ABSTRACT
In this review chapter, photonic properties of graphene device have been presented, posing potential advantages of high-speed electronic response and wide photodetection bandwidth. The high-speed electronic response of photo-generated carriers is attributed to the carrier mobility in graphene photodetectors, which is much higher than those in the conventional semiconductor photodetectors. Meanwhile, the wide photodetection bandwidth is attributed to linear energy−momentum dispersion relation of graphene as a two-dimensional (2D) electron gas that gives rise to no energy bandgap at the neutral Dirac point. To enlighten the photocurrent generation mechanism of graphene devices, in this chapter, band diagrams with voltage bias applied have been presented with the help of laser illumination technique with spatial resolution on graphene. The previously reported theories on change in band structure have also been explained here. Lastly, various techniques
to enhance photocurrent from graphene devices, e.g., asymmetric device structure, graphene stack, and surface plasmonics, have been presented in this chapter. 10.1 IntroductionGraphene as a single-layer atomic carbon crystal with the 2D honeycomb lattice structure has recently attracted enormous attention due to its unique electronic properties [1,2]. In particular, the pioneering reports [3,4] on the quantum electronic properties of graphene obtained from exfoliation of highly oriented pyrolytic graphite (HOPG) inspired many scientists to explore the unknown interesting properties of graphene due to the ease of the fabrication of quantum electronic devices via the formation of graphene as a 2D gas. More fascinating in graphene device is the possibility to demonstrate the quantum electronic properties at room temperature. The unique electronic properties of graphene are attributed to its linear energy−momentum dispersion relation of 2D Dirac electrons which can be controlled by electric and magnetic fields [1,2]. Let us review how the linear energy−momentum dispersion relation and thereby the high carrier mobility is obtained from graphene. Graphene has two atoms per unit cell: A and B. As shown in Fig. 10.1, a low-energy band structure consists of Dirac cones located at two Brillouin zone corners K and K¢. HK x y
v v k ik
k ik = ◊ =
- +
È
Î Í Í
˘
˚ ˙ ˙
σ k 0 0 (10.1)where ν is the graphene Fermi velocity [5]. For each wave vector
k, an eigen-energy of Ek = ±ћν|k| as a linear energy−momentum dispersion relation is obtained. The energy dispersion resembles the energy of relativistic particles which are quantum mechanically described by the Dirac equation. Meanwhile, we are very interested in carrier mobility as a figure of merit on materials property for high frequency device applications. According to the theoretical and experimental results, carrier mobility generally expressed as μ = σ/ne is found to be much higher in graphene than those of the conventional silicon and other semiconductor materials, varying in the range of 103 to 106 cm2V−1s−1 depending on lattice and impurity scattering. When field-
effect transistor (FET) structure is used for the graphene device, the charge carrier density, n, can be determined by n = (7.2 × 1010cm-2V-1)VG, where VG is the gate voltage applied to the device, usually in the range of 0−100 V. That is, the charge carrier density in graphene is <7.2 × 1012 cm-2. According to the relation on effective mass of charge carriers to n, m*= h(n/π)1/2/(2νF), where νF is the Fermi velocity of ~106 ms−1 [1,3], the effective mass in graphene is found to be very low, <0.1m0. By applying μ = σ/ne and the results reported in 2005 by Novoselov et al. [3], carrier mobility of ~2,600 cm2 V−1s−1 is obtained. This result shows the great potential for the mobility in graphene to be enhanced by increasing the mean free path of carriers, that is, by suppressing the scattering of carriers in graphene, as the conductivity of a material can be directly proportional to the mean free path of carriers (l): σ = neμ = (e2/h) kl. In addition, it is very interesting to observe that the mobilities in graphene can remain unchanged near to the room temperature, whereas other materials show a drastic decrease in their mobilities with increasing temperature [6].
