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Multi-response optimization of ultrathin poly-SiGe films characteristics for Nano-ElectroMechanical Systems (NEMS) using the grey-Taguchi technique
Microelectronic Engineering xxx (2013) xxx–xxx
Contents lists available at SciVerse ScienceDirect
Microelectronic Engineering journal homepage: www.elsevier.com/locate/mee
Multi-response optimization of ultrathin poly-SiGe films characteristics for Nano-ElectroMechanical Systems (NEMS) using the grey-Taguchi technique T.B. Asafa a,b,c,⇑, G. Bryce b, S. Severi b, S.A.M. Said c, A. Witvrouw b a
KACST-Intel Consortium Center of Excellence in Nano-Manufacturing Applications, Saudi Arabia Imec, Leuven, Belgium c King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia b
a r t i c l e
i n f o
Article history: Available online xxxx Keywords: Grey-Taguchi SiGe Multi-objective optimization
a b s t r a c t Poly-SiGe can be used for monolithically integrating Micro/Nano-ElectroMechanical Systems (M/NEMS) with its driving circuitry in a MEMS-last approach. For these applications, it is important to have polySiGe films with a low tensile stress, a low resistivity and a high deposition rate. This paper presents a systematic procedure for the simultaneous optimization of these 3 properties for CVD deposited ultrathin (100 ± 5 nm) poly-SiGe films by using the grey-Taguchi approach. Seven process variables were identified as important parameters for controlling the deposition process and the resulting film properties, namely the deposition temperature, the silane, germane, diborane and hydrogen flow rate, the chamber pressure and the shower head-heater spacing. By using 4 different levels for each process variable, 32 unique experiments were defined based on an L32 orthogonal array. The optimal combination of process parameters was determined by applying the grey relational analysis (GRA) for multiple performance characteristics. The analysis of variance (ANOVA) showed that the deposition temperature has the highest influence on the multi-performance characteristics (contributing 41%). The projected optimized process resulted in a 100 nm-thick poly-SiGe film with a tensile stress of 43 MPa, a very low resistivity of 1.39 mO-cm, a deposition rate of 0.34 nm/s, a germanium concentration of 87%, a cauliflower surface morphology with a root-mean-square roughness of 4.2 nm, an elastic modulus of 101 ± 0.81 GPa and a strain gradient of 2.0 102/lm. The optimized film is expected to be desirable as structural layer for M/NEMS applications such as nanoswitches, nanoresonators, biosensors etc. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction Applications of polycrystalline silicon germanium (poly-Si1xGex) films have been successfully demonstrated in various devices [1]. The growing interest in poly-SiGe is largely attributed to its low thermal budget (450 °C) which has proved useful when monolithically integrating Micro/Nano-ElectroMechanical Systems (M/NEMS) with their driving circuitry in the MEMS-last approach [2]. MEMS and NEMS are systems having both electrical and non-electrical (e.g. mechanical) functionality. While MEMS refers to microscopic devices that have a characteristic dimension of less than 1 mm but more than 100 nm, NEMS devices have a characteristic dimension of about 100 nm or less. The fundamental requirements for excellent SiGe M/NEMS structural layers, such as low tensile residual stress, low stress gradient and low sheet resistance, are achievable by effectively identifying the process regime most suitable for the deposition of these films. To achieve the best combination of these characteristics, the process variables can be ⇑ Corresponding author at: Imec, Leuven, Belgium. Tel.: +32 16 28 3525. E-mail address: [email protected] (T.B. Asafa).
optimized to deliver a simultaneous optimal response of all the desired film properties. One of the most widely used multi-response optimization schemes is the grey relational analysis (GRA) [3,4]. GRA is an impact evaluation model that measures the degree of similarity or difference between two sequences based on the grade of relation. This technique has been found helpful to solve many complex and multivariate problems [5]. In this work we utilized the combined Taguchi and GRA to optimize the stress, resistivity and deposition rate of poly-SiGe thin films based on the deposition temperature, germane flow rate, diborane flow rate, silane flow rate, chamber pressure, hydrogen flow rate and heater-shower head spacing. 2. Experimental 2.1. Film deposition and characterization techniques The poly-SiGe films were deposited in a PolyGen chamber of an Applied Materials Centura low pressure chemical vapor deposition (LPCVD) tool on 200 mm silicon wafers on top of a 1 lm SiO2 layer. LPCVD is a deposition technique which works by the thermal
0167-9317/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.mee.2013.03.171
Please cite this article in press as: T.B. Asafa et al., Microelectron. Eng. (2013), http://dx.doi.org/10.1016/j.mee.2013.03.171
T.B. Asafa et al. / Microelectronic Engineering xxx (2013) xxx–xxx Table 1 Experimental parameters and their levels. Symbol
Unit
Deposition temp SiH4 flow rate GeH4 flow rate (10 in % H2) Chamber pressure B2H6 flow rate (1 in % H2) Hydrogen flow rate Shower head-heater spacing
T S G P B H HH
°C sccm sccm Torr sccm sccm mil
-0.20
Stress
150
Parameter levels 1
2
3
4
390 8 120 60 11 500 400
400 10 140 65 13 550 430
415 12 160 70 15 600 470
420 15 180 75 18 650 500
Resistivity
Deposition rate
-0.16 -0.12 -0.08 -0.04
Deposition rate (nm/s)
strain gradient 0 -150 -300 -450 -600 -750
2.2. Grey relational analysis
yi ðjÞ minðyi ðjÞÞ maxðyi ðjÞÞ minðyi ðjÞÞ
ð1Þ
½Y i ðjÞLB ¼
maxðyi ðjÞÞ yi ðjÞ maxðyi ðjÞÞ minðyi ðjÞÞ
ð2Þ
ð3Þ
where yi ðjÞ and Y i ðjÞ are the experimental average and the normalized value of the jth performance characteristic for the ith experiment, and maxðyi ðjÞÞ and minðyi ðjÞÞ are the maximum and minimum values of yi ðjÞ, and NV is the nominal value for the residual stress. The grey relational coefficient bi ðjÞ is computed using Eq. (4) [5]:
mini minj jY o ðjÞ Y i ðjÞj þ kmaxi maxj jY o ðjÞ Y i ðjÞj jY o ðjÞ Y i ðjÞj þ kmaxi maxj jY o ðjÞ Y i ðjÞj
18 16
0.6
14
0.4
12
0.2
10
0.0
8 6
-0.2
4
ð4Þ
where Y o ðjÞ is the ideal normalized value of the jth performance characteristic which is chosen as 1. k (usually between 0 and 1) is
L8 L12 L16 L20 L24 L28 L32
--
Experimental Design Fig. 1. Experimental results.
the distinguishing coefficient and can be adjusted according to the optimization requirement. In our case, it is chosen as 0.8, 0.15 and 0.05 for tensile stress, sheet resistance and deposition rate, respectively. The selection reflects the importance of each output parameter to our thin film development. Finally, the grey relational grade (GRG)i is computed as the average of the grey relational coefficient corresponding to the ith experiment for each performance characteristic using Eq. (5). N
ðGRGÞi ¼
j 1X b ðjÞ Nj j¼1 i
ð5Þ
The GRG provides a ranking of the experimental alternatives [4]. The results of the experiments L1-L32 are provided in Fig. 1 and the details are available in Section B of the supplementary information. The normalized average results, the grey relational
0.70
Grey Relational Grade
½Y i ðjÞHB ¼
bi ðjÞ ¼
0.8
-0.4 2 L4
jyi ðjÞ NVj maxf½maxðyi ðjÞÞ NV; ½NV minðyi ðjÞÞg
20
0.00
The grey relational analysis (GRA) begins with the selection of a suitable orthogonal array and terminates with the experimental verification of the projected improvement (details in Section A of the supplementary information). To perform GRA, the input variables are normalized such that they are comparable in terms of order of magnitude, and dimensionless on a global measurement scale [5]. The normalization process of each performance characteristic depends on the optimization requirement. For the current study, the residual stress is of the nominal-the-better type (NB) with the nominal value chosen as 30 MPa, the deposition rate is of the higher-the-better type (HB) while the sheet resistance belongs to the lower-the-better type (LB). 30 MPa is chosen as the ideal residual stress as a low tensile stress is normally preferred for MEMS structural layers to get flat freestanding structures. A compressive stress can lead to buckling of clamped–clamped beams which are larger than the critical length. A large tensile stress might lead to cracking or structural layer delamination. The normalization equations are given in Eqs. (1)–(3) [7]:
½Y i ðjÞNB ¼ 1
1.0
Resistivity (mOhm-cm)
Process variables
Stress (MPa)
reaction of gaseous precursors at low pressure. Having identified the seven most important deposition variables that influence the deposition process and the resulting film properties (Table 1), we defined the experiments based on the L32 orthogonal array [6]. The deposition time was adjusted accordingly to obtain films with thicknesses of 100 ± 5 nm. The thickness of each film was measured by using the weight difference technique and confirmed with FEI NOVA 200 scanning electron microscopy (SEM). The residual stresses of the films were measured with a Tencor FLX-2320 and the average film resistivity, based on 49 points, was determined with an OmniMap RS75 four-point probe. The crystallinity was determined by X-ray diffraction (XRD) in the glancing incidence mode (D8 Bruker AXS X-ray diffractometer). The elastic modulus was measured with MTS Nano Indenter XP and the surface roughness was measured by using atomic force microscopy (AFM). To determine the strain gradients in the optimized film and a few other films with tensile tress and low resistivity, SiGe nanocantilevers were fabricated by surface micromachining [1]. A patterned Si-oxide layer was used as the sacrificial layer below the SiGe cantilever. This layer was removed by the use of vapor HF to create the freestanding cantilevers. The deflection at the tip of the released cantilever was measured and the strain gradient U was evaluated by using C ¼ 2d=L2 ; where d is the tip deflection and L is the length of the cantilever.
Strain gradient (1/ m)
2
0.65 0.60
Germane Silane
0.55
Pressure
Hydrogen
0.50 0.45 Spacing
0.40 Diborane
0.35
Temperature
1 2 3 4 -- 1 2 3 4 -- 1 2 3 4 Parameter level Fig. 2. Effects plot for selection of optimum parameter levels. An optimum level for a deposition parameter denotes the level at which the grey relational grade is maximum.
Please cite this article in press as: T.B. Asafa et al., Microelectron. Eng. (2013), http://dx.doi.org/10.1016/j.mee.2013.03.171
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T.B. Asafa et al. / Microelectronic Engineering xxx (2013) xxx–xxx Table 2 Results of performance measures for initial and optimal deposition parameters.
Combination level Stress (MPa) Deposition rate (nm/s) Resistivity (mO-cm) Grey relational grade
Initial condition T1S1G1P1B1H1HH1 44 0.16 10.18 0.49
Experimental best condition (L20) T3S1G4P1B4H1HH3 24.7 0.34 3.47 0.96
Optimized condition T3S1G4P2B1H1HH4 43 0.34 1.39 0.98
160 140 E = 101 ± 0.81 GPa
Modulus (GPa)
120 100 80 60 40 20 0
-20 0
10
20
30
40
50
60
Indentation depth (nm) Fig. 3. Glancing incidence XRD spectra of the optimized and the experimental best films.
Fig. 4. Cross-sectional SEM image of the optimized film. The surface topography images from SEM and AFM measurements are shown as insets.
Fig. 5. Nano-indentation curves of the optimized 100 nm thick poly-SiGe films. The rectangle shows the region where the modulus is evaluated. Inset shows the equivalent ten points considered for modulus evaluation.
gives a parameter combination of T3S1G4P2B1H1HH4 which corresponds to the following deposition conditions: T = 415 °C, S = 8 sccm, G = 180 sccm, P = 65 Torr, B = 11 sccm, H = 500 sccm and HH = 500 mil. Analysis of variance (ANOVA) [9,10] was performed to investigate the level of significance of the process parameters on the variation of the responses. ANOVA shows that the deposition temperature, germane flow rate and diborane flow rate contributed about 40.6, 18.1 and 15.2%, respectively to the combined change in the stress, resistivity and deposition rate and are significant at 95.0% confidence level (CL) going by their probability (p) values which are less than 0.05 (Section D of the supplementary information). The implication of this finding is that more attention should be focused on temperature, germane and diborane flow rate if any of the film properties is to be modulated significantly. After evaluation of the optimal parameter combination, a multi-objective verification experiment was conducted using the optimized condition. The projected grey relational grade was computed from Eq. (6).
ðGRGÞprojected ¼ ðGRGÞm þ coefficient, the grey relational grade and the ranking order for the experiments, obtained from Eqs. (1)–(5), are shown in Section C of the supplementary information. Accordingly, experiment L20 has the highest GRG (0.96) which implies the best multiple performance characteristics among the 32 experiments; hence, it is our ‘experimental best’.
7 X ðGRGÞopm ðkÞ ðGRGÞm
ð6Þ
k¼1
3. Results and discussion
where ðGRGÞopm ðkÞ and ðGRGÞm are the optimum grey relational grade for deposition parameter k (obtained from the effects plot of Fig. 2) and the global average of GRG (0.466), respectively. The confirmatory experiment shows that residual stress increases from 44 to 43 MPa while the deposition rate increases from 0.16 to 0.34 nm/s (Table 2). The film resistivity decreases from 10.18 to 1.39 mO-cm and the grey relational grade was doubled. The condition for the experimental best film is also included in Table 2.
3.1. Optimal process condition, ANOVA and confirmation test
3.2. Additional characteristics of the optimized film
The main effects plot (Fig. 2) was computed to select the optimal level of each deposition parameter based on the method described in Ref. [8]. The optimal parameter level is the one with the highest value of GRG for a particular deposition parameter. This
The optimized film is more crystalline than the experimental best film based on the XRD peak parameters of Fig. 3. This is because the diffraction peaks corresponding to the (1 1 1), (2 2 0), and (3 1 1) planes for the optimized film are stronger and sharper.
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T.B. Asafa et al. / Microelectronic Engineering xxx (2013) xxx–xxx
Fig. 6. Array of released nanocantilevers with average strain gradient estimated to be 2.0 102/lm. Insets are top and expanded top views. Each cantilever is 100 nm thick.
The value of the full-width-at-half-maximum (FWHM) is 0.58° for the optimized film compared to 1.14° for the experimental best film indicating that the grain size in the former (15 nm) doubles that of the latter (7.5 nm) (assuming the peak width is solely a function of grain size). Also the resistivities of the two films (Table 2) confirm the higher crystallinity for the optimized film. The Rutherford backscattering spectrometry (RBS) profiles indicate that the germanium concentration in the optimized film is 87% compared to 89% in the experimental best film (profiles are provided in Section E of the supplementary information). The thickness of the optimized film is 100 nm (Fig. 4) while the AFM and top-down SEM images show that the film exhibits cauliflower surface morphology (inset of Fig. 4). The root mean square surface roughness of the optimized film (4.2 nm) is slightly lower than that of the experimental best film (4.6 nm) indicating that the former is more uniform. The optimized film has an elastic modulus of 101 ± 0.81 GPa (Fig. 5 and Section F of the complimentary information). The SEM image of the array of the released cantilevers for the optimized film is shown in Fig. 6. The lengths of the cantilevers vary from 0.8 lm to 7.5 lm while the width is constant (840 nm) (see inserts a and b). The deflections for 3.5, 4.1 and 4.42 lm long cantilevers were 0.13, 0.18 and 0.28 lm, respectively. By putting these values in the strain gradient equation (see Section 2.1), the average strain gradient was calculated to be 2.0 102/
lm. The strain gradient translates to a downward deflection of 10 nm for 1 lm long, 0.84 lm wide and 0.1 lm thick cantilever. This value is considered to be good for applications in nanoswitches, nanoresonators and biosensors among others. The strain gradients for a few films with tensile tress and low resistivity were measured (Fig. 1) and were observed to be higher than that of the optimized film. 4. Conclusions We optimized the properties of ultrathin SiGe films deposited by CVD with the grey-Taguchi approach. The optimal deposition parameters were simultaneously determined for an optimal residual stress (30 MPa), a maximum deposition rate and a minimum sheet resistance. We found that the deposition temperature has, among the other deposition parameters, the strongest influence on the multi-performance characteristics. The order of importance of these deposition parameters is: deposition temperature (40.6%), germane flow rate (18.1%), diborane flow rate (15.2%), silane flow rate (11.3%), chamber pressure (7.1%), hydrogen flow rate (2.0%) and heater-shower head spacing (1%). The optimization resulted in a film with a residual stress, a deposition rate, a film resistivity and a strain gradient of 43 MPa, 0.34 nm/s, 1.39 mO-cm and 2.0 102/lm, respectively.
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T.B. Asafa et al. / Microelectronic Engineering xxx (2013) xxx–xxx
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.mee.2013.03.171. References [1] S. Sedky, Post-Processing Techniques for Integrated MEMS, Aztech House, London, 2006. [2] S. Sedky, M. Gromova, T. Van der Donck, J.P. Celis, A. Witrouw, Sens. Actuators A 127 (2006) 316–323.
[3] [4] [5] [6] [7] [8] [9] [10]
5
Y.-S. Yang, W. Huang, W.-Y. Huang, Thin Solid Films 519 (2011) 4899–4905. S. Singh, Int. J. Adv. Manuf. Technol. 63 (2012) 1191–1202. J.L. Deng, J. Grey System 1 (1989) 1–24. G. Taguchi, Taguchi Methods – Design of Experiments, American Supplies Institute, Dearborn, MI, 1993. K.P. Maity, R.K. Singh, Int. J. Adv. Manuf. Technol. (2012), http://dx.doi.org/ 10.1007/s00170-012-4098-z. J. Anthony, Int. J. Adv. Manuf. Technol. 17 (2001) 134–138. C.C. Tsao, Int. J. Adv. Manuf. Technol. 40 (2009) 41–48. K. Hinkelmann, O. Kempthorne, Design and Analysis of Experiments, John Willey and Sons, New Jersy, 2005.
Please cite this article in press as: T.B. Asafa et al., Microelectron. Eng. (2013), http://dx.doi.org/10.1016/j.mee.2013.03.171
Contents lists available at SciVerse ScienceDirect
Microelectronic Engineering journal homepage: www.elsevier.com/locate/mee
Multi-response optimization of ultrathin poly-SiGe films characteristics for Nano-ElectroMechanical Systems (NEMS) using the grey-Taguchi technique T.B. Asafa a,b,c,⇑, G. Bryce b, S. Severi b, S.A.M. Said c, A. Witvrouw b a
KACST-Intel Consortium Center of Excellence in Nano-Manufacturing Applications, Saudi Arabia Imec, Leuven, Belgium c King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia b
a r t i c l e
i n f o
Article history: Available online xxxx Keywords: Grey-Taguchi SiGe Multi-objective optimization
a b s t r a c t Poly-SiGe can be used for monolithically integrating Micro/Nano-ElectroMechanical Systems (M/NEMS) with its driving circuitry in a MEMS-last approach. For these applications, it is important to have polySiGe films with a low tensile stress, a low resistivity and a high deposition rate. This paper presents a systematic procedure for the simultaneous optimization of these 3 properties for CVD deposited ultrathin (100 ± 5 nm) poly-SiGe films by using the grey-Taguchi approach. Seven process variables were identified as important parameters for controlling the deposition process and the resulting film properties, namely the deposition temperature, the silane, germane, diborane and hydrogen flow rate, the chamber pressure and the shower head-heater spacing. By using 4 different levels for each process variable, 32 unique experiments were defined based on an L32 orthogonal array. The optimal combination of process parameters was determined by applying the grey relational analysis (GRA) for multiple performance characteristics. The analysis of variance (ANOVA) showed that the deposition temperature has the highest influence on the multi-performance characteristics (contributing 41%). The projected optimized process resulted in a 100 nm-thick poly-SiGe film with a tensile stress of 43 MPa, a very low resistivity of 1.39 mO-cm, a deposition rate of 0.34 nm/s, a germanium concentration of 87%, a cauliflower surface morphology with a root-mean-square roughness of 4.2 nm, an elastic modulus of 101 ± 0.81 GPa and a strain gradient of 2.0 102/lm. The optimized film is expected to be desirable as structural layer for M/NEMS applications such as nanoswitches, nanoresonators, biosensors etc. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction Applications of polycrystalline silicon germanium (poly-Si1xGex) films have been successfully demonstrated in various devices [1]. The growing interest in poly-SiGe is largely attributed to its low thermal budget (450 °C) which has proved useful when monolithically integrating Micro/Nano-ElectroMechanical Systems (M/NEMS) with their driving circuitry in the MEMS-last approach [2]. MEMS and NEMS are systems having both electrical and non-electrical (e.g. mechanical) functionality. While MEMS refers to microscopic devices that have a characteristic dimension of less than 1 mm but more than 100 nm, NEMS devices have a characteristic dimension of about 100 nm or less. The fundamental requirements for excellent SiGe M/NEMS structural layers, such as low tensile residual stress, low stress gradient and low sheet resistance, are achievable by effectively identifying the process regime most suitable for the deposition of these films. To achieve the best combination of these characteristics, the process variables can be ⇑ Corresponding author at: Imec, Leuven, Belgium. Tel.: +32 16 28 3525. E-mail address: [email protected] (T.B. Asafa).
optimized to deliver a simultaneous optimal response of all the desired film properties. One of the most widely used multi-response optimization schemes is the grey relational analysis (GRA) [3,4]. GRA is an impact evaluation model that measures the degree of similarity or difference between two sequences based on the grade of relation. This technique has been found helpful to solve many complex and multivariate problems [5]. In this work we utilized the combined Taguchi and GRA to optimize the stress, resistivity and deposition rate of poly-SiGe thin films based on the deposition temperature, germane flow rate, diborane flow rate, silane flow rate, chamber pressure, hydrogen flow rate and heater-shower head spacing. 2. Experimental 2.1. Film deposition and characterization techniques The poly-SiGe films were deposited in a PolyGen chamber of an Applied Materials Centura low pressure chemical vapor deposition (LPCVD) tool on 200 mm silicon wafers on top of a 1 lm SiO2 layer. LPCVD is a deposition technique which works by the thermal
0167-9317/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.mee.2013.03.171
Please cite this article in press as: T.B. Asafa et al., Microelectron. Eng. (2013), http://dx.doi.org/10.1016/j.mee.2013.03.171
T.B. Asafa et al. / Microelectronic Engineering xxx (2013) xxx–xxx Table 1 Experimental parameters and their levels. Symbol
Unit
Deposition temp SiH4 flow rate GeH4 flow rate (10 in % H2) Chamber pressure B2H6 flow rate (1 in % H2) Hydrogen flow rate Shower head-heater spacing
T S G P B H HH
°C sccm sccm Torr sccm sccm mil
-0.20
Stress
150
Parameter levels 1
2
3
4
390 8 120 60 11 500 400
400 10 140 65 13 550 430
415 12 160 70 15 600 470
420 15 180 75 18 650 500
Resistivity
Deposition rate
-0.16 -0.12 -0.08 -0.04
Deposition rate (nm/s)
strain gradient 0 -150 -300 -450 -600 -750
2.2. Grey relational analysis
yi ðjÞ minðyi ðjÞÞ maxðyi ðjÞÞ minðyi ðjÞÞ
ð1Þ
½Y i ðjÞLB ¼
maxðyi ðjÞÞ yi ðjÞ maxðyi ðjÞÞ minðyi ðjÞÞ
ð2Þ
ð3Þ
where yi ðjÞ and Y i ðjÞ are the experimental average and the normalized value of the jth performance characteristic for the ith experiment, and maxðyi ðjÞÞ and minðyi ðjÞÞ are the maximum and minimum values of yi ðjÞ, and NV is the nominal value for the residual stress. The grey relational coefficient bi ðjÞ is computed using Eq. (4) [5]:
mini minj jY o ðjÞ Y i ðjÞj þ kmaxi maxj jY o ðjÞ Y i ðjÞj jY o ðjÞ Y i ðjÞj þ kmaxi maxj jY o ðjÞ Y i ðjÞj
18 16
0.6
14
0.4
12
0.2
10
0.0
8 6
-0.2
4
ð4Þ
where Y o ðjÞ is the ideal normalized value of the jth performance characteristic which is chosen as 1. k (usually between 0 and 1) is
L8 L12 L16 L20 L24 L28 L32
--
Experimental Design Fig. 1. Experimental results.
the distinguishing coefficient and can be adjusted according to the optimization requirement. In our case, it is chosen as 0.8, 0.15 and 0.05 for tensile stress, sheet resistance and deposition rate, respectively. The selection reflects the importance of each output parameter to our thin film development. Finally, the grey relational grade (GRG)i is computed as the average of the grey relational coefficient corresponding to the ith experiment for each performance characteristic using Eq. (5). N
ðGRGÞi ¼
j 1X b ðjÞ Nj j¼1 i
ð5Þ
The GRG provides a ranking of the experimental alternatives [4]. The results of the experiments L1-L32 are provided in Fig. 1 and the details are available in Section B of the supplementary information. The normalized average results, the grey relational
0.70
Grey Relational Grade
½Y i ðjÞHB ¼
bi ðjÞ ¼
0.8
-0.4 2 L4
jyi ðjÞ NVj maxf½maxðyi ðjÞÞ NV; ½NV minðyi ðjÞÞg
20
0.00
The grey relational analysis (GRA) begins with the selection of a suitable orthogonal array and terminates with the experimental verification of the projected improvement (details in Section A of the supplementary information). To perform GRA, the input variables are normalized such that they are comparable in terms of order of magnitude, and dimensionless on a global measurement scale [5]. The normalization process of each performance characteristic depends on the optimization requirement. For the current study, the residual stress is of the nominal-the-better type (NB) with the nominal value chosen as 30 MPa, the deposition rate is of the higher-the-better type (HB) while the sheet resistance belongs to the lower-the-better type (LB). 30 MPa is chosen as the ideal residual stress as a low tensile stress is normally preferred for MEMS structural layers to get flat freestanding structures. A compressive stress can lead to buckling of clamped–clamped beams which are larger than the critical length. A large tensile stress might lead to cracking or structural layer delamination. The normalization equations are given in Eqs. (1)–(3) [7]:
½Y i ðjÞNB ¼ 1
1.0
Resistivity (mOhm-cm)
Process variables
Stress (MPa)
reaction of gaseous precursors at low pressure. Having identified the seven most important deposition variables that influence the deposition process and the resulting film properties (Table 1), we defined the experiments based on the L32 orthogonal array [6]. The deposition time was adjusted accordingly to obtain films with thicknesses of 100 ± 5 nm. The thickness of each film was measured by using the weight difference technique and confirmed with FEI NOVA 200 scanning electron microscopy (SEM). The residual stresses of the films were measured with a Tencor FLX-2320 and the average film resistivity, based on 49 points, was determined with an OmniMap RS75 four-point probe. The crystallinity was determined by X-ray diffraction (XRD) in the glancing incidence mode (D8 Bruker AXS X-ray diffractometer). The elastic modulus was measured with MTS Nano Indenter XP and the surface roughness was measured by using atomic force microscopy (AFM). To determine the strain gradients in the optimized film and a few other films with tensile tress and low resistivity, SiGe nanocantilevers were fabricated by surface micromachining [1]. A patterned Si-oxide layer was used as the sacrificial layer below the SiGe cantilever. This layer was removed by the use of vapor HF to create the freestanding cantilevers. The deflection at the tip of the released cantilever was measured and the strain gradient U was evaluated by using C ¼ 2d=L2 ; where d is the tip deflection and L is the length of the cantilever.
Strain gradient (1/ m)
2
0.65 0.60
Germane Silane
0.55
Pressure
Hydrogen
0.50 0.45 Spacing
0.40 Diborane
0.35
Temperature
1 2 3 4 -- 1 2 3 4 -- 1 2 3 4 Parameter level Fig. 2. Effects plot for selection of optimum parameter levels. An optimum level for a deposition parameter denotes the level at which the grey relational grade is maximum.
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T.B. Asafa et al. / Microelectronic Engineering xxx (2013) xxx–xxx Table 2 Results of performance measures for initial and optimal deposition parameters.
Combination level Stress (MPa) Deposition rate (nm/s) Resistivity (mO-cm) Grey relational grade
Initial condition T1S1G1P1B1H1HH1 44 0.16 10.18 0.49
Experimental best condition (L20) T3S1G4P1B4H1HH3 24.7 0.34 3.47 0.96
Optimized condition T3S1G4P2B1H1HH4 43 0.34 1.39 0.98
160 140 E = 101 ± 0.81 GPa
Modulus (GPa)
120 100 80 60 40 20 0
-20 0
10
20
30
40
50
60
Indentation depth (nm) Fig. 3. Glancing incidence XRD spectra of the optimized and the experimental best films.
Fig. 4. Cross-sectional SEM image of the optimized film. The surface topography images from SEM and AFM measurements are shown as insets.
Fig. 5. Nano-indentation curves of the optimized 100 nm thick poly-SiGe films. The rectangle shows the region where the modulus is evaluated. Inset shows the equivalent ten points considered for modulus evaluation.
gives a parameter combination of T3S1G4P2B1H1HH4 which corresponds to the following deposition conditions: T = 415 °C, S = 8 sccm, G = 180 sccm, P = 65 Torr, B = 11 sccm, H = 500 sccm and HH = 500 mil. Analysis of variance (ANOVA) [9,10] was performed to investigate the level of significance of the process parameters on the variation of the responses. ANOVA shows that the deposition temperature, germane flow rate and diborane flow rate contributed about 40.6, 18.1 and 15.2%, respectively to the combined change in the stress, resistivity and deposition rate and are significant at 95.0% confidence level (CL) going by their probability (p) values which are less than 0.05 (Section D of the supplementary information). The implication of this finding is that more attention should be focused on temperature, germane and diborane flow rate if any of the film properties is to be modulated significantly. After evaluation of the optimal parameter combination, a multi-objective verification experiment was conducted using the optimized condition. The projected grey relational grade was computed from Eq. (6).
ðGRGÞprojected ¼ ðGRGÞm þ coefficient, the grey relational grade and the ranking order for the experiments, obtained from Eqs. (1)–(5), are shown in Section C of the supplementary information. Accordingly, experiment L20 has the highest GRG (0.96) which implies the best multiple performance characteristics among the 32 experiments; hence, it is our ‘experimental best’.
7 X ðGRGÞopm ðkÞ ðGRGÞm
ð6Þ
k¼1
3. Results and discussion
where ðGRGÞopm ðkÞ and ðGRGÞm are the optimum grey relational grade for deposition parameter k (obtained from the effects plot of Fig. 2) and the global average of GRG (0.466), respectively. The confirmatory experiment shows that residual stress increases from 44 to 43 MPa while the deposition rate increases from 0.16 to 0.34 nm/s (Table 2). The film resistivity decreases from 10.18 to 1.39 mO-cm and the grey relational grade was doubled. The condition for the experimental best film is also included in Table 2.
3.1. Optimal process condition, ANOVA and confirmation test
3.2. Additional characteristics of the optimized film
The main effects plot (Fig. 2) was computed to select the optimal level of each deposition parameter based on the method described in Ref. [8]. The optimal parameter level is the one with the highest value of GRG for a particular deposition parameter. This
The optimized film is more crystalline than the experimental best film based on the XRD peak parameters of Fig. 3. This is because the diffraction peaks corresponding to the (1 1 1), (2 2 0), and (3 1 1) planes for the optimized film are stronger and sharper.
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Fig. 6. Array of released nanocantilevers with average strain gradient estimated to be 2.0 102/lm. Insets are top and expanded top views. Each cantilever is 100 nm thick.
The value of the full-width-at-half-maximum (FWHM) is 0.58° for the optimized film compared to 1.14° for the experimental best film indicating that the grain size in the former (15 nm) doubles that of the latter (7.5 nm) (assuming the peak width is solely a function of grain size). Also the resistivities of the two films (Table 2) confirm the higher crystallinity for the optimized film. The Rutherford backscattering spectrometry (RBS) profiles indicate that the germanium concentration in the optimized film is 87% compared to 89% in the experimental best film (profiles are provided in Section E of the supplementary information). The thickness of the optimized film is 100 nm (Fig. 4) while the AFM and top-down SEM images show that the film exhibits cauliflower surface morphology (inset of Fig. 4). The root mean square surface roughness of the optimized film (4.2 nm) is slightly lower than that of the experimental best film (4.6 nm) indicating that the former is more uniform. The optimized film has an elastic modulus of 101 ± 0.81 GPa (Fig. 5 and Section F of the complimentary information). The SEM image of the array of the released cantilevers for the optimized film is shown in Fig. 6. The lengths of the cantilevers vary from 0.8 lm to 7.5 lm while the width is constant (840 nm) (see inserts a and b). The deflections for 3.5, 4.1 and 4.42 lm long cantilevers were 0.13, 0.18 and 0.28 lm, respectively. By putting these values in the strain gradient equation (see Section 2.1), the average strain gradient was calculated to be 2.0 102/
lm. The strain gradient translates to a downward deflection of 10 nm for 1 lm long, 0.84 lm wide and 0.1 lm thick cantilever. This value is considered to be good for applications in nanoswitches, nanoresonators and biosensors among others. The strain gradients for a few films with tensile tress and low resistivity were measured (Fig. 1) and were observed to be higher than that of the optimized film. 4. Conclusions We optimized the properties of ultrathin SiGe films deposited by CVD with the grey-Taguchi approach. The optimal deposition parameters were simultaneously determined for an optimal residual stress (30 MPa), a maximum deposition rate and a minimum sheet resistance. We found that the deposition temperature has, among the other deposition parameters, the strongest influence on the multi-performance characteristics. The order of importance of these deposition parameters is: deposition temperature (40.6%), germane flow rate (18.1%), diborane flow rate (15.2%), silane flow rate (11.3%), chamber pressure (7.1%), hydrogen flow rate (2.0%) and heater-shower head spacing (1%). The optimization resulted in a film with a residual stress, a deposition rate, a film resistivity and a strain gradient of 43 MPa, 0.34 nm/s, 1.39 mO-cm and 2.0 102/lm, respectively.
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Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.mee.2013.03.171. References [1] S. Sedky, Post-Processing Techniques for Integrated MEMS, Aztech House, London, 2006. [2] S. Sedky, M. Gromova, T. Van der Donck, J.P. Celis, A. Witrouw, Sens. Actuators A 127 (2006) 316–323.
[3] [4] [5] [6] [7] [8] [9] [10]
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Y.-S. Yang, W. Huang, W.-Y. Huang, Thin Solid Films 519 (2011) 4899–4905. S. Singh, Int. J. Adv. Manuf. Technol. 63 (2012) 1191–1202. J.L. Deng, J. Grey System 1 (1989) 1–24. G. Taguchi, Taguchi Methods – Design of Experiments, American Supplies Institute, Dearborn, MI, 1993. K.P. Maity, R.K. Singh, Int. J. Adv. Manuf. Technol. (2012), http://dx.doi.org/ 10.1007/s00170-012-4098-z. J. Anthony, Int. J. Adv. Manuf. Technol. 17 (2001) 134–138. C.C. Tsao, Int. J. Adv. Manuf. Technol. 40 (2009) 41–48. K. Hinkelmann, O. Kempthorne, Design and Analysis of Experiments, John Willey and Sons, New Jersy, 2005.
Please cite this article in press as: T.B. Asafa et al., Microelectron. Eng. (2013), http://dx.doi.org/10.1016/j.mee.2013.03.171