advances.sciencemag.org/cgi/content/full/3/4/e1602726/dc1 Supplementary Materials for Selective control of electron and hole tunneling in 2D assembly This PDF file includes: Dongil Chu, Young Hee Lee, Eun Kyu Kim Published 19 April 2017, Sci. Adv. 3, e1602726 (2017) DOI: 10.1126/sciadv.1602726 Supplementary Text fig. S1. The 3D schematic structure of the carristor. fig. S2. Optical images of MIS-C fabrication steps. fig. S3. Optical images of GW-B (or GM-B) fabrication steps. fig. S4. Band alignment of MIS-C and XPS spectra. fig. S5. Schematic representation and I-V curves. fig. S6. ITB-VTB curve for GW-B at different temperatures from 90 to 290 K VG = 0. fig. S7. Electrical transport characteristics of GW-B. fig. S8. Electrical transport characteristics of GM-B. fig. S9. Highly nonlinear dependence of ITB as a function of VTB for experimental (black line) and calculated data (red dots) under zero gate field and T = 300 K. fig. S10. Semilog ITB-VG curves for MIS-C at different VTB from 0.1 to 0.5 V at room temperature. table S1. List of symbols and descriptions used in the study. References (35 41)
Supplementary Text Surface carrier density calculation The applied VTB across MIS structure is divided into two parts, i.e., the voltage drop across the hbn insulator (VBN) and the semiconductor (ϕs), so that the relationship can be written as (14) V V TB ms BN s where ϕms is not negligible. The oxide charges are ignored in this simplified discussion. The potential drop in the insulator can be related to the space-charge density Qs, and is given by VBN=QsdBN/εBN. (S1) By solving the one-dimensional Poisson equation and applying Gauss s law for n-type semiconducting WS2 (35, 36), the Qs at the interface of the heterojunction is as follows: 2 n e e (S2) i e s /kbt s e s /kbt s QS 2WS2k BTND e 1 e 1 ND kbt kbt where εws2=11.5 is the dielectric constant of bulk WS2 (37). The parameters ni and ND=10 16-10 17 cm -3 are the intrinsic carrier density and donor impurity concentration at room temperature (36, 38), respectively. For the non-degenerately doped semiconductor, ni can be obtained from the effective DoS in the conduction band, NC, and the effective DoS in the valence band, Nv. E G ni NCNV exp 2k T B (S3) The surface carrier density neh as a function of VTB as illustrated in Fig. 2B (main text) can be calculated using these equations. 1/2 Analytic model of the carristors When the insulator is a few atomic layers thick (6-7 layers in our case) as in the MIS structure, the time-independent part of the wave function Ψ(x) of the confined electrons at the semiconductor surface does not end abruptly. The problem is to solve for the probability of electron transmission through the insulator barrier for determining the tunneling current. This calculation is performed by applying the effective-mass-approximated one-dimensional Schrodinger s equation as 2 * 2 2 2m d (x) dx [E V(x)] (x) 0, where V(x) is the potential across the barrier 25,26. The solution of Ψ(x) has a general plane waveform of * 2 (x) exp i 2m (EV) x. The value inside the square root is imaginary. The WKB approximation assumes that the potential barrier changes slowly with respect to position, so that the tunneling coefficient can be calculated using Ψ * Ψ by assuming a parabolic dispersion relationship of hbn and is given by (14)
* * xb 2m 2dBN 2emBNTp T exp[ 2 (E V)dx] exp( ) E x 2 a In the case of the rectangular barrier, the distance between the classical turning points xa and xb is the barrier width (dbn). (S4) Based on the above discussion, we modeled the back-gate modulated tunneling current expressed as follows (39) * 4em I (V,V ) A de de T F F h TB TB G 3 0 0 T E 1 2 where ET and E are the transverse and total kinetic energies of the electrons in the semiconductor and F1 and F2 are the respective Fermi-Dirac distribution functions for MGr and WS2. Since the lower integral limit in these integrals corresponds to the WS2 conduction band edge, integrating over the energy range, Equation (S5) is reduced to * 2dBN 2emBNTp * 2 TB TB G 1 FW TB 2 FW (S5) I (V,V ) A AT e F E ev F E (S6) Here, EFW is the energy distance towards the WS2 conduction band. For a positive VTB applied on the MGr, we obtain the relations EFW=eϕs+kBTln(NC/ND) and EFG=EFW-eVTB. Equation (S6) can be written as TB TB G D C U s TB G B f e (V,V ) k T evtb kbt I (V,V ) N N e e e 1 (S7) and (noting that ϕs is a function of two variables, VTB and VG) 1/2 endws2 kt B N 2eN C D WS2 s,vg V 2 TB m EFG ln WS2 2CBN e N D CBN (S8) where CBN=ε0εBN/dBN (εbn 4) 30,31 is the capacitance per unit area of hbn. Equation (S8) is derived from the relations (S1) and (S2), in which the semiconductor charges are approximated QS 2eNDWS2 S for the depletion and weak inversion regime:. This approach is available for transistor-like operation when the interface of MIS-C is near the inversion mode. Alternatively, when the external electrostatic field only minimally changes the interface mode, the terms related to surface potential and other parameters can be replaced to obtain the effective Schottky barrier height. Figure S9 shows the experimental ITB-VTB data and compares it to the simulated data by solving equation (S7) with effective eϕb=230 mev. This value is consistent with the predicted value of the Schottky-Mott model, determined to be approximately 200 mev using an experimentally observed electron affinity of 4.4 ev in ref. (40). The EFG in the above equation significantly depends on the back-gate polarity and the thickness of MGr. If we use single-layer graphene instead of multi-layer graphene, the value is calculated as EFG F n eh (V G) (41). The doping concentration in graphene is inversely proportional to the capacitance of silicon oxide (we used 280-nm-thick SiO2) in the back-gate dielectric. The controllability of the surface potential would be enhanced using high-κ dielectric materials (such as HfO2 or Al2O3) to obtain further improvement in the subthreshold swing parameter. 2
Surface potential calculation Based on equation (S7), the determination of the ϕs relies on measuring the activation energy. One advantage of this technique is that it is available without accurate knowledge of the active contact area. The equation can be rewritten as follows when VTB>>kBT/e e V 2 s TB ln ITB T cons tan t (S9) kt B From the Richardson plot (ln(itb/t 2 ) vs. 1000/T) for different VTB (from 0.2 to 0.6 V), a slope can be extracted at various VTB. The slope follows a linear dependence with -e(ϕs-vtb/ η)/1000kb, thus ϕs can be evaluated in terms of the intercept value.
a Top lead WS 2 hbn Bottom lead MGr SiO 2 Si (back-gate) b fig. S1. The 3D schematic structure of the carristor. (A) Cross-sectional illustration of the device layout with precisely aligned multi-2d-crystals. Left side view (B) and right side view (C) of the carristor.
a MGr b hbn SiO 2 Ti/Au c d WS 2 PR fig. S2. Optical images of MIS-C fabrication steps. (A) Optical image of the bottom lead metallization and the MGr deposition for the electrical interconnection with Ti/Au. A series of optical images of hbn deposition (B), WS2 deposition (C), and negative-tone photoresist (PR) patterning (D). Scale bar is 5 μm.
a b SiO 2 MGr Ti/Au WS 2 c PR d B T1 T3 T2 fig. S3. Optical images of GW-B (or GM-B) fabrication steps. (A) A series optical image of MGr deposition (A), overlapping with WS2 (or MoS2) flake (B), and top leads patterning (C). (D) Optical image of the device after metallization.
a b c N 1s S 2p W G =4.6 eχ Tn =2.46 eχ WS2=4.24 VBM hbn E g = 5 WS 2 E g = 1.3 eχ Tp =1.24 32.08 VBM Intensity (a. u.) Intensity (a. u.) W 4f 188.74 B 1s 157.9 390 395 400 405 Binding energy (ev) 160 162 164 166 Binding energy (ev) fig. S4. Band alignment of MIS-C and XPS spectra. (A) VBO and CBO line-up of the hbn-ws2 heterojunction, showing a hole (electron) barrier height to be 1.24 ev (2.46 ev) with a type-i structure. The relative position of graphene from the vacuum level is included. XPS spectra of N 1s (B) and S 2p state (C) for hbn and WS2, respectively.
a Ti/Au Ti/Au MGr WS 2 or MoS 2 Ti/Au Si (back-gate) 280nm SiO 2 b 400 Linear Log 10-6 10-7 c 800 Linear Log 10-6 10-7 10-8 600 10-8 (na) 200 (A) (na) 400 (A) 0 200-200 -1.0-0.5 0.0 0.5 1.0 Graphene/WS 2 barristor 10-12 -1.0-0.5 0.0 0.5 1.0 fig. S5. Schematic representation and I-V curves. (A) Schematic diagram showing the barristor (GW-B and GM-B) layout. Room-temperature ITB-VTB output curves for (B) GW-B and (C) GM-B at zero VG bias. 0 Graphene/MoS 2 barristor 10-12
10-6 (A) 10-7 10-8 10-12 10-13 10-14 T (K) 290 275 260 245 230 210 190 170 150 130 110 100 90 10-15 -1.0-0.5 0.0 0.5 1.0 fig. S6. ITB-VTB curve for GW-B at different temperatures from 90 to 290 K VG = 0. The two temperature regimes, corresponding to semiconducting and metallic phases, can be observed at low and high temperature, respectively.
a 10-6 b 10-6 10-7 10-7 =-0.5 V 10-8 10-8 /j TB /(A um -2 ) 10-12 10-13 10-14 V G -1.0-0.5 0.0 0.5 1.0-7 -5-3 -1 1 3 5 7 (A) 10-12 10-13 on/off ratio ~1.210 5-15 -10-5 0 5 10 15 V G fig. S7. Electrical transport characteristics of GW-B. (A) Room-temperature semi-log ITB-VTB output characteristics of a typical GW-B under various VG voltage showing current multiplication behavior. (B) Room-temperature semi-log ITB-VG transfer characteristics of the same device at VTB=-0.5 V showing the switching ratio exceeding 1.2 10 5.
a 12 b = 0.5 V (na) 10 8 6 4 2 V G -7-6 -5-4 -3-2 -1 0 1 2 (A) on/off ratio ~ 30 0-1.0-0.5 0.0 0.5 1.0-15 -10-5 0 5 10 15 V G fig. S8. Electrical transport characteristics of GM-B. (A) Room-temperature ITB-VTB output characteristics of a typical GM-B under different various back-gate voltages from VG=2 V to VG=-7 V. (B) Room-temperature semi-log ITB-VG transfer characteristics of the same device.
10-7 Calculated data Experiments 10-8 (A) 10-12 10-13 10-14 10-15 -0.4-0.2 0.0 0.2 0.4 0.6 0.8 1.0 fig. S9. Highly nonlinear dependence of ITB as a function of VTB for experimental (black line) and calculated data (red dots) under zero gate field and T = 300 K.
10-6 10-7 10-8 (A) 10-12 10-13 -0.5-0.4-0.3-0.2-0.1 10-14 10-15 -15-10 -5 0 5 10 15 V G fig. S10. Semilog ITB-VG curves for MIS-C at different VTB from 0.1 to 0.5 V at room temperature.
table S1. List of symbols and descriptions used in the study. Description Symbol Unit Schottky barrier height ϕb V On-state current Ion A Off-state current Ioff A Surface potential ϕs V Graphene Fermi level shift EFG ev Graphene Fermi level EFG ev Quasi-Fermi level for electrons EFn ev Quasi-Fermi level for holes EFp ev Back-gate voltage VG V Bias voltage VTB V Current ITB A Saturation current I0 A Current density JTB Aμm -2 Elementary charge e C Ideality factor η - Boltzmann constant kb evk -1 Absolute temperature T K Rectification ratio RR - Barrier height χtp V Out-of-plane resistivity ρ T Ωμm 2 In-plane resistivity ρ Ω Activation energy EA ev Depletion width WD cm Carrier lifetime τ s Intrinsic carrier density ni cm -3 Transmission coefficient TE - Work function difference ϕms V Graphene work function WG ev WS2 work function Ws ev Richardson constant A * Acm -2 K -2 Active contact area A μm 2 Barrier function Uf - Effective mass of a hole in hbn m * BN kg Electron rest mass m0 kg Barrier thickness dbn nm