Characterization method of thermomechanical parameters for microelectronic materials

Reliability of thermomechanical simulations is critically linked to the accuracy of the mechanical properties that govern the behaviour of structure, like Young's modulus (E) and coefficient of thermal expansion (CTE). For many cases, the values found in literatures are dealing with bulk properties without detailed information on temperature effects. To address such issues, it is necessary to measure the materials parameters as a function of temperature. The measurement of CTE is usually accomplished by evaluating the thermal deflections of a subjected material layer deposited on a substrate, providing that E is known at a specific temperature of experiment. A bilayer method, based on theory of elasticity, is proposed to determine both E and CTE for a given temperature with a good resolution. This paper presents the theoretical analysis, the design and process of the microsystem test structures, and the main calculation results.     

Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations

The novelty of this paper is the use of an efficient beam theory for bending, free vibration and buckling analysis of functionally graded material (FGM) beams on two-parameter elastic foundation. The present theory accounts for both shear deformation and thickness stretching effects by a parabolic variation of all displacements across the thickness, and satisfies the stress-free boundary conditions on the upper and lower surfaces of the beam without requiring any shear correction factor. Due to porosities, possibly occurring inside FGMs during fabrication, it is therefore necessary to consider the vibration, bending and buckling behaviors of beams having porosities in this work. The equation of motion for FGM beams is obtained through Hamilton’s principle. The closed form solutions are obtained by using Navier technique, and then fundamental frequencies are found by solving the results of eigenvalue problems. The validity of the present theory is investigated by comparing some of the present in literature. It can be concluded that the proposed theory is accurate and simple in solving the bending, free vibration and buckling behaviors of FGM sandwich beams.     

A four variable refined plate theory for nonlinear cylindrical bending analysis of functionally graded plates under thermomechanical loadings

In this paper we present a new application for a four variable refined plate theory to analyse the nonlinear cylindrical bending behavior of functionally graded plates subjected to thermomechanical loadings. This recent theory is based on the assumption that the transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The theory accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The material properties are assumed to vary continuously through the thickness of the plate according to a power-law distribution of the volume fraction of the constituents. The non-linear strain-displacement relations in the von Karman sense are used to study the effect of geometric non-linearity. The solutions are achieved by minimizing the total potential energy and the results are compared to the classical and the first-order theories reported in the literature. It can be concluded that the proposed theory is accurate and simple in solving the nonlinear cylindrical bending behavior of functionally graded plates.     

Power MOSFET quality and robustness enhancement with a new QBD characterization performed at probe–die–wafer level

The quality of the gate oxide is a central parameter for power MOSFET devices dedicated to automotive applications. Reliability is systematically evaluated through electrical tests. The purpose of this study is to apply the Q_BD test directly at probe–die–wafer level and to correlate its results with reliability test conclusions. In other words, this new kind of Q_BD test is a monitor of power MOSFET robustness which helps identify extrinsic failures and the process steps responsible. In summary, it is an accurate and fast measurement method of identifying weakened parts and enhancing device quality.     

Analysis of the transverse cracking in hybrid cross-ply composite laminates

A modified shear-lag analysis, taking into account the concept of interlaminar shear stress, is employed to evaluate the effect of transverse cracks on the stiffness reductions in different glass/epoxy and graphite/epoxy hybrid cross-ply laminates. The modified shear-lag model is proposed that assumes interlaminar adhesive layer between two neighbouring layers transferring not only interlaminar shear stress but also normal stress. The stress distribution is solved by the used model which rigorously satisfies the stress equilibrium equations, boundary conditions and the traction continuity at interfaces between layers.     

Smart 3-D Finite-Element Modeling for the Design of Ultra-Low On-Resistance MOSFET

A 3-D electrical finite-element model (FEM) for the design of an ultra-low on-state resistance power MOSFET device is presented. Model building and layer conductivity are discussed to take into account microscopic, technological, and electrical effects, such as metal step coverage and MOS behavior of each elementary cell of the transistor. Model simplifications are also presented to ensure time-efficient simulations. FEM gauging is then achieved, by comparing simulation results to electrical measurements, on devices subjected to top metallization debiasing effects. Simulations show a good agreement with measurements for result errors at less than 2%. The aim of this paper is to provide an accurate estimation of the contribution of parasitic elements such as the shape and number of power bonding wires or top metallization thickness to power device on-state resistance (R_ON). The 3-D electrical FEM is a mandatory first step towards an accurate electrothermal FEM for the design of efficient power products.     

Identification of machine–tool–workpiece system dynamics

The aim of this paper is to present a method to identify the dynamics of a structure composed of a milling machine, a tool and a workpiece. The excitation is obtained as a result of the interrupted cutting of a narrow workpiece width and single tooth milling operations. This provides a pulse-like cutting force. The three components of the cutting force and the relative motion between the tool and the workpiece are measured simultaneously. A method was developed to determine the nine terms of the structural transfer matrix under a single cutting operation and without any assumption on the excitation direction. The proposed method is experimentally validated.     

Dynamic cutting force measuring

Piezoelectric dynamometer are generally used for force measuring. Delivered signals are distorted due to their self dynamic behaviour. Their dynamic characteristics are identified under normal machining operation. The proposed method is based on the interrupted cutting of a specially designed workpiece that provides a strong broadband excitation. The three components of the exciting force and the acceleration of the gravity centre of the dynamometer cover plate are measured simultaneously. Although the input acceleration components are correlated in the frequency bandwidth of interest, a method is presented to determine the nine terms of the dynamometer transfer matrix from only one cutting experiment. Series of different pulse excitations are carried out to validate the proposed method. Then, the determined transfer matrix is used for dynamic cutting force compensation under some milling operations.     

Some observations on the evolution of transversal hygroscopic stresses in laminated composites plates: effect of anisotropy

The transient and non-uniform moisture concentration distributions in laminated composite plates give rise to transient and non-uniform stress fields [Composite Structures 30 (1995) 201; Communication au 12 journées nationales sur les composites, JNC12 (in French), 2000, 969; Composite Structures 55 (4) (2002) 393]. It was shown [Composite Structures 30 (1995) 201; Communication au 12 journées nationales sur les composites, JNC12 (in French), 2000, 969; Composite Structures 55 (4) (2002) 393] that the heterogeneity and the anisotropy of such plate, have an influence on the distribution of transient hygroscopic stresses through the thickness of composite plates. The purpose of this paper is to investigate the effect of anisotropy on the transverse residual stresses and strains in polymer composite systems under long term exposure to hygrothermal environments. The anisotropy is evaluated using the degree of anisotropy introduced from polar representation method of tensors [Communication au 12 journées nationales sur les composites, JNC12 (in French), 2000, p. 969; Composite Structures 55 (4) (2002) 393; Mechanical Behaviour, Design and Application, 1990, p. 29; Computer Aided Design in Composite Material Technology, 1988, p. 243; Proceeding of the seventh International Conference on Composite Materials, 1989, p. 358; Proceedings of the Fifth French Conference on Composite Materials, 1986, p. 267; Eighth International Conference on Composite Materials (ICCM-8), Honolulu (USA), 1991, p. 1; 12th International Conference on Composite Materials (ICCM-12), Paris, 1999; 12th International Conference on Composite Materials (ICCM-12), Paris, 1999; 12th International Conference on Composite Materials (ICCM-12), Paris, 1999; Découplage et quasi-homogénéité pour les stratifiés renforcés par tissus équilibrés”, JNC12, (in French), 2000, p. 265]. The principal objective of this study is to contribute to the understanding and predicting the behaviour of transversal hygroscopic stresses and strains in the studied composites as a function of the degree of anisotropy. The analysis has indicated that: (i) the reduction of degree of anisotropy favours the transversals hygroscopic stresses to be in tensile state, contrary to the thermal stresses where they become in compressive state; (ii) the values of the transverse residual stresses in laminates having the same degree of anisotropy are nearly identical; (iii) from certain value of in-plane degree of anisotropy which is about 38.5% for the used material in this study, the sensibility to the anisotropy is more felt. For inferior values, the transversal residual stresses are nearly identical to those of quasi-isotropic laminates.     

Convection behavior analysis of CMOS MEMS thermal accelerometers using FEM and Hardee’s model

This paper presents convection behavior investigation of CMOS MEMS convective accelerometers using both analytical and FEM techniques. In a first part, a newly developed accelerometer 3D model is used in FEM simulations to model convection behavior as a function of design geometry and temperature. Using various sizes of two different cover shapes, sensitivity reading and its maximum position in cavity are found to be largely affected by both cover size and shape. In addition, a sensor with cavity width of 600 μm produces sensitivity saturation starting at a cavity depth of 200 μm, for both cover shapes. Using FEM data and curve fitting, differential temperature is claimed to be linearly linked to the effective heater temperature to the power of 1.7. Using the same cavity design and from computed heating efficiency values, we found that a 60 μm width heater offers the best efficiency. This cavity and heater designs give an optimal detector position of 120 μm from heater center along the sensitive axis. Moreover, dual axis accelerometers are found to be more power efficient than single axis ones. In the second part, we present Hardee’s spherical model and investigate its possible application on convective accelerometers. It is shown that inner and outer isotherms deformation, caused by accelerometer design and convection process, should be modeled by including sensor geometry parameters in the derived governing equations. Moreover, Hardee’s biasing temperature relation has to be revised if it is to be used for convective accelerometers.