We have investigated low-frequency 1/f noise in the boron nitride–graphene–boron nitride heterostructure field-effect transistors on Si/SiO2 substrates (f is a frequency). The device channel was implemented with a single layer graphene encased between two layers of hexagonal boron nitride. The transistors had the charge carrier mobility in the range from ∼30 000 to ∼36 000 cm2/Vs at room temperature. It was established that the noise spectral density normalized to the channel area in such devices can be suppressed to ∼5 × 10−9 μm2 Hz−1, which is a factor of ×5 – ×10 lower than that in non-encapsulated graphene devices on Si/SiO2. The physical mechanism of noise suppression was attributed to screening of the charge carriers in the channel from traps in SiO2 gate dielectric and surface defects. The obtained results are important for the electronic and optoelectronic applications of graphene.

The most realistic of the proposed electronic applications of graphene are those that do not seriously suffer from the absence of an energy bandgap but rely mostly on graphene's high electron mobility, thermal conductivity, saturation velocity, and a possibility of tuning the charge carrier concentration over a wide range.1,2 These applications are in analog electronics,3–5 high-frequency graphene devices for communications,6,7 and terahertz plasmonic devices,8,9 which benefit from graphene's excellent electron mobility and saturation velocity, as well as in chemical and biological sensing enabled by the ultimately high surface-to-volume ratio and the precise control of the carrier concentration.10–13 For all these applications, the low-frequency electronic 1/f noise is a crucial performance metric (here f is the frequency). The low-frequency noise, usually found at frequencies below 100 kHz, limits the sensitivity and selectivity of all the sensors that rely on an electrical response. It is also responsible for the dominant contribution to the phase noise of the communication systems even when they operate at much higher carrier frequency.14–16 From the fundamental physics point of view, graphene, as a truly two-dimensional material system, presents an interesting testing ground for theories describing the origin and mechanisms of 1/f noise.17–19 

Owing to the importance of the subject, there have been numerous reports on 1/f noise in graphene devices.17–30 Despite some data scatter due to unavoidable differences in graphene and device quality, most of the studies agree on the following characteristics of low-frequency noise in graphene. The low-frequency noise spectral density, SI, in graphene devices is proportional to I2 (here I is the drain–source current). The latter implies that the electrical current does not drive the fluctuations but merely makes them visible as in other homogeneous conductors.31 Although both the graphene layer itself and metal contacts contribute to the 1/f noise, the dominant contribution mostly comes from the graphene channel itself. The results obtained by different groups for micrometer size graphene devices on Si/SiO2 substrates put the current normalized spectral density SI/I2 in the range of 10−9–10−7 Hz−1 at f = 10 Hz.17 A more informative characteristic of 1/f noise level in two-dimensional (2D) materials is the noise spectral density normalized to the device channel area, which we denote as parameter β = (SI/I2)(W×L), where W is the channel width and L is the channel length. Independent studies established that β parameter is in the range from ∼10−8 to 10−7 μm2 Hz−1 for micrometer scale graphene devices on Si/SiO2 substrate. Another important finding reported by several groups17,19,28–30 was that 1/f noise in graphene does not follow the McWhorter model32 conventionally used for description of noise in Si complementary metal-oxide-semiconductor (CMOS) transistors and field-effect transistors (FETs) made of other conventional semiconductors.15 

Different mechanism of noise in graphene calls for investigation of the noise reduction techniques that can be effective for the specific material system. In this letter, we report on the low-frequency noise in the hexagonal boron nitride–graphene–boron nitride (h-BN-G-h-BN) heterostructure field-effect transistors (HFETs) on Si/SiO2 substrates. The mobility in back- and top-gated graphene devices on Si/SiO2 substrates used for noise studies previously was in the range from 1500 to 7000 cm2/V s at room temperature (RT). In our HFETs, graphene channel is screened from defects by the hexagonal BN cap and barrier layers. The latter resulted in RT mobility in the back-gated graphene HFETs in the range from ∼30 000 to 36 000 cm2/Vs and allowed us to study the low-frequency noise in the supported graphene devices operating in the near-ballistic transport regime.33 

The specific structure of h-BN-G-h-BN heterogeneous device channel was selected following the reports of mobility enhancement in graphene devices on h-BN substrate.34–36 We modified the device design by using a thicker h-BN barrier and cap layers for better screening from the defects. Raman spectroscopy (Renishaw InVia) was used to determine the number of atomic planes in the exfoliated graphene samples and to verify the quality of the selected graphene and h-BN layers used for the device fabrication. The devices were fabricated in the following steps. First, h-BN layers (thickness H ∼ 30 nm) were mechanically exfoliated on top of p-doped Si/SiO2 wafer (300 nm of SiO2). Graphene layers were prepared by the same procedure on another Si/SiO2 substrate. Thin viscoelastic materials (Gelpak) adhered to glass slides were used as transparent stamps for the layer transfer. The stamps were spin-coated (Headway SCE) with polypropylene carbonate (PPC). Second, the stamp with PPC was brought into contact with the h-BN layer on a substrate using a micromanipulator. The stage was heated to 40 °C allowing for adherence of h-BN crystal with subsequent lifting of the stamp with attached h-BN layer. Third, the micromanipulator was used for careful positioning of h-BN layer over the graphene layer. Pressing the stamp with h-BN layer on top against monolayer graphene placed on a SiO2 substrate and heating the stage to 40 °C led to the adherence of the graphene layer to h-BN. Repeating these steps, h-BN–graphene–h-BN stacks were formed creating the desired heterostructure. The completed heterostructure was released by heating the stage to 90 °C onto the degenerately doped p-type Si/SiO2 substrate. Finally, the PPC layer was washed out with acetone to leave the assembled stack on the substrate. No cleaning treatments like thermal annealing have been used before and during the assembly process, as well as in the post-fabrication stage.

The fabricated heterostructures were spin coated and heated with a positive resist polymethyl methacrylate (PMMA) two times. Patterning of the assembled stacks was accomplished by electron beam lithography (EBL) (LEO Supra). In order to expose encapsulated graphene edges, the assembled stacks were selectively etched with sulfur hexafluoride (SF6) gas on an inductively coupled plasma system (Oxford Plasmalab) into conventional Hall bar geometries. The samples were rinsed with acetone to remove the resist mask. After the repeated PMMA spin coating procedures, the electrical contacts were patterned with EBL. Immediately before metallization, the graphene edges were exposed to O2 plasma to improve bonding and increase transmission.37,38 The metal leads (10 nm Cr/100 nm Au) were deposited by electron beam evaporation (Temescal BJD). The electrical contacts were made to Cr adhesion layers because the Cr work function is ∼0.16 eV lower than that of graphene.39 The fabricated three-dimensional (3D) Cr/Au electrodes touched the 2D graphene monolayer along the one-dimensional (1D) graphene edge in these devices. This “1D contact” approach is typically advantageous in comparison to conventional “2D contacts” in the sense of separating the layer assembly and metallization processes, lower contact resistance.38 The schematics and optical microscopy image of a representative device are presented in Figure 1. Total of eight devices were studied in this work.

FIG. 1.

(a) Schematics of h-BN-G-h-BN HFET. Note the structure the “one-dimensional” contact to the fully encapsulated graphene layer. (b) Optical microscopy image of a representative graphene encapsulated HFET. The source and drain contacts of the device are denoted with S and D symbols, respectively.

FIG. 1.

(a) Schematics of h-BN-G-h-BN HFET. Note the structure the “one-dimensional” contact to the fully encapsulated graphene layer. (b) Optical microscopy image of a representative graphene encapsulated HFET. The source and drain contacts of the device are denoted with S and D symbols, respectively.

Close modal

Transport measurements were done in a two-probe configuration with the heavily doped Si substrate used as the back-gate. Figure 2 shows the current-voltage (I-V) characteristics of a representative h-BN-G-h-BN HFET with L = 9.45 μm. The effective mobility, μeff, was determined from the channel resistance using the expression

μEFF=LGREFFCG(VGSVD)W,
(1)

where LG is the gate length, CG is the gate capacitance per unit area, REFF=RDSRC1σ0(RDSRC), σ0 is the conductivity at the voltage corresponding to the charge neutrality point, RC is the sum of the drain and source contact resistances, and RDS is the measured drain-source contact resistance. All our measurements were performed in the linear regime at very small currents so that the external VGS was approximately equal to the intrinsic source-gate voltage. The field-effect mobility, μFE, was determined from the transconductance, gm0, in the linear regime using the expression

μFE=gm0CG(VDSIRC)LGW,
(2)

where VDS is the drain-source voltage. In the linear regime at small drain voltages, the internal transconductance was found from

gm0gm(1+RCREFF+RCσ0),
(3)

where gm is the external transconductance. Both the effective and field-effect mobility extractions gave consistent results, and the charge carrier mobility was determined to be greater than 30 000 cm2/Vs at RT and for the carrier concentration of 7 × 1011 cm−2. The low-temperature (T = 77 K) mobility values reached 100 000 cm2/Vs.

FIG. 2.

Current–voltage transfer characteristics of h-BN-G-h-BN HFETs. The source-drain voltage is 10 mV.

FIG. 2.

Current–voltage transfer characteristics of h-BN-G-h-BN HFETs. The source-drain voltage is 10 mV.

Close modal

An estimate for the contact resistance, RC, was obtained by plotting the drain-to-source resistance, RDS, versus 1/(VG − VD), where VG is the gate bias and VD is the Dirac (charge-neutrality point) voltage. An extrapolation of this dependence to 1/(VG − VD) = 0 provides the sum of the drain and source contact resistance RC. For the studied devices, the value of the contact resistance per unit width Rc0=RC×W/2 was ∼ 277 Ω μm. To estimate the charge carrier mean free path (MFP), Λ, we used a conventional relation between the mobility, μ, and electrical conductivity σ=enμ=(2e2/h)kFΛ, where kF=(πn)1/2 is the Fermi wave vector in 2D graphene, h is the Planck's constant, e is the charge of an electron, and n is the carrier concentration. For n = 2 × 1012 cm−2, from the expression Λ=(h/2e)μ(n/π)1/2 we obtained Λ ≈ 0.311 μm. For devices with W ≈ 1 μm and L in the range from 2.5 to 9.45 μm, the electron transport is not yet ballistic, but it approaches this regime. As predicted in Ref. 40, the unique features of the near ballistic response could be revealed by studying “ringing” of the transistor response to short THz pulses.

The low-frequency noise was measured using an in-house built experimental setup with a spectrum analyzer (SRS FFT). The devices were biased with a “quiet” battery–potentiometer circuit. Details of our noise measurement procedures have been reported by some of us elsewhere.18,19,22 Figure 3 shows representative normalized noise spectrum density, SI/I2, for one of the tested devices. The noise is of true 1/fγ type with γ varying from 0.95 to 1.2 with an average γ = 1.09 for a device with the channel W × L = 1.16 × 9.45 μm2. For the device with the channel W × L = 1 × 3.21 μm2, the extracted γ was in the range from 0.84 to 1.27 with an average value of γ = 1.02. Table I lists the γ values for two representative devices. No trend in γ dependence with the device channel area or gate voltage, which would suggest non-uniformity of the charge trap distribution,15 was observed. The noise spectra of all examined devices revealed no traces of the generation-recombination noise. The noise spectrum density of the high-mobility h-BN-G-h-BN HFETs revealed strongly non-monotonic gate-bias dependence, which is in contrast to that described by the McWhorter model in Si CMOS devices.32 

FIG. 3.

Normalized noise spectrum density in h-BN-G-h-BN HFET as a function of frequency for several values of the back-gate bias VG. Note that VG = −7.75 V corresponds to the Dirac point.

FIG. 3.

Normalized noise spectrum density in h-BN-G-h-BN HFET as a function of frequency for several values of the back-gate bias VG. Note that VG = −7.75 V corresponds to the Dirac point.

Close modal
TABLE I.

Parameter γ for low-frequency noise in BN-graphene-BN HFETs.

VG (V)−60−30−10−8−505103060
γ (device A) 1.16 1.04 0.96 1.19 0.95 1.16 0.97 1.12 1.12 1.20 
γ (device B) 1.27 0.84 0.95 1.04 1.02 1.02 0.96 0.94 1.04 1.05 
VG (V)−60−30−10−8−505103060
γ (device A) 1.16 1.04 0.96 1.19 0.95 1.16 0.97 1.12 1.12 1.20 
γ (device B) 1.27 0.84 0.95 1.04 1.02 1.02 0.96 0.94 1.04 1.05 

To better elucidate the non-monotonic type of the noise gate bias dependence we calculated the noise amplitude as A=1Zi=1ZfiSIi/I2, which is a dimensionless noise characteristic analogous to the normalized noise spectral density SI/I2 but averaged over several frequencies (here Z is the number of the frequency data points). Figure 4(a) shows the noise amplitude in our h-BN-G-h-BN HFET as a function of VGS-VD (VD is the Dirac voltage). For comparison, we also show noise amplitude in conventional non-encased graphene FET on Si/SiO2 reported in Ref. 28. The non-encased graphene FET had mobility less than 3000 cm2/Vs. In our high-mobility h-BN-G-h-BN HFETs, the minimum of the noise amplitude was achieved near the Dirac point, similar to that in the conventional graphene FETs.17,28 The McWhorter model predicts that SI/I2 decreases in the inversion regime as ∼(1/n)2. In graphene FETs on Si/SiO2, the noise gate dependence has characteristic “M” shape.17 The noise gate dependence in our h-BN-G-h-BN HFETs is also close to “M” shape and it does not follow the McWhorter model.

FIG. 4.

(a) Noise amplitude as a function of the gate bias with respect to the Dirac point, VGS-VD for h-BN-G-h-BN HFET. The results are shown for the device with the largest channel dimensions. The data for conventional non-encapsulated graphene FET on Si/SiO2 wafer from Ref. 28 are also shown for comparison. (b) Parameter β, which defines 1/f noise level in 2D channels plotted as a function of gate bias for two representative devices.

FIG. 4.

(a) Noise amplitude as a function of the gate bias with respect to the Dirac point, VGS-VD for h-BN-G-h-BN HFET. The results are shown for the device with the largest channel dimensions. The data for conventional non-encapsulated graphene FET on Si/SiO2 wafer from Ref. 28 are also shown for comparison. (b) Parameter β, which defines 1/f noise level in 2D channels plotted as a function of gate bias for two representative devices.

Close modal

The parameter β = (SI/I2)(W × L) is a better characteristic of 1/f noise in 2D materials than Hooge parameter introduced specifically for volume noise.22 For conventional graphene devices on Si/SiO2 substrates, β parameter is ∼10−8 to 10−7 μm2 Hz−1 for micrometer-scale channels.17 In our high-mobility h-BN-G-h-BN HFETs, β was determined to be in the range from 5 × 10−9 to 2 × 10−8 μm2 Hz−1. At small gate biases the noise level was typically below 10−8 μm2 Hz−1 in h-BN-G-h-BN HFETs. Figure 4(b) shows parameter β dependence on the gate bias for two representative devices. On average, 1/f noise in our devices was suppressed by a factor of ×5 – ×10 as compared to that in non-encapsulated graphene devices on Si/SiO2. This is a substantial reduction, which can have practical implications.

We now turn to explanation of a potential mechanism of noise reduction in encased graphene channel devices. It is generally accepted now that the low frequency 1/f noise can be either due to the number of charge carrier fluctuations or due to their mobility fluctuations or both. Depending on which term dominates, one distinguishes the mobility fluctuation or the carrier number fluctuation mechanism of 1/f noise.15 In Si and other metal-oxide-semiconductor field-effect transistors (MOSFETs), the carrier number fluctuations usually dominate and such type of the noise is well described by the McWhorter model.32 The studies that investigate noise in graphene under irradiation19 and magnetic field41 suggested that the mechanism of 1/f noise in graphene is more similar to the mobility fluctuations mechanism (like that in metals).

Owing to graphene's atomic thickness and the fact the mobility is limited by scattering from defects and impurities in SiO2,42–46 the mobility fluctuations will be due to the fluctuations in the scattering cross-sections of defect states in SiO2 gate dielectric. For this reason, irrespective of the specific noise mechanism—carrier number or mobility fluctuations—screening electrons in graphene channel from the defect states in SiO2 by introducing h-BN barrier layer with the thickness of 30 nm should reduce the noise. This conclusion is consistent with reports that 1/f noise was reduced in the suspended graphene devices.23 It is interesting to note that suspended graphene device reported in Ref. [23] had β ∼ 6 × 10−9 μm2/Hz, which is approximately the same noise level as in our encased graphene channel HFETs. While most of noise reduction is likely related to screening of the graphene channel from traps in SiO2, it is possible that capping graphene with h-BN also helps to reduce the noise. It has been shown that the environmental exposure and device ageing increase the level of 1/f noise in graphene devices.17,22 Organic residue and other contaminants on the surface can create either trapping centers for electrons in the channel (carrier number fluctuation noise) or scattering centers (mobility fluctuation noise).

In conclusion, we investigated the low-frequency 1/f noise in the h-BN-graphene-h-BN HFETs with mobility in the range from 30 000 to 36 000 cm2/Vs. It was established that 1/f noise in such device is strongly suppressed as compared to that in non-encapsulated graphene devices on Si/SiO2. Considering that h-BN is chemically stable and produces strong positive effect on mobility in graphene channel, our finding that the h-BN capping and barrier layers result in significant reduction of 1/f noise adds an extra merit to practical electronic applications of graphene-based heterostructures.

The work at UC Riverside was supported, in part, by the Semiconductor Research Corporation (SRC) and Defense Advanced Research Project Agency (DARPA) through STARnet Center for Function Accelerated nanoMaterial Engineering (FAME) and by the National Science Foundation (NSF) project Graphene Circuits for Analog, Mixed-Signal, and RF Applications (NSF CCF-1217382). S.L.R. acknowledges partial support from the Russian Fund for Basic Research (RFBR). The work at RPI was supported by the Army Research Office (Program Manager: Dr. Meredith Reed).

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