Preferential sputtering effects in depth profiling of multilayers with SIMS, XPS and AES

Applied Surface Science 483 (2019) 140–155

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Preferential sputtering effects in depth profiling of multilayers with SIMS, XPS and AES

T

S. Hofmanna,b, G. Zhoub, J. Kovacc, S. Drevc, S.Y. Lianb, B. Linb, Y. Liub, J.Y. Wangb,

⁎

a

Max-Planck-Institute for Intelligent Systems (formerly MPI for Metals Research), Heisenbergstrasse 3, D-70569 Stuttgart, Germany Department of Physics, Shantou University, 243 Daxue Road, Shantou 515063, Guangdong, China c Jozef Stefan Institute, Jamova cesta 39, 1000 Ljubljana, Slovenia b

ARTICLE INFO

ABSTRACT

Keywords: Multilayer profiles Depth resolution Preferential sputtering Layer thickness

Multilayer profiles are studied using the MRI model with extension to preferential sputtering. The results show a clear distinction with respect to the main contributions to the depth resolution, namely surface and interface roughness, and atomic mixing. For dominating roughness, the effect of preferential sputtering is more pronounced for the residual surface composition profile (detected by XPS and AES), but it is zero for the sputtered matter composition profile (detected by SIMS). Dominating mixing results in a strong effect of preferential sputtering on the shape of the profile. While in that case its effect on the XPS or AES depth profile is relatively moderate, its effect on the SIMS depth profile is surprisingly strong and appears to be in contradiction to textbook statements. Interface width, location and layer thickness are always affected by preferential sputtering in XPS and AES depth profiles, but SIMS depth profiles are only affected if the contribution of atomic mixing to depth resolution cannot be ignored. In conclusion, a new definition of multilayer resolution is proposed which is based on the normalized amplitude of the wave-like profiles. The successful application of MRI model extended for preferential sputtering is given for fitting an experimental AES depth profile of an Ag/Ni multilayer.

1. Introduction Multilayers play an important role in many fields of advanced technology and are most common in fabrication and applications of semiconductor quantum well structures. Therefore, there is a general demand of for reliable and quantitative characterization of the fabricated layer structures. Among the various methods for this purpose, sputter depth profiling by ion bombardment in combination with secondary ion spectrometry (SIMS), optical emission (GDOES) or electron spectroscopy (XPS, AES) has proved to be versatile and ubiquitously applicable. Furthermore, the directly measured result is an image of the layer structure, which is however distorted, mainly by matrix dependent sensitivity factors and by sputtering induced artifacts which cause characteristic distortions of the measured profile with respect to the original layer structure [1,2]. The key parameter that characterizes accuracy and precision of any composition-depth profile is the depth resolution [1–4]. A more detailed information is contained in the depth resolution function (DRF) [4–6]. For the description of the latter more than one parameter is necessary. A convenient means for quantification of depth profiles with an appropriate analysis and reconstruction of a measured depth profile is the Mixing-Roughness-Information depth-

⁎

(MRI)- model [2,4–8], with the three parameters atomic mixing (w), roughness (σ) and information depth (λ). In a recent review [4], the present state of the definitions of depth resolution and its measurement for sharp interfaces, single layers and multilayers were summarized without consideration of preferential sputtering. Because of the practical importance of the latter, we have first treated its influence on sharp A/B interfaces [9]. Subsequently, we disclosed the influence of preferential sputtering on delta layer profiles [10]. In this paper, the focus is on the influence of preferential sputtering on depth resolution and profile shape in sputter depth profiling of multilayers. In previous papers it was already pointed out that the basic shape of the depth resolution function (defined irrespective of preferential sputtering) has a profound influence on the effect of preferential sputtering on depth profiles of interfaces [9] and of delta layers [10] which in turn modifies the basic DRF. Furthermore, a marked difference is found between analysis methods which detect the sputtered matter (e.g. SIMS, GDOES) and those which detect the residual surface (e.g. XPS, AES) [9,10]. Therefore, we consider here the result of both methods for DRFs with dominating roughness (symmetric DRF) and with dominating atomic mixing (asymmetric DRF). The presented profiles are all calculated using the numerical solution [6] of the DRF according to the

Corresponding author. E-mail address: [email protected] (J.Y. Wang).

https://doi.org/10.1016/j.apsusc.2019.03.211 Received 6 November 2018; Received in revised form 6 March 2019; Accepted 19 March 2019 Available online 28 March 2019 0169-4332/ © 2019 Elsevier B.V. All rights reserved.

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MRI model with the given parameters for a binary system of analyte A in matrix B and vice versa. As shown earlier, a multilayer system can be described as a linear superposition of the profiles of subsequent interfaces A/B/A/B [5]. It follows that the main difference to the sharp interface profiles considered in ref. [9] is the overlapping of profiles for larger values of the depth resolution Δz [11]. A brief introduction in the basic relations developed in previous publications [9,10] is given in the following: we consider a binary system with the components A and B. The two main simplifications are (a) a constant, composition independent sputtering yield and (b) a constant, sputtering independent density of each component. Therefore, we get a composition independent sputtering rate ratio rA/B = qA / qB = 1 / rB/A, with qA and qB the sputtering rates of species A and B. With that, mass conservation requires the general equation for preferential sputtering [12] with XA, XB being the bulk composition and XsA, XsB the respective surface composition

XAs X rA / B = A XBs XB

and w / σ = 10 for dominating w). Note that the basic MRI parameters are defined irrespective of preferential sputtering (i.e. rA/B = 1). At first, symmetric DRFs are considered with dominating roughness parameter σ. 2. Symmetric (Gaussian) DRF 2.1. Profile of instantaneous surface concentration Interfacial roughness is usually characterized by a symmetric, Gaussian DRF with mean deviation σ. When roughness is dominant, i.e. σ ≫ w, λ, the influence of both atomic mixing (w) and information depth parameters (λ) can be ignored. Since the depth scale does not change with the preferential sputtering rate ratio rA/B, the respective change of an interface or delta layer profile is only seen on the sputtering time scale through the composition dependent sputtering velocity. Let us first consider a multilayer depth profile of alternating layers of A/ B/A/B… with 5 nm thickness of each layer1. To get a better resolved image of the single layer structure in the depth profile, we have confined ourselves to 5 layers with a thicker capping layer as shown in Fig. 1a, where dominating roughness is ensured by setting w / σ = 0.1. With good approximation, the middle part, that is layer 2 of A and layer 3 of B, is representative of the profile of multilayers with a higher number of layers. The total depth resolution (defined by the z axis difference between 16% and 18% of the plateau value at a sharp A/B interface profile [3]) is assumed as Δz(16–84%) = 4 nm which is equal to 2σ for dominating roughness parameter. The calculated sputter depth profile of the surface concentrations XsA and XsB is presented in Fig. 1a–c for (a) rA/B = 1.0, for (b) rA/B = 4.0, and (c) rA/B = 0.25 on the sputtering time scale. Note that we refer to a normalized, constant sputtering rate of B for qB = 1 nm/s. Thus, the profiles resemble measured sputter profiles with AES or XPS intensities if the information depth parameter λ is small enough to be ignored. It is obvious that the profile of layers of A and B in Fig. 1a (rA/B = 1.0) are of the same shape, with the same amplitude and the same apparent layer width. The latter is 5 s or 5 nm for qA = qB = 1 at the 50% concentration or amplitude value (XsA,B(max) + XsA,B(min)) / 2 which is equal to half of the 100% concentration of A and B, Xs0(A,B) = XsA,B(max) + XsA,B(min). The reduced maximum concentration is due to the fact that Δz / d > 0.4 (the relation between amplitude and Δz / d for dominating σ and rA/B = 1 is presented in refs. [5, 11]). In Fig. 1b (rA/B = 4), the faster sputtering rate of A causes a smaller apparent layer width as compared to that of B, and a decrease in maximum and amplitude of concentration. The situation is inverted in Fig. 1c (rA/ B = 0.25), but the amplitude is the same as in Fig. 1b. Note that we get a mirror image of the profiles of layer A and B around the axis XsA,B = 0.5. However, for rA/B ≠ 1, (XsA,B(max) + XsA,B(min) ≠ Xs0(A,B). In Fig. 1b, the profile varies around the mean amplitude value of A, XsA(50%) = 0.27 mole fractions, and of B, XsB(50%) = 0.73 mole fractions for rA/B = 4.0. Exactly opposite values for XsA(50%) and XsB(50%) are obtained for rA/B = 0.25 (Fig. 1c). Starting with the usual multilayer measurement after finding the concentration-time profile (e.g. by λ-correction in XPS), we get the value of Xs0(A,B) by setting the amplitude of both A and B to equal. Then, we can find Xs0(A,B) = (XsA(max) + XsA(min)) / 2 + (XsB(max) + XsB(min)) / 2. Besides the apparent layer thickness, the average concentration of XsA, i.e. the 50% amplitude of the layer species with higher sputtering rate is lower and that of the layer species with lower sputtering rate is higher than the mean value between both 50% amplitudes (see Figs. 1b, c and 2a). This fact can serve as an immediate, semi-quantitative indication of non-negligible preferential sputtering in a measured XPS depth profile as indicated by Fig. 1a, b (for λ → 0, see Section 2.2). Note that there is no mass conservation in XPS

(1)

At any time, the total sputtering rate qt is given by (2)

qA X s A + qB X s B = (XA + XB ) qt

Since XA + XB = 1 mole fraction/nm, the total sputtering rate is [9,10]

qt = qB [X s A (rA/B

(3)

1) + 1]

Therefore, the relation between depth and time scales is determined by qt as [10]

z (t1) =

t1 0

qt (t ) dt = qB

t1 0

[(rA / B

1) XAs + 1]dt

(4a)

and z1

t (z1) = 0

qA XAs

1 dz = + qB XBs

z1 0

1 qB [XAs (rA / B

1) + 1]

dz

(4b)

Similarly to refs. [9, 10], we apply an extended MRI model including preferential sputtering to calculate the expected profiles for given parameters of roughness (σ), atomic mixing (w) and information depth (λ) [2–10]. For λ ➔ 0 and ignoring σ, the basic differential equation on the sputtering time scale describes the time dependence of the surface concentration XsA in the mixing zone with length w as the difference between the incoming flux from the bulk concentration XA(z + w) at location z + w and the sputtered matter qA ∗ XsA and is given by [9,10]

(dX s A /dt) w = qt [XA (z + w )

(qA / qt ) X s A ]

(5)

With the total sputtering rate qt = dz / dt, Eq. (5) can be presented as a function of the sputtered depth resulting in

(dX s A /dz) w = [XA (z + w )

(qA / qt ) X s A ]

(6)

Numerical solution of Eqs. (5) or (6) yields the instantaneous surface concentration XsA as a function of the sputtering time (mole fraction/s) or the sputtered depth (mole fraction/nm), respectively. Convolution with the Gaussian resolution function with parameter σ and/or with the exponential resolution function with information depth parameter λ results in the profile obtained by sputtering. Thus, predictions of the experimentally expected profiles for different values of rA/B and given MRI parameters (w, σ, λ) are enabled. In the following, in close analogy to the previous key publications on the influence of preferential sputtering on depth resolution of profiles of sharp interfaces [9] and of delta layers [10], the predictive results of the r-extended MRI model are presented for the two characteristic branches of the depth resolution function (DRF) [4,5], namely for dominating roughness parameter (σ) and for dominating atomic mixing parameter (w), and differentiate between the two cases by the skewness factor w / σ (we frequently use w / σ = 0.1 for dominating σ

1 For simplicity, we confine our considerations here to equal layer thickness of A and B. For dominating σ and rA/B = 1 we have described the influence of depth resolution of different layer thicknesses elsewhere [2,11], to which our present approach can be easily extended.

141

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a

a

S

S

XA S

0.25 1 4

S

XB

S

MRI d = 5 nm w = 0.2 nm = 0.01nm = 2 nm rA/B =

XA(mole fraction/nm)

XA,XB(mole fraction/s)

MRI d = 5 nm w = 0.2 nm = 0.01 nm = 2 nm rA/B = 1

Sputtering Time t (s)

Sputtered Depth z (nm)

b

XB(mole fraction/nm)

XA,XB(mole fraction/s)

b MRI d = 5 nm w = 0.2 nm = 0.01 nm = 2 nm rA/B = 4

S S

S

XA XB

0.25 1 4

S

S

MRI d = 5 nm w = 0.2 nm = 0.01nm = 2 nm rA/B =

Sputtered Depth z (nm)

Sputtering Time t (s)

c

c

B zamp

A w/ =0.1

XA,XB(mole fraction/s)

XA(mole fraction/nm)

S S

S

XA XB

0.16

S

S

rA/B = 0.25 0.5 1 2 4

0.84 MRI d = 5 nm w = 0.2nm = 0.01nm = 2 nm rA/B = 0.25

B

dA(50%)

Sputtering Time t (s)

Sputtered Depth z (nm)

Fig. 1. a MRI result of the surface concentrations XsA, XsB of a multilayer of 6 layers (3 double layers) of A/B (5/5 nm, 6×) with layer thickness d = 5 nm for dominating roughness parameter σ = 2 nm (λ = 0.01 nm, w = 0.2 nm), rA/ B = 1.0, on the sputtering time scale. b For rA/B = 4. c For rA/B = 0.25.

Fig. 2. a MRI result of the surface concentration of component A, XsA of the multilayer in Fig. 1a–c, for dominating roughness parameter σ = 2 nm, rA/ B = 0.25, 1.0, 4.0 on the sputtered depth scale. b As a, but for surface concentration XsB of component B. c Magnified middle layer of the surface concentration of component A, XsA of the multilayer in a, for dominating roughness parameter σ = 2 nm (w / σ = 0.1), rA/ B = 0.25, 0.5, 1.0, 2.0, 4.0 on the sputtered depth scale. Dash-dotted horizontal lines indicate the layer thickness at 50% amplitude, dA(50%), and dashed vertical lines denote the original position and thickness dA of the layer. Note the different values of the amplitude and of the layer thickness at 50% normalized amplitude for dA(50%)(rA/B = 4.0) < dA(50%)(rA/B = 1.0) < dA(50%)(rA/ B = 0.25) (for numerical values see Table 2, w / σ = 0.1). The width of the interfaces B/A and A/B is indicated by Δzamp and independent of rA/B.

sputter depth profiles in contrast to SIMS depth profiles (see Section 2.3). Another important feature is the value of the relative amplitude (ΔXsA,B = (XsA,B(max) − XsA,B(min)) / Xs0(A,B)) (see Section 3.2) which in our case is symmetrically lowered from 0.57 to 0.42 when either increasing or decreasing the sputtering rate ratio from 1 to 4 or 0.25, respectively (see Table 1 for w / σ = 0.1). 142

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apparent (time scale) and true (depth scale) profile as compared to rA/ B = 1 is obtained. This fact corresponds to a decreased multilayer depth resolution (ΔXsA,B) when the sputtering rates of A and B are different (rA/ B ≠ 1, see Table 1, w / σ = 0.1). It should be noted here, that the determination of the depth resolution after the general definition of the depth distance between 16 and 84% of the flat plateau values [3] (characterizing a total intensity change between 0 and 100%), Δz(16–84%),can only be performed at sharp interfaces. Whereas for delta layers the full width at half maximum, Δz(FWHM) can be related to Δz(16–84%) [2,4,10], such a direct measurement is impossible for multilayers with overlapping profiles [2,4,5,10]. Only for high resolution profiles, if Δz(16–84%) / d < 0.4 (where d is the single layer thickness), the resulting layer profiles do not overlap and the depth resolution can be treated as that for two independent types of interfaces A/B and B/A [2,5,11]. If Δz(16–84%) / d > 0.4 (for rA/B = 1), adjacent profiles overlap and FWHM is no more defined. In this case, the only measurable value which can be used to obtain Δz(16–84%) (and which has been found to be useful in many publications [2,4,5,11,13]) is that of the relative, normalized amplitude of the profile. The value of this amplitude is given by the ratio between the difference of the maximum and minimum intensities and the original 100% value, [IA(max) − IA(min)] / I0,A, or better in terms of surface concentrations [XsA(max) − XsA(min)] / Xs0,A, where I0,A and Xs0,A denote the 100% value of intensity or surface concentration, respectively, of the considered component A (see Section 3.2). Indeed, the constant normalized amplitude ΔXsA, given by the distance between maximum and minimum of XsA, is constant, and for Δz / d = 4 / 5 corresponds to [XsA(max) − XsA(min)] / Xs0,A = 0.57, as shown in Fig. 2a, b and in several publications for rA/B = 1 [2,4,5,11]. In Sections 3.2–3.4 the respective dependencies will be further explained. Since the multilayer amplitude and the depth resolution are additionally influenced by rA/B, there is no simple relation between both quantities.

Table 1 Multilayer depth resolution, given by the relative multilayer amplitudes for XPS and SIMS, ΔIA,B(XPS)(t,z) and ΔIA,B(SIMS)(t,z), respectively (see Section 3.2), on the sputtering time (t) and sputtered depth (z) scale, for dominating σ (w / σ = 0.1) and dominating w (w / σ = 10), and for different values of rA/B and corresponding total depth resolution values Δz(16–84%) after Eq. (11). Single layer thickness d = 5 nm. Small deviations ( ± 0.02) from symmetrical values are due to the error of numerical simulation. w / σ=

rA/B=

0.1 0.1 0.1 10 10 10

0.25 1 4 0.25 1 4

ΔIA,B(XPS) (t) = ΔXsA,B (λ ➔ 0) 0.42 0.57 0.42 0.60 0.73 0.60

ΔIA,B(XPS) (z) = ΔXsA,B (λ ➔ 0) 0.42 0.57 0.42 0.59 0.73 0.60

ΔIA,B (SIMS) (t)

ΔIA,B (SIMS) (z)

0.40 0.58 0.42 0.60 0.74 0.60

0.60 0.58 0.62 0.85 0.75 0.85

Δz (nm)

4.2 4.0 4.0 16.0 4.0 1.1

It is interesting to note that an often-found mistake is to set the apparent thickness value at 50% amplitude between A and B as being equal to the inverse sputtering rate 1 / rA/B. However, as seen from Fig. 1b, the ratio would yield rA/B(incorr) = 2.2 instead of 4. The reason is obvious: the concentration of A between the two interfaces at 50% amplitude only changes between 0.27 and 0.47 of X0A = 1 mole fractions, Therefore we would rather expect a value in the vicinity of the average rA/B(av) = 2.5 (= (qA + qB) / 2), as supported by MRI predictions. Using Eqs. (3) and (6), the profiles of XsA and XsB on the sputtering time scale in Fig. 1a–c are converted into the true depth profiles on the sputtered depth scale with the same MRI parameters and for rA/B = 0.25, 1.0 and 4.0, as presented in Fig. 2a for XsA and in Fig. 2b for XsB. They show the same concentration amplitudes corresponding to the respective conditions as in Fig. 1a–c. However, an obvious change in layer thickness is recognized which is symmetrically different for A and B. This fact is caused by a characteristic and symmetric shift of the interfaces A/B and B/A as already shown in refs. [9, 10]. A closer look to the layer thickness at 50% of the amplitude, dA(50%), is shown in Fig. 2c for the magnified layer 2 of A, The difference is clearly revealed: while for rA/B = 1, the 50% layer thickness of A, dA(50%), is determined as 5.0 nm, in agreement with the original, true layer thickness, dA. For rA/B = 4. dA(50%) is smaller (3.9 nm), and for rA/ B = 0.25 it is larger (6.2 nm). The interface shift and the resulting layer thickness change are summarized in Table 2. It is important to keep in mind that only for non-existing preferential sputtering, the layer thickness at 50% amplitude is equal to the true, original layer thickness. In case of rA/B < 1, the layer thickness of A increases in accordance with its average amount, as indicated by the shift of the 50% line to higher concentration values (> 0.5 mole fraction/nm), and vice versa (cf. Fig. 2c). This fact demonstrates that the instantaneous surface concentration (i.e. the residual amount of matter remaining during sputter removal) is independent from mass conservation (in contrast to SIMS, see Section 2.3) but is inversely proportional to the preferential sputtering rate ratio after Eq. (1). Again, the respective profiles of B are exactly complementary to those of A. Therefore, as obvious from Fig. 2a–c, the same decrease in the amplitude (ΔXsA,B) (see Section 3.2) for rA/B = 4 and 0.25 in the

2.2. Intensity profiles for XPS (AES) Any measured profile is a profile consisting of an intensity (IA) as a function of the sputtering time. For the electron spectroscopies XPS and AES, that means that each thin layer element with thickness d has to be converted to the instantaneously residual surface by the simple relation IA / I0A = [1 − exp(−d / λ)], where λ is the mean electron escape depth and I0A is an appropriate sensitivity factor [2]. Let us assume two different mean escape depth values for the information depth parameter, λ = 0.4 nm (e.g. low energy AES) and λ = 1.6 nm (e.g. high energy AES or XPS). The result for the normalized intensity, IA / I0A(XPS), is shown for rA/B = 1 on the depth scale in Fig. 3a, for rA/B = 4 in Fig. 3b and for rA/B = 0.25 in Fig. 3c. The usually measured intensity versus time profile for A layers is depicted in Fig. 3d and e for rA/B = 4 and 0.25, respectively, where the profiles for λA = 0.4 nm are normalized to the amplitude of those for λA = 1.6 nm to recognize the almost constant profile shift between the maxima and minima. Whereas the shift is equal on both sides of the maxima for rA/B = 1 [2], it is different for rA/ B ≠ 1 (see Table 3). If the electron escape depth λΑ of A is different from that of B, it is

Table 2 Interface shift Δzsh(XSA)(XPS), Δzsh(SIMS) and layer thickness d(50%amp)(XSA)(XPS), d(50%amp)(SIMS) in multilayer profiles by XPS(λ ➔ 0) and SIMS, respectively, for dominating roughness (w / σ = 0.1) and dominating mixing (w / σ = 10) and for different preferential sputtering rate ratios rA/B (d = 5.0 nm). w/σ

rA/B

Δzsh(XSA)1(XPS) (nm) interface, B/A

Δzsh(XSA)2(XPS) (nm) interface, A/B

0.1 0.1 0.1 10 10 10

0.25 1 4 0.25 1 4

−0.58 0 0.50 −1.36 −1.0 −1.05

0.52 0 −0.55 −1.02 −1.0 −1.34

dA(50%amp) (XPS) (nm) 6.1 5.0 3.95 5.34 5.0 4.71

143

Δzsh(SIMS)1 (nm) interface, B/A 0.03 0 0.08 0.72 1.0 1.82

Δzsh(SIMS)2 (nm) interface, A/B 0.10 0 0.05 1.80 1.0 0.7

dA(50%amp) (SIMS) (nm) 4.96 5.0 5.03 3.92 5.0 6.12

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IA/IA(XPS)(mole fraction/nm)

b

IA/IA(XPS)(mole fraction/nm)

a MRI d = 5 nm w = 0.2 nm = 2 nm rA/B = 1 =

= 0.4 nm 1.6 nm

0

0

0.4 nm 1.6 nm

MRI d = 5 nm w = 0.2 nm = 2 nm rA/B = 4

Sputtered Depth z (nm)

Sputtered Depth z (nm)

d normalized with a red line in front MRI d = 5 nm w = 0.2 nm = 2 nm rA/B = 4

IA/IA(XPS)(mole fraction/s)

IA/IA(XPS)(mole fraction/nm)

c MRI d = 5 nm w = 0.2 nm = 2 nm rA/B = 0.25 =

= 0.4 nm 1.6 nm

0

0

0.4 nm 1.6 nm

Sputtered Depth z (nm)

Sputtering Time t (s)

IA/IA,IB/IB(XPS)(mole fraction/nm)

f MRI d = 5 nm w = 0.2 nm = 2 nm rA/B = 0.25 = 0.4 nm 1.6 nm

= 0

0.4 nm(IA/IA) 0

0

Normalized with a red line in front

MRI d = 5 nm w = 0.2 nm = 2 nm rA/B = 4

0.4 nm(IB/IB)

0

0

1.6 nm(IB/IB)

Sputtered Depth z (nm)

Sputtering Time t (s)

g MRI d = 5 nm w = 0.2 nm = 2 nm rA/B = 4 =

IB/IB(XPS)

= B=0.4nm =0.4nm

0

0

IA/IA(XPS)(mole fraction/nm)

e

=1.6nm

B

0

IA/IA(XPS) 144

(caption on next page)

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S. Hofmann, et al.

Fig. 3. a MRI result for the normalized XPS intensity IA / I0A(XPS) of the same multilayer as in Figs. 1, 2, but for rA/B = 1, with mean escape depths λ = 0.4 and 1.6 nm, on the sputtered depth scale. b As a but for rA/B = 4. c As a but for rA/B = 0.25. d MRI results for the XPS intensity IA / I0A(XPS) as in b for rA/B = 4 but normalized to equal amplitude with mean escape depths λ = 0.4 and 1.6 nm, on the sputtering time scale. e As d but for rA/B = 0.25. f MRI profile results for the XPS intensities IA / I0A(XPS) (red line) and IB / I0B(XPS) (blue lines) with mean escape depths λA = λB = 0.4 nm, and λA = 0.4 nm, λB = 1.6 nm. g Diagram IA / I0A(XPS) vs. IB / I0B(XPS) for equal (λA = λB = 0.4 nm, red line) and different (λA = 0.4 nm, λB = 1.6 nm, blue line) λ values of A and B.

frequently found in the literature [2], and we have already demonstrated the consequences for quantification in this way in ref. [9]. To further illustrate this fact for multilayers, let us compare the correlated intensities IA / I0A(XPS) with λΑ = 0.4 nm and IB / I0B(XPS) with λΒ = 0.4 nm or λΒ = 1.6 nm as shown in Fig. 3f. In Fig. 3g, IB / I0B(XPS) is depicted as a function of IA / I0A(XPS) for λA = λB = 0.4 nm (red line) and λA = 0.4 nm, λB = 1.6 nm (blue line). In the former case, a linear relation is obtained, which is typical for a constant sensitivity factor [4]. In the latter case there is a non-linear relationship between IA / I0A(XPS) and IB / I0B(XPS) which indicates an apparent sensitivity factor change but in fact it is caused by comparing two intensities with different λ values in a concentration gradient [2,9]. It is interesting to note that for rA/B ≠ 1, the mutual shift of profile upslope and downslope are different, as shown in Fig. 3d and e for rA/ B = 4.0 and 0.25, respectively, on the sputtering time scale. Table 3

Table 3 Amplitudes ΔIA,B(XPS)(z) and mutual shift Δzsh(λ1,2) of XPS intensity profiles with λ1 = 0.4 nm, λ2 = 1.6 nm for different values of rA/B, on the depth scale, for dominating roughness parameter σ. rA/B

ΔIA,B(XPS)

ΔIA,B(XPS)

Δzsh(λ1,2) (nm)

Δzsh(λ1,2) (nm)

λ1 = 0.4 nm

λ2 = 1.6 nm

Upslope

Downslope

0.50 0.56 0.50

0.39 0.41 0.39

0.25 1.0 4.0

0.78 0.96 1.14

1.17 0.96 0.69

obvious that at the same depth or time IA / I0A(XPS) ≠ 1 − IB / I0B(XPS) and therefore the usually applied normalization of the multilayer in terms of relative concentrations is wrong. Indeed, this is a mistake

b

MRI d = 5 nm w = 0.2 nm = 0.01 nm = 2 nm rA/B = 1 0

MRI d = 5 nm w = 0.2 nm = 0.01nm = 2 nm rA/B = 4 0

IA/IA 0

IB/IB

0

IA/IA

0

Total Sputtering Rate qt(nm/s)

IA/IA,IB/IB(SIMS)(mole fraction/s)

IA/IA,IB/IB(SIMS)(mole fraction/s)

a

0

0

0

IB/IB

Sputtering Time t (s)

Sputtering Time t (s)

IA/IA,IB/IB(SIMS)(mole fraction/nm)

d

IA/IA,IB/IB(SIMS)(mole fraction/s)

c

MRI d = 5 nm w = 0.2 nm = 0.01 nm = 2 nm rA/B = 0.25 0

IA/IA

0

0

0

IA/IA 0

IB/IB rA/B = 0.25 / 1 / 4

0

0

0

IB/IB

MRI d = 5 nm w = 0.2 nm = 0.01 nm = 2 nm

Sputtered Depth z (nm)

Sputtering Time t (s)

IA / I0A(SIMS)

Fig. 4. a Multilayer (as in Figs. 1, 2) profile of the normalized SIMS intensities (=sputtered matter) and IB / I0B(SIMS) on the sputtering time scale for rA/ = 1. B b Normalized SIMS Intensity as in a but for rA/B = 4 (red and blue lines). In addition, the instantaneous total sputtering rate qt (green line) is shown after Eq. (3). c For rA/B = 0.25. d Multilayer (as in Figs. 1, 2) profile of the normalized SIMS intensities (=sputtered matter) IA / I0A(SIMS) and IB / I0B(SIMS) on the depth scale for rA/B = 1 (IA / I0A(SIMS) = XSA ∗ qA / qt). 145

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is determined, and preferential sputtering in a multilayer profile is easily recognized by a smaller apparent thickness on the sputtering time scale. Dominating roughness in the depth resolution function is obvious if the profiles look symmetric, and asymmetry is a clear hint to dominating atomic mixing.

XA,XB(mole fraction/s)

a

MRI d = 5 nm w = 2.36 nm = 0.01 nm = 0.24 nm rA/B = 1

2.3. Intensity profiles for SIMS (GDOES) and sputtered matter Whereas in XPS and AES the remaining, residual surface composition is measured, SIMS and related techniques like GDOES or SNMS measure the instantaneously sputtered matter (indeed, this condition is best fulfilled by the latter techniques [14,15]). If the sensitivity factor I0A,m, of component A in matrix m is constant, then the normalized intensity IA / I0A,m(SIMS)(t) on the sputtering time scale is given by [10].

S S

S

XA XB

S

IA / I 0 A,m (SIMS)(t ) = X s A Sputtering Time t (s)

XA,XB(mole fraction/s)

MRI d = 5 nm w = 2.36 nm = 0.01 nm = 0.24 nm rA/B = 4

S S

S

XB

S

IA / I 0 A,m (SIMS)(z ) = X s A

XA,XB(mole fraction/s)

c

MRI d = 5 nm w = 2.36 nm = 0.01 nm = 0.24 nm rA/B = 0.25

S S

(8)

3. Asymmetric (non-Gaussian) DRF 3.1. Profiles of instantaneous surface concentration

S

S XB

qA /qt

which is presented in Fig. 4d for both A and B components, and for all three different sputtering rates rA/B = 1.0, 4.0, 0.25. This display convincingly shows that –in contrast to the residual surface or XPS (Fig. 2a, b)–the influence of preferential sputtering on the multilayer depth resolution (ΔIA,B, see Section 3.2) in SIMS vanishes if the latter is overwhelmingly determined by roughness. This fact agrees with similar results for single layer profiles in ref. [10]. Numerical values of ΔIA,B are summarized in Table 1 (small deviations are due to the non-zero parameter w (=0.24 nm) for w / σ = 10).

Sputtering Time t (s)

XA

(7)

The MRI result based on Eq. (7) is shown in Fig. 4a for rA/B = 1, and in Fig. 4b and c for rA/B = 4.0 and 0.25, respectively. In Fig. 4b, the instantaneous total sputtering rate is also given, which increases with the relative amount of the faster sputtering component A after Eq. (3). Note that the instantaneous SIMS intensity can increase to values of > 1 mole fraction/s for high sputtering rates as in Fig. 4b for IA / I0A,m(SIMS)(t). However, it is recognized that the integral of each layer of A and B over the sputtering time corresponds to the total amount of matter in each layer, and for the total multilayer structure the average amount of each species is 5 ∗ 3 = 15 mole fractions of A and 15 mole fractions of B. On the real depth scale, the different apparent thicknesses merge into a common depth scale and we get for the sputtered matter or SIMS intensity [10].

b

XA

qA

Let us now consider the other extreme of a depth resolution which is purely determined or at least dominated by the atomic mixing parameter w. This case means that the depth resolution function is asymmetric [2–6,9,10]. Important is the physical difference: Roughness is a morphological property of the sample, whereas atomic mixing is characteristic for the ion-sample interaction. Therefore the parameter w is a key parameter in our basic differential Eqs. (5) and (6). The numerical solution of Eq. (5) for the same A/B multilayer with w = 2.36 nm and w / σ = 10 (corresponding to Δz = 4.0 nm [2,5,10]) results in the sputtering time profile of the surface concentrations XsA, XsB, which is shown in Fig. 5a for rA/B = 1.0, and for rA/B = 4.0 and 0.25 in Fig. 5b and c, respectively. Already for rA/B = 1.0 a strong asymmetry of the profiles is recognized, but the apparent width of both interfaces, A/B and B/A, seem to be the same. Since the amplitude is < 100%, we cannot use the determination of the apparent depth resolution at sharp, isolated interfaces defined as Δt (16–84%) ∗ qav [9] with the average sputtering rate qav = (qA + qB) / 2. However, a relative measure of the interface width is the magnitude of Δtamp(16–84%) between 16 and 84% of the amplitude (note that the region between 16 and 84% of the amplitude has nothing to do with the depth resolution definition, since there is no plateau if the 100% value is not

Sputtering Time t (s) Fig. 5. a MRI result of the surface concentrations XsA, XsB of a multilayer of 6 layers (3 double layers) of A/B (5/5 nm, 6×) with single layer thickness d = 5 nm for dominating mixing parameter w = 2.36 nm (σ = 0.24 nm, λ = 0.01 nm), rA/B = 1.0, on the sputtering time scale. b Multilayer profile as in a, but for rA/B = 4. c Multilayer profile as in a, but for rA/B = 0.25.

summarizes the different amplitudes and profile shifts for different values of rA/B. In summary, XPS and AES depth profiles, IA(t), provide a direct measure of the instantaneous surface concentration profiles XsA(t), as obtained e.g. by well- known conversion relations (see e.g. p. 306 in ref. [2]). Therefore, these methods are very sensitive to preferential sputtering and, according to Eq. (1), they are very useful to determine rA/B by comparison with measurements before sputtering. In practice, IA(t) 146

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a

b XB(mole fraction/nm)

XA(mole fraction/nm

MRI d = 5 nm w = 2.36 nm = 0.01 nm = 0.24 nm rA/B =

S

S

0.25 1 4

MRI d = 5 nm w = 2.36 nm = 0.01nm = 0.24 nm rA/B = 0.25 1 4

Sputtered Depth z (nm)

Sputtered Depth z (nm)

c

d XA(mole fraction/nm)

XA(mole fraction/nm

MRI d = 10 nm w = 2.36 nm = 0.01 nm = 0.01 nm rA/B =

MRI d = 5 nm w = 2.36 nm = 0.01nm = 0.24 nm rA/B =

S

S

0.25 1 4

0.25 1 4

Sputtered Depth z (nm)

Sputtered Depth z (nm)

Fig. 6. a MRI result of the surface concentration of component A, XsA, of the multilayer in Fig. 1a–c, for dominating mixing parameter w = 2.36 nm, rA/B = 0.25, 1.0, 4.0 on the sputtered depth scale. b MRI result of the surface concentration of component B, XsB, of the multilayer in Fig. 1a–c, for dominating mixing parameter w = 2.36 nm, rA/B = 0.25, 1.0, 4.0 on the sputtered depth scale. c MRI result of the surface concentration of component A, XsA, of the same multilayer structure as in a but with layer thickness d = 10 nm, for dominating mixing parameter w = 2.36 nm, rA/B = 0.25, 1.0, 4.0 on the sputtered depth scale. Note the increased multilayer resolution ΔXsA,B. d MRI result of the surface concentration of component A, XsA, of the multilayer in Fig. 1a–c, for dominating mixing parameter w = 2.36 nm, rA/B = 0.25, 1.0, 4.0 on the sputtered depth scale.

attained, but a similar restriction to the useful interval 16–84% appears to be necessary to exclude the long tails and emphasize the steepest and more characteristic part of the interface profile). On the time scale (Fig. 5a), for rA/B = 1.0 this yields Δtamp(16–84%)(B/A) = Δtamp(16–84%)(A/B) = 2.6 s. In contrast, for rA/B = 4.0 (Fig. 5b) and 0.25 (Fig. 5c) the profiles of A and B look dramatically different, and in particular the apparent widths of the interfaces A/B and B/A are different. For rA/B = 4.0 (Fig. 5b), Δtamp(16–84%)(A/B) = 1.0 s, and Δtamp(16–84%)(B/A) = 1.5 s. For rA/ B = 0.25 (Fig. 5c), the relations are opposite, with Δtamp(16–84%)(A/ B) = 5.9 s and Δtamp(16–84%)(B/A) = 4.0 s. Indeed, when the contribution of mixing is prevalent, the typical asymmetric profile shape (see e.g. Fig. 6c) is seen in experimentally measured multilayer profiles, in particular in high resolution profiles (see e.g. ref. [15], and Fig. 12, Sect. 5). In Fig. 6a and b, the profiles of Fig. 5a–c are converted to the depth scale for components A and B, respectively. By determination of the true interface width with reference to 16 and 84% of the amplitude, Δzamp(16–84%) for rA/B = 1.0 we get in Fig. 6a Δzamp(16–84%)(A/ B) = Δzamp(16–84%)(B/A) = 2.8 nm, and for rA/B = 4.0 we get Δzamp(16–84%)(A/B) = 1.7 nm, Δzamp(16–84%)(B/A) = 3.0 nm. For rA/B = 0.25, the latter values for A/B and B/A interfaces are interchanged. From Fig. 6b for component B we get - within about 3% uncertainty caused by very small but non-vanishing σ - the mirror image, Δzamp(16–84%)(B/A) = 1.8 nm and Δzamp(16–84%)(A/B) = 2.9 nm.

As demonstrated earlier [9,10], the contribution of the mixing length varies with w / qA on the time scale and with w / rA/B on the depth scale, valid for the interface A/B [9]. That means for rA/B = 4.0, Δz(16–84%) (A/B) = 2.36 ∗ 1.76 / 4 = 1.0 nm and Δz(16–84%) (B/ A) = 4 / 0.25 = 8.0 nm, in qualitative agreement with the above Δzamp(16–84%) values. For thicker layers, the profile amplitude gets more in the vicinity of the 100% value. Hence, for d = 10 nm as shown in Fig. 6c the respective values for the same Δz are, with Δzamp(16–84%)(A/B) = 2.0 nm and Δzamp(16–84%)(B/A) = 5.5 nm more close to the true interface resolution values. The altered shape of the profile of XsA of the layers of A with respect to those of B when rA/B ≠ 1 is better disclosed in the magnified view of layer 2 of A on the depth scale shown in Fig. 6d. As clearly seen, for rA/ B = 1, the 50% layer thickness of A is equal to the true layer thickness, dA(50%amp) = dA = dB, whereas dA(50%amp) < dA for rA/B > 1, and dA(50%amp) > dA for rA/B < 1, and vice versa for layers of B (see Table 2 for numerical values). 3.2. Towards an alternative definition of multilayer resolution At this stage it becomes obvious that the interfacial width is not a unique function of the interfacial resolution as for rA/B = 1 [2,5,11], but depends additionally on preferential sputtering. In particular, the 147

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IB/IB(XPS)(mole fraction/s)

b

IA/IA(XPS)(mole fraction/s)

a

MRI d = 5 nm w = 2.36 nm = 0.24 nm rA/B = 1 =

= 0.4 nm 1.6 nm

0

0

0.4 nm 1.6 nm

MRI d = 5 nm w = 2.36 nm = 0.24 nm rA/B = 1

Sputtering Time t (s)

Sputtering Time t (s)

d MRI d = 5 nm w = 2.36 nm = 0.24 nm rA/B =0.25

IA/IA(XPS)(mole fraction/s)

IA/IA(XPS)(mole fraction/s)

c

MRI d = 5 nm w = 2.36 nm = 0.24 nm rA/B = 4 =

0.4 nm 1.6 nm

0

0

0.4 nm 1.6 nm

=

Sputtering Time t (s)

Sputtering Time t (s)

IA / I0A(XPS)

Fig. 7. a MRI result for the normalized XPS intensity of the same multilayer as in Figs. 1, 2 and for rA/B = 1, with mean escape depths λ = 0.4 and 1.6 nm, on the sputtering time scale. b MRI result for the normalized XPS intensity IB / I0B(XPS) of the same multilayer as in Figs. 1, 2 and for rA/B = 1, with mean escape depths λ = 0.4 and 1.6 nm, on the sputtering time scale. c MRI result for the normalized XPS intensity IA / I0A(XPS) of the same multilayer as in Figs. 1, 2 and for rA/B = 4, with mean escape depths λ = 0.4 and 1.6 nm, on the sputtering time scale. d MRI result for the normalized XPS intensity IA / I0A(XPS) of the same multilayer as in Figs. 1, 2 and for rA/B = 0.25, with mean escape depths λ = 0.4 and 1.6 nm, on the sputtering time scale.

influence of preferential sputtering increases when the mixing parameter w dominates Δz [5]. Furthermore, the mirror symmetry of the multilayer profiles of A and B means that there is only one multilayer resolution, ΔXsA,B, which is the same for A and B, as already described by the relative amplitude itself, i.e.

X s A,B = [X s A,B (max)

X sA,B (min)]/ X s 0,A,B

The instantaneous, residual surface concentration is equal to the intensity in AES and XPS for λ ➔ 0, and in SIMS the intensity is representative for the sputtered matter and not for XsA,B. Since rA/B = 1 / rB/A, symmetry requires that the multilayer resolution is equal for both values, in accordance with the predicted profiles in all Figs. 1–6. It should be noted, that the above definitions of ΔXsA,B and ΔIA,B values are similar to signal-to-noise figures, i.e. the higher the number the better the multilayer or features therein are resolved (opposite to the definition of depth resolution Δz). The definition is also similar to that in optics, where two adjacent objects (here: layers) are better resolved the higher the intensity valley is between the two maxima (here: amplitude). The value of ΔIA,B can also be used to describe a detection limit ΔIA,B(lim) of the multilayer which is usually defined as ΔIA,B(lim) = 3 ∗ S / N, where S / N is the actual signal-to-noise ratio of the measurement points [2]. It is interesting to note that a similar proposal of an adequate description of multilayer resolution (in terms of the amplitude or envelope of the intensity, Eq. (10)) was already made in 1981 by one of the pioneers in sputter depth profiling, Martin Seah in ref. [13].

(9)

Xs0,A,B

where denotes the 100% value of the respective surface concentration (see Section 2.1). It is obvious that alternatively to ΔXsA,B. we can determine the relative amplitude of the intensity, ΔIA,B, normalized to 100%, which follows directly from the extreme values IA,B(max) and IA,B(min) (as e.g. in Fig. 3b–e or Fig. 4a–d, and in the following Sections 3.3 and 3.4),

IA,B = [IA,B (max)

IA,B (min)]/ I0,A,B

(10)

where I0,A,B is the intensity for A and B when the sensitivity factor corrected intensity of the other component is zero. Formerly, we have called ΔIA,B = Im / I0 [11], but this was only valid for rA/B = 1, where a clear and unique relation between Im / I0 and Δz was possible in contrast to the more complicated relation encountered for rA/ B ≠ 1. Here, we generalize for any value of rA/B and express the multilayer resolution directly by the relative amplitude ΔIA,B. A disadvantage of that approach is that we can only quantitatively compare the achieved multilayer resolution for the same layer thickness and material combination.

3.3. Intensity profiles for XPS (AES) When the MRI model is applied to AES or XPS depth profiles, the information depth parameter λ is taken as the mean electron escape depth. As 148

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IA/IA,IB/IB(SIMS)(mole fraction/s)

b

IA/IA,IB/IB(SIMS)(mole fraction/s)

a

MRI d = 5 nm w = 2.36 nm = 0.01 nm = 0.24 nm rA/B = 1 0

0

IA/IA 0

IB/IB

0

0

IA/IA

MRI d = 5 nm w = 2.36 nm = 0.01 nm = 0.24 nm rA/B = 4

0

0

0

IB/IB

Sputtering Time t (s)

d

IA/IA,IB/IB(SIMS)(mole fraction/s)

IA/IA(SIMS)(mole fraction/nm)

Sputtering Time t (s)

c

0

MRI d = 5 nm w = 2.36 nm = 0.01 nm = 0.24 nm rA/B = 0.25 0

0

0.25 1 4

0

IA/IA

MRI d = 5 nm w = 2.36 nm = 0.01nm = 0.24 nm rA/B =

0

IB/IB

Sputtered Depth z (nm)

Sputtering Time t (s)

IB/IB(SIMS)(mole fraction/nm)

e

MRI d = 5 nm w = 2.36 nm = 0.01nm = 0.24 nm rA/B =

0

0.25 1 4

Sputtered Depth z (nm) Fig. 8. a Multilayer (as in Figs. 1, 2) profile of the normalized SIMS intensities (=sputtered matter) IA / I0A(SIMS) and IB / I0B(SIMS) on the time scale for rA/B = 1. b Multilayer (as in Figs. 1, 2) profile of the normalized SIMS intensities (=sputtered matter) IA / I0A(SIMS) and IB / I0B(SIMS) on the time scale for rA/B = 4. c Multilayer (as in Figs. 1, 2) profile of the normalized SIMS intensities (=sputtered matter) IA / I0A(SIMS) and IB / I0B(SIMS) on the time scale for rA/B = 0.25. d Multilayer (as in Figs. 1, 2) profile of the normalized SIMS intensities (=sputtered matter) IA / I0A(SIMS) on the depth scale for rA/B = 0.25, 1.0, 4.0. e MRI result of the normalized SIMS intensities (=sputtered matter) IB / I0B(SIMS) of a multilayer on the depth scale for rA/B = 0.25, 1.0, 4.0 (IB / I0B (SIMS) = XSB ∗ qB / qt).

already done in Section 2.2, we assume two different values of λ = 0.4 nm (e.g. low energy AES) and λ = 1.6 nm (e.g. high energy AES or XPS). The result for rA/B = 1 is shown for the normalized intensity, IA / I0A,m(XPS) as a function of the sputtering time in Fig. 7a, and for IB / I0B,m(XPS) in Fig. 7b. It is interesting to note that for both components the convolution with the higher λ (of the order of w) leads to an almost symmetric profile [2,4] which masks the asymmetric effect of w, and decreases ΔIA,B. Even for rA/B = 4 (Fig. 7c) or rA/B = 0.25 (Fig. 7d), the higher λ smoothes out sharp peaks and edges and, as expected, causes a characteristic shift of the profile towards

the instantaneous surface. As already explained in Section 2.2, Fig. 7a–d again demonstrates that in the usual case of different values of the electron escape depth λ for A and B, the normalized intensity at corresponding time or depth in the profile does not represent the surface concentration at that location, and therefore IA / I0A ≠ 1 − IB / I0A. Only after conversion of intensities to surface concentrations, quantification is possible because ΔXsA = 1 − ΔXsB is always valid.

149

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a

b

0.98

0.87

IA/IA,m(SIMS)

IA/IA,m(SIMS)

MRI d = 5 nm w = 2.36 nm = 0.01nm = 0.24 nm rA/B =

MRI d = 5 nm w = 2.36 nm = 0.01nm = 0.24 nm rA/B =

0

0

0.25 1 4

0.25 1 4

Sputtered Depth z (nm)

XA (mole fract./nm)

c

d

XA(mole fraction/nm)

MRI d = 5 nm = 0.01 nm rA/B = 4

MRI d = 5 nm = 0.01 nm rA/B = 4 w/ =0.1 w/ =1 w/ =10

S

0

IA/IA,m(SIMS)

w/ =0.1 w/ =1 w/ =10

Sputtered Depth z (nm)

Sputtered Depth z (nm)

e Total Sputtering Rate qt(nm/s)

MRI d = 5 nm w = 2.36 nm = 0.01nm = 0.24 nm rA/B = 0.25 1 4

Sputtered Depth z (nm) IA / I0A,m(SIMS)

Fig. 9. a Profile of layer 2 of A of the normalized SIMS intensities on the depth scale for rA/B = 0.25, 1.0, 4.0. Note the change in layer thickness at 50% amplitude. dA(50%), with rA/B as indicated by the horizontal dash-dotted lines. For rA/B = 1.0, dA(50%) = dA, for rA/B = 4.0, dA(50%) > dA, and for rA/ B = 0.25, dA(50%) < dA (see Table 2). b Normalized SIMS intensity IA / I0A,m(SIMS) as a function of the bulk concentration XA showing apparent matrix effect between both quantities for rA/B = 0.25 and 4.0. c MRI result of the surface concentration XsA (=IA / I0A.m(XPS) for λ ➔ 0), of layer 2 of component A of the multilayer in Fig. 1a for rA/B = 4, and three different values of w / σ = 0.1, 1, 10 (Δz is always 4 nm) on the sputtered depth scale. Note the change of dA(50%amp) (horizontal dashed lines) with w / σ (see Table 2). d Profile of the normalized SIMS intensities (=sputtered matter XA,sp) IA / I0A,m(SIMS) on the depth scale for rA/B = 4.0 and three different values of w / σ = 0.1, 1, 10 (Δz is always 4 nm). Note the change of dA(50%amp) (horizontal dashed lines) with w / σ (see Table 2 and Fig. 10b). e The total sputtering rate qt as a function of the sputtered depth for the values of rA/B in a.

3.4. Intensity profiles for SIMS (GDOES) and sputtered matter

rA/B = 0.25 in Fig. 8b and c are considerably different from Fig. 5b and c. Since those represent the instantaneous surface concentration, there is no requirement of mass conservation. In contrast, the normalized SIMS intensity represents the sputtered matter which should be equal to the bulk composition which is removed by sputtering. In Fig. 8b and c, the areas of

According to Section 2.3 and Eq. (7), the normalized SIMS intensity is presented as a function of the sputtering time for rA/B = 1 in Fig. 8a. Whereas the latter is identical to Fig. 5a, the diagrams for rA/B = 4.0 and for 150

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to demonstrate the dependence of profile shape, interface location and layer thickness on the preferential sputtering rate ratio for the instantaneous surface concentration XsA. For SIMS intensity-depth profiles, Fig. 9a–d show the effect of rA/B on profile shape, amplitude, and on the 50%amp layer thickness usually measured at the location of 50% of the amplitude, i.e. (Imax + Imin) / 2 (note that for rA/B = 1, the 50% amp layer thickness is always equal to the real layer thickness, d(50% amp) = d). Frequently, the layer thickness is determined at a concentration of 50 at.% [17–19]. In case of preferential sputtering, this definition has the disadvantage that in special cases (e.g. for rA/B ≪ 1) the 50% mark may not be attained at all [20] (see e.g. Fig. 8c). Because of the changing shape of the profile, as indicated by the changing layer thickness and amplitude in Fig. 9a, the instantaneously sputtered matter (IA / I0A,m(SIMS) = XsA ∗ qA / qt) is no more equal to the instantaneously removed bulk concentration (IA / I0A,m(SIMS) ≠ XA, for rA/ B ≠ 1). Since the profile for rA/B = 1 represents the case of XA,sp = XA, a comparison of both quantities for rA/B ≠ 1 shows their mutual deviation, as disclosed in Fig. 9b. The straight line is obtained for rA/B = 1, that means no sensitivity factor change, whereas the curved lines for rA/ B = 4.0 and for indicate the change of the sensitivity factor with XA. As seen in Fig. 9b, for rA/B = 0.25, a bulk reference sample of concentration XA = 0.85 corresponds to the multilayer concentration of sputtered matter IA / I0A,m(SIMS) = XsA ∗ qA / qt = 0.98. Thus, when applying this value to the green line maximum for XA = 0.99 in Fig. 9a, the sensitivity factor, I0A,m = 1 is erroneously changed from unity to I0A,m(error) = 0.98 / 0.85 = 1.15 in this case. Thus, we may conclude that the sensitivity factor which is usually obtained from a reference sample with constant (bulk) concentration XA (see e.g. refs. [17, 18]), is no more applicable to quantify multilayer profiles in case of preferential sputtering. This fact is generally ignored in the present literature on quantification of SIMS depth profiles [17,18,21]. Table 2 summarizes the results according to Fig. 9a–d, showing the effect of rA/B (=0.25, 1, 4) on the shift Δzsh of the location of the two types of interfaces B/A and A/B with respect to the original layer interfaces, measured at 50% of the amplitude, and the resulting 50% layer thickness dA(50%amp)(XPS, λ ➔ 0) for the surface concentration (measured by XPS) and dA(50%amp)(SIMS) of the sputtered matter (measured by SIMS). The interface width Δzamp(16–84%) is slightly modified by rA/B and by w / σ but not significantly altered for the present parameter combination (see Table 1). It is interesting to note that the effect of rA/B on the 50% layer thickness is opposite for the XPS and SIMS (see Table 2). Fig. 9e depicts the dependence of the instantaneous total sputtering rate, dz / dt = qt, on the sputtered depth for SIMS depth profiles. The strong asymmetry for rA/B ≠ 1 and dominating w can be explained by the fact that the depth resolution, Δz, and the depth resolution function (DRF), are determined by the apparent mixing length, w ∗ qA / qt. As already shown in ref. [10], in this case, Δz and the DRF become dependent on XsA and therefore they lose their original meaning in the convolution integral. In Fig. 10a, the 50% layer thickness for XPS, dA(50%amp)(XPS, λ ➔ 0) as a function of rA/B is shown for dominating σ (w / σ = 0.1), for increased w (w / σ = 1.0) and for dominating w (w / σ = 10). In Fig. 10b, dA(50%amp)(SIMS) is shown as a function of the same parameters. The difference to Fig. 10a is striking. In XPS, there is a slight decrease of the 50% thickness with increasing rA/B for dominating w, and a considerably stronger effect for dominating σ. In contrast, in SIMS there is no effect at all of rA/B for dominating roughness parameter σ, but a rather strong increase of the layer thickness with increasing rA/B for dominating mixing parameter w (w / σ = 10). The dependence on the increasing mixing parameter on dA(50%) is shown - again for IA / I0A,m(XPS) (λ ➔ 0) and for IA / I0A,m(SIMS) - as a function of w / σ, in Fig. 10c and d, respectively. For both analysis methods, the shape of the dependence at rA/B = 4.0 looks similar. But in XPS depth profiling, the value of dA(50%amp)(XPS) stays always below (for rA/ B = 4.0) or above (for rA/B = 0.25) the original, true thickness. In contrast, dA(50%amp)(SIMS) corresponds to the true depth dA for dominating roughness, and increases with the influence of atomic mixing. This fact

Table 4 Ag/Ni multilayer thickness values determined by HRTEM. The two representative layers shown in Fig. 12b, c are given in boldface. Layer Ag-surface Ni Ag Ni Ag Ni Ag Ni SUM

Thickness (nm) 24.1 19.4 26.9 20.4 25.9 17.6 25.9 18.5 178.7

the A and B profiles seem to be much more similar than those in Fig. 5b and c. Profiles similar to those in Fig. 8b, c are reported in publications of multilayer profiles with appreciable differences in sputtering rates such as Mo and Si [16]. The SIMS intensity profiles on the sputtered depth scale after Eq. (8) are shown in Fig. 8d for component A and in Fig. 8e for component B. It seems that mass conservation can be recognized by the fact that the mass missing on top of the layer of A in Fig. 8d for rA/B = 4 is contained in the increased layer thickness as compared to rA/B = 1. However, the magnified picture of layer 2 of A shown in Fig. 9a shows clear evidence of a preferential sputtering effect. An obvious change in layer thickness of A, dA(50%amp), is recognized which was first described in SIMS profiles of single layers in ref. [10]. To the authors' knowledge the effect of change in multilayer thickness by preferential sputtering has not yet been predicted in the respective literature and seems to be a rather new discovery. However, experimentally this effect was already found in SIMS depth profiles of multilayers as a result of increasing ion beam intensity [17,18], but now it can be explained by the theoretical prediction developed in this paper. Table 1 shows a summary of the predicted influence of the preferential sputtering ratio on ΔIA,B for XPS and SIMS on the time and the depth scale for both dominating σ (w / σ = 0.1) and dominating w (w / σ = 10) in MRI (as demonstrated by the skewness parameter w / σ [4]). The basic difference between XPS and SIMS multilayer profiles is clearly recognized: In XPS, for dominating σ (e.g. w / σ = 0.1), the multilayer resolution on the time and depth scales is always worse for rA/B = 0.25 and 4 (and of the same value), and the effect of rA/B is rather similar but less pronounced for dominating w (e.g. w / σ = 10). While in SIMS, for dominating σ, the dependence of the multilayer depth resolution is exactly the same as in XPS on the time scale, there is a great contrast for the true resolution on the depth scale. In SIMS, the latter is not affected by rA/B ≠ 1 for dominating σ (in accordance with refs. [9, 10]), but ΔIA,B(z) is slightly improved for both rA/B = 0.25 and 4 when w is dominant (see Table 1). 3.5. Influence of preferential sputtering on SIMS depth profiles: effect on profile shape, interfacial width, interface location, layer thickness and sensitivity factor The presented effect of preferential sputtering to SIMS depth profiles appears to contradict the often-cited textbook wisdom that SIMS is independent of preferential sputtering [19,20]. Now we see that this statement is only valid for constant concentration (no profile) or in SIMS depth profiling when roughness dominates the depth resolution and the influence of atomic mixing can be ignored (see Table 1). When the depth resolution is additionally dependent on the amount of atomic mixing, then the effect of preferential sputtering is seen in variations of multilayer resolution (normalized amplitude, see Table 1), interface width (see Section 3.1, Fig. 6a–d), interface location, layer thickness (see Fig. 8d, e, f, and Tables 2 and 4), and sensitivity factor (see Fig. 9b). In Fig. 6d, one layer of the multilayer structure is magnified for clarity 151

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a

b w/

dA(50%amp)(SIMS)

dA(50%amp)(XPS)

0.1 1.0 10

rA/B

w/ 0.1 1.0 10

rA/B

c

d rA/B= 0.25 1 4

rA/B=

dA(50%)(XPS)

dA(50%)(SIMS)

0.25 1 4

w/

w/

e

f w/

IA,B(XPS)(nm)

IA,B(SIMS)(nm)

0.1 1.0 10

rA/B

w/ 0.1 1.0 10

rA/B

Fig. 10. a 50% layer thickness dA(50%amp) vs. rA/B for XsA or IA / I0A,m(XPS, λ ➔ 0) and w / σ = 0.1, 1, 10 (see Table 2). b 50% layer thickness dA(50%amp)(SIMS) vs. rA/B for IA / I0A,m(SIMS) and w / σ = 0.01, 0.1, 10 (see Table 2). c 50% layer thickness dA(50%amp)(XPS) vs. w / σ for XsA or IA / I0A,m(XPS, λ ➔ 0) and rA/B = 0.25, 1.0, 4.0 (see Table 2). d 50% layer thickness dA(50%amp)(SIMS) vs. w / σ for IA / I0A,m(SIMS) and rA/B = 0.25, 1.0, 4.0 (see Table 2). e Multilayer depth resolution in λ-corrected XPS depth profiles, ΔIA,B(XPS) (for λ ➔ 0), as a function of the preferential sputtering rate ratio, rA/B, for layer thickness d = 5 nm and MRI parameters as in a, b. f Multilayer depth resolution in SIMS depth profiles, ΔIA,B(SIMS), as a function of the preferential sputtering rate ratio, rA/B, for layer thickness d = 5 nm and MRI parameters as in a, b.

explains the increasing 50%-layer thickness with increasing primary ion energy experimentally found in refs. [17, 18], quite naturally and without any additional assumption [22]. As already obvious from Fig. 9a, not only the layer thickness, but also the multilayer resolution given by the amplitude, ΔIA,B, changes with rA/B, as shown in Fig. 10e for ΔIA,B(XPS) (=ΔIA,B(XsA) for λ ➔ 0) and I Fig. 10d for ΔIA,B(SIMS).

When comparing both figures, the contrary behavior with rA/B is evident: While for both methods multilayer depth resolution increases with increasing mixing already for rA/B = 1, it decreases for XPS and increases for SIMS symmetrically with increasing and decreasing rA/B. While the absolute magnitude of the effect of preferential sputtering on profile shape, ΔIA,B and dA(50%amp) appears to be rather similar for SIMS and XPS, the sign of the effect is opposite. For SIMS with 152

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taken into account in addition. Because the effect of the electron escape depth in XPS depth profiling is well known and the information depth parameter generally vanishes in SIMS, we confine our considerations to the combination of roughness (σ) and mixing (w). As already shown earlier, when ignoring the information depth parameter λ, the interfacial resolution is given by [9]

a

XA(mole fraction/nm

MRI d = 5 nm w = 1.53 nm = 0.01 nm = 1.53 nm rA/B =

z (16–84%) = [(2

w/ rA/B ) 2]1/2

(11)

As an example, we assume the same magnitude of both parameters and perform the MRI calculations with σ = w = 1.53 nm. For rA/B = 1, this adds up to the same Δz = [(2 ∗ 1.53)2 + (1.67 ∗ 1.53)2]1/ 2 = 4.0 nm as before [10]. According to Eq. (11), for rA/B = 4.0 and 0.25, Δz(A) = 3.1 nm and 10.7 nm, respectively. Since for multilayers, Δz(B) is opposite to Δz(A), there has to be some compromise which results in a much-reduced influence on the respective profile amplitudes. The MRI results for the above example are shown for the surface concentration (=normalized XPS intensity for λ ➔ 0) in Fig. 11a, and for the sputtered matter (=normalized SIMS intensity in Fig. 11b), both on the sputtered depth scale. From both the above figures it is clear that the sputter depth profiles are to some degree between both extremes of dominating σ (Section 2) or dominating w (Section 3). The degree of influence as a function of the skewness parameter w / σ (rA/B = 1) [4], is modified by rA/B (Eq. (11)), demonstrated by the MRI results in Fig. 10c for dA(50%)(XPS) and in Fig. 10d for dA(50%)(SIMS) (see Table 2). The MRI prediction according to Fig. 10a will be applied to an experimental example of an AES depth profile in the next section.

S

0.25 1 4

Sputtered Depth z (nm)

b MRI d = 5 nm w = 1.53 nm = 0.01 nm = 1.53 nm rA/B = 0.25 1 4

5. An experimental example: AES depth profile of an Ag/Ni multilayer quantified with the MRI model

0

IA/IA(SIMS)(mole fraction/nm)

)2 + (1.67

In order to demonstrate an application of the MRI model extended for preferential sputtering on a multilayer we measured and modeled a depth profile of the Ag/Ni multilayer. The sample consists of four Ag/Ni bilayers (nominal thickness Ag (26 nm)/Ni (19 nm), see below) deposited by magnetron sputtering on thin SiO2 layer covering Si substrate. The intensity-sputtering time profile of the Ag/Ni multilayer measured with AES is shown in Fig. 12a. In order to obtain a good depth resolution two symmetrically inclined 1 keV-Ar ion sputter beams were employed in addition to sample rotation. Also a very low angle of electron emission of 15° with respect to sample surface was used. The Ag/Ni multilayer sample was also investigated by TEM microscopy on JEOL JEM-2010F microscope. Actual thickness of individual Ni and Ag layers were measured and are given in Table 4. These data were used for comparison with simulated depth profiles obtained using the MRI model. The Ag/Ni multilayer was chosen since Ag and Ni significantly differ for sputtering rates allowing us to test the MRI model extended to include preferential sputtering. Fig. 12b shows the MRI fitted profiles on the time scale with the MRI parameters w = 3.5 nm, σ = 2 nm, λ = 0.5 nm for Ag (351 eV), and 1.0 nm for Ni (848 eV) and r(Ag/ Ni) = 3.5. The average fitting error is obtained as ε = 5% [24] (Note that ε is relatively high since it is mainly caused by ignoring the obvious backscattering effect of Ag on the Ni profiles [25]). Fig. 12c shows a magnified view of the second Ag layer and the adjacent Ni layer on the depth scale between 40 nm and 120 nm. The original positions of Ag and Ni layers and interfaces between them are also shown. The 50% layer thickness values from fitted depth profile are measured as d(50%) (Ag) = 24.5 nm, and d(50%)(Ni) = 21.4 nm. These values are different from the original layer thickness d obtained by TEM measurements (26.9 nm and 20.4 nm respectively for the considered Ag and Ni layers). This fact is in accordance with the predictions in Section 3.5, for the residual surface analysis values, d(50%amp)(Ag) < d(Ag) and d(50% amp)(Ni) > d(Ni), since r(Ag/Ni) > 1. Although the quantitative analysis of sputter depth profiles by MRI is expected to be difficult because Ag/Ni is a well-known segregation system [26], atomic mixing appears to stabilize at a constant value thus enabling a successful MRI

Sputtered Depth z (nm) Fig. 11. a MRI result of the surface concentrations XSA, XSB of a multilayer of 6 layers of A and B with single layer thickness d = 5 nm for both roughness and mixing parameters, σ = w = 1.53 nm (λ = 0.01 nm), rA/B = 1.0, on the sputtered depth scale. b Multilayer profile of the normalized SIMS intensities (=sputtered matter) IA / I0A(SIMS) on the depth scale for rA/B = 0.25, 1.0, 4.0 (IA / I0A(SIMS) = XSA ∗ qA / qt).

dominating mixing parameter the effect of rA/B is most pronounced. Because of the universal validity of the mass conservation law in sensitivity factor - corrected SIMS, the change in layer thickness is accompanied by a complementary change in the maximum intensity. However, only when the total layer structure, i.e. the integral of the sputtering time or depth is considered, SIMS yields the sputtered matter without any restriction for different sputtering rates of the components [10]. Frequently, sputtering induced roughening is experimentally found to increase with sputtered depth [23]. According to Fig. 10c and d, for XPS profiles that means an increasing influence, and for SIMS profiles a decreasing influence with depth, respectively. However, since in contrast to our assumption of constant Δz, in ref. [23] Δz increases with σ, this fact results in a general reduction of the effect of preferential sputtering with sputtered depth in this case (cf. Eq. (11)). 4. Combination of roughness and mixing parameters Up to now we have considered the two extreme cases of preponderant roughness and preponderant mixing establishing the total depth resolution to clarify their different influence on the profile and the depth resolution. In practice, we generally encounter a combination of these parameters, and in XPS, a non-zero information depth has to be 153

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application to multilayers showing preferential sputtering.

a

Intensity (APPH, arb. u)

Ag(356eV) Ni(848eV) C(272eV) O(510eV) Si(78eV)

6. Summary and conclusion A quantitative description of the influence of preferential sputtering on depth resolution and on the shape of multilayer profiles is presented by the MRI model which is extended to include preferential sputtering. Multilayers of the structure A/B/A/B… are considered as a linear superposition of subsequent interfaces and/or a sequence of single layers. Therefore the results are compatible with that of previous papers on the influence of preferential sputtering on sharp interface and delta layer depth profiles. Thus, the difference of the influence of the main contributions to depth resolution, namely roughness and atomic mixing, on XPS and on SIMS depth profiles is obvious here too. However, because of the overlapping of adjacent layer profiles for insufficient resolution, new aspects come into play. Most important is the fact of the reciprocity of the profiles of both multilayer components A and B which contrasts delta layer profiling and requires a new definition of multilayer resolution that is based on the normalized amplitude of the wavelike profile structure. While the different widths of the two different types of interfaces, A/B and B/A, are already encountered for dominant influence of atomic mixing without preferential sputtering, the skewness parameter given by the ratio of atomic mixing length w and roughness parameter σ tends to increase the effects of preferential sputtering. In turn, these effects cause a respective difference in the location of the interfaces. Thus, a new effect of the influence of preferential sputtering on the layer thickness determined at 50% of the multilayer profile amplitude is predicted in sputter profiling with XPS and SIMS which in the past was experimentally observed in SIMS but to the authors' knowledge was never correctly explained before. An important consequence of the profile shape variation is the fact that in case of preferential sputtering, multilayer profiles cannot be quantified by relative sensitivity factors which are obtained by reference standards with constant bulk concentration. In contrast to XPS and AES, in SIMS the effect of profile shape change is absent when roughness dominates the total depth resolution. The basic difference in sputter depth profiling with XPS and SIMS is caused by the fact that XPS determines the transient residual surface composition where no mass balance is required, whereas SIMS detects the sputtered matter where a strict mass conservation law has to be obeyed for the integral over the total multilayer. Thus, the main result is completely different for XPS and SIMS. Whereas preferential sputtering in XPS profiles causes a decrease in multilayer resolution which is most pronounced for dominating roughness, in SIMS an improvement of multilayer resolution is obtained which vanishes for dominating roughness influence. The gathered insight sheds a new light on old controversies about the question: Does preferential sputtering have an influence on depth resolution and on multilayer profiles? The answer is ambiguous: Yes and No. Yes, for XPS always, but for SIMS only when atomic mixing dominates depth resolution. No, for SIMS when roughness is the dominating contribution and atomic mixing can be ignored.

Sputtering Time t (min)

Intensity (APPH, arb. u)

b

Sputtering Time t (min)

c 20.4nm

21.4nm 24.5nm

S

S

XAg XNi (at.%)

TEM: 26.9nm

Sputtered Depth z (nm)

Acknowledgment

Fig. 12. a The AES experimental intensity-sputtering time profile of an Ag (26 nm)/Ni (19 nm) multilayer (4 double layers) obtained by 1 keV Ar+ sputtering with sample rotation is shown (open diamonds for Ag and open triangles for Ni). b Magnified part (layers 3 and 4) of the profile with I0Ni = 1580 arb. u. (APPH) and I0Ag = 3407 arb. u. (APPH) showing MRI model calculation fitted to the data in a (from 20 to 90 min) on the sputtering time scale with the MRI parameters and q(Ag), q(Ni), rAg/Ni shown below (ε denotes the least squares fitting error). c A magnified view of the second Ag layer and the adjacent Ni layer between 40 nm and 120 nm from b but for the plot of concentration vs. sputtered depth. The original interfaces of the layers are shown by vertical dashed lines. The layer thickness values at 50% of the amplitude are measured as d(50%amp) (Ag) = 24.5 nm, and d(50%amp)(Ni) = 21.4 nm. Note the different values of Δzamp(16–84%)(Ni/Ag) = 12.7 nm, Δzamp(16–84%)(Ag/Ni) = 4.0 nm.

This work was partially supported by the Slovenian Research Agency (ARRS) through the Programme P2-0082 and bilateral project ARRS-BI-CN/17-18-003 between Slovenia and China, and is supported by the Science and Technology Planning Project of Guangdong Province, China (Grant No. 2017A010103021). References [1] K. Wittmaack, Basic aspects of sputter depth profiling, chap. 3 in: D. Briggs, M. P. Seah, eds., Practical Surf. Analysis Vol. 2-Ion and Neutral Spectroscopy, (Wiley, Chichester, UK 1992), pp. 105–175. [2] S. Hofmann, Auger- and X-ray Photoelectron Spectroscopy in Materials Science, Springer Verlag Heidelberg, New York, Dordrecht, London 2013, Chap. 7: quantitative compositional depth profiling, pp. 297–408. [3] ISO 18115-1:2013(E), Surface chemical analysis – vocabulary – part 1: general

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