Supplementary Information for Self-assembled and intercalated film of reduced graphene oxide for a novel vacuum pressure sensor Sung Il Ahn *, Jura Jung, Yongwoo Kim, Yujin Lee, Kukjoo Kim, Seong Eui Lee 3*, Sungyun Kim 4*, and Kyeong-Keun Choi 5 Department of Engineering in Energy and Applied Chemistry Silla University, Busan 67-736 (Republic of Korea) Department of Electrical Engineering Korea Advanced Institute of Science and Technology (KAIST), 9 Daehak-ro, Yuseong-gu, Daejeon 35-7 (Republic of Korea) 3 Advanced Materials Engineering Korea Polytechnic University, Jungwang dong Shihung 49-793 (Republic of Korea) 4 Institute of NT.IT fusion technology, Ajou university, Worldcup ro 6, Youngtong gu Suwon 6499 (Republic of Korea) 5 National Center for Nanomaterials Technology (NCNT) San 3, Hyoja-Dong, Nam-Gu, Pohang 79-784 (Republic of Korea).
. Sheet resistance of spin-coated i-rg versus vacuum pressure a. b. c. 94 59 83 47 7 39 9 5 79 45 6 37 i-rg.5.5.5 86 43 75 43 5 35 n-rg 8 35... 8 6 38 35 7 4... d. e. f. 7 5 36 34 4 33... Temp. ( C) 3 n-rg Fitting Eq. R = 63P 98P +4 i-rg Fitting Eq. R = 986P - 35.4P +867.5 3.5 3 5 R = -77.8ln(P) + 4 R = -34.7ln(P) + 77 4 3 3 R = -554.3ln(P) + 34947 R = -9.4ln(P) + 469 5 R = -656.ln(P) + 3943 R = -39.4ln(P) + 94 9... 9 8... R = -555.7ln(P) + 3934 R = -5.7ln(P) + 499 Figure S. Sheet resistance of spin-coated i-rg (with a PVA/G weight ratio of ) and normal RG (n-rg) as pressure is elevated from 3 torr to ambient air pressure; (a) 3 C, (b) 5 C, (c) C, (d) 5 C, and (e) C. (f) A table of fitting equations used to calculate errors in the pressure readings below torr. Insets are enlarged graphs with fitting curves plotted on a linear scale. The sheet resistances were measured at.67 s intervals as a function of increasing pressure in a vacuum under a constant leakage of approximately 3 3 torr/min.
i-rg n-rg Sensitivity (%) Max. Error (%). Sensitivity and reproducibility of pressure reading from spin-coated i-rg a. b. 3 i-rg n-rg 8 6 7 ~ 5 3 torr 4 7 Time (s) s Air pressure 3 5 5 Temperature ( C) 56 565 57 575 58 3 4 Time (min) Figure S. Sensitivity, maximum error, and reproducibility of pressure readings between. and torr; (a) Sensitivities of RG samples and maximum errors at measurement temperature from 3 to C, (b) Repeated measurement of sheet resistance in spin-coated i-rg at C in the vacuum range between ~ 5 3 and ambient air pressure. Note that the percentage error was calculated as ΔR / R fitting (where ΔR = R real R fitting at a given pressure). 3
3. Theoretical description of resistance behavior in spin-coated i-rg versus vacuum pressures a. b. c. 87 54 86 85 84 83..4 47 4 33 6.5.5.5.5.5.5.5 8 78 75 7.5 d. e. f. 6 45 3 5.5.5.5.5.5.5.5 65 6 55 5 45.5 T ( ) a b 3 834.4 9. 5 777.7 33.8 4666.7 68.79 5 896. 865.7 338.8 8.6.5.5.5 Figure S3. Theoretically calculated standard deviations of the z axis ( ) and resistance of the spin-coated i-rg film as the pressure is increased from 3 to torr; (a) at 3 C, (b) at 5 C, (c) at C, (d) at 5 C, and (e) at C. (f) Table of fitting parameters used for equation () (R= a + b ). Note that the calculated resistances are compared with the experimental data in Figure S. The suggested hypothesis of LVW interaction is theoretically examined in the low pressure regime, with the assumptions that the parallel horizontal layers of hexagonal graphene lattice have a side length of.4 Å connected vertically by polymer pillars of 5 nm radius and the distance between two layers is 6.8 Å. For a pressure of torr and a temperature of 3 K, the number density of air molecules is quite small, about one per 3 nm side cube. Therefore, the pressure equilibrium condition of the graphene sheets seem to play a role in resistance changes at low pressure, rather than the direct action of air molecules inside graphene. In this regime the pres- 4
sure on each atom (~.89 8 J) is small compared with the effects, for example, thermal energy (~ 4.4 J) and VDW minimum energy (~ 3.86 J). Hence, the manifested pressure effect is likely to be a macroscopic effect. For the theoretical calculation, one graphene layer between parallel layers is considered, with the normal direction of the layer along the Z axis, and the average position of the layer in this axis is Z. Supposing that the distances between upper and lower layers are the same, the Z value becomes zero. In smaller length scale (horizontal layer diameter ~5 nm) Z can fluctuate by a few Å since, locally, the layer can be attracted to lower or upper layers by van der Waals attraction. At a larger scale (horizontal layer diameter ~ μm) local parts of the layers can be randomly attracted to the upper or lower layers. If the deformation is symmetric about the Z direction, we can assume that Z = is the average equilibrium position of the layer. The potential energy of the layer along the Z plane can become complex, depending on the size of the layer. In the regime where pressure differences cause a visible change, one can assume that the average position of layer Z changes by ΔZ, since the layer has higher energy by Δ Δ (P is pressure and A is the area of the layer). The probability density also changes by a factor Δ. The resistance is related to mobilities of the charge carriers. When Z has an appreciable standard deviation, the carriers should travel a longer path with potential barriers. We assume that the resistance has a linear relation with the standard deviation of Z. Since the average of Z is, the standard deviation of Z is just. Using the above partition function factor, the following equation can be obtained: () 5
With the given experimental data in Figure and a suitable value for A, the (P vs ) graph correlates with the (P vs R) graph assuming: () (a and b in equation () are T and A dependent) Figure S3 shows (P vs R) and (P vs ) graphs in comparison with the experimental data in Figure S. A is set as 5.5 m, which corresponds to a square with a side length of.9 μm. The fitting parameters are a, b, and in units of Å. As seen in Figure 6, the theoretical description with A is consistent matches with the experimental data. 6
Transmittance (%) HC H H HC H H H H HC H H H H HC H H CH H CH CH H HC H H CH H H HC H CH H H CH CH CH H H H CH CH CH CH Intensity (a. u.) 4. A schematic of reaction-based self-assembly for the preparation of i-rg a. H i-rg Fabric to remove water (5 o C) Hot plate (75 o C) Fabric to remove water (5 o C) Hot plate (75 o C) Fabric to remove water (5 o C) Hot plate (75 o C) PVA H H H H PVA RG n G + NH NH Δ i-rg b. 9 8 7 Ref. P P P3 G c. 8 6 4 C-C 6 5 C-N C- C=C() 4 3 4 Wavenumber (cm - ) 75 8 85 9 95 Binding Energy (ev) Figure S4. (a) A schematic of reaction-based self-assembly of i-rg, (b) FT-IR spectra of the samples after heat-treatment at C for min, (c) XPS spectrum of sample Ref. RG formed by the RSA method. 7
.6 mm 5. A test device using patterned IT electrodes a. b. Four point probe Glass substrate Electrode 6 4 i-rg % error 4 3 i-rg.5.6 mm 9.. Figure S5. Properties of a pressure sensor using IT electrodes; (a) A diagram of the test device structure and a microscope image of the active area, (b) Results of sheet resistance measurements in the device with increasing pressure. 8
Sensitivity ( -5 torr - ) 6. Sheet resistance of RSA i-rg at high vacuum pressures a. b. 9 ~ 76 torr (RP on) 88 8 6 86 ~ -3 torr (TMP on) 4 84 ~ -6 torr 8 6 8 4 3 Time (min).5.5.75 PVA/G ratio Figure S6. (a) Sheet resistance of RSA i-rg (P3) with increasing vacuum pressure from ambient air pressure to approximately -6 torr at C (RP and TMP indicate the rotary and turbo molecular pumps, respectively), (b) Sensitivity of pressure readings within the pressure range used in (a). Note that the sensitivity is calculated as ΔR/R max P. Here, P = P max P min and ΔR = R max R min, where R max and R min are the maximum and minimum sheet resistance, respectively, in the pressure range between -6 and 76 torr. 9