石墨烯PN结的电流理论特性研究

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1、 本 科 生 毕 业 论 文（设计）石墨烯PN结的电流理论特性研究Theoretical study of electronic transport properties of graphene PN junctions 姓名与学号 3071102254 指导教师 年级与专业 电子科学与技术07级 所在学院 信息与电子工程学系 摘要在本文中，基于第一性原理计算，我们检验了金属接触对于石墨烯的掺杂影响。之后，我们使用金属接触构建了石墨烯PN结结构。我们通过电流电压特性曲线和透射率曲线研究了石墨烯PN结的电流传输性质。尽管石墨烯PN结在导通正向电流和抑制反向电流这一特点上和传统PN结有所相似，但仍

2、然有很多新颖的现象存在于石墨烯PN结中。我们还研究了使用六方氮化硼衬底时石墨烯PN结的电流传输情况。PN结在电子器件中非常重要，对于石墨烯PN结的研究将会促进石墨烯电子这一后硅时代很有前景的领域的发展。关键词：石墨烯PN结掺杂第一性原理氮化硼 AbstractIn this work, we examined the effects of metal contacts on the doping type of graphene based on first-principles calculation. Then we used the metal contacts technique to

3、 construct several kinds of graphene PN junctions. We explore the current transport mechanism through the PN junctions by their current-voltage characteristic and transmission plots. Graphene PN junctions behaved like traditional PN junctions by transmitting positive current and suppressing negative

4、 current, also there are some novel phenomena in graphene PN junctions that are different from traditional PN junctions. We also inspect the situations where h-BN substrate was used. PN junctions are very importing in electronic and optoelectronic devices, and the study of graphene PN junctions will

5、 put forward the development of graphene electronics, a very promising technology in the post-Silicon era. Keywords: graphenePN-junctiondopingfirst-principlesBNContent1. Introduction12. Method23. Results83.1 Doping graphene with metal contacts83.2 Cu|graphene Au|graphene PN junction103.3 Cu|graphene

6、 Pt|graphene PN junction133.4 Cu|graphene|BN Au|graphene|BN PN junction153.5 Cu|graphene|BN Pt|graphene|BN PN junction173.6 Cu-graphene junction184. Conclusion195. Acknowledgement20References20Appendix22浙江大学本科生毕业论文 石墨烯PN结的电流理论特性研究1. IntroductionGraphene, a monolayer material consists of carbon atoms

7、 tightly packed into honeycomb lattices, has been the focus of many heated researches since its first discovery in 2004 by A.K.Geim and K.S.Novoselov1. As a novel material, graphene has several outstanding properties that make it promising in various kinds of applications23. Among them, the applicat

8、ion of graphene in micro-/nano-electronic devices has attracted much attention. Graphene has many good and unique electrical properties that fit the development of better devices. For instance, the mobility of charge carriers in graphene is extremely high (as high as 15,000cm2/Vs under room temperat

9、ure145); the energy dispersion relationship of graphene is linear around dirac point5; the charge carriers in graphene are massless relativistic fermions and their behavior can be described by Dirac equation5. Compared with a previously found similar material, carbon nanotuble, graphene is capable o

10、f much higher current density and compatible with todays planar fabrication technology.In the application of graphene in electronic devices, a very important problem to be considered is the issue of the contact between graphene and other materials such as metals and dielectrics. It is of great signi

11、ficance because of these contacts not only affect the performance of the devices, but also control the transport of charge carriers and functionalize the devices, in which circumstances we call the contacts “junctions”. In traditional semiconductor technology, PN junctions and Schottky junctions are

12、 two simple representatives of junctions and constitute more complicated junctions6. In the sphere of graphene electronics, some experimental and theoretical work has been done with regard to graphene junctions. Previous work711 has proved when graphene is in contact with metals, it can be doped, re

13、sulting from the electron/hole transfer between graphene and metals due to their different work functions. To be specific, copper (Cu), silver (Ag) and Aluminum (Al) induced n-type doping in graphene, while platinum (Pt) and gold (Au) induce p-type doping in graphene. Researchers also studied the is

14、sue of charge carriers transporting through graphene junctions. It is pointed out theoretically that the probability a charge carrier goes through a junction depends on its incident angle, and when the carrier vertically moves through a junction, the probability of transmission is one910. Meanwhile,

15、 some experimental work has shown the current-voltage characteristic of a graphene PN junction is linear16.In this work, we studied the influence of metal contacts on graphene and the carrier transport phenomenon through a metal contacts induced graphene PN junction. Pervious graphene PN junctions u

16、nder study were formed mostly by chemical doping8 or electrostatic doping12. These strategies are either instable or complicated, for chemical molecules are easy to desorb and split-gate technique requires high fabrication precision. The idea of using metal contacts to construct graphene PN junction

17、s makes use of the inherent electrodes in an integrated circuit and is promising in future industrial application.2. MethodIn this work, we used first-principles calculations based on density functional theory (DFT) and Non Equilibrium Greens Function (NEGF) to obtain the simulation results. For a g

18、iven system, first-principles calculations were used to get the energy dispersion relationship (E-k curve). In this scenario, we observed the position of Fermi level to decide the doping type and dose of the system. For a current transport structure, we used NEGF method to solve Landauers equation,

19、getting the information of transmission as well as I-V curve.First, we studied the influence of metal contacts on graphene. We used three metals: copper (Cu), gold (Au) and platinum (Pt). For all three metals, their (111) surfaces were in contact with a monolayer graphene. The lattice constant of gr

20、aphene is set to its optimized value, 2.445, and the lattice constants of metals were adjusted accordingly. This adjust is reasonable as the mismatch with the optimized lattice constants for metals is just 0.8% 3.8%. Fig.1 shows how the lattices of graphene and metals are matched. Fig.2 shows the gr

21、aphene-metal structures we built. Based on our observation, metals with more than 3 layers have almost the same calculation results as metals with 3 layers. Hence we can use 3-layer metal to simulate bulk metal. For the distance between graphene and metals, we chose 3.3 for Cu(111)-graphene and 3.5

22、for Au/Pt(111)-graphene by referring to literature7.Fig.17. The lattice matching of graphene on (a) Cu(111) with 2 carbon atoms and 1 metal atom per layer in a unit cell and (b) Au(111) and Pt(111) with 8 carbon atoms and 3 metal atoms per layer in a unit cell.Fig.2. The unit cell of Cu(111)-graphen

23、e contact (left) and Au/Pt(111)-graphene contact (right). Second, we studied the current transport properties through a metal contacts induced PN junction. We set up the structure in a “left electrode channel right electrode” mode, and Cu, Au, Pt were used for both the electrode contacts and the dop

24、ing materials for graphene. Graphene was chosen as the channel material. By choosing different metals for left and right electrode, we doped the graphene differently on the left and on the right, namely one side of the graphene was n-type doped and the other side is p-type doped. Fig.3 and Fig.4 sho

25、w the structures of Cu|graphene Au|graphene PN junction and Cu|graphene Pt|graphene PN junction. Furthermore, recent discoveries showed that a novel substrate or gate dielectric, hexagon Boron Nitride (h-BN), has a significant influence on the performance of graphene based devices1314, so we tried g

26、raphene-BN stacking layer as our second channel material. Fig.5 and Fig.6 show the structures of Cu|graphene|BN Au|graphene|BN PN junction and Cu|graphene|BN Pt|graphene|BN PN junction. (For both calculation and fabrication compatibility, we left a buffer zone between the left and right side, so the

27、 structure is actually a PIN junction.)Fig.3. The structure of Cu|graphene Au|graphene PN junction.Fig.4. The structure of Cu|graphene Pt|graphene PN junction.Fig.5. The structure of Cu|graphene|BN Au|graphene|BN PN junction.Fig.6. The structure of Cu|graphene|BN Pt|graphene|BN PN junction.Last, we

28、studied the current transport properties through a metal-graphene Schottky junction. This study not only revealed the mechanism of metal-graphene junctions but also helped to understand the calculation results of the above structures. We chose Cu as the metal. Fig.7 shows the structure of Cu-graphen

29、e junction.Fig.7. The structure of Cu-graphene junction.Some calculation details are as follows. For the calculation of graphene on metals, we used double-zeta polarization as the basis size for pseudo atomic orbital of every element. Ceperly and Alders exchange functional was used in the Local Dens

30、ity Approximation method15. The pseudo atomic orbital bases were generated by achieving the energy shift that made the Fermi level of each element as the optimized value. A 50501 k-grids was used for sampling. For the calculation of current transport structures, we used single-zeta as the basis size

31、 for pseudo atomic orbital of every element. Ceperly and Alders exchange functional was used in the Local Density Approximation method. The pseudo atomic orbital bases were generated by achieving the energy shift that made the Fermi level of each element as the optimized value. A 8011 k-grids was us

32、ed for sampling. The range of contour integration was chosen as 3eV of Fermi levels.3. Results3.1 Doping graphene with metal contactsFig.8, Fig.9 and Fig.10 show the band structure of graphene on Cu(111), Au(111) and Pt(111) respectively. The high symmetry points we chose in the k-space were M, and

33、K. From the figures we can see that Cu can induce n-type doping in graphene and Au and Pt can induce p-type doping in graphene. These results are consistent with previous results in literature714.Fig.8. Band structure of graphene on Cu(111). The dirac point of graphene lies on K point, and the red d

34、ashed line shows the position of Fermi level, which is above the dirac point, Hence, graphene is n-type doped or electron doped in contact with Cu.Fig.9. Band structure of graphene on Au(111). The dirac point of graphene lies on K point, and the red dashed line shows the position of Fermi level, whi

35、ch is below the dirac point. Hence, graphene is p-type doped or hole doped in contact with Au.Fig.10. Band structure of graphene on Pt(111). The dirac point of graphene lies on K point, and the red dashed line shows the position of Fermi level, which is below the dirac point. Hence, graphene is p-ty

36、pe doped or hole doped in contact with Pt.3.2 Cu|graphene Au|graphene PN junctionFig.11 shows the current transport properties of a Cu|graphene Au|graphene PN junction in an I-V curve. We noticed that when we applied the same voltage forward and backward on the junction, we got different currents, a

37、nd the current was larger when positive voltage was applied on the Au|graphene side. Considering Cu|graphene is the n-type side and Au|graphene is the p-type side, this junction behaves just like traditional PN junctions: current from P side to N side is larger than current flowing reversely. Beside

38、s, we also found the I-V curve was not as linear as showed in previous literature16. Specifically, there is a S-shaped “kink” effect when the junction is forward biased at 0V 1V. This finding was issued experimentally3 and our work firstly brings up this phenomenon in an ab initio point of view.Fig.

39、11. The current-voltage characteristic of a Cu|graphene Au|graphene PN junction.To further explore the mechanism of the PN junction, we plotted the transmission (conductance) under several bias voltages in Fig.12 Fig.15. We found the transmission is not symmetrical for electrons and holes, and the c

40、hanging of the small transmission peak around Fermi level with voltage offered an explanation for the “kink” effect3.Fig.12. Transmission (in the unit of quantum conductance) plot of a Cu|graphene Au|graphene PN junction when biased at -0.3V.Fig.13. Transmission (in the unit of quantum conductance)

41、plot of a Cu|graphene Au|graphene PN junction when biased at 0V.Fig.14. Transmission (in the unit of quantum conductance) plot of a Cu|graphene Au|graphene PN junction when biased at +0.5V.Fig.15. Transmission (in the unit of quantum conductance) plot of a Cu|graphene Au|graphene PN junction when bi

42、ased at +1.0V.3.3 Cu|graphene Pt|graphene PN junctionFig.16 shows the current transport properties of a Cu|graphene Pt|graphene PN junction in an I-V curve. Also we plotted transmissions under several voltages in Fig.17 Fig.20. Similar results were get. The only thing to notice is that after substit

43、uting Au with Pt, the current became smaller, indicating a better contact between graphene and Au.Fig.16. The current-voltage characteristic of a Cu|graphene Pt|graphene PN junction.Fig.17. Transmission (in the unit of quantum conductance) plot of a Cu|graphene Pt|graphene PN junction when biased at

44、 0V.Fig.18. Transmission (in the unit of quantum conductance) plot of a Cu|graphene Pt|graphene PN junction when biased at +0.5V.Fig.19. Transmission (in the unit of quantum conductance) plot of a Cu|graphene Pt|graphene PN junction when biased at +1.0V.Fig.20. Transmission (in the unit of quantum c

45、onductance) plot of a Cu|graphene Pt|graphene PN junction when biased at +1.5V.3.4 Cu|graphene|BN Au|graphene|BN PN junctionFig.21 shows the current transport properties of a Cu|graphene|BN Au|graphene|BN PN junction in an I-V curve. Besides the current transport properties we got from Cu|graphene A

46、u|graphene PN junctions, there are some novel phenomena that interested us. First, the current becomes smaller. This makes sense as compared with graphene, a good conductor, h-BN is an insulator. Also our previous work showed when stacked on a single layer h-BN, graphenes zero band gab will be opene

47、d, and we shall expect the current is suppressed. From our calculation, the current of a Cu|graphene|BN Au|graphene|BN PN junction is reduced to about 0.1 times that of a Cu|graphene Au|graphene PN junction. Another interesting aspect is that the I-V curve of a Cu|graphene|BN Au|graphene|BN PN junct

48、ion is more nonlinear than that of a Cu|graphene Au|graphene PN junction, namely the linearity of the current-voltage characteristic is decreased after graphene is put on a monolayer h-BN substrate. To illustrate this problem, we explored the transmission of the structure, which was plotted in Fig.2

49、2. To our surprise, this transmission plot is very much different from the transmission plot of the structures without BN substrate. In the Cu|graphene|BN Au|graphene|BN PN junction, the transmission of the channel is discrete. There are several transmission peaks, and the value of transmission is a

50、lmost zero outside these peaks. The discrete transmission is responsible for the relatively large nonlinearity of the I-V curve. Moreover, the discrete transmission reminded us of the carrier transport in molecular electronics. Hence, the influence of BN substrate on graphene is not only band gap op

51、ening but also transmission discretization. The last thing to notice is that in the I-V curve, when the bias voltage is between 1.0V and 1.5V, the junction seems to have negative differential resistance. This phenomenon needs confirmation by denser samplings of bias voltage and its causation needs f

52、urther exploration.Fig.21. The current-voltage characteristic of a Cu|graphene|BN Pt|graphene|BN PN junction.Fig.22. Transmission (in the unit of quantum conductance) plot of a Cu|graphene|BN Au|graphene|BN PN junction with no bias voltage.3.5 Cu|graphene|BN Pt|graphene|BN PN junctionFig.23 shows th

53、e current transport properties of a Cu|graphene|BN Pt|graphene|BN PN junction in an I-V curve. Most of the properties and trends remain unchanged, while there are two issues which need to pay attention to. First, the I-V curve is of good linearity compare with previous structure. This can be explain

54、ed by the transmission plot in Fig.24. The transmission peaks are close to each other, and the value of transmission outside these peaks is not zero, making the transmission continuous rather than discrete. Hence the I-V curve is linear. Second, the current of this structure is extremely small (arou

55、nd 0.00001 times the current of the structure without BN substrate), and the reason is still unclear.Fig.23. The current-voltage characteristic of a Cu|graphene|BN Au|graphene|BN PN junction.Fig.24. Transmission (in the unit of quantum conductance) plot of a Cu|graphene|BN Pt|graphene|BN PN junction

56、 with no bias voltage.3.6 Cu-graphene junctionFig.25 shows the current transport properties of a Cu-graphene junction in an I-V curve and Fig.26 shows the transmission plot. In this junction, we got higher positive current / negative current ratio when applied the same voltage, which indicating its

57、potential application in rectification devices. The transmission is also discrete. From the transmission plot, we had an interesting discovery that under small bias voltage, the current contains only one kind of charge carriers, holes. This might be useful in some electron/hole valve devices.Fig.25.

58、 The current-voltage characteristic of a Cu-graphene junction.Fig.26. Transmission (in the unit of quantum conductance) plot of a Cu-graphene junction with no bias voltage.4. ConclusionIn this worked, we first examined the effects of metal contacts on the doping type of graphene. It turns out that C

59、u induced n-type doping in graphene, while Au and Pt induced p-type doing. Then we used the metal contacts technique to construct several kinds of graphene PN junctions, using different metals (Cu, Au, Pt) and different channel materials (graphene, graphene|BN). We explore the current transport mech

60、anism through the PN junctions by their current-voltage characteristic and transmission plots. Graphene PN junctions behaved like traditional PN junctions by transmitting positive current and suppressing negative current, though its rectification effect was not that obvious. The transmission of a gr

61、aphene PN junction is asymmetrical to electrons and holes, and when graphene is stacked on a monolayer BN substrate, the transmission will become discrete. In the current-voltage characteristic of grpahene PN junctions, there was a S-shaped kink effect, in consistent with previous work. It can be ex

62、plained by the changing of the shape of transmission plot. PN junctions are very importing in electronic and optoelectronic devices, and the study of graphene PN junctions will put forward the development of graphene electronics, a very promising technology in the post-Silicon era.5. Acknowledgement

63、The author would like to thank Dr. Yang Xu for careful and patient guidance, and Zhendong Guo, Haiyuan Gao, Chun Zhao and Meijiao Li for helpful discussions.References:1 A.K.Geim and K.S.Novoselov, Science 306, 666 (2004).2 K.F.Mak, C.H.Lui, J.Shan and T.F.Heinz, Phys. Rev. Lett. 102, 256405 (2009).3 I.Meric, M.Y.Han, A.F.Young, B.Ozyilmaz, P.Kim and K.L.Shepard, Nat. Nanotechnol. 3, 654 (2008).4 K.S.Novoselov, D.Jiang, F.Schedin, T.J.Booth, V.V.Khotkevich, S.V.Moroz