273 ISSN 1392 - 1207. MECHANIKA. 2012 Volume 18(3): 273-279 Residual stress in a thin-film microoptoelectromechanical (MOEMS) membrane K. Malinauskas*, V. Ostaševičius**, R. Daukševičius***, V. Grigaliūnas**** *Kaunas University of Technology, Kęstučio 27, 44312 Kaunas, Lithuania, E-mail: [email protected]**Kaunas University of Technology, Kęstučio 27, 44312 Kaunas, Lithuania, E-mail: [email protected]***Kaunas University of Technology, Studentų 65, 51369 Kaunas, Lithuania, E-mail: [email protected]****Kaunas University of Technology, Savanorių 271, 50131 Kaunas, Lithuania, E-mail: [email protected]http://dx.doi.org/10.5755/j01.mech.18.3.1880 1. Introduction Microoptoelectromechanical systems (MOEMS) is not some special class of microelectromechanical sys- tems (MEMS) but in fact it is MEMS merged with micro- optics which involves sensing or manipulating optical sig- nals [1]. There are numerous membrane-based MOEMS devices involved in various precise measurements such as pressure sensors, accelerometers as well as resonators, mi- cromotors and capacitive micromachined ultrasonic trans- ducers (CMUTs). In MEMS devices such as CMUTs, the width of a membrane is typically 50 - 100 μm while the gap height reaches 0.1 μm in order to maximize device efficiency. Hence, the aspect ratio of these microdevices is as high as 1:1000. Only 0.01 degrees initial membrane bow puts the membrane in contact with the bottom substrate, making the device inoperable. During design stage it is necessary to consider all possible initial membrane deflec- tion contributors in order to ensure proper device opera- tion. There is a need to emphasize that all the derived ana- lytical formulations and simulation studies assume an ini- tially flat membrane shape. This contributes to unexpected device response as compared to theoretical response. MOEMS devices frequently employ free-standing thin- film structures to reflect or diffract light. Stress-induced out-of-plane deformation must be small in comparison to the optical wavelength of interest to avoid compromising device performance. A principal source of contour errors in micromachined structures is residual strain that results from thin-film fabrication and structural release. Surface micromachined films are deposited at temperatures signifi- cantly above ambient and they are frequently doped to im- prove their electrical conductivity. Both processes impose residual stresses in the thin films. When sacrificial layers of the device are dissolved, residual stresses in the elastic structural layers are partially relieved by deformation of the structural layers. Stress gradients through the thickness of a micromachined film are particularly troublesome from an optical standpoint, because they can cause significant curvature of a free-standing thin-film structure even when the average stress through the thickness of the film is zero. The relationship between stress and curvature in thin-film structures is an active area of research, both for the devel- opment of MOEMS technology and for the fundamental science of film growth [2]. To summarize there are three main factors that cause a membrane-based structure to bow: 1) residual stress developed during the deposition; 2) the effect atmospheric pressure on the membrane (constant ~ 0.1 MPa); 3) thermal stress contribution during deposition. 2. Thin-film stress The formation of thin films during fabrication of a MOEMS device typically takes place at an elevated tem- perature and the film growth process gives rise to the thin film stress. Two main components that lead to internal or residual stresses in thin films are thermal stresses and in- trinsic stresses. Thermal stresses are induced due to strain misfits as a result of differences in the temperature de- pendent coefficient of thermal expansion between the thin film and a substrate material such as silicon. Meanwhile, intrinsic stresses are generated due to strain misfits en- countered during phase transformation in the formation of a solid layer of a thin film. Residual or internal thin film stress therefore can be defined as the summation of the thermal and intrinsic thin film stress components [1] R T I (1) where R is the residual thin film stress, T is the thermal stress component, I is the intrinsic stress component. 3. Governing equations for stress in thin films Between a film and substrate the stress is predom- inantly caused by incompatibilities or misfits due to differ- ences in thermal expansion, phase transformations with volume changes and densification of the film [1]. Simple solutions of mechanics of materials are therefore employed to study the mechanical residual stress induced in thin films. The solution that will be discussed here involves the biaxial bending of a thin plate [2]. After a film is deposited onto a substrate at an elevated temperature, it cools down to a room temperature. When the film/substrate composite is cooled, they contract with different magnitudes because of different coefficients of thermal expansion between the film and the substrate. The film is subsequently strained elastically to match the substrate and remain attached, causing the substrate to bend. This along with the intrinsic film stress developed during film growth, gives rise to a total residual film stress [2-6]. A relationship between the biaxial stress in a plate and the bending moment will now be discussed. Parts of the derivation are based on Nix’s analysis [2]. Fig. 1 presents free body diagram illustrating bending moment acting on a plate. From Fig. 1 the bending moment per unit length along the edge of the plate M, is
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Residual stress in a thin-film microoptoelectromechanical (MOEMS)
membrane
K. Malinauskas*, V. Ostaševičius**, R. Daukševičius***, V. Grigaliūnas**** *Kaunas University of Technology, Kęstučio 27, 44312 Kaunas, Lithuania, E-mail: [email protected]
**Kaunas University of Technology, Kęstučio 27, 44312 Kaunas, Lithuania, E-mail: [email protected]
***Kaunas University of Technology, Studentų 65, 51369 Kaunas, Lithuania, E-mail: [email protected]
****Kaunas University of Technology, Savanorių 271, 50131 Kaunas, Lithuania, E-mail: [email protected]
http://dx.doi.org/10.5755/j01.mech.18.3.1880
1. Introduction
Microoptoelectromechanical systems (MOEMS)
is not some special class of microelectromechanical sys-
tems (MEMS) but in fact it is MEMS merged with micro-
optics which involves sensing or manipulating optical sig-
nals [1]. There are numerous membrane-based MOEMS
devices involved in various precise measurements such as
pressure sensors, accelerometers as well as resonators, mi-
cromotors and capacitive micromachined ultrasonic trans-
ducers (CMUTs). In MEMS devices such as CMUTs, the
width of a membrane is typically 50 - 100 μm while the
gap height reaches 0.1 μm in order to maximize device
efficiency. Hence, the aspect ratio of these microdevices is
as high as 1:1000. Only 0.01 degrees initial membrane bow
puts the membrane in contact with the bottom substrate,
making the device inoperable. During design stage it is
necessary to consider all possible initial membrane deflec-
tion contributors in order to ensure proper device opera-
tion. There is a need to emphasize that all the derived ana-
lytical formulations and simulation studies assume an ini-
tially flat membrane shape. This contributes to unexpected
device response as compared to theoretical response.