**2.3. Electrical Properties of Graphene**

The electronic properties of graphene are one of the prominent cases that relating experimental researches have dealt with. The controllable continuous transformation of charge carriers from holes to electrons was one of the most notable features in pioneering researches.

An example of the gate (or gate electrode is a region at the top of the transistor whose electrical state determines whether the transistor is on or off) dependence in single-layer graphene is shown in Fig. 4a. This dependency is much weaker in multiple layers of graphene because electric field is screened by the other layers.

graphene (from 1 to 10 layers), it can be expertized that interlayer resistance, 1/ *G*″, remains almost constant and pretty smaller than the resistance between graphene and its nongraphene environment [61]. Indeed, the interlayer thermal conductance of bulk graphite is ∼ 24 GW m

It must be remarked that surface effects are able to decrease the thermal conductivity of graphene because of the sensitivity of phonon propagation to surface or edge perturbation, and as a result of this, the in-plane thermal conductivity of freely suspended graphene is drastically lower than a graphene nanoribbon or a graphene contacted with a substrate.

**Figure 3.** (a) Thermal conductivity *κ* as a function of temperature for representative data of suspended graphene [55], SiO2-supported graphene [64], ~20-nm-wide graphene nanoribbons (GNRs)[63], suspended single-walled CNTs (SWCNTs)[66], multi-walled CNTs (MWCNTs)[67], type IIa diamond, graphite in-plane and out-of-plane. Additional data for graphene and related materials are also summarized in Ref.[54]. (b) Room temperature ranges of thermal con‐ ductivity data κ for diamond [57], graphite (in-plane) [54], carbon nanotubes (CNTs) [54], suspended graphene [54, 55],

It has been seen that the in-plane thermal conductance *G* of graphene can reach a significant fraction of the theoretical ballistic limit in sub-micrometer samples, owing to the large phonon mean free path (*λ* ≈ 100 to 600 nm in supported and suspended samples, respectively). However, thermal properties of graphene could be highly tunable, so that makes it useful for heat- sinking applications when we regulate it in ultra-high thermal conductivity, and it is useful for thermoelectric applications when it is regulated for ultra-low thermal conductivity.

The electronic properties of graphene are one of the prominent cases that relating experimental researches have dealt with. The controllable continuous transformation of charge carriers from

holes to electrons was one of the most notable features in pioneering researches.

SiO2-supported graphene [64], SiO2-encased graphene [65], and GNRs [63].

**2.3. Electrical Properties of Graphene**

spacing and the *c* axis thermal conductivity are assumed.

–2 K –1 if the typical 3.35- *A*°

8 Graphene - New Trends and Developments

The high electronic mobility of graphene permits the development of quantum hall effect (an effect that is visible in conductor and semiconductors materials; when there are both electrical and magnetic field at the same time in a conductor or semiconductor material, it can arise an electric potential perpendicular to the magnetic field that causes electric current perpendicular to the magnetic field) at low temperatures and high magnetic fields, for both electrons and holes (Fig. 4b) (Novoselov, et al., 2005; Zhang, et al., 2005). As seen in Fig. 4b, at room tem‐ perature, the Hall conductivity *σ*xy reveals clear plateaus at 2*e*<sup>2</sup> /*h* for both electrons and holes, while the longitudinal conductivity *ρ*xx approaches zero. (Quantum Hall effect is measured by *<sup>σ</sup>* <sup>=</sup>*<sup>υ</sup> <sup>e</sup>* <sup>2</sup> *<sup>h</sup>* , where "*e*" is the elementary charge, *h* is the Planck' constant, and *υ* is the "filling factor."

If *υ* is an integer, it will be an "integer quantum hall effect," and if *υ* is a fraction, it will be a "fractional quantum Hall effect." Here, at room temperature, the filling factor of graphene is *υ*=2.)

**Figure 4.** (a) The resistivity of a single layer of graphene vs. gate voltage. (b) The quantum Hall effect in single-layer graphene. Figures taken from (Novoselov, et al. (2005).

For sensing or transistor application, we should utilize the strong gate dependence of gra‐ phene. To do this, we should cut graphene into narrow ribbons because graphene does not have a band gap, and thus resistivity variation is small. However, graphene in narrow ribbons, makes an opening in the band gap that is proportional to the width of the ribbon by increasing the momentum of charge carriers in the traverse direction when shrinking them. This band gap in carbon nanotubes is proportional to its diameter. The opening of a band gap in graphene ribbons has recently been observed in wide ribbon devices lithographically patterned from large graphene flakes (Han, et al., 2007) and in narrow chemically synthesized graphene ribbons (Li, et al., 2008).
