## Abstract

Accurate optical emission spectroscopy (OES) measurements are necessary for plasma semiconductor processing and for optical emission analysis. In this paper we investigate the effects of self-absorption on the most important neutral Argon spectra lines. One of these Argon spectral lines (750 nm) is frequently used for actinometry. The experiment is performed in a reactive ion etch (RIE) capacitively coupled plasma (CCP) system. A comprehensive design of experiments has been created to establish all plasma conditions, power, pressure and gas flow rate which affect the Argon emission intensity by self-absorption. The results are then compared to theoretical calculated line ratios.

© 2012 OSA

## 1. Introduction

Plasma processing applications are of major importance for scientific and technological semiconductor manufacturing. Non-intrusive plasma diagnostic techniques, like optical emission spectroscopy (OES), are frequently used for measurement of electron density, electron temperature, gas temperature, plasma etch/deposition rate and wafer surface modification/interaction. For accurate measurement and prediction of these parameters, it is important to know the density of reactive species. The density is linked with external system parameters i.e. power, pressure, flow rate, etc. This can be determined by using optical diagnostic techniques like Laser-induced fluorescence (LIF) and/or OES actinometry.

Laser-induced fluorescence [1, 2] is an accurate and powerful technique for determining the density of the plasma species. However due to the bulky nature and complexity of the laser and optical systems it cannot be easily used in an industrial setting. OES actinometry is a more viable option.

Actinometry is a well known OES based technique for determination of reactive particle density. First introduced by Coburn and Chen [3] for estimating atomic fluorine density, developed for atomic oxygen by Walkup et al. [4], and improved upon by Katsch et al. [5]. The technique requires a small amount of an inert gas to be added to the plasma and to monitor the inert gas emission intensities simultaneously with the buffer gas to estimate the reactive particle density. Knowledge of the electron collision cross sections, the spectroscopic data of emission lines (i.e. frequency), Einstein’s coefficients and the electron energy distribution function (EEDF) is necessary in order to determine the atomic density. OES actinometry for monitoring oxygen [6] and nitrogen [7] can be used as a real time sensor for process control.

Our main goal for this work is to study the self-absorption of Argon. Argon is frequently used as an actinometer and for testing purposes it contains many well resolved, easily identifiable spectral lines, almost regardless of the spectral device resolving power.

Self-absorption is an effect when a photon emitted by an atom at one point in a light source may be absorbed by a different atom before it has a chance to escape from the source; this photon may be lost as a contribution to the original spectrum line either as a result of radiative decay to a different lower level or through collisional de-excitation of the absorbing atom. Self-absorption is a resonance process, and it is an important measurement for accurate OES diagnostics because it will have the effect of distorting and broadening the spectral lines and therefore produce larger width and incorrect line intensities [8]. In the same way that the probability of emission is greatest at the centre of the line, the probability of absorption is also greatest at the centre [9].

The transfer of radiation throughout inhomogeneous plasma has significant impact on the spectral lines shape. Optically thin conditions must prevail at the line centres, or appropriate corrections must be made when using the OES data for quantitative analysis. Many authors report large variations of widths and shifts within a multiplet without trying to determine the cause of these irregularities which are, most likely, caused by misidentification of lines or by the presence of self-absorption.

Several techniques exist for determining the effect of self-absorption. The most straight forward method is to check line intensity ratios within multiplets which abide by so-called LS-coupling rules [9]. The reduction in the observed intensity of the strongest or metastable line within the multiplet, in respect to the weakest spectral line in the same multiplet shows that self-absorption is present [8]. A variation of this technique is to vary the concentration of the species under study and then to observe variations in the intensity ratio with decreased concentration. While the spectral line ratio remains constant within the lines multiplet these plasmas are optically thin and do not require any correction for self-absorption.

A second technique to quantify self-absorption is to double the optical path length by placing a concave mirror at two focal lengths behind the plasma. Then if the increase in signal intensity, except for reflection and transmission losses, doubles there is no self-absorption. This technique however is difficult to implement in many setups (as ours) when the plasma is enclosed inside a stainless steel chamber with a limited number of viewports and the mirror itself would start to become etched, increasing the transmission losses.

Another technique for checking the self-absorption in homogeneous pulsed sources is to introduce an additional movable obstacle between the cathode and anode. By changing the position of the movable obstacle it’s possible to change the observed plasma length without significantly changing the plasma impedance. Plasma parameters remain constant while the observation length is changed, as in the previous case, by measuring the line shapes with two plasma lengths it is possible to determine the self-absorption.

For pulse plasma sources another possible check for the self-absorption could be to measure the full width at half maximum of the emission spectral line during plasma decay as discussed herein [10].

For comparison with the results, theoretical line ratios are calculated using line strengths, statistic weights, spectral line wavelengths and Einstein coefficients [11, 12].

## 2. Experimental setup & diagnostics

The experiments are performed in an Oxford Instruments plasma lab 100 reactive ion etch (RIE) chamber. The experimental setup is illustrated in Fig. 1 .

The chamber is configured as a parallel plate, capacitive discharge reactor driven by a 13.56 MHz radio-frequency (RF) power supply with automatic matching unit. Both electrodes are made of aluminium, 50 mm apart. The top grounded electrode is 290 mm in diameter, shower head gas inlet optimized for RIE. The cooled bottom powered electrode consists of a wafer clamp with helium backside cooling and holds a 200 mm diameter silicon wafer. When a wafer is not in use the lower electrode is protected by a quartz plate. Chamber volume is 15.31 litres. Max power for the system is up to 600 Watts. Total pressure of the system can be up to 1 Torr (133 Pa). The mass flow controllers for the gases used, Argon and Oxygen, can be set for a maximum of 50 standard cubic centimetres per minute (sccm) flow rate.

The OES spectrums were taken with a Horiba Jobin Yvon Czerny-Turner design Auto MicroHR spectrometer with focal length of 140 mm and spectral resolution of 0.25 nm at 400 nm wavelength. The spectrometer uses a Sygnature – Toshiba TCD 1304AP Linear Charge-couple device (CCD) with 3648 x 1 pixels, with a pixel size of 8 µm x 200 µm and spectral range of 200 nm to 1100 nm. Two gratings (1200 grooves/mm, 32 mm x 32 mm grating size) with blaze at 330 nm and 630 nm are present in the system. The slit entrance size is variable, for our experiments it is set at 10 µm for all measurements. The resolving power of the spectrometer can be seen in Fig. 2 .

For accurate results, the measure of the systems quantum efficiency has been performed according to a technique described by Milosavljević et al. [7, 13]. In this work we used a tungsten halogen calibration source, LSB 020, LSK 115 No. 18, 100 W, 6.60 A, power supply LSN 111.

Quantum efficiency of the system is show in Fig. 3 .

JMP^{®} desktop statistical software, for performing simple and complex statistical analyses, has been used to create a design of experiments (DOE) and when all the data has been collected, to explore, understand and visualize the results. Its main advantage is that it links statistical data with graphics, so that a large amount of multidimensional data can be easily shown and worked with.

A DOE was designed to evaluate which process inputs have the most significant impact on the process outputs, and what the target level of those inputs should be to achieve the most desired output. For the work presented here, to evaluate the self-absorption and the importance of the plasma input parameters on the self-absorption, a 360 step DOE was designed. The input parameters under evaluation are: 10 different values of power in watts, 9 different values of pressure in mTorr, and 5 different values for each flow rate of Ar and O_{2} in sccm. Without DOE a full-factorial experimental run would contain 2250 experimental steps.

## 3. Results

All the Argon spectral lines used for calculating the self-absorption are listed in Table 1
. These lines are part of the transition 4s-4p and contain five separate multiplets. The lower energy levels (*E _{i}*) vary between 11.55 to 11.83 eV and the upper energy levels (

*E*) vary between 12.90 to 13.48 eV [12].

_{k}The technique which is used to calculate the self-absorption involves evaluating the ratios of emission spectra from the same multiplet. With the energy levels of the spectral lines from the same multiplet being similar, there should be no change in the ratios due to changes in power, pressure or gas flow rate if there is no self-absorption [8, 14].

Theoretical line ratios are calculated using Eq. (1) [11]:

where, g_{k}is the upper level statistical weight, λ is the wavelength and A

_{ki}is the transition probability value. Results for Eq. (1) are shown in Table 2 for the selected Argon spectral lines.

The intensities (areas) of all spectral lines shown in Table 1 are evaluated for all the DOE design steps. The area means the integral intensity of the curve (the spectral line shape). The Quantum Efficiency of the spectrometer (Fig. 2) is taken into account for all intensities. The ratios are then calculated according to the rules already mentioned at end of the introduction section. The results are inputted into JMP statistical software were a prediction profiler model is used to create the results shown below.

The changing slopes for all parameters as shown in Fig. 4 for the 750/826 nm ratio indicates that self-absorption is present. The decreasing slope for rising power and pressure and increasing slope for rising gas flow with Argon gas increase being the most significant parameter affecting the slope. This is as expected since the more gas is introduced into the system the higher the gas density and thus the higher the probability of the light interacting with other atoms or molecules which will absorb its energy. The large ratio values on the y-axis are changing from 18 to 6. This is due to the large variation in intensity between the high intensity of spectral line at 750 nm and low intensity of spectral line at 826 nm.

The following graphs illustrate the rest of the Argon spectral line ratios from Table 1. The reproducibility of the results is very high, taking into account the 360 experimental runs.

Figures 4-11 shows the linear trends due to the selected DOE model, which has reduced the full set of experimental runs by a factor of six. Main purpose of this approach is to check for the presence of self-absorption. The reported linear trends of the self-absorption for the emission spectral lines gives significant information regarding the effect of the external experimental parameters on the self-absorption for the selected spectral lines.

## 4. Discussion

We have recorded Argon emissions from the ultraviolet, visible and near infrared spectrums. The selected Argon spectral line emissions are presented in Table 1. Unfortunately Argon spectra lines from the ultraviolet spectrum (around 420 nm) from 4s-5p transition have been recorded as single lines at the multiplet. Moreover for the range of experimental conditions covered by this work, the recorded spectral lines from this transition were difficult to measure. In the case of the other Argon spectral lines which belong to the visible and near infrared spectra, which have been selected, only those that have significant intensity, can be easily separated from neighboring spectra lines and the spectroscopic data are known. Self-absorption has the most significant impact on the highest intensity spectral lines within multiplets and on those spectral lines which the lower energy level is the metastable one. Therefore Table 1 contains Argon spectral lines which follow all the mentioned criteria. In addition to these criteria, Table 1 contains the Argon spectral lines with the lower intensity in the multiplet. We are assuming that those low intensity spectral lines are not affected by self-absorption [8]. This assumption is important for the approach and there is known methods [10] which can be used for checking this. The method [10] is for a pulse plasma source and our plasma generator has a continuous wave form at 13.56 MHz which is equivalent to about 74 ns time interval. For a pulse plasma source it is easy to find the line profile in conditions of negligible self-absorption. On the contrary, for continuous plasma sources with the time scale of 10’s of ns (plasma decay/creation) it is very difficult to find the line profile in conditions of negligible self-absorption.

Theoretical spectral line ratios for optical absorption are calculated and presented in Table 2 using Eq. (1). The selected spectral line ratios shown in Table 2 are the ratios between the high intensity spectral lines and the lower intensity spectral lines or the ratio between spectral lines which the lower energy level is the metastable and the lowest intensity from the multiplet. Table 2 is used for comparing with experimental results. Any deviation between experimental and theoretical data is an indication of self-absorption within that multiplet.

The graphs from Figs. 4 to Fig. 11 present trends of different spectral line ratios vs. external experimental parameters, such as power, pressure, Oxygen flow and Argon flow. Self-absorption for the Argon 750 nm spectral line shown in Fig. 4 is significant with changing power, Oxygen flow and Argon flow. However for changing pressure the self-absorption of this spectral line is not so significant. These results are based on the assumption that the 826 nm Argon spectral line is not affected by self-absorption, this spectral line being the weakest line in the multiplet. Unfortunately there is no other spectral line in the multiplet which can be used for checking the self-absorption.

Summarizing all other graphs, from Figs. 5 to Fig. 11, the results are shown in Table 3 . It can be seen from this table that the amount of self-absorption for changing power from 35 to 550 watts results in self-absorption importance from 0 to 38%, keeping all other parameters constant. Increasing the pressure from 20 to 900 mTorr and keeping all other parameters constant results in self-absorption influence on the selected Argon spectral lines from 14 to 38%. Oxygen flow, increasing from 15 to 45 sccm, results in a self-absorption influence from 0 to 41%, keeping all other parameters constant. Gas flow of Argon, increasing from 15 to 45 sccm, results in a self-absorption influence from 30 to 60%, keeping all other parameters constant.

It can be clearly seen from Table 3 how self-absorption is important for all selected Argon spectral lines, the increase in Argon flow having the most significant impact on the self-absorption.

For example, the spectral lines 801 nm and 750 nm, from Fig. 2, have been affected by self-absorption by 11% and 38%, respectively. These percentages are applied to the whole area (i.e. the integral intensity of spectral line curve), not only to the line peak (i.e. the height of the spectral line).

Table 4 represents some of the theoretical results from Table 2 and experimental results from Figs. 4 to Fig. 11.

The chosen Argon spectral lines (Table 4) have none or very small self-absorption as presented in Table 3. The constant difference amongst measured (S_{E}) and calculated (S_{Th}) theoretical line intensity ratios can be explained by taking into account the high uncertainties ( ± 50%) of the used transition probabilities as explained in reference [15]. There are some experimental techniques [16] which can be used for correction of transition probabilities.

Furthermore the plasma discharge in many experimental setups is inhomogeneous and therefore any optical diagnostics have to take this into account. The position of optical ports could be side-on or end-on and the viewports themselves play important roles in the observation of the plasma spectral emission. In the case of side-on observation (this work), there are two experimental approaches for collecting the light emission from the plasma. The first one collects the light along the radial directions of the chamber and represents the integral light emission effect, i.e. includes plasma emission across the whole chamber diameter (this work). The second approach involves using a set of focusing lenses, which gives the possibility to move the focusing point from the centre of the discharge toward the viewport, and then applying Abel’s inversion procedure it is possible to get a radial spectral distribution curve. The second method is very time consuming and with the extensive experimental campaign (360 experimental runs) it is not practical. The method used, in this work, for checking the self-absorption, uses as the input parameter the ratio of the spectral lines and therefore it is not so sensitive to the plasma variations (inhomogeneity).

As shown in Table 3, the impact of self-absorption is very significant for the 750 nm Argon spectral line. The 750 nm Argon spectral line is very important for Actinometry calculation [3–6], therefore the 750 nm Argon spectral line must always be checked and corrected for self-absorption. Also the Quantum Efficiency of the spectral device needs to be taken into account.

Figure 12 shows the Actinometry results, including self-absorption contribution and quantum efficiency of the spectrometer for atomic oxygen. The power is varied from 100 to 300 Watts, the pressure is kept constant at 100 mTorr, the Oxygen flow is set to 48 sccm and the Argon flow is set to 2 sccm. The self-absorption for the 750 nm Argon line is calculated as being approximately 25% for the range of RF power.

The Actinometry results show that the Oxygen atomic density is reduced due to the increase in the area of 750 nm Argon line. However the self-absorption of Oxygen is not being taken into account for this work, only for the Argon spectral lines, which would need to be evaluated, in order to have more accurate results.

## 5. Conclusion

Self-absorption has been widely neglected or its importance overlooked for plasma diagnostics. In this paper the influence of self-absorption on neutral Argon spectral lines for a range of parameters in an RIE plasma chamber has been studied. Almost all the measured Argon spectral lines have been affected, up to some level, by self-absorption. Some Argon spectral lines shapes are changed by self-absorption up to 60%. One of the most widely used Argon spectral line for plasma diagnostics, 750 nm, has its intensity affected by self-absorption by up to 40%.

There is fluctuation of the weight in the importance of self-absorption for the range of external parameters such as RF power, gas flow rate and total gas pressure. The gas flows have shown the most significant contribution on the self-absorption.

Correction of self-absorption is a necessary step for OES based plasma diagnostics. In the case of Actinometry calculation correction of self-absorption could change the final result up to 20%.

For the measured Argon spectral lines which are not affected by self-absorption there is a discrepancy between theoretically calculated and measured spectral line ratios. This difference can be attributed to the high uncertainties ( ± 50%) with the used transition probabilities.

## Acknowledgments

This material is based upon works supported by Science Foundation Ireland under grant No.08/SRC/I1411, Precision Strategic Research Cluster (SRC) and EU IMPROVE project. The authors are grateful to B. Dolinaj for help. V. Milosavljevic is grateful to the Ministry of Education and Science of the Republic of Serbia under grant No. OI171006.

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