Fabrication and electrical transport properties of embedded graphite microwires in a diamond matrix
J. Barzola-Quiquia, T. Lühmann, R. Wunderlich, M. Stiller, M. Zoraghi, J. Meijer, P. Esquinazi, J. Böttner, I. Estrela-Lopis
aa r X i v : . [ c ond - m a t . m e s - h a ll ] F e b Fabrication and electrical transport properties of embeddedgraphite microwires in a diamond matrix
J. Barzola-Quiquia, ∗ T. L¨uhmann, R. Wunderlich,M. Stiller, M. Zoraghi, J. Meijer, and P. Esquinazi
Institute for Experimental Physics II, University of Leipzig, 04103 Leipzig, Germany
J. B¨ottner and I. Estrela-Lopis
Institute of Medical Physics and Biophysics,University of Leipzig, 04107 Leipzig, Germany (Dated: February 26, 2018)
Abstract
Micrometer width and nanometer thick wires with different shapes were produced ≈ µ m belowthe surface of a diamond crystal using a microbeam of He + ions with 1.8 MeV energy. Initialsamples are amorphous and after annealing at T ≈ ρ (2K) /ρ (315K) ≈ . T = 200 K was measured and can be well understoodtaking spin-dependent scattering processes into account. The used method provides the meansto design and produce millimeter to micrometer sized conducting circuits with arbitrary shapeembedded in a diamond matrix. PACS numbers: 81.05.ug, 78.30.Am, 73.63.-b, 61.82.Ms
1. INTRODUCTION
Diamond is a natural allotrope of carbon,transparent, insulating and the hardest naturalmaterial on earth. Vavilov and coworkers [1]have shown that it is possible to induce graphi-tization in diamond by ion irradiation. One ofthe first works trying to change the transportcharacteristics of diamond showed that one canproduce conducting regions by carbon implan-tation on the diamond surface [2]. The valueand temperature dependence of the resistivity ofion implanted diamond layers was found to besimilar to that of amorphous carbon producedby sputtering [2, 3]. In a recently published ∗ Corresponding author: Tel.:+49 341 9732765,E-mail: [email protected] (Jose Barzola-Quiquia) study, micro-channels were fabricated in single-crystal diamond using a microbeam of He + ionsin the MeV energy range [4]. The conductivityof the microchannels was improved substantiallyby annealing treatment, achieving values similarto polycrystalline graphite [4]. The possibility tocreate a relatively long conducting path of mi-crometer or even narrower width inside diamondis interesting for possible electrical device appli-cations where the main electronic circuit remainswell protected by the highly insulating and bio-compatible diamond matrix.On the other hand, early studies of 100 keVnitrogen and carbon implanted into nano dia-monds, show ferromagnetic hysteresis even atroom temperature [5], and recent studies on mi-crometer small areas on single crystal diamond fter irradiation with 2.2 MeV proton micro-beams provided hints on the existence of mag-netic order [6, 7]. The authors found that for flu-encies below 8 . × cm − , a very weak mag-netic response was observed at room tempera-ture. In both mentioned studies, the origin ofthe magnetism was related to the defects pro-duced by the irradiation.In this work, a similar technique as in Ref. [4]was used to produce conducting microwires be-neath the diamond surface using He + irradia-tion. After two annealing steps, different de-grees of graphitization of the microwire werereached. Our aim was also to check, whetherthose conducting structures can show some de-gree of magnetic order. As was shown in severalworks in the past, defects like vacancies and/ornon-magnetic ions within the graphite structureas well as in a large number of materials, cantrigger magnetic order even above room tem-perature, a phenomenon called defect-inducedmagnetism (DIM) [8]. Therefore, one can ex-pect that a defective graphitic structure, like theone we produce within the diamond structure byion irradiation and after annealing, may showsome magnetic response. The possibility of hav-ing conducting and magnetic microwires withina pure diamond matrix provides a further inter-esting option for future application.
2. EXPERIMENTAL DETAILS2.1. Preparation of sub-micrometerwidth and millimeter long graphite wires
To produce a graphite-like microwire (GLM)inside diamond, we used a polished single crys-tal (100) diamond of the company Element Six,with a nitrogen concentration < < .
05 ppm. The diamondsample was produced by chemical vapor deposi-tion (CVD) with dimension 2 . × . × . .The He + ion irradiation used to produce thewires in diamond was realized using a very sta-ble high-energy ion nanoprobe in the linear ac- celerator LIPSION at the University of Leipzig.The wires within the diamond structure was pro-duced with a microbeam of 1.8 MeV energy andan ion current of 2.4 nA.In our accelerator facilities, using the high-energy ion nanoprobe, we can obtain a sub-micrometer ion beam diameter [9] using a twomagnetic quadrupole double lens system. Also,to produce the long size microwire inside the di-amond, we need a high ion current and energystability. This two important conditions are ful-filled with the ion accelerator Singletron TM fromthe Dutch company High Voltage EngineeringEuropa B.V. [10]. The ability to produce com-plex two dimensional structures (2D) is obtainedwith the help of a raster unit, which is locatedbetween the quadrupole lenses and the sample.Using a self-made program we can produce anydesired 2D structure by deflection of the ionbeam. According to our experimental condi-tions, we can continuously deflect the He + ionbeam within a total area of (1780 × µ m .As examples, using a beam diameter of ≈ µ m,a microwire of similar width, see Fig. 1(a), insidea diamond substrate was produced and after an-nealing, we have graphitized the wire. As a proofof the ability of our ion nanoprobe to producecomplex structures (see also other structures insupplementary information), we have prepareda graphitized loop, see Fig. 1 (b-d), which canbe used to generate small magnetic fields and/ormicrowave fields in order to manipulate, e.g., thespin states of NV centers in diamond. The im-ages in Fig. 1 were obtained with a self madeconfocal optical microscopy implemented with alens (Olympus MPlanApo 100x/NA0.95), a laserbeam with λ = 532 nm and a lateral and depthresolution of ≈
300 nm and ≈ µ m respectively.Summarizing, we are able to produce long wireswith a width of ≈ µ m and desired shape.These results show the possibilities to produce2D graphitized structures inside diamond for fu-ture applications. ig. 1. Image of graphitized structures. (a)Confocal image of a wire with a width in theorder of ≈ µ m. (b) Confocal image of a wire inshape of a loop. All images taken after annealing(c) 3D sketch of the loop (d) optical picture ofthe wire loop showing the current-voltage ( I − V )contacts at the surface of the diamond. After irradiation of diamond with He + ionsof energy and fluence similar to the ones weused in this work, an amorphous phase is pro-duced at the region where the irradiated ionsstop [1]. By annealing at high temperatures,this amorphous carbon region can later be trans-formed into graphite or back to diamond struc-ture, which is correlated to the density of va-cancies produced by the irradiation. There ex-ists an estimated critical vacancy density N v0 ∼ cm − [11] to induce graphitization in thematerial after ion irradiation at room tempera-ture and after annealing. According to other ex-perimental work and supported by molecular dy-namics simulation, the critical density necessary to graphitize the surface [12] was determined to N v0 ≈ × cm − . Raman measurements in-dicate that after annealing above T ≈
700 K thegraphitization process begins by formation andgrowth of sp bonded nanoclusters [12].We have irradiated the diamond sample withHe + ions using a fluence of φ = 5 . × cm − ,which gives a vacancy density N v & × cm − in a specific depth, see Fig. 2(a) estimated fromMonte-Carlo simulation done by SRIM [13]. Theprogram simulates the atomic-displacement cas-cades in solids on the base of the binary-collisionapproximation to construct the ion trajecto-ries [14]. For the calculations we have assumeda dislocation energy of 52 eV [15]. This va-cancy density is around the minimum valuefor graphitization after annealing of the ion-produced amorphous carbon phase.To facilitate the transport measurements per-formed in this study, the produced GLM had di-mension of 15 µ m width, 1350 µ m total lengthand a estimated thickness of 130 ± ≈ . µ m beneaththe diamond surface, which was verified by con-focal micro-Raman spectroscopy (CRS), see Sec-tion 3 3.1.After He + irradiation, the sample was firstannealed at T ≈ P ≈ × − mbar (heatingrate of 15 K/min and cooling rate of 10 K/min)for 4 hours for the first and for 2 additionalhours in the second annealing treatment. Afterthe first and also after the second annealing pro-cess the sample was placed in an oxygen plasmachamber at room temperature in order to removethe conducting carbon-based thin layer formedat the surface after the annealing, to avoid anycontribution to the transport measurements. .2 2.4 2.6 2.8 3.0 3.20246810121416 (d) V a c an cy den s i t y N v ( c m - ) Depth d ( m)N v = 9x10 cm -3 (a) (b) (c) He-ion
Fig. 2. Sketch of the sample and contact prepa-ration. (a) SRIM simulation showing the va-cancy density versus the penetration depth forthe fluence and energy (see main text) used inthis work. (b) In the first irradiation step, themicrowire was produced without a mask, after-wards, the diamond substrate was covered usinga copper grid. (c) The sketch shows how con-tacts from the embedded wire were grown on thesubstrate surface. (d) Sketch of the amorphouscarbon region (top) and the region transformedinto graphite (bottom) by annealing at high tem-peratures.
The contacts for the electrical measurementshave to be done at the surface of the substrate. For this purpose we used a commercial coppergrid used for transmission electron microscopy(2000 mesh), having the advantage that the gridhas a wedge shape allowing a continuous changeof the He + ions penetration depth inside the di-amond sample, see Fig. 2(b-d). At the surfaceof the sample and at a distance of ≈ µ m,square-like contacts with dimension of ≈ × µ m were prepared in direct electrical contactwith the embedded microwire, Fig. 2(c). A sim-ilar but more complicated method was alreadyused in Ref. [4]. Afterwards, the electrodes weremade by sputtering of Cr/Au directly at the topof the square-like regions at the surface, after anelectron beam lithography process. Finally, thecontacts to the chip carrier, where the samplewas fixed for the transport measurements, wereproduced using silver paste and gold wires.Resistance measurements were carried outusing the conventional 4-points method usingan AC Bridge (Linear Research LR-700) in thetemperature range of 2 K to 310 K. For thecurrent-voltage ( I–V ) measurements, we usedthe Keithley DC and AC current source (Keith-ley 6221) and a nanovoltmeter (Keithley 2182).The resistance and its magnetic field depen-dence were measured with a commercial cryo-stat from Oxford Instruments with a supercon-ducting solenoid that provides a maximum fieldof ± λ =532 nm, a lateral resolution of ≈
300 nm andaxial resolution of ≈
900 nm.
3. RESULTS AND DISCUSSION3.1. Raman results
To get information about the structural prop-erties of the measured wire produced inside thediamond sample, we have used CRS, which isprobably the only method to get information
000 1250 1500 17500123456
Diamond G D I n t en s i t y ( a r b . un i t s ) Raman shift (cm -1 ) CR3 CR2 CR1 (a) (b) (c)
Fig. 3. Raman results measured at the surfaceand inside the diamond substrate. The curvesCR1 and CR3 were obtained fixing the focus ofthe Raman microscope at the surface (CR1) onthe as-received sample, and in a depth of 3 µ m(CR3) after irradiation and second annealing.The curve CR2 was obtained from the measure-ments at the surface after He + irradiation andthe second heat treatment. The continuous linesthrough the experimental curves are the fits tothe data. The insets show confocal Raman im-ages, in (a) the loop shown in Fig. 1 can be seen,(b) the image shows a close up of a graphite wireand (c) shows an area perpendicular to the sur-face, i.e. as function of the sample depth. Thebright part represents the G -graphite peak.about the microstructure produced inside the di-amond without destroying it. Fig. 3 shows theRaman results.The curve named CR1 in Fig. 3 was mea-sured at the surface of the as-received diamondsample. The Raman peak at ≈ − is the characteristic peak for carbon in the diamondstructure. The small bump at ≈ − isrelated to the appearance of disorder at the sur-face of the sample during the polish process [16].The curve CR3 obtained after irradiation andthe second annealing was measured with the fo-cus at ≈ µ m depth from the diamond sur-face. The results confirm the estimated depthfrom the SRIM calculations. The results of thecurves CR2 and CR3 show three characteristicpeaks, one at ≈ − corresponding to thediamond structure, a second peak due disordergraphite, the so-called D peak at ≈ − .The third and the most important peak for thecharacterization of graphite structure, called the G -peak, appears at ≈ − as a conse-quence of the double degenerate zone center E g mode.Our Raman results resemble those obtainedin [12], specially for similar annealing tempera-tures. The results CR2 and CR3 can be verywell fitted using Gaussian functions centered atthe aforementioned Raman peaks. The resultsare shown as continuous black lines in Fig. 3and describe very well the experimental results.From the fits we get also information about thepeak intensity I G and I D corresponding to the G and D peak respectively.From these results it is possible to estimatethe crystal size [17] L a using Eq. (1): L a (nm) = (2 . × − ) λ l (cid:18) I D I G (cid:19) − , (1)which correlates the crystal size L a with the inte-grated intensities of the D and G peaks and thelaser excitation wavelength λ l = 532 nm. Us-ing this equation, we obtain L a = 8 ± et.-al. usingtransmission electron microscopy [18], where di-amond samples were irradiated with He + ionsusing a fluence between 3 × − × cm − followed by an annealing for 1 h at 1400 ◦ C. .2. Temperature Dependence of theElectrical Resistance After the first annealing the sample shows (atlow temperatures) non-linear
I–V curves, indi-cating that non graphitized regions remain in thesample which act like barriers. It has been shownthat, whenever a barrier is present between theconducting grains, the resistance R ( T ) and mag-netoresistance ( M R ) depend on the applied cur-rent like in multi-wall carbon nanotubes bun-dles [19]. Here we do not discuss the R ( T ) and I–V results after the first annealing (see supple-mentary information) because our interest lies inthe behavior of the transport properties in theOhmic regime, without any influence of poten-tial barriers, this is obtained after the secondannealing treatment.The resistance results after the second an-nealing are shown in Fig. 4. The experimen-tal results from 2 K to 315 K are shown as opensymbols. The observed temperature dependenceis clearly different from the one we obtainedafter the first annealing treatment. The resis-tance ratio R A (2K) /R A (315K) ≈ .
275 is oneorder of magnitude smaller than the one afterthe first annealing, and of the same order as fornano-graphite films [20] and few layer graphenefilms [21, 22]. The current-voltage curves aftersecond annealing are linear in all measured tem-perature range and are shown in the supplemen-tary information.The temperature dependence of the resis-tance, see Fig. 4, indicates the existence of twodifferent regions, one below and the other above T ≈
75 K. We have identified (see supplemen-tary information) that the dominant mechanismat high temperatures is the so-called Mott vari-able range hopping (VRH) [23], given as: R V RH ( T ) = R M exp "(cid:18) T T (cid:19) / , (2)where T is a characteristic temperature coeffi-cient defined as: T = 18 k B ξ N ( E F ) , (3) R(T=300K)=1873 R A ( T ) / R A ( T = K ) T (-1/4) (K -1/4 ) Exp Fit
Temperature T (K) R A ( T ) / R A ( T = K ) Fig. 4. Temperature dependence of the resis-tance (after the second annealing). The insetshows the resistance versus T − / . The continu-ous lines are the fits results.and ξ is the localization length, N ( E F ) the den-sity of states at the Fermi level and R M is a con-stant prefactor. In order to fit the resistance overall the measured temperature range, we need toinclude an extra transport mechanism in parallel(we have also checked other configurations, seesupplementary information) given as: R A ( T ) − = R V RH ( T ) − + R m ( T ) − , (4)with R m ( T ) = R + R a T + R b · exp( − E a /k B T ) , (5)a metallic-like contribution, which dominates atlow temperatures. The coefficients R , R a , R b as well as the activation energy E a are free pa-rameters. R a residual temperature indepen-dent resistance that we include in the metallic-like contribution only, provides a saturation ofthe resistance at low temperatures. The contri-bution R m ( T ) was already used to explain the M (Ω) T , Mott (K) R (Ω) R a (Ω)686.66 723.6 2431.31 20.08 R b (Ω) E a (meV) N ( E F ) (eV − cm − )276.4 1.96 2 . × TABLE I. Summary of parameters obtained af-ter fitting the resistance R A ( T ) using Eq. (4).temperature dependence of the resistance in bulkgraphite [24], few layer graphene samples [22, 25]and nano-graphite thin films [20]. Its origin isrelated to certain interfaces formed between thegraphite crystallites. We can fit the experimen-tal resistance data to Eq. (4) very well. Theresults are shown as continuous lines in Fig. 4and the fitting parameters are listed in Table I.The inset of Fig. 4 shows clearly the temper-ature ranges where each transport mechanismdominates the electric transport. We have as-sumed a localization length of ξ ≈ . N ( E F ) ∼ . × eV − cm − ,which is of the same order as reported forgraphitic materials [27] and multi-walled carbonnanotubes [28]. Values of N ( E F ) of several or-ders of magnitude lower than our result werefound for similar ion irradiated diamond, butthese samples were not annealed [2, 29] or evenmeasured when a barrier was present [29]. Fi-nally, the calculated resistivity of the GLM is ρ (300 K) = 7 . . . × − Ωm, one order of mag-nitude larger than bulk graphite in-plane resis-tivity ( ρ (300 K) = 0 . × − Ωm) [21, 22, 30] orthe resistivity of few layer graphene ( ρ (300 K) =3 . . . × − Ωm) [21, 22] and three orders ofmagnitude lower than pure amorphous carbon( ρ (300 K) > − Ωm) [31, 32]. However, theGLM resistivity is comparable to other nano-graphite thin films prepared by chemical vapor deposition and aerosol assisted chemical vapordeposition ( ρ (300 K) = 3 . . . × − Ωm) [20].From experiments it is known that the resistiv-ity ratio between the in-plane ( ρ a ) and out-of-plane ( ρ c ) resistivity in graphite is in the orderof ρ c /ρ a ≈ − [30, 33], indicating thatthe transport in our sample is dominated bythe in-plane resistivity. Further, it means thatthe produced GLM have nano-crystals with apreferential c -axis normal to the substrate sur-face. The obtained transport characteristics ofthe produced GLM are important for future ap-plications, because the resistivity and its tem-perature dependence make this GLM interest-ing to be used for electronic circuits in a broadtemperature range. To obtain any information of the magneticproperties of the GLM there are no experi-mental methods other than transport becausethe wire is not only embedded inside the dia-mond matrix but also its mass is too small tobe measured with commercial magnetometers.The magneto-transport measurements at differ-ent constant temperatures were done with anexternal magnetic field applied perpendicular tothe current and main axis of the GLM. The re-sults of the magnetoresistance
M R defined as
M R = [ R ( B ) − R (0)] /R (0) are shown in Fig. 5.We observe a magnetic field dependence ofthe resistance, which is positive at T = 2 K, andnegative in the field range of -3 T < B < T >
10 K the
M R is negative in all the field range. The pos-itive
M R at very low temperatures can be un-derstood as a consequence of the strong Lorentzcontribution. This tends to vanish at high tem-peratures. The negative
M R can be attributedto a spin dependent scattering process. Dueto the relatively high temperatures and mag-netic field range where the negative
M R is ob-served, we can rule out weak localization ef-fects. According to the theory developed by -5 -4 -3 -2 -1 0 1 2 3 4 5 -0.50.00.51.01.5
2K 5K 10K 15K 20K 25K 50K 75K 200K H(T) M R x M agne t o r e s i s t an c e M R x Applied field H (T)
Fig. 5. Magnetoresistance at different constanttemperatures. The inset shows the
M R obtainedat T
20 K. The lines through the points arefits to Eq. (6). The results were shifted by aconstant in the vertical axis in order to facilitatea detailed view.Toyozawa [34] and later modified by Khosla andFischer [35], the
M R of systems with localizedmagnetic moments can be described using thefollowing equation:
M R = − P ln(1 + P B ) + P B P B . (6)The free parameters P and P depend on sev-eral factors such as a spin scattering amplitude,the exchange integral, the density of states atthe Fermi energy, the spin of the localized mag-netic moments and the average magnetizationsquare [34, 35]. The parameters P and P de-pend on the conductivity and the carrier mobil-ity. In general, Eq. (6) contains two competi-tive terms. The first term describes the negative T ( K ) P P (1 / K) P (1 / K) P (1 / K)2 0.1643 0.0300 0.02053 0.163165 0.013 1.68 0.00936 0.0508110 0.0114 1.6428 0.00541 0.0013315 0.0148 1.00675 0.0015 4.075E-720 0.017 0.668 1E-4 3.07E-7TABLE II. Summary of parameters obtained af-ter fitting the
M R using Eq. (6).contribution due to a spin-dependent scatteringmechanism ( s - d usually in d -band ferromagnets, s - p in p -band ferromagnets [36]). The secondterm describes a positive M R due to the usualLorentz force contribution. Using this equationwe have fitted our experimental results. Theyare shown as continuous lines in the inset ofFig. 5 and the corresponding parameters arelisted in Table II. The fits describe very wellthe experimental results at all measured tem-peratures, indicating the existence of spin de-pendent scattering in our GLM, however, this isnot an evidence of magnetic order. Similar re-sults were already observed in magnetic sampleswhere the magnetic order was triggered by de-fects, as in proton irradiated graphite [37], pro-ton irradiated ZnO:Li microwires [38], as well asin samples with magnetic elements like in sin-gle multi-walled carbon nanotubes filled with Fenanorods [39].The magnetic scattering contribution in oursamples can be explained as a consequence ofdefects present in the disordered graphite struc-ture of the microwire. Because of the prepara-tion method used to produce the microwire, wecan rule out the presence of magnetic impurities.The almost zero MR for temperatures T &
200 Kopens the possibility to use GLMs in a deviceunder application of high magnetic fields. . CONCLUSION In this work we have prepared a graphitizedwire of 1350 µ m length and lateral area of ≈ µ m ×
130 nm inside a diamond matrix bymeans of He + irradiation and heat treatment.After annealing, the resistivity of the microwireis only one order of magnitude larger comparedto graphite. Also, its temperature dependencecan be well described by the parallel contributionof VRH and a metallic-like conduction, similarhas been observed in other carbon based mate-rials. The measured magnetoresistance can bewell described by a semi empirical model, whichtakes into account a spin dependent transportmechanism used to describe the M R of mag-netic diluted semiconductors as well as magneticcarbon-based materials, related to the defect-induced magnetism.In summary, the low resistivity ( ρ (300 K) =7 . . . × − Ωm), the small resistivity ratio ( ρ (2K) /ρ (315K) ≈ . in-situ the human body. ACKNOWLEDGMENTS
We thank F. Bern for technical support in themagnetoresistance measurements.[1] V. S. Vavilov, V. V. Krasnopevtsev, Y. V.Miljutin, A. E. Gorodestsky, and A. P.Zakharov, “On structural transitions inion implanted diamond,” Radiation Effects , 141–143 (1974).[2] J.J. Hauser, J.R. Patel, and J.W. Rodgers,“Hard conducting implanted diamond lay-ers,” Appl. Phys. Lett. , 129–130 (1977).[3] J.J. Hauser and J.R. Patel, “Hopping con-ductivity in c-implanted amorphous dia-mond, or how to ruin a perfectly good dia-mond,” Solid State Commun. , 789–790(1976).[4] F. Picollo, D. Gatto Monticone, P. Oliv-ero, B.A. Fairchild, S. Rubanov, S. Prawer,and E. Vittone, “Fabrication and electri-cal characterization of three-dimensional graphitic microchannels in single crystal di-amond,” New Journal of Physics , 053011(2012).[5] S. Talapatra, P. G. Ganesan, T. Kim,R. Vajtai, M. Huang, M. Shima, G. Ra-manath, D. Srivastava, S. C. Deevi, andP. M. Ajayan, “Magnetic properties ofpoint defects in proton irradiated dia-mond,” Phys. Rev. Lett. , 097201 (2005).[6] T. N. Makgato, E. Sideras-Haddad,S. Shrivastava, M. Madhuku, K. Sekonya,A. Pineda-Vargas, and D. Joubert, “Mag-netization effects in proton micro-irradiateddiamond,” arXiv:1409.2997.[7] T. N. Makgato, E. Sideras-Haddad, M. A.Ramos, M. Garcia-Hernandez, A. Climent-Font, M. Munoz-Martin, A. Zucchiatti, . Shrivastava, and R. Erasmus, “Magneticproperties of point defects in proton irradi-ated diamond,” J. Magn. Magn. Mat. ,76–80 (2016).[8] P. Esquinazi, W. Hergert, D. Spemann,A. Setzer, and A. Ernst, “Defect-inducedmagnetism in solids,” Magnetics, IEEETransactions on , 4668–4674 (2013).[9] D. Spemann, T. Reinert, J. Vogt, T. Butz,K. Otte, and K. Zimmer, “Novel test sam-ple for submicron ion-beam analysis,” Nucl.Instr. and Meth. B , 186–192 (2001).[10] D. J. W. Mous, R. G. Haitsma, T. Butz,R.-H. Flagmeyer, D. Lehmann, andJ. Vogt, “The novel ultrastable hvee 3.5 mvsingletron tm accelerator for nanoprobe ap-plications,” Nucl. Instr. and Meth. B ,31–36 (1997).[11] C. Uzan-Saguy, C. Cytermann, R. Brener,V. Richter, M. Shaanan, and R. Kalish,“Damage threshold for ion-beam inducedgraphitization of diamond,” Appl. Phys.Lett. , 1194–1196 (1995).[12] R. Kalish, A. Reznik, S. Prawer, D. Saada,and J. Adler, “Ion-implantation-induceddefects in diamond and their annealing:experiment and simulation,” Physica Sta-tus Solidi A-Applied Research , 508–524 (1974).[15] D. Saada, J. Adler, and R. Kalish, “Trans-formation of diamond (sp ) to graphite(sp ) bonds by ion-impact,” Int. J. Mod.Phys. C , 61 (1998).[16] Z. Ma, J. Wu, W. Shen, L. Yan, X. Pan,and J. Wang, “Etching of CVD diamondfilms using oxygen ions in ECR plasma,”Appl. Surf. Sci. , 533–537 (2014).[17] L. G. Cancado, K. Takai, T. Enoki,M. Endo, Y. A. Kim, H. Mizusaki, A. Jo-rio, L. N. Coelho, R. Magalhaes-Paniago,and M. A. Pimenta, “General equation forthe determination of the crystallite size L a of nanographite by raman spectroscopy,”Appl. Phys. Lett. , 163106–3 (2006).[18] S. Rubanov, B. A. Fairchild, A. Suvorova,P. Olivero, and S. Prawer, “Structuraltransformation of implanted diamond layersduring high temperature annealing,” Nucl.Instr. and Meth. B , 5054 (2015).[19] J. Barzola-Quiquia, P. Esquinazi, M. Lin-del, D. Spemann, M. Muallem, and G.D.Nessim, “Magnetic order and supercon-ductivity observed in bundles of double-wall carbon nanotubes,” Carbon , 16–25(2015).[20] J. L. Cholula-Diaz, J. Barzola-Quiquia,H. Krautscheid, U. Teschner, and P. Es-quinazi, “Synthesis and magnetotransportproperties of nanocrystalline graphite pre-pared by aerosol assisted chemical vapor de-position,” Carbon , 10–16 (2014).[21] J. Barzola-Quiquia, J.-L. Yao, P. R¨odiger,K. Schindler, and P. Esquinazi, “Sample ize effects on the transport characteris-tics of mesoscopic graphite samples,” Phys.Stat. Sol. (a) , 2924–2933 (2008).[22] M. Zoraghi, J. Barzola-Quiquia, M. Stiller,A. Setzer, P. Esquinazi, G. H. Kloess,T. Muenster, T. L¨uhmann, and I. Estrela-Lopis, “Influence of rhombohedral stackingorder in the electrical resistance of bulkand mesoscopic graphite,” Phys. Rev. B ,045308 (2017).[23] N. F. Mott, “Conduction in glasses contain-ing transition metal ions,” J. Non-Cryst.Solids , 1–17 (1968).[24] K. Matsubara, K. Sugihara, andT. Tsuzuku, “Electrical resistance inthe c direction of graphite,” Phys. Rev. B , 969–974 (1990).[25] N. Garcia, P. Esquinazi, J. Barzola-Quiquia, and S. Dusari, “Evidence forsemiconducting behavior with a narrowband gap of Bernal graphite,” New Journalof Physics , 053015 (14pp) (2012).[26] T. L¨uhmann,
3D Ionenstrahlschreiben inDiamant zur Erzeugung von Graphitstruk-turen und deren Charakterisierung , Mas-ter’s thesis, University Leipzig, Germany(2015).[27] K. G. Raj and P. A. Joy, “Cross over from3D variable range hopping to the 2D weaklocalization conduction mechanism in disor-dered carbon with the extent of graphitiza-tion,” Phys. Chem. Chem. Phys. , 16178–16185 (2015).[28] Z. H. Khan, M. Husain, T. P. Perng,N. Salah, and S. Habib, “Electrical trans- port via variable range hopping in an in-dividual multi-wall carbon nanotube,” J.Phys.: Condens. Matter , 475207 (7pp)(2008).[29] P. Olivero, G. Amato, F. Bellotti, S. Borini,A. Lo Giudice, F. Picollo, and E. Vittone,“Direct fabrication and iv characterizationof sub-surface conductive channels in di-amond with mev ion implantation,” Eur.Phys. J. B , 127132 (2010).[30] H. Kempa, P. Esquinazi, and Y. Kopele-vich, “Field-induced metal-insulator transi-tion in the c-axis resistivity of graphite,”Phys. Rev. B , 241101(R) (2002).[31] A. Grill, “Electrical and optical propertiesof diamond-like carbon,” Thin Solid Films , 189193 (1999).[32] J.J. Hauser, “Hopping conductivity inamorphous carbon films,” Solid State Com-mun. , 1577–1580 (1975).[33] Y. Kopelevich, J. H. S. Torres, R. R.da Silva, F. Mrowka, H. Kempa, and P. Es-quinazi, “Reentrant metallic behavior ofgraphite in the quantum limit,” Phys. Rev.Lett. , 156402–1–4 (2003).[34] Y. Toyozawa, “Theory of localized spinsand negative magnetoresistance in themetallic impurity conduction,” J. Phys.Soc. Japan , 986–1004 (1962).[35] R. Khosla and J. Fischer, “Magnetoresis-tance in degenerate CdS: Localized mag-netic moments,” Phys. Rev. B , 4084–4097(1970).[36] O. Volnianska and P. Boguslawski, “Mag-netism of solids resulting from spin polar- zation of p orbitals,” J Phys: CondensMatter , 073202 (19pp) (2010).[37] P. Esquinazi, J. Barzola-Quiquia, D. Spe-mann, M. Rothermel, H. Ohldag,N. Garc´ıa, A. Setzer, and T. Butz,“Magnetic order in graphite: Experimentalevidence, intrinsic and extrinsic difficul-ties,” J. Magn. Magn. Mat. , 1156–1161(2010).[38] I. Lorite, C. Zandalazini, P. Esquinazi,D. Spemann, S. Friedl¨ander, A. P¨oppl,T. Michalsky, M. Grundmann, J. Vogt, J. Meijer, S.P. Heluani, H. Ohldag,W.A. Adeagbo, S.K. Nayak, W. Hergert,A. Ernst, and M. Hoffmann, “Study ofthe negative magneto-resistance of singleproton-implanted lithium-doped ZnO mi-crowires,” J. Phys.: Condens. Matter ,256002 (2015).[39] J. Barzola-Quiquia, N. Klingner, J. Kr¨uger,A. Molle, P. Esquinazi, A. Leonhardt, andM. T. Martinez, “Quantum oscillations andferromagnetic hysteresis observed in ironfilled multiwall carbon nanotubes,” Nan-otechnology , 015707 7(pp) (2012)., 015707 7(pp) (2012).