Characterization of the ion angle distribution function in low-pressure plasmas using a micro-electromechanical system

Our modern society is concealed in a world that is enabled by plasma processes. Without the use of various low pressure plasmas for deposition and structuring of layers in microelectronics, today’s highly digitized world would not be possible. The last processor that was realized without plasma etching is the Intel 80386 from 1985.¹ Also, by the development of the plasma etching processes, the number of transistors could be increased in the last 35 years from some hundred thousand to over $100× 10 9$ billion transistors in a processor. The miniaturization at the transistor level required for this was accompanied by the progressive technical development of plasma reactors in order to be able to realize ever smaller structures on ever larger substrates. Today’s dry etching systems are technically highly complex systems that are capable of simultaneously structuring trillions of nanometer-sized structures on 300 mm wafers.

However, this development led to the fact that today’s production systems have a very large number of process parameters (e.g., deep silicon etching—approximately 50 process parameters). Due to the large number of process parameters, the design of experiments (DOEs) is only applicable to a very limited extent. Therefore, the use of plasma analytical methods is desirable as they narrow down the parameter space and provide process characterization data faster than processing hundreds of wafers and analyzing them afterward, e.g., by transmission electron microscopy.

The two main plasma characteristics describing the direct ion bombardment of the substrate surface are the ion energy distribution function (IEDF) and the ion angle distribution function (IADF). For the characterization of the IEDF, planar miniaturized retarding field energy analyzers (RFEAs, Impedans Ltd.) are widely used in both research and industry.² Section II will show that various concepts have been tested over the years for the experimental determination of the IADF, but none of the methods has yet been able to establish itself in the production environment. Although simulations of plasma etching processes show that the IADF has a significant influence on the etching results,³ the measurement of IADF remains confined to academic research. The sensor concept presented here could bridge this gap between academic research and industrial application, as the MEMS shown here represent a significant miniaturization of the methods used to date.

The paper is organized as follows. In Sec. II, the state of the art of IADF sensors is presented and their applicability in an industrial environment is critically examined. The manufacturing of the used MEMS, the system integration, and the applied calculations for the determination of the IADF are described in Sec. III. Section IV is devoted to the measurements and discussions. Main conclusions are summarized in Sec. V.

The methods used to measure the (IADF) often employ grids with different potentials, each serving distinct functions. The uppermost grid, referred to here as the aperture grid, ensures that the plasma perceives a planar surface and that the sheath remains undisturbed. For this purpose, it is essential that the openings of the aperture grid are smaller than the Debye length of the plasma being examined. Other grids are utilized to prevent plasma electrons from entering the sensor system or to function as retarding field energy analyzers for measuring the ion energy distribution function. For the sake of clarity, these additional grids are not depicted in the description of the measurement methods for determining the IADF.

Special test structures⁴ allow the analysis of the ion angle distribution function by means of subsequent cross-sectional analyses by electron microscopy in combination with simulations of the ion trajectories. For this purpose, cavities with a defined entrance opening are first created using conventional silicon technology, see Fig. 1. This entrance opening acts as a pinhole during ion bombardment. Depending on the angular distribution of the incident ions, a specific etching profile results at the bottom of the cavity.

Segmented, ring-shaped electrodes in combination with a pinhole^5,6 allow measurements of the ion angle distribution function by means of spatially resolved detection of the ions. The ions enter the sensor through a defined pinhole and are detected by ring-shaped electrodes, see Fig. 2. Depending on which ring electrode the incident ions hit, they can be assigned to a corresponding incidence angle range.

Charge-coupled device (CCD) in combination with a pinhole⁷ follow a similar measuring principle as the ring-shaped electrodes explained above. The ions also enter the sensor via a defined pinhole. However, they are not detected via ring electrodes but optically via a CCD camera, see Fig. 3. In order for this to succeed, the ions are spatially resolved within the sensor and converted into an electron avalanche by an microchannel plate (MCP). The resulting electrons are in turn spatially resolved by means of a phosphorescent screen into a luminescent signal that can be detected by the CCD camera.

Tiltable Faraday cup in combination with a pinhole⁸ allow measurements of the angle-dependent ion current and thus the IADF by tilting a Faraday cup using a defined entrance aperture as a tilting point, see Fig. 4. By choosing an appropriate distance between the pinhole and the detector, only ions from a certain angular acceptance range can reach the Faraday cup and be detected. Tilting is typically achieved through a mechanical feedthrough and a rod to which the sensor is attached.

Tiltable quadrupole mass spectrometer (QMS) in combination with a pinhole⁹ allows the characterization of the IADF. Due to the distance between the pinhole and the entrance aperture of the QMS, angular selection occurs. Additionally, a QMS is equipped with electrostatic lenses at the entrance, which also contribute to angular selection due to their acceptance angle. By mechanically tilting the QMS, the IADF can be detected, see Fig. 5.

In some publications, the mass spectrometer is rigidly mounted to characterize the ion distribution and the ion source is moved to change the angle between the ion source and the measurement system.¹⁰ 

Rigid quadrupole mass spectrometer in combination with a simulation of the ion trajectories^11,12 also allows a determination of the IADF. However, the simulations required for this are complex, as the calculations must cover the range of ion trajectories between the substrate and the QMS entrance aperture as well as within the QMS. In some cases, the simulations are not solvable at all due to the complex geometric conditions.¹¹ Furthermore, the simulations have to be adapted to the specific chamber geometry of the plasma system.

A tiltable microchannel plate^13,14 selectively filters incident ions within a specific angular range determined by the hole geometry. The holes patterned into the plate must have a high aspect ratio for a small acceptance angle. The ions, which can pass the microchannel plate due to their small angle of incidence are detected by an electrode, see Fig. 6. To measure the IADF, the whole system is tilted mechanically over the angular range of the expected IADF. This is typically achieved through a mechanical feedthrough and a rod to which the sensor is attached, see Fig. 6.

Defined lateral field drift¹⁵—the basis of this measurement system is formed by several electrically conductive grids stacked on top of each other, as used in planar RFEAs, see Fig. 7. The basic principle of this analyzer is based on the variation of the kinetic energy of incident ions perpendicular to the wafer surface due to the electric fields between the various grids. Due to the homogeneous electric field between the respective gratings, the energy component $E =$ parallel to the surface remains unchanged. However, as the perpendicular energy component $E ⊥$ is changed, there is a change in the ion angle within the sensor, see Fig. 7. Ions with different energy and incidence angles can be separated and detected by varying the lattice potentials. This sensor is distributed by Impedans Ltd.

Reusability is not given with the special test structures. This method, as the name already shows, is not a sensor, but a test structures for one-time use.

Special equipment or modifications are required for most of the solutions presented. As a result, these sensors cannot and will not be used in industrial plants. For the following systems, the wafer chuck must be substantially modified so that the measurements can be conducted at wafer level. This also requires a differential pumping system in the area under the chuck in order to avoid further collisions and thus a falsification of the IADF.

• Segmented, ring-shaped electrodes in combination with a pinhole.

• CCD detector in combination with a pinhole.

• Tiltable Faraday cup in combination with a pinhole.

• Tilting quadrupole mass spectrometer (QMS).

• Tilting microchannel plate.

The necessary extensive changes would probably affect the etching results and the transferability of the knowledge gained to unmodified production systems. Only special research systems have pinholes in the wafer holder as well as the necessary free space to install the measuring system below the wafer holder.

Stepless angular measurement of the incident ions is not possible with all sensors. Sensors based on ring electrodes as well as sensors based on lateral drift in grid stacks allow only the classification of the ions into certain angular ranges. Sensors based on lateral field drift are mainly suitable for health checks of plants due to the wide distinguishable angular intervals of $3 °$⁠.

These capabilities and limitations of existing IADF measurement techniques are summarized in Table I.

The main shortcoming of the tiltable microchannel plate, as shown in Fig. 6, is the need for a mechanical feedthrough to tilt the microchannel plate. Such feedthroughs exist only in specially built or modified equipment. This shortcoming is overcome by the sensor presented here, which integrates the perforated plate into a micro-electromechanical system (MEMS). Due to their small dimensions in the millimeter range, these MEMS should be able to be inserted into existing plasma systems without additional modifications. They can be placed on the substrate holder instead of the substrate, allowing the ion angular distribution function to be measured.

The sensor system presented in this paper consists of three main components:

• Aperture: This area is exposed to the plasma. Through a perforated area, ions can enter the sensor system. The diameter of the openings in the perforated area should be chosen to be smaller than the Debye length so that the plasma boundary layer is not disturbed and a flat substrate surface is simulated. The thickness of the perforated region shall be selected to produce openings with a low aspect ratio so that no angular selection occurs at this perforation.

• Angular filter MEMS: This element is used for angular selection of ions. The perforation of the element to be tilted, hereafter called the plate, selects the ion angles based on their angle of incidence perpendicular to the surface of the plate. For this purpose, the perforation of the plate must consist of holes with high aspect ratio. Ions whose incidence angle is larger than the acceptance angle of the holes are absorbed by the sidewalls of the holes and cannot reach the detector. To acquire the ion angle distribution function, the plate is tilted along one axis using an AlN based piezoelectric actuator. The symmetrically constructed opposite side of the MEMS does not serve as an actuator but as a sensor for the achieved tilting of the moving element. The ion angle distribution function results directly from the tilt angle dependent measurement signal of the ion current at the detector.

• Ion detector: Below the MEMS element is a gold electrode that detects the ions that have passed through the angle filter.

The starting point for the realization of the aperture grid was the assumption that relevant low-pressure plasmas have a Debye length greater than 50  $μ$m.^16–19 Therefore, the opening diameter $d Si$ of the aperture grid was set to 30  $μ$m so that the plasma would perceive a planar sensor surface and not be disturbed by the sensor structure. A honeycomb structure with a bridge width of 5  $μ$m was chosen, focusing on the optimal ratio of stability to open area. In this work, the size of the opening $d Si$ is always referred to as the inner diameter, i.e., the distance between two opposite sides of the hexagon, see Fig. 8.

(100) Si wafers with a diameter of 150 mm, a thickness of 400  $μ$m, and a resistivity of 0.020  $Ω$ cm were used to fabricate the aperture wafers. The process flow can be divided into several steps. First, the wafers were prepared, which included the following processes: marking of the wafers, RCA clean, thermal oxidation (1000 nm $SiO 2$⁠), and $N 2$-annealing at $700 °$C for 30 min. This initial situation is shown in Fig. 9(a). Subsequently, the openings of the honeycombs were transferred into the silicon oxide, which later served as a hardmask for the Si patterning. The grid area was set to 4.8  $×$ 4.8  $mm 2$⁠. The wafer front side was spin-coated with photoresist (OiR 906/12 1.3  $μ$m), the honeycomb structures were exposed and developed. Honeycomb structures with 30  $μ$m openings and 5  $μ$m bridge widths were implemented. The wafer front side was then subjected to 1000 nm $SiO 2$ dry etching, followed by plasma resist removal. The opened oxide hardmask is sketched in Fig. 9(b).

The wafer was then thermally oxidized again (70 nm  $SiO 2$⁠), and 100 nm  $Si 3 N 4$ was deposited using low-pressure chemical vapor deposition (LP-CVD) in order to create the necessary hardmask on both sides for the upcoming KOH etching step, see Fig. 9(c).

Photoresist (OiR 906/12 1.7  $μ$m) was spincoated on both the wafer front and backside, and exposure of the Si pits on the wafer backside was carried out. The photoresist was developed, followed by 100 nm $Si 3 N 4$ dry etching, 1070 nm $SiO 2$ wet etching, plasma resist removal, and wet etching of the Si pits using KOH until a residual membrane thickness of 30  $μ$m was achieved. The wafers with the prepared Si pits on the wafer backside are shown in Fig. 9(d). The remaining 1070 nm $SiO 2$ was wet etched to remove $SiO 2$ residues at the edges of the Si pits, and 100 nm $Si 3 N 4$ dry etching was performed on the wafer backside. The already patterned $SiO 2$ hardmask on the front side remained protected from this $SiO 2$ wet etching as it was covered by $Si 3 N 4$⁠.

Then, the 100 nm $Si 3 N 4$ layer and the 70 nm $SiO 2$ were dry etched on the front side of the wafer to restore the $SiO 2$ hardmask originally structured in the previous steps, see Fig. 9(e). This hardmask was then used to etch the opening of the honeycomb through the Si membranes fabricated earlier. The backside of the Si grid was stabilized for the following 30  $μ$m silicon dry etching (Bosch process) via spray-coating of photoresist (AZ4999, 8  $μ$m) on the wafer backside. The photoresist was then removed using plasma resist removal. Silicon dioxide wet etching exposes the Si surface again. To make the distribution of electric fields more homogeneous, the conductivity of the wafer surface was increased by full-area Al deposition, see Fig. 9(f). Due to the large honeycomb openings compared to the used Al layer thickness of 500 nm as well as the directional characteristic of the used magnetron sputtering, the Al deposition on the sidewalls of the honeycomb structures can be neglected. The finished grids are shown in Fig. 8.

The following bridge widths were tested: 1, 2, 3, 4, and 5  $μ$m. Bridge widths greater than or equal to 2  $μ$m could be produced with high yields (>95%). For bridge widths of 1  $μ$m, the yield collapsed to below 25% during the Si dry etching. Probably, the heat input from this plasma-based process and the poor heat dissipation due to the narrow bridges generated during the etching process lead to thermal stress in the honeycomb structure, which causes the bridges to break. The measurements shown in this paper were performed using grids with 5  $μ$m bridge width and 30  $μ$m opening.

In Fig. 10, the schematics of the fabricated AlN MEMS with 6 $×$ 6  $mm 2$ footprint are shown. Based on this figure, it is visible that the actual MEMS area in the center of the chip is much smaller at 2 $×$ 2  $mm 2$⁠. This layout was chosen so that the electrode areas for contacting the various MEMS elements are outside the area that is bombarded with ions and other plasma particles due to the 4.8 $×$ 4.8  $mm 2$ aperture. The piezoelectric actuator and sensor are covered by the upper Al electrode. In operation, the upper Al electrode is grounded, and only the lower electrode, protected from ion bombardment, serves as the signal path.

Figure 10 shows also a detailed view of the chip center. The tiltable angle filter plate is connected by Si-bridges to two piezoelectric cantilevers. These Si-bridges serve as torsion springs in resonant operation. One of these cantilevers is actively excited and deflects the angular filter plate, while the second cantilever is passively moved and used as a piezoelectric tilt sensor. The MEMS design and finite element analysis (FEA) process for optimization of the leverage effect is described by our research group previously.²⁰ 

The moving plate in the center of the MEMS is 800 $×$ 800  $μ m 2$⁠. For angular selection of the incident ions, this plate was perforated on an area of 700 $×$ 700  $μ m 2$⁠. For this purpose, holes with a diameter of 2  $μ$m were etched into this 30  $μ$m thick silicon plate at intervals of 2  $μ$m. The holes are arranged on a hexagonal grid with 2  $μ$m spacing between the hole edges.

To fabricate piezoelectric MEMS on 150 mm wafers, SOI wafers with a 30  $μ$m thick device silicon layer, 1.5  $μ$m silicon oxide [buried oxide (BOX)], and a 575  $μ$m handle silicon layer were used. Both the device and the handle layer p-Si had a resistance of 1–30  $Ω$ cm. After an initial RCA clean, lithography was performed and 1  $μ$m of Si was dry etched to transfer alignment marks into the silicon, including photoresist stripping. Another RCA clean was conducted afterward.

In the next step, wet thermal oxidation was carried out to create a 1.5  $μ$m thick oxide layer, which later served as a hardmask for the ion angle selection holes as well as an insulator between the lower electrode and the device silicon. Afterward, lithography and $SiO 2$ dry etching were performed to open the contacts to the device silicon, including photoresist stripping, see Fig. 11(a). Another RCA clean was conducted.

PVD deposition of 20 nm Ti, 100 nm Pt, and 600 nm AlN followed. The Ti served as an adhesion promoter, Pt forms a (111) orientation with a hexagonal surface, which is necessary as a seed layer for the required piezoelectric (002) crystal orientation of AlN. Then, 500 nm of $SiO 2$ hardmask for the following AlN echting was deposited using PE-CVD. Lithography and dry etching, including photoresist stripping, were performed to prepare the 500 nm $SiO 2$⁠. Wet etching was conducted with 85% $H 3 PO 4$ at $80 °$C. Subsequently, the $SiO 2$ hardmask was selectively removed by wet etching.

PVD deposition of 800 nm tungsten followed, which served as a hardmask for the patterning of the lower Ti/Pt electrode using Cl–Ar plasma. The remaining tungsten hardmask was then removed by dry etching, see Fig. 11(b). A 50 nm thick $SiO 2$ layer was deposited using PE-CVD to close pinholes in the AlN and thus improve insulation properties. The uniformly deposited $SiO 2$ was then patterned using lithography and dry etching, so that this 50 nm layer remained only on the previously patterned AlN.

Subsequently, 500 nm of Al was deposited and patterned, serving as both the top electrode and the bond pad on Pt, see Fig. 11(c). Then, 2.3  $μ$m OiR906-17i photoresist, including hexamethyldisilazane pretreatment, was spin-coated, and the Si holes (2  $μ$m in diameter, 2  $μ$m spacing between hole edges) for the later angle selection were transferred into the photoresist. The holes were transferred into the initially deposited 1.5  $μ$m thick thermal oxide, which later served as a hardmask. The photoresist layer was removed by photoresist stripping, see Fig. 11(d).

7  $μ$m AZ2945 was spin-coated, and the device Si structures were transferred into the photoresist. The 1.5  $μ$m thermal oxide was then dry etched to subsequently pattern the 30  $μ$m device Si. Photoresist stripping followed, see Fig. 11(e).

7.6  $μ$m of AZ4999 photoresist was spray-coated on the front and exposed, so that the resist was removed only on the chip center to be perforated, with the already patterned $SiO 2$ hardmask, while the rest of the wafer remained protected for the subsequent Si etching process. The ion filter holes with a 2  $μ$m diameter were patterned into the 30  $μ$m thick device Si by dry etching. The oxide layer between the device and handle silicon served as an etch stop. Photoresist stripping followed, see Fig. 11(f).

7.6  $μ$m AZ4999 photoresist was spray-coated on the front as protective resist, and 13  $μ$m AZ 10XT 520cp photoresist was spin-coated on the back. The photolithography on the wafer backside with the layout of backside pits in the handle Si was then performed. The thermal oxide on the wafer backside was opened by dry etching. Subsequently, the 575  $μ$m thick backside Si layer was patterned by dry etching down to the oxide layer between the device and handle layer. The photoresist was removed by photoresist stripping.

The 1.5  $μ$m thick BOX was removed by a blanket $SiO 2$ dry etch on the wafer backside (wafers were placed face down), see Fig. 11(g). Finally, the wafers were diced to prepare the single chips which were mounted and wire bonded to printed circuit boards (PCBs), see Fig. 11(h). A completed MEMS, including the holes for ion incidence angle filtering, is shown in Fig. 12.

A gold electrode is used to detect the ions after passing through the angle filter. This gold electrode is part of a printed circuit board on which the MEMS is bonded. Via wire bonds, the MEMS is electrically connected to the printed circuit board, which carries the signals to the outside via U.FL connectors. The wire connections are discussed in more detail in Sec. III B. The diameter of the gold electrode was chosen with 300  $μ$m in such a way that for all relevant tilt angles (⁠ $α< 20 °$⁠) of the sensor the complete surface of the gold electrode is always in the transmission area of the angle filter, see Fig. 13. A larger electrode surface would lead to the fact that with large deflection angles only a part of the electrode is bombarded by ions. This effect would influence the measurements as an additional angle dependence and was suppressed by selecting a small electrode.

For industrial applications, it is important to note that the front end of line (FEOL) is particularly sensitive to potential metallic contamination. If necessary, a setup should be implemented where essential yet undesirable metals, such as gold used for wire bond pads, are positioned in covered areas of the sensor system that are shielded from the plasma.

A test vehicle milled from aluminum was used to insert the assembly consisting of an aperture wafer and a MEMS on circuit board with ion detector into a plasma reactor. Figure 13 sketches a cross section including dimensions. Figure 14 shows the test vehicle with the aperture wafer removed. The use of this test vehicle offers several advantages for the initial testing of the sensor principle thanks to its simple design.

• The aluminum-coated aperture wafer and the housing of the test carrier are electrically connected to each other via the mechanical contact. As the aluminum housing rests on the grounded lower electrode, the aperture wafer is also grounded.

• Due to the large diameter of the lid wafer (150 mm), the plasma is undisturbed in the area of the aperture grid, since the next stage occurs only at the wafer edge at the wafer clamp. Thus, the ion angle distribution function in the measurement region is not distorted by the presence of the sensor itself.

• The printed circuit board with the MEMS is connected via U.FL cables to a printed circuit board on which the necessary cables toward the electrical feedthrough are soldered.

These angle can be increased by reducing the distance between the PCB with MEMS and the aperture. However, this did not seem to be necessary for the principle verification since typical angle distribution functions are only a few degrees wide. Therefore, the measurement range was limited to $± 10.0 °$⁠. This angle range covers typical ion angle distributions as they occur for high aspect ratio dielectric etching at process pressures in the single-digit Pascal range.²¹ These simulations have shown a maximum ion incidence angle of $4 °$⁠.

Due to the limitation of the MEMS used here, it cannot achieve the necessary tilt angle $α MEMS$ of approximately  10 $°$ in the static operating mode, which is required to fully characterize the IADF. In order to achieve the necessary tilt, the sensor must be operated resonantly. Attempts to measure the ion current impinging on the ion collector below the resonantly oscillating MEMS with temporal resolution have not yet been successful due to the small ion currents <1 nA. Therefore, the ion current at the collector was measured on a time-averaged basis $I RMS$ and a method for extracting the IADF from the time-averaged current $I RMS$ for different MEMS amplitudes $α amp$ was developed.²² The following explanation details how the width $σ$ and mean $μ$ of the IADF can be determined from the time-averaged ion currents $I RMS$ measured at the ion collector for different MEMS amplitudes $α amp$⁠.

These equations enable the calculation of the RMS ion current $I RMS$ at the detector based on the assumed ion angular distribution $IADF( ϕ Ion,μ,σ)$ and the amplitude $α amp$ set at the sensor. When this is performed for all amplitudes $α amp$ set in the experiment, an expected measurement curve is obtained, see Fig. 22. The measured RMS ion current $I RMS$ decreases with increasing MEMS amplitude, as the time the MEMS spends near the $0 °$ tilt angle decreases with increasing amplitude. However, since the MEMS always passes the $0 °$ tilt angle, albeit with increasing angular velocity, the RMS current never drops to zero but only decreases steadily with increasing amplitude. The IADF centroid $μ$ and the width $σ$ of the IADF can be iteratively determined by varying the parameters, minimizing the deviation between the measured curve and the simulated curve.

To stimulate the MEMS, a Tektronix AFG31000 arbitrary function generator was used with a sinusoidal signal of amplitude $V MEMS , act$ and frequency $f$⁠.

The charge signal of the piezoelectric tilt sensor was converted into a voltage signal and amplified using a low-noise transimpedance amplifier with adjustable gain (Femto, DLPCA-200). A gain of $10 6$ was used (gain accuracy $±1%$⁠). The transimpedance amplifier was operated in low noise AC mode. Both bandwidth limiting and bias voltage were disabled. This signal was recorded and digitized using a NI-DAQmx USB-6363 (BNC) measurement box. The amplitude of the signal was determined via fast Fourier transformation.

For the current measurement at the ion collector, a Keithley 236 source measuring unit was used. The system integrated for 20 ms per measurement, and subsequently, 32 of these measurements were averaged. The measurement error in the utilized range amounts to $0.3%±100 fA$ with a noise of 20 ppm. Typical values for the measured ion current $I RMS$ ranged between 150 pA and 10 nA.

During the measurements, the device silicon of the MEMS, including the perforated movable area, was subjected to a voltage of $−$60 V to prevent plasma electrons from passing through the hole array. This ensured that only ions contributed to the measurement.²⁴ 

In order to achieve the necessary tilting of the MEMS of approx. 10 $°$⁠, the silicon of the spring elements must be twisted to such an extent that it leaves the linear range of Hook’s law. This is reflected in the equation of motion by a nonlinear restoring force $αx+β x 3$⁠. For a detailed mathematical treatment of such a Duffing oscillator, please refer to other publications.^25–27 For the present work, it is only relevant that a nonlinearity $β≠0$ leads to a stiffening for $β>0$ or an softening $β<0$⁠. Stiffening leads to a higher restoring force and thus to a shift of the resonant frequency to higher values.

The dynamic behavior of the resonator in the steady state is investigated by creating an amplitude-frequency curve. The AC excitation frequency $f$ is gradually increased (upward sweep) and decreased (downward sweep) by 1 Hz around the fundamental frequency $f 0$ of the resonator. After a transient time of 1.5 s, the output voltage $V MEMS , sens$ is measured, which is a measure for the tilt of the MEMS $α MEMS$ (see Sec. IV B 2).

Figure 23 shows such a frequency-amplitude curve at a pressure of 5 Pa. The excitation was carried out with a voltage between 25 and 325 mV. It is clearly observable how the nonlinearity develops with increasing excitation voltage and thus force, and how the hysteresis steadily increases. The inclination of the resonance curve to the right is due to a stiffening of the system $β>0$⁠.

For further investigation of the system, this hysteresis is significant in that the system cannot simply be set to a target frequency and amplitude. The steady-state behavior of the oscillator is influenced by the previous state of the oscillator due to the hysteresis. To achieve the maximum possible deflection $α MEMS$ for a given excitation voltage $V MEMS , act$⁠, the excitation frequency $f$ must be increased step by step up to the jump-down frequency.

To ensure that the tilt angle of the MEMS $α MEMS$ is always known during sensor operation in a vacuum, a calibration curve for the tilt sensor signal $V MEMS , sens$ as a function of the mechanical tilt angle $α MEMS$ was recorded before the plasma measurements. For this purpose, different MEMS amplitudes $α amp$ and the corresponding sensor signals $V MEMS , sens$ were measured using vacuum-LDV. The measurements shown in Fig. 24 clearly demonstrate the linear relationship between the amplitude of the MEMS tilt angle $α amp$ and the internal MEMS tilt sensor signal $V MEMS , sens$ as well as the pressure independence of this correlation. Based on previous measurements of similar MEMS by our research group,²⁸ it is known that this linear relationship exists at least up to a tilt angle $α$ of 13.9 $°$⁠, thus covering the measurement range used here.

For proof of principle, the test vehicle including the MEMS was placed in a CCP plasma reactor, see Fig. 25. The upper electrode was driven, and the test vehicle was placed on the grounded bottom electrode. The measurements shown here were all performed at 1 Pa pressure in argon atmosphere and 30 W generator power (13.56 MHz).

To ensure that the measurement signal indeed depends on the ion current, a control measurement was initially conducted with the plasma turned off. This measurement showed no dependence of the ion current signal on the MEMS oscillation across the entire range of mechanical oscillations from $0 °$ to $10 °$ tilt angle. The measured ion current only randomly fluctuated between the resolution limits of the measurement system, with a step size of 10 fA, see Fig. 26. This was expected and was merely intended to confirm that there is no crosstalk between the excitation signals of the MEMS and the measurement signal at the ion collector.

To investigate potential coupling of plasma excitation into the measurement electronics on the MEMS sensor and the collector, and to ensure that no ions reach the ion collector, the entrance grid of the aperture wafer was covered with the Kapton tape. This ensures that electric fields from the plasma excitation can penetrate the system while ions cannot pass through, allowing these factors to be characterized separately. This control measurement, conducted with the plasma turned on, also produces noise in the measurement signal, similar to previous crosstalk measurements. This was expected because the measurement systems use input low-pass filters to filter out the 13.56 MHz plasma excitation frequency.

To measure the IADF the MEMS amplitude $α amp$ was varied while simultaneously measuring the RMS ion current $I RMS$ under the MEMS ion angle filter at the ion collector. The obtained measurement data and the resulting angle distribution are shown in Fig. 27. The method used to fit the parameterized IADF is described in Sec. III C. During these measurements, no interference from heating of the MEMS due to energy input from the plasma was observed. Heating the chip would result in a shift of the resonance frequency, but this shift would be evident in the detection of the MEMS amplitude $α amp$ across the different frequencies employed in this study. Nevertheless, a shift in the resonant frequency would not pose a problem for the fundamental measurement principle, provided that the desired amplitudes $α amp$ are achieved. If necessary, adjustments to the frequency range and excitation amplitude $V MEMS , act$ may be required.

To further verify whether really the IADF is measured, the entire sensor system was mechanically tilted relative to the sheath while the plasma conditions remained unchanged. To do this, the entire circuit board was tilted by 3.6 $°$ by placing nuts with a total height of 4.2 mm on one side at a distance of 67 mm from the contact point of the circuit board. This mechanical tilting should result in a shift of the IADF mean $μ$ by the corresponding angle. Since the aperture wafer is still located above the tilted MEMS, the sheath is not deformed and the mechanical tilting results in a tilt relative to the sheath.

The measurements carried out in this way and the IADF fitted from them show the expected shift of the mean value $μ$⁠, see Fig. 28. The mean value $μ$ of the IADF shifted to $3.8 °$⁠, which agrees well with the mechanical tilting of the system by $3.6 °$⁠.

The measurements presented suggest that the MEMS sensor is capable of characterizing the ion angle distribution function. The comparison of the background measurement with the actual measurements, along with the reflection of the mechanical tilt relative to the plasma boundary in the measurement data, demonstrates that the presented measurements correlate with the ion angular distribution function.

However, at higher amplitudes $α amp$⁠, there is a deviation between the measured values and the fit. Possible causes, which are to be investigated in future work, include

• The assumption that the ion angular distribution is Gaussian may be incorrect. Detailed plasma simulations using Particle in Cell methods at the reactor level are necessary. These simulations can account for symmetry-breaking effects caused by various parts of the vacuum chamber, potentially explaining the non-Gaussian ion angular distribution function. These comprehensive 3D simulations are inherently time-intensive but are required to adequately consider the various attachments and components of the vacuum chamber.

• The MEMS plate may deform due to the dynamic load caused by resonant motion or may already be deformed in the static state due to layer stresses.

• The electric fields occurring between the individual components, as well as the electric fields in the holes for angular selection, may lead to a sufficiently strong deviation from the currently used approach of ion motion without external forces, which relies solely on a geometric filter effect.

• Other angle-dependent effects may occur, which have not been considered so far. For example, the angle dependence of secondary electron generation at the detector could lead to a deviation that has not been accounted for. However, literature values suggest that these effects should be negligible for angles below $30 °$⁠.

• The scattering and reflection behavior of ions at grazing incidence on the sidewalls of the silicon holes must be investigated. Suitable binary collision Monte Carlo simulations, such as SDTrimSP or TRIDYN, which accurately reproduce the angular distribution of sputtered particles, are ideal for this purpose.²⁹ 

For the first time, it has been demonstrated that the ion angle distribution function in low-pressure plasmas can be characterized using a micro-electromechanical system. This innovative measurement principle represents a significant breakthrough in terms of geometric dimensions compared to previous sensor concepts. As a result, it offers new opportunities for measuring ion angle distribution functions in both basic research and industrial settings, particularly because the sensor can be entirely fabricated from CMOS-compatible materials.

Further steps to advance this sensing principle will involve measurements with a static or quasi-static MEMS based on recent developments from our research group.²⁸ This approach would eliminate the need to fit the Ion Angle Distribution Function (IADF), as opposed to the resonant measurement shown here, and allow for direct measurement of the IADF. This advancement would enable the detection of asymmetric structures in the ion angular distribution. Additionally, it is desirable to further evaluate the presented system in a facility equipped with a mass spectrometer to measure the IADF, allowing for a comparison between our novel system and this state-of-the-art method. It is also conceivable to use MEMS with two tilting axes,³⁰ which would enable solid angle-resolved measurements.

To expand the potential fields of application, the electronics used must be made robust against the electromagnetic fields present in production plants through the use of filter technology. In addition, system properties such as durability must be examined under real production conditions. Furthermore, it is conceivable to develop a self-sufficient sensor system without cables, integrating the energy supply, MEMS, and data acquisition into a miniaturized system. Once these challenges are addressed, the system should be tested in both pulsed CCP systems, commonly used for dielectric etching in production tools, and in ICP sources, which enable precise adjustment of plasma parameters. This would provide additional characterization capabilities in micro- and nanoelectronics manufacturing, helping to maintain the viability of Moore’s law in a cost- and resource-efficient manner for the coming years.

Symbol Description

$A rel$

Relative hole area

$d Si$

Diameter of the holes in the silicon

$GT$

Geometric transfer function (filter effect of holes)

$IADF$

Ion angle distribution function

$I ion$

Ion current (unfiltered)

$I filtered$

Ion current (filtered)

$I RMS$

RMS ion current (filtered)

$T$

MEMS period

$t$

Time

$t Si$

Silicon thickness

$V MEMS , act$

MEMS amplitude actuator voltage

$V MEMS , sens$

MEMS amplitude tilt sensor voltage

$α amp$

MEMS tilt angle, amplitude of the oscillation

$α crit$

Acceptance angle of the ion filter holes

$α max$

MEMS tilt angle, largest possible tilt angle

$α MEMS$

MEMS tilt angle

$Δ x$

Virtual displacement of the hole center point

$μ$

Mean of the ion angular distribution function

$ω$

Angular frequency (MEMS oscillation)

$ϕ ion$

Ion incidence angle (deviation from orthogonality)

$σ$

Width of the ion angular distribution function

$Θ$

MEMS phase angle

This study is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—Project No. 335529250 and by the European Union (EU-ESF), the Sächsische Aufbaubank SAB, and the free state of Saxony within the research group “E-PISA,” FK:100310500.

The authors have no conflicts to disclose.

M. Melzer: Conceptualization (equal); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Software (lead); Visualization (equal); Writing – original draft (lead). K. Meinel: Formal analysis (supporting); Methodology (equal); Writing – review & editing (equal). C. Stoeckel: Conceptualization (equal); Formal analysis (supporting); Methodology (equal); Resources (equal); Supervision (equal); Visualization (equal); Writing – review & editing (equal). T. Hemke: Formal analysis (supporting); Writing – review & editing (equal). T. Mussenbrock: Conceptualization (equal); Formal analysis (supporting); Funding acquisition (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal). S. Zimmermann: Conceptualization (equal); Formal analysis (supporting); Funding acquisition (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.