Wafer-scale graphene quality assessment using micro four-point probe mapping

Micro four-point probes (M4PP) provide rapid and automated lithography-free transport properties of planar surfaces including two-dimensional materials. We perform sheet conductance wafer maps of graphene directly grown on a 100 mm diameter SiC wafer using a multiplexed seven-point probe with minor additional measurement time compared to a four-point probe. Comparing the results of three subprobes we find that compared to a single-probe result, our measurement yield increases from 72%–84% to 97%. The additional data allows for correlation analysis between adjacent subprobes, that must measure the same values in case the sample is uniform on the scale of the electrode pitch. We observe that the relative difference in measured sheet conductance between two adjacent subprobes increase in the transition between large and low conductance regions. We mapped sheet conductance of graphene as it changed over several weeks. Terahertz time-domain spectroscopy conductivity maps both before and after M4PP mapping showed no significant change due to M4PP measurement, with both methods showing the same qualitative changes over time.

Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. graphene are well established, methods for assessing the quality [21,22] and homogeneity of wafer-scale graphene are required to mature graphene-based technologies. Despite these advances in growth and processing, graphene inhomogeneity remains an issue for large-scale graphene. Areas of bilayer graphene are very difficult to eliminate and affect device properties [23][24][25].
In addition, significant variations in sheet conductance and carrier density are challenging to eliminate on large scale [18,[26][27][28]. Finding accurate strategies to probe thin-film properties is important for future research into the optimisation and commercialisation of graphene. Ideally, these methods should not require any wafer dicing (so the characterized wafer can be further processed), or contact with liquids or polymers so to not change the properties of the material [29]. Several techniques can probe thin-film properties without lithography.

Micro-Raman spectroscopy
Due to extensive work on the Raman spectral response of graphite and carbon nanotubes [30] prior to the graphene research boom, micro-Raman analysis was a tool that fit easily into the toolbox of the early graphene researcher. Therefore micro-Raman spectroscopy has become one of the key technologies used in the characterization of graphene because it is able to imply many metrics of graphene quality, including, but not limited to, number of layers [31,32], defect density [33,34], strain [35,36], and doping [37,38].
The resolution of micro-Raman depends on the laser wavelength and objective, full width at half maximum is typically <1 μm. Although micro-Raman is useful for graphene characterisation the technique cannot obtain direct measurement of sheet conductance ( ) G .

Terahertz time-domain spectroscopy
Terahertz time-domain spectroscopy (THz-TDS) is a non-contact method where a THz pulse attenuated by graphene is translated into G S [39,40]. Graphene G S measurements can be performed in either transmission-mode [41] or reflection-mode [42]. The beam spot diameter of a 1 THz pulse is ≈1 mm, however, for typical graphene the mean free path for one pulse is ≈10 nm [21]. This results in each THz pixel being the average of ≈10 nm transport properties in an mm-sized area. The probed area must be several millimetres away from metal contacts/ contamination, as the large number of carriers can significantly affect the THz signal [43]. THz-TDS can also extract G S for graphene on polymer [44] and has been used for tracking graphene properties before and after processing [43,45].

Micro four-point probes
Micro four-point probes (M4PPs) consist of micron-sized metalcoated cantilevers that are attached to a silicon carrier [46]. The electrodes are brought into contact with the sample using a strain gauge sensor to detect the surface [47]. G S is then measured using lock-in technique applying dual configuration van der Pauw type correction [48]. G S measured with M4PPs typically have errors less than 0.1% [49] even when measuring in confined regions on a scale similar to the probe size [50]. Hall measurements are also possible [51] as well as determination if current flows in a 1D or 2D path [28,52,53]. The resolution and probing area of M4PPs is on the order of the probe pitch ≈10 μm. Fully automated M4PP systems are commercially available and are typically used for G S characterisation of metallic and semiconductor thin films [54].

G S mapping of graphene
The discussed methods can all be used to generate high resolution spatial maps of graphene properties. Micro-Raman cannot probe G , S and there are several differences between G S maps obtained via THz-TDS and M4PP. M4PP has higher spatial resolution (≈10 μm versus ≈mm) whereas THz-TDS probes on the order of 10 nm versus 10 μm for M4PP. The differences in mean-free path could lead to different results if graphene has grain boundaries between 10 nm and 10 μm, which should be considered when choosing a mapping method or performing analysis. Transmission-mode THz-TDS has specific wafer requirements: the substrate should be flat on both sides and be (near) transparent in the THz range. Reflection-mode THz-TDS does not require a specialized THz-transparent wafer, but has a lower tolerance for alignment error. M4PP does not have any specific wafer requirements other than a substrate that is less conducting than the thin film to be measured. But M4PP requires probes to be in direct contact with graphene.
Previously we have analyzed a 100 mm diameter graphene-coated SiC wafer using G S maps obtained via THz-TDS and a single-probe M4PP [28] in order to examine wafer-scale variations. During this study a potential weakness of the M4PP method became apparent, dead pixels could occur because of failed contact for an individual probe engage (all four electrodes are required to be in good electrical contact for any measurement to be performed) or due to probe failure typically after few thousands measurements. In order to make the M4PP technique more robust we repeated the measurements with an equidistant seven-point probe, enabling us to significantly increase measurement yield, as well as provide novel homogeneity information that can be applied to thin film analysis in general.

Methods
Graphene was grown on a four-inch silicon carbide wafer as described previously [28,55]. Electrical measurements were performed with a CAPRES microRSP-A300 using lock-in technique at 12 Hz, and with a current of 250 μA. In this work we have used a probe with seven nickel-coated electrodes as shown in figure 1(a), which are based on three-way flexible electrodes [56,57] to minimize lateral forces. The right-hand-side of figure 1(a) shows a strain gauge, which is used to control the contact force when the probe is engaged on the surface [47]. A low contact force and three-way flexible electrodes [56,57] are used to prevent unnecessary damage to the probe and surface. During a single engage of the probe to the surface, electrical measurements were performed in A-configuration, and then B-configuration as During each engage a total of 24 resistance measurements were performed (8 for each subprobe). These multiplexed measurements enabled a variety of error-checking measures to increase result accuracy as previously described [58]. Firstly, because the measurements were performed with lock-in technique, the phase of each individual measurement was assessed, and individual resistance measurements rejected if outside a set tolerance. The sheet resistance (R S ) is determined from the modified van der Pauw equation [48,50] using resistance values measured in A configuration (R A ) and B configuration ( All accepted sheet resistance values were then subjected to a median filter and the mean of the remaining sheet resistance values á ñ R S which pass the filter gave a single sheet conductance = á ñ -G R S S 1 value for the subprobe. If no á ñ R S values pass the filters with the set tolerances, then we define the sheet conductance = G 0 S in subsequent analysis and mapping. Probes were replaced automatically every 2000 engages from the M4PP probe cassettes loaded in the microRSP-A300. In order to combine the three subprobe maps (figures 2(a)-(c)) to the combined map ( figure 2(d)), each pixel G S values from all subprobes that had previously passed the median filter, were combined using an additional median filter. The median of the remaining values is used for the combined subprobe map. In this work our phase tolerance was 1°, and all median filter tolerances were 2%.

Results and discussion
Wafer-scale G S maps performed with each of the three subprobes are shown in figures 2(a)-(c) with a map combining the data from all three subprobes is shown in figure 2(d). Previously, M4PP data from this wafer was compared with a THz-TDS conductance map [28]. Here, we compare G S results obtained from different subprobes during the same probe engage. For a perfectly uniform material using multiple subprobes provides a redundancy in the measurement, in case of subprobe failure or localized sample defects. In either case, a measurement from one of the other subprobes may be successful.
Qualitatively, all the subprobe maps in figures 2(a)-(c) are similar, each having different regions where no G S values passed the filters described in the methods section. The most prominent of these features appear as annulus sectors (circular ring sectors) and are attributed to subprobe failure as it matches the spiral-like measurement order. Thus, there is no reason to attribute these measurement failures to the local thin-film properties.
When G S from the three subprobes are combined ( figure 2(d)) all the null-G S annulus sectors disappear. We then find that for this combined map only 385 out of 11 310 engages did not return an accepted G S value (10 925 accepted, 97%). In contrast, the successful measurements for individual subprobes was 9528 (84% accepted), 9135 (81% accepted) and 8163 (72% accepted), for subprobe 1, subprobe 2, subprobe 3, respectively. For our measurements choosing more than one subprobe offered a level of measurement redundancy, with significant higher measurement yield from 72%-84% to 97%. Although some regions of the wafer have over an order of magnitude lower G , S by studying the R A /R B ratio of the measurements (figure S1 is available online at stacks.iop.org/NANO/31/225709/mmedia), it can be concluded that this graphene does not exhibit any significant quasi 1D electrical behaviour.
Increasing the number of subprobes also increases the total measurement time. The time to measure one subprobe, disengage, move and reengage took approximately five seconds. Measurement time was increased by one second per additional subprobe. Three subprobes were chosen as a good compromise between measurement yield and measurement time. For a non-uniform sample, multiple subprobe analysis can reveal the spatial and quantitative information about the extent of inhomogeneities.
Multi-subprobe G S maps can be a useful metrology tool for evaluating the variation in thin film/2D material quality across a wafer. With a wafer map of G S enough data is available to perform analysis that would otherwise be impossible or imprecise with a linescan, reduced-area map, or single probe scan. For example, a comparison between G S values for different subprobes can be compared to give an insight into homogeneity on the order of the probe length. Figure 3(a) shows a uniformity map of figure 2(d), which was calculated using the relative standard deviation of each pixel and its 15 nearest neighbours (uniformity maps for different number of nearest neighbours are shown in figure S2). The singlesubprobe uniformity maps for data from figures 2(a)-(c) are shown in figures S3(a)-(c), where the lack of data coverage conceals many uniformity features. Homogeneity is known to be important for two-dimensional device performance [59,60], so it is important to know if the entire wafer, or certain areas are suitable for device processing.
The subprobe-to-subprobe conductance correlation is shown in figure 3(b), where four regions are defined: G S <0.3 mS (black region), 0.3 mSG S <0.75 mS (blue region), 0.75 mSG S <7.5 (green region), 7.5 mSG S (red region). We observe good subprobe-to-subprobe agreement for high and low values of G , S the blue and red regions, but poorer agreement in the green region. The fact the subprobe-to-subprobe error decreases again for the red region shows the subprobe-subprobe error is not simply proportional to the magnitude of G , S and is likely an indication the green region has variations on the order of the probe length, a result which is in good agreement with previous analysis [28]. When figure 2(b) is replotted using the colourscale from figure 3(b), we in fact do observe most of the green pixels as a transition area separating the regions of high and low values of G .
S Because the width of the transition areas are significantly larger than the size of the probe, it can be concluded this data represents a true variation in the sample G .

S
When the G S data for all subprobes is plotted as a histogram three distinct peaks emerge, as shown in figure 3(c), where the peaks are labelled I through III, and in addition between peak II and peak III a plateau in the data where the counts are roughly constant. Measurements representing the three peaks all originate from connected regions of graphene. The plateau between the second and third peak originates from measurements made in the transition area. Representing the data as a histogram allows for easy comparison of changes to the wafer over time.
G S was also mapped at different times over several weeks using THz-TDS and M4PP, expanding on the work from [28]. After the maps shown above, a THz-TDS map of the wafer was performed, followed by an additional M4PP map, and then by a second THz-TDS map. Damage to graphene is easily detected by THz-TDS, for example damage attributed to mishandling by using a wafer tweezer is visible when comparing figure S4b and figure S4d, with the damage features matching the dimensions of the tweezer tines. Histogram analysis of the THz-TDS/M4PP maps are shown in figure S5 and show that the two THz-TDS maps are almost identical, suggesting that the intervening M4PP map has not made significant changes the sample. These repeated maps suggest that the contact forces used to directly probe of graphene with an M4PP is very well controlled by the strain gauge and microRSP-A300 hardware and lead to no significant graphene damage.
Overall, we observe slightly higher G S values in the M4PP map in comparison to both THz-TDS results, which is expected due to the fact that M4PP analyses G S over micron-sized areas whereas THz-TDS at 1 THz probes over tens of nanometres [21]. We also note that peak I and II observed in figure 3(d) have now combined as part of the change in G S over time. The progression of wafer changes over nine weeks are shown in figure S4. The changes over time are quantitatively similar for both M4PP and THz-TDS showing that either method has the resolution required to track changes in graphene over time.
We have the following recommendations when G S mapping graphene. THz-TDS and M4PP both provide information about graphene uniformity. Both methods deliver equivalent results in some cases-for uniform graphene where the G S on the few-nm scale matches that on the μm scale. THz-TDS is faster, non-contact and performs well on uniform samples. However, when device processing requires G S knowledge on the order of microns to millimetres, then M4PP mapping is still preferred. If metal is present near test regions M4PP mapping is more reliable than THz-TDS. Beyond graphene, 2D materials/thin films of various THz opacities are possible to map with a M4PP system. Generally, choosing to use a M4PP with more than four electrodes allows for additional subprobe measurements while adding negligible additional measurement time. This also allows a level of measurement redundancy for failed measurements, and allows insightful additional analysis. We have shown in figure 2 that a higher accuracy G , S with fewer dead pixels was achieved by combining the data from subprobes into a single map. In addition, the combined map can be used via both uniformity assessment (e.g. Figure 3(a)) and subprobecorrelational assessment of G S to determine spatial quality. The technique is sensitive enough to track changes in the graphene over time.

Conclusion
In summary, we have investigated wafer conductance maps of graphene using multiple subprobe M4PPs. Combining subprobes increased measurement yield from under 85% to 97% without adding significant measurement time. G S varied across the wafer by over an order of magnitude, leading to local regions with different G S landscapes. Producing waferscale analysis can be used to determine overall growth quality, identify graphene areas which are suitable for further device processing, or to reject/accept an entire wafer and such analysis can be performed for M4PP maps of other materials. The M4PP map was compared to THz-TDS which showed qualitatively similar maps, even when the wafer changed over many weeks, further suggesting that M4PP produces accurate G S data. THz-TDS conductivity maps performed before and after the M4PP mapping showed no decrease in conductivity attributable to the M4PP process.