The sheet resistance of graphene under contact and its effect on the derived specific contact resistivity

CARBON

8 2 ( 2 0 1 5 ) 5 0 0 –5 0 5

Available at www.sciencedirect.com

ScienceDirect journal homepage: www.elsevier.com/locate/carbon

The sheet resistance of graphene under contact and its effect on the derived specific contact resistivity Song-ang Peng a, Zhi Jin a,*, Peng Ma a, Da-yong Zhang a, Jing-yuan Shi a, Jie-bin Niu a, Xuan-yun Wang a, Shao-qing Wang a, Mei Li a, Xin-yu Liu a, Tian-chun Ye a, Yan-hui Zhang b, Zhi-ying Chen b, Guang-hui Yu b a

Department of Microwave Devices and Integrated Circuits, Institute of Microelectronics, Chinese Academy of Sciences, Beijing 100029, China State Key Laboratory of Functional Material for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, China b

A R T I C L E I N F O

A B S T R A C T

Article history:

It is normally assumed that the sheet resistances under and outside the metal contact are

Received 28 May 2014

identical when deriving specific contact resistivity of graphene from transmission line

Accepted 1 November 2014

model. We considered the contact end resistance and obtained the sheet resistance under

Available online 7 November 2014

contact of 670 X/h, which is much different from that outside the contact of 1840 X/h. Considering the difference, the value of specific contact resistivity is determined to be 3.3 · 106 X cm2, which is three times as large as the unmodified value. This indicates that the difference between the sheet resistances under and outside the contact affects the derived specific contact resistivity of graphene significantly.  2014 Elsevier Ltd. All rights reserved.

1.

Introduction

Graphene is considered to be the most promising candidate for future high-speed electronics applications because of its high carrier mobility (exceeding 200,000 cm2/V s) and large saturation velocity (vsat = 5.5 · 107 cm/s) [1–6]. As the graphene field effect transistors (GFETs) are scaled down, an ultralow metal/graphene contact resistance is required to achieve the high intrinsic speed [7–10]. The specific contact resistivity (qc) is always used to describe the real contact in metal/semiconductor contact [11,12]. In GFETs, the value of qc can be estimated from the contact resistance by fitting the total resistance curve of the device [13]. But, this method can be only valid for the devices without access region, in which

* Corresponding author: Fax: +86 10 62021601. E-mail address: [email protected] (Z. Jin). http://dx.doi.org/10.1016/j.carbon.2014.11.001 0008-6223/ 2014 Elsevier Ltd. All rights reserved.

the parasitic resistance only includes metal/graphene contact resistance. In addition, it also requires that the Dirac point of the GFET locates at the measured range of gate voltage. Therefore, the transmission line model (TLM) is always used to extract qc in graphene devices [14–18]. In this case, the sheet resistances beneath and outside the ohmic contact are usually considered to be the same. It is satisfied in conventional metal/semiconductor contact, because the bulk semiconductor under metal is not affected significantly by the metal. However, being atomically thin, the properties of graphene under the electrodes can be significantly altered due to the doping induced by the work function difference, as well as the chemical interaction between graphene and metal [19–24]. Hence, the sheet resistance underneath the

CARBON

8 2 ( 2 0 1 5 ) 5 0 0 –5 0 5

metal contact is quite different from that in the channel region. It will make a significant effect on the value of qc for metal/graphene contact. In this letter, we present the additional contact end resistance to modify the normal TLM. The sheet resistance of graphene under the metal (RSK) and in channel (RSH) are extracted to be 670 X/h and 1840 X/h, respectively. As a result, the value of specific contact resistivity (qc) is determined to be 3.3 · 106 X cm2, which is three times as large as the unmodified value.

2.

Experimental

The TLM test structures were fabricated on the single-layer graphene that was grown on Cu foil by chemical vapor deposition (CVD) method. The graphene film was transferred onto a highly resistive silicon substrate (3000 X cm) with 300 nm thick silicon oxide. The morphology of transferred CVD-grown graphene film onto SiO2/Si substrate was examined with optical microscopy and atomic force microscopy (AFM), as shown in Fig. 1(a) and (b). They show that the graphene is continuous with a few small bilayer islands. The quality of the graphene was further characterized by Raman spectroscopy (LabRAM HR Raman system with a laser wavelength of 473 nm, 100· objective lens). In the Raman spectroscopy results shown in Fig. 1(c), typical G and 2D bands were observed at 1582 and 2704 cm1, respectively. The ratio of 2D/G peaks was 3.0, indicating monolayer graphene [25,26]. The electron-beam lithography was used to define the TLM structures, multiple two point probe structures with varying channel lengths from 4 lm to 14 lm and fixed contact length (L) of 1 lm. Pd/Au (15/50 nm) was deposited as ohmic contacts by e-beam evaporation. The dielectric film was deposited on the channel region consisting of 1 nm thick oxide Al layer and 16 nm thick Al2O3 layer using atomic layer deposition (ALD). It is identical with the structure of top-gated device. After patterning graphene sheet with dielectric layer with photolithography, a dilute solution of H3PO4 and oxygen plasma treatment were employed to etch the unwanted Al2O3 and graphene respectively. Finally, Ti/Au (20/200 nm) metal stacks were deposited as external pads. All the current–voltage measurements on TLM test structures were carried out in vacuum at room temperature using four probes through B1500 semiconductor parameter analyzer.

3.

501

Results and discussion

Fig. 2(a) shows the scanning electron microscope (SEM) micrograph of a TLM test structure. The width (W) of the defined graphene strip is 20 lm. Fig. 2(b) shows the transfer characteristics of each GFET in TLM structures at VDS of 0.1 V. The ambipolar behavior is observed with positive shift of neutrality voltage point (VDirac), indicating p-type doping of the graphene. It can be attributed to the adsorption of oxygen and water molecules during graphene growth and transfer process [27,28]. The electron conduction branches are suppressed and lead to asymmetry of these curves, which can be explained as the intrinsic property of p–n junction caused by the p-type doping graphene under Pd contact [29–31]. The result is different from the ideal Pd/graphene contact where graphene is considered to be n-type doped because of work-function difference, as well as the strong interaction between them [20,21]. The p-type doped graphene under Pd can be attributed to the separation between metal and graphene induced by the residual resist during GFET processing. In this case, the effect of Pd on the Fermi-level of graphene is weakened and electron doping from the Pd cannot thus balance the heavily p-type doping level in the graphene layer. This results in the p-type doped graphene under the contact [16,23,32]. In addition, as the channel is scaled down, VDirac shifts more positively with drain current increasing. This can be related to the effect of the various channel resistances in these different scale GFETs. In shorter channel device, the channel resistance becomes smaller than that in longer channel device, which results in an increase in the drain current. In addition, the Fermi level in channel will be affected by the contact-doping induced charge transfer more seriously. Thus, it leads to the shift of Dirac point [20,33]. According to Kim’s theory, the carrier mobility can be extracted by fitting the total resistance (RT) to the expression [34]:  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1Þ RT ¼ RC þ Nsq =elFE n2 þ n20 ; where e is the electron charge, n is the field-modulated carrier concentration, n0 is the residual carrier concentration, Nsq is the number of squares of the channel area, RC is the metal/ graphene contact resistance and lFE is the intrinsic field-effect mobility of graphene channel. Fig. 2(c) shows the

Fig. 1 – Optical and AFM (a and b) image of CVD-grown graphene transferred onto SiO2/Si substrate. (c) The Raman spectra for the graphene simple. (A color version of this figure can be viewed online.)

502

CARBON

8 2 ( 2 0 1 5 ) 5 0 0 –5 0 5

Fig. 2 – (a) SEM micrograph of a completed graphene TLM test structure; (b) transfer characteristics of the various channel scale GFETs measured in TLM test structure in vacuum. (c) Measured total resistance versus gate voltage along with the fitting result. (A color version of this figure can be viewed online.)

measured and fitting RT for 10 lm channel length device as a function of gate voltage. Fitting the experimental data to this expression yields lFE value of 1100 cm2/V s and RC of 410 X lm. The relative low carrier mobility may be attributed to the damage from the fabricating process. Fig. 3(a) shows the schematic of energy dispersion in graphene sheet representation under and outside contact and in channel. In the traditional metal/semiconductor contact, the sheet resistances in channel and under contact are assumed to be the same because of the stable bulk material feature. However, the electrical propriety of graphene is sensitive to the adjacent environment. In traditional semiconductor material, the sheet resistance (Rh) is defined as [11]: Z t R ¼ 1= nðxÞlðxÞdx; ð2Þ 0

where the n(x) represents the carrier concentration of the material, l(x) is the carrier mobility and t is the film thickness. In atomically thick graphene, the carrier concentration depends on the Fermi level. Their relationship can be pffiffiffiffiffiffi hvF pn, where vF is the Fermi velocity. expressed as: EF ¼  The graphene beneath metal contacts will be doped either p- or n-type depending on the difference of work functions

between the metal and graphene, as well as the metal–graphene interaction. It leads to the different Fermi level positions of graphene in channel and beneath contact, which results in the different sheet resistances in the two regions. Based on the first-principle calculation, the graphene under Pd contact is n-type doped due to the strong interaction between pz sates of graphene and d states of metal [20]. However, the graphene under Pd contact in our device revels p-type doping according to the suppressed electron branch as discussed in Fig. 2(b). This may be due to more heavily p-type doping of intrinsic graphene originated from the water molecule, oxygen molecule and charge impurities on the surface or beneath the graphene film. When graphene sheet comes into contact with metal layer, the Fermi level (EF) under metal layer is closer to the Dirac point comparing with that in channel region due to the opposite doping from the Pd layer. To accommodate the Fermi-level difference, charge transfer occurs between the contact and channel regions, which results in the energy band bending at the interface of these two regions. Hence, when current flows from graphene to metal, it encounters four types of resistance (as seen in Fig. 3(b)): the sheet resistance of the metal (RM), the specific contact resistivity (qc), the sheet resistance of graphene under contact

Fig. 3 – (a) Schematic of energy dispersion in graphene sheet representation under contact and in channel; (b) schematic of transmission line model for the metal/graphene contact. (A color version of this figure can be viewed online.)

CARBON

8 2 ( 2 0 1 5 ) 5 0 0 –5 0 5

(RSK) and the sheet resistance of graphene in channel region (RSH). Because RM is much smaller than RSK and RSH, it is assumed that the current flows preferentially in the metal following the path of least resistance and that it enters metal from the graphene near the contact edge. The specific contact resistivity is always used to describe the real contact, which is defined as X cm2. Up to now, the reported qc in metal/graphene contact is usually obtained through the normal TLM test. However, in these cases, the sheet resistances in channel and contact region are assumed to be equal. This will result in a deviation from the precise value of qc in GFETs. As a result, the TLM test should be made some modification based on the equations below [11,35]: RT ¼

2RSK LT RSH LX þ ; W W

ð3Þ

LT ¼

rffiffiffiffiffiffiffi qc ; RSK

ð4Þ

where RT is the total resistance between any two contacts including the resistances of probing pads, contact and the graphene channel, LX is the gap between the contacts and LT is the transfer length. The transfer length is defined as the distance over which the current drops to 1/e of the total current [11,24]. Comparison of LT to the actual contact length L indicates whether the current is restricted to the edge of the contact or flows into the complete contact. Fig. 4(a) shows a plot of I–V characteristics of six devices in TLM test structures with the same channel width and different channel lengths. All the curves are linear, indicating their ohmic contact properties. The slopes of the curves represent the total resistance (RT) in each device, which consists of the resistance of graphene in channel and twice the contact front resistance. The inset of Fig. 4(a) shows the measurement structures for RT deriving. The measured RT versus contact spacing of TLM structures with the gaps varying from 4 to 14 lm are shown in Fig. 3(b). The correlation coefficient of the linear fit is 0.99, indicating that the quality of graphene is uniform. According to Eq. (3), RSH can be obtained from the slope of the fitting line. The slope is 92.0, yielding an experimentally determined value for RSH = 1840 X/h. Unlike the former

503

reports, where the LT is obtained from the intersection of the fitting line curve for RT = 0, the value of LT cannot be extracted from that curve in the modified TLM test [12,16,17]. Therefore, the additional parameters named contact front resistance (RCF) and contact end resistance (RCE) are needed to calculate the accurate values of LT and qc [11,35]. The physical meanings of RCF and RCE can be understood through the transmission line model. Based on the solution for the transmission line equations, the potential distribution under the contact is determined by both qc and RSK based on the following expression [7,36]: pffiffiffiffiffiffiffiffiffiffiffiffi I qc RSK cosh½ðL  xÞ=LT  VðxÞ ¼ ; ð5Þ sinhðL=LT Þ W where L is the contact length and I is the total current flowing into the contact region. RCF is defined as the voltage drop across the interface layer at the edge of the contact, V(x = 0), to the total current flowing into the contact, I(x = 0) = I. It can be expressed as: pffiffiffiffiffiffiffiffiffiffiffiffi RSK qC Vðx ¼ 0Þ q ¼ RCF ¼ cothðL=LT Þ ¼ C cothðL=LT Þ: ð6Þ Iðx ¼ 0Þ W WLT To obtain RCF in TLM test structures, the voltage and current at same contacts are measured, as shown in the inset of Fig. 4(a). The value of RCF can be given by the y-intercept of the RT as a function of contact spacing. As shown in Fig. 3(b), the y-intercept is at 46.5, implying the value for RCF = 23.3 X. In addition, the contact front resistance is simply the contact resistance RC and it can also be expressed as RCF = (RSK · LT)/W. Thus, the contact resistance per unit width is 465 X lm, which is consistent well with that extracted from the fitting results in Fig. 2(c). Meanwhile, the ratio of the voltage at x = L to the total current is defined as the contact end resistance, RCE. According to Eq. (5), RCE can be expressed as: pffiffiffiffiffiffiffiffiffiffiffiffi RSK qC Vðx ¼ LÞ 1 q 1 ¼ ¼ C RCE ¼ : ð7Þ Iðx ¼ 0Þ sinhðL=LT Þ WLT sinhðL=LT Þ W Fig. 5 shows the voltage between the contacts 2 and 3 as a function of the current flowing from the contacts 1 to 2. This is the measurement of contact end resistance (shown in the inset of Fig. 5). The feature of this I–V curve is linearity,

Fig. 4 – (a) I–V characteristics of each GFET in TLM test structure. The inset shows the measured schematic of contact front resistance. (b) Measured TLM resistance values versus contact spacings of 4 lm to 14 lm. (A color version of this figure can be viewed online.)

504

CARBON

8 2 ( 2 0 1 5 ) 5 0 0 –5 0 5

4.

Conclusion

In summary, we present a modified TLM test to determine the specific contact resistivity in metal/graphene contact. Because of the extra doping from the contact metal caused by the interaction between graphene and metal, the RSK and RSH are quite different. Considering the difference, the value of specific contact resistivity is determined to be 3.3 · 106 X cm2, which is three times as large as the unmodified value. This indicates that the difference between the sheet resistances under and outside the contact affects the derived specific contact resistance of graphene significantly.

Acknowledgments Fig. 5 – Measured current flowing across contacts 1–2, with the voltage between contacts 2 and 3. Inset: the measured schematic of contact end resistance. (A color version of this figure can be viewed online.)

This work was subsidized by National Science and Technology Major Project (Grant No. 2011ZX02707.3), the National Natural Science Foundation of China (No. 61136005), and Chinese Academy of Sciences (KGZD-EW-303).

indicating that no potential barrier appears in the contact end resistance. The RCE is extracted to be 10.5 X according to the slope of the I–V curve in Fig. 5. RCF and RCE are used to determine LT and qc. Combing Eqs. (6) and (7), the ratio of RCE to RCF is:

R E F E R E N C E S

RCE 1 ¼ : RCF coshðL=LT Þ

ð8Þ

The ratio is calculated to be 0.45 based on the obtained results, we can then obtain LT = 0.70 lm. However, according to the normal TLM, the value of LT is extracted to be only 0.25 lm, which is half of the intersection of the fitting line curve in Fig. 4(b). In our device, the contact length is much longer than LT, indicating the current crowding at the contact edge. This means that the current cannot flow across the total contact length and it is the feature of large contact resistance in our device. This may be attributed to suppressed current injection from metal induced by the relative small density of states for graphene, as well as the contamination at the interface of the metal/graphene contact. The RSK can be extracted from Eq. (3) by introducing the calculated LT. The x-intercept of the fitting curve in Fig. 4(b) is 0.5, yielding an experimentally determined value for RSK = 670 X/h. The value is quite different from that of RSH, indicating that the normal TLM measurement should be modified to characterize the metal/graphene contact. Finally, the qc can be obtained according to Eq. (4) for the value of 3.3 · 106 X cm2. However, if we use the normal TLM, the specific resistivity can be expressed as: qc = RC · LT · W, yielding to a value of 1.2 · 106 X cm2. This is only one third of the modified value, suggesting that RSK affects significantly the derived qc in metal/graphene contact. We can also substitute LT and qc into Eqs. (6) and (7), yielding the calculated RCF = 26.1 X and RCE = 11.8 X, respectively. The values are in close agreement with the extracted results. This further indicates the reliability of the method. It should be noted that our study is only suited for the TLM structure, because that multi-probe configuration is needed.

[1] Novoselov KS, Geim AK, Morozov SV, Jiang D, Zhang Y, Dubonos SV, et al. Electric field effect in atomically thin carbon films. Science 2004;306:666–9. [2] Liao L, Lin YC, Bao MQ, Cheng R, Bai JW, Liu Y, et al. Highspeed graphene transistors with a self-aligned nanowire gate. Nature 2010;467:305–8. [3] Wu YQ, Jenkins KA, Garcia AV, Farmer DB, Zhu Y, Bol AA, et al. State-of-the-art graphene high-frequency electronics. Nano Lett 2012;12:3062–7. [4] Lin YM, Dimitrakopoulos C, Jenkins KA, Farmer DB, Chiu HY, Grill A, et al. 100-GHz transistors from wafer-scale epitaxial graphene. Science 2010;327:662. [5] Lin YM, Valdes-Garcia A, Han SJ, Farmer DB, Meric I, Sun Y, et al. Wafer-scale graphene integrated circuit. Science 2011;332:1294–7. [6] Han S, Jenkins KA, Garcia AV, Franklin AD, Bol AA, Haensch W. High-frequency graphene voltage amplifier. Nano Lett 2011;11:3690–3. [7] Wu YQ, Lin YM, Bol AA, Jenkins KA, Xia F, Farmer DB, et al. High-frequency, scaled graphene transistors on diamond-like carbon. Nat Lett 2011;472:74–8. [8] Parrish KN, Akinwande D. Impact of contact resistance on the transconductance and linearity of graphene transistors. Appl Phys Lett 2011;98:183505-1–3. [9] Hsu A, Wang H, Kim KK, Kong J, Palacions T. Impact of graphene interface quality on contact resistance and RF device performance. IEEE Electron Device Lett 2011;32:1008–10. [10] Franklin AD, Han SJ, Bol AA, Perebeinos V. Double contacts for improved performance of graphene transistors. IEEE Electron Device Lett 2012;33:17–9. [11] Schroder DK. Semiconductor material and device characterization. 3rd ed. United States: John Wiley & Sons, Inc.; 2006. p. 135–47. [12] Robinson JA, Bella ML, Zhu M, Hollander M, Kasarda R, Hughes Z, et al. Contact graphene. Appl Phys Lett 2011;98:053103-1–3. [13] Huang BC, Zhang M, Wang YJ, Woo J. Contact resistance in top-gated graphene field-effect transistors. Appl Phys Lett 2011;99:032107-1–3.

CARBON

8 2 ( 2 0 1 5 ) 5 0 0 –5 0 5

[14] Xia FN, Perebeinos V, Lin YM, Wu YQ, Avouris P. The origins and limits of metal–graphene junction resistance. Nat Nanotechnol 2011;6:179–84. [15] Venugopal A, Colombo L, Vogel EM. Contact resistance in few and multilayer graphene devices. Appl Phys Lett 2010;96:013512-1–3. [16] Moon JS, Antcliffe M, Seo HC, Curtis D, Lin S, Schmitz A, et al. Ultra-low resistance ohmic contacts in graphene field effect transistors. Appl Phys Lett 2012;100:203512-1–3. [17] Li W, Liang Y, Yu DM, Peng LM, Pernstich KP, Shen T. Ultraviolet/ozone treatment to reduce metal–graphene contact resistance. Appl Phys Lett 2013;102: 183110-1–5. [18] Smith JT, Franklin AD, Farmer DB, Dimitrakopoulos CD. Reducing contact resistance in graphene devices through contact area patterning. ACS Nano 2013;7:3661–7. [19] Giovannetti G, Khomyakov PA, Brocks G, Karpan VM, van den Brink J, Kelly PJ. Doping graphene with metal contacts. Phys Rev Lett 2008;101:026803-1–4. [20] Khomyakov PA, Giovannetti G, Rusu PC, Brocks G, van den Brink J, Kelly PJ. First-principles study of the interaction and charge transfer between graphene and metals. Phys Rev B 2009;79:195425-1–195425-12. [21] Gong C, Hinojos D, Wang W, Nijem N, Shan B, Wallace RM, et al. Metal–graphene–metal sandwich contacts for enhanced interface bonding and work function control. ACS Nano 2012;6:5381–7. [22] Song SM, Park JK, Sul OJ, Cho BJ. Determination of work function of graphene under a metal electrode and its role in contact resistance. Nano Lett 2012;12:3887–92. [23] Nagashio K, Moriyama T, Ifuku R, Yamashita T, Nishimura T, Toriumi A. Is graphene contacting with metal still graphene? IEDM 2011;27:2.4.1–4. [24] Nagashio K, Toriumi A. Density-of-states limited contact resistance in graphene field-effect transistors. Jpn J Appl Phys 2011;50:070108-1–6.

505

[25] Ferrari A C, Meyer J C, Scardaci V, Casiraghi C, Lazzeri M, Piscanec S, et al. Raman spectrum of graphene and layers. Phys Rev Lett 2006;97:187401-1–4. [26] Jin Z, Su Y B, Chen J W, Liu X Y, Wu D X. Study of AlN dielectric film on graphene by Raman microscopy. Appl Phys Lett 2009;95:233110-1–3. [27] Shin DW, Lee HM, Yu SM, Lim KS, Jung JH, Kim MK, et al. A facile route to recover intrinsic graphene over large scale. ACS Nano 2012;6:7781–8. [28] Chan J, Venugopal A, Pirkle A, McDonnell S, Hinojos D, Magnuson CW, et al. Reducing extrinsic performancelimiting factors in graphene grown by chemical vapor deposition. ACS Nano 2012;6:3224–9. [29] Low T, Hong S, Appenzeller J, Datta S, Lundstrom MS. Conductance asymmetry of graphene p–n junction. IEEE Trans Electron Devices 2009;56:1292–9. [30] Huard B, Sulpizio JA, Stander N, Todd K, Yang B, GoldhaberGordon. Transport measurements across a tunable potential barrier in graphene. Phys Rev Lett 2007;98:23680-1–4. [31] Williams JR, DiCarlo L, Marcus CM. Quantum hall effect in a gated-controlled p–n junction of graphene. Science 2007;317:638–41. [32] Moriyama T, Nagashio K, Nishimura T, Toriumi A. Carrier density modulation in graphene underneath Ni electrode. J Appl Phys 2013;114:024503-1–8. [33] Nagashio K, Ifuku T, Moriyama T, Nishimura T, Toriumi A. Intrinsic graphene/metal contact. IEDM 2012;68:4.1.1–4. [34] Kim SY, Nah JH, Jo I, Shahrjerdi D, Colombo L, Yao Z, et al. Realization of a high mobility dual-gated graphene fieldeffect transistor with Al2O3 dielectric. Appl Phys Lett 2009;94:062107-1–3. [35] Reeves GK, Harrison HB. Obtaining the specific contact resistance from transmission line model measurements. IEEE Electron Device Lett 1982;3:111–3. [36] Berger HH. Models for contacts to planar devices. Solid State Electron 1971;15:145–58.