Electronic and optical properties of a-C from tight-binding molecular dynamics simulations
Introduction
Amorphous carbon (a-C) is a very interesting material from several points of view. Tetrahedral a-C (ta-C) is a form of a-C, which contains a high percentage of sp3 bonds. Its diamond-like properties, such as high hardness [1], [2], make it an important material ideal for mechanical purposes [3], [4]. Applications of ta-C include hard protective coatings and stiff membranes. It is also a biocompatible material suitable for biomedical coatings, and it has promising applications in microelectromechanical devices (MEMs).
Carbon can be found in three hybridizations, sp3, sp2 and sp1 based on the hybridized orbitals of its second (L) shell electrons. In the sp3 configuration (as in diamond), four equivalent 2sp3 hybrid orbitals are tetrahedrally oriented around the atom forming strong covalent σ bonds. In the sp2 hybridization (as in graphite), there are three equivalent 2sp2 orbitals distributed on a certain plane and forming angles of 120° to each other. In addition, one unhybridized 2p orbital is left. This configuration results to in-plane strong covalent σ bonds and weak π bonds out of plane. Finally, in the twofold coordinated sp1 configuration, two linear 2sp1 orbitals are formed, and two 2p orbitals are left, which forms linear σ bonds and two π bonds in vertical directions, respectively.
An interesting subject of research on a-C is the study of its electronic structure and optical properties, which are related with the hybridization state. Thus, the optical properties are particularly interesting as they can provide accurate although indirect determination of the chemical state of a-C (sp3/sp2 ratio), and they are essential for many applications where optical transparency is required, such as in protective coatings on lenses and optical systems [5]. The optical properties of a-C are dominated by the π–π* and σ–σ* electronic transitions, which show up as distinct features in the dielectric function spectra [6], [7], [8]. The π–π* contribution originates exclusively from sp2 carbon atoms and particularly from the transition of π-bonded electrons to π* antibonding states. On the other hand, the σ–σ* transition comes from the σ-bonded electrons participating in the covalent bonds of both sp3 and sp2 carbon atoms [6], [7].
Despite the intensive investigations, the optoelectronic properties of a-C are not fully understood, and many issues, such as the variation of the optical gap and of other quantities as a function of the sp3 fraction and the role of defects and disorder, remain unclear. We aim at addressing this kind of problems. In the present work, we make the first step towards this direction. We present a computational approach to the study of the optoelectronic properties of a-C, which is based on tight-binding (TB) molecular dynamics (TBMD) simulations. We study various a-C networks generated by quenching from the liquid. We compute the electronic structure, the dielectric functions and the optical gap. We validate our results by comparing to experimental results acquired by spectroscopic ellipsometry (SE) from a wide variety of a-C and ta-C samples.
Section snippets
Tight-binding molecular dynamics simulations
Tight-binding molecular dynamics (TBMD) is more accurate and transferable than empirical schemes because it provides a quantum-mechanical description of the interactions. On the other hand, while less accurate than ab initio approaches, it yields greater statistical precision and allows for the use of larger cells, which compensate in part the sacrifice in accuracy.
In the tight-binding (TB) method, in general, the system is described by the Hamiltonian:
The first term
Results and discussion
The amorphous carbon networks used in this work have been constructed previously [13]. Here, we analyze three typical a-C cells with 86%, 75%, 45% sp3 content. In addition, we use a WWW network, which has 100% sp3 bonded atoms. The first step of our study is to calculate the electronic density of states (EDOS) of the various networks. This is defined for every energy E by the eigenvalues ɛi of our system:where N is the total number of the eigenstates. Fig. 1 shows the EDOS of
Conclusions
We have studied computationally the electronic properties of a-C networks with varying sp3/sp2 content, using tight-binding molecular dynamics with the environment-dependent model. We calculated the electronic density of states (EDOS), the dielectric function and the fundamental gap of various networks. All networks show semiconducting behavior. We have also found that the EDOS is dominated by the σ and π occupied states and the σ* and π* unoccupied states, resulting to two distinct peaks in
References (21)
Mater. Sci. Eng., R
(2002)- et al.
Sens. Actuators
(2002) - et al.
Diamond Relat. Mater.
(2003) Phys. Rev. Lett.
(1994)- et al.
Appl. Phys. Lett.
(1999) - (2002)
Diamond Relat. Mater.
(2003)- et al.
Diamond Relat. Mater.
(2004) - et al.
Phys. Rev. B
(1996) - et al.
J. Phys. Condens. Matter
(1992)