A novel interferometric characterization technique for 3D analyses at high pressures and temperatures

The measurement was performed by employing an MSA-500 micro system analyzer (Polytec GmbH) featuring a green LED 525 nm (spectral width of 510–550 nm) for illumination. The topography measurement is based on white light interferometry. It makes use of a built-in video camera, the LED illumination and a special interference objective scanned by a piezo-driver. For topography measurements through glass, Michelson-type 4×-interferometer objectives contain a slot for a compensation glass to adjust the optical path of the interferometer setup. Dimensions of the compensation glass were adjusted to closely match the optical path length between the test and reference arm. In order to acquire good contrast fringes, the tolerances between the compensating element and the cover glass of the chamber were kept as low as possible and a matched cover glass (borosilicate; BK7) from the same sheet was employed [15].

In the measurement set-up, the sample is positioned on an adjustable pedestal beneath the cover glass and surrounded by a layer of hydraulic fluids. The thickness of the fluid layer (e.g. water) can be altered by changing the height of the pedestal. The optimal thickness of the fluid layer was determined, based on optical path calculations. A schematic demonstration of the interferometer objectives with a compensation glass plate for measurements through the protective glass and water layer is presented in figure 1. The optical path length of the test beam was derived as a function of the thicknesses of water layer $({{d}_{{\rm w}}})$, sample $({{d}_{{\rm s}}})$ and the glass plates (${{d}_{{\rm G}1}}$ and ${{d}_{{\rm G}2}}$), as well as the ratio of refractive indices of glass $\newcommand{\e}{{\rm e}} ({{\eta}_{{\rm G}}})$ to water $\newcommand{\e}{{\rm e}} ({{\eta}_{{\rm W}}})$ at the average wavelength of 525 nm. Accordingly, the height of the pedestal (D) was extracted from equations (1)–(3).

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Considering an ideal case of zero optical path difference (figure 1), which can be described as:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{\eta}_{{\rm w}}}{{d}_{{\rm w}}}+{{\eta}_{{\rm G}}}{{d}_{{\rm G}1}}={{\eta}_{{\rm G}}}{{d}_{{\rm G}2}},\nonumber \end{align} \tag{ 1 }$$

the ideal thickness of the water layer will be expressed, as follows:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{d}_{{\rm w}}}=\frac{{{\eta}_{{\rm G}}}}{{{\eta}_{{\rm w}}}}~\times \left| {{d}_{{{{\rm G}}_{2}}}}-{{d}_{{{{\rm G}}_{1}}}} \right|.\nonumber \end{align} \tag{ 2 }$$

Therefore, the exact height of the pedestal, by taking into account all possible discrepancies ($\Delta d$), can be determined from equation (3):

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle D={{d}_{{\rm s}}}+{{d}_{{\rm w}}}+\Delta d.\nonumber \end{align} \tag{ 3 }$$

The pressure chamber, as shown schematically in figure 2, was designed and fabricated from stainless steel. The chamber comprises an optical access for the microscopic observation, where glass slides in different thicknesses can be inserted. The chamber contains a volume of about 1 cm³ for positioning the samples. A resistive heating rod, driven by a feedback controlled power supply, was incorporated to adjust chamber temperature from ambient temperature up to 200 °C. A type J thermocouple sensing element was located at the inner top side of the adjustable pedestal. Its thermal information was used to control the temperature in the chamber, especially on top of the pedestal. The estimated distance from the sensing element to the specimen was about 0.3–0.4 mm.

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The pressure regulator was driven by a spindle pump (MTR mini HD 106, Germany) capable of generating supply pressures up to 100 bar. The pressurized fluid (water/oil) was transferred through a stainless steel plumbing run, and then directed through the orifice.

It is noteworthy to mention that, since the presented chamber was in fact an upgraded version of our initial set-up without temperature module, the medium—water—came to use in the first place. However it was revealed that water cannot be implemented as a medium for higher temperatures. Although above 40 bar water can be kept in the liquid state even up to 200 °C, it gets highly aggressive towards any kind of sealing. Therefore, the medium was changed from water to a hydraulic transparent oil (Di-2-ethylhexyl Sebacate, Hallstar, Inc), generally known as Sebacate. As its boiling temperature is in the range of 232 °C–249 °C, it is well suited for the high temperature measurements. Conclusively, distilled water and the Sebacate were determined as the medium for room temperature and high temperature examination, respectively. The sealing of the chamber at high temperature was facilitated by means of metal c-ring seal on the medium side and a flat metal ring on the glass side, whereas at room temperature silicone rubber seals could be utilized.

It was also found, that the specimen did not necessarily lie flat on the support but rather tilted by some degrees in the horizontal plane. To readjust the specimen in the plane, the whole chamber is mounted into a goniometer with the specimen located at its tilt center, as illustrated in figure 2.

A MEMS package with the thickness of 170 µm featuring several sensing microstructures was employed as specimen in this study. The typical feature sizes in this specimen were in the order of 25 µm and below. All the samples were coated with a conformal layer of platinum (10 nm in thickness) to ensure high reflectivity. These thin and flexible sensing microstructures, which will be denoted as 'beams', are elastically deflecting when the corresponding package is exposed to hydrostatic pressure. The measurements were carried out with a speed of 3 µm s⁻¹ and a sampling increment of 89 nm. In the second part of this study, the accuracy and tolerances of the measurements were evaluated via a standard step-height measurements. Correspondingly, a reference step-height sample (Silicon, CTR AG) and a stylus profilometer (DektakXT, Bruker) were utilized.

Optical path length $({{D}_{{\rm opt}}})$ for a homogenous medium is the product of the geometrical path length $({{D}_{{\rm geom}}})$ and the index of refraction of the medium:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{D}_{{\rm opt}}}=\eta \times {{D}_{{\rm geom}}}.\nonumber \end{align} \tag{ 4 }$$

Optical path length concept is significant because it helps to determine the phase of light which governs the interferences of light. If a wave travels through various media, then the optical path length of each medium needs to be calculated to discover the total optical path length [16, 17].

The refractive indices of air, water and Sebacate oil were 1, 1.33 and 1.45, respectively [18]. Correspondingly, the real deflection of the beams $(\Delta D_{n}^{{\rm air}})$ which is defined as the difference between the initial position of the structure at 0 bar ($D_{0}^{{\rm air}}$) and the position under pressure at n bar $(D_{n}^{{\rm air}})$ is associated to the optical thickness in water and oil by:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \Delta D_{n}^{{\rm air}}=D_{0}^{{\rm air}}-D_{n}^{{\rm air}}=\frac{{{D}_{{\rm opt}_{0}^{{\rm water}}}}-{{D}_{{\rm opt}_{n}^{{\rm water}}}}}{{{\eta}_{~{\rm water}}}}=\frac{{{D}_{{\rm opt}_{0}^{{\rm oil}}}}-{{D}_{{\rm opt}_{n}^{{\rm oil}}}}}{{{\eta}_{~{\rm oil}}}}.\nonumber \end{align} \tag{ 5 }$$

The elastic deflection of the beams induced by hydrostatic pressure was investigated at different pressures up to 100 bar. A small pressure load step was used to ensure a linear elastic response of the specimen. 3D images of the sample under 0, 20, 30 and 100 bar are depicted in figure 3, rendering the deflection of the beams in accordance to the applied pressure. As one can perceive, under dynamic pressure, the beams underwent elastic deformation, yielding to transformation from a planar structure to a saddle-like configuration.

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The deflection induced by pressure in the middle of beam was successively derived from the measurements by data analysis software (TMS 3.5, Polytec). In figure 4 the average deflection of a typical beam versus the applied pressure is plotted. The specimen was pressurized up to 100 bar and depressurized down to 0 bar without any detectable crack formation through the beams, which verified the functionality of the package under pressure. As a result of this in situ monitoring, an in-depth understanding of deflection and mechanical stability of the sensitive beams under pressure was achieved. Hence, the proposed technique was proven to be a versatile, nondestructive method for performance monitoring and reliability testing of these specimens.

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Repeatability of the measurement system was verified by measuring the deflection of several packages under the pressure span. Analogous to room temperature measurements, the deflection regime of the specimen was also assessed at elevated temperature. As aforementioned, with respect to the measurement media at elevated temperature, water was substituted with oil. Figure 4 compares the average deflection of a typical beam at 25 and 180 °C. As implied from this plot, the deflection of the beam at 180 °C is higher than the one in room temperature, which can be attributed to the temperature-dependence of the Young's modulus.

Measurement tools and systems have always some tolerance and disturbance that will introduce a degree of uncertainty [19, 20]. In order to evaluate the precision of measurements, especially at high temperatures and pressures, a step-height reference sample was utilized as shown in figure 5(a). The nominal height of this step was validated by the stylus profilometer to be 2.82  ±  0.05 µm in air, thereby 4.095 in oil after deploying equation (5). This nominal height is depicted as a line in figure 5(b) together with the measured values up to 180 °C. As one can see, the results were highly reliable with a measurement tolerance (standard deviation) of less than  ±0.4 µm. As implied from this figure, both measurement accuracy and precision, i.e. deviation between the measured and actual values and the spread of the measured values respectively, were slightly affected by the temperature change. As a matter of fact, due to a light dispersion phenomenon, the quality of signals at high temperature was lower than that of room temperature. This phenomenon corresponds to the unwanted scattering as some light rays might bend a way when they pass through an inhomogeneous path from colder area (higher refractive index) to the warmer area adjacent to the heated chamber. Possible fluctuation in the fluid layer due to a temperature gradient which can be ascribed to the Rayleigh–Bénard convection effect [21] and irregularities in the refractive index of this layer can also be postulated as the reasons for weaker signals at higher temperature. The precision of high temperature measurements were further improved by a spike removal filtering. No systematic error due to a thermal drift effect [22] was detected, that could be attributed to the large distance (>40 mm) between the measuring unit and the locally heated area inside the chamber. Moreover, no systematic shift in the refractive index of the Sebacate oil was identified in the temperature and pressure span of measurements, at least to the detection limit of the instrument. The results also indicate a measurement tolerance of  ±0.4 µm over the whole pressure range, revealing no discernible effect of pressure on the precision of the measurement.

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The lateral resolution of the measurement is dependent on the objective itself. By using the 4×  objective, the lateral resolution (pixel size) for the measurements is 1.6  ×  1.6 µm, while the field of view will be as big as 2.2  ×  1.7 mm. As a matter of fact, higher magnification objectives could lead to a superior lateral resolution in the range of 100  ×  100 nm, however the field of view would be limited down to 180  ×  130 µm.