Up-scaling graphene electronics by reproducible metal-graphene contacts

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Norman Washington
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1 Supporting Information Up-scaling graphene electronics by reproducible metal-graphene contacts Kamal Asadi 1,*, Eugene C. Timmering 2, Tom C. T. Geuns 2, Amaia Pesquera 3, Alba Centeno 3, Amaia Zurutuza 3, Johan H. Klootwijk 2, Paul W. M. Blom 1,Dago M. de Leeuw 1,4 1 Max-Planck Institute for Polymer Research, Ackermannweg 10, D-55128, Mainz, Germany 2 Philips Research Laboratories, High Tech Campus 4, 5656 AE, Eindhoven, The Netherlands 3 Graphenea S.A., Tolosa Hiribidea 76, Donostia-San Sebastian, Spain 4 King Abdulaziz University, Abdullah Sulayman, Jeddah, Saudi Arabia * asadi@mpip-mainz.mpg.de 1

2 I. Graphene growth and transfer The quality of the graphene grown on Cu was investigated using Raman spectroscopy. We measured the Raman spectra of graphene before and after transfer. Figure S1 shows the Raman spectra of as-grown graphene (Figure S1a) and of the transferred graphene on a smooth Si monitor wafer (Figure S1b). Figure S1. a) and b) Raman Spectra of two different graphene samples from the same batch. Subsequently, we inspected the transfer quality with optical microscopy. The photographs shown in Figure S2 and Figure S3 were taken on Si monitor wafer and on the wafer with prepatterned Au stripes. Both images show that clean transferred graphene films can be obtained using the conformal transfer technique. 2

3 Figure S2. Optical image of transferred graphene on a smooth Si monitor wafer. Figure S3. Optical image of graphene deposited by conformal transfer on the pre-patterned wafer with gold strips (the bright strips). 3

4 II. Transfer Line Method (TLM) 1 A thorough explanation of different TLM methods is given in Refs. 11 and Here we give a brief summary. As depicted in Figure S4a, a TLM test structure consists of stripes of metal contacts with variable spacing, d, between them that are applied on a piece of semiconductor. The contacts and the semiconductor have a well-defined geometry. The semiconductor has a length, Z, and width, W. The contacts have a fixed contact length, L. The contact width should be larger than or at least equal to the width of semiconductor layer, W. Otherwise, the current can flow through the region beyond the test structure. a b d Z W L R T (Ω) c L t d L t 2L t Slope=R SH /W 2R c Electrode spacing, d (µm) Figure S4. TLM analysis. a) TLM test structure in which the semiconductor and the contacts all have a well-defined geometry. b) Schematic of a TLM plot. c) Schematic of transfer length, L t, for current transfer from contacts into graphene and vice versa. The essential requirement for a TLM test is a uniform sheet resistance of the semiconductor both under the contact area and between the contacts. Under these conditions the sheet resistance, contact resistance and other device parameters can reliably be determined as follows. A constant 4

5 current is forced between two neighboring contacts, and the voltage drop is measured. The total resistance between that pair of contacts, assuming a uniform sheet resistance and similar contact resistances then reads as: = + 2 (S1) R T depends linearly on the spacing between the contacts. As shown in Figure S4b, by plotting the total resistance versus the spacing, and by linear fitting the data, one obtains the sheet resistance of the semiconductor from the slope and the contact resistance, 2R C, from the intercept with the total resistance axis. Moreover, from the intercept of the linear fit with the spacing axis one obtains a length scale called the transfer length, L t, which is the length scale over which most of the current is transferred from the contact to the semiconductor and vice versa, as depicted in Figure S4c. III. Circular Transmission Line Method (CTLM) Circular test structures consists of a conducting circular inner electrode of radius, L, surrounded by a conducting outer region with a gap spacing, d, as shown in Figure S5a. The CTLM geometry has the following advantage over the TLM geometry: it eliminates the need for patterning of the graphene layer. The surrounding contact is grounded and therefore the current can only flow from the central contact to the surrounding contact. Hence the CTLM geometry eliminates parasitic currents. It is therefore not necessary to pattern the graphene layer to be measured. 5

6 a c d L Raw injection resistance data Corrected injection resistance data b SiO 2 (gate dielectric) V Total Resistance (Ω) Y = 0.480X R 2 = Y = 0.421X+1.98 R 2 = Highly n-doped Si (back gate) Gap spacing (µm) Figure S5. CTLM analysis. a) Schematic of CTLM test structure. b) Cross section of one single device in a CTLM test structure with conformal graphene layer on top of the contacts. The middle contact represents the circular inner electrode and the side contacts represent the surrounding outer electrode. c) Typical corrected and uncorrected CTLM data for current injection into graphene. We performed four-point probe resistance measurements, and gated four-point probe measurements on the CTLM test structures with graphene conformal transferred to the test structure. A constant current was forced between the inner and outer electrode and the voltage drop was measured between the two electrodes, as shown in Figure S5b. For the gated four-point probe experiments, a constant current was forced between the inner and outer electrode. The voltage drop between the electrodes was recorded as a function of gate bias. Graphene is deposited on top of the metal electrodes. Hence the requirement for the uniformity of the sheet resistance on top of the metal electrodes and in the gap is met. The total resistance between the inner and the outer contacts is: 6

7 = + + ln 1+ (S2) where I 0,1 and K 0,1 denote the modified Bessel functions of the zero and first order. For L >> 4L t, the Bessel function ratios I 0 /I 1 and K 0 /K 1 tend to unity and R T becomes: = + + ln 1+ (S3) When L >> d the above formula simplifies to = +2 (S4) where C is geometrical correction factor: = 1 + (S6) The correction factor, C, is necessary to take into account the circular geometry of the CTLM layout as compared to the linear geometry of the TLM layout. The experimental CTLM data needs to be corrected for the geometry. The total resistance as a function of gap spacing, d, before and after data correction is shown in Figure S5c. The slope of the linear fit gives R sh /2πL and the intercept is 2R C. For the uncorrected data the linear fit clearly underestimates the sheet resistance and overestimates the contact resistance and the transfer length. Corrected data produce a high quality linear fit, with correct values of extracted device parameters. Furthermore the CTLM structure in combination with conformal graphene transfer allows determining the specific contact resistance, ρ C. The major requirement is uniformity of the sheet resistance of the graphene layer. The current flows through the lowest resistance path. For current injection from the graphene to the metal, charge carrier encounter two resistances: ρ C and 7

8 R sh, as depicted in Figure S6. The potential distribution under the contact is therefore determined as: = (S7) where I is the current flowing into the contact. The voltage is highest near the contact edge x = 0. In the CTLM test structure used in our work, L is 320 µm. Transfer length is in between 1-3 µm. Hence L>>L t and therefore the voltage drops nearly exponentially with distance. At x=l t from the contact edge, the voltage drops by 1/e. From Eq. S7, one can therefore calculate the specific contact resistivity as: = (S8) Figure S6. Current extraction from graphene to the contact. The same holds also for the injection process, with the direction of current arrow being reversed. The black resistors represent graphene sheet resistance. The red resistors represent the contact specific resistivity. References 1. Schroder, K. S.; Semiconductor Material and Device Characterization; 3 rd ed., Wiley: New Jersey,

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