Button shear testing for adhesion measurements of 2D materials

Two-dimensional (2D) materials are considered for numerous applications in microelectronics, although several challenges remain when integrating them into functional devices. Weak adhesion is one of them, caused by their chemical inertness. Quantifying the adhesion of 2D materials on three-dimensional surfaces is, therefore, an essential step toward reliable 2D device integration. To this end, button shear testing is proposed and demonstrated as a method for evaluating the adhesion of 2D materials with the examples of graphene, hexagonal boron nitride (hBN), molybdenum disulfide, and tungsten diselenide on silicon dioxide and silicon nitride substrates. We propose a fabrication process flow for polymer buttons on the 2D materials and establish suitable button dimensions and testing shear speeds. We show with our quantitative data that low substrate roughness and oxygen plasma treatments on the substrates before 2D material transfer result in higher shear strengths. Thermal annealing increases the adhesion of hBN on silicon dioxide and correlates with the thermal interface resistance between these materials. This establishes button shear testing as a reliable and repeatable method for quantifying the adhesion of 2D materials.


Introduction
The integration of two-dimensional (2D) materials into semiconductor devices is gaining momentum as the technology matures [1][2][3] .One of the remaining challenges is the adhesion, or lack thereof, of the 2D films to adjacent layers due to their van der Waals (vdW) nature 4,5 .
Adhesion ultimately affects the device reliability, but also 2D layer transfer methods 6,7 .
The double cantilever beam method [33][34][35] is applicable to gather information on the average adhesion of large area interfaces in the millimeter range but cannot be applied for local measurements in the micrometer range.A promising method for some applications is scratch testing [36][37][38] .However, the mechanical properties of all materials in a sample stack, such as hardness, influence the critical load in a scratch test 39 .This limits the comparability of multilayer systems or of measurements on different substrates.Four-point bending as an established adhesion measurement method 40,41 was recently used to assess the adhesion of transition metal dichalcogenides (TMDC) 42 .All methods can be categorized by their ratio of forces perpendicular (mode I) and parallel (mode II) to the surface, or a mix.
Here, we introduce button shear testing as a quantitative method for determining the shear strengths of 2D materials.Button shear testing is an established method for adhesion measurements in typical semiconductor technologies and materials [43][44][45][46][47][48] , which yields rapid and conclusive results based on vast existing knowledge.We demonstrate the feasibility of the method for different 2D materials and substrate combinations and its application in evaluating the effect of sample treatments on adhesion.

Button shear testing
The graphene samples were based on commercial chemical vapor deposited (CVD) monolayer graphene on copper.This was transferred onto three different substrates by a wet-etching process 49 before button fabrication, (a) 250 nm silicon dioxide (SiO2) deposited with oxygen and tetraethyl orthosilicate precursors (TEOS SiO2), (b) 250 nm silicon nitride deposited from ammonia and dichlorosilane (Si3N4), and (c) 90 nm silicon dioxide grown by thermal oxidation of silicon (thermal SiO2).A subset of TEOS SiO2 and thermal SiO2 substrates was treated with oxygen (O2) plasma before graphene transfer.CVD hexagonal boron nitride (hBN) was also transferred from a copper growth substrate onto O2 plasma-treated thermal SiO2 substrates by a wet-etching process 49 , and subsets with hBN were annealed up to 1000 °C between the transfer process and button fabrication.Metal-organic chemical-vapor-deposited (MOCVD) molybdenum disulfide (MoS2) 50,51 and MOCVD tungsten diselenide (WSe2) 52 was transferred from the sapphire growth substrate onto O2 plasma-treated thermal SiO2 substrates.
Schematic cross-sections of all samples are shown in Supplementary Fig. 1.
Buttons were fabricated by spin-coating polymethyl methacrylate (PMMA) onto the samples to create a 5 µm PMMA film.A 20 nm thick aluminum hard mask deposition followed by a lithography process step led to structures (buttons) with typical lateral dimensions of 60 x 100 µm.Anisotropic dry etching of the PMMA film in an oxygen (O2) plasma produced the desired buttons (Fig. 1a,b).Polystyrene as an alternative button material did not lead to a cuboid button cross-section after O2 plasma-etching and was excluded from the shear experiments (Supplementary Fig. 2).
Button shear test measurements were performed with a DAGE4000Plus pull-shear tester.
The stage with the sample moved with a defined speed to create contact between the fixed shear head and the button (Fig. 1c).The lateral displacement of the stage was then recorded while the force that acts on the shear head was measured by the cartridge.The force increased as the shear head made contact with the buttons.The force reached a maximum at a certain point where the shearing of the button started, moving it slightly on the target (see Fig. 1b).After the initiation of the shear process, less force was required to maintain the shear process, and the measurement was stopped.The maximum recorded force corresponds to the force that is required to initiate the shear process.This is expected to occur at the weakest spot of the interface underneath the button and is labeled as critical shear force FC within this work.
Reference button shear tests were performed on samples with PMMA on thermal SiO2 and button lengths of 20, 40, and 60 µm.Typically button shear tests use button sizes in the millimeter range and measure FC in the Newton range 43 .However, 2D materials today must be expected to have cracks, holes, or other defects [53][54][55] that influence their mechanical properties 32,56,57 in such millimeter-range contact areas.We therefore implemented a measurement routine based on smaller buttons to overcome this challenge.A button length of 60 µm was established as a minimum for reproducible results by these initial experiments because smaller buttons with 20 µm and 40 µm button length show very low and scattered FC (Fig. 1d).PMMA is a soft material with low elastic modulus compared to other assistance layers in shear testing experiments with 2D materials 58 .That leads to button deformation near the contacted button edge, hence, the ratio of forces perpendicular (mode I) and parallel (mode II) to the surface varies along the shear path 43,59 .The pronounced mixed mode near the contacted edge can be the reason for the very low FC at small button lengths 60 .The influence of plasma on PMMA edges 61,62 is an additional possible reason for the FC variability with smaller button lengths.
Shear tests were further performed on a calibration sample that consists of a step in the (100) silicon surface.This step can be considered as a button that cannot be sheared off to assess the accuracy of the force and displacement measurement.Ideally, the measured force before contacting the stable obstacle is zero and jumps to a very high value upon contact.Here, we chose a shear speed of 1 µm s -1 to be able to stop the measurement in time and prevent damage to the tool.A large cartridge with high internal stiffness and a small cartridge for small forces were compared (Fig. 2a).The large cartridge delivered correct displacement values, but the noise in the force data before contact made reliable force measurements impossible.The small cartridge produced no noise in the force data and was chosen for the experiments.However, the pronounced force-dependent stiffness of the small cartridge leads to non-reliable displacement measurements.A multipoint calibration may reduce this effect, but there are several other system-dependent influences on the displacement measurement 45 .Therefore, no quantitative evaluation of the displacement was performed, but FC was extracted only from the force data.Dividing FC by the button area 100 µm x 60 µm leads to the area-independent shear strength τC.
The influence of the shear speed was evaluated on samples with PMMA on thermal SiO2 because shear speed effects strongly influence τC 31,35,48 .τC at low shear speeds below 5 µm s -1 was significantly lower than at high shear speeds (Fig. 2b,c).Similar trends were observed in previous studies 48,[63][64][65][66] and can be assigned to viscoelastic properties of PMMA [67][68][69][70] .We chose a shear speed of 10 µm s -1 for the experiments with 2D materials to prevent a significant influence of the viscoelastic properties of PMMA.

Graphene
The shear strength of graphene on the three substrates TEOS SiO2, Si3N4, and thermal SiO2 was measured with the optimized parameters of a small cartridge and 10 µm s -1 shear speed.
Fig. 3a compares τC of graphene on as deposited TEOS SiO2 (1.55±0.31MPa), Si3N4 (2.88±0.31MPa), and thermal SiO2 (2.68±0.11MPa).We correlated these results with the surface roughness sa of the substrates and the surface roughness of graphene on the substrates as the roughness is known to influence the adhesion of a 2D material 21,71 .AFM roughness data show that bare TEOS SiO2 has a roughness of sa = 0.76 nm and graphene on TEOS SiO2 has a lower roughness of sa = 0.64 nm.On the smoother substrate thermal SiO2 the roughness remains at sa = 0.22 nm without and with graphene.On Si3N4 the roughness increases from sa = 0.30 nm without graphene to sa = 0.42 nm with graphene (see Fig. 3b-d andTable 1).This increase in roughness may be attributed to PMMA residues from the wet etching transfer process 72,73 and limits the validity of roughness measurements on transferred CVD-grown graphene.However, the lower roughness of graphene on TEOS SiO2 compared to bare TEOS SiO2 is an indication that the graphene does not fully follow the TEOS SiO2 morphology.This behavior on rough substrates is predicted in theoretical studies 74,75 and leads to a smaller effective interface area and finally to a smaller adhesion 76 .
The TEOS SiO2 and thermal SiO2 samples were further exposed to O2 plasma.This was not the case for the Si3N4 sample, because an O2 plasma would have modified the surface to an undefined silicon-oxide-nitride composition 8 .The O2 plasma treatment increased τC of graphene on TEOS SiO2 to 2.21±0.33 MPa, but we did not observe a significant change on thermal SiO2 (2.77±0.32MPa, Fig. 3a).AFM measurements show that the roughness of our oxides did not change significantly after the O2 plasma, and hence this was ruled out as the reason for the different behavior (Table 1).However, several other potential explanations for the influence of the plasma treatment on adhesion remain: O2 plasma reduces the water (H2O) contact angle (CAwater), increases the surface energy 8,21,23 , and reduces carbon contamination on the surface 8 .Contact angle measurements showed that the applied O2 plasma reduced the CAwater from 7.3 ° to 3.0 ° for TEOS SiO2 and from 42.7 ° to 2.7 ° for thermal SiO2, (Fig. 3e-g and Table 1).Since the reduction of CAwater is more pronounced on thermal SiO2, which showed no significant change in τC, we rule this effect out as the main contributor.X-ray photoelectron spectroscopy (XPS) measurements of C 1s peak on TEOS SiO2 (Fig. 3h) and thermal SiO2 (Fig. 3i) before and after O2 plasma show that the reduction of carbon contamination on the surface is more pronounced on TEOS SiO2, which confirms previous investigations 8 .Therefore, we conclude that the adhesion increase is dominated by the effect of surface cleaning.We note that only buttons with visibly intact graphene underneath were included in the assessment.This is because the high CAwater caused cracking and partial delamination of graphene during the drying process in some cases.Buttons on areas with partially delaminated graphene were excluded to evaluate only pure graphene-substrateinterfaces (see also Supplementary Fig. 3).In all cases, delamination at the substrate-graphene interface occurred.This was confirmed by optical microscopy (Supplementary Fig. 4) and Raman measurements (Supplementary Fig. 5).Minor graphene residues are found predominantly near the contacted button edge.The pronounced mixed mode at the contacted button edge is a likely reason for this observation 60 .

Hexagonal boron nitride
hBN is of interest as a 2D dielectric for encapsulating electrically active 2D materials like graphene or semiconducting TMDCs 1,77,78 .In many integration schemes, hBN is therefore in contact with a three-dimensional substrate like SiO2.We have investigated the adhesion of hBN on thermal SiO2 with O2 plasma cleaning.The τC of 4.43±0.95MPa is significantly higher on this substrate compared to graphene, which was 2.77±0.32MPa, but also shows a higher standard deviation (Fig. 3a).This is in contrast with the work by Rokni and Lu 25 , who compared the adhesion of graphene and hBN on a silicon oxide substrate and measured a larger interfacial adhesion energy in the case of graphene.However, the high adhesion energy was only apparent when the graphene was pressed onto the substrate by a pressure of at least 3 MPa before measurement, and their experiments were conducted with (nearly) defect-free exfoliated 2D materials.They hypothesized that the large adhesion energy values for graphene on silicon oxide arose from non-vdW forces, i.e. hydrogen bonds (e.g.C-H…O-Si) or maybe even covalent bonds (e.g.C-O-Si) 25 .In our case, we expect a higher defect density of the CVDgrown hBN compared to the CVD-grown graphene because the growth processes are less mature 53 .As an indication of the defect density of graphene and hBN used in this work, we provide laser scanning microscope images, AFM measurements, and Raman measurements in Supplementary Fig. 6.A higher defect density can drastically increase the adhesion, e.g. by hydrogen bonds as shown for graphene on polymers 30,32 .This finding could be used to engineer 2D materials with defects at well-defined locations as a reasonable integration scheme to achieve sufficient adhesion of 2D-3D heterostructures if one can tolerate the altered electronic properties of the material at the defect sites.Thermal annealing is an established post-process treatment to reduce polymer residues 79,80 , remove interfacial water residues 81 , and increase the adhesion 9,37 .Thermal annealing is also expected to lead to a more conformal contact of 2D materials with the respective substrates 9,82 and to a larger effective interaction area of the van der Waals forces.We performed button shear tests with hBN on plasma-treated thermal SiO2 samples before and after thermal annealing in N2 atmosphere.The focus was on temperatures from 100 °C to 400 °C, which are typical annealing temperatures compatible with the back end of the line in silicon technology.
Anneals up to 1000 °C were additionally executed to investigate possible effects above this regime.The button shear test showed that annealing up to 300 °C -400 °C significantly increases the adhesion, in line with recent results for graphene 9,38 .Higher temperatures have only a minor additional influence on the adhesion, which may also lie within the standard deviation of the single measurements (Fig. 4a).
We performed scanning thermal microscopy (SThM) to determine the thermal conductivity (or thermal resistance) [83][84][85] of the multilayer hBN on thermal SiO2 samples before and after annealing as a measure of the conformal contact of the 2D material with its substrate. 9,82In SThM, the measured thermal signal in Volt corresponds to the thermal interface resistances (TIRs) between the layers for a system of ultrathin layers 86 .This, in turn, correlates with high adhesion as shown for other material systems [87][88][89] .The thermal signal (V) in the hBN samples decreases significantly from 4.0 V to 3.1 V after a 400 °C anneal (Fig. 4b), but a subsequent anneal at 1000 °C does not further decrease the thermal signal, which remained at 3.2 V. We assume that the TIR between the Si and the thermal SiO2 remained unaffected by annealing at 400 °C and 1000 °C, and attribute the TIR reduction to a change in the hBN and thermal SiO2 interface.This is in good agreement with the adhesion measurement data.Measurements with different probe tips and comparative measurements on a similar sample demonstrate the reproducibility of the results.Additional SThM measurements for hBN on bulk Si samples show a similar behavior (Supplementary Fig. 7).
Neuman et al. showed for graphene that slight deformations occur when the 2D material follows a substrate's roughness, leading to nanometer strain variations 90 .We therefore employed Raman measurements to corroborate our hypothesis that the hBN forms a more conformal contact with the SiO2 substrate upon annealing.Our Raman data of E2g peaks of the hBN on thermal SiO2 before and after thermal annealing show a slight increase of the fullwidth at half-maximum (FWHM) ΓE 2g with higher anneal temperatures (histograms in Fig. 4e).
This is a signature of increased strain variation, which influences the position of the E2g peak of hBN.The peak broadening is caused by overlapping subpeaks of different strain values in different directions 91 , and serves to explain the increased adhesion upon annealing.

Molybdenum disulfide and tungsten diselenide
We transferred MoS2 and WSe2 with lateral dimensions of approximately one by one centimeter onto thermal SiO2 with O2 plasma cleaning and created buttons on top of and next to the TMDCs.Supplementary Fig. 8 shows Raman spectra of MoS2 and Wse2 films on SiO2.with the same measurement method can be used as references.Few publications compare the adhesion of MoS2 on SiO2 with graphene on SiO2.They consistently conclude lower adhesion energy for MoS2 on SiO2 compared to graphene on SiO2 by blister test 10,14 , spontaneously formed blisters 92 intercalation of nanoparticles 18 , and AFM techniques 25,93 .The button shear test also assigns a slightly lower shear force to MoS2 compared to graphene (τC = 2.77±0.32MPa) on thermal SiO2 with O2 plasma cleaning.τC of WSe2 is significantly higher and exhibits a gradient over the film.τC of WSe2 is highest at columns three to five and gradually decreases to columns eight and nine.The reason for this observation remains unclear, although one possible explanation may be non-uniform drying after wet transfer.This data shows that button shear testing can reveal nonuniformities in 2D material samples and may be used to optimize deposition, transfer, and subsequent device fabrication process steps regarding uniformity and adhesion on a wafer scale.
Control of the mechanical properties of the button material is crucial for reproducible results.
As discussed previously, the relatively soft PMMA leads to button deformation and pronounced mixed mode near the contacted button edge.Variations in button fabrication can lead to changes in the PMMA properties, hence, to changes in the measured shear strength 60 .
Table 2 compares the button shear testing method with other adhesion measurement methods for 2D materials in the literature.It compares favorably in terms of accuracy and measurement effort and provides fraction mode data for 2D materials on standard semiconductor substrates like silicon.surface roughness is beneficial for the strong adhesion of graphene on its substrate.We further used the method to explore means of enhancing adhesion, in particular, O2 plasma treatments of SiO2 surfaces before graphene transfer or post-transfer annealing after a wet transfer of hBN.
Our work thus introduces a reliable adhesion measurement technique for 2D materials and provides measurement parameters that can be utilized for quantifying and enhancing the adhesion of 2D materials on rigid substrates.Button shear testing may thus play a crucial role in the development of 2D materials for commercial semiconductor production.

Reference sample
A reference sample without 2D material was fabricated by spin-coating polymethyl methacrylate in chlorobenzene onto an oxidized silicon wafer to create a 5 µm PMMA film.A 20 nm thick aluminum (Al) hard mask was deposited by thermal evaporation.S1805 resist was used to define structures (buttons) with typical lateral dimensions of 60 x 100 µm.The alkaline developer in this process simultaneously etched the Al hard mask.A myplas-III © tool from Plasma Electronic was used to structure the PMMA in an O2 plasma.The buttons were tested both after the removal of the Al film as the last processing step and with the Al film remaining on top of the buttons.We observed no differences in the delamination behavior.The presence of Al provided a higher optical contrast and, hence, faster identification of buttons, so the process option with Al on top of the buttons was chosen for our experiments.A schematic cross-section of the reference sample can be found in Supplementary Fig. 1a.The reference sample was used for button shear test measurements with different button dimensions in Fig. 1d and with different shear speeds in Fig. 2b,c.

Calibration sample
A calibration sample was fabricated by a lithography process step on blank (100) silicon followed by anisotropic wet etching in potassium hydroxide (KOH) solution.This creates a step in the silicon that can be considered as button that cannot be sheared away.A schematic cross-section of the calibration sample can be found in Supplementary Fig. 1b.The calibration sample was used for button shear test measurements with different cartridges in Fig. 2a.

Graphene samples for button shear testing
Our graphene samples were based on commercial chemical vapor deposited (CVD) monolayer graphene on copper.This was transferred onto three different substrates by a wet-etching process before button fabrication, (a) 250 nm silicon dioxide deposited with oxygen and tetraethyl orthosilicate precursors (TEOS SiO2), (b) 250 nm silicon nitride deposited from ammonia and dichlorosilane (Si3N4), and (c) 90 nm silicon dioxide grown by thermal oxidation of silicon (thermal SiO2).A subset of TEOS SiO2 and thermal SiO2 substrates was treated with O2 plasma before graphene transfer.A schematic cross-section of the graphene samples for button shear testing can be found in Supplementary Fig. 1c-g.

hBN samples for button shear testing
Our hBN samples were based on commercial CVD monolayer hBN, transferred onto O2 plasma-treated thermal SiO2 substrates.Thermal annealing of hBN samples was conducted in nitrogen atmosphere with a hold time of two hours in a Jipelec Jetfirst 300 tool between the transfer process and button fabrication.A schematic cross-section of the hBN samples for button shear testing can be found in Supplementary Fig. 1h-i.

MoS2 and WSe2 samples for button shear testing
The MoS2 and WSe2 samples were based on MOCVD-grown few-layer MoS2 and WSe2 on sapphire substrates.After spin-coating with PMMA, the TMDC was delaminated from sapphire by KOH/H2O and transferred onto O2 plasma-treated thermal SiO2 substrates.A schematic cross-section of the MoS2 and WSe2 samples for button shear testing can be found in Supplementary Fig. 1k and Supplementary Fig. 1l, respectively.
hBN samples for Scanning thermal microscopy (SThM) measurements SThM samples were prepared by growing 15 nm of thermal oxide on silicon.A lithography step and wet-etching of SiO2 with hydrofluoric acid (HF) created areas with blank Si surface for referencing and normalization of the thermal signal.Multilayer hBN (15 nm) was transferred onto this substrate from copper foil using wet-etching transfer 49 .SThM measurements were performed at the edge of the transferred hBN area to be able to compare the thermal signal with and without hBN.A schematic cross-section and top view of the hBN samples for SThM measurements can be found in Supplementary Fig. 1j.

Button shear testing
Button shear test measurements were performed with a DAGE4000Plus pull-shear tester from Nordson Corporation.The samples with the processed buttons were placed into the sample holder of the tool.The shear head with a width of 100 to 120 µm was mounted into a cartridge, positioned 2 µm above the substrate surface, and a few tens of µm in front of a button.
The stage with the sample moved with a defined speed to create contact between the fixed shear head and the button (Fig. 1c).The lateral displacement of the stage was then recorded while the force that acts on the shear head was measured by the cartridge.The force increased as the shear head made contact with the buttons.The force reached a maximum at a certain point where the shearing of the button started, moving it slightly on the target (see Fig. 1b).After the initiation of the shear process, less force was required to maintain the shear process, and the measurement was stopped.The maximum recorded force corresponds to the force that is required to initiate the shear process.This is expected to occur at the weakest spot of the interface underneath the button and is labeled as critical shear force FC within this work.
Dividing FC by the button area 100 µm x 60 µm leads to the area-shear strength τC.

AFM roughness measurements
AFM roughness measurements were performed on the substrates TEOS SiO2 without O2 plasma, TEOS SiO2 with O2 plasma, Si3N4, thermal SiO2 without O2 plasma, and thermal SiO2 with O2 plasma and on graphene on TEOS SiO2 without O2 plasma, graphene on Si3N4, and graphene on thermal SiO2 without O2 plasma with a Bruker Dimension ICON AFM with Nanoscope V Controller.We used ScanAsyst-Air tips with a nominal radius of = 2 nm and a spring constant of knom = 0.4 N m -1 in ScanAsyst-Mode.Every sample was scanned at two different positions.Before and after scanning the samples, a calibration scan on a PA01 tip characterization sample from MikroMasch Europe was conducted to exclude tip degradation during the scan.The measurements were performed under ambient atmosphere (T = 21 °C, RH = 55 %).

XPS measurements
XPS measurements were performed on a Thermo Fisher Scientific ESCALAB Xi + with an Al K alpha source at 1486.6 eV.TEOS SiO2 samples and thermal SiO2 samples were analyzed by XPS initially, exposed to the O2 plasma afterwards, and finally characterized by XPS again.

SThM measurements
SThM measurements were performed with a Bruker Dimension ICON AFM with the Nanoscope V Controller.Here, we used a VITA-DM-NANOTA-200 tip and a VITA Module to evaluate the thermal interface resistance (TIR) of hBN to both SiO2 and Si after thermal annealing.Multiple measurements were recorded before and after the annealing process.A plane correction was applied to remove thermal drifts that are common in SThM measurements.The mean value of the thermal signal of the respective area was determined by the software Gwyddion 2.58.This mean thermal signal was normalized such that the thermal signal of Si = 0 V and the thermal signal of SiO2 on Si = 1 V. Constant TIRs between Si and SiO2 are assumed.

Raman measurements
Raman measurements were performed on hBN before and after anneal with a 532 nm laser, 240 s integration time, and a 100x objective with a Horiba LabRAM Evolution HR system.A linear baseline correction and a fitting with a Lorentz-Gauss profile of the hBN E2g peak and the neon reference lines were performed to evaluate the hBN signal.

Fig. 1
Fig. 1 Illustration of button geometry and shear test mechanism.a Colored scanning

Fig. 2
Fig. 2 Characterization of cartridge and influence of shear speed.a Force vs.

Fig. 4
Fig. 4 Influence of thermal annealing on a hBN -thermal SiO2 interface.a Shear strength

Fig. 5
Fig. 5 correlates the measured shear strength with the button position on, partly on, or next to

Table 2 .
Comparison of adhesion measurement methods of 2D materials.