Density Functional Based Tight Binding (DFTB) Study on the Thermal Evolution of Amorphous Carbon

Density functional based tight binding (DFTB) model is employed to study the sp3-to-sp2 transformation of diamond-like carbon at elevated temperatures. The understanding could lead to the direct-growth of graphene on a wide variety of substrates.


I. INTRODUCTION
Graphene is a promising material that can replace tindoped indium oxide (ITO) as the next-generation large-area transparent conducting electrodes (TCE). A particular advantage of using graphene (assuming defect-free) is its unique two-dimensional electron gas properties at room temperature, leading to exceptionally high mobility [1]. A common method to grow large area graphene is by chemical vapor deposition (CVD) [2]. However, such method requires deposition temperature of approximately 1000 °C [ 3 ]. Furthermore, the produced graphene film needs to be transferred to the substrate of interest. Research is on-going to circumvent these limitations and a recent approach has been to investigate graphene growth from amorphous carbon (a-C) [4]. Understanding the graphitization mechanism of a-C is essential to produce quality graphene.
In 2013, Barreiro et al. reported the growth of graphene from catalyst-free a-C by current-induced annealing [ 5 ]. They observed the structural evolution both with in-situ transmission electron microscopy and with molecular dynamics simulation [5], and a-C clusters were simulated as part of the work. An intriguing observation was the formation of long fibers stem from the clusters at elevated temperature. These clusters with fibers acted as carbon source and were able to heal up defects on a graphene sheet [5].
In this work, we performed molecular simulation using DFTB method on a-C cluster to further understand the transformation dynamics of sp 3 to sp 2 , as well as the origin and process by which the carbonous fibers emerged.

II. SIMULATION DETAILS
An amorphous carbon cluster with diameter 1 nm was constructed using the Materials Visualizer within the Materials Studio environment, as shown in Fig. 1. The molecular dynamics simulation was performed using the DFTB+™ which includes the van der Waals interaction. The dynamics were performed at temperatures of 300K, 723K (TFT annealing temperature), 1200K, 1500K and 2000K. Duration of each dynamical simulation was 10 ps with 1 fs time-step to satisfy the Verlet assumption. Geometry optimization (structural relaxation) was performed prior to the dynamics simulation. Canonical Nose-Hoover isothermal constrained ensemble was used to supply heat to the system at constant volume and temperature.

III. RESULTS AND DISCUSSION
The DFTB dynamics simulation on the a-C cluster revealed a progressive increase in the population of sp 2 sites as the temperature was raised in a stepwise manner. Fig. 2 shows the difference in the sp 3 population between 300K and 2000K. There were only two sp 3 sites remained in the cluster at the end of 2000K annealing which is consistent with the work reported in Ref. 5. In the absence of substrate effect the free-standing a-C cluster also expectedly evolved into a fullerene-like structure instead of graphitic layer [5]. Stone-Wales defect commonly found on graphene sheet [6] can also be seen in the outer surface of the annealed cluster. 5and 7-member rings were observed on the outer surface of the cluster. Further study will focus on ways to minimize the defects during transformation and to promote formation of 6member carbon rings.
This work provided detailed insight into the process by which a tetrahedral sp 3 transformed into a planar sp 2 at elevated temperature. The bond connecting the carbon atom on top of the tetrahedral and the center atom (indicated by an 'X') weakened and eventually dissociates as the bond length increases, as illustrated in Fig. 3.  Highly reactive carbonous "fiber structures" responsible for graphene formation and defect healing has been reported [5] but no detail was given as to how they developed. This work shed some light on the process. Fig. 4 shows two snapshots taken from the same dynamic trajectory at 1200K. The cyan colored box highlights the dissociation of a sp 3 site occurred at time equals 6.77 ps, leading to a simultaneous emergence of a 7-member ring and a "fiber structure".

IV. CONCLUSIONS
A molecular simulation based on DFTB was performed on a-C cluster to investigate the sp 3 -sp 2 transformation process in detail including the formation of highly reactive carbonous fiber structure. Understanding of such processes will enable the direct deposition of graphene from a-C on a wide variety of substrate, which is essential for the massproduction of cost effective graphene-based transparent electrode. Fig. 4. Two snapshots taken from the same trajectory at 1200K. The enclosed cyan colored box shows (a) before and (b) after the sp 3 bond was transformed into sp 2 , giving rise to a 7-member sp 2 carbon ring and a "fiber structure".