intensity of the beam of these secondary ions by a factor of 3–5 in comparison with Bi+. Similar profiles were also obtained for structure no. B. The secondaryion beam intensity was averaged for each GexSi1 – x layer; based on these data, calibration curves were constructed. Figure 2 shows the dependences of the intensity of the + GeCs+ and GeCs 2 secondaryion beam on the germa nium concentration x. For GeCs+ ions, this depen + dence is far from linear (RL = 0.986). For GeCs 2 ions, the degree of linearity is higher (RL = 0.997); however, in our opinion, these data do not allow us to speak about a complete lack of matrix effects. The calibration curves based on expression (1) (Fig. 3a) show the linear dependence of the intensity on x/(1 – x); the coefficients K1 and correlation coef ficients RL are listed in Table 3. We found that higher correlation coefficients in the MCs+ approach up to 0.9997 can be obtained using, instead of (1), another expression for normalization GeCs1(2)/(GeCs1(2) + SiCs1(2)) = K4x. (4) The calibration curves based on expression (4) are shown in Fig. 3b, the coefficient K4 and correlation coefficient are given in Table 4. We can see that the degree of linearity of the obtained dependences appears higher than in [12] for a similar TOF.SIMS5 system and is close to the best data for the Cameca sys tem with a magneticsector mass spectrometer. 3.2. Calibration of the Germanium Concentration Scale in Negative Secondary Ions The profiles of the emissionintensity distribution of 30Si, 74Ge, and Ge2 negative secondary ions are shown in Fig. 1b. Such measurements for structures no. A and no. B were performed for two energies of 1 + and 2keV sputtering cesium ions and Bi+ and Bi 3 probe ions. We note that the 70Ge isotope was used for the determination of germanium in the studies men tioned above, since the main line of the 74Ge isotope in the mass spectrum of secondary ions is overlapped with the lines of 29Si2O and 28Si30SiO cluster secondary ions, which distorts the results at low germanium con centrations. The TOF.SIMS5 system has a very high mass resolution, M/ΔM > 10000, which allows the separation of these cluster lines and the 74Ge line. Therefore, in this study, we used the main germanium 74Ge isotope which has the largest concentration. The dependence of the 74Ge intensity on x is nonlinear; furthermore, this dependence is nonmonotonic for Bi+ probe ions (Fig. 4). Figure 5 shows the calibration dependence based on expression (3); the correspond SEMICONDUCTORS
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74
Ge/30Si
7 6 5 4 3 2 1 0
0
0.2
0.4
0.6
0.8
1.0
1.2 1.4 x/(1 − x)
Fig. 5. Calibration curve based on expression (1) for a Cs sputteringion energy of 2 keV for probing with Bi+ ions.
ing coefficients K3 and RL for various energies of Cs ions and Bi+ and Bi3 probe beams are given in Table 5. As seen in Fig. 5, the linearity of the dependence of the ratio 74Ge/30Si on x/(1 – x) is retained in the whole studied range to x = 0.6. The correlation coefficient for all analysis conditions of Table 5 exceeds 0.9995. The results obtained differ from the data of [13] for a similar TOF.SIMS5 system, where a significant devi ation from linear dependence (3) was observed at ger manium concentrations x > 0.33. Along with linear dependence (3), the nonlinear dependence of the ratio Ge/Si for cluster secondary Table 5. Calibration coefficients and correlation coefficient for negative secondary ions according to expressions (3), (5), and (6) Measured ions and number K
74Ge/30Si,
Cs ion energy, keV
Probe ions
K
RL
1
Bi Bi3
4.5 5.11
0.9995 0.9999
2
Bi Bi3
4.55 5.24
0.9998 0.9996
1
Bi Bi3
2.51 2.65
0.9996 0.9996
2
Bi Bi3
3.14 3.1
0.9997 0.9999
1
Bi Bi3
1.39 1.32
0.998 0.9987
2
Bi Bi3
2.1 1.9
0.9983 0.9975
K3
(Ge2/30Si)1/2, K5
Ge2/74Ge, K6
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Ge2/30Si
x, %
(a)
(a)
16 10
1 2 3
12 8 1 4 0
0
0.4
0.2 30
0.6
0.8
1.0
1/2
0.1
1.2 1.4 x/(1 − x)
200
300
(Ge2/ Si)
(b)
500 600 Depth, nm
(b)
4
40
3
30
2
1 2 3
20
1 0
400
x, %
10
0
0.2
0.4
0.6
0.8
1.0
1.2 1.4 x/(1 − x)
0
Fig. 6. Calibration curves for Ge2 cluster secondary ions: ratios (a) Ge2/30Si and (b) (Ge2/30Si)1/2.
ions was observed in [6], Ge2/Si ∝ [x/(1 – x)]1.78. Based on these data, it was stated in [6, 8] about the possible compensation of matrix effects using Ge2 sec ondary ions; however, we know of no concrete results in this direction. Figure 6a shows the dependence of the ratio Ge2/30Si on x/(1 – x). In the initial x portion to 0.4, the best approximation of this dependence is quadratic, Ge2/30Si ∝ [x/(1 – x)]2. This more clearly follows from Fig. 6b showing the dependence (Ge2/30Si)1/2 on x/(1 – x). In the range 0 < x < 0.4, this dependence is approximated with very high accuracy by the linear expression (Ge2/30Si)1/2 = K5[x/(1 – x)].
(5)
The parameters of this approximation are given in Table 5; the correlation coefficient also exceeds 0.9995. The beam intensities of 30Si, 74Ge, and Ge2 nega tive ions are measured simultaneously in a single anal
220
200
240
260 Depth, nm
Fig. 7. Germanium concentration depth profiles in struc ture no. C, measured using calibrations (3) and (4): (1) GeCs/(GeCs + SiCs), (2) GeCs2/(GeCs2 + SiCs2), and (3) 74Ge/30Si.
ysis mode; it is easy to see that expressions (3) and (5) can be transformed to the form in which the 30Si emis sion intensity is lacking, Ge2/74Ge = K6[x/(1 – x)],
(6)
2
where K6 = K 5 /K 3 . Table 5 lists the parameters of linear approxima tion (6), obtained from the measured profiles of the distribution of secondary ions (Fig. 1b). We can see that the error of linear approximation (6) appears sig nificantly higher than that of expressions (3) and (5). The main contribution to this error is made by the low Ge concentration region in which the values of both the numerator and denominator on the lefthand side of expression (6) are small. At the same time, the application of Ge2/Ge calibration can have advan tages at high germanium concentrations near 1, where SEMICONDUCTORS
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x, %
40 1 2 3
(a) 1 2 3
10
30
1115
1
20 0.1 10 0.01 0
200
220
240
260
280 Depth, nm
Fig. 8. Germanium concentration depth profiles in two layers of structure no. C, measured using calibrations (3), (5), (6): (1) 74Ge/30Si, (2) (Ge2/30Si)1/2, and (3) Ge2/Ge.
the error of normalization to Si will be a problem for expression (3). Thus, in measuring GexSi1 – x structures in the mode of negative secondary ions upon sputtering with Cs ions, the Ge calibration variants can be extended, and expressions (5) and (6) can be used along with expression (3). 3.3. Quantitative Depth Profiling of the Germanium Concentration Using Various Calibration Modes In this section, we present the results of the quanti tative analysis for GexSi1 – x/Si heterostructures, obtained using the TOF.SIMS5 system with various variants of Geconcentration calibration according to expressions (3), (4), (5), and (6). Figures 7 and 8 show the x profiles in structure no. C with 10 “thick” layers using calibrations (3), (4) and (3), (5), (6), respec tively. It clearly follows from Figs. 7b and 8, where only two GexSi1 – x layers are shown in more detail, that all these calibration variants are equivalent and yield completely identical x profiles in the case at hand. Figures 9 and 10 show the x profiles in structure no. D with Ge δ layers. Figures 9a and 9b were obtained in the mode of negative secondaryion mea surements for linear (3) and nonlinear (4), (5) calibra tions. Figure 10 compares calibration (3) and the + MCs+ mode with maximum sensitivity, i.e., the GeCs 2 mode (GeCs+ measurement data are not presented due to the low signaltonoise ratio). We can see that the results are different for the structure with thin Ge layers using different calibrations, which indicates dif ferent depth resolution in the measurements. Among the used modes of quantitative analysis, the largest concentration x in Ge δ layers is recorded for calibra SEMICONDUCTORS
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50
0
100 Depth, nm
x, % 20
15
(b) 1 2 3
10
5
0 110
115
120
125
130 Depth, nm
Fig. 9. Germanium concentration depth profiles in struc ture no. D, measured using calibrations (3), (4), (5): (1) 74Ge/30Si, (2) (Ge2/30Si)1/2, and (3) Ge2/Ge.
x, % 20 1 2 15
10
5
0 110
115
120
125
130 Depth, nm
Fig. 10. Germanium concentration depth profiles in the third layer of structure no. D, measured using calibrations (3) and (4): (1) GeCs2/(GeCs2 + SiCs2) and (2) 74Ge/30Si.
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x, % 20
15
2 keV 1 keV
10
5
0 110
115
120
125
130 Depth, nm
Fig. 11. Germanium concentration depth profiles in the third layer of structure no. D, measured using calibra tion (3) for 74Ge/30Si at various energies of sputtering cesium ions.
effect of nonsteadystate processes on the emission of elemental and cluster ions is still to be clarified in more detail. We also note that we cannot determine the depth resolution from Figs. 9 and 10 directly from the profile width; all curves have close profile widths despite the different values of x at the maximum. A different situ ation arises in the depth profiling of structure no. D using the same type of secondary ions and different energies of sputtering Cs ions (Fig. 11). The x profiles measured with energies of 1 and 2 keV differ in terms of their maximum values and widths. Furthermore, the profile shifts to the surface at higher sputteringion energies. These differences in the profiles of x at vari ous sputteringion energies can be completely explained by the MRI model [21]. Such a result once more shows that quantitative depth profiling using dif ferent secondary ions for measuring one element does not fit the Hoffman model and requires a new model description. 4. CONCLUSIONS
74Ge/30Si
tion (3) based on elemental secondary ions. Other x measurement modes (Figs. 9b and 10) lead to lower concentrations x at the δlayer maximum; hence, these modes have worse depth resolution. Cur rently, the cause of the difference in the depth resolu tion seems ambiguous. Depth profiling in all these modes was performed during sputtering with Cs ions with the same energy of 1 keV, at the same angle of incidence on the sample surface. Therefore, all arti facts of ion sputtering, i.e., atomic mixing, surface roughness development, and instrumental error, are identical. According to the MRI (mixingroughness information depth) model [19], the difference in this case can be associated with different escape depths of different secondary ions used in the calibrations. However, according to available concepts on the for mation and emission of cluster secondary ions, their escape depth should be minimum, which contradicts the observed results indicating depthresolution deg radation. In our opinion, more probable is the other cause of different depth resolutions, i.e., the difference in the time of achieving steadystate emission condi tions for cluster and elemental secondary ions during the transition process. More complex ñluster second ary ions require longer sputtering times than elemental ions, which probably manifests itself in depth resolu tion degradation. We note that the MRI model is valid only for steadystate sputtering conditions and cannot be applied to nonsteadystate processes. Its known modification for describing nonsteadystate pro cesses is applicable only for the very beginning of the surface sputtering process [20]. It is clear that when the sputtering front passes through sharp interfaces or thin layers, nonsteady state processes will also play an important role. The
It was shown that two types of ions, i.e., MCs+ clus ter secondary ions and Ge– and Si– negative elemental ions, can be used for quantitative determination of the germanium concentration in GexSi1 – x structures by the SIMS method using a TOF.SIMS5 system. In the germanium concentration range from 0 to 0.6, both of these approaches have linear calibration dependences with a correlation coefficient close to unity (above 0.9995). The calibration line slopes were experimen tally determined for two energies of sputtering Cs ions + during probing with Bi+ or Bi 3 ions. The lack of matrix effects in GexSi1 – x structures is not confirmed for any of the secondaryion types in these approaches. Linear calibration is provided only for the ratio of Ge and Si secondary ions or their combinations for which matrix effects are compensated. It was first shown that the quadratic dependence of the ratio Ge2/30Si on the ratio x/(1 – x) is provided in the germanium concen tration range from 0 to 0.4. Based on this study, two new variants for calibrating (Ge2/30Si)1/2 and Ge2/Ge secondary ions, which have a linear dependence on x/(1 – x), are proposed. The calibration coefficients for these secondary ions were determined for various analysis conditions The effect of nonsteadystate processes on the emission of elemental and cluster ions is still to be clarified in more detail. All proposed calibration modes were tested upon the quantitative depth profiling of GexSi1 – x/Si hetero structures. For structures with thick GexSi1 – x layers (~10 nm), the measured x profiles are identical for all the abovelisted calibration variants. This justifies the validity of their use in SIMS practice. For structures with thin layers (
