Biaxial initial stress characterization of bilayer gold RF-switches

Microelectronics Reliability 45 (2005) 1776–1781 www.elsevier.com/locate/microrel

Biaxial initial stress characterization of bilayer gold RF-switches K. Yacinea, F. Flourensa, D. Bourriera, L. Salvagnaca, P. Calmonta, X.Lafontanb, Q.-H. Duongc, L. Buchaillotc, D. Peyroua, P. Ponsa, R. Planaa a

LAAS-CNRS, 7 avenue Roche, 31077 Toulouse Cedex 04, France NOVAMEMS, 14 quai du 19 mars 1962, 09700 Saverdun, France c IEMN, ISEN Dpt, CNRS UMR 8520, Cité Scientifique, Av. H. Poincaré Contact : [email protected] b

Abstract An analysis has been conducted to determine the biaxial initial stress state of gold bilayer switches. Results have shown that the sensitivity of the sacrificial photoresist layer to process parameters make the wafer curvature technique unreliable to determine the initial stress state of the evaporated gold seed layer. An analytical method based on the cantilever deflection method is proposed to determine the biaxial stress state on this layer. Assumptions were validated numerically using FEM and cantilevers gold bilayer of various length were elaborated and characterized. Ó 2005 Elsevier Ltd. All rights reserved.

1. INTRODUCTION RF switches are often obtained with coplanar wave guide and metallic bridge or cantilever. The performances of these switches are almost related to the bridge or cantilever stiffness and height over the lines. These two characteristics are particularly sensitive to the initial stress state in the metallic layers. Lots of work have been done to determine Young’s modulus and initial stress states using various techniques as presented in Table 1. A large scatter can be observed from one laboratory to another for both characteristics. This indicate that mechanical properties might be very sensitive to technological process parameters especially for the initial stress state that is influenced by the underneath substrate and multi physic phenomenon. In order to determine the initial stress state of suspended structures of complex geometries, specific cells of test structures including cantilevers have been designed and fabricated on specific location of wafers.

Mechanical properties of gold Young’s modulus (GPa)

Initial stress state (MPa)

Characterisation techniques Nanoindentation test Nanoindentation test Membrane deflection Resonant frequency of microbeam Membrane deflection Membrane deflection Deflection of cantilevers X-Ray

Litterature

Ref

86-102 (*) 72 (*) 53-55 (*) 35.2-43.9 (**)

[1] [2] [3] [4]

35.4 (**) 10-12 (*) 40.1-43.8 (**)

[5] [3] [4]

100-250 (*)

[6]

Tab 1. Review of the mechanical properties of evaporated(*) and electroplated Gold (**)

This was done in order to study structures that are following the switch technological process described below. A gold seed layer is first deposit on a four inches silicon wafer. Then a photoresist sacrificial layer is

0026-2714/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.microrel.2005.07.093

K. Yacine et al. / Microelectronics Reliability 45 (2005) 1776–1781

patterned in order to fix the cantilever anchorage. A first gold evaporated seed layer (0.2µm thick) is then deposit followed by an electroplated layer (around 1.6 µm thick). In the next step the cantilever is patterned with classical wet bath. Finally the cantilever is released by solvent and dried in CO2 dryer. Investigations have been carried out to determine the initial stress state of electroplated and evaporated gold layer using the wafer curvature technique and the cantilever deflection method.

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(IV). The initial stress was deduced from wafer curvature measurement using a mechanical profilometer after each step.

2. WAFER CURVATURE TECHNIQUE Stoney’s formula is one of the most important and straightforward tools for initial and thermomechanical stress analysis. In its basic form, it allows to evaluate the stress state of a thin film deposited on a well known substrate through a single layer analysis. In the case of a uniform thin film deposited on a massive wafer, the initial stress in the film can be deduced from equation 1.

σf =

E s t s2 6 R t f (1-ν s )

(1) where E is the Young’s modulus of the substrate

νs is the Poisson coefficient of the substrate ts is the thickness of the substrate tf is the thickness of the film R is the curvature radius of the wafer due to the stress relaxation.

The following method was used in order to evaluate the initial stress of electroplated gold: to reproduce the switch composition, a uniform thin film of evaporated gold with the proper thickness was deposited on a silicon wafer. The biaxial initial stress state was extracted from the differential curvature of the wafer before and after the electroplated gold deposit was determined to be 7.5MPa +/- 2.5MPa. This technique was used to investigate the couple evaporated gold / sacrificial photoresist. This characterization is not easy to handle because the photoresist characteristics are altered throughout the technological process history. Figure 1 presents the evolution of the stress relaxation for a uniform photoresist deposit on a Silicon wafer and subjected to the gold switch process: - a soft cure at 105°C during 1 min (I) - an hard cured at 150°C during 1 min10’ (II) - 1h in the vacuum chamber of the evaporation apparatus (III) - 20 h in ambient atmosphere and temperature

Figure 1. Initial stress evolution after each technological process step

These results indicate that the photoresists is probably creeping after step II. Stress relaxation continues to evolve after 20 hours in a linear trend. Another wafer was subjected to the same process with a deposition of gold in step III, then the gold layer was etched in liquid bath (KI + I2) and the stress was determined to be 8MPa after less than 1 h from the gold deposition. This shows that the gold deposit or the gold etchant tends to accelerate the relaxation phenomenon. And that the evaporated gold initial stress cannot be deduced from this technique. 3. CANTILEVER DEFLECTION METHOD 2.1. Effect of biaxial stress relaxation Consider a cantilever composed of a bi-layer of the same material (cf. fig2) but subjected to different (but constant) initial stress states along its axis. E, σu1 = cte

t1 = 2.8 µm

E, σu2 = cte

t2 = 0.2 µm

L

z W

x

Figure 2. Cantilever bilayer There exists a simply and straightforward formulation between the out of plane deflection of the

K. Yacine et al. / Microelectronics Reliability 45 (2005) 1776–1781

cantilever due to the uni-axial initial stress state (σu1 and σu2) relaxation [1] : 3 t1 t 2 σ u1 − σ u2 w= L² eq. 2 3 E (t1 + t 2 ) where E is the Young modulus (80GPa for gold). t1 is the thickness of the first layer t2 is the thickness of the second layer

Assuming that there is initial in-plane stress (biaxial stress) in the two gold layers (σb1 and σb2), the result of this analytical approach has to be extrapolated. If one considers each layer independently without regards to the interface, the relaxation of the initial biaxial stress in each direction can be decoupled. According to the Hooke's law, the free relaxation in the section plane induces a subsequent relaxation of the initial stress lengthways :

σ u1 = (1 − ν) σ b1 (3) σ u2 = (1 − ν) σ b2 where υ is the Poisson coefficient (0.42 for gold).

Simulations on Abaqus6.4/Ideasv9 were run to check this hypothesis. 3 dimensionnal models were build in order to take account of the deformation induced by the biaxial stress state. Results indicate that the cantilever profile calculated from eq.2 and simulated with extrapolated bi-axial stresses (cf. eq.3) are within 1% different in terms of deflection. 2.2. Effect of boundary conditions

For ideally clamped cantilever multilayers, the mean initial stress is relaxed in the in plane direction and the out of plane deflection is only sensitive to the initial gradient through the thickness. Due to technological process, the cantilever are usually not ideally clamped but T-shaped. In that case, the cantilever may rotate at the clamped condition when releasing the mean initial stress state [2]. This will result in an additional linear trend to the quadratic out of plane deflection profile described in eq.2. Simulations on Abaqus/Ideas were run to calculate the deflection profile of experimental structure which geometry was measured using an optical profilometer. The cantilever profile has been measured before the sacrificial photoresist etching to evaluate the rotation at the clamped boundary as well as the accuracy of the analytical solution in that case. Figure 3 shows the linear and quadratic counterparts of the out of plane deflection profile of gold bilayer cantilever subjected to bi-axial initial stress. Results show that the rotation

at the clamped boundary is not negligible. However extracting the quadratic shape of the profile in the real boundary condition gives the same results that in ideally clamped condition. 100

Deflection (µm)

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Initial deflection profile Quadratic trend

80

2

y = 1,22E-04x + 8,64E-03x + 6,05E-02 2 R = 1,00E+00

Linear trend

60

Analytical solution

40 2

y = 1,23E-04x + 4,44E-16x - 1,71E-13 2 R = 1,00E+00

20 0 0

200

400

600

800

1000

Length (µm)

Fig. 3. Decomposition of the quadratic and linear trend of the simulated cantilever initial profile with real boundary conditions and comparison with the analytical solution (L = 800µm, σb1 = 7.5MPa, σb2 = -75MPa) 2.3. Polynomial approximation of the cantilever profile

Experimental cantilever profile after stress relaxation is presented on figure 4. It can be noticed that the geometric profile is influenced by the technological process at the vicinity of the non ideal clamped condition and that the dispersion from cantilever to cantilever profiles seemed independent of the cantilever lengths according to the theory. Therefore this dispersion could be understood as an experimental dispersion.

Experiments

Fig. 4. : Cantilever profiles after stress relaxation The precision of the analytical formulation (cf. eq.2) is determined by the quality of the polynomial interpolation of the experimental profile. As presented

K. Yacine et al. / Microelectronics Reliability 45 (2005) 1776–1781

on figure 5, a straightforward manner would be to approximate the experimental initial profile with a polynomial interpolation of degree 2 : y= ax2 +bx+c. (4) where a, represents the quadratic trend b represents the linear trend c represents the unknown origin of the parabola

0,2

Residual (µm)

0,15

However the study of the residual (difference between the interpolate curve and the experimental characteristic) show that although the sum of the residual equals zero it does not follow a Gaussian distribution. Thus the calculation of the mean quadratic coefficient over the full profile may give rise to error. In addition the approximation is not accurate at the vicinity of the clamped condition where the interpolation is very sensitive to profile irregularities and where the sensitivity to the quadratic coefficient is very poor. Thus each profile has been investigated using a polynomial interpolation on different part of the profile avoiding the first 50 µm of the profile (cf. Figure 6) in order to center the residual and to get a gaussian distribution of the residual (cf. Figure 7).

Residual (µm)

25 20

0 15 -0,05

10

-0,1

86

141

196

252

307

362

417

472

527

Cantilever1 Cantilever2 Cantilever3 Cantilever4 Cantilever5 Cantilever6

1,0E-04

8,0E-05 0

100

200

583 -5

Part Part

30

Part

25

Part

20

Part

15

300

400

500

Fig. 8. : Evolution of the quadratic coefficient as a function of the partition for all cantilevers 1,5E-02 1,0E-02 5,0E-03

2

y = 9,74E-05x + 2,60E-03x + 1,23E+00 1 2 R = 1,00E+00 2 2 y = 8,42E-05x2 + 1,18E-02x - 3,71E-01 R 2 = 1,00E+00 3 y = 9,04E-05x2 + 8,44E-03x + 4,87E-02 R = 1,00E+00 2 4 y = 9,49E-05x2 + 9,09E-03x - 6,59E-02 R = 9,99E-01 5 y = 1,16E-04x2 - 2,06E-02x + 7,96E+00 2 R = 9,99E-01

0,0E+00 -5,0E-03 0 -1,0E-02 -1,5E-02

10

-2,0E-02

5

-2,5E-02

100

200

300

400

500

Cantilever1 Cantilever2 Cantilever3 Cantilever4 Cantilever5 Cantilever6

Length (µm)

0 0

100

200

300

400

600

Length (µm)

Coefficient b

Deflection (µm)

1,1E-04

9,0E-05

Fig. 5. : Polynomial interpolation of a cantilever profile and evolution of the residual as a function of the length 35

600

1,2E-04

Length (µm)

40

500

1,3E-04

0 31

-0,2

400

The evolution of quadratic coefficient “a” and linear “b” as a function of the selected partition of each cantilever profile are reviewed in figures 8 and 9.

5

-0,15

300

3. RESULT AND DISCUSSION

30

0,05

200

Fig. 7. : Evolution of the residual after the polynomial interpolation of each partition

35

2

y = 1,07E-04x - 1,24E-01x + 3,55E+01 2 R = 1,00E+00

0,1

100

-0,1

Length (µm)

Coefficient a

0,15

0 -0,05 0

-0,2

40

Experimental profile Residual

0,1 0,05

-0,15

Deflection (µm)

0,2

1779

500

600

Length (µm)

Fig. 6. : Polynomial interpolation of a cantilever profile and using different partition along the length

Fig. 9. : Evolution of the linear coefficient as a function of the partition for all cantilevers

600

K. Yacine et al. / Microelectronics Reliability 45 (2005) 1776–1781

thick deposit of evaporated (2µm thick) and electroplated gold (3µm thick) thin films that has been subjected to a near technological process. Ten indents were performed using the Berkovich tip to evaluate the Young’s modulus in each case. Result are reported on figure 10.

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V.38, p4125-4128, 2003 [6]. S. Brennan, A. Munkholm, O.S. Leung, W.D. Nix, " XRay measurements of the depth dependance of stress in gold films ", Physica, V.B283, p 125-129, 2000 [7] Youn-Hoon Min and Yong-Kweon Kim, In situ measurement of residual stress in micromachined thin films using a specimen with composite layered cantilever, J. Micromech. Microeng. V.10 (2000) 314-321 [8] W. Fang and J.A. Wickert, Determining mean and gradient residual stresses in thin films using micromachined cantilevers J. Micromech. Microeng. V.6 (1996) 301-309

Fig. 10. : Determination of Young’s modulus for evaporated and electroplated gold Young’s modulus of evaporated and electroplated gold were determined to be respectively 92±7GPa and 82±2GPa. These results indicate that the value of the deposit are very closed to the gold bulk value.

References [1]. Sebastien Rigo, "Microcaractérisation des matériaux et structures issues des technologies microsystèmes",thesis, institut nationnal polytechnique de Toulouse, 2003 [2]. Xiadong Li, Bharat Bhushan, Kazuki Takashima, ChangWook Baek, Yong-Kweon Kim, M. Fischer, "Mechanical characterisation of micro/nanoscale structures for MEMS applications using nanoindentation techniques", Ultramicroscopy 97 (elsevier), p481-494, 2003 [3]. H. D. Espinoza, B. C. Prorok, M. Fischer, "A methodology for determining mechanical properties of freestanding thin films and mems materials", Journal of the mechanics and physics of solids, V.51, p47-67, 2003 [4]. Chang-Wook Baek, Yong Kwean Kim, Yoomin Ahn, Yong-hyup Kim, "Measurement of the mechanical properties of electroplated gold thin films using micromachined beam structures", Sensors and actuators, 2004 [5]. H. D. Espinoza, B. C. Prorok, M. Fischer, "Size effect on the mechanical behaviour of gold thin films",J. Mat. Science,