A Method of Minimizing Mechanical Stresses in a Sensitive Element of Micromechanical Devices at Packaging
Over many years a particular attention has been paid to microelectromechanical systems (MEMS) SE packaging due to its significance for final parameters of the finished device . Among lots of proposed concepts for decoupling a primary transducer or SE, the worthiest solutions have appeared due to the following trend: SE package is much more efficient if the required parameters of mechanical decoupling are set beforehand in a silicon intermediate layer or support chip. One of the support chip functions is to minimize mechanical stresses that happen, for example, as a result of thermal linear expansion of a device package base with installed SE.
At present there are several fundamental trends in microsystem technology (MST) that are most package- sensitive. One of these covers integrated pressure transducers whose operation principle is based in some cases on the piezoresistive effect. The application of this effect as the key operation principle has been widely spread due to relatively high accuracy of SE  measuring characteristics and the simplicity of the structure using piezoresistors. But there are some few factors that can deteriorate output characteristics. The most critical are mechanical stresses which contribute to an output signal — applied external medium pressure ratio. The mechanical stresses contribution can result in a shift and ratio zero drift, hysteresis occurrence in an operation cycle, response time change under rapidly changing temperature. Therefore, to design a high-precision PMS it is necessary to match the designed PMS SE components with minimal mechanical stresses on transient interfaces in the SE membrane-device package system, or to make sure of compensating for negative factors influence.
Undoubtedly, struggling for a maximal result you face with both positive and negative aspects in designing the finished product. If you consider SE accuracy as a priority parameter, then the second most important criterion is simplicity of its manufacturing process. So, both criteria have been used for further consideration and selection of support chips as SE constituent part. The support chip structure should provide a minimal undesirable components contribution to an output signal and the support chip itself can be fabricated in a unique cycle based on microelectronic devices processing line.
Among relatively inexpensive PMS SEs, the most popular has appeared to be mechanical decoupling with a package formed as a massive support chip whose height is several fold greater than a SE chip thickness (model I illustrated in Fig. 1a)  or similar support chip but already mounted on a ceramic pipe (model II shown in Fig. 1b). SE membrane installed in this way to a first approximation enables partial removal of mechanical stresses related to SE packaging.
A SE membrane is assembled on a support chip (model I and II) by gluing, soldering and doping . Along with other techniques, a support chip of model I is more often manufactured by electro-stimulated (anodal) bonding of several silicon wafers or borosilicate glass which is joined with SE chip . However, from the technological viewpoint a mechanical decoupling of such a type is not always effective and justified due to an increased amount of operations and applied engineering in comparison to a silicon wafer standard processing cycle. Besides, a significant disadvantage of this concept is a requirement that all layers that are constituent parts of a SE and support chip match the material thermal expansion coefficient (TEC). In addition, anodal bonding of two chips leads to pre-stressed state in a SE membrane that has negative effect on piezoresistors characteristics and causes initial bridge unbalance in an electric circuit to which SE is hooked up. The abovementioned case will be illustrated below by PMS SE output signal dependence on applied external pressure (Fig. 8).
An alternative approach to designing a support chip form is based on using predefined planar and bulky temperature compensation elements [5, 6] in its structure. Among already existing support chip structure variations, there have been presented those capable of minimizing mechanical stresses and whose structure does not introduce an additional negative functional, such as the appearance of SE dependence on acceleration. Fig. 2a, b shows two types of support chips (model III and IV) whose geometry has temperature compensators of elastic stresses, and Fig. 3 illustrates model V offered by the authors in this research.
Support chips whose structure consists of temperature compensators of elastic stresses can be formally divided into two classes. The first class covers chips capable of compensating for mechanical stresses affecting along XY plane (Fig. 2b and Fig. 3) (rectangular coordinate system). The second class includes chips that also minimize stresses along XY plane and may cover direction along Z axis as well (Fig. 2a).
EXPERIMENTAL PART. ANALYZING MECHANICAL STRESSES IN SUPPORT CHIP
While analyzing mechanical stresses in the highlighted various structures, dimensions and materials they are made of have been borrowed from the descriptions of operating PMS SEs . To take into account some critical moments of a mathematical model, the final structure consisted of the following operating layers: a chip with PMS membrane, support chip, a package base or ceramic pipe which functions as a SE component. A SE was considered to be manufactured from single-crystalline silicon as well as a support chip with temperature compensators for models II-V. For model I a chip with membrane was placed on borosilicate glass. Model I and III package base was made of kovar. As for models II, IV and V, their package fixing is done by a ceramic pipe and copper tube, the latter being package-welded.
To choose an optimal structure among various class samples, an analysis has been made for a few similar models. Below are the results of simulation by a finite element method for support chips characterized by the most optimal functionality among each class representatives.
As seen in Fig. 4a, if a SE is installed on a support chip made from borosilicate glass under temperature alteration (the base with a support chip is heated up), a membrane appears to be mechanically strained resulting in a negatively bended membrane in the gas flow reverse direction. A membrane of model II behaves similarly when a massive silicone base is located on a ceramic pipe with no temperature compensators. This joint effect from mechanical stresses of opposite directions will result in output signal decaying, and an external observer might make an improper assumption that the measuring gas flow pressure has been reduced. The analogous situation occurs in relation to negative temperature area but a membrane bend and mechanical stress effect are directed the same way in this case.
In comparison to a glass-made support chip with the maximum membrane chip contact area, model III has contact area of no more than 30 % of the lower base facet but models II, IV and V interact primarily by a ceramic pipe which afterwards is mounted inside a copper tube rigidly welded to the package. In this case the contact area with the ceramic pipe for models II, IV and V does not exceed 30 % either. Therefore, reducing the support chip contact area with the package as it has been demonstrated in Figs. 5 and 6 makes it possible to decrease strain distribution zones, which is also true for model II. However, as for model II, thermal expansion of a ceramic pipe with a support chip is mounted on due to symmetry will cause initial strain of a SE membrane affecting SE output characteristics.
A support chip in the form of a corrugated surface (model III) possesses radial symmetry, and as distance relative to a chip center increases, mechanical stresses totally relax. The advantage of this structure is that among the investigated analogs this type of a support chip is the least exposed to mechanical stresses related to temperature variations because the entire corrugated surface functions as a bulky temperature compensator. According to  a variation of support chip lateral parameters and corrugated surface wall thickness makes it possible to diminish material stress states up to 95 %. Moreover, model III and V structure does not require auxiliary sealing, and such a SE version fits both an absolute sensor and differential pressure. The disadvantage of corrugated support chips is a fabrication complexity to obtain specified (target) crystallographic surfaces by liquid etching from both chip sides and their brittleness (fragility) while being assembled  and in highly defective areas.
Compared to model III structure, in model IV support chip where package bonding is done by a suspension and tube, strains caused by similar temperature fluctuations are also minimal and do not affect a SE performance. All temperature changes related to external medium are neutralized by a ceramic pipe at the first stage and afterwards by a suspension at the end of which there is a base to fix a tube. The advantage of this structure is simplicity in manufacturing a support chip whose key element is a base to bond a ceramic pipe and flat suspension joining the base with the rest part of the chip. Radial symmetry of the base and its location site enable mechanical package decoupling with minimal suspension interaction. A burden for this type of a support chip and SE itself relates to a necessity to fabricate for absolute pressure sensor SE an additional protection cover for SE membrane sealing. Moreover, the system even with a highly rigid suspension, as in this variant, can function as a mechanical fluctuation concentrator that is a structure disadvantage.
By its geometrical properties the suggested support chip of model V is sufficiently simple in production due to a necessity of merely single-side modification for a wafer surface curvature. From the viewpoint of silicon technology and production, a similar solution has a number of advantages as likelihood technology errors and inaccuracies are minimized. A chip temperature compensator geometry looks like a set of complicated concentric rings whose structure is not through. Therefore, as mentioned above, this model will not need additional sealing.
OBTAINING PMS SE OUTPUT CHARACTERISTICS IN TEMPERA¬TURE VARIATION MEDIUM
To define contribution of mechanical stresses that can be transferred to a SE membrane and to obtain its output characteristics in temperature variations medium the following analysis stages have been realized:
Using CAD Comsol Multiphysics 20 micron-thick SE has been modeled (Fig. 7a).
Basing on the analysis of the most strained membrane areas and the obtained results, the sites for allocating piezoresistors have been chosen (Fig. 7b).
Afterwards SE piezoresistors have been hooked up to a bridge circuit resulting in output characteristics — ratio of Uout output signal to membrane-applied pressure.
Having obtained SE output characteristics when a membrane is not exposed to mechanical stresses, we have taken into account temperature warm-up-cooling resulting in characteristics plotted in Fig. 8.
According to the given plots (Fig. 8) the dependence of output signal for various support chips suffers from a linear shift along Uout axis, which relates to mechanical stresses caused by the medium temperature variations. As mentioned before, in models I and II in positive temperature area a lowering is observed (Fig. 8a) as a result of two counteracting mechanical stress types. Under negative temperatures signal level is going up, which speaks for coincided directions of internal and external stresses (Fig. 8b). As for model III, the ratio does not vary within entire temperature range, which proves high efficiency of SE support chips with corrugated surface. Support chip characteristics of models IV and V suffer inconsiderable shift, which also proves their efficiency in minimizing elastic fields while decoupling SE from a device package.
In the course of the work five types of support chips have been tested. The analysis made by a finite elements method under thermal expansion-compression of a device package body has demonstrated that a support chip of models I and II requires strict TEC materials matching between all layers being constituent parts of the membrane-support chip-package system. In this case PMS SE output signal of model I depends heavily on temperature, even if variation is the slightest.
Among the offered number of support chip models, model III has shown the best PMS SE-obtained output characteristics with the least mechanical stress transferred from a package body to SE membrane. The minimum value of the transferred mechanical stress is achieved by thinning a support chip corrugated surface wall which has been thoroughly described in . Besides, peculiarities of a support chip complicated curvature and material in use impede its production.
Having analyzed the design results and the simplicity of models IV and V structure from the production viewpoint, the preference was given to the development of this type of support chip with planar temperature compensation elements in its structure, as the model is the least labor-intensive and is the best in terms of strength. The ratio of Uout output signal and applied pressure of SE based on these models is slightly dependent on the medium temperature, which complies with the target requirement that undesirable contributions to output characteristics should be minimized. The support chip of model V proposed by the authors fits both an absolute sensor SE and differential pressure, which makes it a worthier solution in comparison to the highlighted support chips.
NOVELTY OF RESULTS
The authors consider the following points and results in this paper as novel:
1. An original variant of a support crystal design with planar temperature compensation elements has been proposed. It allows reducing the transmission of parasitic effects to the SE of PMS and, thereby, reducing undesirable components in the output characteristic Uout from the applied pressure.
2. The design of the model V support crystal is less expensive in terms of technology as compared to the designs of support crystals with similar characteristics.
3. The proposed model of the support crystal design is universal and applicable to microsensors of absolute and differential pressure.
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