Interface States in Bilayer Graphene Encapsulated by Hexagonal

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Interface States in Bilayer Graphene Encapsulated by Hexagonal Boron Nitride Kayoung Lee, En-Shao Liu, Kenji Watanabe, Takashi Taniguchi, and Junghyo Nah ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b16625 • Publication Date (Web): 15 Nov 2018 Downloaded from http://pubs.acs.org on November 16, 2018

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ACS Applied Materials & Interfaces

Interface States in Bilayer Graphene Encapsulated by Hexagonal Boron Nitride Kayoung Lee,1,2,* En-Shao Liu,1 Kenji Watanabe,3 Takashi Taniguchi,3 and Junghyo Nah1,4 1

Microelectronics Research Center, The University of Texas at Austin, Austin, TX 78758 USA

2

School of Materials Science and Engineering, Gwangju Institute of Science and Technology, Gwangju 61005, South Korea 3

National Institute for Materials Science, 1-1 Namiki Tsukuba, Ibaraki 305-0044, Japan.

4

Department of Electrical Engineering, Chungnam National University, Daejeon 34134, South Korea *

[email protected]

Abstract The threshold voltages at the onset of conduction for electron and hole branches can provide information on band gap values or the interface states in a gap. We measured conductivity of bilayer graphene encapsulated by hexagonal boron nitride as a function of back and top gates, where another bilayer graphene is used as a top gate. From the measured conductivity the transport gap values were extracted assuming zero interface trap states, and they are close to the theoretically expected gap values. From a little discrepancy an average density of interface states per energy within a band gap (Dit) is also estimated. The data clearly show that Dit decreases as a bilayer graphene band gap increases rather than being constant. Despite the decreasing trend of Dit, interestingly the total interface states within a gap increases linearly as a band gap increases. This is because of ~ 2  1010 cm-2 interface states localized at band edges even without a band gap, and other gap states are equally spread over the gap.

Keywords: bilayer graphene, transport gap, band gap, interface states, hexagonal boron nitride

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Bernal stacked bilayer graphene is distinctive from monolayer graphene as the inversion symmetry can be easily broken via a transverse electric field (E-field)1. The E-field induced onsite electron energy asymmetry gives rise to a tunable band gap2,3, a variety of quantum Hall phases4–8, exotic valley transport9,10, etc. Such tunability renders bilayer graphene more promising for dynamically tunable device applications. E-field induced band gap of bilayer graphene has been investigated theoretically and experimentally using various techniques for years. General picture of band structure of bilayer graphene is understood based on the tight-binding model2,4,11. Ab initio density functional theory further confirms the tight-binding idea, but results in stronger screening of the external interlayer potential yielding a little smaller band gap compared to tightbinding calculations12,13. Several infrared spectroscopic measurements showed band gap values as a function of back-gate bias14–16, which agrees well with self-consistent tight-binding14,16 or ab initio density functional theory calculation15. Temperature (T) dependent measurements at high E-fields have shown the thermal activation energy approaching half of theoretical band gap values17–19. But at relatively small E-fields conduction paths through localized states hamper the extraction of thermal activation energy20,21. Fermi energy measurement using double bilayer graphene heterostructures also provided band gap values in agreement with ab initio density functional theory calculation8. Another straightforward measure of a band gap is probing a transport gap. Conduction of gapped semiconductor is suppressed when its Fermi energy is located inside a gap. A finite gate bias is required to move Fermi energy to a conduction or valence band edge at which electrical conduction appears. The threshold bias is thus almost linearly dependent on band gap values. The transport gap of bilayer graphene on oxide dielectrics was measured at different E-fields using dual-gated structures22. At a finite E-field, bilayer graphene conductivity shows threshold voltages


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along the electron and hole branches, analogous to the threshold voltages seen in a conventional bulk semiconductor with a band gap. However, the size of the measured transport gap is far larger than theoretical band gap values because of numerous localized states inside the transport gap. Here we perform the transport gap measurement on high quality double bilayer graphene heterostructures with hexagonal boron nitrides (hBN) dielectrics. hBN provides nearly pristine environment for graphene and induces negligible localized states and potential fluctuation compared to oxide dielectrics. We compare our measured transport gap with theoretical gap values, and extract interface states in bilayer graphene encapsulated by hBN, providing a detailed analysis of the variation of gap states as a function of gap size.

Figure 1: (a) A schematic which describes the vertical structure of our device (upper), and a micrograph of sample #1 (lower). (b) Conductivity of sample #1 as a function of VTG and VBG, measured at T = 1.5 K.

Figure 1(a) lower micrograph shows one of our double bilayer graphene heterostructures, and the upper schematic describes the vertical structure of the device. Samples are fabricated using a general dry transfer process, elaborated in Ref.8,23. Double bilayer graphene heterostructures can be considered as dual-gated bilayer graphene systems using the top bilayer graphene as a top-gate with relatively low density of states compared to a conventional metal gate. Back-gate bias (VBG)



is applied on the highly degenerate Si substrate, and top-gate bias (VTG) is applied on the top bilayer graphene. Bottom bilayer graphene conductivity (σ) was measured as a function of VBG and VTG using a conventional low-current lock-in technique while grounded in average. Figure 1(b) shows the measured conductivity of the bottom bilayer graphene of sample #1 at T = 1.5 K. Here, conductivity lower than 0.05 mS is presented as black, which is indeed along the diagonal charge neutrality line. VBG and VTG control carrier densities of the bottom (nB) and top (nT) bilayer graphene and corresponding chemical potentials of the bottom (μB) and top (μT) bilayers, as described by8,24 eVBG = e2(nB + nT)/CBG + μB (1) eVTG = −e2nT/CTG − μT + μB (2). CBG and CTG are capacitances of back-gate and top-gate dielectrics, and e is electron charge. VBG and VTG in Eqs. (1) and (2) are referenced with respect to the bias values at nB = nT = 0 (double charge neutrality point, DNP, at which both top and bottom graphene have zero carrier density). Using a dual-gated structure both carrier density and E-field across the bottom bilayer graphene (EB) can be independently controlled. EB is given by EB = enB/2ɛ0 + enT /ɛ0 + EB0 (3) where EB0 is a built-in E-field in the bottom bilayer graphene at DNP by unintentional doping25, and ɛ0 is vacuum permittivity. At nB = EB = 0 Eq. (1) and Eq. (3) yield EB0 = −enT /ɛ0 = CBGVBG/ɛ0, where VBG is the difference between the VBG values at DNP and at the nB = EB = 0 point25. nB = EB = 0 point is identified as the charge neutrality point (Dirac point) with a highest conductivity as marked in Fig. 1(b) [point (i), minimum band gap point], which is expected to have a minimum band gap. From that point EB increases along the charge neutrality line. We note that in Fig. 1(b)


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the black region with a vanishing conductivity gradually increases as EB increases, which means a higher gate bias is required to gain conductivity at a higher EB.

Figure 2: (a) nB, (b) nT, and (c) EB calculated as a function of VBG and VTG for sample #1.

Our previous study in double bilayer graphene heterostructures provides a direct chemical potential measurement technique and measured chemical potential of bilayer graphene as a function of carrier density8,24. Using this μ vs n dependence for bilayer graphene Eqs. (1) and (2) are solved self-consistently and yield carrier density and corresponding chemical potential vs VBG and VTG. Figure 2(a, b) show the calculated nB and nT, respectively, as a function of VBG and VTG for sample #1, and Fig. 2(c) presents EB consecutively calculated using nB and nT. Figure 3(a, b) shows conductivity of the bottom bilayer graphene at different EB values as a function of nB, measured at T = 1.5 K in samples #1 and #2. Even at EB = 0, σ is non-zero at nB = 0 [point (i), minimum band gap point] because of thermally excited carriers and disorder in graphene. By contrast, at a finite E-field σ becomes vanishing at nB = 0 [point (ii)] and remains vanishing up to a finite threshold |nB| [point (iii)], which increases with the E-field. Sample #2 was measured with more number of data points, and thus threshold points are clearer compared to sample #1. Note that here nB denotes the carrier density calculated neglecting band-gaps, rather than the actual mobile carrier density in gapped graphene. At a non-zero E-field a finite gate bias is required to move Fermi energy to either a conduction or valence band edge. Therefore,



conductivity of gapped bilayer graphene remains vanishing until applying a finite threshold bias, VBG′ and VTG′ for VBG and VTG respectively. Such behavior was observed previously in dual-gated bilayer graphene systems with oxide dielectrics22, but our current systems with hBN dielectric layers show noticeably reduced threshold |nB|. This is thanks to reduced interface states, and it allows us to extract transport gaps (Δ) closer to actual band gap values.

Figure 3:

Conductivity of the bottom bilayer graphene as a function of nB at different EB, measured in (a) sample #1 and (b) sample #2, at T = 1.5 K. (c) The extracted transport gap values as a function of an E-field. Transport gaps were measured in the bottom bilayer graphene of sample #1 (blue open) and sample #2 (red open). We also include the transport gaps measured in bilayer graphene with oxide dielectrics, Sample A and Sample B, data from Ref.22 (light and dark green), and a gap value in sample #1 measured using a chemical potential measurement technique8 (blue closed) for comparison. Dashed line represents theoretically calculated gap values12.

The transport gap extraction mechanism previously used for dual-gated bilayer graphene systems with oxide dielectrics22 can be employed for our current system. However, the change of top graphene chemical potential is considered rigorously here because of low density of states in graphene. When only VBG′ is applied while keeping VTG constant as the bias value at point (ii), VBG′ induces the changes in a Si back-gate electron density δnBG , a bottom graphene Fermi level δ𝜇B_BG, and a top graphene Fermi level δμT_BG. Note that the change in a top graphene electron density by VBG′ is then −δnBG because there is no carriers in the bottom bilayer graphene. In the same manner, when only VTG′ is applied while keeping VBG constant as the bias value at point (ii), VTG′ induced the changes in a top graphene electron density δnTG , a bottom graphene Fermi level ACS Paragon Plus Environment

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δμB_TG, and a top graphene Fermi level δμT_TG. Here the change in a back-gate electron density by VTG′ is then −δnTG . Writing VBG′ (or VTG′) as the sum of changes in Fermi level and electrostatic potential using Poisson equation yields – e2 δnBG eVBG ′ = + δ𝜇B_BG (4) CBG eVTG ′ =

– e2 δnTG – δμT_TG + δ𝜇B_TG (5). CTG

Considering electrostatic potential difference between top-gate (or back-gate) and bottom graphene when VBG′ (or VTG′) is applied using Poisson equation leads to the following relation: δ𝜇B_BG = – e2 δnBG /CTG + δμT_BG (6) δ𝜇B_TG = – e2 δnTG /CBG (7). Eqs. (4) and (5) can be then converted into eVBG ′ = eVTG ′ =

CTG (δ𝜇B_BG – δ𝜇T_BG ) + δμB_BG (8) CBG CBG δ𝜇B_TG – δ𝜇T_TG + δ𝜇B_TG (9) CTG

Using δ𝜇B_BG + δ𝜇B_TG = Δ/2 we obtain the transport gap Δ=

2e 2CTG (CBG VBG ′ + CTG VTG ′) + (δ𝜇T_BG + δ𝜇T_TG ) (10) CBG + CTG CBG + CTG

Here, any disorder induced interface states are not considered. Figure 3(c) shows the extracted transport gap values for samples #1 and #2. The sample #1 gap data probed using our another chemical potential probing technique8 are also included, which can be done only at DNP. The transport gap values measured in samples #1 and #2 are surprisingly close to the theoretically expected gap values (dashed line)12.

Multiple wide-range temperature dependent

measurements17,18,20,21 were performed to extract thermal activation energies, but only at an E-field



higher than 0.5 V/nm valid gap values were produced. Infrared spectroscopy15,16 provided band gap values, which is in agreement with theoretical tight-binding calculation, but the number of data points is limited also for small E-field regime. In Fig. 3(c) we also show the transport gap measurement data performed on bilayer graphene with oxide dielectrics (Samples A and B)22. Samples A and B are on SiO2 substrate and encapsulated by Al2O3. The transport gaps extracted from the samples with oxide dielectrics are significantly larger than the theoretical values. This feature is a clear distinction from that of samples #1 and #2, bilayer graphene with hBN dielectrics. SiO2 substrates induce spatial disorder and numerous impurities in graphene resulting in interface trap states within a gap17,20,26–28. Those gap states should be filled up first to induce carriers in a conduction or valence band, which requires additional bias across the dielectric. In contrast, the transport gaps measured in sample #2 with hBN dielectrics agrees very well with the theoretical expectation, showing negligible disorder and gap states. This confirms that encapsulating graphene with hBN protects the pristine quality of graphene and presumably general two-dimensional materials as well.

Figure 4: (a) Dit (left axis) and total gap states, Dit, (right axis) extracted from transport gap data of bilayer graphene with oxide dielectrics22 as a function of theoretical gap values for an applied E-field. Closed and open symbols mark Samples A and B respectively. (b) Dit (left axis) and Dit (right axis) extracted for sample #1. Closed and open symbols represent two opposite E-field directions.


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Sample #1 has transport gap values slightly larger than the calculation, and we extracted the information about gap states from a little discrepancy. Taking into account the density of gap states in bilayer graphene, Eq. (8) and Eq. (9) are corrected into CTG (δ𝜇B_BG – δ𝜇T_BG ) e2 Dit δ𝜇B_BG eVBG ′ = + + δμB_BG (11) CBG CBG eVTG ′ =

CBG δ𝜇B_TG e2 Dit δ𝜇B_BG + – δ𝜇T_TG + δ𝜇B_TG (12) CTG CTG

where Dit is average density of gap states per energy. Then the corrected transport gap is given as

=

2e(CBG VBG ′ + CTG VTG ′ ) + 2CTG (δ𝜇T_BG + δ𝜇T_TG ) CBG + CTG + e2 Dit

(13)

By equating Δ to the theoretically calculated gap value and using Dit as a fitting parameter, we extract Dit as a function of an applied E-field. Figure 4(a) shows the calculated Dit and total gap states Dit   for Sample A and B, bilayer graphene with oxide dielectrics, as a function of theoretical gap value. The obtained Dit values vary from 6  1012 to 9  1012 cm-2/eV, and a band gap (E-field) dependence is not observed. This gap-size-independent Dit indeed leads to the linearly increasing total gap-states as a band gap increases as shown in Fig. 4(a). The linear fit yields averaged Dit = 7.3  1012 cm-2/eV. Fig. 4(b) shows the Dit and total gap states extracted from sample #1 as a function of band gap. Interestingly, the extracted Dit in sample #1 decreases as a band gap increases, distinctive from the behavior seen in samples with oxide dielectrics. This suggests that Dit is mostly concentrated at a certain energy range, presumably near the band edges. Despite the decreasing trend of Dit with an increasing band gap, interestingly the total interface states in a gap shows a clear linearity with an increasing band gap. The linear fit to the total interface states vs gap provides a gap state increasing rate as 7.8  1011 cm-2/eV with an intercept of ~ 2  1010 cm-2 at zero band gap. The standard error of the extrapolated intercept value is ~ 1 



109 cm-2. This reveals ~ 2  1010 cm-2 interface states localized at band edges even without a band gap, and 7.8  1011 cm-2/eV density of gap states per energy equally spread over the gap regardless of the gap size. The intercept values from Fig. 4(a) data are ~ 6  109 cm-2 and ~ 6  1010 cm-2 for Samples A and B respectively both with a standard error of ~ 4  1010 cm-2, comparable to the intercept value. This suggests that the density of interface states localized at band edges of samples with oxide dielectrics can range up to 1011 cm-2. Several studies17,20,29 provide the estimation of charge density in fluctuating potentials (puddles), which is in the range of 2  1011 ~ 1012 cm-2 for graphene on SiO2 and ~ 2  109 cm-2 for graphene on hBN. However, there have been no detailed study showing the variation of gap states as a function of gap size and the density of interface states localized at band edges. In summary, we measured conductivity of bilayer graphene encapsulated by hBN as a function of carrier density and transverse E-field. Similar to dual-gated bilayer graphene with oxides as dielectrics, our samples show finite threshold voltages for the onset of conduction, which increase as the E-field increases. Surprisingly, the extracted transport gaps are far closer to the theoretically expected gap values, in contrast to those of graphene on oxide dielectrics. This confirms that encapsulating graphene with hBN protects the pristine quality of graphene and presumably general two-dimensional materials as well. Our study also suggests that our simple transport gap measurement method is reliable and can be utilized to probe a band gap of other high quality semiconductors or to extract rich information about interface states.


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Acknowledgements This work was supported by NRI-SWAN. K. L. acknowledges support from the Korean National Research Foundation (NRF) funded by the Korea government (MSIT) with the grant number NRF-2018R1C1B3002733 and NRF-2013M3A6B1078873.



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Interface States in Bilayer Graphene Encapsulated by Hexagonal

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