Doctor of Philosophy
School of Engineering Physics
Al-Tikrity, Shareef Faik Sultan, The electronic and optical properties of graphene, Doctor of Philosophy thesis, School of Engineering Physics, University of Wollongong, 2013. http://ro.uow.edu.au/theses/4013
This thesis describes theoretical and experimental studies into the optical response of single and multiple layer graphene in the terahertz to infrared regime and provides a description of some the unique characteristics of graphene.
In this work, the Schrödinger time-dependent equation is employed for gapless and gapped graphene in monolayers and bilayers to specify the optical and electronic characteristics and describe the electronic transitions in the structuring of the honeycomb lattice that depend on the Hamiltonian equation and include applied electric field. The energy band dispersion and wave function are calculated by using a quantum mechanical approach, together with the tight-binding model, and a comparison with Bloch's theory is included in order to satisfy the theoretical details and provide a description of the low energy bands of graphene. Furthermore, this procedure has been used to study the interband transitions. The Boltzmann formula has also been used to describe the intraband transitions. To analyze our results, models for the optical response of graphene single layers and bilayer are taken into account, based on the electronic system described by the Fermi-Dirac distribution at different temperatures and in the most important frequency regime.
The linear and nonlinear optical conductivity and current density have been calculated to first and the third order for single-layer gapped and gapless graphene and bilayer graphene. It is demonstrated that the third order nonlinear response includes single frequency and frequency tripling nonlinear terms.
In the present results, single layer graphene on a SiO2 substrate layer shows a strong response in the p-n junction regime in the nonlinear optical conductivity. It is also shown that the conductivity can be negative within a limited range of frequencies, depending on the bias voltage (Vb) and when (hω < eVb). In the terahertz regime, the negative conductivity increases with increasing relaxation time and gate voltage, and with decreasing temperature. In this kind of p-n junction, the nonlinear optical response in the gapped and gapless graphene shows a strong response under forward bias. Also, the negative conductance provides a unique mechanism for photon generation in graphene and could be used for developing coherent terahertz radiation sources.
In the both the weak field and the strong field Fermi-Dirac distribution, the linear and nonlinear current density of single-layer gapped and gapless graphene has been calculated as a function of temperature. In gapless graphene, the nonlinear current effect increases with temperature up to room temperature, and is very much stronger than the linear current density. The third order nonlinear optical response in strong field is asymmetric between μ > 0 μ < 0and and can be stronger than that in weak field. The nonlinear optical response in gapped graphene is stronger than in gapless graphene under weak field at zero to finite temperature, and it increases with increasing temperature with a finite gap. The linear and the nonlinear optical responses in gapped graphene are affected by the strong field (under the Fermi-Dirac distribution) but the opposite is true with the linear gapless graphene.
For bilayer graphene, the optical conductivity can be affected by changing the temperature. Increasing the temperature from low to room temperature leads to a decrease in the optical conductivity where there is an electric field of 1000 V/cm. In addition, the nonlinear optical response decreases gradually with increasing frequency. Also, the single frequency nonlinear response is greater than the frequency tripled nonlinear response in different frequency ranges.
The critical electric field plays an important role in equalizing the linear and nonlinear optical responses at a specific field of ~ 103 V/cm. Also, the critical field increases with increasing frequency or temperature.
It is demonstrated that the second order response in single and bilayer gapless and gapped graphene is equal to zero in both the strong field and the weak field regimes due to the inversion symmetry of the graphene structure.
Transmittance spectra from the terahertz to the infrared range in the multilayer sample (Graphene on substrate) and single layer samples (graphene only) at room temperature could be feasibly collected and were useful due to the high mobility of electrons in graphene at room temperature. Fourier transform spectroscopy is used to describe the transmittance of graphene and graphite films under room pressure and in vacuum. In the present results, graphene multilayer on Si substrate has low resistance at room temperature, less than that of the silicon alone. In addition, a new method was developed to calculate the transmittance and reflectance through multiple layers. This method is demonstrated to be more accurate than the classic (general) method. The theoretical and experimental results also show good convergence at short and long wavelengths.
Finally, the highly tunable and strong optical properties of graphene-based materials make graphene a new alternative candidate to most of the semiconductor materials. Also, the high transmittance and low resistance of graphene represent a remarkable result. Therefore, we suggest that graphene could be a candidate for developing optoelectronics devices and graphene-based optical applications, as well as being useful for building innovative devices for nonlinear terahertz applications.