Nanoscale Direct Mapping of Noise Source Activities on Graphene Domains Hyungwoo Lee,† Duckhyung Cho,† Shashank Shekhar,† Jeongsu Kim,† Jaesung Park,‡,⊥ Byung Hee Hong,‡ and Seunghun Hong*,†,§ †
Department of Physics and Astronomy and Institute of Applied Physics, ‡Department of Chemistry, and §Department of Biophysics and Chemical Biology (WCU Program), Seoul National University, Seoul 151-747, Korea ⊥ Center for Electricity & Magnetism, Korea Research Institute of Standards and Science, Daejeon 305-340, Korea S Supporting Information *
ABSTRACT: An electrical noise is one of the key parameters determining the performance of modern electronic devices. However, it has been extremely difficult, if not impossible, to image localized noise sources or their activities in such devices. We report a “noise spectral imaging” strategy to map the activities of localized noise sources in graphene domains. Using this method, we could quantitatively estimate sheet resistances and noise source densities inside graphene domains, on domain boundaries and on the edge of graphene. The results show high activities of noise sources and large sheet resistance values at the domain boundary and edge of graphene. Additionally, we showed that the top layer in doublelayer graphene had lower noises than single-layer graphene. This work provides valuable insights about the electrical noises of graphene. Furthermore, the capability to directly map noise sources in electronic channels can be a major breakthrough in electrical noise research in general. KEYWORDS: low-frequency noise, graphene, finite element method, noise imaging, atomic force microscopy
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spectral density (PSD) was measured on the graphene. Then, the map was analyzed by a computational method based on a finite element method (FEM) analysis and a differential method, enabling the mapping of the distribution of localized electrical noise sources in the graphene. This measurement and analysis method was named here as the “noise spectral imaging (NSI)” method because the PSD image was utilized to obtain the noise source distribution on electronic channels. Using the NSI method, we could map the distribution of noise sources on the domain boundary and the edges of single-layer graphene (SLG). In case of double-layer graphene (DLG), we found that the top layer exhibited a lower current noise level than the bottom layer as predicted previously.23 Until now, although electrical noises have been a serious problem in many nanoand microelectronic devices, only very limited methods have been developed to study the noises in such devices. Our method allows one to image the localized noise source distribution in electronic channels such as graphene and should have a significant impact on modern electronics in general.
ne of the key parameters determining the performance of electronic devices can be an electrical noise.1,2 Previous studies suggested that various localized noise sources in an electronic channel can generate electrical current noises. Examples of such noise sources include charge traps,3 domain boundaries of channel materials,4−6 channel edges,7 and impurities.8 However, it has been very difficult, if not impossible, to directly image the distribution of localized electrical noise sources in a device channel. Thus, most of the previous studies about electrical noises have relied on rather complicated analyses based on electrical measurement of multiple devices.9,10 For example, graphene has recently attracted significant interest because of its superb electrical transport characteristics.11−13 The characteristics of electrical noises in graphene channels have been studied using multiple graphene devices14−21 or conducting atomic force microscopy (AFM),22 which indirectly indicated the existence of various localized noise sources such as charge traps in the underlying substrates and defects in domain boundaries and edges. However, previous methods could not enable the mapping of localized noise sources in a graphene channel. Herein, we report a method for the direct imaging of electrical noise sources and their activities in graphene domains. In this method, a conducting AFM tip made a direct contact with a graphene surface, and the map of electrical noise power © 2016 American Chemical Society
Received: August 5, 2016 Accepted: November 8, 2016 Published: November 8, 2016 10135
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the low conductance near the boundary.28 This result clearly shows that we had a clean and wrinkle-free graphene layer, which is essential for the reliable noise analysis and mapping via our NSI method.22 The Raman spectroscopy was utilized to confirm the quality of the measured graphene film (Figure S1). The sharp symmetric 2D peak at 2682 cm−1 in the Raman spectrum indicates the high quality of the graphene film. The 2D/G ratio was ∼2 in the spectrum, showing that the graphene film was a monolayer. To estimate the sheet resistance Rs (x,y) at each point from the measured I (x,y) values, we developed an iterative method based on a computational algorithm coded in Agros2D (http:// agros2d.org). Details of the method are described in the Supporting Information. Figure 2c shows the calculated map of the sheet resistance Rs (x,y). The averaged sheet resistance value far from the domain boundary (marked by (i)) was ∼900 Ω, which is consistent with the previously reported sheet resistance of SLG on a SiO2 substrate.24,25 However, note that the sheet resistance near the domain boundary (marked by (ii)) was estimated as ∼1491 Ω, and it was much higher than that inside the domain. Previous study indirectly indicated that the resistance on the domain boundary can be rather high compared with that in the domain due to various defects.28 However, our work allowed us to directly estimate the specific sheet resistance values of the domain boundaries. This result clearly shows that our method can be a versatile tool for the analysis of two-dimensional nanostructures. While taking the topography and the current maps, we could also measure the current noise PSD SI. Figure 2d shows the map of current-normalized PSD SI/I2 measured at 548 Hz on the same regions of the graphene. Note that the PSD values change abruptly at the domain boundaries, and they sometimes appeared larger at the domain boundaries than those inside the domains. The results imply that the domain boundaries contributed significantly to the electrical current noises in the SLG channel. One common theoretical model to describe electrical current noises in electronic channels is the number fluctuation model, where individual noise sources trap and release charge carriers with a relaxation time τ.1,3 The repeated trap-and-release of charge carriers results in the current fluctuations whose PSD is proportional to ∼1/f 2. If the current channel has a large number of noise sources with different τ, the noise PSDs of the different noise sources are averaged out and result in the noise spectra proportional to 1/f. Previous reports suggested that the low-frequency noise in graphene is generated mainly via carrier number fluctuations caused by noise sources in the graphene or underlying substrates, and in this case, the PSD values from the graphene channels should decrease under increased gate bias voltages with a scaling parameter close to ∼2.29,30 We measured the currents and the noise PSD of our graphene sample versus gate voltage in order to evaluate its basic device characteristics and the sources of electrical noises (Figure S2 in the Supporting Information). The graphene device exhibited a typical gating effect of single-layer graphene with a Dirac point voltage of ∼20.9 V. The scaling parameter of the noise PSD versus gate bias plot was estimated as ∼1.94, which is close to 2. It indicates that the low-frequency noise of our graphene sample was originated from the number fluctuation of charge carriers in the graphene channel.29 Various localized noise sources have been suggested in the number fluctuation model for graphene. One example can be the charge traps buried in underlying SiO2 substrates, which can trap and detrap charge
RESULTS AND DISCUSSION Experimental Setup. Figure 1 shows a schematic diagram depicting our experimental setup. A SLG sheet was grown via a
Figure 1. Schematic diagram depicting the experimental setup for the noise spectral imaging method. A Pt probe made a direct contact with a graphene sample, and it was utilized to measure the topography, electrical currents, and current noise PSD simultaneously. A homemade spectrum analyzer was utilized to measure the PSD of the measured currents. The graphene sample consisted of a SLG channel transferred on a SiO2 substrate (oxide thickness ∼300 nm) and a metal electrode (Ti/Au thickness ∼10/30 nm). Note that the graphene channel can have various noise sources such as charge traps at the oxide layer, domain boundaries, and edge regions.
chemical vapor deposition method24,25 and transferred onto a SiO2 substrate (oxide thickness ∼300 nm). A metal electrode (Ti/Au ∼ 10/30 nm) was fabricated on the sample by a thermal evaporation method. For the current and the noise measurement, a Pt-based conducting probe (25Pt300B, Park Systems) installed on an AFM (XE-70, Park Systems) made contact with the surface of a graphene sample. Then, a bias voltage was applied to the metal electrode of the graphene sample by a DC power supply. The current signals through the probe were converted to voltage signals by a low-noise preamplifier (SR570, Stanford Research Systems), and the PSD of the converted voltage signals with a specific frequency was measured by a homemade spectrum analyzer.26 Using this system, we could obtain the AFM topography map, the current map, and the map of noise PSD with a specific frequency on the graphene sample, simultaneously. Noise Source Distribution on the Domain Boundary of a Single-Layer Graphene. Figure 2a,b shows the AFM topography and current maps of a SLG, respectively. The topography map indicates that the surface of our graphene sample was clean, and there were no significant wrinkles or surface roughness on it. For the current mapping, the bias voltage of 0.04 V was applied to the metal electrode, and the current output was measured using the conducting AFM tip. The current map exhibited clear domains (bright regions) separated by the boundaries with low currents (dark regions). The low conductance at the domain boundary can be associated with the lattice disordering at the boundary.27 It was previously reported that irregular atomic structures at domain boundary could induce a finite energy gap, which led to 10136
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Figure 2. Noise source distribution at the domain boundary. (a) AFM topography image of a SLG sample. (b) Current image of the sample. The bias voltage of 0.04 V was applied to the sample through a metal electrode. (c) Sheet resistance map of the SLG sample. (d) Currentnormalized noise PSD map (at 548 Hz) of the SLG sample. (e) Current-normalized noise PSD versus frequency measured far from the domain boundary (blue circles) and near the domain boundary (red circles). When the noise spectrum was measured near the domain boundary, the 1/f 2 behavior was observed at a rather low-frequency condition near or below ∼10 Hz. (f) Schematic diagram depicting a small piece of graphene generating electrical noises. (g) Schematic diagram showing the network model to describe the graphene layers. The graphene channel was modeled as a network circuit of small graphene pieces with resistances and noise sources. (h) Noise source density map of the SLG sample. It was calculated from the measured current-normalized noise PSD and sheet resistance maps. Note that the domain boundary exhibited high density noise sources.
carriers resulting in current fluctuations.9,10 On the other hand, graphene itself can have various noise sources such as defects at domain boundary28,31−33 and dangling bonds at the edge of graphene channels.34 However, such localized noise sources were just suggested, and the actual distribution of them on a graphene channel has not been imaged before. Because our system includes a spectral analyzer, we can place a conducting AFM probe on a specific location of the graphene and measure noise spectra from that location. Figure 2e shows the current-normalized PSD SI/I2, which was measured at two different positions (marked by dotted circles in Figure 2d): (i) far from the domain boundary and (ii) near the domain boundary. A network analyzer (SR770 FFT network analyzer,
Stanford Research Systems) was utilized to measure the noise spectrum, and the bias voltage of 0.04 V was applied to the metal electrode of our SLG sample. Note that the PSD measured far from the domain boundary (blue circles in Figure 2e) showed typical 1/f behaviors. It indicates that there existed a large number of noise sources in the current paths, resulting in the averaged spectra of the noises caused by many different noise sources. On the other hand, when we measured noise spectra near the domain boundary (red circles in Figure 2e), we observed 1/f 2 behaviors at a rather low-frequency condition near or below ∼10 Hz. Previous works showed that when noise sources exist in a nanoscale junction, the noises by the noise sources are enhanced compared with those in a rather wide 10137
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ACS Nano electrical channel, and they generate large electrical noises with 1/f 2 behaviors.35−39 Presumably, in our works, when an AFM tip was on a domain boundary with a rather high density of noise sources, some noise sources could exist inside the small tip−graphene junction area and the electrical noises by the noise sources were enhanced, generating 1/f 2 noises at a lowfrequency condition. In this case, the 1/f 2 noises should represent mainly the noise enhancement effect by the tip− graphene junction, while 1/f noises could be considered as the summation of noises from many noise sources in our graphene channels.35−39 Note that such 1/f 2 noises decayed quickly with an increased frequency, and we could observe 1/f noises at a high-frequency regime even near domain boundaries (Figure 2e). Thus, in our experiments, we mapped electrical noises at a rather high-frequency condition with only 1/f noises (Figure 2d) so that we could avoid an unexpected noise enhancement effect by the tip−graphene junction and use the measured noise map to estimate the density of noise sources. We performed a differential analysis to obtain the density map of noise sources on the graphene channel. Note that a 1/f 2 component in the noise spectra decays much faster than a 1/f component, and the noise spectra exhibited only 1/f behavior at a rather high-frequency condition (Figure 2e). It indicates that the noise at a rather high-frequency condition was an averaged noise from multiple noise sources near and away from the AFM tip−contact area. In this case, we can assume that individual noise sources can independently trap and detrap charge carriers with different relaxation time τ, and the noise source density could be calculated from the PSD data in Figure 2d using Wiener-Khintchine theorem.39 The detailed calculation method is shown in the Supporting Information. In brief, let us consider a graphene layer on a SiO2 substrate (Figure 2f). The PSD of mean-square fluctuation in the number of occupied charge traps in the small segment of graphene in the area of ΔxΔy can be written as ∞
ΔS Nt(f , x , y) =
ΔSI(f , x , y) = =
neff (f , x , y) =
(1)
ΔS =
4τ(E , x , y , z) f
(2)
Here, we define an effective noise source density neff as 4τ(E , x , y , z)
∫ 1 + [2πf ·τf (E , x , y , z)]2
neff (f , x , y) ≡ f
f
× Nt(Ef , x , y , z)dz
(5)
ΔSI(f , x , y) (ΔC)2 f × 2 kT ΔxΔy (I )
(6)
(I )2 kT n (Δl)2 . (ΔC)2 f eff
Furthermore, assuming that Δl is
small, the sheet resistance and the effective noise source density of each graphene segment at (x,y) can be approximated as the averaged values of those of four graphene channels at (x ± Δl/2, y ± Δl/2) connecting the node with four neighboring nodes. Using the estimated Rs (x,y) values (Figure 2c), the effective noise source density neff (x,y) at each point could be calculated from the SI (f,x,y) values at the corresponding node at (x,y) (details in the Supporting Information). Figure 2h shows the calculated map of the effective noise source density neff. The averaged noise source density inside the domain (marked by (i)) was ∼0.8 × 1010 cm−2 eV−1. The noise sources in the domain can be attributed to the charge traps in the underlying SiO2 substrate and some defects in the graphene. Previous works suggested that the effective oxide trap density of general SiO2 substrates ranged from 109 to 1010 cm−2 eV−1, which is also consistent with our results.9 However, the effective noise source density near the domain boundary (marked by (ii)) was estimated as ∼1.2 × 1010 cm−2 eV−1, which was ∼1.5 times higher than that inside the domain. The high density of noise sources near the domain boundary can be attributed to lattice disordering and defects located in the
∫ 1 + [2πf ·τf (E , x , y , z)]2
× Nt(Ef , x , y , z)dz
(I )2 kT neff (f , x , y)ΔxΔy (ΔC)2 f
It is worth discussing a few interesting aspects of neff. First, in the common case of 1/f noise, ΔSI is proportional to 1/f. Thus, fΔSI ∼ constant and neff (f,x,y) ∼ neff (x,y). Furthermore, considering that neff is the integrated value of the charge trap density over the z-direction, it can be a convenient value to represent the effective surface density of noise sources in the two-dimensional graphene channels. In order to estimate the effective noise source density from the measured data, we adopted a network model as depicted in Figure 2g (details in the Supporting Information). Here, the layer of a graphene channel was modeled as a two-dimensional network on a x−y plane composed of small graphene segments of a square shape with its area of (Δl)2. A graphene segment at a (x,y) was assumed to have a sheet resistance Rs (x,y) and an effective noise source density neff (x,y). Each node at a (x,y) can be considered as a point where a conducting AFM tip was placed to measure I (x,y) and SI (f,x,y) in our experiments. Each node at (x,y) is connected with four neighboring nodes through small graphene channels with its area of (Δl)2, a sheet resistance Rs (x ± Δl/2, y ± Δl/2), and effective noise source density neff (x ± Δl/2, y ± Δl/2). We can estimate that each connecting graphene channel has a resistance of ΔR ∼ Rs, and from eq 5, it generates the current noise of
where the Nt, τ, and f are the density of charge traps over the space and energy, a trapping time constant, and a frequency, respectively.9,10 The integral over z ranged from 0 to oxide thickness Tox (Figure 2f) to account for charge traps buried in underlying oxide layers9,10 as well as those in the graphene layer. The trap occupancy function can be written as f t(E) = [1 + exp{(E − Ef)/kT}]−1, where Ef is Fermi level energy. At a rather low temperature T, f t(1 − f t) in eq 1 behaves like a delta function around the Fermi level,1 and eq 1 after the integral over E can be approximated as ΔS Nt(f , x , y) = ΔxΔy kT
(I )2 ΔS Nt(f , x , y) (ΔC)2
Then the effective noise source density can be written as
4τ(E , x , y , z)
× ft (1 − ft )Nt(E , x , y , z)dz dE
(4)
Assuming the charge carrier number as ΔC and the electrical current as I in the graphene segment, the PSD of the current noises generated by the segment ΔxΔy can be written as9
∫−∞ ∫ 1 + [2πf ·τ(E , x , y , z)]2
ΔS Nt(f , x , y) = ΔxΔy
kT neff (f , x , y)ΔxΔy f
(3)
Then eq 2 can be rewritten as 10138
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map shows that the graphene sample consisted of a SLG sheet (height ∼ 1.0 nm) and included no wrinkle or surface roughness. Previously, it was reported that the height of a single-layer graphene on a SiO2 substrate is typically measured as ∼0.8 nm, and the result was explained by a repulsive interaction between the graphene and SiO2,41 which is consistent with our result. The edges in the topography images appeared rather smeared presumably due to the tip convolution effect. In this experiment, we utilized a rather blunt probe with its contact area diameter of ∼10 nm to minimize the scratching of rather weak graphene edges and form a stable electrical contact. The current map was measured under the bias voltage of 0.04 V on the sample. The map shows that there were no leakage currents through the underlying SiO2 layer or any insulating residual defects on the graphene surface. Under the high-frequency condition (548 Hz) with 1/f noise characteristics, we measured the map of current-normalized PSD SI/I2 (Figure 3c). The PSD values appeared high at the edge of the graphene. This indicates that the edge of graphene also contributed significantly to the current noise in the SLG. We measured the noise spectra after placing a conducting AFM probe on the position away from (blue circles in Figure 3d) and near (red circles in Figure 3d) the edge of the SLG. When the tip was away from the graphene edge, we could observe typical 1/f noise behaviors. However, the PSD measured near the edge region exhibited the 1/f 2 noise characteristics under the lowfrequency conditions (below ∼10 Hz), which indicates that there exist noise sources in direct contact with a conducting probe near the edge of graphene just like graphene domain boundaries. It should also be noted that the 1/f 2 component disappeared at a rather high-frequency condition, and we could observe only a 1/f component. We also applied the FEM-based computational analysis on the measured current map to obtain the sheet resistance map. Figure 3e shows the map of sheet resistance values, which are consistent with the reported sheet resistance values of a SLG on SiO2 substrates.42,43 Note that the regions near the graphene edge (marked by (ii)) exhibited a three times larger sheet resistance value than that of the regions far from the edge (marked by (i)). The high resistance near the edge region can be associated with the presence of edge disorders hindering the charge transport.44 The map of estimated effective noise source density neff is shown in Figure 3f. As expected, the noise source density of region (ii) near the edge region was ∼1.5 times higher than that of region (i) far from the edge region. The high noise source density near the edge region can be associated with dangling bonds at the edge of graphene. It was previously reported that the dangling bonds or disorders at the edge region generate edge states,45,46 and the edge states can trap or detrap the charge carriers in the channel. The trap/detrap processes by edge states cause the number fluctuation of charge carriers, and it is also the well-known origin of low-frequency noise.40 Our spectral analysis indicates that such defect sites near the edge can be significant noise sources in graphene channels. Noise Source Distribution on a Double-Layer Graphene. We also utilized our method to analyze the noises in a DLG (Figure 4). Figure 4a shows a schematic diagram of the NSI measurement on the DLG. Here, we utilized a rather large piece of SLG with a small region covered by another SLG flake, forming a DLG only on that region. An electrode was connected to the SLG part, and a conducting AFM probe was utilized to measure the topography and the maps of
Figure 3. Noise source distribution at the edge of a graphene piece. (a) AFM topography image of a SLG sample. (b) Current image of the sample. The bias voltage of 0.04 V was applied to the electrode of the sample. (c) Current-normalized noise PSD map (at 548 Hz) of the SLG sample. The current noise was rather high at the edge region. (d) Current-normalized noise PSD versus frequency measured far from the edge (blue circles) and near the edge of graphene (red circles). When the noise spectrum was measured near the edge, the 1/f 2 behavior was observed at a rather lowfrequency condition near or below ∼10 Hz. (e) Sheet resistance map of the SLG sample. (f) Noise source density map of the SLG sample. This result indicates a rather large noise source density at the edge of graphene layers, presumably due to dangling bonds and lattice disordering. 10139
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Figure 4. Noise spectral imaging of double-layer graphene. (a) Schematic diagram showing the NSI measurement on a DLG sample. (b) AFM topography image of the DLG sample. (c) Current image of the DLG sample. The bias voltage of 0.04 V was applied to the sample. (d) Noise source density map of the DLG sample. The averaged values of noise source density at regions marked with labels (i) (on the SLG), (ii) (near the edge of the DLG stack), and (iii) (on the DLG stack) in panel (d) were ∼7.1 × 109, ∼8.2 × 109, and ∼5.6 × 109 cm−2 eV−1, respectively.
electrical currents and noise PSD. For the current measurement, we applied the bias voltage of 0.04 V to the sample through the electrode. Figure 4b,c shows the topography and the current image of the DLG region, respectively. The topography values along the dashed white line in the topography image are also presented in Figure 4b. The result shows that the height of the second layer was ∼0.4 nm, which is close to the reported thickness of a graphene layer. Note that the current measured on the DLG region (dark region) was actually lower than that on the SLG region (bright region). Presumably, it is because the electrode was connected to the SLG regions, and there existed a rather high contact resistance between two graphene layers.47 We also measured the noise PSD map (Figure S5 in the Supporting Information) and utilized it to estimate the neff map (Figure 4d). Here, we applied the bias voltage of 0.04 V on the electrode of the sample, and the noise PSD at 173 Hz was mapped. Note that the edge of the DLG flake also exhibited a high noise source density similar to that of the SLG in Figure 3f. It is also interesting to note that the noise source density of the DLG stack regions appeared ∼0.79 times lower than that on the SLG region. Noise sources in a graphene channel on a SiO2 substrate can exist in the SiO2 as well as in the graphene layer itself.23,47 In particular, the charge traps in the SiO2
substrate can trap or release the charge carriers in the graphene layer, generating significant current noises. Previous study predicted that, in the case of a DLG on a SiO2, the bottom layer in the DLG can screen the SiO2 traps from charge carriers in the top layer, and the effect of the SiO2 traps as noise sources could be reduced.23,47 In this case, the overall effective noise source density in a DLG stack region could appear lower than that in a SLG layer as we observed (Figure 4d). Our method allowed us to estimate this effect quantitatively, which clearly shows the versatility of our strategy.
CONCLUSIONS In summary, we have developed a NSI method for the direct imaging of noise sources and their activities in multiple graphene domains. In this method, a conducting AFM probe made a direct contact with a graphene surface, and the maps of electrical currents and noise PSD were measured on the graphene. Then, the maps were analyzed by a computational method based on a FEM analysis and a differential method based on a network model, enabling the mapping of the sheet resistance and the effective noise source density of graphene layers. Using the NSI method, we found that noise sources of high densities exist near the domain boundary and the edge of graphene, and those noise sources may significantly contribute 10140
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REFERENCES
to the noise characteristics of graphene-based devices. We could also quantitatively study the screening effect of noises in DLG using the NSI method. These results show that our method is a simple but powerful tool to study the electrical noises in graphene. Furthermore, the imaging capability of noise sources should be a significant breakthrough in the basic study of noises and the applications of nanoelectronic devices in general.
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METHODS Graphene Sample Preparation. First, a graphene sheet grown by a chemical vapor deposition method was transferred onto a clean SiO2 substrate (oxide thickness ∼300 nm). After the substrate with acetone and ethanol was rinsed, a Ti/Au (10/30 nm) electrode was fabricated on the graphene channel via thermal evaporation through a shadow mask. Note that we did not use the etching process or lithography methods, which should have helped to keep the graphene surface clean. Noise Measurement. A conducting AFM system (XE-70, Park Systems) was utilized with a conducting AFM probe based on Pt (25Pt300B, Park Systems). After the conducting probe made direct contact with the graphene surface, a bias voltage was applied to the metal electrode of the sample by a function generator (DS345, Stanford Research Systems). During all imaging and measurements in this article, the contact force was maintained as 1 μN via an AFM force feedback circuit in the XE-70. The output current was converted to amplified voltage signals by a low-noise preamplifier (SR570, Stanford Research Systems), and the PSD was measured by a homemade spectrum analyzer. The homemade spectrum analyzer consists of a band-pass filter and a RMS-DC converter. We utilized the band-pass filter included in the preamplifier SR570 to measure the signal within the frequency of interest. We built the RMS-DC converter circuit using an AD737 chip (Analog Devices). Finally, the PSD signals could be obtained by dividing the converted DC signals by the bandwidth of filters.
ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.6b05288. Detailed methods for the calculation of the sheet resistance map and noise source density map (PDF)
AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. ORCID
Duckhyung Cho: 0000-0002-9675-926X Author Contributions
H.L. designed and performed the measurements and noise analysis. D.C. developed the analysis method for the sheet resistance mapping. S.S. and J.K. measured the noise spectra. J.P. and B.H.H. contributed to the sample preparation and Raman analyses. S.H. planned and supervised the project. The manuscript was written through contributions of all authors. Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS This work was supported by the National Research Foundation (NRF) Grant (No. 2013M3A6B2078961). B.H.H. thanks Graphene Research Center at Advanced Institute of Convergence Technology. S.H. also acknowledges support from the NRF Grant (Nos. 2014M3A7B4051591 and 2015M3C1A3002152). 10141
DOI: 10.1021/acsnano.6b05288 ACS Nano 2016, 10, 10135−10142
Article
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