제8회 EDISON SW 활용 경진대회 Effects of biaxial strain on Performance of Graphyne TFET/MOSFET Jihoon Byun and Hyeongu Lee because band gap of channel material significantly affects the device performance. In this project, the Introduction strain effects on electronic properties were reproduced The alltrope of carbon has been steadily studied and biaxially strained graphyne TFETs and nMOSFETs because it shows unique physical properties. Since are investigated by quantum transport simulations. fullerens were observed for the first time in 1985 [1], Computational Method carbon system has attracted attention in the field of nanoelectronics in that the remarkable properties Graphyne ( ) has a hexagonal lattice structure could open many opportunities beyond Moore’s law. with 12 atoms in a primitive unitcell as shown in Fig. 1 Among the allropes, graphene, which consists of sp2- (a). First-principles calculations are performed with the hybridized carbon network system with a linear energy use of density functional theory (DFT) in the basis of a dispersion relation, has been the most intensely linear combination of atomic orbitals (LCAO) using studied because of its high electrical, thermal SIESTA code. The exchange-correlation interacionts are mobilities. However, the applications to treated by the genralized gradient approximation (GGA) nanoelectronics are hindered because pristine with Perdew-Burke-Ernzerhof (PBE) functional. The graphene has zero band gap which limits achievable Brillouin zone is sampled using 15 x 15 x 1 Monkhorst- on-off current ratios.[2] As an alternative materials, Pack grid. The k grid points are tested to converge total other alltropes with non-zero band gap, such as energy as shown in Fig. 2 (a). The lattice consant of graphane, graphene oxide and graphyne, has attracted unstrained graphyne is optimized to 6.497 using much attention. Of that, graphyne especially has polynomial fitting. The atomic structures of strained interesting electronic properties. It was theoretically graphyne were fully relaxed until the maximum force found that band gap of graphyne can be linearly became less than 1− Hartree/Bohr. tunned by strain.[3] Graphyne can have advantages over graphene in nanodevice design and application due to the property of band gap variation under strain. Although strain effects on physcial properties of graphyne has been theoretically investigated, few studies have been made for tranport properties. Strain Fig.1 (a) Primitive unit cell of graphyne (b) effects on graphyne transistors should be investigated Transport super cell (c) Device model 15 40 제8회 EDISON SW 활용 경진대회 Atomistic transport properties are investigated using structure is 0.45 eV. Both of then are on M point and nonequilibrium Green’s function formalism. The the variation of two data is only 1 %. It is known that electrostatic effects are considered by adding the the band structure of unstrained graphyne was potential to each unit cell as shown in eq.1.[4] For successfully reproduced. quantum transport simulation, the rectangular supercells are formed which consists of 24 atoms as shown in Fig.1 (b). In this project, the transport properties along armchair direction are only investigated. The transport unitcell structure were relaxed until the maximun force became less than 1−. The hamiltonians (H) from DFT calculataions are Fig 3. Band structure data, reference (left) imported eq.1. eq.1 and eq.2 are self-consistently reproduced (right) calculated using in-house tool. Fig 4. shows the band gap variation under biaxial ( − − − Σ)� = � tensile strain. ‘H-strain' means biaxial strain and ‘M-M’ 2 = − − + indicates special k point of conduction band minima and valence band maxima. It can be shown that the tendencies of band gap variation with increase of srain are the same. Fig 2. k point samping test and lattice constant optimized Results and Discussion Fig 4. band gap variation under strain, reference 1. Reproduce (left) reproduced (right) Fig 3. (b) shows the band structure of unstrained graphyne, which was reproduced in this project. 2. TFET simulation Referecne data is black solid line as shown in Fig 3. (a). Comparing two data, the band gap of reference band Device model is shown as in Fig. 1 (c). Each source, structure is 0.46 eV and that of reproduced band channel, drain length is 10 nm. Doping profile is p-i-n 16 40 41 제8회 EDISON SW 활용 경진대회 and doping density of p, n is 12− . Channel thickness is 0.1 nm and equivalent oxide thickness (EOT) is 0.45 nm. According to ITRS 2015 benchmark, supply voltage is set 0.4 V. In TFET simulation, off-current is − 1 targeting low power device. Fig 7. (a) Band edge profile of 4%, 10% strained graphyne at on-curren state. Dashed line indicates the energy level of the highest transmission peak (b) Effective mass variation Fig 7. (a) shows band edge profile of 4%, 10% Fig 5. Transfer characteristic curve (left) on- strained graphyne at on-current state. Red arrow current variation (right) indicates dominant tunneling length and blue arrow Fig 5. (a) shows transfer characteristic curves of indicates dominant tunneling barrier height. Fig 7. (b) strained graphyne. The current decreases in off-region shows variation of electron, hole effective mass by as strain increases. Minimum off current of unstrained strain. Strain induces heavier effective mass, longer graphyne is almost 10 order higer than that of 10 % tunneling length and higher barrier height. These strained graphyne. Fig 5. (b) shows variation of on- factor degrades on-current performance of TFET. current with strain. On-current exponentially decreases Longer tunneling length and higher tunneling barreir with increases of strain. height result from increase of band gap due to strain. The increase of effective mass with increase of band gap is general properties. 3. MOSFET simulation Off-current is 1−1 targeting high performance device. Fig 6. on-off ratios (left) SS (right) Performance spectrum of on-currnet vs on-off ratios is shown in Fig 6. (a). The maximun on-off ratios exponentially increases by strain. Fig 6. (b) shows SS decreases as strain increases. Low SS and high on- current enhances switching performace. Strain induces low SS, but lower on-current. It means that strain engineering can optimize graphyne TFET performance. 17 42 제8회 EDISON SW 활용 경진대회 Fig. 8 Device performance parametric of how this bandgap variation due to strain affects device MOSFETs performance of TFETs, MOSFETs. For TFETs, the increase of band gap induces lower on-current, off-current, SS Fig. 8 shows transfer curve, on-off ratios and SS of and higher on-off ratio and for MOSFETs it induces graphyne nMOSFETs. The tendencies are similar to lower on-current, off-current, but doesn’t affect SS. On- TFETs. Strain induces lower on-current, lower off- current changes exponentially in TFETs while on- current and higer on-off ratio. However the on-current currrent linearly changes in MOSFETs. Strain effets can lineary decreases while the on-current of TFETs be useful design factor because it changes trade-off exponentially decreases. It implies that transport parameters.’ mechanisms of TFETs, MOSFETs are different. While strain decreases SS of TFETs, it doesn’t affect SS of MOSFETs. SS of MOSFETs is closer to 60 meV/dec Acknowledgement which is thermionic limit. This research was supported by the EDISON Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Science & ICT(NRF-2011-0020576) References [1] Hirsch, Andreas. "The era of carbon allotropes." Nature materials 9.11 (2010): 868. [2] Meric, Inanc, et al. "Current saturation in zero- bandgap, top-gated graphene field-effect Fig 9. on-current vs effective mass of MOSFETs transistors." Nature nanotechnology 3.11 (2008): 654. [3] Yue, Qu, et al. "Mechanical and electronic properties For MOSFETs, on-current is domiantly determined by of graphyne and its family under elastic strain: theoretical effective mass. As shown in Fig 9., strain induces predictions." The Journal of Physical Chemistry heavier effective mass and lower on-current. C 117.28 (2013): 14804-14811 [4] Shin, Mincheol, Woo Jin Jeong, and Jaehyun Lee. "Density functional theory based simulations of silicon Conclusion nanowire field effect transistors." Journal of Applied Physics 119.15 (2016): 154505. In this project, I reproduced the referecen data that . graphyne has non-zero band gap and tensile strain linearly increases the band gap. Further, I investigated 18 42 43.