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Gas transport mechanisms that characterize the hermetic behavior of MEMS packages are fundamentally different depending upon which sealing materials are used in the packages. In metallic seals, gas transport occurs through a few nanoscale leak channels (

Hermeticity of the MEMS package is a measure of the ability to maintain an acceptable level of stable and sometimes inert ambient in the cavity. It impacts device reliability and hence lifetime expectancy. Poor hermeticity can lead to ingress of contaminants, ambient gases and moisture, thereby causing performance degradation. Good hermeticity is essential for compliance with performance and reliability standards.

A schematic of a typical MEMS package of interest is shown in ^{−3} cm^{3}.

The most commonly used sealing materials to provide hermeticity are low-melting point eutectics such as AuSn [

It is important to note that gas transport mechanisms in the two sealing materials are completely different. The helium fine leak test [

_{cavity}^{−4} cm^{3}) and metal-sealed packages (_{cavity}^{−4} cm^{3}). The test conditions include a bombing time of 6 hours at 4 atm (gauge) and a dwell time of 10 minutes. In the experiment, individual packages as well as batches containing multiple identical packages were tested; in the batch tests 20 polymer-sealed packages and 54 metal-sealed were used. The signals obtained from the batch tests and single package tests are shown in

The normalized signal of the polymer-sealed packages is similar to that of the single package signal (

The above results clearly indicate the different gas transport mechanisms exist in the two packages. In metallic seals, gas transport occurs through a few nanoscale leak channels (

In this review article, the techniques to measure true leak rates of MEMS packages with the two sealing materials are described and discussed: a helium mass spectrometer based technique for metallic sealing and a gas diffusion based model for polymeric sealing [

In both molecular gas conduction and gas diffusion, the gas flux can be described by the gas conductance equation in a general form as [^{2}sec), _{tube}_{0} is the universal gas constant (8.3145 J/molK),

In gas conduction, gas molecules travel through a nanoscale channel and thus can be regarded as a Cartesian 1-D flow problem. The pressure gradient inside the flow channel is developed almost instantaneously, and transient effects are negligible. Thus, the gas transport can be predicted by simply considering the conduction equation (

Conductance can be expressed in terms of the channel dimensions, fluid properties and ambient conditions. The exact expression depends on the nature of the flow regime. Gas flow is divided into three regimes based on the nature of the flow as determined by the ratio of the characteristic dimension of the leak channel (the radius of the circular cross section, ^{−8} cm, Air: 3.7 × 10^{−8} cm [

The three flow regimes [

Analytical expressions for conductance in the molecular and viscous regimes are available in the literature [_{T}_{m}_{v}

In contrast to gas conduction, gas diffusion takes place through the entire sealing area. Multi-dimensional modeling is necessary to account for the actual sealing layer structure. In addition, the gas pressure gradient inside the sealing material develops very slowly (usually on the order of hours to days). The conductance equation based on Fick’s first law cannot model such a slow pressure gradient development and hence Fick’s second law has to be considered.

Fick’s second law is derived from the principle of mass continuity for an infinitesimal volume as:
^{3}), ∇ is the gradient operator and ^{2}/sec). Using the linear Henry’s law (^{2}/m^{2}) and

The permeability

The cavity of a typical MEMS package has a rectangular (or square) shape. Many parameters are required to define the structure of the cavity and the surrounding seal, and hence the rectangular shape is not most ideal for a parametric study. In this study we consider an axisymmetric model, which is much more effective for the parametric study. Although simplified, the axisymmetric model effectively represents the gas diffusion behavior of the actual cavity structure.

An axisymmetric model is formulated to illustrate the transient boundary conditions. Its normalized form will be utilized later for an extensive parametric study. A schematic diagram of the axisymmetric model is illustrated in _{a}_{c}_{i}_{i}h_{c}

The helium mass spectrometer based leak testing has been widely used in the industry for fine leak detection [

The output of the spectrometer is the measured leak rate (_{i}

The equivalent standard leak rate (_{a}_{a}_{i}

For relatively large packages, there exists one-to-one correspondence between the initial apparent leak rate and the true leak rate in the fine leak domain (less than 10^{−4} atm-cm^{3}/s). As the package volume becomes smaller (less than 10^{−3} cm^{3}), however, the one-to-one correspondence vanishes [

The consequence of this loss of one-to-one correspondence is that the initial apparent leak rate no longer carries quantitative meaning; for example, a package with a higher true leak rate (

To cope with the problem, a method to extract the true leak rate using the Helium mass spectrometer has been developed. The method utilizes the complete profile of the apparent leak rate collected by the mass spectrometer and determines the true leak rate by performing a non-linear regression analysis. The theoretical limit of true leak rates that can be measured by the fine leak test was studied previously [

The first step comprises of “bombing” the specimen with helium, _{b}_{b}_{dwell}

Ideally the spectrometer should measure only the helium leaking out of the package, _{zero}

For quantitative characterization of the true leak rate, stable apparent leak rate data must be utilized for consistency and accuracy. Therefore, the data to be used for a subsequent regression analysis should be taken only after the zero signal becomes negligible. We introduce a new parameter called _{dwell}_{zero}_{p}

An approach similar to the one outlined in reference [

The test is divided into three phases, viz. bombing, preprocessing, and measurement phases. For the purpose of mathematical modeling, the preprocessing phase is further divided into two sub-phases, the dwell phase and the zero signal phase, since the downstream pressure of each sub-phase is different (1 atm and vacuum for the dwell and zero signal phases, respectively). In each phase, the ratio between

During the bombing phase, the upstream pressure, _{u}_{b}_{i}_{i}_{b}_{b}

In this phase the internal cavity pressure is the upstream pressure, _{u}_{u}_{i}_{b}_{d}

The internal cavity pressure is still the upstream pressure, _{u}_{u}_{i}_{b}_{dwell}_{d}

The internal cavity pressure is the upstream pressure, _{u}_{i}_{b}_{p}

The task of inferring _{a}_{a}

It is important to recall that viscous conduction dominates only when the leak channel opening (the true leak rate) is large and/or the average pressure is high. When the viscous contribution is high, helium leaks out fast during the preprocessing time. As a result, the internal pressure, and thus the pressure differential, drops so fast that the effect of the viscous conduction becomes insignificant after the preprocessing time. In other words, even when the viscous conduction is high after bombing, the contribution of viscous conduction decreases rapidly and the flow can be assumed molecular during the

The apparent leak rate can be modeled as:
_{a}_{helium}

Under idealized conditions, the two unknowns (Ω and _{a}

The least-squares method has been used in a regression analysis. The basic assumption that underlies this approach is that there are always differences between experimental results and theoretical values. Their relationship can be expressed using the error function, ϒ, as:
_{k}_{k}_{a}_{i}_{a}

The method was implemented for a MEMS package. The package enclosed MEMS devices and comprised of a silicon cap bonded to a silicon substrate by means of a metallic seal. The overall package dimensions are 2.5 mm × 2.5 mm × 0.7 mm. The internal cavity volume, ^{−4} cm^{3}.

The zero signal is a noise signal and should be excluded when the true leak rate is to be measured. Although it can vary slightly from an instrument to an instrument, the zero signal time can be measured experimentally simply by operating the mass spectrometer without any specimen inside the test chamber. Representative zero signals are shown in ^{−10} atm-cm^{3}/s after ∼150 s.

The following procedure was used in the experiment:

A single package was subjected to pressurized helium (_{b}_{b}

It was transferred into the spectrometer in time, _{dwell}

Data recording started after the zero signal time _{zero}

The apparent leak rate signal was measured using a commercial helium fine leak tester (Model DGC 1001, Alcatel). The data was recorded at 5 Hz and the results of Package 1 are shown in

The data of the measurement phase was utilized to determine the true leak rate through the regression analysis. The data was trimmed at a value of ^{−10} atm-cm^{3}/s in order to negate the effect of the stabilized zero signal (10^{−10} atm-cm^{3}/s) on the regression. The analysis was conducted using MATLAB, and yielded a true leak rate value of 3.12 × 10^{−7} atm-cm^{3}/s with the goodness of fit, R^{2}, equal to 0.995. The experimental data of the measurement phase are replotted in _{a}^{2}, the regression results and the experimental data are nearly identical. It is to be noted that only a few experimental data points are shown in

The robustness of the technique was assessed by testing Package 1 again with different dwell times: 5 minutes (Case A) and 20 minutes (Case B). The apparent leak rate profile of each case and the corresponding regression fits are shown in

The regression technique yields the true leak rate values of 2.99 × 10^{−7} atm-cm^{3}/s (Case A) and 3.20 × 10^{−7} atm-cm^{3}/s (Case B), which have less than 4% variation compared with the value of the reference case (3.12 × 10^{−7} atm-cm^{3}/s). These consistent values validate the efficacy of the proposed method.

The value of Ω was treated as an unknown in the regression analysis. It is tempting to utilize the experimentally measured value of Ω to reduce the number of unknowns in

In practice, the experimental value of Ω inherently contains uncertainties associated with the instrument, in particular, Helium mass spectrometer, and can be very unstable. If large, the uncertainties in Ω can affect the true leak rate, and it is suggested that the value of Ω treated as an unknown as proposed in this study.

An effective numerical scheme is developed to solve the governing equations (

As illustrated in

An effective modeling scheme is proposed to avoid the user-defined algorithm (this scheme will be referred to as “effective volume”). A schematic illustration of the effective volume scheme is shown in ^{3}; note that gas density can be interpreted as gas concentration inside the imaginary polymer), ^{3}) and

The effective volume scheme transforms the original single material diffusion problem with transient boundary conditions into a bi-material gas diffusion problem with fixed boundary conditions. Consequently, the Nernst distribution law should be considered for mass continuity at the cavity-polymer seal interface [the inner surface of the polymer seal, _{c}_{p}

The effective volume modeling scheme can be readily implemented using commercial finite element analysis (FEA) software packages. Not all commercial FEA software packages offer the mass diffusion analysis function, but the current problem—namely, a diffusion analysis of a multi-material system subjected to an isothermal condition—can be solved by the thermal diffusion (or heat transfer) analysis function adopting the well-established thermal-moisture diffusion analogy [

The basic principle of the optical leak test [

The optical/mechanical configuration is shown schematically in

The surface topology of the package is documented by a classical laser interferometry configuration called Twyman/Green interferometry [

The optical/mechanical configuration of the actual experimental setup is illustrated in

Any high pressure gas tank can be used as the source of gas. A mechanical regulator located on the tank reduces the gas pressure from the tank pressure value (∼70 atm) to 7 atm. This lower pressure gas is then supplied to a PID controller (TESCOM ER3000). The PID controller has an internal sensor, which is used in conjunction with PID logic and user defined PID parameters to reduce gas pressure to the desired pressurization value. An additional pressure sensor (TESCOM 200-1000-2527) is screwed into the pressure vessel in order to read the pressure inside the chamber, which can detect any large leakage of gas due to an accidental failure/rupture of the chamber gaskets and seals. The uncertainty of measurement using this pressure regulation setup is ±0.02 atm (±0.3 psi).

The deformation,

The fringe patterns are processed further by the Fast Fourier Transform (FFT) method [

The original fringe pattern of the specimen before pressurization is shown in

The package used in the experiment consists of a glass cap bonded to a silicon substrate using a photo-definable adhesive polymer. The cavity was fabricated through a lithography process. All the processes were conducted in a controlled nitrogen environment (0.9 bar). The height of the silicon substrate, the glass cap and the polymer seal are 120 μm, 500 μm and 46 μm, respectively. The overall package dimensions are 4.6 mm × 4.5 mm. The cavity dimensions are 2.22 mm × 2.86 mm, which yields an internal cavity volume of ∼ 3 × 10^{−4} cm^{3}.

In order to obtain the calibration curve, the pressure in the chamber was increased to 4 atm (gauge) in steps of 0.25 atm and the surface deformation was recorded at each step. The deformation-induced deflections are plotted as a function of the applied external pressure and bombing time in _{max}

After the calibration curve was obtained, the package was subjected to a constant bombing pressure of 4 atm (gage) and the deflections were measured as a function of time. The bombing pressure was maintained for 600 h. There was no noticeable deflection change after 600 h, indicating that the cavity pressure was equal to the bombing pressure. At this point, the “release” stage was initiated by closing the helium gas valve and opening the chamber to the atmospheric environment (0 atm of helium). The surface deflection was also documented regularly during the release stage. Representative fringe images and corresponding 3D maps are shown in

The effective deflections obtained from the 3-D maps are plotted in

A finite element model based on the effective-volume scheme was built to simulate the cavity pressure evolution during the bombing and release stage. The modeling prediction is compared with the experimental data in

It is to be noted that the two diffusion properties (diffusivity and solubility) required for the modeling were not known in advance. Instead they were determined through an inverse analysis [

Two distinctively different techniques were reviewed to measure true leak rates of MEMS packages with different sealing materials: a Helium mass spectrometer based technique for metallic sealing and a gas diffusion based model for polymeric sealing. The governing equations were reviewed and the measurement procedures were discussed. The true leak rates of MEMS packages with micro to nanoliter cavity volumes can be measured accurately by combining the two techniques.

The author acknowledges and thanks A. Goswami and C. Jang of Apple Inc. for their contributions in related technical papers [

Schematic illustration of a MEMS package and the length of the leak channel, l.

Helium leak test signals for (_{cavity}^{−4} cm^{3}) and (_{cavity}^{−4} cm^{3}). Test parameters include a bombing pressure of 4 atm (gage), a bombing time of 6 h and a dwell time of 10 min.

Schematic diagram of the geometry of 1-D axisymmetric case (the top and bottom surfaces are adiabatic).

Representative zero signals.

(

Apparent leak rates and the corresponding regression fits of Package 1 with various dwell times: Case A = 5 min; Case B = 20 min. The reference case has a dwell time of 10 min (

Schematic illustration of (

Schematic illustration of the optical leak test.

Schematic illustration of (

Illustration of FFT analysis: (

(

Cap surface topographical contour maps (the units in the scale are μm and the cavity location is indicated by the dotted box) at the beginning and the end of (

Effective chip surface deflections during the bombing and release stages; the encircled values correspond to the contour maps shown in

Cavity pressure evolutions measured by the optical leak test are compared with the numerical predictions.