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Graphene is an ideal two-dimensional crystal with the advantages of high conductivity, unique physical and chemical properties, and high specific surface area. Especially, because of its super excellent electronic properties, graphene may substitute the traditional semiconductor silicon material and carbon nanotube, thus creating a new nanoscale electronic device. In addition, multilayer graphene with ultra-wide spectral absorption characteristics and unique photoelectric properties is an ideal material for photovoltaic devices. However, the zero band gap and semi-metality of graphene both limit its application in space detectors such as the microelectronic industries and satellites. Opening and regulating the graphene band gap by physical methods has become one of the key means to further expand its applications. Research work has shown that the doping of elements can significantly change the electronic structure of graphene, thereby regulating the optical properties of graphene. In order to provide an insight into electronic properties of graphene and tune its electronic band structure and optical properties effectively, electronic and optical properties of Ni-doped multi-layer graphene are studied and a number of interesting results are obtained. The calculation are carried out by the CASTEP tool in Materials Studio software based on the first-principles of ultrasoft pseudopotential of density functional theory. The models of three typical doping positions relative to carbon atoms are constructed. After structural optimization, it is obtained that " above the center of two carbon atoms” is the most stable doping structure. By using the method of local density approximation, the band structure, density of states, dielectric constant, reflectivity and refractive index of the models are calculated. The results show that an enhanced energy band gap can be achieved after nickel-doping, and reach up to 0.604 eV. Besides, peaked phenomenon of density of states at Femi level can be observed, which is accomplished by enhancing the plasma energy. Furthermore, the calculations show that the imaginary part of permittivity and refractive index increase after nickel-doping, suggesting that the optical absorbing performance is improved. All these results provide theoretical guidance for further exploring the optical properties of graphene.
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Keywords:
- graphene /
- first principle /
- Ni-doping /
- electronic structure /
- optical properties
1. 引 言
自2004年英国曼彻斯特大学的Geim和Novoselov[1,2]用机械剥离法成功获得石墨烯以来, 掀起了石墨烯的研究热潮[3—5]. 石墨烯具有高比表面积、高导电性及优异的力学、热学性能, 可广泛应用于新型锂电池负极材料、超级电容电极材料[6]、显示电子器件[7]和半导体器件[8]等领域. 然而, 作为一类综合性能优异的碳纳米材料, 石墨烯自身的光吸收性能不佳, 单层石墨烯的吸光率仅为2.3%; 但随着层数增多, 多层石墨烯的吸光率呈增大趋势[9].
研究发现, 具有超宽光谱吸收特性及独特光电性能的多层石墨烯是制作光电器件的理想材料. 然而石墨烯的零带隙半金属性限制了其在微电子工业和卫星等太空探测器领域的应用, 通过物理化学方法打开和调控石墨烯带隙成为进一步拓展其广泛应用的关键手段之一. Schedin等[10]通过在石墨烯表面吸附气体分子, 测试分析了带隙大小与载流子浓度和电阻变化率的关系, 研制的石墨烯探测器有望应用于机敏探头等. Reddy等[11]利用化学气相沉积法研究了氮掺杂石墨烯层的受控生长, 结果表明这种方法制得的石墨烯可逆电容量是本征石墨烯可逆电容量的两倍. 文献[12—14]将B, N, Al等元素掺入石墨烯及碳纳米管, 发现掺入杂质元素可改变其结构特性和化学敏感度. 已有研究工作[15,16]表明, 通过元素掺杂可以显著改变石墨烯电子结构, 从而调控石墨烯的光学特性.
晶格常数匹配性是保障掺杂体系稳定的前提. 过渡金属元素镍的晶格常数与石墨烯的晶格常数(2.46 Å)较为匹配, 且石墨烯本身为半金属性, 掺杂镍不会显著改变石墨烯的结构. 此外, 双层石墨烯的费米能级附近的两支能带有分离的趋势, 有可能会因外界原子的引入对费米能级附近的色散关系产生重要影响[17]. 本文选用镍原子对双层石墨烯和三层石墨烯进行层间掺杂, 以期打开石墨烯的带隙, 提高其吸光性能. 以AB型双层石墨烯和ABA型三层石墨烯为研究对象, 探讨镍元素掺杂对多层石墨烯体系的能带、态密度(DOS)和光吸收系数的影响规律及作用机理.
2. 计算方法
采用基于密度泛函理论平面波赝势方法的Materials Studio软件的CASTEP模块, 优化几何结构和计算电子结构. 利用局域密度近似处理电子间相互作用的交换关联能. 平面波截断能设置为800 eV, 在结构优化中, 自洽收敛值取1.0 × 10–6 eV/atom, 总能量收敛小于1.0 × 10–5 eV/atom. 最大Hellmann-Feynman力取为0.03 eV/Å, 最大应力小于0.05 GPa. 最大原子位移小于1 × 10–3 Å, Brillouin区的K点采用Monkorst-Park空间网格取法. 对于多层石墨烯掺杂前后的结构优化采用11 × 11 × 1的K点, DOS及光学特性相关计算采用21 × 21 × 1的K点. 为消除石墨烯双层与双层之间沿Z方向产生的相互作用, 晶体模型的真空层厚度选为20 Å.
图1(a)和图1(b)分别是镍原子掺杂的双层石墨烯原胞模型的俯视图和侧视图, 模型采用2 × 2超胞AB堆垛的双层石墨烯, 超胞晶格常数设置为a = b = 4.92 Å, 双层石墨烯结构优化后的晶格参数为a = b = 4.884 Å, 与文献[18, 19]中双层石墨烯的晶格参数极为接近.
图 1 镍原子掺杂的双层石墨烯的(a)俯视图和(b)侧视图; 镍原子掺杂的三层石墨烯的(c)俯视图和(d)侧视图(蓝色代表石墨烯, 绿色代表镍原子)Fig. 1. (a) Top view and (b) side view of bilayer graphene cell (marked as blue) doped with nickel (marked as green); (c) top view and (d) side view of trilayer graphene cell (marked as blue) doped with nickel (marked as green).为确保掺杂体系的稳定性, 镍原子在石墨烯原胞中的掺杂位置需经过测试确定. 计算了镍原子位于层间某碳原子上方、层间某碳环中心上方以及两个碳原子中心上方三种情形下对应体系的总能量, 优化得到的最低总能量依次为–1969.360, –1969.362和–1970.120 eV. 可见, 两个碳原子中心的上方为镍原子层间掺杂的稳定位. 图1(c)和图1(d)分别是镍原子掺杂的三层石墨烯原胞模型的俯视图和侧视图, 计算可得镍原子掺杂三层石墨烯的稳定位亦为两个碳原子中心的上方.
3. 结果与讨论
图2(a)和图2(b)分别为镍原子层间掺杂双层石墨烯前后的能带图, 图2(c)和图2(d)分别为三层石墨烯和镍掺杂三层石墨烯的能带图. 由图2可知, 双层和三层石墨烯均为零带隙(圆圈标识), 而掺杂镍原子的双层体系存在0.604 eV的直接带隙, 掺杂体系呈半导体性. 掺杂镍原子的三层石墨烯体系亦为半导体性, 且出现0.514 eV的直接带隙. 掺杂体系产生直接带隙较间接带隙而言, 具有较好的导电能力[20,21].
图 2 能带图 (a)双层本征石墨烯; (b)镍掺杂双层石墨烯; (c)三层本征石墨烯; (d)镍掺杂三层石墨烯Fig. 2. Energy band diagram for (a) bilayer graphene, (b) Ni-doped bilayer graphene, (c) trilayer graphene, (d) Ni-doped trilayer graphene.图3(a)—(d)为镍掺杂前后的双层和三层石墨烯的态密度(DOS)对比图. 双层和三层石墨烯, 如图3(a)和图3(b)所示, 费米能级EF位于DOS谷的最小值处, 呈现半金属特性. 由于过渡金属镍的掺杂, Ni-d轨道的DOS产生尖峰效应, 表明掺杂后的石墨烯体系电子局域性增强, 如图3(c)所示. EF位于金属Ni-d主导态之间, 自由电子行为源自d轨道电子. 石墨烯中掺入镍会使EF从能量最小值移出, 如图3(c)和图3(d)所示, 明显可见在EF处Ni-d带对DOS的贡献显著; 且掺杂三层石墨烯体系(图3(d))在EF处的DOS比掺杂双层石墨烯体系(图3(c))明显增大, 所以掺杂的三层石墨烯体系的电导率高于掺杂的双层石墨烯体系, 表明三层石墨烯的掺杂体系应具有比双层石墨烯的掺杂体系更高的等离子体频率[22].
图 3 DOS (a)双层本征石墨烯(D); (b)三层本征石墨烯(T); (c)镍掺杂双层石墨烯(D-Ni); (d)镍掺杂三层石墨烯(T-Ni)Fig. 3. Density of states diagram for (a) bilayer graphene (D), (b) trilayer graphene (T), (c) Ni-doped bilayer graphene (D-Ni), (d) Ni-doped trilayer graphene (T-Ni).介电常数虚部
ε2 是表征电子在占据态和非占据态之间的跃迁及损耗特性的重要参量. 考虑到三层石墨烯和双层石墨烯的性质类似, 且双层石墨烯的掺杂效果更直观(能隙打开最大), 故以双层石墨烯为例. 图4是双层石墨烯和镍掺杂的双层石墨烯的介电常数实部ε1 和虚部ε2 随能量的变化情况, 由图可知, 掺杂后的ε1 和ε2 均比未掺杂的增大; 且掺杂后的双层石墨烯体系在1.5—3.0 eV能量区间(可见光波段)的跃迁增强. 这是由于镍的3p态贡献的电子使导带底存在大量的过剩电子, 并使晶体内部的载流子即电子的浓度增加. 晶格中的镍离子束缚着附近的过剩电子, 在外加交变电场的作用下, 被束缚的过剩电子会克服一定的势垒而不断往复运动, 从而引起极化弛豫和损耗.
图 4 镍原子掺杂前后的双层石墨烯的介电常数Fig. 4. Dielectric constant of the Ni-doped bilayer graphene and bilayer graphene.晶体内部的光吸收主要源自电子的带间跃迁. 根据费米黄金定则, 介电常数的虚部
ε2 可表示为[23]ε2(ω)=(4π 2e2m2ω2)∑|Pc,v|2δ(Ec−Ev−ℏω), (1) 式中的求和扩展到整个导带c和价带v, P为动量跃迁矩阵, E为电子能级,
ℏ 是约化普朗克常量, ω为光子频率, m是电子的有效质量, e是电子的电荷. δ函数使带间电子跃迁的能级差恰好等于入射光子的能量. 由(1)式可知, 由介电常数的虚部就可判断材料的光吸收性能.由图4可见, 掺杂后介电常数的虚部(D-Ni
ε2 )在可见光波段(390—760 nm)比掺杂前(Dε2 )的有明显提升, 即掺杂后的双层石墨烯在可见光波段损耗增强, 则相应的吸光能力也增强.复折射率
nc=n+iκ ,nc 的实部n是固体折射率, 反映介质对电磁波的色散, 其虚部κ为消光系数, 表征介质对电磁波的吸收[24,25]:κ(ω)=1√2[(ε21+ε22)1/2−ε1]1/2, (2) ε1=n2−κ2,ε2=2nκ. (3) 吸收系数
α(ω)=4kπλ0=ωncε2(ω). (4) 由(3)和(4)式可知, 吸收系数与消光系数成正比, 如图5所示, 在可见光波段(390—760 nm), 掺杂镍原子的双层石墨烯的折射率虚部(消光系数)比掺杂之前的高, 表明损耗大, 吸光性能好.
图 5 双层石墨烯掺杂前后的折射率与波长的关系Fig. 5. Refractive index versus wavelength for the Ni-doped bilayer graphene and pure bilayer graphene.由图6可知, 相同层数的石墨烯体系, 相比本征石墨烯, 掺杂镍原子的石墨烯其反射率R有所降低. 掺杂之后的双层石墨烯在可见光波段的反射率都低于0.1, 掺杂之后的三层石墨烯在可见光波段的反射率都低于0.15, 即镍原子的层间掺杂有效降低了石墨烯的反射率. 本征石墨烯[26]随着层数的增加, 透射率T依次下降2.3%, 进行层间掺杂后透射率下降更快, 且计算证明镍原子掺杂能有效降低石墨烯体系的反射率, 故由
A+R+T=1 可知, 镍原子的层间掺杂能有效提升石墨烯的吸光性能.
图 6 掺杂前后的单层、双层和三层石墨烯的反射率Fig. 6. Comparison of reflectivity of monolayer, bilayer and trilayer graphene with and without Ni doping.4. 结 论
运用基于局域电荷密度近似密度泛函理论的第一性原理方法, 计算分析了镍原子掺杂双层和三层石墨烯体系的能带结构、DOS和光学性质. 研究发现, 在层间掺杂镍原子, 能打开多层石墨烯体系的带隙, 最大带隙可达0.604 eV; 镍原子掺杂后的石墨烯体系电子局域性增强, 且d轨道的DOS产生尖峰效应, 体系等离子能量增强. 镍掺杂后的多层石墨烯体系的介电常数虚部和消光系数均得到提高, 对可见光的吸收能力增强.
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图 1 镍原子掺杂的双层石墨烯的(a)俯视图和(b)侧视图; 镍原子掺杂的三层石墨烯的(c)俯视图和(d)侧视图(蓝色代表石墨烯, 绿色代表镍原子)
Fig. 1. (a) Top view and (b) side view of bilayer graphene cell (marked as blue) doped with nickel (marked as green); (c) top view and (d) side view of trilayer graphene cell (marked as blue) doped with nickel (marked as green).
图 2 能带图 (a)双层本征石墨烯; (b)镍掺杂双层石墨烯; (c)三层本征石墨烯; (d)镍掺杂三层石墨烯
Fig. 2. Energy band diagram for (a) bilayer graphene, (b) Ni-doped bilayer graphene, (c) trilayer graphene, (d) Ni-doped trilayer graphene.
图 3 DOS (a)双层本征石墨烯(D); (b)三层本征石墨烯(T); (c)镍掺杂双层石墨烯(D-Ni); (d)镍掺杂三层石墨烯(T-Ni)
Fig. 3. Density of states diagram for (a) bilayer graphene (D), (b) trilayer graphene (T), (c) Ni-doped bilayer graphene (D-Ni), (d) Ni-doped trilayer graphene (T-Ni).
图 4 镍原子掺杂前后的双层石墨烯的介电常数
Fig. 4. Dielectric constant of the Ni-doped bilayer graphene and bilayer graphene.
图 5 双层石墨烯掺杂前后的折射率与波长的关系
Fig. 5. Refractive index versus wavelength for the Ni-doped bilayer graphene and pure bilayer graphene.
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[1] Geim A K N, Novoselov K S 2007 Nature Mat. 6 183
Google Scholar
[2] Geim A K 2009 Science 324 1530
Google Scholar
[3] Zhao M Z, Xu H, Xiong C X, Zheng M F, Zhang B H, Xie W K, Li H J 2018 Appl. Phys. Express 11 082002
Google Scholar
[4] Zhang B H, Li H J, Xu H, Zhao M Z, Xiong C X, Liu C, Wu K 2019 Opt. Express 27 3598
Google Scholar
[5] Yan Z L, Xiong X, Chen Y, Ouyang F P 2014 Superlattice Microst. 68 56
Google Scholar
[6] 褚颖, 刘娟, 方庆, 蒋利军 2009 电池 39 220
Google Scholar
Zhu Y, Liu J, Fang Q, Jiang L J 2009 The Battery 39 220
Google Scholar
[7] 琚成, 贾芸芳 2014 太赫兹科学与电子信息学报 12 325
Google Scholar
Ju C, Jia Y F 2014 Inf. Elect. Eng. 12 325
Google Scholar
[8] Liu Y P, Xia Q L, He J, Liu Z W 2017 Nanoscale Res. Lett. 12 93
Google Scholar
[9] 陈英良, 冯小波, 侯德东 2013 物理学报 62 187301
Google Scholar
Chen Y L, Feng X B, Hou D D 2013 Acta Phys. Sin. 62 187301
Google Scholar
[10] Schedin F, Geim A K, Morozov S V, Hill E W, Blake P, Katsnelson M L, Novoselov K S 2007 Nature Mater. 6 652
Google Scholar
[11] Reddy A L M, Srivastava A, Gowda S R, Gullapalli H, Dubey M, Ajayan P M 2010 ACS Nano 4 6337
Google Scholar
[12] Denis P A, Faccio R, Mombru A W 2009 ChemPhysChem 10 715
Google Scholar
[13] Chi M, Zhao Y P 2009 Comput. Mater. Sci. 46 1085
Google Scholar
[14] Endo M, Hayashi T, Hong S H, Enoki T, Dresselhaus M S 2001 J. Appl. Phys. 90 5670
Google Scholar
[15] Jiang Q G, Ao Z M, Jiang Q 2013 Phys. Chem. Chem. Phys. 15 10859
Google Scholar
[16] Rafique M, Shuai Y, Hussain N 2018 Physica E 95 94
Google Scholar
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