Rapid subsurface damage detection of SiC using inductivity coupled plasma

This paper proposes a method for the rapid detection of subsurface damage (SSD) of SiC using atmospheric inductivity coupled plasma. As a plasma etching method operated at ambient pressure with no bias voltage, this method does not introduce any new SSD to the substrate. Plasma diagnosis and simulation are used to optimize the detection operation. Assisted by an SiC cover, a taper can be etched on the substrate with a high material removal rate. Confocal laser scanning microscopy and scanning electron microscope are used to analyze the etching results, and scanning transmission electron microscope (STEM) is adopted to confirm the accuracy of this method. The STEM result also indicates that etching does not introduce any SSD, and the thoroughly etched surface is a perfectly single crystal. A rapid SSD screening ability is also demonstrated, showing that this method is a promising approach for the rapid detection of SSD.


Introduction
Single crystal silicon carbide (4H-SiC) is considered one of the most promising third-generation semiconductor materials with applications in many cutting-edge fields, including electronics, optics, and graphene growth [1]. 4H-SiC has many excellent properties, such as a wide bandgap, low thermal expansion coefficient, high specific stiffness, good size stability, and high radiation resistance [2,3]. Despite these advantages, 4H-SiC is a typical difficult-to-machine material because of its high hardness and strong chemical inertness [4,5]. Furthermore, subsurface damage (SSD) is more easily introduced into this type of hard and brittle material during the machining process. SSD impairs the mechanical, electronic, and optical * Author to whom any correspondence should be addressed.
Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
properties of materials [6][7][8]. Thus, it is necessary to remove all SSD for advanced applications.
As a typical difficult-to-machine material, the processing of SiC wafers usually takes hours, especially the last polishing step, which removes all SSD introduced by previous slicing, grinding, and lapping steps [9]. The typical material removal rate (MRR) of SiC via the chemical mechanical polishing (CMP) method is ∼100 nm h −1 [10]. Moreover, this process consumes a large amount of slurry, which can be toxic, contaminative, and expensive [11,12]. To minimize the duration of CMP, a precision measurement method of the SSD layer thickness is indispensable.
SSD can be detected using destructive and nondestructive methods. Destructive methods include taper polishing, crosssectional microscopy, and etching, while nondestructive methods include x-ray scanning, laser scattering, and ultrasonic probing [13]. A nondestructive method can achieve in-process detection and will not destroy the sample. However, the detection accuracy and efficiency are relatively low. Destructive methods, in contrast, are more mature and have better reliability and accuracy. Thus, this type of method is widely used in industry and academia at present [13]. The most widely used destructive method is taper polishing, which is based on removing the material to form a taper or dimple that crosses the SSD layer to the damage-free matrix and observing the revealed surface to measure the SSD thickness [14]. To operate destructive SSD detection methods, a material removal method that does not introduce new SSD is indispensable. Conventional methods that meet this demand have been applied in SSD detection including CMP, chemical etching, and magnetorheological finishing (MRF) [15][16][17]. For CMP, the main drawback is the low MRR for SiC and the massive consumption of slurry, which is expensive and toxic [10][11][12]. Chemical etching uses hydrofluoric acid (HF) solution, which is hypertoxic. In addition, SiC does not react with HF at room temperature because of its excellent chemical inertness [18]. Among the destructive methods, MRF is most widely used. However, MRF often introduces Fe contamination into the sample [19]. Moreover, the MRR is not very high for SiC, and the general MRR is below 0.2 µm min −1 [20]. To increase the MRR of MRF, diamond abrasives are often used, which might introduce new damage [21]. Furthermore, MRF needs to collocate with a subsequent etching step to open cracks [13]. This etching step will be difficult for SiC because it is inert in all known aqueous etching solutions at room temperature [18]. To further develop the SSD detection technique, a novel SSD-free material removal method is needed.
Plasma etching is generally considered an 'ion-assisted gas-surface chemistry mechanism' process, and ion bombardment is the main cause of plasma-induced damage. However, damage induced by atmospheric pressure inductivity coupled plasma etching (ICPE) can be very low. ICP can achieve a higher etching rate under no substrate bias because of the much higher ion-to-neutral flux ratio and a much larger active species production rate compared to capacitively coupled plasma [22]. Furthermore, the incident energy for atmospheric ICP can be even lower because of the short mean free path; thus, the etching process is free of structural damage [23]. Recently, the application of atmospheric ICP as a potentially efficient machining method has been studied by many researchers. For instance, reactive atom plasma technology by Fanara et al, atmospheric pressure plasma polishing by Jin et al, and ICPE by Dai et al have achieved SSD-free processing of fused silica based on ICPE [24][25][26]. Furthermore, Dai et al discussed the surface damage evolution of fused silica under ICPE and compared it with that of the MRF method, implying that ICP could be a promising method for SSD detection [26].
Precision detection of SSD using ICPE is difficult because the etching spot is relatively large, in the range of centimeters. The spread radicals reach an even larger area, resulting in whole surface etching. Meanwhile, the deposition of fluorocarbon particles covers the original surface. It is imprecise to measure the SSD thickness by comparing the last trace of the SSD layer and the remainder of the surface. Meanwhile, confocal microscopy for large areas loses accuracy because of pixel-limited resolution [27]. In this study, a cover was used to protect the raw surface and produce a shorter transition between the SSD-free matrix and the original surface. The position of the mask was optimized via plasma simulation.
SiC was chosen as the cover material considering that a highly reactive and high-temperature plasma jet is needed to prevent the introduction of new contamination. Furthermore, a demonstration of rapid SSD detection was performed to help understand the influence of several lapping parameters.

Materials
Single-crystal Si slices (40 × 40 mm) were used to study the single spot etching behavior of ICP. Commercially available on-axis sliced and epi-ready 4H-SiC wafers (SICC Co., Ltd, Shandong, China) were used in this study, and the thicknesses were 650 µm and 370 µm, respectively. The wafers were cut into 10 × 10 mm slices. All experiments were conducted on the Si (0001) face, which is the most commonly used face for electronic device applications [28].

ICPE
The ICPE process was performed on the apparatus shown in figure 1(a). A three-channel gas supporting system is connected to a quartz torch, which consists of three concentric tubes. The inner tube is supplied with reactive gas, which is a mixture of CF 4 and oxygen in this case. The addition of oxygen can greatly reduce the deposition of fluorocarbons on the surface [29]. The second tube is supplied with pure argon at a flow rate of 1.5 slm as the plasma ignition gas. The outer tube is supplied with cooling gas, which is pure argon at a flow rate of 18 slm. The bottom part of the quartz torch is placed concentrically in an inductance coil. This inductance coil is connected to a matcher, which is connected to radio frequency (RF) power (27.12 MHz, 1000 W). During operation, the RF power generates an RF changing electronic field in the center of the inductance coil, which excites the gas passing through the coil and transforms it into a dense plasma jet. The sample to be etched is placed on a thermal insulation platform wafer holder that is connected to a three-axis numerical control (NC) platform. As shown in figure 1(b), the entire ICPE device is installed inside an enclosed metal chamber with an electromagnetic interference shielded window and connected to a ventilation system to prevent possible health damage from electromagnetic radiation and toxic exhaust.

The numerical simulation of atmospheric ICP torch
To have a better understanding of the temperature and velocity distribution of the ICP jet, we did a numerical simulation of atmospheric ICP torch conducted by COMSOL Multiphysics 5.4. In the case of atmosphere pressure, inductively coupled plasma is assumed to be under local thermodynamic equilibrium conditions. Hence, it can become a conductive fluid through interactions with electromagnetic fields in the simulation. Many assumptions were made to reduce the computational cost.
We combine the Navier-Stokes, heat, and Maxwell equations to describe the motion of the conducting fluid in an electromagnetic field. The governing equations of the torch model are summarized as follows: The Navier-Stokes equations for laminar flow module: Conservation of mass: Momentum conservation equation: where ρ is the fluid density, u is the velocity vector, p is the pressure, µ is the dynamic viscosity of the fluid, I is the identity matrix, and F is the Lorentz force acting on the fluid.
The heat transfer equation for heavy particles: where Q is the heat source, T is the temperature, C p is the specific heat capacity, k is the thermal conductivity.
The first term represents the enthalpy transport, the second term represents the joule heating, and Q rad is the volumetric net radiation loss. Maxwell equations were used to solve the magnetic field: where H is the magnetic field, J is the plasma current density, B is the magnetic flux density, A is the potential vector, σ is the electrical conductivity, E is the RF electric field, ω is the angular frequency, and D is the displacement current. Equations (1)-(9) were solved by a finite element method based on COMSOL software. The ICP torch is modeled to be a fully axisymmetric configuration, which is shown in figure 2. The ICP simulation uses the same model size and etching parameters as the experiment. The temperature of the quartz tube and the temperature of the ambient air are assumed to be 300 K under atmospheric pressure. The temperature data were collected from the exposed upper surface of the SiC sample. The velocity data were collected above the aforementioned surface with a distance of 0.01 mm.

SSD screening demonstration
A set of samples was prepared using various lapping parameters to demonstrate the rapid SSD screening ability of the ICPE method and to obtain the optimized lapping parameters for a high MRR with low SSD thickness. Lapping experiments were performed on the Si face of the epi-ready SiC substrate using diamond lapping discs of 500-3000 grits. All experiments were conducted using a metallographic grinding polishing machine from Laizhou Weiyi Experimental Machinery Manufacture Co., Ltd. The detailed lapping parameters are listed in table 1.

Characterization and measurement
Optical emission spectrometry (OES, Ocean optics USE4000) was used to determine the composition of radicals in the

Plasma diagnostics
In this method, ICPE was the chosen approach for removing materials from the substrate surface and forming a taper that serves as the window for measuring the SSD depth. The ICPE of SiC should be a pure chemical process without mechanical force and, thus, does not introduce new SSD, ensuring accurate SSD measurements. The process is based on the chemical reaction expressed as equation (10) [30]: SiC + mF + nO → SiF m + CO n + CF m (m = 1 to 4, n = 1 to 2).
The reactive plasma must contain sufficient amounts of F and O radicals to ensure that the reaction progresses. Thus, plasma diagnostics of ICP were implemented before the etching operation. An optical photo of the ICP jet is shown in figure 3(a). OES was used to confirm the presence of etching radical compositions in the plasma. OES data were collected from the normal analysis zone of the ICP jet, and the results are shown in figure 3(b). When CF 4 was added to the plasma, distinctive peaks corresponding to CF X and the typical C 2 swan system were observed [31][32][33]. The peaks representing fluorine radicals are difficult to detect because they overlap with the strong peaks of argon emissions. However, the strong peaks of CF X and C 2 prove the sufficient dissociation of CF 4 , which generates a substantial amount of fluorine radicals as another major product [34]. The atomic oxygen peaks at 777 nm and 844 nm represent the transitions O (3p5P→3s5S) and O (3p3P→3s3S), respectively [35]. The OES results indicate that this ICP jet contains abundant F and O radicals that are capable of etching SiC.

Etching characteristics
The etching behavior of ICP was studied to make it a predictable tool for taper fabrication. Here, a 40 × 40 Si slice was used to explore the profile change of ICP torch etching. A single spot was etched on Si for 2 min. Optical photos of the samples are shown in figure 4(a), where 1 is the as-received sample, and 2 is the sample after single spot etching by ICP. The size of the ICPE pits is approximately 3 cm. Since we used an ICP torch with a diameter below 2 cm, the larger etching pits are due to the deflection of the plasma jet when it hits the sample surface and the flow and diffusion of radical. The cross-sectional profile of 1 and 2 along the diagonal is shown in figure 4(b). The profile change exceeds the size of the etching pits and stretches to the entire surface. Because of reaction consumption, a limited lifetime, and dilution by air, the concentration of etching radicals decreases as the distance from the torch increases. Thus, the etching depth decreases along the pit radius.   particles on the surface area should be the deposited fluorocarbon polymers [36]. This result could explain the profile change outside the etching pits, where accumulated fluorocarbon polymer covers the initial surface. Furthermore, the adsorption of deposited particles increases with decreasing temperature, which has a consistent trend with the distance from the heat source, i.e. the plasma center. Consequently, the entire initial surface of the sample will be deformed, either by etching from plasma or occlusion by deposition particles, and it is impracticable to identify the raw surface after unobstructed etching. Nevertheless, marking the position of the raw surface is crucial in destructive SSD detection; hence, a raw surface protective countermeasure is needed during ICPE [13].

SSD detection
Masks of photoresist or deposited metal are often used in the plasma etching process to protect certain areas. In this study, a mask was used for that purpose. To resist the high temperature and highly reactive radicals from the ICP torch, a slice of 4H-SiC was used as the mask. The entire rapid SSD measurement process is listed as follows: (a) ICP is ignited as described in section 2. (b) As illustrated in figure 5, the SiC sample for the SSD measurement is partially covered by a smaller piece of SiC to protect a portion of the original surface as a reference plane to measure the SSD depth. (c) The covered sample is then moved directly under the ICP flame by the three-axis NC platform and etched for 2 min. (d) After etching, the SiC cover is released, and the etched SiC sample is cleaned with DI water and alcohol. (e) After cleaning, the etching profile is observed via CLSM. The depth of the SSD layer is obtained by comparing the vertical distance between the protected original surface (z1) and the last trace of the SSD layer (z2).
A taper that gradually deepens is needed to observe the SSD depth successfully. Considering the ease of CLSM operation and avoiding stitching measurement to ensure accuracy, the lateral length of the taper should be controlled within 100 µm. Moreover, the etching rate should increase along the exposed sample surface and cover the 100 µm observation zone mentioned above. The etching rate is governed by the Arrhenius equation listed in equation (11): where n F is the concentration of fluorine radicals on the surface, A is the pre-exponential factor, Ea is the activation energy of the etching reaction, R is the universal gas constant, and T is the absolute temperature of the sample surface. For this specific reaction, A, Ea, and R are constant values. Thus, we only need to study the temperature and radical concentration. According to figure 4, the lateral distance between the plasma center and the sample (d p-s ) significantly affects the etching behavior. Hence, we studied the influence of d p-s on these two factors that affect the etching rate using COMSOL Multiphysics. Figures 6(a)-(c) show the temperature simulation of the etching process for three sample positions in which d p-s equals 0.5 mm, 5 mm, and 9 mm, respectively. Figure 6(d) shows the temperature of the observation zone, which is on the surface of the sample and ranges from the mask boundary to the exposed part of the sample 100 µm away horizontally. With increasing d p-s , the sample moves to the edge of the plasma, and the temperature gradually decreases. However, the temperature of each sample is uniform, fluctuating within 1 • C. This result might be due to the excellent thermal conductivity of SiC. Thus, the etching rate difference due to temperature change can be neglected. As the calculation of the reactive radical concentration on the surface can be complicated, we studied the flow rate of the plasma as an approximation to facilitate the investigation. Figures 6(e)-(g) show the simulation of the flow rate of the three experiments. The flow rate on the sample surface should be zero. Here we chose the flow rate from the area 10 µm above the observation zone, the aforementioned indicator of the flow condition near the surface, and the data are plotted in figure 6(h). The velocity variation increases with d p-s . A larger flow rate change induces a larger etching rate difference. Accordingly, the sample stack should be placed in the outer region of the plasma, and d p-s = 9 mm was used in the subsequent experiments.
ICPE for SSD measurement was conducted on the Si face of the SiC sample with an SiC cover and d p-s = 9 mm. The morphology changes before and after etching are shown in figure 7. The lapped SiC surface (figure 7(a)) shows an actinomorphic trajectory pattern, which is caused by the periodic eccentricity lapping process [37]. Figure 7(b) shows the same sample after SSD reveals etching. The left part is the covered area, where no visual difference can be observed. The right part is the etched area, where a glazed surface implies the removal of the damaged layer. A distinctive boundary is observed between the covered and etched areas. Figure 7(c) is a schematic of the etching boundary area, which is marked by the red rectangle in figure 7(b). The red arrows 1-3 represent the covered area, transition etched area, and throughout etched area, which are shown in figures 7(e)-(g), respectively. Figure 7(d) is the SEM image of the original surface. No discrepancy can be observed within the area of the etched SiC sample under the protection of the SiC cover (figure 7(e)), which indicates that the SiC cover efficiently suppresses the etching of SiC beneath it. Thus, the surface under the SiC cover can be used as a reliable initial reference plane for measuring the thickness of the SSD layer. Figure 7(f) shows the area near the edge of the SiC cover, where radical flow can reach   and react with the sliced SiC sample surface. Meanwhile, the edge of the SiC cover confines the radical flow from some directions; thus, the SSD layer is only partially removed. Many cracks are revealed by the plasma etching, suggesting that the revealed plane is inside the SSD layer. Figure 7(g) shows the surface of the sliced SiC sample far from the protection of the SiC cover. Without any protection, the SSD layer is fully etched. Cracks completely vanish on the surface, indicating that the surface is damage-free [13]. The island structure remaining on the surface is caused by the uneven etching rate between the damaged layer and damage-free matrix [38]. ICPE in this part crossed the bottom of the SSD layer.
To measure the vertical distance between the original surface and the bottom of the SSD layer, CLSM was employed, and the results are shown in figure 8. The 2D CLSM image is shown in figure 8(a), and the 3D image is shown in figure 8(c). A very clean taper was formed via ICPE. For figures 8(a) and (b), the left side of the SiC sample exploded under ICP, while the right side was under the protection of the SiC cover. The right side retained its original morphology, suggesting that no etching occurred in this area, which agrees with the SEM result in figure 7(e). The left side underwent etching of dense ICP, and the original morphology was totally removed. A slope structure caused by the partial protection of the SiC cover edge links the original surface and deeply etched area. A gradual reduction in crack density can be observed along the taper, analogous to that of the MRF taper method, representing thinning of the SSD layer [39]. The deepest crack disappears in the bottom of the SSD layer. After that spot, all SSDs were removed, and only perfect SiC remained. A crosssectional profile was extracted along the last crack trace, as depicted in figure 8(b). The blue rectangle in figure 8(b) indicates the position of the last crack. The vertical distance to the original surface is 1.128 µm, which is also the depth of the SSD layer. figure 8(b) also demonstrates that the total etching depth is approximately 4 µm, which is more than three times the measured SSD layer thickness. In this case, the etching depth is sufficient to penetrate the SSD layer, suggesting that the result is accurate.
To further confirm the accuracy of the SSD measurement, FIB was used to cut a cross section of the etched sample, and STEM was employed to directly observe the SSD layer. Figure 9(a) shows the area under the protection of the SiC cover: Cracks, stress and amorphous layers can be clearly observed. The depth of the SSD layer is approximately 1.06 µm, which matches the ICPE sample. Higher magnification images of areas A and B are shown in figures 9(b) and (c), which represent the typical crack region and deformed region of the SSD layer. The cross section of the part where SSDs are fully removed by ICPE is depicted in figure 9(d). A visually uniform SiC interface was observed, indicating that the SSD layer was removed. The high resolution transmission electron microscope (HRTEM) of the interface region shown in figure 9(e) further proves this point. Perfectly crystalline 4H-SiC was observed immediately below the interface, and the image corresponds to the <11-20> face of 4H-SiC [40]. This result proves that only single crystal 4H-SiC remained on the crack-free surface formed by ICPE, and no new SSD was introduced. The selected area electron diffraction (SAED) pattern in figure 9(f) shows a typical diffraction pattern along the [11][12][13][14][15][16][17][18][19][20] zone axis of 4H-SiC, which agrees with the HRTEM image and further supports the good crystallinity of the remaining substrate [41]. The results demonstrate that ICPE of SiC is a rapid, SSD-free method that produces accurate SSD measurements, making it a promising approach for SSD detection of SiC.

Rapid SSD screening demonstration
The ability of the ICPE method to rapidly and accurately detect the thickness of the SSD layer enables us to quickly screen and find the optimal lapping parameters. Here, we demonstrate  this rapid screening ability using ICPE to study the influence of lapping parameters, including granularity, lapping pressure, and revolution velocity. Twelve sets of samples were lapped using the parameters listed in table 2.
With the assistance of rapid ICPE, only 2 min of etching are needed to reveal the SSD layer of each sample. Meanwhile, the system operates in an atmospheric environment, which eliminates time-consuming vacuum process in normal plasma etching. In addition, this method does not require a subsequent etching step for opening cracks, which is indispensable for the traditional MRF method. Furthermore, the NC platform can load multiple samples. The entire SSD revelation process for 12 samples is completed within 30 min. Figure 10(a) shows the influence of lapping pressure on the MRR and SSD of the SiC sample (sample number [1][2][3][4]. MRR increases linearly with increasing pressure. However, the SSD changes at a much lower rate because the gap between the sample and diamond disc decreases with increasing lapping pressure. The number of abrasive particles that undertake the load also increases, so the contact pressure remains constant. This causes the relevant SSD thickness to remain constant [42]. However, the MRR increases quickly as the number of effective abrasive particles increases. Granularity has a similar influence over the MRR and SSD layers (sample number [5][6][7][8], as shown in figure 10(b). This is because grain size directly affects the cut depth of each grain. In figure 10(c), representing sample number 9-12, the MRR increases with the revolution velocity because a higher cutting speed removes more material in unit time. However, if cut depth remains the same, no obvious change trend of SSD can be observed, which means that SSD is not sensitive to lapping revolution velocity. In summary, granularity has the greatest effect on SSD thickness, followed by pressure. Revolution velocity has no clear influence on SSD thickness.

Conclusion
Atmospheric ICPE, an SSD-free material removal method, was used to perform rapid SSD detection of SiC. The plasma diagnosis and etching behavior study showed its capability for fast material removal. Plasma flow simulation was used to optimize the etching position, and rapid SSD detection finished within 2 min. As confirmed via STEM, the ICPE process did not introduce new SSD, and the SSD layer thickness determined by STEM matched well with that of the ICPE method. A demonstration of rapid scanning was demonstrated on 12 samples to study the influence of lapping parameters on SSD. The results indicate that ICPE is a promising SSD detection method. It is rational to further propose that by altering the composition of the etching gas, ICPE could be a general method for SSD detection in a wide range of materials.