Quantification of High Resolution Pulsed RF GDOES Depth Profiles for Mo/B₄C/Si Nano-Multilayers

Abstract

Pulsed-radio frequency glow discharge optical emission spectrometry (Pulsed-RF-GDOES) has exhibited great potential for high resolution (HR) depth profiling. In this paper, the measured GDOES depth profile of 60 × Mo (3 nm)/B₄C (0.3 nm)/Si (3.7 nm) was quantified by employing the newly extended Mixing-Roughness-Information depth (MRI) model. We evaluated the influences of the thickness and sputtering rate on the depth profile of very thin layers. We demonstrated that a method using the full width at half maximum (FWHM) value of the measured time-concentration profile for determining the sputtering rate and the corresponding thickness was not reliable if preferential sputtering took place upon depth profiling.

1. Introduction

Glow discharge optical emission spectrometry (GDOES) was initially developed for measuring the composition distribution of conductive thick films [1]. By introducing the Pulsed-Radio Frequency (RF) power, conductive and nonconductive thin film materials, including inorganic oxide and organic materials could be measured [2]. Currently, Pulsed-RF-GDOES has become a general and powerful depth profiling technique due to its extremely high sputtering rate in the order of 1 μm/min [3,4], all elements detectable (including hydrogen), and high depth resolution on the order of ~1 nm [5,6]. Research has demonstrated that Pulsed-RF-GDOES is very suitable for depth profiling from thick layers (more than hundred micrometers) to thin layers (several nm) [7,8].

The quantification of a monolayer depth profile has even shown that the depth resolution of Pulsed-RF-GDOES could sometimes reach the sub-nanometer range thanks to flexibility in adjusting the pulsed radio frequency parameters [9]. However, it is a great challenge for such ultrathin layers to come back to the original in-depth concentration profiles since all the distortion effects resulting from the GDOES depth profiling must be taken into account, i.e., preferential sputtering, atomic mixing from sputtering, surface/interface roughness resulting from sputtering, and/or sample nature or preparation, and the information depth from the analyzer. For this purpose, the Mixing-Roughness-Information (MRI) model [10] was proposed and further developed for the quantitative analysis of different kinds of depth profiles [11,12,13,14,15,16,17,18].

Mo/Si multilayers as reflective coatings have been widely used in free electron lasers and extreme ultra-violet (EUV) tools [19]. However, the high operating temperature of EUV tools results in the interdiffusion of Mo and Si atoms and, consequently, causes failure of the reflective coatings [20]. In order to enhance the thermal stability of Mo/Si multilayers under thermal loading, B₄C barrier films with excellent optical properties are usually sandwiched into multilayer films [21,22]. The B₄C barriers are usually extremely thin—less than 1 nm. Therefore, the characterization of multilayers with such ultrathin B₄C barriers becomes extremely difficult. Depth profiling by Pulsed-Rf-GDOES is one suitable solution to this challenge.

In this paper, the influences of the thickness and sputtering rate of inserted ultrathin (delta) layers (BC layers) on the depth profiles of elements A and D in an A/BC/D multilayer are quantitatively evaluated by the extended MRI model. As an example, the measured high resolution Pulsed-Rf-GDOES depth profiles of 60 × Mo (3 nm)/B₄C (0.3 nm)/Si (3.7 nm) nano-multilayer structure is quantitatively reconstructed. The sputtering rate of each element and the individual layer thicknesses in the Mo/B₄C/Si multilayer are obtained accordingly.

2. Extended MRI Model

The MRI model is a rather general, versatile, and frequently used method for quantitatively analyzing the measured depth profiles of multilayer obtained by AES, XPS, SIMS, and GDOES [9,23,24,25,26]. Recently, the conventional MRI model has been extended to a multi-elemental thin film system [27]. In this extended MRI model, the effect of roughness on the reconstructed in-depth concentration profile is expressed as:

$$X_A^{\sigma }(z)=\frac{1}{\sigma \sqrt{2\pi }}{\displaystyle \underset{z-\infty }{\overset{z+\infty }{\int }}{X}_A^0}(z^{\prime })\cdot \exp [\frac{{(z-z^{\prime })}^2}{2{\sigma }^2}]d{z}^{\prime }$$

(1)

where $X_A^0$ is the original distribution of composition concentration, σ is the roughness parameter, and z’ is an integral variable. The effects of atomic mixing and preferential sputtering are taken into account by the following equations [27]:

$$\frac{d{X}_i^S(z)}{dz}=\frac{-J_i/J+X_i^{\sigma }(z+w)}{w}$$

(2)

$$J_i/J=\frac{q_i{X}_i^S}{{\displaystyle \sum _i^m{X}_i^S{q}_i}}$$

(3)

where $X_i^{\sigma }(z+w)$ is the molar concentration of element i at the depth of z + w after considering the effect of roughness. $X_i^s$ is the surface concentration in mole fraction. w is the mixing length, and m is the number of elements. J_i (atom*m⁻²*s⁻¹) is the sputtered yield of element i in unit time, and J is the total sputtered yield in unit time. q_i represents the sputtering rate of pure element I, and q_t is the total sputtering rate. In most cases, the instantaneous sputtering rate can be estimated assuming a linear dependence on composition [28,29]. Therefore, converting the time scale (i.e., the measured depth profile) to the depth scale (i.e., the in-depth concentration profile), could be carried out by the following equation

$$t={\displaystyle \underset{0}{\overset{z}{\int }}\frac{1}{q_t}}dz={\displaystyle \underset{0}{\overset{z}{\int }}\frac{1}{{\displaystyle \sum _i^m{X}_i{q}_i}}}dz.$$

(4)

The contribution of information depth caused by the detected signal coming from the several sublayers underneath the surface layer to the normalized intensity is treated as follows [10,17]:

$$\frac{I_A}{I_0}(z)=X_A^S(z){\displaystyle \underset{z}{\overset{z+w}{\int }}\frac{1}{\lambda }}\exp [-\frac{(z-z^{\prime })}{\lambda }]d{z}^{\prime }+{\displaystyle \underset{z+w}{\overset{+\infty }{\int }}{X}_A^{\sigma }}(z^{\prime })\cdot \frac{1}{\lambda }\cdot \exp [-\frac{(z-z^{\prime })}{\lambda }]d{z}^{\prime }$$

(5)

where λ is called the information depth. Due to the low average energy of sputtered atoms in GDOES depth profiling, only the atoms of the topmost layer of sample are sputtered out and collected by the spectrometer. The atoms of the sublayers underneath of the surface layer have almost no influence on the detected signals; therefore, the λ could be set to zero, similarly to with SIMS depth profiling.

3. Simulation and Discussion

To illustrate the extended MRI model for a periodical multilayer (3×A/BC/D) with a delta layer of BC in each period, the sputter depth profiles were simulated with the same MRI parameters but with different sputtering rates or thickness values of the delta layer. For the following simulation, the original molar concentration of component B in the delta layer of BC was 0.8, the thickness of A layer (d_A) was 5 nm, and the total thickness of the BC layer (d_BC) and D layer (d_D) in each period maintained a constant value of 5.5 nm. For example, the thickness of D layer was 5 nm if the thickness of BC layer was 0.5 nm. To evaluate the influences of the sputtering rate and thickness of the delta layer (BC layer) on the depth profiles of components A and D, the simulations were carried out with constant MRI parameters of w and σ (2 nm). The parameters used for the simulations of Figure 1, Figure 2and Figure 3 are listed in

Table 1. The parameters used for the simulations of Figure 1, Figure 2 and Figure 3.

Figure	qA (nm/s)	qB (nm/s)	qC (nm/s)	qD (nm/s)	w (nm)	σ (nm)	dA (nm)	dBC (nm)	dD (nm)
Figure 1	8	change	qC = qB	8	2	2	5	0.5	5
Figure 2	8	3	3	8	2	2	5	change	5.5-dBC
Figure 3	8	3	3	change	2	2	5	0.5	5

.

Figure 1 shows the time-concentration profiles of the components A, D, and B in multilayers of 3×A/BC/D with the BC layer thickness of 0.5 nm for different sputtering rates of element B. Figure 1a shows that the time-concentration profiles of component A with q_B = 8 nm/s (black line) are almost the same as that with q_B = 6 nm/s (red line) but quite different when compared to the ones with low sputtering rates of q_B = 1 and 3 nm/s. As indicated in Figure 1a, the time difference in the second valley of the profiles for q_B = 6 and 1 nm/s is 0.4 s; therefore, the time difference in the last valley of the profiles would be 12 s if the periodic number of multilayers is 60.

Similar results were obtained in the time-concentration profiles for component D as indicated in Figure 1b; however, the time difference in the second valley of the profiles for q_B = 6 and 1 nm/s is 0.6 s. Figure 1c shows that the peak values of component B increased with sputtering time, particularly for a low sputtering rate of component B, e.g., q_B = 1 nm/s. This is because more atoms of B remain on the surface due to its low sputtering rate, and the sputtered yield is proportional to its concentration and the individual sputtering rate.

Figure 2 shows the time-concentration profiles of the components A, D, and B in multilayer of 3×A/BC/D for different thickness values of BC layer. As shown in Figure 2a−c, a small change in the thickness of BC layer may cause a notable change in the time-concentration profiles, particularly, for the component B. The concentration profile of component B changes not only the shift of the profile but also the concentration value. Meanwhile, Figure 2a,b shows that, with decreasing the thickness of BC layer, the concentration of A or D increases. Therefore, if there is no BC layer in between the A and D layers, the concentration of A or D will increase under the condition that the total thickness of each cycle is the same for the two-layer structures of A/BC/D and A/D.

Figure 3 shows the time-concentration profiles of components A, D, and B in multilayers of 3×A/BC/D for different sputtering rates of element D with a constant thickness of the delta layer. Clearly, with increasing the sputtering rate of element D, both the shift of the concentration profile and the total sputtering time for the whole multilayer decrease accordingly. Moreover, the increasing sputtering rate of element D leads to a decrease of the peak value of element D and an increase of that of element A. This is because a fast sputtering rate implies less atoms remaining on the surface consequently providing a decreasing peak value. In the simulations of Figure 3a−c, the layer thickness values of components A, D, and BC are 5, 5, and 0.5 nm, respectively, and the sputtering rates of elements A and B are constant values of 8 and 3 nm/s, respectively.

In practice, it is typical to take the FWHM of the measured time-concentration profile as the layer thickness by Δt(50%)*q(sputtering rate). The FWHM, i.e., Δt(50%) in the time-concentration profile is the time difference corresponding to 50% of the amplitude of each layer as shown in Figure 4a. However, based on the above simulation, the total sputtering time for the whole multilayer decreases with increasing the sputtering rate of element D so that the FWHMs of elements A and D decrease too as shown in Figure 4b. According to the simulation results of Figure 3a,b, the layer thickness values of elements A and D determined by Δt(50%)*q(sputtering rate) are displayed as a function of the sputtering rate of element D in Figure 4c.

Clearly, the determined thickness values in terms of FWHM are different from the real one of 5 nm. This indicates that the method using the FWHM of the measured time-concentration profile to determine the layer thickness is not reliable for multielement film systems due to preferential sputtering because the low sputtering rate of the BC layer has a strong impact on the concentration profiles of elements A and D. Similarly, it is also not reliable to predict the sputtering rate from the FWHM of measured time-concentration profile of multielement thin film when there is preferential sputtering.

4. Quantification of Measured Pulsed RF GDOES Depth Profile of Mo/B₄C/Si Multilayer

We applied the extended MRI model to quantitatively analyze the measured Pulsed-RF-GDOES depth profiles of a Mo/B₄C/Si multilayer, which is composed of a 60-layer periodic superlattice with a total thickness of 420 nm deposited on a Si(111) wafer. The details about the material layers thickness and the GDOES measurement are described in [30]. The main points are briefly summarized as follows. The total thickness of the Mo/B₄C/Si multilayer and the individual layer thickness values of the Mo, Si, and B₄C layers in each period were determined as 7.00 ± 0.05, 3.0 ± 0.2, 3.7 ± 0.2, and 0.3 nm, respectively, by HR-TEM and GIXRD techniques.

The experimental conditions of the pulsed RF GDOES measurement were as follows: argon pressure of 550 Pa, sputtering power of 17 W (corresponding to the average Ar⁺ sputtering energy of 50 eV), pulse frequency of 5 KHz, and duty cycle of 0.25. The emission intensities of excited sputtering atoms at 386.411 nm (Mo), 251.611 nm (Si), 249.678 nm (B), and 156.144 nm (C) wavelengths were recorded as a function of the sputtering time, and the results of the measured GDOES depth profile are displayed in Figure 5.

Clearly, the measured GDOES depth profile of 60 × Mo (3 nm)/B₄C (0.3 nm)/Si (3.7 nm) nano-multilayer correctly represents the corresponding layer structure and features a high-depth resolution as demonstrated with the B and C elemental profiles corresponding to the distinguished B₄C (0.3 nm) layer structure. A closer check of the measured depth profiles of B and C shows that the peak/valley positions are almost coincident, indicating that the sputtering rates of B and C could be regarded as the same. However, the intensity of the C signal and the whole C profile exhibit a continuous decrease with the sputtering time likely coming from residual surface contamination. For simplicity, the C profile will not be considered for quantification. For a better view of the fitted profile, the measured depth profile in the range of 15 to 35 s of sputtering time was selected for quantification.

When depth profiling a multilayer and analyzing sputtered elements, as in SIMS and GDOES depth profiling, a matrix effect may exist [31,32]. To investigate whether a matrix effect exists in this GDOES depth profiling of Mo/B₄C/Si multilayer, the plot of the intensity of Mo + B against that of Si + C is displayed in Figure 6. The obtained straight line implies that the sensitivity factors at each point of experimental data are almost the same, indicating no matrix effect at all in this GDOES depth profiling of the Mo/B₄C/Si multilayer.

With respect to the MRI parameters used for simulation, the atomic mixing length of w can be obtained by the Stopping and Range of Ions in Matter (SRIM) calculation [33,34]. From the SRIM code for Ar ions with an energy of 50 eV, the w values for the elements Mo, Si, and B(C) are 0.3, 0.8, and 0.6 nm, respectively. The roughness parameter σ can be measured by Atomic Force Microscopy (AFM), which is 0.7 nm after the sputtering of 30 periods for the Mo/B₄C/Si multilayer [30].

We demonstrated in Figure 3 that it was not reliable to predict the individual sputtering rate directly from the corresponding FWHM and its thickness if the sputtering rate of the B₄C layer is different from the ones of Mo or Si. This fact causes difficulty for the estimation of sputtering rates of elements in the Mo/B₄C/Si multilayer. Fortunately, the depth profiles of a binary Mo/Si multilayer with the same total thickness as that of the Mo/B₄C/Si multilayer were measured by GDOES under the same conditions in [30]. For comparing the difference of depth profiles between Mo/B₄C/Si and Mo/Si multilayers, the maximum peak value and the total sputtering time are listed in

Table 2. The maximum peak value and total sputtering time of the measured GDOES depth profiles for the Mo/B₄C/Si and Mo/Si multilayer samples.

Sample	60 × Mo (3 nm)/B4C (0.3 nm)/Si (3.7 nm)	60 × Mo (3.5 nm)/Si (3.5 nm)
Max. value of Mo peak	19.6	22.3
Max. value of Si peak	2.5	2.9
Total sputtering time	49 s	44 s

.

With the help of the above estimated parameters for simulation, the measured GDOES depth profiling data (open circles) were fitted by the extended MRI model, and the best results are plotted as solid lines in Figure 7a−c, respectively, for the elements Mo, B, and Si. The fitting MRI parameters are the atomic mixing length of 0.6 nm, the roughness parameter of 0.7 nm, and the sputtering rate of element Mo/B(C)/Si of 8.53/4.3/8.95 nm/s. The relative errors between the experimental data and the MRI fitted results are 5.5% for Mo, 6.7% for Si, and 12.5% for B.

As demonstrated by Figure 2a,b, if a B₄C layer is introduced in between Mo and Si layers, the peak value of Mo or Si in the Mo/B₄C/Si multilayer will decrease as compared with that in the Mo/Si multilayer. By Figure 1a,b, if the sputtering rate of the B(C) element is less than that of the Mo or Si element, the total sputtering time of Mo or Si in the Mo/B₄C/Si multilayer will increase as compared with that in the Mo/Si multilayer. Both facts were confirmed by the identical GDOES measurements for the Mo/B₄C/Si and Mo/Si multilayers as shown in Table 2.

Therefore, the average sputtering rate of Mo and Si could be estimated as about 9.5 nm/s by the total thickness (420 nm) and sputtering time (44 s) for the Mo/Si multilayer. Based on the simulation results presented in Figure 1 with respect to the variation of the peak value and total sputtering time, the sputtering rate of element B or C could be estimated to be half that of the element Mo or Si. This estimated value is reasonable by considering the relative sputtering rate. According to the experimental data in [35], the sputtering yields for argon ions with energy of 500 eV were 1, 1.1, and 0.4 (atoms/ion) for Si, Mo, and B/C, respectively.

The fitting error for the B depth profile is relatively larger due to the smaller intensity value and some scattered peak/valley points as shown in Figure 7c. According to the obtained MRI parameter values from fitting the measured GDOES depth profiling data, the depth resolution was then calculated as about 1.1 nm, indicating high-resolution depth profiling measurements [9].

By fitting the measured GDOES depth profiling data, the individual layer thickness in the Mo/B₄C/Si multilayer structure could be determined accurately as listed in

Table 3. The determined individual layer thickness by fitting the measured GDOES depth profiling data of the Mo/B₄C/Si multilayer.

No. of period	Mo (nm)	B4C (nm)	Si (nm)
1	3.00	0.30	3.90
2	2.90	0.30	3.98
3	2.90	0.30	3.98
4	2.90	0.30	3.80
5	3.00	0.30	3.82
6	3.00	0.29	3.90
7	3.00	0.30	3.80
8	3.00	0.29	3.70
9	3.00	0.30	3.70
10	3.00	0.30	3.70
11	3.00	0.30	3.70
12	3.00	0.30	3.70
13	3.00	0.30	3.70
14	3.00	0.30	3.70
15	3.00	0.30	3.70
16	3.00	0.30	3.70
17	3.00	0.30	3.70
18	2.80	0.30	3.60
19	2.80	0.30	3.60
20	3.00	0.30	3.60
21	3.00	0.32	3.60
22	3.00	0.32	3.50
23	3.00	0.30	3.70
24	3.00	0.30	3.70
25	3.00	0.30	3.70

. Clearly, the determined individual layer thickness is consistent with the one determined by HR-TEM and/or GIXRD techniques within an absolute error of 0.2 nm. Therefore, the reconstruction of the measured depth profile could provide an alternative way to determine the individual layer thickness in nano-multilayer structures.

5. Conclusions

The extended MRI model developed for multi-element thin films was successfully applied to quantify the measured GDOES depth profiling data of 60 × Mo (3 nm)/B₄C (0.3 nm)/Si (3.7 nm), and the MRI simulation results were in good agreement with the experimental data. With decreasing the sputtering rate of BC layer, the total sputtering time for depth profiling of the A/BC/D multilayer increased, and both the concentration values of element A and D decreased.

When a BC layer was introduced in between the A and D layers, even a small change of thickness could cause a large change in the time-concentration profiles of element A and D with respect to the total sputtering time and concentration. It is not reliable to determine the sputtering rate according to the measured FWHM in the time-concentration profile of multi-element layers when there is preferential sputtering.