Theoretical Prediction on the Versatile Electronic Properties of Graphdiyne and

YU Yang WANG Guo LIAO Yi



Theoretical Prediction on the Versatile Electronic Properties of Graphdiyne and Its Nanoribbons Composed of Hexaethynylbenzene and Tetraethynylethene①

YU Yang WANG Guo②LIAO Yi

(100048)

Fourteen atomically thin two-dimensional graphdiynes composed of hexaethynyl- benzene and tetraethynylethene were proposed and investigated using density functional theory. Being different from the traditional graphdiyne, these structures have versatile electronic properties. They can be metals, semimetal, or semiconductors, depending on the coupling patterns and proportions of monomers. One hundred and thirty one one-dimensional nanoribbons cutting from these structures have band gaps larger than 0.4 eV. They have high carrier mobilities. Especially, the hole mobility reaches the order of 105cm2×V-1×s-1. This is caused by small valence band deformation potential constants and explained by crystal orbital analysis. Both the two- and one-dimensional structures have very small formation energies of 32～37 meV per carbon atom. Furthermore, a seamless electronic device composed of theabove metallic electrodes and semiconducting nanoribbon has a high conductance of 11.7mS and the device can be switched off with gate voltage. These imply that the proposed graphdiynes are good candidates for high speed electronic devices.

graphdiyne, tetraethynylethene, carrier mobility, density functional theory;

1 INTRODUCTION

Atomically thin two-dimensional materials have attracted much attention due to the exfoliation of graphene[1]. As a monolayer structure, graphene has many appealing properties, such as high carrier mobility, outstanding electronic properties, and capability of being a substrate[2–6]. The properties are drastically different from those of bulk forms. Thus versatile properties of two dimensional materials are needed to be explored. As an allotrope of graphene, graphdiyne has also attracted extensive attention since it was synthesized[7]. There are cavities in the structure of graphdiyne. The unique structure makes it a good candidate for gas separation[8]. Also, it can be applied in energy field because of its capability of lithium ion storage[9]. The highly conjugated triple bonds in graphdiyne bring it outstanding electronic properties, such as being a semiconductor with high carrier mobility. Therefore, it has promising applica- tions in electronics, photovoltaics, and catalysis[8, 10, 11].

For electronics, graphdiyne is a semiconductor with a high carrier mobility of 7.1 × 102cm2×V-1×s-1[12]. Theoretical calculations indicated that the carrier mobility should be much higher for single-crystal graphdiyne and its nanoribbons[13, 14]. Fortunately, ordered and crystalline graphdiynes were synthesized in state-of-the-art experiments[15–17]. This should significantly elevate the performance of the graphdiyne in electronics. The graphdiyne was synthesized through cross-coupling reaction exclu- sively using hexaethynylbenzene[7]. In fact, more structures that contain acetylenic linkages were proposed.-graphdiyne was predicted to have Dirac cones[18]while its nanoribbons have tunable band gaps[19]. Moreover, our previous work indicated that 6,6,18-graphdiyne and its nanoribbons are semi- conductors. The nanoribbons have high carrier mobilities[20]. It is worth noting that 6,6,18-gra- phdiyne was assumed to be also synthesized by cross-coupling reaction by using 1:1 hexaethynyl- benzene and tetraethynylethene. Like graphdiyne, 6,6,18-graphdiyne and its nanoribbons do not have versatile electronic properties. They are all semicon- ductors. Metallic electrodes, such as copper, are required to compose electronic devices. In addition, the type of coupling between hexaethynylbenzene and tetraethynylethene as well as the proportion of the two monomers may vary. Different allotropes of graphdiyne are needed to be explored, because different structures, like semi-metallic graphite and insulating diamond, may have different electronic properties. In the present work, several graphdiynes composed of hexaethynylbenzene and tetraethynyle- thene (GDYHT) with different proportions and different coupling patterns were constructed and investigated using density functional theory. The GDYHTs can be metals, semimetal, or semicon- ductors. Also, an all-GDYHY seamless electronic device composed of metallic electrodes and semi- conducting nanoribbon was proposed.

2 METHOD

Fourteen two-dimensional GDYHYs were cons- tructed with different proportions of hexaethynyl- benzene and tetraethynylethene. The monomers are shown in Figs. 1(a) and 1(b). They can couple either with the same or different type of molecules. The number of the same type of coupled molecules can be used to name the GDYHYs. For example, the unit cell indicated by a rectangle in Fig. 1(c) contains three hexaethynylbenzene molecules and one tetraethynylethene molecule, so the structure is called GDYHY-31. The first number represents the number of hexaethynylbenzene molecules in the unit cell, while the second refers to that of tetraethynylethene molecules. In some cases, four numbers are needed to name the GDYHYs. As shown in Fig. 1(d), the unit cell of GDYHY-2121 contains alternately two hexaethynylbenzene molecules, one tetraethynyle- thene molecule, two hexaethynylbenzene molecules, and one tetraethynylethene molecule. The reason is that GDYHY-21 does not exist, because two hexaethynylbenzene molecules and one tetra- ethynylethene can not compose a repeatable unit cell. Following this nomenclature, the 6,6,18-graphdiyne should be called GDYHY-11 here. The proposed fourteen two-dimensional GDYHYs are GDYHY-13, GDYHY-31, GDYHY-22, GDYHY-15, GDYHY-51, GDYHY-24, GDYHY-42, GDYHY-33, GDYHY-1212, GDYHY-2121, GDYHY-1311, GDYHY-3111, GDYHY-2211, and GDYHY-1414. For one-dimensional GDYHY nanoribbons (GDYHYNRs), only structures along horizontal extended direction have smooth edges. The nanori- bbons can be obtained by cutting fragments from the two-dimensional structures. The numbers of hexa- ethynylbenzene and tetraethynylethene molecules are expressed alternately after abbreviation. For example, GDYHYNR-422 means that the unit cell contains four hexaethynylbenzene molecules, two tetra- ethynylethene molecules, and four hexaethynylben- zene molecules. If the first number refers to the tetraethynylethene molecules, an apostrophe is used. For example, the unit cell of GDYHYNR-1’21 contains alternately one tetraethynylethene molecule, two hexaethynylbenzene molecules, and one tetraethynylethene molecule.

The geometrical optimization and calculations of electronic properties were carried out using CRYSTAL14 program[21, 22]. The band gap is an important parameter for semiconductors in elec- tronics. In order to accurately describe the band gaps[23], the HSE06 hybrid density functional[24]was used. Bloch functions constructed from the standard 6-21G(d,p) basis set in the program were adopted. Five parameters 8, 8, 8, 8, and 18 were used to control the accuracy of the calculation of the bielectronic coulomb and exchange series. In the first Brillouin zone, a dense Monkhorst-Pack sampling with 81-points was used. The k-point sampling is ten times denser when calculating the band structures, since their quality affects the fitting of effective masses.

Fig. 1. Structures of (a) hexaethynylbenzene and (b) tetraethynylethene monomers, unit cells of (c) GDYHY-31 and (d) GDYHY-2121

Carrier mobility is a central parameter in electronics. Under deformation potential theory[25], carriers are mostly scattered by longitudinal acoustic phonons when the wavelength of an electron is much longer than the lattice constant of a semiconductor. The carrier mobility of a one-dimensional structure[26]can be obtained by

in which1D=0∂2/∂2is the stretching modulus along one-dimensional direction,0is the equili- brium lattice constant,is the total energy,*=2[∂2/∂2]-1is the carrier effective mass,is the energy at frontier band edge, and1=0δ/δis the deformation potential constant. In order to obtain the stretching modulus and deformation potential constant, deformed structures with lattice constants of 0.990, 0.9950, 1.0050, and 1.010were also calculated. Usually, semiconductors do not have a sharp density of states near the frontier band edges. Carriers in energy range more thanBcould participate in the conduction process. In this work, 10B[27]was used as an energy range for fitting effective masses. The deformation potential theory was successfully applied to similar materials, such as graphene[28]and its nanoribbons[5, 29].

The current-voltage (-) characteristics of the electronic device was calculated through the Landa- uer-Büttiker formula[30]based on the nonequilibrium Green’s function method

in which(,) is the transmission coefficient at energyand bias voltage, andL() andR() are Fermi-Dirac distribution functions at the left and right electrodes. Norm-conserving pseudopoten- tials[31]and variationally optimized pseudoatomic localized basis functions[32, 33]included in the OPENMX program[34]were used. Each atomic orbital was described by a primitive orbital. Since the HSE06 hybrid density functional is not available in this program, the PBE density functional[35]was adopted. The energy cutoff was 150 Ry, and 131-points were used along the transport direction.

3 RESTULTS AND DISCUSSION

The band structures of fourteen two-dimensional GDYHYs are shown in Fig. 2. In these structures, GDYHY-13, GDYHY-33, GDYHY-1212, and GDYHY-1311 are metals, while the other ten structures have direct band gaps. The direct band gaps are beneficial to possible optical applications. The band gaps are 0.21, 0.22, 0.11, 0.68, 0.37, 0.77, 0.57, 0.23, and 0.54 eV for the semiconducting GDYHY-15, GDYHY-22, GDYHY-24, GDYHY-31, GDYHY-42, GDYHY-51, GDYHY-2121, GDYHY- 2211, and GDYHY-3111, respectively. GDYHY- 1414 can be viewed as a semimetal with band gap of 0.01 eV. The GDYHYs with different coupling patterns and proportions have versatile electronic properties; thus should be useful in electronics. This is different from that of graphdiyne, which is only a semiconductor. The optimized lattice constants are all 9.44 Å along horizontal direction, indicating that the lattices of hexaethynylbenzene and tetra- ethynylethene are commensurable. The formation energies of the fourteen GDYHYs are in a narrow range of 33～37 meV per atom with respect to graphene. The small formation energies indicate that they may be experimentally approachable. The narrow range also implies the compensability.

Fig. 2. Band structures of two-dimensional GDYHYs. The top half from left to right is for GDYHY-13, GDYHY-33, GDYHY-15, GDYHY-22, GDYHY-24, GDYHY-31, and GDYHY-42, respectively; the bottom half is for GDYHY-51, GDYHY-1212, GDYHY-1311, GDYHY-1414, GDYHY-2121, GDYHY-2211, and GDYHY-3111, respectively. Fermi levels are denoted by dotted lines

With the development of computer industry, an electronic device becomes smaller and smaller. One-dimensional material can further reduce the device size, and the conduction in circuit should be essentially one-dimensional. For this reason, several one-dimensional GDYHYNRs cut from the two- dimensional GDYHYs were calculated. They are all semiconductors with direct band gaps at the center of the first Brillouin zone. The band structures of GDYHYNR-11, GDYHYNR-22, GDYHYNR-422, and GDYHYNR-224241 shown in Fig. 3 were taken as examples. The band structures are denser when the unit cell contains more atoms. The band gaps are 1.82, 0.71, 0.45, and 0.45 eV, respectively. The narrowest GDYHYNR-11 has the largest band gap due to quantum confinements, and the band gap generally decreases when the width increases. The frontier bands are smooth and parabolic near band edges. These should be favorable to small effective masses, which are essential for high speed electronic devices.

Fig. 3. Band structures of one-dimensional GDYHYNR-11, GDYHYNR-22, GDYHYNR-422, and GDYHYNR-224241 (from left to right). Fermi levels are denoted by dotted lines

As shown in Fig. 4(a), one hundred and thirty one GDYHYNRs have band gaps larger than the minimum value 0.4 eV[36]for electronic devices. Among these GDYHYNRs, the narrowest one is GDYHYNR-11 that contains two monomers in a unit cell while the widest one is GDYHYNR-424242 that contains eighteen monomers. The names of eight GDYHYNRs have two numbers. The narrowest and widest ones are GDYHYNR-11 and GDYHYNR-42. Thirty-three GDYHYNRs have three numbers in their names, such as GDYHYNR-11’1 and GDYHYNR-424. There are twenty-four, thirty-six, seventeen, eight, and five GDYHYNRs in the four-, five-, six-, seven-, and eight-number series, such as GDYHYNR-1221 and GDYHYNR-4242, GDYHYNR-12’221 and GDYHYNR-42424, GDYHYNR-113131 and GDYHYNR-424242, GDYHYNR-12’12121 and GDYHYNR-3111311, GDYHYNR-11212121 and GDYHYNR-31113111, respectively. Large band gap is necessary to obtain high on/off ratio of electronic devices. The band gaps of these GDYHYNRs are in the range of 0.40～1.82 eV. Among these structures, ten GDYHYNRs with width smaller than 50 Å have band gaps larger than 1 eV. There are thirteen GDYHYNRs with width larger than 100 Å. Their band gaps are all smaller than 0.5 eV. The band gap depends on the coupling pattern and the width. However, no GDYHYNR is metallic. Therefore, the GDYHYNRs can be used as semicon- ducting scattering region in electronic devices. In these structures, there are four hydrogen atoms at the two uncoupled edges. The formation energies of these GDYHYNRs are in a narrow range of 32～36 meV per carbon atom with respect to graphene and hydrogen molecule. The small values are similar to those of two-dimensional GDYHYs, and imply that they should be energetically approachable in experiments.

The widths of the one hundred and thirty one GDYHYNRs are in the range of 15～133 Å. The largest width is comparable to the size of an electronic device in modern central processing unit. Unlike the electronic properties, the mechanical properties of GDYHYNRs are relatively simple. In Fig. 4(b), the stretching modulus generally increases with the width. Linear fitting can be applied with a correlation coefficient of 0.96. The slope is 11 eV×Å-2. The Young's modulus is 0.5 TPa when the atomic thickness of 3.4 Å (the interlayer thickness of graphite) is considered. The value is quite large to obtain high carrier mobilities, but is smaller than the value of 1.34 TPa[29]of graphene nanoribbons. The smaller value does not imply that the strength of the triple bond is weaker than that of the double bond. The reason is that there are cavities in the GDYHYNRs due to the connection pattern.

Fig. 4. (a) Band gaps, (b) stretching moduli, (c) hole and (d) electron effective masses, (e) valence and (f) conduction band deformation potential constants, (g) hole and (h) electron mobilities of GDYHYNRs

Because the valence and conduction bands are almost symmetric, the hole and electron effective masses as shown in Figs. 4(c) and 4(d) are similar. The hole effective masses are in the range of 0.16～0.650. Only the narrowest GDYHYNR-11 has the largest hole effective mass 0.650. Those of fifteen GDYHYNRs are in the range of 0.30～0.410. The values of the rest one hundred and fifteen GDYHYNRs are smaller than 0.300. For electron effective masses, the values are in the range of 0.13～0.540. Those of five nanoribbons GDYHYNR-11, GDYHYNR-1’2121, GDYHYNR- 313131, GDYHYNR-111, and GDYHYNR-21 are 0.54, 0.37, 0.37, 0.36, and 0.350, respectively. The other one hundred and twenty six GDYHYNRs have electron effective masses smaller than 0.300. The narrowest GDYHYNR-11 has the largest hole and electron effective masses, while the values are generally smaller for wider GDYHYNRs. Smaller effective masses are beneficial to high carrier mobilities.

As shown in Fig. 4(e), the valence band defor- mation potential constants of the most GDYHYNRs are in the range of 0.71～1.09 eV. A narrow structure GDYHYNR-21 has a large value of 1.25 eV, while the values of six structures GDYHYNR-422, GDYHYNR-424, GDYHYNR-22421, GDYHYNR- 22422, GDYHYNR-32422, and GDYHYNR-224241 are about 0.54 eV. On the other hand, the conduction band deformation potential constants shown in Fig. 4(f) are much larger. They are in the range of 4.35～4.90 eV. Although some structures have smaller values while some other ones have larger values, the difference is small compared to the whole value. Therefore, the difference of the conduction band deformation potential constants has small impact on the carrier mobilities than that of the valence band deformation potential constants has.

In Fig. 4(g) and 4(h), the hole and electron mobility of GDYHYNRs are in the ranges of 1586～342849 and 115～7665 cm2×V-1×s-1, respectively. Thirty three GDYHYNRs have hole mobilities larger than 1 × 105cm2×V-1×s-1. The hole mobility of each GDYHYNR is much higher than the electron mobility, which is quite different from that for ordinary semiconductors, such as silicon. The high hole mobility is rare. Generally, the carrier mobility increases with the width because of larger stretching modulus. The effective masses also have some influence, but the effect is smaller than that comes from the deformation potential constants (especially for hole mobilities). The hole mobility of GDYHYNR-21 with the largest valence band deformation potential constant is 4397 cm2×V-1×s-1. On the other hand, the values of six structures GDYHYNR-422, GDYHYNR-424, GDYHYNR- 22421, GDYHYNR-22422, GDYHYNR-32422, and GDYHYNR-224241 with the smallest valence band deformation potential constants are 220262, 298337, 206872, 260450, 294601, and 342849 cm2×V-1×s-1, respectively, because the carrier mobility depends on powers of deformation potential constant. The electron mobilities do not depend significantly on the conduction band deformation potential constants, but increase almost linearly with the width (or stretching modulus). The reason is that the difference between the conduction band deformation potential constants is quite small compared with the whole value, which has been discussed above.

The unbalanced deformation potential constants result in the unbalanced carrier mobilities. The deformation potential constant is proportional to the stiffness of frontier band edge against lattice defor- mation. To elucidate this phenomenon, the highest occupied and the lowest unoccupied crystal orbitals (HOCO and LUCO) at the top of valence band and bottom of conduction band are compiled and shown in Fig. 5. A structure GDYHYNR-422 that has high carrier mobilities was taken as an example. In Figs. 5(a) and 5(b), the HOCO and LUCO are not uniformly distributed on all the atoms, but mainly on the two tetraethynylethene fragments and some atoms in the adjacent hexaethynylbenzene fragments. The orbitals on the benzene ring and the double bonds in the tetraethynylethene fragments for HOCO are parallel to the one-dimensional deformation direction. However, it is vertical for LUCO. Thus the HOCO is delocalized and the LUCO is localized with respect to the extended direction. The bonds in the delocalized HOCO should be stiffer to the deformation than those in the localized LUCO, because the conjugated bonds are easier to adjust during deformation. Thus the valence band defor- mation potential constant 0.54 eV is much smaller than the conduction band deformation potential constant 4.63 eV. The orientation of crystal orbitals makes GDYHYNRs have high hole mobilities.

Fig. 5. (a) HOCO and (b) LUCO of GDYHYNR-422

The above discussions are based on infinitely long structures. However, a real electronic device has finite size. For this reason, an all-GDYHY seamless electronic device was constructed. As indicated in Fig. 6, the left and right electrodes are metallic GDYHY-33. The central scattering region is com- posed of GDYHYNR-22 and two cells of GDYHY- 33. This electronic device avoids undesirable contact between metal electrodes and GDYHYNR. It uses the same type of materials as electrodes and scattering region. Thus the contact should be ohmic. In Fig. 6(a), there is a gap near the Fermi level, indicating semiconducting characteristics. The gap is about 0.4 eV. In Fig. 6(b), the current is quite small when the bias voltage is less than 0.4 eV. After this threshold, the current increases almost linearly with the bias voltage. The semiconducting device is switched on. At 1.0 V, the current is 11.7mA. The conductance is as high as 11.7mS. The high conductance indicates high performance of the electronic device. When a gate voltage of 5 V is applied, the current reduces to 1.1mA at this bias voltage. The on/off ratio is in the order of 10. Thus the device can be switched off with a gate voltage. These indicate that the GDYHYs and GDYHYNRs can be used as a small size electronic device.

Fig. 6. (a) Transmission spectrum (Fermi level is set to 0) and (b)-characteristics of an all-GDYHY electronic device. The left and right electrodes are indicated by rectangles

4 CONCLUSION

Fourteen atomically thin two-dimensional GDYHTs were constructed and investigated using density functional theory. The calculations indicate that the GDYHTs can be metals, semimetal, or semiconductors, depending on the coupling patterns and proportions of monomers. This is different from the situation for graphdiyne, which is a semicon- ductor. Also, one hundred and thirty one one- dimensional GDYHTNRs cut from the two-dimen- sional structures are all semiconductors with band gaps of 0.4～1.82 eV. The lattice constants of GDYHTs along the one-dimensional direction as well as those of GDYHTNRs are all 9.44 Å, implying the commensurability between the lattices of hexaethynylbenzene and tetraethynylethene frag- ments.The formation energies of GDYHYs and GDYHTNRs are in the narrow ranges of 33～37 and 32～36 meV per carbon atom, respectively, which imply that they should be experimentally appro- achable. The widths of GDYHYNRs are in the range of 15～133 Å. The largest width is comparable to the size of an electronic device in modern central pro- cessing unit. The stretching modulus increases almost linearly with the width. The Young's modulus is 0.5 TPa. This is smaller than that of graphene because of cavities, but is large enough to obtain high carrier mobilities. The hole and electron effective masses are in the ranges of 0.16～0.65 and 0.13～0.540, respectively. The valence and conduction band deformation potential constants are 0.54～1.25 and 4.35～4.90 eV, respectively. The smaller valence band deformation potential constants are explained by the delocalized HOCO at the top of valence band. The unbalanced deformation potential constants result in the unbalanced carrier mobilities. The hole and electron mobilities are as high as 1586～342849 and 115～7665 cm2×V-1×s-1, respec- tively. Furthermore, a seamless electronic device composed of metallic GDYHY electrodes and semiconducting GDYHYNR scattering region was constructed. The conductance is as high as 11.7mS at bias voltage of 1 V and the electronic device can be switched off with an on/off ratio of about 10 when a gate voltage of 5 V is applied. The proposed GDYHYs and GDYHYNRs can be good candidates for high speed electronic devices.

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18 January 2018;

30 March 2018

① This work was supported by the National Natural Science Foundation of China (No. 21203127) and the Scientific Research Base Development Program of the Beijing Municipal Commission of Education

. E-mail: wangguo@mail.cnu.edu.cn

10.14102/j.cnki.0254-5861.2011-1947