Large-Scale Graphene on Hexagonal-BN Hall Elements: Prediction of

Aug 31, 2016 - A graphene Hall element (GHE) is an optimal system for a magnetic sensor because of its perfect two-dimensional (2-D) structure, high c...
3 downloads 0 Views 4MB Size
Download PDF
Large-Scale Graphene on Hexagonal-BN Hall Elements: Prediction of Sensor Performance without Magnetic Field Min-Kyu Joo,†,‡,# Joonggyu Kim,‡,# Ji-Hoon Park,† Van Luan Nguyen,† Ki Kang Kim,§ Young Hee Lee,*,†,‡ and Dongseok Suh*,‡ †

Center for Integrated Nanostructure Physics (CINAP), Institute for Basic Science (IBS), Suwon 16419, Republic of Korea Department of Energy Science, Sungkyunkwan University, Suwon 16419, Republic of Korea § Department of Energy and Materials Engineering, Dongguk University, Seoul 04620, Republic of Korea ‡

S Supporting Information *

ABSTRACT: A graphene Hall element (GHE) is an optimal system for a magnetic sensor because of its perfect two-dimensional (2-D) structure, high carrier mobility, and widely tunable carrier concentration. Even though several proof-of-concept devices have been proposed, manufacturing them by mechanical exfoliation of 2-D material or electron-beam lithography is of limited feasibility. Here, we demonstrate a high quality GHE array having a graphene on hexagonal-BN (h-BN) heterostructure, fabricated by photolithography and large-area 2-D materials grown by chemical vapor deposition techniques. A superior performance of GHE was achieved with the help of a bottom h-BN layer, and showed a maximum current-normalized sensitivity of 1986 V/AT, a minimum magnetic resolution of 0.5 mG/Hz0.5 at f = 300 Hz, and an effective dynamic range larger than 74 dB. Furthermore, on the basis of a thorough understanding of the shift of charge neutrality point depending on various parameters, an analytical model that predicts the magnetic sensor operation of a GHE from its transconductance data without magnetic field is proposed, simplifying the evaluation of each GHE design. These results demonstrate the feasibility of this highly performing graphene device using large-scale manufacturing-friendly fabrication methods. KEYWORDS: graphene, hexagonal boron nitride, magnetic field sensor, large-area graphene device, graphene Hall element, chemical vapor deposition

W

because of its extremely high mobility, ambipolar operation, and one-atom layer thickness, as well as its low carrier density.6,10−14 These unique and beneficial characteristics enable the graphene Hall element (GHE) to be a high performance magnetic sensor having larger Hall-effect current sensitivity (SI) and smaller minimum magnetic resolution (Bmin) compared with silicon-based magnetic sensors.6,7,10,12,13 In one investigation, the Bmin value was reduced to around 0.5 mG/Hz0.5 at the 3 kHz frequency domain for a GHE, which was encapsulated between exfoliated hexagonal-BN (h-BN) and fabricated by electron-beam lithography (EBL).13 However, these mechanical exfoliation and EBL techniques are only useful for proof-of-concept experiments, and are not feasible for quality-controlled mass manufacturing. Instead, large-area materials synthesized by chemical vapor deposition (CVD) in

ith the increasing use of smart devices, there is an urgent need to extend their capabilities by incorporating chip-based sensors with diverse functions, for example, gyroscope, proximity, and pressure sensors. The Hall-effect magnetic sensor (Hall sensor) is one of them, potentially applicable in the fields of biomedical, electromagnetic, and mechatronic engineering.1−4 Material properties required for a Hall sensor include (i) a thin active channel, (ii) high carrier mobility, and (iii) a narrow band gap, based on its operating principle.3,5−7 While commercial Hall sensors based on silicon-related materials are widely manufactured and used, there have also been many efforts to improve their performance. Active channels consisting of III−V compounds and having two-dimensional (2-D) electron-gas configurations have achieved a thin channel depth and high mobility.2,8−10 However, exploration to find better Hall sensor materials continues to be driven not only for performance but also by economic reasons. Recently, monolayer graphene has been considered as a channel material appropriate for Hall sensor application © 2016 American Chemical Society

Received: July 8, 2016 Accepted: August 31, 2016 Published: August 31, 2016 8803

DOI: 10.1021/acsnano.6b04547 ACS Nano 2016, 10, 8803−8811

Article

www.acsnano.org

Article

ACS Nano

RESULTS AND DISCUSSION Manufacturing-Friendly Design of GHE in Terms of Material and Fabrication. In the device design stage, we focused on two things. First, the GHE devices are composed of large-area graphene and h-BN layers, both of which are prepared by CVD methods instead of mechanical exfoliation. Second, they are fabricated using standard photolithography techniques instead of electron-beam lithography. Figure 2 shows the overall fabrication procedures of the GHE arrays. Initially, a 20 nm-thick h-BN film was synthesized directly on a 4-in. SiO2/Si wafer by plasma-enhanced CVD (PECVD). Then, the full-coverage monolayer graphene grown by CVD on copper foil was transferred onto the h-BN/SiO2/Si substrate.15 After that, symmetric crossbar-shaped GHE channel areas were defined using a standard photolithography process, followed by oxygen-plasma reactive-ion etching. Finally, metal electrodes consisting of a Cr/Au (3/70 nm) bimetal layer were formed through the combined processes of photolithography, thermal evaporation of metals and lift-off. The relevant optical images at each fabrication step are included in Figure 2. Structural Analysis of GHE Using Raman Spectroscopy. Due to its atomically smooth surface and absence of charged impurities, an h-BN layer has been considered as a suitable dielectric substrate for graphene transistors.16 To make a highly performing GHE magnetic sensor, we used a CVDgrown large-area h-BN layer as a substrate for our graphene device although this CVD thin-film may contain some degree of structural defects.17,18 The sample quality of CVD-grown graphene/h-BN heterostructure was evaluated using Raman spectroscopy. Two prominent Raman peaks corresponding to the “G” mode and “2D” mode of monolayer graphene are observed at 1586 cm−1 and 2675 cm−1, respectively in Figure 3a. Since they are almost equal to the intrinsic values of the G (∼1582 cm−1) and 2D (∼2677 cm−1) peak positions,19−21 the bottom h-BN thin-film in our sample also plays a role of optimal substrate for graphene. One small peak located at 2454

combination with conventional photolithography fabrication are preferred for the practical fabrication of large-scale GHE arrays. Here, we demonstrate a CVD-based, photolithographically patterned, highly sensitive GHE array having graphene on a hBN structure. Although the large-area materials and fabrication methods were applied, the relative standard deviation of the field-effect mobility (μFE) was less than ∼10% (see Figure S1 in the Supporting Information, SI). Not only the superior device performance, but also the deep understanding and analysis for the operation principle of this GHE magnetic sensor were studied, which will help the promotion of 2-D materials toward more practical applications in the field of electronic devices. The entire characterization sequences for the GHE device are summarized in Figure 1.

Figure 1. Hall effect magnetic resolution measurement concept. Hall effect and low frequency (LF) noise characteristics of the GHE are combined to estimate the limit of Bmin. VH (= V+ − V−) is the Hall voltage difference obtained from Hall bar probes and SA is the absolute magnetic sensitivity estimated from the slope of Hall measurement. SV is the voltage power spectral density occurring from voltage fluctuations across the Hall bar.

Figure 2. Large area GHE arrays on h-BN heterostructure. Three-dimensional fabrication process schematics of CVD-based and photolithographically patterned GHE arrays on h-BN heterostructure. Representative optical images of the GHE array at each step are shown at the bottom of the figure, where the length (L = 160 μm) and width (W = 50 μm) of the GHE are well-defined by conventional photolithography. Post-thermal annealing was carried out between each step for better adhesion of h-BN and complete removal of residual polymers on the graphene surface. 8804

DOI: 10.1021/acsnano.6b04547 ACS Nano 2016, 10, 8803−8811

Article

ACS Nano

even though they are located nearby. The D peak (red longdashed line) is observed at 1344 cm−1 and might be created during the graphene transfer process onto h-BN thin film. The E2g phonon mode of polycrystalline h-BN (orange long-dashed line) appears at 1377 cm−1, agreeing with the range of reported values.23−26 The remaining peak at 1457 cm−1 can be attributed to the third-order transverse optical mode of a silicon substrate (olive long-dashed line).27,28 From a pre- and postannealing comparison, no evidence is observed for a blue-shift of graphene’s G and 2D peaks. All such results indicate that a hBN thin film below monolayer graphene plays an important role in preventing unwanted hole-doping by the silicon oxide substrate (see Figure S2 in the SI).29 Electrical and Magnetic Sensor Properties of GHE. Figure 4a presents the dependence of the GHE drain current on the back-gate voltage (ID − VBG) at several drain voltages (VD = 10 mV, 100 mV, 1 V, and 10 V). These ID − VBG transfer curves exhibit the V-shaped ambipolar behavior typically observed in graphene field-effect transistors. The negligible hysteresis during a VBG sweep indicates that h-BN enables to provide an inert and clean surface to the graphene, as discussed

Figure 3. Raman spectroscopy of GHE. Raman spectra of monolayer graphene on a h-BN thin film heterostructure in the (a) whole and (b) magnified low-frequency regions.

cm−1 corresponds to the G* band associated with a double resonance Raman process.19,22 Additional analysis of the disorder-related “D” peak is shown in Figure 3b. The Raman spectrum (violet circles) below 1500 cm−1 is decomposed into individual Lorentzian lines (longdashed lines) due to the known peak positions of the D mode of monolayer graphene and the E2g phonon mode of h-BN,

Figure 4. Hall effect sensitivity of GHE. (a) Drain current (ID) curves as a function of back-gate bias (VBG) as a function of VD. (b) Relevant energy band diagram in GHE to explain the spatial hole-doping effect on VCNP for a given VBG condition. (c) Linear Hall effect characteristics of GHE for different ID values (at room temperature). (d) Experimentally obtained Hall effect sensitivity (SI) characteristics for various ID values, and (e) its contour plot as a function of VBG and ID. (f) Analytically predicted drain bias dependence of Hall effect sensitivity. 8805

DOI: 10.1021/acsnano.6b04547 ACS Nano 2016, 10, 8803−8811

Article

ACS Nano in the previous Raman analysis section.29 The mean value of the field-effect mobility (μFE) ranges from 1700 cm2/(V s) to 3500 cm2/(V s), depending on the GHE array. It is worth noting that the voltage at charge neutrality point (VCNP) corresponding to the minimum channel conductance moves substantially as VD increases. This VCNP shift related to VD can be understood in terms of hole-doping effects in the region near the drain electrode.30,31 For the clear description about this hole-doping effect, a simplified energy diagram for the large VD bias condition is shown in Figure 4b. When the back-gate voltage induces an overall n-doping in the graphene channel, the large VD bias pushes the Fermi level down to make a local p-doping region near the drain electrode. Such a carrier-type conversion along the channel originates from graphene’s intrinsic Dirac-cone band structure.32,33 The movement of the VCNP with increasing VD bias results from the interaction between the spatially inhomogeneous carrier concentration and the heated graphene channel due to the deficiency of charge carriers at the carriertype conversion region. In particular, the heating effect will limit the ranges of device-control parameters, which will be discussed in the last section of this article. The representative linear responses of Hall voltage (VH) as a function of magnetic field (B) between −5 kG and 5 kG at the fixed VBG = 2.5 V with various ID conditions are plotted in Figure 4c. The absolute Hall sensitivity SA (= ∂VH/∂B) can be obtained from the linear VH slope at specific ID and VBG bias conditions, where the current-normalized Hall sensitivity (SI = SA/ID) is equivalent to the conventional Hall effect current sensitivity. Therefore, under the assumption that the magnitude of the hole mobility is similar to that of the electron;3,5,12,14 n(VBG , VCNP) ⎞ ⎫ SA r α⎛ ⎟⎪ ≈− H ⎜ ID e ⎝ n(VBG , VCNP)2 + n02 ⎠ ⎪ ⎬ ⎪ COX n(VBG , VCNP) ≈ (VBG − VCNP) ⎪ ⎭ e

Prediction of Magnetic Sensor Performance from Electrical Properties of GHE. Because the conventional twoband model given in eq 1 does not describe the experimentally observed shift of the maximum SI as a function of ID, we developed an analytical model that incorporates the transconductance (gm = ∂ID/∂VBG) of the GHE. In fact, SI is equivalent to the Hall coefficient, i.e., SI is inversely proportional to the carrier concentration n(VBG,VCNP) in principle, which can be alternatively described using the voltage difference (VBG − VCNP) and the capacitance COX as expressed in eq 1. Additionally, the empirically determined gm can be considered to correct for possible errors originating from the VCNP estimation with respect to VD. Then SI can be expressed in the form of eq 2, ⎛ r α ⎞⎛ ∂V ⎞⎛ 1 ⎞ S I = − ⎜ H ⎟⎜ H ⎟⎜ ⎟ ⎝ e ⎠⎝ ∂B ⎠⎝ ID ⎠ ⎞⎛ 1 ⎞ eID ⎛ r α ⎞⎛ ≈ − ⎜ H ⎟⎜ ⎟⎜ ⎟ ⎝ e ⎠⎝ COX(VBG − VCNP) ⎠⎝ ID ⎠ ⎛ r α ⎞⎛ ∂I ⎞ g = −⎜ H ⎟⎜ D ⎟ ∝ −rHα m IDCOX ⎝ IDCOX ⎠⎝ ∂VBG ⎠

(2)

It is very interesting that the final form of eq 2 indicates that the Hall sensitivity SI can be expressed using parameters such as gm and ID, which can be experimentally obtained without magnetic field. In other words, it implies that the magnetic sensor performance of GHE can be predicted from the normal (i.e., no B field) transconductance data, with no actual experiment under magnetic field. To check the validity of the above arguments, we plotted simulation curves in Figure 4f by combining the experimental transconductance data in Figure 4a and the analytical model in eq 2. When these simulated SI curves (rHα used as a fitting parameter has been set to the numerical value 3) are compared to the SI curves in Figure 4d measured under magnetic fields, the shape and the trend of SI with respect to ID in both graphs are quite similar. Therefore, it confirms that the behavior of SI as a function of VD, and the value of VBG corresponding to the maximum of SI, can be fitted well using this approach. Furthermore, the electrical input parameters ID (or VD) and VBG giving the maximum SI can be predicted well, without a full parameter mapping of the response under magnetic field conditions. This can greatly reduce the effort to find optimal bias conditions for GHE performance. As a result of the direct relation between SI and the transconductance data via eq 2, several features of SI observed in Figure 4d can be intuitively understood in relation to the ID − VBG curves in Figure 4a. For example, no significant variation of SI up to ID ≈ 200 μA is attributed to the small variation of VCNP seen in Figure 4a. The degradation of the maximum SI magnitude at large VD (or ID) in Figure 4d can be also explained in terms of the VCNP shift as discussed in Figure 4b, where local hole-doping near the drain electrode and inhomogeneous thermal heating in the highly resistive region of the GHE degrades the sensor performance.10,30 (See Figure S3 in the SI for the additional 2-D contour plot data of SI obtained from different GHE devices using eq 2). From this contour plot, the optimal input bias conditions as well as the performance limitations of a GHE magnetic sensor can be actually predicted without magnetic field. Theoretically predicted VBG locations for the SI maxima as a function of ID

SI =

(1)

where rH, α, COX, e, n0, and n(VBG,VCNP) denote the Hall factor, the geometrical correction factor, the oxide capacitance, the elementary unit charge, the residual carrier concentration, and the carrier concentration as a function of VBG and VCNP, respectively. By taking the first derivative of eq 1, it can be easily calculated that the maximum magnitude of SI is rHα/ (2n0e) when n(VBG,VCNP) equals n0,12 which is independent of ID by definition. However, it should be noted that the position and magnitude of maximum SI changes as a function of ID in the experimental data, indicating a need for revision of the above model. Figure 4d shows the VBG-dependence of the Hall effect sensitivity SI for selected ID values, while Figure 4e displays the variation of SI as a two-dimensional contour plot, as a function of ID (from 10 μA to 1 mA with 10 μA steps) and VBG (from −30 to 30 V with 0.1 V steps). A slightly asymmetric shape of SI related to the type of majority charge carriers is observed, and can be ascribed to the difference between field-effect mobility of electrons and holes, as well as to the scattering mechanisms involved in the carrier transport through graphene. In Figure 4e, we can clearly notice that the maximum value of SI is strongly dependent on the ID and VBG bias conditions. As the driving current ID of the Hall sensor increases, the maximum value of SI decreases gradually and VCNP is positively shifted. 8806

DOI: 10.1021/acsnano.6b04547 ACS Nano 2016, 10, 8803−8811

Article

ACS Nano

where SV is the voltage power spectral density), the lowfrequency (LF) noise measurement (with a frequency range 5 Hz−1 kHz) was carried out to obtain SV as a function of ID and VG in Figure 6. Initially, we confirmed that the LF noise characteristics are independent of the ID direction due to the symmetrical cross bar shape of the GHE device. The representative SV curves are presented in Figure 6a for the hole- and electron-dominant regimes, which are controlled by the VBG. Both curves show a general 1/f trend at low frequencies and eventually saturate to thermal Nyquist noise level at higher frequencies as a result of random thermal motion of carriers in graphene together with uniformly distributed traps around the interface.34−36 Since this thermal noise can be regarded as the minimum LF noise floor, the equivalent resistance value can be extracted from the definition of voltage power spectrum density (SV = 4kBTR, where kB, T, and R are the Boltzmann constant, the absolute temperature, and the equivalent resistance value, respectively).36 The calculated thermal noise was approximately 1−2 × 10−16 V2/Hz, which is equivalent to the resistance range of 6−12 kΩ. Because such a result matches well with the resistance values obtained in Figure 4a, it confirms the consistency of our noise experiment results. Furthermore, the small magnitude of LF noise can be ascribed to the effect of graphene/h-BN heterostructure. When we consider the VD normalized SV curves (= SV/VD2) with respect to different ID (see Figure S4 in the SI), it turns out that the LF noise levels are roughly same in both carrier types, and the dependence of

showed good agreement with the experimentally obtained data under magnetic field as shown in Figure 5. And small deviations

Figure 5. Comparison between analytical model and experiment. Direct comparison between theoretically predicted VBG values that correspond to the maximum value of SI and values obtained from the magnetic experiments, as a function of ID.

can be attributed to contact-resistance effects, neglected scattering mechanisms, and different geometrical correction factors between electron and hole carriers. The Minimum Magnetic Resolution of GHE. For the estimation of a minimum magnetic resolution (Bmin = SV 0.5/SA,

Figure 6. Limit of magnetic resolution. (a) The voltage power spectrum of hole- and electron-dominant regimes (left and right panels, respectively) with respect to different ID. (b) Experimentally obtained SA contour plot. (c) The absolute value of Bmin of hole- and electrondominant regimes (panels as above) with respect to different ID. (d) Experimentally obtained Bmin contour plot (the red dashed area) at f = 300 Hz. For the comparison, the 2-D contour plot (back ground panel) is overlapped behind Bmin graph. 8807

DOI: 10.1021/acsnano.6b04547 ACS Nano 2016, 10, 8803−8811

Article

ACS Nano Table 1. A Performance Comparison in GHEs graphene

type

SI (V/AT)

μ (cm2/(V s))

lithography

Bmin (mG/Hz0.5) at 300 Hz

ref 42 ref 41 ref 7 ref 10 ref 13 this work for holes this work for electrons best GHE

CVD epitaxial CVD CVD exfoliated

1200 1021 800 2093 4100 1447 1535 1986

2500 3000 5100 6900 NA 1600−1700 1900−2100 3500−3700

photolithography EBL EBL EBL EBL

NA ∼66 (calculated) ∼20 ∼7 ∼0.5 0.5−30 1−90 NA

CVD

photolithography

Figure 7. Dynamic range measurement of GHE. (a) Schematic illustration for the effective dynamic range measurement setup. (b) Characteristic curve for the small AC magnetic field (BAC) detection under a large DC magnetic field (BDC) by the measurement of AC Hall voltage (VH_AC) signal. (c) BAC dependence of VH_AC at different VBG with the condition of ID = 1 mA, f = 10 kHz, and BDC = 0.5 T.

a function of ID for both electron- and hole-dominant regimes in Figure 6c and plotted again in the form of two-dimensional graph at f = 300 Hz in Figure 6d. Even though the smallest SV is achieved at VBG ≈ VCNP, the abrupt reduction of SA (see the background SA contour plot in Figure 6d), makes Bmin increased rapidly near VD when ID ≤ 200 μA. However, when the driving current ID exceeds 200 μA, the Bmin value ranges from 0.5−30 mG/Hz0.5 irrespective of VBG (see the red dashed area and values in Figure 6d), which is comparable to the best reported value using the EBL technique.13 Various performance parameters of Hall elements in literature are listed in Table 1.7,10,13,41,42 This confirms the superiority of our GHE device in terms of performance compared with Si and III/V semiconductor-based Hall elements and in the aspects of materials and fabrication methods compared with other reported GHEs. Dynamic Range of GHE. As a magnetic field sensor, a dynamic range, defined as the range of minimum detectable ef fective magnetic f ield in the presence of a strong static B f ield, is one of the important parameters characterizing the sensor performance, especially in the application of a biomedical signal

the LF noise amplitude on VBG shows a typical trend with a minimum at VCNP as reported previously.37,38 In addition to LF noise properties, the trend of SA (rather than SI) with respect to ID and VBG should be examined to determine the bias condition of this GHE device for the larger SA and the better Bmin values. The blue and the red portions in Figures 6b corresponds to the maximum SA operation range of the GHE device with hole- and electron-majority carriers, respectively. Except for the region near VCNP where SA is close to zero, the entire operating region in terms of carrier concentration, in other words, VBG becomes broader as ID increases. In an alternative approach, the optimal bias ranges can also be deduced by the analytical method proposed above using eq 2, where the contour plot of SA with the relationship SA = −rHαgm/COX and gm ≈ ID /(VBG − VCNP) from the carrier drift model gives roughly the similar tendency (see Figure S5 in the SI for details and limitation of this analytical method).35,36,39,40 After SA and SV values are determined, the frequency dependence of the absolute Bmin (= SV0.5/SA) can be obtained as 8808

DOI: 10.1021/acsnano.6b04547 ACS Nano 2016, 10, 8803−8811

Article

ACS Nano

Figure 8. Thermal heating effects on GHE. Imaged temperature contour of GHE for ID = 1 mA (left panel), 3 mA, 5 mA, and 7 mA (right panel) at VBG = 200 V, respectively.

CONCLUSION We have made a centimeter-scale magnetic-field sensor chip having GHE arrays to utilize graphene’s advantageous features as a Hall sensor, such as its complete two-dimensional properties, high carrier mobility, and largely controllable carrier density. For the development to practical manufacturing level, CVD-synthesized two-dimensional materials (graphene and hBN) and photolithography-based fabrication processes were employed instead of mechanical exfoliation and electron-beam lithography. Even in such situations, the best results we obtained (i.e., 1986 V/AT for the current-normalized sensitivity, 0.5 mG/Hz0.5 for the minimum magnetic resolution at f = 300 Hz, and a minimum dynamic range of ∼74 dB at B = 0.5 T and f = 10 kHz) are mostly equivalent to or superior than the values in the literature. A suggested analytical model predicting magnetic sensor performance of GHE without the actual measurement under magnetic fields will help us to determine the sensor parameters for an optimized operational condition. The combination of CVD-grown two-dimensional materials with photolithography will definitely promote the advance of this prototype GHE to the practical manufacturing level.

detection. Figure 7a shows the schematics of the experimental setup for the dynamic range measurement (see Experimental Methods and Figure S6 in the SI for details). With the help of a coil-shaped electromagnet installed on top of the GHE device, small amplitude AC magnetic field (BAC) can be applied to the GHE in addition to the large static DC magnetic field (BDC) simultaneously. Then AC Hall voltage signal (VH_AC = V + − V−) can be extracted using the conventional lock-in method. Figures 7b represents the conceptual dynamic range characteristic curves with the linear relationship between BAC and VH_AC at a finite BDC condition. After the calibration of BAC as a function of external bias applied to the coil (see Figures S6a and S6b in the SI), a dynamic range measurement of GHE was carried out with ID = 1 mA and f = 10 kHz under BDC = 0.5 T as displayed in Figure 7c, which is plotted in the same way as in inset of Figure 7b. In the tested GHE sample, the larger VH_AC value was obtained for the larger VBG because the maximum gm was found at around VBG ∼ 75 V (see Figure S6c in the SI). For comparison, the overall linear relationship between VH_AC and BAC in the absence of BDC and the magnified graph at low BAC are given in Figures S6d and S6e, respectively (see also Figure S6f in the SI for the full range data of Figure 7c). As the BAC decreases, the linearity between the Hall voltage and the magnetic field is maintained down to the level of BAC = 1 G irrespective of VBG. This gives the minimum effective dynamic range of ∼74 dB at B = 0.5 T, which is equivalent to the case of ultrasensitive CMOS magnetic sensor.43 The feasibility of GHE as a practical magnetic sensor is also demonstrated in combination with a programmable microcontroller board, “Arduino”. (See Figure S7 in the SI and the Supporting Video S1). Thermal Heating Effects on GHE. To investigate the effect of Joule heating, the temperature distribution images of the GHE device operated in the heavily electron-doped region are presented in Figure 8 with ID ranging from 1 to 7 mA at VBG = 200 V. As ID increases, the hot spot corresponding to the most resistive area in the device gradually appears inside the channel and moves along the direction from the source to the drain electrode. From the fact that a large ID bias varies the position of CNP owing to the spatial hole doping near the drain electrode, an inhomogeneous heating occurs significantly at the CNP because of the ambipolar nature of graphene, which is observed as a hot spot in Figure 8. Accordingly, the shift of the hot spot can be interpreted as a direct evidence for hole-doping near the drain electrode. This induces a large variation of SI and the LF noise characteristics of the device, which results in the performance degradation of GHE.

EXPERIMENTAL METHODS Device Fabrication. A 20 nm thick polycrystalline h-BN film was synthesized directly on 4-in. SiO2/Si wafer by plasma-enhanced CVD.44 The full-coverage high-quality CVD-grown monolayer graphene on copper foil (3 × 9 cm2) was transferred onto the hBN/SiO2/Si substrate by the well-developed bubbling transfer technique.15 Symmetric cross-shaped GHEs having different active channel areas (L × W) were defined ranging from 60 × 12 μm2 to 240 × 120 μm2 through standard photolithography and oxygen-plasma reactive ion etching (AFS-R4T, ALL FOR SYSTEM). Electrodes consisting of Cr/Au metal layers (3/70 nm) were also patterned using conventional photolithography processes, followed by thermal evaporation of bilayer metals and established lift-off sequences. The post-thermal annealing process was carried out at each step for 2 h under a flow of Ar/H2 = 500/100 sccm at T = 350 °C for the adhesion of h-BN and the complete removal of residual polymers on the surface of graphene. The geometrical factors of channel length, width, and the thickness of monolayer graphene on h-BN heterostructure were confirmed by optical microscopy (Axio imager 2, CARL ZEISS) and atomic force microscopy (SPA 400, SEIKO). Optical, Electrical, and Thermal Characterizations. Raman spectroscopy (XperRam 200, Nano Base) was performed to characterize the quality of monolayer graphene on the h-BN doublelayer structure. Electrical transport experiments, including the Hall effect measurements, were carried out at room temperature under high vacuum using a cryostat (PPMS, Quantum Design Inc.) and 8809

DOI: 10.1021/acsnano.6b04547 ACS Nano 2016, 10, 8803−8811

Article

ACS Nano commercial semiconductor characterization systems (4200-SCS, Keithley Instruments and B1500A, Keysight Technologies). Lowfrequency noise characteristics were measured using a customized LF noise measurement system in a metal shielding box, consisting of a battery container, a low noise voltage amplifier (SR5113, Signal Recovery), and a data acquisition system (DAQ-4431, National Instruments).45 Dynamic range measurement data was obtained by commercial semiconductor analyzer (B1500A, Agilent) and lock-in amplifier (SR830, Stanford research) in PPMS. The spatial temperature image of a GHE during its operation was obtained from an infrared thermal-imaging microscope system (InfraScope III, Quantum Focus Instruments). The static DC bias was supplied by a conventional semiconductor analyzer (Agilent 4156C, Agilent Technologies) at ambient conditions inside a metal shielding box.

(6) Xu, H.; Zhang, Z.; Shi, R.; Liu, H.; Wang, Z.; Wang, S.; Peng, L.M. Batch-Fabricated High-Performance Graphene Hall Elements. Sci. Rep. 2013, 3, 1207. (7) Xu, H.; Huang, L.; Zhang, Z.; Chen, B.; Zhong, H.; Peng, L.-M. Flicker Noise and Magnetic Resolution of Graphene Hall Sensors at Low Frequency. Appl. Phys. Lett. 2013, 103, 112405. (8) Kunets, V. P.; Black, W. T.; Mazur, Y. I.; Guzun, D.; Salamo, G. J.; Goel, N.; Mishima, T. D.; Deen, D. A.; Murphy, S. Q.; Santos, M. B. Highly Sensitive Micro-Hall Devices Based on Al0.12In0.88Sb/InSb Heterostructures. J. Appl. Phys. 2005, 98, 014506. (9) Bando, M.; Ohashi, T.; Dede, M.; Akram, R.; Oral, A.; Park, S. Y.; Shibasaki, I.; Handa, H.; Sandhu, A. High Sensitivity and Multifunctional Micro-Hall Sensors Fabricated Using InAlSb/InAsSb/InAlSb Heterostructures. J. Appl. Phys. 2009, 105, 07E909. (10) Huang, L.; Zhang, Z.; Chen, B.; Ma, X.; Zhong, H.; Peng, L.-M. Ultra-Sensitive Graphene Hall Elements. Appl. Phys. Lett. 2014, 104, 183106. (11) Huang, L.; Xu, H.; Zhang, Z.; Chen, C.; Jiang, J.; Ma, X.; Chen, B.; Li, Z.; Zhong, H.; Peng, L.-M. Graphene/Si CMOS Hybrid Hall Integrated Circuits. Sci. Rep. 2014, 4, 5548. (12) Chen, B.; Huang, L.; Ma, X.; Dong, L.; Zhang, Z.; Peng, L.-M. Exploration of Sensitivity Limit for Graphene Magnetic Sensors. Carbon 2015, 94, 585−589. (13) Dauber, J.; Sagade, A. A.; Oellers, M.; Watanabe, K.; Taniguchi, T.; Neumaier, D.; Stampfer, C. Ultra-Sensitive Hall Sensors Based on Graphene Encapsulated in Hexagonal Boron Nitride. Appl. Phys. Lett. 2015, 106, 193501. (14) Manzin, A.; Simonetto, E.; Amato, G.; Panchal, V.; Kazakova, O. Modeling of Graphene Hall Effect Sensors for Microbead Detection. J. Appl. Phys. 2015, 117, 17B732. (15) Nguyen, V. L.; Shin, B. G.; Duong, D. L.; Kim, S. T.; Perello, D.; Lim, Y. J.; Yuan, Q. H.; Ding, F.; Jeong, H. Y.; Shin, H. S.; Lee, S. M.; Chae, S. H.; Vu, Q. A.; Lee, S. H.; Lee, Y. H. Seamless Stitching of Graphene Domains on Polished Copper (111) Foil. Adv. Mater. 2015, 27, 1376−1382. (16) Dean, C. R.; Young, A. F.; Meric, I.; Lee, C.; Wang, L.; Sorgenfrei, S.; Watanabe, K.; Taniguchi, T.; Kim, P.; Shepard, K. L.; Hone, J. Boron Nitride Substrates for High-Quality Graphene Electronics. Nat. Nanotechnol. 2010, 5, 722−726. (17) Lu, G.; Wu, T.; Yuan, Q.; Wang, H.; Wang, H.; Ding, F.; Xie, X.; Jiang, M. Synthesis of Large Single-Crystal Hexagonal Boron Nitride Grains on Cu−Ni Alloy. Nat. Commun. 2015, 6, 6160. (18) Bresnehan, M. S.; Hollander, M. J.; Wetherington, M.; LaBella, M.; Trumbull, K. A.; Cavalero, R.; Snyder, D. W.; Robinson, J. A. Integration of Hexagonal Boron Nitride with Quasi-freestanding Epitaxial Graphene: Toward Wafer-Scale, High-Performance Devices. ACS Nano 2012, 6, 5234−5241. (19) Malard, L. M.; Pimenta, M. A.; Dresselhaus, G.; Dresselhaus, M. S. Raman Spectroscopy in Graphene. Phys. Rep. 2009, 473, 51−87. (20) Ahn, G.; Kim, H. R.; Ko, T. Y.; Choi, K.; Watanabe, K.; Taniguchi, T.; Hong, B. H.; Ryu, S. Optical Probing of the Electronic Interaction between Graphene and Hexagonal Boron Nitride. ACS Nano 2013, 7, 1533−1541. (21) Lee, J. E.; Ahn, G.; Shim, J.; Lee, Y. S.; Ryu, S. Optical Separation of Mechanical Strain from Charge Doping in Graphene. Nat. Commun. 2012, 3, 1024. (22) Gupta, A.; Chen, G.; Joshi, P.; Tadigadapa, S.; Eklund. Raman Scattering from High-Frequency Phonons in Supported n-Graphene Layer Films. Nano Lett. 2006, 6, 2667−2673. (23) Gorbachev, R. V.; Riaz, I.; Nair, R. R.; Jalil, R.; Britnell, L.; Belle, B. D.; Hill, E. W.; Novoselov, K. S.; Watanabe, K.; Taniguchi, T.; Geim, A. K.; Blake, P. Hunting for Monolayer Boron Nitride: Optical and Raman Signatures. Small 2011, 7, 465−468. (24) Hoffman, D. M.; Doll, G. L.; Eklund, P. C. Optical Properties of Pyrolytic Boron Nitride in the Energy Range 0.05 - 10 eV. Phys. Rev. B: Condens. Matter Mater. Phys. 1984, 30, 6051−6056. (25) Yang, W.; Chen, G.; Shi, Z.; Liu, C.-C.; Zhang, L.; Xie, G.; Cheng, M.; Wang, D.; Yang, R.; Shi, D.; Watanabe, K.; Taniguchi, T.; Yao, Y.; Zhang, Y.; Zhang, G. Epitaxial Growth of Single-Domain

ASSOCIATED CONTENT S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.6b04547. (1) Relative standard deviation of the field-effect mobility of GHE samples; (2) Post annealing effect on Raman spectroscopy of a GHE; (3) Calculated Hall effect current sensitivity (SI) of GHE based on analytical model; (4) Voltage power spectrum (SV) normalized by drain voltage; (5) Numerically calculated SA; (6) Limitation of Bmin of GHE based on low frequency noise model; (7) Dynamic range measurement of GHE; (8) Feasibility of GHE as a magnetic sensor application using the Arduino (PDF) Video S1 (ZIP)

AUTHOR INFORMATION Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Author Contributions #

These authors (M.K.J. and J.K.) contributed equally to this work. Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work was supported by the Institute for Basic Science (IBS-R011-D1) (Y.H.L.) and by the National Research Foundation of Korea (NRF-2013R1A1A1076063) (D.S.), funded by the Ministry of Science, ICT & Future Planning, Republic of Korea. REFERENCES (1) Pankhurst, Q. A.; Connolly, J.; Jones, S. K.; Dobson, J. Applications of Magnetic Nanoparticles in Biomedicine. J. Phys. D: Appl. Phys. 2003, 36, R167−R181. (2) Kazakova, O.; Gallop, J. C.; Cox, D. C.; Brown, E.; Cuenat, A.; Suzuki, K. Optimization of 2DEG InAs/GaSb Hall Sensors for Single Particle Detection. IEEE Trans. Magn. 2008, 44, 4480−4483. (3) Popovic, R. S. Hall Effect Devices; CRC Press: Boca Raton, FL, 2003. (4) Thiaville, A.; Belliard, L.; Majer, D.; Zeldov, E.; Miltat, J. Measurement of the Stray Field Emanating from Magnetic Force Microscope Tips by Hall Effect Microsensors. J. Appl. Phys. 1997, 82, 3182−3191. (5) Baltes, H. P.; Popovic, R. S. Integrated Semiconductor Magnetic Field Sensors. Proc. IEEE 1986, 74, 1107−1132. 8810

DOI: 10.1021/acsnano.6b04547 ACS Nano 2016, 10, 8803−8811

Article

ACS Nano Graphene on Hexagonal Boron Nitride. Nat. Mater. 2013, 12, 792− 797. (26) Song, Y.; Zhang, C.; Li, B.; Ding, G.; Jiang, D.; Wang, H.; Xie, X. Van der Waals Epitaxy and Characterization of Hexagonal Boron Nitride Nanosheets on Graphene. Nanoscale Res. Lett. 2014, 9, 367. (27) Han, G. H.; Rodríguez-Manzo, J. A.; Lee, C.-W.; Kybert, N. J.; Lerner, M. B.; Qi, Z. J.; Dattoli, E. N.; Rappe, A. M.; Drndic, M.; Johnson, A. T. C. Continuous Growth of Hexagonal Graphene and Boron Nitride In-Plane Heterostructures by Atmospheric Pressure Chemical Vapor Deposition. ACS Nano 2013, 7, 10129−10138. (28) Spizzirri, P.; Fang, J.-H.; Rubanov, S.; Gauja, E.; Prawer, S. Nano-Raman Spectroscopy of Silicon Surfaces. arXiv preprint; arXiv:1002.2692, 2010. (29) Pirkle, A.; Chan, J.; Venugopal, A.; Hinojos, D.; Magnuson, C. W.; McDonnell, S.; Colombo, L.; Vogel, E. M.; Ruoff, R. S.; Wallace, R. M. The Effect of Chemical Residues on the Physical and Electrical Properties of Chemical Vapor Deposited Graphene Transferred to SiO2. Appl. Phys. Lett. 2011, 99, 122108. (30) Bae, M.-H.; Ong, Z.-Y.; Estrada, D.; Pop, E. Imaging, Simulation, and Electrostatic Control of Power Dissipation in Graphene Devices. Nano Lett. 2010, 10, 4787−4793. (31) LeeEduardo, J. H.; Balasubramanian, K.; Weitz, R. T.; Burghard, M.; Kern, K. Contact and Edge Effects in Graphene Devices. Nat. Nanotechnol. 2008, 3, 486−490. (32) Geim, A. K.; Novoselov, K. S. The Rise of Graphene. Nat. Mater. 2007, 6, 183−191. (33) Das Sarma, S.; Adam, S.; Hwang, E. H.; Rossi, E. Electronic Transport in Two-Dimensional Graphene. Rev. Mod. Phys. 2011, 83, 407−470. (34) Ghibaudo, G.; Roux, O.; Nguyen-Duc, C.; Balestra, F.; Brini, J. Improved Analysis of Low Frequency Noise in Field-Effect MOS Transistors. Phys. Status Solidi A 1991, 124, 571−581. (35) Schroder, D. K. Semiconductor Material and Device Characterization; John Wiley & Sons: New York, 2006. (36) Von Haartman, M.; Ö stling, M. Low-Frequency Noise in Advanced MOS Devices; Springer: Berlin, 2007. (37) Kaverzin, A. A.; Mayorov, A. S.; Shytov, A.; Horsell, D. W. Impurities as a Source of 1/f Noise in Graphene. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 85, 075435. (38) Balandin, A. A. Low-Frequency 1/f Noise in Graphene Devices. Nat. Nanotechnol. 2013, 8, 549−555. (39) Habibpour, O.; Vukusic, J.; Stake, J. A Large-Signal Graphene FET Model. IEEE Trans. Electron Devices 2012, 59, 968−975. (40) Brews, J. R. A Charge-Sheet Model of the MOSFET. Solid-State Electron. 1978, 21, 345−355. (41) Panchal, V.; Cedergren, K.; Yakimova, R.; Tzalenchuk, A.; Kubatkin, S.; Kazakova, O. Small Epitaxial Graphene Devices for Magnetosensing Applications. J. Appl. Phys. 2012, 111, 07E509. (42) Shi, R.; Xu, H.; Chen, B.; Zhang, Z.; Peng, L.-M. Scalable Fabrication of Graphene Devices through Photolithography. Appl. Phys. Lett. 2013, 102, 113102. (43) Wang, H.; Kosai, S.; Sideris, C.; Hajimiri, A. In An Ultrasensitive CMOS Magnetic Biosensor Array with Correlated Double Counting Noise Suppression, Microwave Symposium Digest (MTT), 2010 IEEE MTTS International, 23−28 May 2010; 2010; pp 616−619. (44) Park, J.-H.; Park, J. C.; Yun, S. J.; Kim, H.; Luong, D. H.; Kim, S. M.; Choi, S. H.; Yang, W.; Kong, J.; Kim, K. K.; Lee, Y. H. Large-Area Monolayer Hexagonal Boron Nitride on Pt Foil. ACS Nano 2014, 8, 8520−8528. (45) Joo, M.-K.; Kang, P.; Kim, Y.; Kim, G.-T.; Kim, S. A Dual Analyzer for Real-Time Impedance and Noise Spectroscopy of Nanoscale Devices. Rev. Sci. Instrum. 2011, 82, 034702.

8811

DOI: 10.1021/acsnano.6b04547 ACS Nano 2016, 10, 8803−8811