ABSTRACT
The word superlattice (SL) literally denotes a periodic array of thin layers of two crystalline materials or quantum structures of distinctly different bandgaps that are capable of controlling the transmission of electrons (or holes) [1-5]. SL structures are conventionally formed by depositing ultrathin layers of specic elements such as from groups III-V and II-VI in order to obtain superior electrical and optical properties compared to present silicon devices [6-9]. Well-dened conned structures, created by employing some sophisticated deposition techniques, can yield an exceptionally high mobility of electron (or hole) gas [10]. The superb electronic and optical properties, although not yet having extensive commercial applications in nanoelectronics, created a huge interest in theoretical understanding of hybrid structures [11]. Smooth layers of amorphous materials such as a-Si:H and a-Si3N4 were employed for making articial SL structures; however, they could not produce a strong evidence of resonant tunnelling [12]. Following this idea, a multilayered carbon SL structure has been developed (at Cambridge University, United Kingdom), which was successful in explaining the enhanced optical properties [13]. One of the major successes in this eld was the observation of resonant tunnelling with negative differential resistance
(NDR) from the quantum well structure of carbon that also showed high-frequency transport (at the University of Surrey, United Kingdom) [14]. Understanding of resonant transmission in disordered carbon systems has remained incomplete until the theoretical explanation of electron transmission was recently given (at the University of the Witwatersrand, South Africa) [15]. These studies can be extended to understand the microstructure and electronic properties of low-dimensional materials such as quantum dots and quantum wires consisting of two or more phases. In fact, a quantum well structure model of amorphous carbon was envisioned by a number of researchers due to the presence of sp2 and sp3 (and other low concentration) phases [16-18]. However, sufcient theoretical analysis has not been given to show the connectivity between these two phases that explain the resonant tunnel features within a carbon structure [19-20]. Although optical and mechanical properties of multilayered carbon lms were found to be useful [21-24], this subject did not offer convincing evidence for application in nanoelectronics. In fact, over many years, a large amount of work involving rigorous calculation of 3D SL structures were performed to understand the mechanical properties of the bulk material [22-23]. In a-C lms, the quasi-one-dimensional (q-1D) building block of SL has not
Introduction ............................................................................................................................................................................. 1025 Motivation for Studying Carbon SL ....................................................................................................................................... 1027 Graphene Superstructures ....................................................................................................................................................... 1028
Transport in Defective Graphene ....................................................................................................................................... 1028 Transport through Carbon Clusters .................................................................................................................................... 1028
Multilayered SL Structures of Disordered Carbon ................................................................................................................. 1032 Carbon RTDs ...................................................................................................................................................................... 1034 Carbon 1D Filamentary Channels ...................................................................................................................................... 1034 High-Frequency Applications of Carbon RTD .................................................................................................................. 1034
Proposed Carbon 1D Superstructures: Disorder Effects in the Electronic Structure of Carbon ............................................. 1037 Uncorrelated Disorder ........................................................................................................................................................ 1040 Correlated Disorder ............................................................................................................................................................ 1041 Nitrogen Doping................................................................................................................................................................. 1042
3D SL Structures Applied to UNCD Films............................................................................................................................. 1044 Temperature-Dependent Conductivity at Zero Magnetic Fields ........................................................................................ 1046 Magnetoresistance and 3D Anisotropic Transport ............................................................................................................. 1046 AMR Study for the Analysis of SL Structures ................................................................................................................... 1048
Conclusion .............................................................................................................................................................................. 1049 Acknowledgments ................................................................................................................................................................... 1050 References ............................................................................................................................................................................... 1050
been found unlike in some organic molecular polymeric structures [25-26]. At present, only a few model structures are proposed for weakly disordered carbon mimicking the organic molecules and weakly disordered SL structures of semiconductors. The proposed models may need further improvement through the introduction of some rational ideas. Nevertheless, the effect of disorder and its connection to energy bandgap in carbon have been introduced at present to understand the electronic transport properties. Due to exibility of carbon-carbon bonds in the hybrid structures, the electron mobility in disordered carbon chains will be much smaller compared to other rigid (strictly periodic) carbon nanostructures, namely, graphene, nanotubes, and even insulating diamond lms [27-30]. On the other hand, the limitations of pure carbon structures in real device applications fostered a trend of achieving hybrid materials, for example, ultrananocrystalline diamond (UNCD) lms (a mixture of diamond nanocrystals and graphene layers) (Figure 625a and b), graphene on diamond, and diamond-like carbon (DLC) (Figure 625c and d) [32-38]. Furthermore, related heterostructures such as lled carbon nanotubes, functionalized graphene, diamond nanorods wrapped with graphene, and multilayered carbon structures (Figure 626a through d) can be included in this group [39-42]. One of the
main motivations for studying hybrid structures is to compare with GaAs SL structures and produce better (and cheaper) electronics than silicon, a material which is less responsive in the high-frequency range [43-45]. In this article, we shall discuss on resonant transmission of electrons and their relationship with microstructure (and disorder level) of pure and nitrogen doped a-C SL. The following topics are addressed:
1. Motivation for developing carbon SL and heteros tructures
2. Articial SL structures of graphene and carbon clusters 3. Multilayered SL structures of disordered carbon. 4. Theoretical analysis of carbon SL structures: a. q-1D chain b. Uncorrelated disorder c. Correlated disorder d. Nitrogen doping of SL structures 5. Electronic transport in 3D carbon SL structures
made of diamond and graphene: a. Weak localization b. Magnetoresistance (MR) at high elds c. Angular dependent MR 6. Future directions and conclusions
FIGURE 625 Hybrid structures formed by a mixture of sp3 and sp2 carbon phases: (a) Ultra-nanocrystalline diamond lms. (From Bhattacharyya, S. et al., Appl. Phys. Lett., 79, 1441, 2001.) (b) Predicted microstructure of graphene diamond system. (From Churochkin, D. and Bhattacharyya, S., EPL, 100, 67004, 2012.) (c) Diamond incorporated with graphene. (From Yu, J. et al., Nano Lett., 12, 1603, 2012.) (d) High-frequency graphene device constructed on diamond-like carbon lms. (From Wu, Y. et al., Nature, 472, 74, 2011.)
Information science depends on the (1) availability of quantum states (density), (2) connectivity between states, and (3) lifetime of states (speed). The information stored in the potential wells should be neither too deep nor too shallow. The material should have high mobility of carriers for fast communication. Nitrogen or nitrogen vacancy centers in diamond have been identied as qubits for quantum information science with great optical properties [46]. Unfortunately, these centers are not accessible electrically since the potential is too deep and also do not interact with environment due to the interference of disordered carbon layers present on the diamond surface [47]. On the contrary, graphene does not have
a (sufciently large) bandgap to store information over a long time [48]. Carbon as a rigid and strong material in general has several advantages in handling or manipulation. Rather than combining with other light elements to form a stable solid object, carbon atoms nd their counterpart within other carbon atoms; hence, the superstructures of carbon can be formed. One can imagine that carbon atoms can change their conguration(s) from sp2C to sp3C and back to sp2C by utilizing the available energy differentiating these two phases. One structure can complement with its counterpart easily through controlling disorder level. However, the main disadvantage is the structural disorder that arises from the exibility of carbon-carbon bonds as well as their ability to accept many forms of disorder. This material (burnt off into gaseous CO2)
FIGURE 626 Various forms of carbon hybrid structures: (a) Diamond-lled nanotubes. (From Zhang, J. et al., Angew. Chem. Int. Ed., 52, 3717, 2013.) (b) Functionalized grapheme. (From Souto, S. et al., Phys. Rev. B, 57, 2536, 1998.) (c) Diamond nanorods. (From Arenal, R. et al., Phys. Rev. B, 75, 195431, 2007.) (d) Multilayered superlattice structures showing the periodic variation of density and stress with thickness. (From Mathioudakis, C. et al., Phys. Rev. B, 65, 205203, 2002.)
may not be compared with other semiconductors e.g., Si since the oxide form of silicon is compatible with Si and can be utilized as a gate dielectric layer. Although gated structures of nanotubes and graphene have shown some interesting transport properties, over a long period of research, they did not yield much commercial value since the effect of disorder has not been overcome [49]. In contrast, tunnel structures made from organic molecules have some real applications overcoming the effect of disorder [50,51]. Can it be possible to make resonant tunnel devices using thin layers of carbon that are intermediate to molecules and solid-state devices? This point is addressed currently. It seems one has to nd the ultimate or nest elementary q-1D structure of (pure) carbon that can act as a backbone for the hybrid structure and carry information over a long path. Stimulated by high magnetic eld and high frequency, it is possible to carry information at high speed unlike in bioorganic molecular structures [52-55] and also can couple to the environment. We would like to search for the microstructural unit of carbon by comparing carbon SL structures of different forms, articially created or in natural systems that might be extended in other related hybrid/ organic/molecular and even in biological systems.
