Elsevier

Thin Solid Films

Volume 482, Issues 1–2, 22 June 2005, Pages 151-155
Thin Solid Films

Electronic and optical properties of a-C from tight-binding molecular dynamics simulations

https://doi.org/10.1016/j.tsf.2004.11.133Get rights and content

Abstract

Although the structural and mechanical properties of a-C have been theoretically investigated in detail, this is not so for the optoelectronic properties. Many issues remain unclear, such as the influence of disorder and intrinsic defects on the localization of the electron states and on the optical transitions. Here, as a first step towards solving this kind of problems, we present a computational approach to the study of the optoelectronic properties of a-C. This is based on tight-binding (TB) molecular dynamics (TBMD) simulations using a reliable environment-dependent Hamiltonian. The a-C networks were generated by quenching from the liquid. The electronic density of states of all simulated networks show that the material is semiconducting, and that the gap is clearly controlled by the separation of the π and π* peaks. A Tauc gap analysis shows that the optical gap varies between 2.7 and 0.3 eV. We analyze the dielectric functions as a function of the sp3 fraction. We also compare the computational results with experimental dielectric function spectra revealing considerable consistency between theory and experiment.

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 ππ* and σσ* electronic transitions, which show up as distinct features in the dielectric function spectra [6], [7], [8]. The ππ* 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 σσ* 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:H=nψn|HTB|ψn+Erep.

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:ρ(E)=i=1Nδ(Eεi),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

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