二维硅烯的电学性能以及金属纳米线的输运性质的第一原理计算
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摘要
在过去的几十年里，集成电路的发展遵守摩尔定律，即在保证性能提高以及平均每个晶体管成本降低的前提下，每12到18个月特征尺寸按比例减小。这些制备要求导致集成电路的复杂性日益增加，所以人们所要克服的技术挑战的数目以及困难程度也会显著增加。
首先，本文讨论集成电路的一个主要元件—金属氧化物半导体场效应晶体管。在高速晶体管应用中，栅极需要对电场做出迅速反应，这就需要栅极的长度较短并且载流子迁移率较高。但是当栅极的长度较短时，通常晶体管中会出现短沟道效应，这会严重的阻碍晶体管性能的进一步提高。幸运的是，按比例缩小原理预测当栅极和沟道区域很薄时，晶体管能够避免出现短沟道效应。而沟道材料最薄的可能性是单层原子膜。
硅烯是石墨烯的硅类似物，是硅的蜂窝状单层原子膜。由于硅烯和石墨烯的结构相类似，硅烯在费米能附近也具有线性色散关系，相应的理论结果预测硅烯也具有非常高的载流子迁移率并且其值接近于石墨烯的载流子迁移率。此外，硅烯具有能够与现有的硅基技术相兼容的额外优势。因此，本文研究硅烯材料作为沟道材料应用在高性能场效应晶体管的可能性。首先密度泛函理论杂化相关交换函数计算了表面卤族功能化硅烯的结构和电学性能。表面功能化硅烯的结构稳定性增加。并且随着表面功能化元素氟、氯、溴、碘的变化，其能隙是非线性变化的，这主要是由于硅硅成键和硅卤族原子成键对能隙贡献的相互竞争所导致的。此外，氟化硅烯(1.469eV)和碘化硅烯(1.194eV)的能隙值分别接近于传统沟道材料砷化镓和大块硅的能隙值，因此其有可能应用在场效应晶体管的沟道材料。
然而，上述表面功能化的硅烯不再具有硅烯所固有的高速载流子迁移率，因此接下来采用硅烯和基底相互作用把硅烯的能隙打开的同时保持其非常高的载流子迁移率。我们选取了一些常用二维基底来研究控制硅烯/基底异质结构的能隙大小的因素。界面结合为范德华力的硅烯/基底异质结构的稳定性增加并且其载流子迁移率不会显著减小。此外，所有的异质结构都打开一个较小的能隙值(0.004~0.156eV)，并且层间距更小的结构具有更大的能隙。硅烯/Si(111)异质结构具有较强的层间作用力，其能隙值能够满足场效应晶体管在室温下执行的要求。所以，硅烯/Si(111)异质结构是硅烯应用在高速场效应晶体管的一个潜在途径。最近一篇文献报道了硫化钼表面成功生长了硅单层膜并且其具有蜂窝状结构，接下来范德华力修正的密度泛函理论计算了这种硅烯/硫化钼异质结构的结构和电学性能。结果表明硅烯和硫化钼基底之间是范德华力结合，因此在费米能附近硅烯的线性能带基本上不发生变化，所以这种异质结构仍然具有非常高的载流子迁移率。同时本征的界面偶极破坏了硅烯的晶格对称性从而打开了异质结构的能隙。此外，异质结构的能隙在外电场作用下是线性变化的。因此，硫化钼是硅烯材应用在高速开关设备和声子设备中的潜在的基底材料。
接着，本文研究了集成电路中连接各个元件之间的内连线。根据摩尔定律的发展，集成电路中芯片的持续减小不可避免的导致内连线尺寸的持续减小。目前集成电路中使用的是铜内连接，这是因为除了银以外铜的电导率最大，而电导率是内连线应用的一个最重要的因素。然而，随着内连线的尺寸逐渐接近电子平均自由程，逐渐显著的表面散射和晶界散射作用会导致内连线电导率的大幅降低。理论模型结果表明纳米结构的电导率随着尺寸的变化是各向异性的，由此可以推测随着尺寸减小可能会出现其他金属材料的电导率大于铜。因此，本文比较计算了小尺寸铝和铜纳米线的电导，探讨铝替换铜内连线的可能性。密度泛函理论结合兰道公式计算了最大直径为3.6纳米的铝和铜纳米线的输运性质。与经典理论相反，小尺寸铝纳米线的电导大于铜。这主要是由不同的电子结构所导致的，从而导致铝的3p电子数对电导的贡献更大。同时，铝纳米线较大的轴向收缩对电导的增加有少量贡献。因此，铝纳米线有可能作为下一代内连线应用在集成电路中。
According to the Moore’s law, the size scaling in digital logic has enabled thecomplexity of integrated circuits to double every12to18months, leading to significantimprovements in performance and diminutions in price per transistor, and also theincrements in the number of challenge.
First, one of the most important parts in integrated circuits is investigated, themetal-oxide-semiconductor field effect transistor (FET). For high-speed applications, FETsshould respond quickly to variations in the voltage applied between the gate and source; thisrequires short gates and fast carriers in the channel. Unfortunately, the FETs with short gatesfrequently suffer from short channel effects. Scaling theory predicts that a FET with a thinbarrier and a thin channel region will be robust against short-channel effects down to veryshort gate lengths. The possibility of having channels that are just one atomic layer thick isperhaps the most attractive feature of silicene for use in transistors.
Silicene, the Si analogue of graphene, is a promising material for electronic applicationswhile its linear band structures in Fermi energy suggest the high carrier mobility. Moreover,it supplies an ideal interface with the existing Si devices and takes advantage of tractablematerial technology. Thus, the possibility of silicene as the channel in FETs is studied. Theelectronic structures and band gaps of silicene adsorbed with halogen elements are studiedusing the density functional theory based screened exchange local density approximationmethod. It is found that the structural stability increases for silicene with surfacefunctionaliztion. Moreover, the band gaps of silicene adsorbed with F, Cl, Br and I have anonmonotonic change as the periodic number of the halogen elements increases. This isattributed to the transfer of contributions to band gaps from Si–Si bonding to Si–halogenbonding. In addition, the band gap values of silicene with F and I functionalization are closeto those of GaAs and bulk Si, thus those are potential to be used as the channels in FETs.
However, the high carrier mobility of silicene is broken seriously by the surfacefunctionalization. Our calculations show that opening a sizeable band gap of silicene withoutdegrading its carrier mobility can be realized by silicene/substrate hybrid structures withnoncovalent interface interactions. Several possible two-dimensional semiconductingsubstrates are selected to find the factors those control the magnitude of band gap. It is found that the more notable charge redistribution in two sublattices of silicene and thus a largerband gap are characterized by a smaller interlayer distance. Thus, the opened band gap inhybrid structures with SiH/π interaction has reached the technique requirement ofroom-temperature operation in FETs. Recently, it was reported that the Si single layer withhoneycomb structure grew on the MoS2substrate. Thus, the geometric and electronicproperties of silicene paired on MoS2substrate are studied systematically by using densityfunctional theory with van der Waals correction. It is found that the nearly linear banddispersion can be preserved in the heterobilayers due to the weak interface interactions.Meanwhile, the band gap is opened because of the sublattice symmetry broken by theintrinsic interface dipole. Moreover, the band gap values could be effectively modulatedunder an external electric field. Therefore, a way is paved for the silicene/MoS2heterobilayers as the candidate materials for logic circuits and photonic devices.
Finally, we investigate the interconnect that connects the parts in integrated circuits. Inkeeping with the Moore’s law, the miniaturization of chip dimensions also creates the needto downscale interconnects. The bulk conductivity of presently used Cu is superior to nearlyall conventional metals (except Ag), while the electrical conductivity is one of essentialrequirements for interconnects. However, as the size approaches the electron mean free path,the electrical conductivity deviates downward from their bulk value seriously induced bysurface and grain boundary scatterings. Thus, we study the structural and quantum transportproperties of Al and Cu nanowires with diameters up to3.6nm using density functionaltheory combined with the Landauer formalism. Contrary to the classical electronic behavior,the conductance of Al wires is larger than that of Cu. This is mainly attributed to the largercontribution of conductance channels from Al-3p, which is determined by the chemicalnature. Meanwhile, the stronger axial contraction of Al wires plays a minor role toconductance. This makes Al wires possible candidate of interconnects in integrated circuits.
首先，本文讨论集成电路的一个主要元件—金属氧化物半导体场效应晶体管。在高速晶体管应用中，栅极需要对电场做出迅速反应，这就需要栅极的长度较短并且载流子迁移率较高。但是当栅极的长度较短时，通常晶体管中会出现短沟道效应，这会严重的阻碍晶体管性能的进一步提高。幸运的是，按比例缩小原理预测当栅极和沟道区域很薄时，晶体管能够避免出现短沟道效应。而沟道材料最薄的可能性是单层原子膜。
硅烯是石墨烯的硅类似物，是硅的蜂窝状单层原子膜。由于硅烯和石墨烯的结构相类似，硅烯在费米能附近也具有线性色散关系，相应的理论结果预测硅烯也具有非常高的载流子迁移率并且其值接近于石墨烯的载流子迁移率。此外，硅烯具有能够与现有的硅基技术相兼容的额外优势。因此，本文研究硅烯材料作为沟道材料应用在高性能场效应晶体管的可能性。首先密度泛函理论杂化相关交换函数计算了表面卤族功能化硅烯的结构和电学性能。表面功能化硅烯的结构稳定性增加。并且随着表面功能化元素氟、氯、溴、碘的变化，其能隙是非线性变化的，这主要是由于硅硅成键和硅卤族原子成键对能隙贡献的相互竞争所导致的。此外，氟化硅烯(1.469eV)和碘化硅烯(1.194eV)的能隙值分别接近于传统沟道材料砷化镓和大块硅的能隙值，因此其有可能应用在场效应晶体管的沟道材料。
然而，上述表面功能化的硅烯不再具有硅烯所固有的高速载流子迁移率，因此接下来采用硅烯和基底相互作用把硅烯的能隙打开的同时保持其非常高的载流子迁移率。我们选取了一些常用二维基底来研究控制硅烯/基底异质结构的能隙大小的因素。界面结合为范德华力的硅烯/基底异质结构的稳定性增加并且其载流子迁移率不会显著减小。此外，所有的异质结构都打开一个较小的能隙值(0.004~0.156eV)，并且层间距更小的结构具有更大的能隙。硅烯/Si(111)异质结构具有较强的层间作用力，其能隙值能够满足场效应晶体管在室温下执行的要求。所以，硅烯/Si(111)异质结构是硅烯应用在高速场效应晶体管的一个潜在途径。最近一篇文献报道了硫化钼表面成功生长了硅单层膜并且其具有蜂窝状结构，接下来范德华力修正的密度泛函理论计算了这种硅烯/硫化钼异质结构的结构和电学性能。结果表明硅烯和硫化钼基底之间是范德华力结合，因此在费米能附近硅烯的线性能带基本上不发生变化，所以这种异质结构仍然具有非常高的载流子迁移率。同时本征的界面偶极破坏了硅烯的晶格对称性从而打开了异质结构的能隙。此外，异质结构的能隙在外电场作用下是线性变化的。因此，硫化钼是硅烯材应用在高速开关设备和声子设备中的潜在的基底材料。
接着，本文研究了集成电路中连接各个元件之间的内连线。根据摩尔定律的发展，集成电路中芯片的持续减小不可避免的导致内连线尺寸的持续减小。目前集成电路中使用的是铜内连接，这是因为除了银以外铜的电导率最大，而电导率是内连线应用的一个最重要的因素。然而，随着内连线的尺寸逐渐接近电子平均自由程，逐渐显著的表面散射和晶界散射作用会导致内连线电导率的大幅降低。理论模型结果表明纳米结构的电导率随着尺寸的变化是各向异性的，由此可以推测随着尺寸减小可能会出现其他金属材料的电导率大于铜。因此，本文比较计算了小尺寸铝和铜纳米线的电导，探讨铝替换铜内连线的可能性。密度泛函理论结合兰道公式计算了最大直径为3.6纳米的铝和铜纳米线的输运性质。与经典理论相反，小尺寸铝纳米线的电导大于铜。这主要是由不同的电子结构所导致的，从而导致铝的3p电子数对电导的贡献更大。同时，铝纳米线较大的轴向收缩对电导的增加有少量贡献。因此，铝纳米线有可能作为下一代内连线应用在集成电路中。
According to the Moore’s law, the size scaling in digital logic has enabled thecomplexity of integrated circuits to double every12to18months, leading to significantimprovements in performance and diminutions in price per transistor, and also theincrements in the number of challenge.
First, one of the most important parts in integrated circuits is investigated, themetal-oxide-semiconductor field effect transistor (FET). For high-speed applications, FETsshould respond quickly to variations in the voltage applied between the gate and source; thisrequires short gates and fast carriers in the channel. Unfortunately, the FETs with short gatesfrequently suffer from short channel effects. Scaling theory predicts that a FET with a thinbarrier and a thin channel region will be robust against short-channel effects down to veryshort gate lengths. The possibility of having channels that are just one atomic layer thick isperhaps the most attractive feature of silicene for use in transistors.
Silicene, the Si analogue of graphene, is a promising material for electronic applicationswhile its linear band structures in Fermi energy suggest the high carrier mobility. Moreover,it supplies an ideal interface with the existing Si devices and takes advantage of tractablematerial technology. Thus, the possibility of silicene as the channel in FETs is studied. Theelectronic structures and band gaps of silicene adsorbed with halogen elements are studiedusing the density functional theory based screened exchange local density approximationmethod. It is found that the structural stability increases for silicene with surfacefunctionaliztion. Moreover, the band gaps of silicene adsorbed with F, Cl, Br and I have anonmonotonic change as the periodic number of the halogen elements increases. This isattributed to the transfer of contributions to band gaps from Si–Si bonding to Si–halogenbonding. In addition, the band gap values of silicene with F and I functionalization are closeto those of GaAs and bulk Si, thus those are potential to be used as the channels in FETs.
However, the high carrier mobility of silicene is broken seriously by the surfacefunctionalization. Our calculations show that opening a sizeable band gap of silicene withoutdegrading its carrier mobility can be realized by silicene/substrate hybrid structures withnoncovalent interface interactions. Several possible two-dimensional semiconductingsubstrates are selected to find the factors those control the magnitude of band gap. It is found that the more notable charge redistribution in two sublattices of silicene and thus a largerband gap are characterized by a smaller interlayer distance. Thus, the opened band gap inhybrid structures with SiH/π interaction has reached the technique requirement ofroom-temperature operation in FETs. Recently, it was reported that the Si single layer withhoneycomb structure grew on the MoS2substrate. Thus, the geometric and electronicproperties of silicene paired on MoS2substrate are studied systematically by using densityfunctional theory with van der Waals correction. It is found that the nearly linear banddispersion can be preserved in the heterobilayers due to the weak interface interactions.Meanwhile, the band gap is opened because of the sublattice symmetry broken by theintrinsic interface dipole. Moreover, the band gap values could be effectively modulatedunder an external electric field. Therefore, a way is paved for the silicene/MoS2heterobilayers as the candidate materials for logic circuits and photonic devices.
Finally, we investigate the interconnect that connects the parts in integrated circuits. Inkeeping with the Moore’s law, the miniaturization of chip dimensions also creates the needto downscale interconnects. The bulk conductivity of presently used Cu is superior to nearlyall conventional metals (except Ag), while the electrical conductivity is one of essentialrequirements for interconnects. However, as the size approaches the electron mean free path,the electrical conductivity deviates downward from their bulk value seriously induced bysurface and grain boundary scatterings. Thus, we study the structural and quantum transportproperties of Al and Cu nanowires with diameters up to3.6nm using density functionaltheory combined with the Landauer formalism. Contrary to the classical electronic behavior,the conductance of Al wires is larger than that of Cu. This is mainly attributed to the largercontribution of conductance channels from Al-3p, which is determined by the chemicalnature. Meanwhile, the stronger axial contraction of Al wires plays a minor role toconductance. This makes Al wires possible candidate of interconnects in integrated circuits.
引文
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