- Email: [email protected]
Wavelet monitoring of spatial surface roughness for plasma diagnosis
Available online at www.sciencedirect.com
Microelectronic Engineering 84 (2007) 2810–2816 www.elsevier.com/locate/mee
Wavelet monitoring of spatial surface roughness for plasma diagnosis Byungwhan Kim *, Woo Suk Kim Department of Electronic Engineering, Sejong University, 98, Kunja-Dong, Kwangjin-Ki, 143-747 Seoul, Republic of Korea Received 27 February 2006; received in revised form 12 December 2006; accepted 9 February 2007 Available online 21 February 2007
Abstract To maintain device yield, plasma status should be stringently monitored. In this study, a new monitoring method for plasma diagnosis is presented. The method was based on a wavelet detection of surface roughness measured by atomic force microscopy. The wavelet enabled us to analyze spatial variations of surface roughness in vertical, lateral, and diagonal components. The sensitivity of spatial variation was examined in terms of a ratio pattern for the variations in process parameters. The ratio patterns were defined by the numerical values characterizing wavelet-decomposed images. The method was applied to the etching of a silicon oxynitride film in a C2F6 inductively coupled plasma. The process parameters involved include radiofrequency source power, bias power, pressure, and C2F6 flow rate. Applicability of this method was evaluated without or with respect to a fixed reference condition. In the case of a non-reference condition, a particular ratio for the diagonal component demonstrated the highest sensitivity to the variations in all parameters, but C2F6 flow rate. It is also noticeable that this ratio showed a strong correlation with actual surface roughness measurements. Meanwhile, in the case of one fixed reference, all ratio sensitivities were much higher than those for actual measurements for each component. A particular ratio for the lateral component yielded the highest sensitivity compared to other components. The proven high sensitivity indicates that the presented method can be effectively used for monitoring plasma conditions. 2007 Elsevier B.V. All rights reserved. Keywords: Plasma; Monitoring; Atomic force microscopy; Wavelet
1. Introduction In manufacturing integrated circuits, plasmas play a crucial role in depositing or etching fine patterns. To maintain process quality and device yield, plasma status should be stringently monitored and accurately diagnosed. Plasma status can be tracked by monitoring in situ or ex situ measurements. For in situ diagnostic, radicals or plasma impedance have been measured by optical emission spectroscopy [1], radiofrequency (RF) impedance sensor [2], or quadruple mass spectroscopy [3,4]. Rather than relying on a subsidiary diagnostic system, an equipment component such as a radiofrequency (RF) match network has been utilized for plasma monitoring [5] or for detecting an etch endpoint [6]. In the context of ex situ diagnostics, the etch rate is the most widely monitored in actual manu*
Corresponding author. Tel.: +82 2 3408 3729; fax: +82 2 3408 3329. E-mail address: [email protected] (B. Kim).
0167-9317/$ - see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2007.02.006
facturing sites. An etching profile measured with scanning electron microscope has recently been utilized for plasma monitoring [7]. This study demonstrated an improved diagnosis compared to conventional approaches based on the etch rate or approximated profile slope. Another etch characteristic that might be utilized for plasma diagnosis is the surface roughness of etched feature. This is supported by the report that the surface roughness was sensitive to the variations in process parameters [8]. It is therefore anticipated that by examining a variation in surface roughness plasma status can be monitored. Up to now, there has been no report regarding a plasma monitoring based on etched surface roughness. In this study, a new monitoring technique for plasma diagnosis is presented. This is accomplished by applying a wavelet to detect spatial variations of surface roughness. Previously, the wavelet transformation technique has been applied to the etching profile [7] or the match network sensor data [9]. The proposed technique was applied to the
B. Kim, W.S. Kim / Microelectronic Engineering 84 (2007) 2810–2816
etching of silicon oxynitride (SiON) film conducted in a C2F6 inductively coupled plasma (ICP) [10]. The surface roughness was measured by atomic force microscopy (AFM). Plasma status was varied by experimentally adjusting process parameters. The sensitivity of surface roughness is examined not only as a function of process parameters, but also in three (vertical, lateral, and diagonal) directions for a given parameter variation. The fault sensitivity of the proposed technique is also compared to that based on AFM measurement. 2. Experimental Schematic of an ICP etch system is shown in Fig. 1. The equipment was explained in detail [11]. Test patterns were fabricated on SiON wafers. Using a PECVD system, SiON films were deposited by about 4.09 lm thickness at 150 W rf power, 135 sccm N2O flow rate, and 45 sccm SiH4 flow rate, 350 C substrate temperature, and 0.2 Torr pressure. The refractive index of the deposited SiON films was about 1.46. To fabricate a Ni mask layer, photoresist patterns were first formed. A magnetron sputtering method was used to subsequently deposit Ni film of about 0.3 lm thickness on the patterned photoresist. The sputtering continued for 1 h at 8 mTorr pressure, 100 W rf power, and 6 sccm Ar flow rate. By removing the photoresist with acetone, Ni mask layer was formed. The SiON films were etched in a C2F6 ICP with the variations in the process parameters, including the source power, bias power, pressure, and C2F6 flow rate.. In all experiments, the etching time was set to 10 min. Images of surface roughness were taken by the AFM. 3. Wavelet theory A wavelet has an efficient space-frequency localization, which enables to examine local variations of signals or images at multiple levels. Fundamentals of discrete wavelet
13.56 MHz RF Power Matching Network
∼
Planar Coil Quartz Window Plasma Wafer Holder
High Vacuum Pump (Turbo+Rotary)
13.56 MHz RF Power
Fig. 1. Schematic of inductively coupled plasma etch system.
2811
transformation (DWT) [12] are briefly explained. When the DWT is applied to a function f, f can be approximated as X XX f ðtÞ ¼ ðf ; uj0;k Þuj0;k þ ðf ; Wj;k ÞWj;k ð1Þ k
j>j0
k
where u is an orthonormal basis for the scaled subspace Vj of a central subspace Vo. The other W forms an orthonormal basis for the subspace Wj, the complement of Vj. Both ðf ; uj0 ;k Þ and (f,Wj,k) are called the approximation (or scale) and detail (or wavelet) coefficients, respectively. As represented in (1), f can be approximated as the sum of the approximation of f at level j0 plus the details about f at j > jo. For a signal of length 2n, the decomposition is conducted n times, yielding n levels of different scales. The filter matrix initially of size n · n consists of two scaling and wavelet filters, each placed on the first and second half of the filter matrix, respectively. The wavelet filter produces the detailed parts of a signal, corresponding to the wavelet coefficients. The other scaling filter provides an approximated description of the signal, which is used as representative of the signal at the next decomposition. Filtering the signal with the filter matrix produces a filtered signal of the same length as the original one. The filtered signal obtained at this scale 1 contains approximated and detailed parts. In the next scale 2, only the approximation part is filtered by the down-scaled filter by a factor of two. In other words, the size of the filter matrix is reduced to n/2. This process is repeated until the scale n is reached. For an image such as an AFM photo, meanwhile, the decomposition is successively conducted by a pair of low and high pass filters, separately in two directions. The low and high pass filters provide the approximation and details of the image, respectively. The decomposition is first applied to each row of an image array. The high pass and low pass sub-images thereby obtained are each separately filtered columnwise, resulting in 4 sub-images corresponding to low–lowpass, low–highpass, high–lowpass, and high–highpass row column filtering, respectively. The DWT of two-dimensional image is mathematically detailed [12]. 4. Results 4.1. Wavelet characterization of surface roughness An image taken with AFM is shown in Fig. 2. The etching to obtain the AFM image was conducted at 400 W source power, 60 W bias power, 9 mTorr pressure, and 45 sccm C2F6 flow rate. The AFM image was subsequently transformed into an image represented in only black and white colors. The transformed image is shown in Fig. 3. The DWT was applied to this image at the scale level of 1 and the results are displayed in Fig. 4. As illustrated in Fig. 4, the original image was transformed into the approximated and detailed parts. The detailed part was further divided into the vertical (V), lateral (L), and diagonal (D) components. Both vertical and diagonal components were characterized
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B. Kim, W.S. Kim / Microelectronic Engineering 84 (2007) 2810–2816
Fig. 2. AFM image taken at 400 W source power, 60 W bias power, 9 mTorr pressure, and 45 sccm C2F6 flow rate.
Fig. 3. The processed AFM image in black and white colors.
in ‘‘0’’ or ‘‘255’’. The remaining lateral component was represented in ‘‘1’’, ‘‘9’’, or ‘‘16’’. The total number of numerical values comprising each component was 2304. The characterized number patterns corresponding to each component are depicted in Fig. 5. The variations in each pattern are expected to be different depending on plasma conditions. In other words, the detailed variations in each number pattern can provide useful clues to track or diagnose a variation in plasma condition. This is investigated as a function of process parameters. 4.2. Ratio sensitivity to process parameters To investigate the sensitivity of wavelet-transformed AFM patterns to the variations in process parameters, various ratios of numbers were defined and they are shown in Table 1. As shown in Table 1, a ratio characterizes a relative portion of any number with respect to the other number or to the total number of all entities (i.e., 2304) as stated earlier. For example, #0/2304 is the ratio of the total number of ‘‘0’’ to that of ‘‘0’’ and ‘‘255’’, which is 2304. The sensitivity of these ratios is examined as a function
of process parameters. It should be noted that in plotting all Figs. 6–8 appearing later the other parameters, but the one of interest were set to their default values. The default values are 700 W, 60 W, 9 mTorr, and 45 sccm, for the source power, bias power, pressure, and C2F6 flow rates, respectively. First, the source power was varied from 400 to 1000 W with the increment of 200 W. For each component, the ratio sensitivity to the source power variations are depicted in Fig. 6a–c. To facilitate the comparison, the ratio for #0/#255 in Figs. 6a and c was scaled with the largest value, because they were numerically too large. As seen in Fig. 6a, almost all ratios vary little with the source power variations in the range between 400 and 800 W. In contrast, all ratios substantially vary as the power increased from 800 to 1000 W. This implies a significant variation in the surface roughness and this could be ascertained by the corresponding experimental data. Actually, the surface roughness drastically increased from 1.79 to 2.27 nm. Among the four ratios, the ratio symbolized as the triangle seems to show the highest sensitivity to the power variations. To find out any correlation, both variations in the ratio and actual surface roughness measurement were compared. Interestingly, the variation of #0/#255 was consistent with the surface roughness variation in the reverse fashion for all power variations. The reverse fashion means that in each power interval the ratio increases (or decreases) as the surface roughness decreases (or increases). Due to the strong correction and high sensitivity, the identified ratio can be used to monitor the variations in surface roughness or plasma conditions. Fig. 6b shows the ratio sensitivity to the power variations for the lateral component. As displayed in Fig. 6b, the ratio corresponding to #16/#255 yields the smallest sensitivity. The sensitivities of the other two ratios seem to be almost comparable. The ratio sensitivity for the diagonal component is shown in Fig. 6c. The sensitivity of each ratio appears to be similar to that already observed in Fig. 6a. However, for each ratio pattern, enhanced sensitivity of the diagonal component is demonstrated over the vertical component. As seen in Figs. 6a or c, the ratio of #0/#255 yields the highest sensitivity to the power variations. The #0/#255 for the diagonal component shows enhanced sensitivity compared to that for the vertical component. In each power interval, the #0/ #255 also demonstrates enhanced sensitivity over the ratio sensitivity of #1/#2304 or #9/#2304 for the lateral component. In consequence, the most effective ratio for plasma monitoring is determined as 0/#255 for the diagonal component. As noticed earlier, the diagonal component demonstrated the highest ratio sensitivity to the source power variations. This was also true for the variations in other parameters. Therefore, the ratio sensitivity for other parameters is examined only for the diagonal component. The results are shown in Fig. 7a–c. Fig. 7a shows the ratio sensitivity to the bias power variation. As depicted in Fig. 7a, the ratio of #0/#255 is seen to yield the highest sensitivity to the power variations. This is identical to that
B. Kim, W.S. Kim / Microelectronic Engineering 84 (2007) 2810–2816
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Magnitude of Wavelet Coefficients (a.u.)
Fig. 4. Wavelet transformed AFM image.
300
250
200
Vertical
Lateral
Diagonal
150
100
50
0 1
167
333
499
665
831
997 1163 1329 1495 1661 1827 1993 2159
Number
Fig. 5. Wavelet coefficients for vertical, lateral, and diagonal component.
Table 1 Ratios defined for each wavelet component Wavelet components
Ratios
Vertical Lateral Diagonal
#0/2304, #255/2304, #0/#255, #255/#0 #1/2304, #9/2304, #16/#255 #0/2304, #255/2304, #0/#255, #255/#0
for the source power variation. It has been reported that the surface roughness generally increases with increasing the bias power, mainly due to enhanced ion bombardment
[13]. In the current etching experiment, this report is partly supported by the increasing surface roughness from 2.2 to 2.5 nm on increasing the bias power from 45 to 90 W. From this perspective, the variation of the identified ratio is consistent with the surface roughness variation in the reverse fashion. Interestingly, these results are in good agreement with those obtained for the source power variation. The ratio sensitivity to the pressure variation is depicted in Fig. 7b. The highest sensitivity is observed for the ratio of #0/#255. This observation coincides with that identified for the variation either in the source power or bias power. It is also interesting that the variation of the identified ratio is consistent with the corresponding surface roughness variation in most of pressure range, 8–12 mTorr. This can be ascertained by referring to the experimental measurements, 2.51, 2.24, and 2.96 nm, measured at 8, 10, and 12 mTorr, respectively. The ratio sensitivity to the variations in C2F6 flow rate is shown in Fig. 7c. Among the ratios, the ratio of #255/#0 exhibits the highest sensitivity to the flow rate variations. Meanwhile, the variation of #0/#255 is very similar to the surface roughness variation. This can be verified by observing the roughness measurements, 2.14, 1.42, 1.42, and 1.74 nm, respectively. In consequence, the sensitivity analysis reveals that there exists one particular ratio yielding the highest sensitivity for each parameter varia-
Ratio of Sensitivity for L-AFM
B. Kim, W.S. Kim / Microelectronic Engineering 84 (2007) 2810–2816
Ratio Sensitivity for V-AFM
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1.2 1.0 0.8 0.6 0.4
#0/2304 #0/#255
#255/2304 #255/#0
0.2 0.0 400
600
800
1.2 1.0 0.8 0.6
#1/2304
#16/2304
0.2 0.0
1000
400
600
Source Power (W) Ratio Sensitivity for D-AFM
#9/2304
0.4
800
1000
Source Power (W)
1.2 1.0 0.8 0.6 #0/2304 #0/#255
0.4
#255/2304 #255/#0
0.2 0.0 400
600
800
1000
Source Power (W)
1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0
#0/2304 #0/#255
#255/2304 #255/#0
45 75 Bias Power (W)
Ratio Sensitivity for D-AFM
30
Ratio of Sensitivity for D-AFM
Ratio Sensitivity for D-AFM
Fig. 6. (a) Ratio sensitivity for vertical component as a function of source power, (b) ratio sensitivity for lateral component as a function of source power and (c) ratio sensitivity for diagonal component as a function of source power.
90
1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0
1.2 1.0 0.8
40
#255/2304 #255/#0
0.4 0.2 0.0 6
#0/2304 #0/#255
30
#0/2304 #0/#255
0.6
8 10 Pressure (mTorr)
12
#255/2304 #255/#0
50
60
C2F6 Flow Rate (sccm) Fig. 7. (a) Ratio sensitivity for the diagonal component as a function of bias power, (b) ratio sensitivity for the diagonal component as a function of pressur and (c) ratio sensitivity for the diagonal component as a function of C2F6 flow rate.
tion. Interestingly, the identified ratio (#0/#255) was same for all parameters but C2F6 flow rate. Also, this particular ratio was strongly correlated to the actual roughness measurements. All these results indicate that the identified ratio can be utilized to monitor plasma states.
4.3. Ratio sensitivity to one fixed reference Next, the ratio sensitivity is evaluated with respect to one fixed reference condition. In the case of the source power variation, the reference condition was set to 400 W
4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0
#0/2304 #0/#255
Percent Sensitivity for L-AFM (%)
Percent Sensitivity for V-AFM (%)
B. Kim, W.S. Kim / Microelectronic Engineering 84 (2007) 2810–2816
#255/2304 #255/#0
600
800
16 14 12 10 8 6 4 2 0
1000
#1/2304
#9/2304
600
800 Source Power (W)
Percent Sensitivity for D-AFM (%)
Source Power (W)
5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0
#0/2304 #0/#255
2815
#16/2304
1000
#255/2304 #255/#0
600
800
1000
Source Power (W)
Fig. 8. (a) Percent sensitivity for the vertical component as a function of source power, (b) percent sensitivity for the lateral component as a function of source power and (c) percent sensitivity for the diagonal component as a function of source power.
where x indicates a level of the source power. The PSs were calculated for various ratios depicted in Figs. 6a–c, and the calculated PSs are illustrated in Figs. 8a–c. As depicted in Fig. 8a, the ratio of #255/#0 for the vertical component yields the highest sensitivity. This is also true for the diagonal component. For the lateral component, the ratio of #16/#255 demonstrates the highest sensitivity, which is numerically much larger than that corresponding to #255/#0. In consequence, monitoring the ratio of #16/ #255 for the lateral component seems to be the most effective in detecting plasma variations for the source power variation. As conducted in the case of source power, the ratio sensitivity to the reference condition was calculated for other process parameters. The reference conditions were 30 W, 6 mTorr, and 30 sccm for the bias power, pressure, and C2F6 flow rate, respectively. For a given parameter variation, the ratios exhibiting the highest sensitivity are shown in Table 2 for each component. To facilitate the comparison, the total percent sensitivity (TPS) was calculated for the ratios shown in Table 1. The TPS is simply the sum of PSs defined in (2). For example, the TPS for the source power is calculated as TPS ¼
1000 X x¼600
Table 2 The ratios with the highest sensitivity determined for each wavelet component Parameters
V
L
D
SP BP P C2F6 Flow Rate
#255/#0 #0/#255 #0/#255 #0/#255
#16/#255 #16/#255 #16/#255 #16/#255
#255/#0 #0/#255 #0/#255 #0/#255
The results are displayed in Fig. 9. In Fig. 9, the abbreviations of SP, BP, and P represent the source power, bias power, and pressure, respectively. As illustrated in Fig. 9, the TPS is also compared to another TPS calculated with actual surface roughness measurements. It is common that each TPS for each component demonstrates a higher sensitivity for all parameter variations compared to the TPS for the actual measurement. Another common observation is
35 30
Total Sensitivity
with setting other parameters to their default values already mentioned. The sensitivity was measured in terms of the percent sensitivity (PS) defined as Ratiox Ratio400 PSx ¼ 100ð%Þ ð2Þ Ratio400
Raw L
25
V D
20 15 10 5 0 SP
BP
P
C2F6
Process Parameters
PSx
ð3Þ
Fig. 9. Comparison of total percent sensitivity as a function of process parameters.
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B. Kim, W.S. Kim / Microelectronic Engineering 84 (2007) 2810–2816
that the TPS for the lateral component yields the highest sensitivity for all parameter variations. This is not consistent with the component (i.e. diagonal) already noticed in the case of the non-reference condition. This inconsistency implies that depending on the monitoring schemes different components and ratios should be monitored. 5. Conclusions In this study, a new monitoring technique was presented. Compared to in situ-based monitoring techniques, the presented one is differentiated in that it was based on ex situ etch measurement. The main idea for plasma monitoring was to utilize a spatial variation of surface roughness measured by atomic force microscopy. Wavelets played a crucial role in characterizing detailed variations in surface roughness. Applying the wavelet enabled us to analyze the ratio sensitivity in three components as a function of process parameters. The proposed technique was evaluated in two situations, with or without a reference condition. In the case of the no reference condition, a particular ratio yielding the highest sensitivity existed for nearly all parameter variations. This was more transparent as the plasma was monitored with respect to one reference condition. Moreover, the identified ratio yielded a much higher sensitivity than that measured on the basis of actual measurement. All these results indicate that the presented technique can be applied to strictly monitor plasma conditions. It is expected that by combining the ex situ monitoring technique with the current in situ monitoring plasma status could be more stringently detected. The effectiveness of the presented technique may further be improved by
detailing spatial surface roughness with a more sophisticated AFM. Acknowledgements This study was supported by ‘‘System IC 2010’’ Project of the Korea Ministry of Commerce, Industry, and Energy, and partly by the MIC (Ministry of Information and Communication), Korea, under the ITRC (Information Technology Research Center) support program supervised by the IITA (Institute of Information Technology Advancement) (IITA-2006-C109006030030). References [1] J.O. Stevenson, P.P. Ward, M.L. Smith, R.J. Markle, Sur. Interf. Anal. 26 (1998) 124. [2] S. Bushman, T.F. Edgar, I.J. Trachtenberg, J. Electrochem. Soc. 144 (1997) 721. [3] H. Sugai, K. Nakamura, Y. Hikosaka, M. Nakamura, J. Vac. Sci. Technol. A 13 (1995) 887. [4] R.H.M. van de Leur, A.J.G. Shellingerhout, J.E. Moij, F. Tuinstra, Appl. Phys. Lett. 52 (1988) 1005. [5] B. Kim, C.J. Lee, J. Vac. Sci. Technol. A 18 (2000) 58. [6] M. Kanoh, M. Yamage, H. Takada, Jpn. J. Appl. Phys. 40 (2001) 1457. [7] B. Kim, W. Choi, M.T. Lim, J. Vac. Sci. Technol. B 21 (2003) 2329. [8] B. Kim, H.J. Choi, B.T. Lee, J. Vac. Sci. Technol. A 20 (2002) 424. [9] B. Kim, S. Kim, Chemometr. Intell. Lab. Syst. 65 (2003) 231. [10] B. Kim, D. Lee, N. Kim, B. Lee, J. Vac. Sci. Technol. A 23 (2005) 520. [11] B. Kim, S. Kim, S.C. Ahn, B.T. Lee, Thin Solid Films 434 (2003) 276. [12] L. Prasad, S.S. lyengar, Wavelet Analysis with Applications to Image Processing, CRC Press, Boca Raton, FL, 1997. [13] B. Kim, K. Kim, B.T. Lee, Appl. Surf. Sci. 217 (2003) 261.
Microelectronic Engineering 84 (2007) 2810–2816 www.elsevier.com/locate/mee
Wavelet monitoring of spatial surface roughness for plasma diagnosis Byungwhan Kim *, Woo Suk Kim Department of Electronic Engineering, Sejong University, 98, Kunja-Dong, Kwangjin-Ki, 143-747 Seoul, Republic of Korea Received 27 February 2006; received in revised form 12 December 2006; accepted 9 February 2007 Available online 21 February 2007
Abstract To maintain device yield, plasma status should be stringently monitored. In this study, a new monitoring method for plasma diagnosis is presented. The method was based on a wavelet detection of surface roughness measured by atomic force microscopy. The wavelet enabled us to analyze spatial variations of surface roughness in vertical, lateral, and diagonal components. The sensitivity of spatial variation was examined in terms of a ratio pattern for the variations in process parameters. The ratio patterns were defined by the numerical values characterizing wavelet-decomposed images. The method was applied to the etching of a silicon oxynitride film in a C2F6 inductively coupled plasma. The process parameters involved include radiofrequency source power, bias power, pressure, and C2F6 flow rate. Applicability of this method was evaluated without or with respect to a fixed reference condition. In the case of a non-reference condition, a particular ratio for the diagonal component demonstrated the highest sensitivity to the variations in all parameters, but C2F6 flow rate. It is also noticeable that this ratio showed a strong correlation with actual surface roughness measurements. Meanwhile, in the case of one fixed reference, all ratio sensitivities were much higher than those for actual measurements for each component. A particular ratio for the lateral component yielded the highest sensitivity compared to other components. The proven high sensitivity indicates that the presented method can be effectively used for monitoring plasma conditions. 2007 Elsevier B.V. All rights reserved. Keywords: Plasma; Monitoring; Atomic force microscopy; Wavelet
1. Introduction In manufacturing integrated circuits, plasmas play a crucial role in depositing or etching fine patterns. To maintain process quality and device yield, plasma status should be stringently monitored and accurately diagnosed. Plasma status can be tracked by monitoring in situ or ex situ measurements. For in situ diagnostic, radicals or plasma impedance have been measured by optical emission spectroscopy [1], radiofrequency (RF) impedance sensor [2], or quadruple mass spectroscopy [3,4]. Rather than relying on a subsidiary diagnostic system, an equipment component such as a radiofrequency (RF) match network has been utilized for plasma monitoring [5] or for detecting an etch endpoint [6]. In the context of ex situ diagnostics, the etch rate is the most widely monitored in actual manu*
Corresponding author. Tel.: +82 2 3408 3729; fax: +82 2 3408 3329. E-mail address: [email protected] (B. Kim).
0167-9317/$ - see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2007.02.006
facturing sites. An etching profile measured with scanning electron microscope has recently been utilized for plasma monitoring [7]. This study demonstrated an improved diagnosis compared to conventional approaches based on the etch rate or approximated profile slope. Another etch characteristic that might be utilized for plasma diagnosis is the surface roughness of etched feature. This is supported by the report that the surface roughness was sensitive to the variations in process parameters [8]. It is therefore anticipated that by examining a variation in surface roughness plasma status can be monitored. Up to now, there has been no report regarding a plasma monitoring based on etched surface roughness. In this study, a new monitoring technique for plasma diagnosis is presented. This is accomplished by applying a wavelet to detect spatial variations of surface roughness. Previously, the wavelet transformation technique has been applied to the etching profile [7] or the match network sensor data [9]. The proposed technique was applied to the
B. Kim, W.S. Kim / Microelectronic Engineering 84 (2007) 2810–2816
etching of silicon oxynitride (SiON) film conducted in a C2F6 inductively coupled plasma (ICP) [10]. The surface roughness was measured by atomic force microscopy (AFM). Plasma status was varied by experimentally adjusting process parameters. The sensitivity of surface roughness is examined not only as a function of process parameters, but also in three (vertical, lateral, and diagonal) directions for a given parameter variation. The fault sensitivity of the proposed technique is also compared to that based on AFM measurement. 2. Experimental Schematic of an ICP etch system is shown in Fig. 1. The equipment was explained in detail [11]. Test patterns were fabricated on SiON wafers. Using a PECVD system, SiON films were deposited by about 4.09 lm thickness at 150 W rf power, 135 sccm N2O flow rate, and 45 sccm SiH4 flow rate, 350 C substrate temperature, and 0.2 Torr pressure. The refractive index of the deposited SiON films was about 1.46. To fabricate a Ni mask layer, photoresist patterns were first formed. A magnetron sputtering method was used to subsequently deposit Ni film of about 0.3 lm thickness on the patterned photoresist. The sputtering continued for 1 h at 8 mTorr pressure, 100 W rf power, and 6 sccm Ar flow rate. By removing the photoresist with acetone, Ni mask layer was formed. The SiON films were etched in a C2F6 ICP with the variations in the process parameters, including the source power, bias power, pressure, and C2F6 flow rate.. In all experiments, the etching time was set to 10 min. Images of surface roughness were taken by the AFM. 3. Wavelet theory A wavelet has an efficient space-frequency localization, which enables to examine local variations of signals or images at multiple levels. Fundamentals of discrete wavelet
13.56 MHz RF Power Matching Network
∼
Planar Coil Quartz Window Plasma Wafer Holder
High Vacuum Pump (Turbo+Rotary)
13.56 MHz RF Power
Fig. 1. Schematic of inductively coupled plasma etch system.
2811
transformation (DWT) [12] are briefly explained. When the DWT is applied to a function f, f can be approximated as X XX f ðtÞ ¼ ðf ; uj0;k Þuj0;k þ ðf ; Wj;k ÞWj;k ð1Þ k
j>j0
k
where u is an orthonormal basis for the scaled subspace Vj of a central subspace Vo. The other W forms an orthonormal basis for the subspace Wj, the complement of Vj. Both ðf ; uj0 ;k Þ and (f,Wj,k) are called the approximation (or scale) and detail (or wavelet) coefficients, respectively. As represented in (1), f can be approximated as the sum of the approximation of f at level j0 plus the details about f at j > jo. For a signal of length 2n, the decomposition is conducted n times, yielding n levels of different scales. The filter matrix initially of size n · n consists of two scaling and wavelet filters, each placed on the first and second half of the filter matrix, respectively. The wavelet filter produces the detailed parts of a signal, corresponding to the wavelet coefficients. The other scaling filter provides an approximated description of the signal, which is used as representative of the signal at the next decomposition. Filtering the signal with the filter matrix produces a filtered signal of the same length as the original one. The filtered signal obtained at this scale 1 contains approximated and detailed parts. In the next scale 2, only the approximation part is filtered by the down-scaled filter by a factor of two. In other words, the size of the filter matrix is reduced to n/2. This process is repeated until the scale n is reached. For an image such as an AFM photo, meanwhile, the decomposition is successively conducted by a pair of low and high pass filters, separately in two directions. The low and high pass filters provide the approximation and details of the image, respectively. The decomposition is first applied to each row of an image array. The high pass and low pass sub-images thereby obtained are each separately filtered columnwise, resulting in 4 sub-images corresponding to low–lowpass, low–highpass, high–lowpass, and high–highpass row column filtering, respectively. The DWT of two-dimensional image is mathematically detailed [12]. 4. Results 4.1. Wavelet characterization of surface roughness An image taken with AFM is shown in Fig. 2. The etching to obtain the AFM image was conducted at 400 W source power, 60 W bias power, 9 mTorr pressure, and 45 sccm C2F6 flow rate. The AFM image was subsequently transformed into an image represented in only black and white colors. The transformed image is shown in Fig. 3. The DWT was applied to this image at the scale level of 1 and the results are displayed in Fig. 4. As illustrated in Fig. 4, the original image was transformed into the approximated and detailed parts. The detailed part was further divided into the vertical (V), lateral (L), and diagonal (D) components. Both vertical and diagonal components were characterized
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B. Kim, W.S. Kim / Microelectronic Engineering 84 (2007) 2810–2816
Fig. 2. AFM image taken at 400 W source power, 60 W bias power, 9 mTorr pressure, and 45 sccm C2F6 flow rate.
Fig. 3. The processed AFM image in black and white colors.
in ‘‘0’’ or ‘‘255’’. The remaining lateral component was represented in ‘‘1’’, ‘‘9’’, or ‘‘16’’. The total number of numerical values comprising each component was 2304. The characterized number patterns corresponding to each component are depicted in Fig. 5. The variations in each pattern are expected to be different depending on plasma conditions. In other words, the detailed variations in each number pattern can provide useful clues to track or diagnose a variation in plasma condition. This is investigated as a function of process parameters. 4.2. Ratio sensitivity to process parameters To investigate the sensitivity of wavelet-transformed AFM patterns to the variations in process parameters, various ratios of numbers were defined and they are shown in Table 1. As shown in Table 1, a ratio characterizes a relative portion of any number with respect to the other number or to the total number of all entities (i.e., 2304) as stated earlier. For example, #0/2304 is the ratio of the total number of ‘‘0’’ to that of ‘‘0’’ and ‘‘255’’, which is 2304. The sensitivity of these ratios is examined as a function
of process parameters. It should be noted that in plotting all Figs. 6–8 appearing later the other parameters, but the one of interest were set to their default values. The default values are 700 W, 60 W, 9 mTorr, and 45 sccm, for the source power, bias power, pressure, and C2F6 flow rates, respectively. First, the source power was varied from 400 to 1000 W with the increment of 200 W. For each component, the ratio sensitivity to the source power variations are depicted in Fig. 6a–c. To facilitate the comparison, the ratio for #0/#255 in Figs. 6a and c was scaled with the largest value, because they were numerically too large. As seen in Fig. 6a, almost all ratios vary little with the source power variations in the range between 400 and 800 W. In contrast, all ratios substantially vary as the power increased from 800 to 1000 W. This implies a significant variation in the surface roughness and this could be ascertained by the corresponding experimental data. Actually, the surface roughness drastically increased from 1.79 to 2.27 nm. Among the four ratios, the ratio symbolized as the triangle seems to show the highest sensitivity to the power variations. To find out any correlation, both variations in the ratio and actual surface roughness measurement were compared. Interestingly, the variation of #0/#255 was consistent with the surface roughness variation in the reverse fashion for all power variations. The reverse fashion means that in each power interval the ratio increases (or decreases) as the surface roughness decreases (or increases). Due to the strong correction and high sensitivity, the identified ratio can be used to monitor the variations in surface roughness or plasma conditions. Fig. 6b shows the ratio sensitivity to the power variations for the lateral component. As displayed in Fig. 6b, the ratio corresponding to #16/#255 yields the smallest sensitivity. The sensitivities of the other two ratios seem to be almost comparable. The ratio sensitivity for the diagonal component is shown in Fig. 6c. The sensitivity of each ratio appears to be similar to that already observed in Fig. 6a. However, for each ratio pattern, enhanced sensitivity of the diagonal component is demonstrated over the vertical component. As seen in Figs. 6a or c, the ratio of #0/#255 yields the highest sensitivity to the power variations. The #0/#255 for the diagonal component shows enhanced sensitivity compared to that for the vertical component. In each power interval, the #0/ #255 also demonstrates enhanced sensitivity over the ratio sensitivity of #1/#2304 or #9/#2304 for the lateral component. In consequence, the most effective ratio for plasma monitoring is determined as 0/#255 for the diagonal component. As noticed earlier, the diagonal component demonstrated the highest ratio sensitivity to the source power variations. This was also true for the variations in other parameters. Therefore, the ratio sensitivity for other parameters is examined only for the diagonal component. The results are shown in Fig. 7a–c. Fig. 7a shows the ratio sensitivity to the bias power variation. As depicted in Fig. 7a, the ratio of #0/#255 is seen to yield the highest sensitivity to the power variations. This is identical to that
B. Kim, W.S. Kim / Microelectronic Engineering 84 (2007) 2810–2816
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Magnitude of Wavelet Coefficients (a.u.)
Fig. 4. Wavelet transformed AFM image.
300
250
200
Vertical
Lateral
Diagonal
150
100
50
0 1
167
333
499
665
831
997 1163 1329 1495 1661 1827 1993 2159
Number
Fig. 5. Wavelet coefficients for vertical, lateral, and diagonal component.
Table 1 Ratios defined for each wavelet component Wavelet components
Ratios
Vertical Lateral Diagonal
#0/2304, #255/2304, #0/#255, #255/#0 #1/2304, #9/2304, #16/#255 #0/2304, #255/2304, #0/#255, #255/#0
for the source power variation. It has been reported that the surface roughness generally increases with increasing the bias power, mainly due to enhanced ion bombardment
[13]. In the current etching experiment, this report is partly supported by the increasing surface roughness from 2.2 to 2.5 nm on increasing the bias power from 45 to 90 W. From this perspective, the variation of the identified ratio is consistent with the surface roughness variation in the reverse fashion. Interestingly, these results are in good agreement with those obtained for the source power variation. The ratio sensitivity to the pressure variation is depicted in Fig. 7b. The highest sensitivity is observed for the ratio of #0/#255. This observation coincides with that identified for the variation either in the source power or bias power. It is also interesting that the variation of the identified ratio is consistent with the corresponding surface roughness variation in most of pressure range, 8–12 mTorr. This can be ascertained by referring to the experimental measurements, 2.51, 2.24, and 2.96 nm, measured at 8, 10, and 12 mTorr, respectively. The ratio sensitivity to the variations in C2F6 flow rate is shown in Fig. 7c. Among the ratios, the ratio of #255/#0 exhibits the highest sensitivity to the flow rate variations. Meanwhile, the variation of #0/#255 is very similar to the surface roughness variation. This can be verified by observing the roughness measurements, 2.14, 1.42, 1.42, and 1.74 nm, respectively. In consequence, the sensitivity analysis reveals that there exists one particular ratio yielding the highest sensitivity for each parameter varia-
Ratio of Sensitivity for L-AFM
B. Kim, W.S. Kim / Microelectronic Engineering 84 (2007) 2810–2816
Ratio Sensitivity for V-AFM
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1.2 1.0 0.8 0.6 0.4
#0/2304 #0/#255
#255/2304 #255/#0
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600
800
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1.2 1.0 0.8 0.6 #0/2304 #0/#255
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1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0
#0/2304 #0/#255
#255/2304 #255/#0
45 75 Bias Power (W)
Ratio Sensitivity for D-AFM
30
Ratio of Sensitivity for D-AFM
Ratio Sensitivity for D-AFM
Fig. 6. (a) Ratio sensitivity for vertical component as a function of source power, (b) ratio sensitivity for lateral component as a function of source power and (c) ratio sensitivity for diagonal component as a function of source power.
90
1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0
1.2 1.0 0.8
40
#255/2304 #255/#0
0.4 0.2 0.0 6
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8 10 Pressure (mTorr)
12
#255/2304 #255/#0
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C2F6 Flow Rate (sccm) Fig. 7. (a) Ratio sensitivity for the diagonal component as a function of bias power, (b) ratio sensitivity for the diagonal component as a function of pressur and (c) ratio sensitivity for the diagonal component as a function of C2F6 flow rate.
tion. Interestingly, the identified ratio (#0/#255) was same for all parameters but C2F6 flow rate. Also, this particular ratio was strongly correlated to the actual roughness measurements. All these results indicate that the identified ratio can be utilized to monitor plasma states.
4.3. Ratio sensitivity to one fixed reference Next, the ratio sensitivity is evaluated with respect to one fixed reference condition. In the case of the source power variation, the reference condition was set to 400 W
4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0
#0/2304 #0/#255
Percent Sensitivity for L-AFM (%)
Percent Sensitivity for V-AFM (%)
B. Kim, W.S. Kim / Microelectronic Engineering 84 (2007) 2810–2816
#255/2304 #255/#0
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16 14 12 10 8 6 4 2 0
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Percent Sensitivity for D-AFM (%)
Source Power (W)
5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0
#0/2304 #0/#255
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#16/2304
1000
#255/2304 #255/#0
600
800
1000
Source Power (W)
Fig. 8. (a) Percent sensitivity for the vertical component as a function of source power, (b) percent sensitivity for the lateral component as a function of source power and (c) percent sensitivity for the diagonal component as a function of source power.
where x indicates a level of the source power. The PSs were calculated for various ratios depicted in Figs. 6a–c, and the calculated PSs are illustrated in Figs. 8a–c. As depicted in Fig. 8a, the ratio of #255/#0 for the vertical component yields the highest sensitivity. This is also true for the diagonal component. For the lateral component, the ratio of #16/#255 demonstrates the highest sensitivity, which is numerically much larger than that corresponding to #255/#0. In consequence, monitoring the ratio of #16/ #255 for the lateral component seems to be the most effective in detecting plasma variations for the source power variation. As conducted in the case of source power, the ratio sensitivity to the reference condition was calculated for other process parameters. The reference conditions were 30 W, 6 mTorr, and 30 sccm for the bias power, pressure, and C2F6 flow rate, respectively. For a given parameter variation, the ratios exhibiting the highest sensitivity are shown in Table 2 for each component. To facilitate the comparison, the total percent sensitivity (TPS) was calculated for the ratios shown in Table 1. The TPS is simply the sum of PSs defined in (2). For example, the TPS for the source power is calculated as TPS ¼
1000 X x¼600
Table 2 The ratios with the highest sensitivity determined for each wavelet component Parameters
V
L
D
SP BP P C2F6 Flow Rate
#255/#0 #0/#255 #0/#255 #0/#255
#16/#255 #16/#255 #16/#255 #16/#255
#255/#0 #0/#255 #0/#255 #0/#255
The results are displayed in Fig. 9. In Fig. 9, the abbreviations of SP, BP, and P represent the source power, bias power, and pressure, respectively. As illustrated in Fig. 9, the TPS is also compared to another TPS calculated with actual surface roughness measurements. It is common that each TPS for each component demonstrates a higher sensitivity for all parameter variations compared to the TPS for the actual measurement. Another common observation is
35 30
Total Sensitivity
with setting other parameters to their default values already mentioned. The sensitivity was measured in terms of the percent sensitivity (PS) defined as Ratiox Ratio400 PSx ¼ 100ð%Þ ð2Þ Ratio400
Raw L
25
V D
20 15 10 5 0 SP
BP
P
C2F6
Process Parameters
PSx
ð3Þ
Fig. 9. Comparison of total percent sensitivity as a function of process parameters.
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that the TPS for the lateral component yields the highest sensitivity for all parameter variations. This is not consistent with the component (i.e. diagonal) already noticed in the case of the non-reference condition. This inconsistency implies that depending on the monitoring schemes different components and ratios should be monitored. 5. Conclusions In this study, a new monitoring technique was presented. Compared to in situ-based monitoring techniques, the presented one is differentiated in that it was based on ex situ etch measurement. The main idea for plasma monitoring was to utilize a spatial variation of surface roughness measured by atomic force microscopy. Wavelets played a crucial role in characterizing detailed variations in surface roughness. Applying the wavelet enabled us to analyze the ratio sensitivity in three components as a function of process parameters. The proposed technique was evaluated in two situations, with or without a reference condition. In the case of the no reference condition, a particular ratio yielding the highest sensitivity existed for nearly all parameter variations. This was more transparent as the plasma was monitored with respect to one reference condition. Moreover, the identified ratio yielded a much higher sensitivity than that measured on the basis of actual measurement. All these results indicate that the presented technique can be applied to strictly monitor plasma conditions. It is expected that by combining the ex situ monitoring technique with the current in situ monitoring plasma status could be more stringently detected. The effectiveness of the presented technique may further be improved by
detailing spatial surface roughness with a more sophisticated AFM. Acknowledgements This study was supported by ‘‘System IC 2010’’ Project of the Korea Ministry of Commerce, Industry, and Energy, and partly by the MIC (Ministry of Information and Communication), Korea, under the ITRC (Information Technology Research Center) support program supervised by the IITA (Institute of Information Technology Advancement) (IITA-2006-C109006030030). References [1] J.O. Stevenson, P.P. Ward, M.L. Smith, R.J. Markle, Sur. Interf. Anal. 26 (1998) 124. [2] S. Bushman, T.F. Edgar, I.J. Trachtenberg, J. Electrochem. Soc. 144 (1997) 721. [3] H. Sugai, K. Nakamura, Y. Hikosaka, M. Nakamura, J. Vac. Sci. Technol. A 13 (1995) 887. [4] R.H.M. van de Leur, A.J.G. Shellingerhout, J.E. Moij, F. Tuinstra, Appl. Phys. Lett. 52 (1988) 1005. [5] B. Kim, C.J. Lee, J. Vac. Sci. Technol. A 18 (2000) 58. [6] M. Kanoh, M. Yamage, H. Takada, Jpn. J. Appl. Phys. 40 (2001) 1457. [7] B. Kim, W. Choi, M.T. Lim, J. Vac. Sci. Technol. B 21 (2003) 2329. [8] B. Kim, H.J. Choi, B.T. Lee, J. Vac. Sci. Technol. A 20 (2002) 424. [9] B. Kim, S. Kim, Chemometr. Intell. Lab. Syst. 65 (2003) 231. [10] B. Kim, D. Lee, N. Kim, B. Lee, J. Vac. Sci. Technol. A 23 (2005) 520. [11] B. Kim, S. Kim, S.C. Ahn, B.T. Lee, Thin Solid Films 434 (2003) 276. [12] L. Prasad, S.S. lyengar, Wavelet Analysis with Applications to Image Processing, CRC Press, Boca Raton, FL, 1997. [13] B. Kim, K. Kim, B.T. Lee, Appl. Surf. Sci. 217 (2003) 261.