SUPPLEMENTAL MATERIAL
Improvement of Graphene–Metal Contact Resistance by Introducing
Edge Contacts at Graphene under Metal
Seung Min Song, Taek Yong Kim, One Jae Sul, Woo Cheol Shin, Byung Jin Choa)
Department of Electrical Engineering, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon, Korea
a) Author to whom correspondence should be addressed. Electronic mail: bjcho@ee.kaist.ac.kr
1
1. CVD source and its properties
The graphene used in this work was synthesized on Cu thin film by inductive coupled plasma
chemical vapor deposition (ICP-CVD) in our laboratory. The synthesized graphene was then transferred
onto a target substrate by the conventional wet transfer method with PMMA. PMMA was removed by
thermal annealing in a H2/Ar ambient at ~400°C. Hall mobility and the sheet resistance of the astransferred graphene were measured to be ~903.62 cm2/Vs and ~693.17 Ω/□, respectively, at room
temperature as shown in Fig.S1. Representative Raman spectrum ofe graphene is plotted in Fig. S2.
2. Transfer characteristics
Figure S3 shows ID - VG and RTotal(=VD/ID) – VG curves. RTotal at VG lower than -20 V approaches
to be 2×Rc due to the lower resistance of graphene channel. Since the contact resistance in Fig. 1(d) is
extracted at VG=0 V, the contact resistance at VG~-40 V could be lower.
3. Simulation details
For the simulation of the model in Fig. 2(c) in the main manuscript, MATLAB program was used.
By introducing a unit distance of ΔL for simulation, each unit contact resistance and the unit sheet
resistance were modeled as ΔRc = ρc/ΔL/W and ΔRs = Rs×ΔL/W, individually. In addition, Rce which
represents the edge contact resistance at x = Lgr (red dashed line in Fig. 2(a)) was also included in the
model. There are three fitting parameters in the model; contact resistance (Rce), unit contact resistance
(ΔRc) and unit sheet resistance (ΔRs). However, Rce can be assumed to be infinite in the case of Lgr =
100 μm since the metal covers all the surface and there is no edge contact. Thus, in the first step, ΔRc
and ΔRs can be obtained from fitting the measured Rc in Fig. 2(d). Since there is only one result (mean
value of Rc in the case of Lgr = 100 μm) to fit, various combinations of Rs and ρc can be obtained (as
shown in Fig. S4(a)) for the case of the proposed devices with graphene antidot arrays. The values are
then applied for all the cases of Lgr, and the Rce is finally extracted as shown in Fig. S4(b). It is clear
2
that the smallest deviation of Rce is observed when Rs = 5~6 Ω/□, accordingly ρc = 4.1~4.9 kΩ·μm2 and
Rce = 16.9~18.6 Ω.
The parameters of ρc and Rs in Fig. S4(b) are, however, obtained only from the case of Lgr = 100
μm and the extraction process must include all the cases.
To determine the optimal values, the
parameters based on the above values are re-extracted from all the cases of Lgr and the result is plotted
in Fig. S5. As Rce increases to 21 Ω, the smallest standard deviation of ρc (std(ρc)) decreases and the
corresponding Rs approaches to ~8 Ω/□ as shown in Fig. S5(a). Since std(ρc) are almost constant for Rs
higher than 8 Ω/□ and Rce higher than 21 Ω, the optimal values are chosen to be Rs ≈ 8 Ω/□, ρc ≈ 3.17
kΩ·μm2 and Rce ≈ 21 Ω. In the case of the control devices, ρc shows little difference with Rce as seen in
the inset of Fig. S5(b) and it may be due to its short Lt which leads to negligible dependence on Rce. As
Rce could be assumed to be independent on the presence of holes in graphene, Rce for control device is
the same as that of the proposed devices with graphene antidot arrays (~ 21 Ω).
3
Figures
(a)
4
Count
3
2
1
0
400
(b)
600
800 1000 1200 1400
2
Hall mobility [cm /Vs]
1600
5
Count
4
3
2
1
0
200
400
600
800
1000
Sheet resistance [Ohm/sq]
1200
Figure S1. Distribution of (a) Hall mobility and (b) sheet resistance of the as-transferred graphene
synthesized by ICP-CVD method. The average values of Hall mobility and the sheet resistance at
room temperature are ~903.62 cm2/Vs and ~693.17 Ω/□, respectively.
4
Raman Intensity [a.u.]
1500
2000
2500
-1
wave number [cm ]
Figure S2. Raman spectrum of the as-transferred graphene on SiO2/Si substrate. The Raman
spectrum was measured at a wavelength of 514.53 nm.
5
ID [A/m]
(a) 200
Sum of antidot perimeters
0
213 m
902 m
9512 m
150
100
50
-40
W/L=30/10
VD=100 mV
-20
0
20
40
60
VG [V]
(b)
RTotal [km]
4
3
Sum of antidot perimeters
0
213 m
902 m
9512 m
2
W/L=30/10
VD=100 mV
1
-40
-20
0
20
40
60
VG [V]
Figure S3. (a) Transfer characteristics and (b) the total resistance (VD/ID) of graphene devices with or
without graphene antidot arrays.
6
(a) 13.5
12.0
w/ antidots (Lgr=100 m)
2
c [km ]
10.5
9.0
7.5
6.0
4.5
3.0
(b)
2
3
40
35
4
5
Rs [/]
6
7
8
9
10
w/ antidots
Rce
30
Rce []
1
8
std (Rce)
25
6
20
4
15
2
10
5
0
1
2
3
4
5
6
7
8
9
std(Rce) []
0
0
Rs [/]
Figure S4. Extraction of parameters from simulation with the model shown in Fig. 2(c). The devices
are with graphene antidot arrays in contact area. (a) Extracted ρc and Rs in the case of Lgr = 100 μm
and (b) corresponding edge contact resistance (Rce) and its standard deviation for the all cases of Lgr.
7
5
std(c) [km ]
4
(b)
0
w/ holes
Rce=17 
Rce=18 
3
Rce=19 
2
Rce=21 
Rce=20 
1
w/o holes
Rce=17 
1.8
8
c [km ]
2
Rce=18 
2
ave(c) [km ]
2
(a)
1.5
6
Rce=19 
1.2
Rce=20 
0.9
Rce=21 
0.6
200 300 400 500 600
Rs [/]
4
0
2
4
6
Rs [/]
8
10
Figure S5. Re-extraction of the parameters with the consideration of all Lgr. (a) Extracted standard
deviation (std(ρc)) and (b) average (ave(ρc)) of contact resistance with sheet resistance (Rs) and edge
contact resistance (Rce). The inset is the extracted ρc against Rs with different Rce values for the
control devices. The relatively small deviation with Rce indicates the negligible role of Rce in control
devices due to the short transfer length.
8