Chapter 2 Design Technique for Microsystems Packaging and Integration
2.3 Mechanical Design
is no noise generated during its operation.
A typical TEC device is comprised of numerous thermoelectric cooling units, which are serial in terms of electrics, while parallel in terms of thermophysics. Each two thermocouples are electrically insulated by a heat-conducting ceramic sheet.
The performance of TE cooler is usually evaluated by Figure of Merit (FOM), namely,
FOM = α2s
ρTEkTE. (2.14)
where as is the Seebeck coefficient, and ρTE is the electrical resistivity of TEC. Typical values of FOM range from 0.02 K−1 to 0.05 K−1. Recently, the FOM of the MEMS-based TEC samples have had a magnitude increase.
Standard design rules are generally adopted in thermal management design, namely, a whole-set selection of TEC, heat-sink fins, and power supply for TEC. To increase cooling capability, TECs need to work in parallel with each other. For comparatively low tempera-tures in chips, TECs need to be connected in serial.
With the progress of MEMS technology, integration of miniaturized TEC and microsystem chips is close to being realized. Figure 2.12 illustrates the array elements of such a novel miniaturized TEC, whose refrigerating coefficient of performance is 0.3 and can be used in wireless communications directly.[14]
Figure 2.12 Miniaturized TEC codesigned and manufactured with microsensors
2.3 Mechanical Design[15−18]
2.3.1 Importance of Mechanical Design
In order to further reduce the package’s signal delay and improve its density between circuits so as to build on the rapid development of the integrated circuits, high-precision interconnections, fine packaging structure, and high functional density should be taken into consideration. With the functional density increasing, the problems of thermal stress, thermal-mechanical failure, and mechanical performance failure become increasingly serious,
26 Chapter 2 Design Technique for Microsystems Packaging and Integration and studying the mechanical performance becomes necessary. Especially with the develop-ment of multipins and fine pitches of bare chips packaging, and the microminiaturization of the multilayer surface electrode for mounting, package strength becomes increasingly im-portant, and the issue of reliability becomes more and more prominent. At the same time, with the adoption of new technologies, materials, processes, and structures, a great change will take place in micromechanical performance, especially microcracks induced by stress, structural deformation of components, and substrates induced by temperature variation, all of which can result in increased stress problems.
2.3.2 Basic Concept in Mechanical Design
Mechanical terms include: thermal mismatch, stress, deformation, strain, Hooke’s law, stress yield strength, fatigue, etc.
In microsystem packaging design, the stress change mainly comes from the following:
(1) Thermal condition’s variation.
Electronics packages contain different kinds of materials, and the temperature distribution is usually not uniform. Thermal stress will occur inside the package during the manufac-turing process because of mismatches in geometrical shape, thermal expansion coefficients, and material compound in the different parts. Therefore, mechanical design usually has a close relation ship with thermal management.
(2) External force.
On one hand, external forces come from manufacture, assembly, test, and usage. On the other hand, numerous force-sensitive structures in MEMS devices, such as inertial devices and mechanical sensors, can with stand different external forces.
(3) Inherence in microsystems.
A large number of MEMS devices, including MEMS switches, relays, micropumps, mi-crovalves, microjets, micromirrors, etc. cannot work correctly unless they are driven by corresponding forces, such as electrostatic force, electromagnetic force, fluid pressure, me-chanical force generated by piezoelectric materials, and thermal driving force. High temper-ature and pressure may occur in some local areas.
2.3.3 Mechanical Design Method
Mechanical analysis is an old but young technique. Various theories and experimental methods, solutions for specific problems, and high-efficiency computing tools cannot be presented seriatim here. In general, mechanical design methods can be divided into three categories: theoretic analysis solutions, numerical calculations, and computer-aided analysis.
1. Theoretical Solutions for Mechanical Problems
In a Cartesian coordinate system, the control equations of thermal stress and strain theory can be written as
2.3 Mechanical Design 27 Heat transfer and thermal stress in the electronics packaging occur in two stages: tran-sient state (switch on/off) and steady state (in operation). In the two stages, as for thermal stress and strain theory, temperature distributions, T (xi, t), in the package are obtained from the solution of thermal conduction Equation 2.15 under certain initial and boundary conditions, while displacement components, u, v, and w, in the package are determined from the solutions of Equations 2.16, 2.17, and 2.18 under certain boundary conditions of stress and displacement, and with temperature distribution obtained above as an essential bound-ary condition. Thermal stress components (σx, σy, σz, τxy, τyz, τzx) and strain components (εx, εy, εz, γxy, γyz, γzx) can be achieved from the solution of displacement partial differential equations.[2]
In Equations 2.15−2.18, u, v, and w are displacement components in the directions of x, y, z, respectively; Xx, Yy, Zz are the force components in the directions of x, y, z, respectively; α is the linear coefficient of thermal expansion; k is the heat conductivity; ν is Poisson’s ratio; λ is the Lam´e constant; G is the shear modulus; T is the transient absolute temperature; ρ is the mass density; Cv is the heat capacity per unit mass object; t is time;
and W is the thermal energy generated per unit volume per unit time.
2. Numerical Simulation Method
Except for a very few single and ideal problems, most packaging problems cannot get their displacement, stress, and deformation distribution from the analytical method. A numerical simulation is needed to solve these problems. Among the available numerical tools, the finite element method (FEM) is one of the widely used tools in mechanical analysis.
Presently, some of the design software packages that are widely used assist in the de-sign of microsystems packaging, such as ABAQUS, ANSYS, possess powerful FEM-based calculation modules for mechanical analysis.
Figure 2.13 shows the structural design diagram of a high-temperature package in the power-MEMS design. Metal tubes are sintered together with a silicon wafer by a glass powder binder at a temperature of about 1000◦C. This packaging structure can work in a wide temperature range, from room temperature to 600◦C. Moreover, the structure is very precise, and the interface precision is within micrometers. Therefore, it is important to study the temperature-dependent displacement and stress by using ANSYS. The main steps include the following:
Tube OD
Tube ID
Glass OD
Metal pipe
Glass binder Silicon
X H
Figure 2.13 Packaging structure of metal/glass/silicon structure
(1) Establish a model and assume the initial and the boundary conditions. The dimen-sions, thermal-expansion coefficient, Young’s modulus, and Poisson’s ratio of the studied
28 Chapter 2 Design Technique for Microsystems Packaging and Integration packaging structures should be determined in advance. Owing to the axisymmetric feature, the three-dimensional problem can be solved by a two-dimensional axisymmetric model.
(2) A typical mesh is shown in Figure 2.14. For areas with complicated structures, areas with high stress gradients or areas needing specific attention, a denser mesh is required to obtain more precise information.
(3) Calculate the displacement variation in the whole temperature range and work out the corresponding stress distribution. Typical displacement variations and stress distributions are shown in Figure 2.15a, b.
(4) Find out whether the result meets the requirement, and adjust parameters to recal-culate if necessary.
(5) Conduct structural design, fabrication, and experimental tests according to the nu-merical simulation result, compare them with the simulative data and modify the model if necessary.
(a) Typical displacement distribution (b) 3D von Mises stress distribution Figure 2.15 Displacement and stress distribution