Author: Sharma, Akshdeep
Date published: December 1, 2011
(ProQuest: ... denotes formulae omitted.)
In micro-electro-mechanical systems (MEMS) technology surface micromachining is widely used for creating thin film mechanical structures. There has been great interest in studying mechanical properties of thin films. The mechanical properties are very critical to the microstructure devices and can also influence the productivity and quality of these structures [1, 2]. One of the most important mechanical proprieties of thin films is the residual stress. Excessive compressive or tensile stress results in buckling, cracking, splintering and sticking problems. In particular, the residual stress is very important in MEMS applications and in cases where the thin film is designed to be a moving part. The mechanical displacement of the film is largely affected by the stress.
The investigation is concentrated on the development of two techniques buckling and rotation [3-5]. The buckling technique is based on the buckling of a beam when exceeding a critical strain level. Therefore, an array with different beam lengths is required. The rotation technique, on the other hand, converts the extension or contraction of the material into a rotation, which can be easily measured. These structures have been designed, simulated, fabricated and tested experimentally, using thin Au plated film. Both techniques have been shown to be promising methods for simple and accurate onchip thin-film strain measurements. The results of stress calculation using each method are discussed and compared with conventional wafer curvature to calculate the average stress.
2. Test Structures
Presently, it is very difficult to predict the residual stress from a growth process because the residual stress is strongly affected by deposition conditions and follows fabrication processes. Many techniques of stress measurement in thin films have been studied and proposed in the past several decades. The conventional method is measuring the wafer curvature to calculate the average stress using the Stoney's equation . The stress can also be determined by nanoindentation technique . The most popular and simplest method is the micromachining technique as it does not require special equipment and can be done by in situ measurements.
This paper focus on the test structures fabricated by micromachining technique used for residual stress measurement. Essentially, the test structure under stress is released after removing the underlying sacrificial layer. The structure will deform by increasing or decreasing the dimension of the structure because of the residual stress. The residual stress can thus be derived from this deformation. Several types of test structures for residual stress measurement are described in detail as follows.
2.1. Buckling Techniques
Stress in the thin film results in an extension or contraction of the released structure. This is basic principle of the stress measurement by buckling technique. The typical device normally used is a micro bridge. A micro bridge can only measure compressive stress. A micro bridge, under compressive stress buckles after release. The stress can be expressed using critical buckled bridge dimensions as Eq.
where E is the elastic modulus, v is Poisson's ratio and E/ (l-v) is the biaxial modulus, L is the length of the critical buckled bridge, and h is the thickness of the bridge.
For tensile stress, the conversion structures shown in Fig. 1 are needed. The ring structure in Fig. 1(a) can be used to measure tensile stress only. When the freestanding structure is released, the ring deforms to an oval under tensile stress and the central beam becomes compressive. After removing the sacrificial layer in Fig. 1(b), the diagonal beams convert the tensile stress into compressive stress in the central beam and the compressive stress causes the central beam to buckle. On the other hand, in the presence of compressive stress, outer beams get buckled . Stress value can be derived from the maximum displacement of the central beam of a Guckel ring  as
where h is the film thickness, Rc critical buckel radius.
2.2. Rotational Techniques
The micromachined rotating structures as first presented by Drieenhuizen et al.  is shown in Fig. 2. The structure consists of two test beams and a rotating indicator beam. One end of each test beam is anchored to the substrate and the other is connected to the indicator. When the test beams are released by etching away the sacrificial layer, they are elongated or contracted due to the residual stresses. The test beams are slightly separated at the connection to the indicator beam, thus create a rotating deflection of the indicator beam. The deflection is directly proportional to the residual stress. Its direction corresponds to the type of stress, i.e. tensile or compressive stress. The residual stress can be calculated using Eq. 3, where LA, LB, W, O and d are defined in Fig. 2(a). The CF is correction factor that consider the effect turning point width. The deflection of the indicator can be determined quite easily using an optical microscope or SEM.
One of the improved test structures is the double indicator structure shown in Fig 2(b) . It can increase the sensitivity of the measurement by using two symmetrical structures as shown in Fig. 2(b).
In this way, the double deflection can be measured. Under-etching and technology variations are eliminated. The stress can also be calculated by using the Eq. (3).
2.3. Long-short Beam Strain Sensor
The long-short beam strain sensor is designed by Pan and Hsu . Fig. 3 schematically shows the strain sensor.
The sensor is comprised of a pair of long and short cantilever test beams with different lengths, long test beam and short test beam. The two beams are connected by a tip beam as an indicator. After the freestanding part is released, the two test beams will extend or contract due to residual stress in the thin film. The displacement (d) caused by the deflection of two test beams can be read out using indicator and vernier by optical microscope or SEM. The stress is given by:
where ? is the conversion factor related to geometrical parameters of the structure . This sensor can measure both tensile and compressive residual stress.
3. Fabrication Process Steps
Fig. 4 shows the schematic view of process steps for test structures as a part of RF MEMS switch fabrication . A set of microstructures were realized using surface micromachining techniques, on a 2" diameter P-type <100> oriented silicon wafer. A thermal oxide was grown on the substrate, and then a conventional positive tone photoresist was deposited and patterned as a spacer layer. After that, the wafer was deposited with a chromium adhesion layer and gold seed layer by sputtering technique. Then a second photoresist was deposited and patterned, to work as a mould for the electroplating of a structural layer. The 2 µ?? thick gold was plated by using a commercial sulphite bath solution. Wet etching methods were used to remove the photoresist mould and seed layer followed by a dry etching process to remove the sacrificial photoresist layer without generating suction forces between membranes and surface.
4. Results And Discussion
4.1. Stress Measurement Using Wafer Curvature
Stress on thin films was investigated based on wafer curvature. Wafer curvature measurement is done by scanning the surface using profiler (AMBIOS XP-I). Silicon wafers are pre-stressed by depositing a ?µ?? thick oxide using a wet oxidation process. Wafer curvature is measured before and after the electroplated Au thin film deposition. Due to the change in curvature after deposition, the intrinsic stress of the film can be deduced, using the Stoney's formula (Eq. 5). This equation yields a reasonable estimation of the stress in the thin films, considering the film thickness tf much smaller than the substrate thickness ts.
where, Es and vs are respectively the substrate Young's modulus and Poisson' s ratio, R8 and Rsf the measured curvature radii before and after film deposition. The accuracy of the film stress measurement is about 10 %. A better accuracy can be obtained for small radius of curvature equivalent to highly stressed thin film. The measured average stress for 2 µ?? thick electroplated gold is 117.2 MPa and is tensile in nature.
4.2. Stress Grathent Measurement
The total stress in a material is the sum of the mean residual stress and the stress grathent and can be written as:
The stress grathent can be extracted from the deflection amplitude of different suspended cantilevers. When the structure is released, the stress s? is relaxed and only the stress grathent acts on the beam. The bending moment due to the stress grathent is written as:
A linear stress grathent can be approximated and the resulting stress is defined as:
where γ is the linear stress grathent. Combining (7) with (8), ? can be written as
where I is the moment of inertia of a rectangular beam. The moment of inertia at the endpoint of a cantilever is expressed as (Equ.10) and the stress grathent is calculated from the displacement amplitude.
The displacement at the edge of the cantilever is measures with an optical profiler (Veeco Wyko NT 9800), as shown in Fig. 5. The stress grathent 3. 48×10^sup -4^µ^sup -1^ is extracted from the fit of the tip deflection versus the cantilever length curve in Fig. 6.
4.3. Stress Measurement from Devices
On chip test structures were designed to measure either compressive or tensile stress in the structural layer. According to wafer curvature measurement, a tensile stress was expected in the Au film and Guckel rings were fabricated to measure this stress. As shown in Fig. 7, tensile stress tends to stretch the rings towards the anchors, inducing compressive moment on the central part. Stress value can be calculated from the ring dimensions for which buckling of the central part occurs. Stress value of the film can be derived from the maximum displacement of the central beam of the ring. The accuracy of this technique depends on the ability to find the closest set of rings for which small variation of beam length induces buckling. The closest buckled set in an array is 110-120 µ?? inner diameters. The 3D optical profiler images of the ring array and SEM micrograph of critical buckle central beam of inner diameter 120 µ?? are presented in Fig. 7. Accordingly calculated stress was 126.8, 106.5 MPa for beam central radius 55, 60 µ?? respectively. Considering the fact that the optimal ring for which the beam begins to buckle should be placed between the two rings. The calculated stress value is in good agreement with the 117 MPa tensile stress measured using wafer curvature. The SEM micrograph of critical buckle diamond structure is shown in Fis. 8.
4.4. Stress Measurement Using Rotation Structures
The pointer structure magnifies tip deflection, measured using SEM shown in Fig. 9. This pointer displacement is used for residual stress measuerment. Similar is the case with double indicator and long short beam strain sensor shown in Fig. 10 and 1 1 respectively.
Several types of stress measurement methods including buckling technique, rotating technique, double indicator and long-short beam strain sensor have been reviewed. We have designed, fabricated and characterized the test structures for each method and results are shown in Table 1 . The in situ residual stress has been measured for the same film by using different methods. It only requires a single structure and can also be used for tensile and compressive stress measurement. The double indicator structure is practically preferable for the stress monitoring because of its high reliability, easier calculation and higher accuracy.
The present work is supported by SAC (ISRO) Ahmadabad. The authors are thankful all the member of Sensors and Nanotechnology Group for their help in fabrication of the devices. The author would also like to thank CSIR (Council of Scientific and Industrial Research) Government of India for their financial grant.
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1 Akshdeep SHARMA, 1 Deepak BANSAL, 1 Maninder KAUR, 1 Prem KUMAR, 2 Dinesh KUMAR, 3 Rina SHARMA and 1 K. J. RANGRA
1 Sensors and Nanotechnology Group, Central Electronics Engineering Research Institute (CEERI)/
Council of Scientific and Industrial Research (CSIR), Pilani, Rajasthan 333031, India
Dept. of Electronics Science, Kurukshetra University, Kurukshetra, Haryana, India
3 National Physical Laboratory (NPL), NewDelhi-110 012, India
E-mail: firstname.lastname@example.org, email@example.com, firstname.lastname@example.org,
Received: 29 June 2011 /Accepted: 16 November 2011 /Published: 28 December 2011