Influence of disordered edges on transport properties in graphene
D. Smirnov, G. Yu. Vasileva, J. C. Rode, C. Belke, Yu. B. Vasilyev, Yu. L. Ivanov, R. J. Haug
IInfluence of disordered edges on transport properties in graphene
D. Smirnov, a) G. Yu. Vasileva,
1, 2
J. C. Rode, C. Belke, Yu. B. Vasilyev, Yu. L. Ivanov, and R. J. Haug Institut für Festkörperphysik, Leibniz Universität Hannover, 30167 Hannover, Germany Ioffe Institute, Russian Academy of Sciences, 194021 St. Petersburg, Russia
The influence of plasma etched sample edges on electrical transport and doping is studied. Through electricaltransport measurements the overall doping and mobility are analyzed for mono- and bilayer graphene samples.As a result the edge contributes strongly to the overall doping of the samples. Furthermore the edge disorder canbe found as the main limiting source of the mobility for narrow samples.Since its discovery in 2004 graphene was praised asa new material with different possibilities in technicalapplications . It shows high mobility on silicon/silicondioxide substrates on which it can be easily gated. The-oretical mobility limits were calculated and confirmed invarious experimental studies . Transferring graphene onbetter and smoother substrates, e. g. Boron Nitride ,or removing the substrate completely , lifted that limitand mobilities of over · cm / Vs were measured .However these values only refer to non structured sam-ples with undamaged edges. Edge disorder, introduced byvarious structuring techniques, can further limit the trans-port properties. Its negative impact is visible in mesoscopictransport measurements in graphene on silicondioxid as well as on Boron Nitride . Furthermore Ramanspectroscopy and chemical doping studies hint to-wards the edge disorder not only as a mobility limit buta further doping source. Investigations of different kindof edge disorder were performed in previous studies ongraphene nanoribbons (GNR) . It was shown that plasmaetched or similar prepared GNR exhibit disordered sampleetches and can lead to a reduction of conductance hint-ing to a further scattering mechanism . Furthermore theinfluence of such disorder on electrical transport was stud-ied on samples with varying width and an effect ontransport properties was observed. Such disorder was alsoconfirmed through Raman spectroscopy studies of GNRsedges . However a quantified evaluation of these edge ef-fects were not presented, yet.In this letter a quantified study is performed on mono-and bilayer samples. All flakes were structured in a simi-lar Hall bar geometry with areas of different width. Thatspecific shape allows to investigate the edge doping as wellas the influence of edge disorder on the electrical transportin samples with equal bulk doping. Several graphene flakeswere investigated within the scope of this study, showingsimilar results. In this letter, a monolayer and a bilayersample are presented.The sample preparation was done as following: Grapheneflakes were placed on a silicon/ silicondioxide substrate. Af-terwards the number of layers was analyzed using opticalmicroscopy . Plasma Oxygen Etching was used to edgethe flakes into the geometrical shape, shown in Fig. 1(b).It is a Hall bar, which is divided into three different re-gions, named "wide", "middle", and "thin". Each part has a) Electronic mail: [email protected] (c) µ m R ( k Ω ) U BG (V) (a) R ( k Ω ) U BG (V)0 40-40 (d) ML BL Thin Middle Wide420 0.40.30.20.10.0 R ( k Ω ) B -1 (T -1 )3210 0.40.30.20.10.0 R ( k Ω ) B -1 (T -1 ) Thin Middle Wide (b)(e) (f ) A B C µ m A B C
FIG. 1. (a) An atomic force microscope picture showing themonolayer sample using false colors. The contact positions arerepresented through yellow areas. (b) a schematic picture ofthe Hall bar sample geometry. Four probe resistance measure-ments over the different width areas for mono- (c) and bilayer(d) sample. (f) and (g) show the Shubnikov- de Haas measure-ments versus the inverse magnetic field for mono- and bilayer,respectively. the same length but differs in width. The length of eacharea is . µ m for the monolayer sample and . µ m for thebilayer, respectively. The Hall bar width is different forevery area: µ m (wide), µ m (middle), and . µ m (thin)for the monolayer and . µ m , µ m , and . µ m for thebilayer sample. Figure 1(a) shows an Atomic Force Micro-scope (AFM) image of a monolayer device. To reduce theoverall doping the samples were mechanically cleaned bythe AFM in contact mode . Afterwards chromium/ goldcontacts were evaporated. After the preparation process,the samples were loaded into a He evaporation cryostatand measured at a base temperature of . and a per-pendicular magnetic field up to
13 T . The resistance wasmeasured with a lock-in amplifier using an AC current of
100 nA with a frequency of .
777 Hz . a r X i v : . [ c ond - m a t . m e s - h a ll ] M a y The characterization of the samples was conducted foreach area using a four terminal set-up. Magnetotransportmeasurements were performed to confirm the number oflayers. Figure 1(e) and (f) show the longitudinal resistanceversus the inverse magnetic field. Shubnikov-de Haas os-cillations are visible and the Berry phase can be extractedthrough extrapolation to zero. The Berry Phase is π for themonolayer as expected and π for the bilayer sample, whichconfirms the previous contrast analysis. Figure 1(c) and (d)show the resistance measurements versus the backgate volt-age U BG for different areas and samples. For each area afield effect is observed. However the position and the resis-tance of the charge neutrality point differs. In both casesthe mono- and the bilayer sample follow the same trend.The thin part of both samples exhibits the highest resis-tance reaching
33 kΩ for the monolayer sample and
45 kΩ for the bilayer sample at the charge neutrality point. Theresistance decreases with increasing width as expected forthe geometry. In contrast, the dependence of the chargeneutrality point position is not that simple. The overalldoping of both samples is in the positive backgate voltageregion, meaning that both samples are p-doped. Howeverthe doping concentration differs for every area. Because ofthe AFM cleaning the bulk of both samples can be ruledout as the origin of the doping change. However a disor-dered edge can act as a p-doping source, as was shown inprevious works . To analyze the amount of edge doping inthese samples a simple approach is proposed. The overalldoping amount of the sample N O = n O A , is the sum of thebulk doping N B = n B A and the edge doping N E = n E L , N O = N B + N E , with n O , n B , n E being the doping concentration and A, L, W the area, length, and width of the doped region.One can rewrite that approach to the doping concentration,leading to a width dependence: n O = n B + n E · W .
From the backgate voltage at the charge neutrality pointthe overall doping can be calculated for all areas and bothsamples.Figure 2(a) shows the overall doping concentration plot-ted versus the inverse Hall bar width. For both samples alinear dependence of the doping concentration is observed.Using the bulk-edge-doping approach shown above, the in-dividual doping contributions components can be calcu-lated for both samples. The bulk doping concentration is p B = 6 . · m − and n B = 2 . · m − for the mono-and bilayer, respectively. The edge doping concentration is p E = 6 . · m − for the monolayer and an almost equalconcentration of . · m − for the bilayer sample lead-ing to effective 2D-doping at the edge. To demonstrate thecontribution of the doping components the actual dopingamount is calculated for the thinnest area for the bilayersample, where electrons P B ≈ and holes N E ≈ are introduced into the system through the bulk and theedge. One can clearly see the domination of the edge dop-ing in this area. It is higher than the bulk contribution n D op i ng ( m - ) -1 ( µ m -1 ) (b) L E (a) ML BL
FIG. 2. (a) Dependence of the overall doping on sample width.The overall doping was plotted versus the inverse area width forthe mono- (blue) and bilayer (red) sample. The shown data hasa linear dependence which is clarified with a dashed line. (b) Aschematic picture of a sample with a perfect and a disorderededge to clarify their doping contribution. by a factor of ≈ . , introducing holes as a main dopingtype. Such charge localization at sample edges was ob-served in ultra thin graphene nanoribbons . Furthermoreit was found that additional edges in form of a cut or de-fects in the graphene bulk constitute a p-doping source andcan be used to create p-n junctions .It is clear that the edge of the sample can be seen asa doping source. Furthermore we can assume that theadatoms causing the edge p-doping are oxygen compoundsthat adjusted itself on the graphene edge during the plasmaoxygen structuring process, as is shown in a schematic inFig. 2(b) (orange lines). To calculate the efficiency for edgedoping, it is first assumed that a dangling bond can con-tribute to the overall doping by a count of doping carrier.However, assuming a zigzag edge, it is only possible onceper .
246 nm , as is shown in Fig. 2(b). Taking into accountthat every side of the sample contributes to the edge dop-ing an approximate efficiency of . is calculated for themonolayer. As one can extract from the slopes in Fig. 2(a),the bilayer exhibits almost the same edge doping contribu-tion and doping efficiency as the monolayer sample. Fur-thermore the doping efficiency of the plasma etched edgesis comparable to an intentional chemical edge doping withhydrogen silsesquioxane, which was investigated in Ref. 16.The resulting efficiency is only slightly higher (0.85) thanof the observed values in the presented study.We further analyze the effect of the disordered plasmaetched graphene edge on the electrical transport. The mo-bility was calculated from the measured resistance versusthe backgate-voltage shown in Fig. 1(c) and (d). For thisanalysis the resistance was split up into two different parts: R SR component caused by short range resistance and R LR caused by long range resistance. Both components can beseparated using the constant mobility Ansatz . In con-trast to the doping the short range resistance componentstays almost constant throughout all sample areas:
290 Ω (wide),
260 Ω (mid), and
240 Ω (narrow) for the monolayerand
340 Ω (wide),
320 Ω (mid),
275 Ω (narrow) for the bi-layer sample, respectively. Figure 3(a) and (b) shows thecomparison between the short and the long range resis-tance component for a fixed charge carrier concentrationfor mono- and bilayer sample, respectively. As one cansee the short range component undergoes a slight changeof ≈
50 Ω and is tiny compared to the change in the longrange resistance, which is in the order of kΩ . Furthermorethe difference of the short range component with chang-ing width is quite small in comparison to the total shortrange resistance amount. The origin of the short rangecomponent can be located in the bulk and the edge of thesample. However the fact that the short range resistancestays almost constant while the width and with that thearea changes indicates that the main short range scatter-ing contributors are located at the edge of the investigatedsamples, which has the same length for all the samples.Subsequently, the constant mobility is calculated fromlong range resistance component, i. e. the overall resis-tance after subtracting the short range component. Theresults are shown in Fig. 3(c) and (d). For both samplesthe mobilities differ with changing width. Additionally themonolayer exhibits a significantly higher mobility for ev-ery region as the bilayer, which is an expected behavior forincreasing number of layers . Interestingly, an overall de-pendence similar to the doping analysis can be observed:The highest mobility is obtained for the wide region (mono-layer: / Vs , bilayer: / Vs ) and the lowestfor the narrow region (monolayer: / Vs , bilayer: / Vs ). The middle section exhibits an intermedi-ate mobility / Vs for mono- and / Vs forbilayer. Furthermore a significant difference between holesand electrons was not observed.Hence it follows the same trend as the overall doping, theinverse mobility is plotted versus the inverse width, whichis shown in Fig. 3(e). Equivalent to the overall doping con-centration it is showing a linear increase with inverse widthin the measurement range. The dependence of the mobil-ity on the width is hinting towards an additional scatteringmechanism at the sample edges. Since this correlation isdetected in the mobility calculated from the long range re-sistance component, the origin of this mechanism is mostlikely caused by the additional edge doping shown above.By fitting the data in Fig. 3(e) linearly and extrapolatingto an infinite sample width, the bulk mobility componentcan be estimated to . ± .
05 m / Vs for the bilayer and . ± / Vs for the monolayer sample. Both bulk mo-bilities exceed the measured mobilities proving the limitingnature of the edge disorder. However it is important tonotice, that these same results are an extrapolation of theobserved mobilities and not measured.As stated above, previous analysis were performedon the topic of edge disorder leading to an increasingresistance . Our sample geometry allowed to investi-gate the edge disorder systematically excluding other ef-fects. By extracting the electronic properties from the fieldeffect for every different region we were able to analyzethe short and the long range component independently.Our results show that the edge affects both, however, thelong range far more than the short range resistance, subse-quently influencing the overall mobility greatly. Therefore µ - ( - V s / c m ) -1 ( µ m -1 )1 0-40U BG (V)403020100 µ ( c m / V s ) (c) U BG (V)0 µ ( c m / V s ) (d) (e) ML BL ML BL -1 ( µ m -1 )20010 R ( k Ω ) (b) LR SR804 R ( k Ω ) (a) LR SR
FIG. 3. Analysis of the effect of the edge disorder on the elec-trical transport: (a) and (b) show the long (black) and short(red) range resistance for a fixed charge carrier concentration of p = 6 . · / cm for the mono- and bilayer, respectively. (c)and (d) show the mobility plotted versus the backgate voltagefor the monolayer and bilayer, respectively. (e) shows the de-pendence of the inverse mobility of different areas on the inversewidth. The linear behavior is presented through dashed lines. the edge doping can be seen as a strong scattering mech-anism determining the electrical properties even in large, µ m -sized samples.In conclusion, we have reported an investigation of theinfluence of the edge disorder on the electrical transportin mono- and bilayer graphene. Our devices allowedto investigate the dependency of various properties onthe width of each single sample. We showed how theedge influences the electrical transport greatly, dominatesthe overall doping, and acts as an additional scatteringmechanism.We acknowledge the financial support by the DFGvia SPP 1459 and the Russian Foundation for BasicResearch (Grant No. 13-02-00326 a). We are grateful toA. P. Dmitriev, for helpful discussions. Authors D. S. andG. Yu. V. contributed equally to this work. K. S. Novesolelov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang,S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov,
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