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Ultrahigh Conductivity in Two-dimensional InSe via Remote Doping at Room Temperature Xin-Yi Liu, Ji-Chang Ren, Shufang Zhang, Miguel Fuentes-Cabrera, Shuang Li, and Wei Liu J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b01589 • Publication Date (Web): 28 Jun 2018 Downloaded from http://pubs.acs.org on June 29, 2018

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The Journal of Physical Chemistry Letters

Ultrahigh Conductivity in Two-dimensional InSe via Remote Doping at Room Temperature Xinyi Liu,1 Ji-Chang Ren,1 Shufang Zhang,2 Miguel Fuentes-Cabrera,3 Shuang Li1* and Wei Liu1* 1

Nano and Heterogeneous Materials Center, School of Materials Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China

*Email: [email protected] and [email protected] 2

School of Materials Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China

3

Center for Nanophase Materials Sciences, and Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States

ACS Paragon Plus Environment

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ABSTRACT

Conductivity of two-dimensional (2D) materials, which largely determines the efficiency and reliability of nanodevices, is proportional to the product of carrier concentration and mobility. Conventional doping, such as ionic substitution or introduction of vacancies, increases carrier concentration and decreases carrier mobility due to the scattering or trapping of carriers. Here, we propose a remote-doping strategy that enables the simultaneous enhancement of both parameters. Density functional theory calculations in 2D InSe reveal that adsorbing the molecule tetrathiafulvalene TTF and applying a 4% external tensile strain, which leads to an increase in the carrier concentration of the TTF-InSe system that is 13 orders of magnitude higher than that of the pristine counterpart, whereas the carrier mobility is enhanced by 35% compared to the InSe monolayer. As a consequence of the synergetic role of molecule doping and strain engineering, ultrahigh conductivity of 1.85 × 105 S/m is achieved in the TTF-InSe system at room temperature. TOC GRAPHICS


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Indium selenide (InSe) has low effective mass of conductive electrons and moderate band gap,1,2 which makes it very attractive for applications in superfast electronics.3 Recently, twodimensional (2D) InSe was mechanically exfoliated;4,5 and few-layer InSe possesses chemically inert surfaces and exhibits a high environmental stability.6-8 Applications of InSe-based devices with high efficiency and high reliability demand ultrahigh electrical conductivity, which is dominated by the carrier concentration and the carrier mobility. Carrier mobility can be increased by increasing the number of layers in 2D InSe, however carrier mobility practically saturates at ten layers.6 Conventional chemical doping, such as ionic substitution or vacancies, can enhance the carrier concentration of semiconductors.9-11 These routes, however, would also introduce impurity scattering in the system, which causes a significant reduction in the carrier mobility.12 To date, enhancing carrier concentration of 2D materials without sacrificing carrier mobility is a challenging task. In this Communication, we show that this challenge could be solved by “remote doping”,13,14 which refers to a synergic combination of the physisorption of organic molecules and the strain engineering on 2D materials and both processes can be readily realized in experiments.15-17 To demonstrate the validity of this approach, we systematically study the interactions

of

several

organic

molecules,

including

tetracyanoethylene

(TCNE),

tetracyanoquinodimethane (TCNQ), tetrafluorotetracyanoquinodimethane (F4TCNQ), and tetrathiafulvalene (TTF), with InSe monolayers. Using density-functional theory (DFT) with the many-body dispersion (MBD) method,18,19 we find that the physisorbed molecules create a doping level, assisting thermally excitations of electronic carrier, and increase the carrier concentration of the InSe monolayer. The intrinsic carrier mobility of the substrate is remained, since the lattice deformation and the impurity scattering are excluded in the host material.13,20


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Furthermore, the superimposition of tensile strain would reduce the ionization energy, and more importantly, lead to the promotion of both the carrier mobility and carrier concentration of the system. As a consequence, we achieve an ultrahigh conductivity of 1.85 × 105 S/m in the TTFInSe system at room temperature, which is 3.7 times larger than that of MoS2. The remote doping avenue is expected to be a straightforward, non-destructive, and effective method, which can be generally applied to enhance the conductivity of many other 2D materials.

Figure 1. (a) Structures of TTF, TCNE, F4TCNQ, and TCNQ molecules. (b) Side view of the most favorable adsorbed structures for the TTF-InSe, TCNE-InSe, F4TCNQ-InSe, and TCNQ-InSe systems. The brown, blue, white, light blue, yellow, purple, and green spheres represent C, N, H, F, S, In, and Se atoms, respectively. For each system the adsorption height between the molecule and the InSe monolayer is also indicated. (c) Top view and side view of the pristine InSe and band structure of the single-layer InSe. The Brillouin path is set as M (0, 1/2, 0) – K (1/3, 2/3, 0) – Γ (0, 0, 0) – M (0, 1/2, 0). (d) Band structures of the adsorbed systems. The horizontal red lines indicate the Fermi level, which is set to zero. The flat level around the Fermi level is the doping level, which is mostly attributed to the organic molecules. The distance between the doping level and the VBM or CBM is the ionization energy, which is denoted as Ed for TTF-InSe, and as Ea for the other three systems.

The interactions of TTF, F4TCNQ, TCNQ, and TCNE molecules with the InSe monolayer were first investigated. For each molecule, we fully relaxed all possible adsorption


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configurations shown in Figure S1 with the PBE+vdW method,21 and subsequently determined their corresponding adsorption energies using the state-of-the-art PBE+MBD approach.19,22,23 Note that the MBD method, which computes the long-range correlation energy through the coupled harmonic oscillator model Hamiltonian and treats dipolar van der Waals (vdW) interactions to all orders in perturbation theory beyond the pairwise correction scheme, has been demonstrated to treat supra-molecules, molecular crystals, layered nanostructures, and adsorption systems very well.24-27 Despite the distinct chemical structures of the four molecules (Figure 1a), the vdW forces are found to largely dominate the interactions between all the adsorbates and the InSe monolayer. As shown in Table 1, the positive adsorption energies from PBE (endothermic) become negative (exothermic) after including vdW interactions; the PBE+MBD adsorption energies are consistently larger than those from PBE+vdW, which is attributed to the many-body correlation effects and Coulomb-screening within the substrate. Table 1. Adsorption energy (Eads) with the PBE+MBD, PBE+vdW, and PBE methods, charge transfer (∆q)a with Bader charge analysis, ionization energy (Ei), and effective masses for electrons (me* ) of the TTF, F4TCNQ, TCNQ, and TCNE modified InSe monolayers. m0 is the mass of free electron.

Systems TTF-InSe F4TCNQ-InSe TCNQ-InSe TCNE-InSe Pristine InSe a

Eads (eV) PBE+MBD PBE+vdW −0.59 −0.74 −0.71 −0.93 −0.54 −0.70 −0.40 −0.45

PBE 0.01 0.31 0.17 0.05

∆q (e)a

Ei (eV)

me*/m0

+0.13 −0.26 −0.12 −0.17

0.40 0.73 1.14 1.25

0.185 0.182 0.182 0.182 0.185

A negative ∆q indicates that electrons transfer from the InSe monolayer to the molecules, and vice versa.

Figure 1b shows the most preferable adsorption structures for each molecule on the InSe monolayer. In all cases, one would expect a physisorptive nature of bonding due to the large adsorption heights (3.29 to 3.56 Å) between the molecule and the Se atom in the topmost layer. Interestingly, we find that the bending behaviour of adsorbed TTF is opposite to that of TCNE, F4TCNQ, and TCNQ. This is presumably because the Se atoms on the surface expose the lone


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pair p electrons, which causes a Pauli repulsion effect on the lone pair p electrons located in the centre of TTF (for S atoms), but at the edges in the other molecules (for N and F atoms). The different bending structures induce dipole electric filed pointing in the opposite direction. Consequently, TTF donates electrons to the substrate and exhibit n-type doping, while TCNE, F4TCNQ, and TCNQ accept electrons and exhibit p-type doping on InSe. The above findings can be confirmed by the Barder charge analysis28 results, which are shown in Table 1. Based on the optimized adsorption structures, we next proceed to investigate their electronic conductivity σ. For n-type semiconductor, the product of mobility µ and carrier concentration n determines the conductivity as σ = nqµ, where q is the unit electron charge constant. We first determine the carrier mobility using the Drude model, which is expressed with the formula: µ = −qτ/m*. Here, m* and τ denote the effective mass and the relaxation time of carriers, respectively. Note that m* can be estimated by calculating the second derivative of band energy with respect of momentum of carrier, m* = ±ћ2(d2Ek/dk2)−1.29 The hybrid DFT-HSE exchange-correlation functional,30 which corrects for large part of the self-interaction error in the exchange energy, can obviously modify the size of band gap and even affect the magnetic properties in materials.31 According to our calculations, we also found that the CBM (conduction band minimum) computed with HSE is significantly sharper than that with PBE (c.f. Fig. S3), which means a lighter effective mass and this value agrees better with the experimental value.6 Thus, in our study, the hybrid DFT-HSE exchange-correlation functional were utilized to calculate energy band structures for all the studied systems. From Figs. 1c and 1d, it can be deduced that (1) the effective mass of holes in intrinsic InSe is significantly larger than the mass of electrons; and (2) molecule physisorption leads to an energetic shift of InSe conductive bands, their shapes are slightly changed due to the weak binding at the interface. As a result of this, an almost identical


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effective mass of electrons for the pristine and molecule-adsorbed InSe was obtained (c.f. Table 1). Due to the poor performance of the p-type InSe, and thus its limited applicability in superfast electronics, we focus on the n-type TTF adsorbed InSe system from now on. Since the effective mass is practically unchanged unpon adsorption, the main roles for the mobility may be modified by relaxation time. The relaxation time is directly related to the scattering mechanisms of the carriers. Note that the carrier density of semiconductors is normally lower than that of metals, which can be treated as nondegenerate gas. Thus, electron-electron interaction can be safely ignored here. Further, impurity scattering can also be excluded, since no impurity has been introduced into the host material. The only scattering mechanism left is electron phonon interaction. Based on perturbation theory, electron-phonon interaction can be estimated by fully calculating electron phonon coupling matrix. However, given the size of our systems, we use the following approximation: since there is only one valley for conductive band, and this valley locates at the center of the Brillouin Zone, we can adopt the long wave approximation for the carrier scattering. Due to the nature of single valley of the system, momentum transfer can also be ignored here. Therefore, we can safely apply the commonly used deformation potential method proposed by Bardeen and Shockley,32,33 to estimate the relaxation time of the carrier. In this case, τ = 2ћ3C/(3kBTm*D2), where the deformation potential constant D is calculated by simultaneously expanding (contracting) lattices of InSe, i.e. D = dVedge/dε, with Vedge, the energy change of the CBM for electrons under the appropriate perturbation, ε stands the strength of perturbatively deformed lattices. The elastic modulus C is derived from (∂2E/∂ε2)/S0, where E represents the total energy and S0 stands for the area of the system. In this manner, the relaxation time is determined by the elastic modulus, effective masses and deformation potential constant, all independent of the adsorbed molecules. Therefore, in the


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proposed remote-doping, if the adsorbed organic molecules interact weakly with InSe, the mobilities of InSe remain practically unaltered. The other main parameter that affects electric conductivity is carrier concentration. In the limit of (EC − EF) >> kBT, the electron carrier concentration can be calculated with the formula n = NCexp[−(EC − EF)/2kBT].34 NC presents effective level density of the conduction band, the number of energy levels in the unit energy, EC is the minimum value of conduction band, kB is the Boltzmann constant, and T is the temperature. For the doping system, carrier concentration is described as following:34 n = (NCND)1/2exp(−Ei/2kBT)

(1)

where ND is the doping concentration, and Ei denotes the ionization energy, which are determined by the distance between the doping level and the valence band maximum (VBM) or conduction band minimum (CBM). The ionization energies were obtained from the partial density of states (PDOSs) of the systems (Figure S6). In analogy to traditional doping method, the localized doping states are pinned deeply in the gap of InSe, forming a deep doping level (Fig. 1d). The TTF-InSe system has the smallest ionization energy of 0.4 eV (Table 1); however, this value is still too large for the thermal excitation of carriers. In light of Eq. (1), a smaller Ei value is required in order to boost thermal excitation and further increase n. Here arises the question: how can we reduce the ionization energy in the TTF-InSe system? One practical method is to introduce the concept of partial strain, i.e. the strain is only applied to the substrate, but not to the adsorbed molecule. Since the adsorbates are weakly bound on the InSe monolayer, only the substrate can feel the effect of strain. In this context, one may assume


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that the band edges of InSe would shift under applied strain, but the energy level of the molecule remained pinned in the gap.

Figure 2. (a) Adsorption energies (Eads) using the PBE+MBD method. (b) Charge transfer (∆q) with Bader charge analysis. (c) Ionization energies (Ei) using the hybrid HSE06 functional for F4TCNQ, TCNQ, TCNE, and TTF modified InSe at different strain conditions. (d) Carrier concentration (n) of the TTF-InSe as a function of temperature under different strain. The red lines indicate the systems with 4% tensile strain, blue and black lines indicate the unstrained systems and the systems with 4% compressive strain, respectively.

To prove this assumption, we carried out a series of calculations by applying strains on adsorbed systems. Remarkably, promotion of electronic conductivity by strain occurs in three different ways: strain stabilizes the physical adsorption, increases the interfacial charge transfer and reduces the ionization energy. As shown in Figs. 2a and 2b, the binding energy and charge transfer of all adsorption systems studied here increase with tensile strain, whilst decrease with compressive strain. In contrast, the ionization energy decreases at 4% tensile strain and increases at 4% compressive strain (see Fig. 2c). Notably, charge transfer and ionization energy change most in TTF-InSe system. Specifically, the charge transfer at 4% tensile strain is twice of that of


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the unstrained counterpart; the ionization energy drops to 0.10 eV, suggesting that tensile strain turns the deep doping into a shallow one. The large reduction in the ionization energy is a consequence of the large shift of CBM under 4% tensile stain, which reduces the energy gap between the doping level and the CBM level. The carrier concentration of TTF-InSe as a function of temperature under stain was also determined using Eq. (1). In this case ND = 4.16 × 1020 cm−3, and NC = 2 × (me* kBT/2πћ2)3/2.35 As shown in Fig. 2d, the carrier concentration increases (decreases) when the tensile (compressive) strain is applied, due to the decrease (increase) of ionization energy.

Figure 3. (a) Carrier concentrations n of TTF modified InSe and pristine InSe with different strains at room temperature. (b) Carrier mobility (µ) as a function of tensile strain (ε) at different temperature (T). The isotropic strain ε is defined as ε = ∆a/a0, where a0 is the equilibrium lattice constant and ∆a is the deformation of a0. The carrier mobility decreases with increasing the temperature and almost saturates at 300 K.

Due to the significant reduction of ionization energy of TTF-InSe, the carrier concentration of TTF-InSe with 4% tensile strain at room temperature (3.99 × 1018 cm−3) is thirteen orders of magnitude higher than for the pristine InSe (3.65 × 105 cm−3; Figure 3a). Therefore, molecule doping injects carriers to substrates and increases carrier concentration, which is up to 1.25 × 1016 cm−3 for TTF-InSe and is eleven orders of magnitude higher than for the pristine InSe;


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applied strain, on the other hand, can further increase the carrier concentration by reducing the ionization energy. To investigate the influence of external strains on the mobility of the pristine InSe monolayer, we calculated the carrier mobility using the formula µ = 2qћ3C/3kBT(me*)2D2.32,33 The calculated me* and D values are shown in Table 1; where C for InSe is 76 N m−1.36 Here we assume the values of D, me*, and C are all independent of the temperature.33,35,37 Figure 3b shows that the carrier mobility of InSe is significantly enhanced with the increased tensile strain, due to the reduction of both the deformation potential and effective masses for electrons (c.f. Table 2). Table 2 also shows that the mobility decreases with increasing temperature, since more phonons are involved in scattering at higher temperature. Table 2. Calculated effective masses of electrons in the unit of free-electron mass (me* /m0), deformation potentials (D, in eV)a, and carrier mobilities (µ, in 103 cm2 V−1 s−1) of 50 K and 300 K at different strain conditions.

Strain

D

me*/m0

µ (50 K)

µ (300 K)

−4%

3.535

0.210

12.452

2.075

−3%

3.771

0.201

11.956

1.993

−2%

3.838

0.194

12.368

2.061

−1%

3.983

0.189

12.102

2.017

0

3.940

0.185

12.912

2.152

1%

3.960

0.180

13.507

2.251

2%

3.920

0.176

14.428

2.405

3%

3.830

0.173

15.632

2.605

4%

3.673

0.171

17.402

2.900

a

D is calculated with the equation: D = dVedge/dε. Here Vedge is the energy change of the CBM for electrons under appropriate strains, and ε denotes the strain.

Based on the above analysis, it can be concluded by the combined method of molecule doping and strain, it is possible to simultaneously improve the carrier concentration and carrier mobility. For comparison, the carrier concentration and carrier mobility of other materials,


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together with TTF-InSe (4% strain) at room temperature, are given in Fig. 4a. According to our calculations, an ultrahigh conductivity (1.852 × 105 S/m) at room temperature is achieved in TTF-InSe with 4% tensile strain, which is superior to other semiconductor materials (Figure 4b). The enhanced conductivity is attributed to the higher carrier concentration and larger carrier mobility at 4% tensile strain, doped with the TTF molecule.

Figure 4. (a) Conductivity σ, carrier mobility µ and carrier concentration n of TTF-InSe with 4% tensile strain as functions of temperature T. The carrier concentration and conductivity increase while the mobility decreases with increasing temperature, revealing typical semiconductor characteristics. (b) Scatter diagram with carrier mobility as x-axis and carrier concentration as yaxis of TTF-InSe with 4% tensile strain and other semiconductor materials at room temperature. The black dashed lines present the isolines of different conductivity value σ, which is defined as σ = nqµ. Here the value of carrier concentration, mobility and conductivity is taken from literature.38-43

In summary, we have systematically investigated the electronic structures properties of InSe monolayer with and without adsorbed molecules. Our results show that physisorption of organic molecules on InSe increases the carrier concentration without introducing lattice defects. More importantly, a combination of molecule doping and substrate strain improves the carrier concentration and carrier mobility simultaneously. In particularly, an ultrahigh conductivity of 1.85 × 105 S/m at room temperature was achieved when a 4% tensile strain is applied to the TTFInSe system. It should be noted that the electronic conductivity can also benefit from the screening effects introduced by the charge carriers and the adsorbed molecule, both of which can weaken the electron phonon scattering. The former is attributed to the free electron, and the latter


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originates from large dielectric difference between the molecule and InSe, and thus the Coulomb potential that the carrier felt can also be reduced;44 this issue deserves future attention as it might provide more ways to further improve the electronic conductivity of “remotely doped” systems. COMPUTATIONAL METHODS Structural optimizations based on density-functional theory (DFT) were carried out with the plane-wave basis set Vienna Ab initio simulation package (VASP) code,45,46 along with the generalized gradient approximation (GGA) of Perdew-Burke-Ernzernhof (PBE) for exchange and correlation functional.47,48 A kinetic energy cutoff of 450 eV was used in the simulations. For geometry relaxation calculations, the Brillouin Zone sampling used was 4×4×1 in the Monkhorst-Pack grid.49 The vacuum thickness was set to 20 Å. Because the GGA-PBE exchange correlation functional tends to underestimate the bandgap of semiconductors, the screened hybrid HSE06 functional, which was implemented in the Fritz Haber Institute ab initio molecular simulations (FHI-aims) code, was utilized to determine the electronic band structure of InSe systems. For adsorption energy calculations we also employed the PBE+MBD method, which accurately considers the nonlocal many-body dispersion interactions. We carried out Bader charge analysis to investigate the electron transfer between doping molecules and substrates.

ACKNOWLEDGMENT We acknowledge supports from the NSF of China (51602155, 51722102, 21773120), the Fundamental Research Funds for the Central Universities (30918011340, 30917011201) and Jiangsu Key Laboratory of Advanced Micro&Nano Materials and Technology. ASSOCIATED CONTENT Supporting Information


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Supporting Information available: Possible adsorption configurations and adsorption energies of different molecules on InSe, the charge transfer between the molecules and monolayer InSe, calculated CBM (conduction band minimum) with PBE and HSE, band structures and the partial density of states (PDOSs) of InSe under different strain conditions, carrier mobility of the InSe monolayer as a function of strain under different temperature, PDOSs of adsorbed systems under different strain conditions, Strain-dependent adsorption energy, charge transfer, ionization energy, and band gaps of different adsorption systems, and the values of carrier mobility, carrier concentration, and conductivity of the InSe-based systems and other semiconductor materials at room temperature. Notes The authors declare no competing financial interests. REFERENCES (1)

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Ultrahigh Conductivity in Two-Dimensional InSe ... - ACS Publications

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