Gap state analysis in electric-field-induced band gap for bilayer graphene

The origin of the low current on/off ratio at room temperature in dual-gated bilayer graphene field-effect transistors is considered to be the variable range hopping in gap states. However, the quantitative estimation of gap states has not been conducted. Here, we report the systematic estimation of the energy gap by both quantum capacitance and transport measurements and the density of states for gap states by the conductance method. An energy gap of ~250 meV is obtained at the maximum displacement field of ~3.1 V/nm, where the current on/off ratio of ~3 × 103 is demonstrated at 20 K. The density of states for the gap states are in the range from the latter half of 1012 to 1013 eV−1cm−2. Although the large amount of gap states at the interface of high-k oxide/bilayer graphene limits the current on/off ratio at present, our results suggest that the reduction of gap states below ~1011 eV−1cm−2 by continual improvement of the gate stack makes bilayer graphene a promising candidate for future nanoelectronic device applications.

The main issue of downscaling in the Si field-effect transistors (FETs) is the short channel effect in which the gate control is weakened by the drain bias. Based on an analysis of the electrical potential distribution in the channel region, it is well known that the short channel effect can be neglected when the channel length is ~6 times longer than the scaling length ε ε λ = ( )/( ) t t N ch ch ox ox 1,2 , where N, ε ch , ε ox , t ch , and t ox are the effective gate number, dielectric constants for the channel and gate insulator, and thickness of the channel and the gate oxide. This perspective attracts great attention to two-dimensional (2D) layered channels in the FET application because of their rigidly controllable atomic thickness (t ch < 1 nm), as well as the low dielectric constant (ε ch = ~4) for typical 2D layered channels 3,4 . Although old-but-new 2D channels, such as transition metal dichalcogenides, black phosphorus, and so on, have been intensively investigated recently [5][6][7][8][9] , bilayer graphene with an electrostatically tunable band gap still has an advantage over the high performance device from the viewpoint of mobility due to the smaller effective mass (m BLG = ~0.037 10 , m BP = 0. 13 11 , and m MoS2 = ~0.37 12 ).
The suppression of conductivity in bilayer graphene has so far been reported by many researchers by applying an external electrical field [13][14][15][16][17][18][19][20][21][22][23][24] . Optical spectroscopic measurements, such as angle-resolved photoemission spectroscopy 25 and infrared spectroscopy 14,26,27 , confirmed the band gap formation. However, the large current on/off ratio (I on /I off ) of ~10 6 is obtained only at the quite low temperature of 300 mK 17 , not at room temperature. The reason is explained by the variable range hopping in gap states 13,15,[17][18][19] . Therefore, the main target issue for bilayer graphene is a low current on/off ratio at room temperature. At the zero-order approximation, there will intrinsically be no interface states in bilayer graphene because there are no dangling bonds on the basal plane, compared with P b centers in the SiO 2 /Si system, assigned by the electron spin resonance measurement [28][29][30] . Although the strong disorder at the channel edge was expected to act as a main conduction path, the transport measurement in the Corbino geometry excluded this idea 19  Contrary to the transport measurement, the extraction of the quantum capacitance (C Q ) through the capacitance measurements (C-V) of bilayer graphene provides direct information on the density of states (DOS) of bilayer graphene, consequently, the energy gap (E G ), because it is regarded as the energy cost of inducing the carriers in graphene and is directly related as C Q = e 2 DOS 31 . Although there are a few reports on C Q measurement for bilayer graphene [32][33][34] , the comparison of E G estimated both from I-V and C-V has not been done yet. Moreover, in principle, the mobile carrier response to a small-signal alternating current voltage at a certain frequency is measured in the C-V measurement. The capture and emission process of mobile carriers at the trap levels distributed throughout the band gap can be extracted as a deviation from the ideal carrier response without any trap levels under the assumption of the equivalent circuit. This technique is known as the conductance method 34 .
In this work, we present the systematic extraction of E G as a function of the displacement field (D), which determines the band structure of bilayer graphene, from both I-V and C-V. The conductance measurements are carried out to extract D it and τ it ; then, the possible origins of the gap states are discussed.

Bilayer graphene FTEs with a high quality top gate insulator
Recently, we have demonstrated a considerable suppression of the low-field leakage through high-k Y 2 O 3 on monolayer graphene by applying high-pressure O 2 annealing 35 . The same process was applied to bilayer graphene FETs. The improved electrical quality of the insulators provides access to the large displacement field (D = ~3.1 V/nm) in this study. Although there are several conventions for D, we adopt the most widely used definition of BG  BG  TG  TG  TG  TG  0  0 in this study 14 , where ε BG , ε TG , d BG , d TG , V BG , and V TG are the dielectric constants, the insulator thickness, and the gate voltages for back-and top-gate insulators, respectively.
is the charge neutrality point to give the minimum resistance in the top-gated region.
To suppress the hysteresis in drain current-gate voltage curves, the SiO 2 surface was converted to be hydrophobic (siloxane group) by annealing the SiO 2 /Si substrate in a 100% O 2 atmosphere at 1000 °C prior to the graphene transfer 36 . Then, the conventional back-gated bilayer graphene FETs containing source and drain electrodes were fabricated on ~90 nm SiO 2 /n + -Si substrates by the mechanical exfoliation of Kish graphite. This device was annealed under Ar/H 2 gas flow at 300 °C for 3 hours to remove the resist residue on the bilayer graphene channel. Subsequently, Y 2 O 3 , with a thickness of ~6 nm, was deposited on bilayer graphene FETs by the thermal evaporation of Y metal in the O 2 atmosphere at P O2 = 10 −1 Pa 35 . Then, high-pressure annealing was carried out in a 100% O 2 atmosphere at ~100 atm and 300 °C. Finally, the top gate electrode was patterned, followed by annealing at 300 °C for 30 s under 0.1% O 2 gas flow. The lack of a Raman D band measured through Y 2 O 3 indicated that no detectable defects were introduced into the bilayer graphene by the high-pressure O 2 annealing, as shown in Supplementary  Fig. S1c.

Estimation of E G by C-V and I-V
We first focus on the capacitance measurement to determine E G through the C Q extraction. Figure 1a shows the total capacitance (C Total ) between the source and top gate electrodes, obtained by sweeping V TG at different V BG , which were measured at the frequency of 1 MHz in a vacuum of ~1 × 10 −5 Pa at 20 K. Figure 1b is the counter plot of C Total . The C Total reduction at the Dirac point with increasing V BG indicates the decrease in the DOS by the gap formation because of the strong contribution of C Q . The hysteresis in the bidirectional C-V curves is quite small (~0.1 V for a V TG = ± 4 V sweep) 35 . As shown in Supplementary Fig. S2, the frequency dependence of C Total is clearly observed in the gap region, suggesting the existence of trap sites. The gradual saturation of the capacitance with increasing frequency from 200 kHz to 1 MHz suggests that C Total measured at 1 MHz is close to the ideal capacitance without any response to the trap site. Therefore, the C-V measurement in Fig. 1a was carried out at 1 MHz.
The slope of the dotted black line at the charge neutrality point of ( , Fig. 1b corresponds to the capacitive coupling ratio between the top gate and back gate, that is, − 0.0412 = − C BG /C TG . Using C BG = 0.038 μ Fcm −2 for SiO 2 with d BG = 90 nm and ε BG = 3.9, C TG is estimated to be 0.93 μ Fcm −2 .
In the course of this study, the typical C TG value is ~1.2 μ Fcm −2 , depending on the Y 2 O 3 thickness. The C TG value is considerably high compared with those reported previously for both monolayer and bilayer graphene, as shown in Fig. 1c. Based on C TG and C BG , the white dotted lines indicate the constant D, whose values are shown at the periphery of the counter plot of Fig. 1b. The maximum D at the Dirac point in this study is ~3.1 V/nm, which is quite high compared with other reports.
The simplified equivalent circuit model of the device is shown in Fig. 2a, where V ch and C para are the charging voltage and the parasitic capacitance. The Fermi energy (E F ) and the band structure of bilayer graphene are independently controlled by changing V TG and V BG . It should be noted that the contribution of C BG is implicitly involved in C Total through C Q and V ch , in Fig. 2a. Based on the equivalent circuit of Fig. 1a, C Q was extracted along the constant D lines, i.e., the constant band structure, by using C para as a fitting parameter. Figure 2b shows C Q as a function of E F for different constant D values. At D = 0 V/ nm, the extracted C Q is fitted reasonably well with the theoretical value for bilayer graphene calculated by the tight-binding model 37 by selecting C para = 0.91 μ Fcm −2 . The charging energy required to induce carriers in bilayer graphene is denoted by E F , which is expressed as E F = eV ch . V ch can be expressed by the The detailed calculation method is explained in Supplementary Fig. S3. The C Q value at the Dirac point for D = 0 V/nm is consistent well with the theoretical value because the DOS for bilayer graphene at the Dirac point is larger than the residual carriers induced externally by the charged impurities at the SiO 2 surface 38 . With increasing D, the reduction of C Q is clearly observed because the scattering issue, which strongly contributes to the conductivity in I-V, can be neglected in C-V. It should be emphasized that the DOS within the gap region almost reaches zero, which is not observed in the previous report for bilayer graphene with the h-BN top gate 33 . Moreover, the van Hove Singularity (vHS) is also observed near the valence band edge, as shown by arrows. The appearance of the vHS is asymmetric, that is, a valence band edge for negative D and a conduction band edge for positive D (not shown in Fig. 2b), which is consistent with previous data 33 . This phenomenon is explained by the near-layer capacitance enhancement effect 39 . Figure 2c shows E G as a function of absolute value for D, determined from the C-V data. E G was defined as the energy between inflection points for the conduction and valence sides in Fig. 2b. E G is roughly ~300 mV at D = 2.5 V/nm.  We now consider the transport properties for the same device. Figure 3a shows the conductivity (σ) measured as a function of V TG for different V BG at 20 K. The conductivity at the Dirac point decreases with increasing V BG , again indicating the band gap opening. The maximum I on /I off is ~3 × 10 3 for D = ~3.1 V/nm. Figure 3b shows the maximum mobility as a function of D for different regions of pnp, ppp, and so on, whose positions are shown in Supplementary Fig. S4a. In terms of the determination of carrier mobility using the Drude model (σ = enμ), the carrier density (n) is estimated by the integration of the differential capacitance of ′ C Total , that is, , because of the large contribution of C Q . Otherwise, n is overestimated. However, the carrier density at the access region between the source (drain) and topgate is assumed to be consistent with that at the main channel region just below the topgate electrode for the mobility estimation. Shortening this access region by the self-alignment process 40 is important to extract the mobility more precisely and to improve the device performance.
Moreover, the subthreshold swing (S) is plotted as a function of temperature, as shown in Fig. 3c. The S value (~600 mV/dec) extrapolated to room temperature is considerably larger than the theoretical lower limit of 60 meV/dec at room temperature 41 , suggesting the large contribution of the gap states. Figure 3d compares the present mobility and I on /I off at 20 K with previously reported data. All the data for I on /I off are selected at 20 K from the literature, while the temperature for the mobility is not limited to 20 K. The mobility in the present study is not very high because it includes the contact resistance. In contrast, I on /I off in the present study is quite high in spite of the direct deposition of high-k oxide on bilayer graphene without any organic buffer layer.
To determine E G from the viewpoint of the transport, we study the temperature dependence of σ at different D ranging from 0 to 3.1 V/nm. Figure 4a shows the temperature dependence of σ as a function of V TG − V DP at V BG = − 60 V. So far, the temperature dependence of the conductivity in bilayer graphene is explained by the sum of three terms, the thermal activation (TA) at the high temperature region, nearest neighbor hopping (NNH) at the intermediate temperature range and variable range hopping (VRH) in a two-dimensional system of localized states at the low temperature region, as follows 17,18 , where σ TA 0 , σ NNH 0 and σ VRH 0 are prefactors and E 0 , T 0 and k B are the activation energy, the hopping energy and the Boltzmann constant. Since the lowest temperature in this study is 20 K, the contribution of VRH may not be observed. The conductivity at the Dirac point is plotted as a function of temperature and fitted by two combinations of TA + NNH and TA + VRH, as shown in Fig. 4b,c, respectively. All the conductivity data are well fitted with respect to T −1 for TA + NNH, while the plot with respect to T −1/3 does not show clear linear behavior below T = 100 K. The present data can be explained by TA + NNH for the temperature range above 20 K. This is consistent with the previous report where VRH was  Fig. S4). (c) Subthreshold swing (S) as a function of temperature. The slope is nearly linear (dS/dT = ~1.1 mV/K). (d) Comparison of I on /I off and mobility with those reported previously for bilayer graphene. The temperature for I on /I off data was fixed at 20 K. For the mobility, the temperature is not limited to 20 K, and both two-probe and four-probe data are shown here.
Scientific RepoRts | 5:15789 | DOi: 10.1038/srep15789 observed at below 5 K 13,17,18 . Extracted E G and E 0 are plotted as a function of D in Fig. 2c, respectively, along with the results obtained in infrared absorption studies 14 . E G determined by I-V is reasonably consistent with the previous infrared absorption data, while E G determined by C-V is slightly larger. This difference is discussed later. Moreover, E 0 increases with D and reaches 2.8 meV at D = 3.1 V/nm, which is high compared with previous reports 18 .

Estimation of D it and τ it
To gain insight into the interface properties, the gap states in the electrostatically opened-band gap are quantitatively analyzed using the conductance method. The equivalent circuit of the device is shown in the left of Fig. 5a, where R it and C it are the resistance and capacitance associated with the interface traps, their product C it R it is defined as τ it , and R s is the series resistance. It should be noted that R it and C it have been neglected due to roughly no electrical communication of carriers with trap sites at 1 MHz in Fig. 2a. Here, when this equivalent circuit is converted into C p , in parallel with G p , as shown in the right of Fig. 5a, the relation between G p and D it can be given as the following 42 , , where f 0 is the frequency at ω ( / ) G p max . The accurate estimation of D it is possible because G p /ω does not include C Q , which is the advantage of the conductance method. However, if there is leakage conductance (G leak ), indicated by the dotted line in the left of Fig. 5a, it is quite difficult to separate the two conductance contributions. The key issue to extract D it quantitatively is the fabrication of a highly reliable top gate insulator on bilayer graphene without any leakage current. This has been achieved by the high-pressure O 2 post-deposition annealing of Y 2 O 3 . Figure 5b shows G p /ω as a function of f for E F from − 74 to − 28 meV, where the band structure was fixed as constant at D = − 1.5 V/nm, i.e., E G = ~150 meV. It should be emphasized that G p was measured under the constant band structure along the constant D line by controlling V TG and V BG at the same time.
To prevent the contribution of a minority carrier response to the conductance, especially for small band gap semiconductors, the measurement temperature was lowered as much as possible, i.e., 20 K (k B T = ~1.7 meV). This quite low temperature is only possible in bilayer graphene because the majority carriers do not freeze due to the doping by the external gate control, unlike substitutionally doped semiconductors. The more detailed measurement conditions are described in the method section. Clear peaks were observed in the G p /ω-f relation, suggesting the detection of a trap-detrapping sequence of carriers with gap states. The τ it value is evaluated to be ~4 μ s. In Fig. 2a, it is assumed that the contribution of C it is roughly negligible in C Total , measured at 1 MHz. According to this τ it value, this assumption is roughly, but not completely, reasonable. Therefore, E G estimated by C-V may be slightly overestimated due to the contribution of C it . Figure 5c shows D it as a function of E G for different D. D it is in the range from the latter half of 10 12 to 10 13 eV −1 cm −2 . The energy dependence of D it is not so obvious. Although this value is slightly smaller than that for MoS 2 43 , it is larger compared with those of Si 44 . The large amount of gap states at the interface of high-k oxide/bilayer graphene limits I on /I off at present. The much lower D it could be achieved for dual-gate bilayer graphene heterostructure with h-BN. In general, the conductance method is applied to the metal-oxide-semiconductor (MOS) capacitor, where the current is injected from the back side through the semiconductor substrate, whose series resistance, including back side contact, can be removed by measuring the impedance at the high-frequency limit (see Method). The interface trap conductance can be precisely measured. In contrast, in the present FET structure, the carriers are injected from the side of the channel through the source and drain 43,45 . The channel resistance may contribute to G p in the equivalent circuit. To avoid this, a device with a relatively short channel was used at the expense of the channel area, which increased C para in this study compared with typical value of ~0.2 μ Fcm −2 35 . Supplementary Figure S5b compares τ it with the channel time constant (τ ch = R DP C DP , where R DP and C DP are the measured resistance and capacitance at the Dirac point), suggesting that τ it is dominant. Therefore, the present D it measurement is reliable.
Finally, let us discuss the origin of the gap states. As mentioned before, no detectable defects are observed by the Raman D band. Therefore, the trap sites formed by defects are ignored in this discussion. Two possible origins are discussed here, as shown in Fig. 5d. One is the external origin, that is, the border trap 46 . The carriers in bilayer graphene electrically communicate with trap sites, such as the oxygen vacancy (dotted box) at the surface of oxides, because π electrons stay on the surface of bilayer graphene. The other is the internal origin. The local breakdown of A-B stacking 47,48 results in the stacking of two monolayers 49 , leading to the different band structure. In this case, E F stays within E G at some momentum space, while the real states exist at another momentum space, which may macroscopically act as gap states. Here, let us consider the dominant origin of the gap states. From the viewpoint of the time constant, the former origin will be a more time-consuming process than the latter because the rate limiting process is the tunneling between bilayer graphene and trap sites at the oxide surface 50 . On the other hand, if A-B stack breaking is the dominant origin of the gap states, D it should decrease with increasing D, which is consistent with the observation in Fig. 2b. This, however, does not appear to be clear in the conductance measurement in Fig. 5c because other devices show almost no difference in D it for different D. If T 0 in VRH is extracted at the low temperature region below 5 K, the D dependence of D it can be discussed more in detail because T 0 is inversely proportional to the density of states for the localized states 51 . Further detailed measurements are required to understand the D dependence of D it . Although it is difficult to determine the dominant origin of the gap states at present, the quantitative recognition of the current status for D it in this study does provide the realistic comparison with other semiconductor channels in terms of the interface quality.

Conclusions
We have succeeded in extracting critical information on the interface quality, that is, D it and τ it for gap states. At the large displacement field of ~3 V/nm, they are in the range from the latter half of 10 12 to 10 13 eV −1 cm −2 and ~4 μ s, respectively. The large amount of gap states at the interface of high-k oxide/ bilayer graphene limits the I on /I off ratio at present. Many trials to characterize the interface properties for other 2D layered channels, as well as bilayer graphene, will help in understanding the origin of the gap states. The improvement of gap states below ~10 11 eV −1 cm −2 is the first step for bilayer graphene devices to be a promising candidate for future nanoelectronic applications.

Methods
The transport measurement of the device was performed using a Keysight B1500A semiconductor analyzer in a Nagase low-temperature prober in a vacuum of ~10 −5 Pa. The capacitance measurement and conductance method under the constant D conditions were performed by controlling both the Keysight 4980 A LCR meter and the Keithley 2450 source meter for the back gate. The top gate electrode was connected to the high terminal, while the source and drain electrodes was connected to the low terminal. For the conductance measurement, G p should be measured accurately by reducing the contribution of R s in the equivalent circuit in the right side of Fig. 5a. Therefore, ozone treatment was performed for 5 min before the metal deposition to remove the resist residue at the source/drain contact 52 , which reduces the contact resistance. Then, R s was estimated as follows. For the equivalent circuit in Fig. 5a ( . Therefore, R s at the accumulation side was estimated to be 29.4 kΩ by taking the high-frequency limit (ω→ ∞), as shown in Supplementary Fig. S5a. Finally, G p can be accurately estimated by removing R s in the equivalent circuit in the right side of Fig. 5a. For the D it measurement at the valence band side, E F is scanned along negative D (− 1.5 and − 3 V/nm). The access region modulated only by the back gate is always p-type (black line on the dashed-dotted vertical line at V TG = 0 V in Fig. 1b), from which a hole is injected into the main channel under the top gate to ensure majority carrier response, and vice versa for the conduction band side at the positive D. Therefore, D it distributed throughout E G can be measured using the single FET device, unlike the MOS capacitor.