Understanding Graphenes Thermal Properties - Case Study Example

Understanding graphene’s thermal properties: A phonon perspective December 17, Table of Contents Table of Contents 21. Introduction 3 2. Scope of this paper and main objectives 4 3. The structure of graphene 5 4. Phonon molecular dynamics 7 5. Mechanisms of heat conduction in graphene 7 6. Thermal conductivity of graphene: significance of edges and substrates 9 7. The thermal conductivity of graphene ballistic limit 10 8. Thermal transportation in few-layer Graphene 11 9. Features of conduction of heat in 2D crystals 12 10. Relationship between the 2-D and 3-D (key difference between metals and graphene in terms of thermal conductivity) 14 11. A correlation between the 2D and 3D with respect to thermal conductivity 14 12. Conclusion 15 References 16 Abstract Graphene has attained great attention from various researchers and scientists due to its extraordinary and unique thermal properties [1]. Moreover, it is able to transport electrons at almost zero resistance [5]. However, much of the properties as well as details pertaining graphene are still unknown. Contextually, graphene has been used especially in matter physics as well as in material sciences. Its study is strictly based on 2-D which exhibits a wide variety of applications. Essentially, high thermal conductivity of graphene is as a result of strong bonding between the carbons atoms while out of flow thermal heat is constrained by weak forces due to van der Waals coupling [5]. This paper focuses on discussing the thermal properties of graphene paying from a phonon perspective. In addition, the paper examines the key differences between metals and graphene in terms of their thermal conductivity. The heat flow in graphene can be turned on by various means such as phonon diffusing by substrates or interfaces. Ultimately, the study and analysis of the properties of graphene owes the great number of applications ranging from electronic and structural uses among others. Keywords: graphene, phonon, thermal conductivity, 1. Introduction Graphene is a 2-D material usually developed of a lattice of hexagonal arrangement of carbon atoms [2]. It is also known as a single layer of graphene while other terms commonly used are bilayer or trilayer graphene stratum. Evidently, graphene thermal attributes are obtained by analyzing the crystal anisotropic nature. The strongest bonds are because of the in plane covalent sp2 between the carbon atoms which are significantly stronger than the sp3 diamond bonding. Seemingly, the planes of graphene on the graphite crystal are due to weak van der Waal forces between them. Elimination of heat loss in electronic devices has been a problem encountered by various researchers in an electronic industry. Therefore, the industry has put more efforts and resources in searching for better materials, which dissipates less heat to improve innovations of the next generations of integrated circuits (ICs) designs as well as 3-D electronic devices. Apparently, thermal properties issues have been encountered both in the photonic and optoelectronic devices [4]. Fundamentally, materials ability to conduct heat is based on the arrangement of atomic structure. The restructuring of atomic structure will alter the thermal properties of a material on a nanometer scale [15]. Primarily, nanowires and bulk crystals don’t allow transfer of charges or heat due to high components of photons, dispersion or scattering of photon. Studies shows that the K divergence in 2-D crystals is due to insufficient crystal anharmonicity. Crystal anharmonicity normally restores thermal equilibrium thus requires the need of limiting the system size and introduction of disorder to achieve the significance of the value of K. 2. Scope of this paper and main objectives There are number of papers in open literature regarding the study of graphene’s thermal behaviour. A great deal of them focuses on the numerical/simulation study, based on heat transfer equations. However, they have used heat transfer equation. Nevertheless, there are very little details on the origin of those equations as well as their physical understandings/interpretation and the whole picture is not clear. Thus the objective of this review is to analyse graphene’s thermal properties based on elaborated lattice dynamics fundamentals. The following objectives were considered in this present paper: (1) The paper is aimed at analysis of the graphene thermal properties, and (2) To analyse the most important property that distinguishes graphene from other metals. Thus, this study scientifically investigates and analysis the understanding of fundamental lattice dynamics and associated role in thermal conduction based on the available literature and using the knowledge learned from this course and answers some critical questions as mentioned above. As such, the paper is much focused to avoid survey style. 3. The structure of graphene Since the material’s performance and properties is a function of its structure, it is very important to understand the structure of graphene in order to appreciate its high thermal conductivity. Figure 1 gives a clear understanding of the various allotropes of carbon in existence. 2D crystal is an atomic plane with single layer while 100 layers are considered a thin film of 3D material. Electronic structure advances drastically with various layers approaching the 3D limit of at least 10-20 layers of graphite material . Figure 2 illustrates the atomic arrangement of graphene and how one atom is bonded to the next atom. Figure 1: Various allotropes of carbon Figure 2: The atomic structure of graphene Graphene unlike other materials is uniquely identified by two characteristics. Perfect order is a distinct property of graphene, usually located in its sheets . This property means no existence of atomic defects such as vacancies. Indeed, this property implies that the sheets of graphene are completely pure with traces of carbon atoms being available. Secondly, the properties of graphene correlates with the type of unbounded electrons . It implies that the electrons at room temperature are highly charged and thus move faster as compared with electrons movement in other metals or semiconductors . It has strength of about (~ 130 GPa) and a thermal conductivity K of (~ 5000 W/m.K), which is termed as the best; for the sake of comparison pure copper has a thermal conductivity of (~ 400 W/m.K). In particular, the electronic structure of graphene is unique and different from metals. Graphene is a non-metal component; the electrons are arranged in a pi-bonds model that allows the next atoms to be interconnected as they travel from one atom to another. In contrast with metals in which electric charge is carried by free mobile electron, the graphene on the other hand engages with the lattice in a massless manner . Such properties uniquely define the grapheme 4. Phonon molecular dynamics Molecular dynamics (MD) is one of the fundamental concepts in determining and calculating graphene properties such as thermal properties . However, the technique can be constrained by the amount of bulk graphene. A relationship is derived based on MD, that is, the thermal conductivity depends on the length of graphene component. The relationship signify that graphene material has a very long (mean) free path phonon. Compressive or tensile forces are applied alongside the temperature slope of graphene, thermal conductivity significantly reduces. In addition, graphene with zigzag boundaries alongside the slope of the temperature have higher thermal conductivity as compared with graphene with armchair boundary . 5. Mechanisms of heat conduction in graphene Intensely, there are a variety of thermal properties of graphene material as described below; 1. Thermal conductivity of graphene: Intrinsic; very high in plane thermal conductivity Materials thermal conductivity is related with the heat per flux unit area and the temperature slope. The relationship is based on the following formula [9]; The negative sign designates that the heat flows from a high temperature region to a low temperature region. Graphene is strongly affected by interfacial interactions, atomic defects, and edges. The formula is mainly used if the samples size have greater than the optimum free path whereby (L>λ). Presumably, the layer of the graphene is taken to be graphite interlayer spacing h ≈ 3.35 [12]. The in-plane thermal conductivity of graphene at normal room temperature is recognized to have the highest of nearly 2000-4000w. In case of any disorder or residue will induce more phonon scattering as well as lowering the values. Contextually, phonon is defined by the following expression; J=Polarization phonon branches; two transverse acoustic branches, one longitudinal acoustic branch u- Phonon group velocity τ- Is the phonon relaxation time ω is the phonon frequency C is the heat capacity [20] Technically, the optimum free path is correlated with relaxation of time given as Λ = τυ. This property leads to ballistic conductance at room temperature. This property is normally understood in details by the examination of the principle of the structure of the band. Particularly, when a phonon is absorbed, it can cause huge momentum change to an electron with less energy change [16]. Apparently, two elaborate distinctive phonon transports exist. They include the diffusive and ballistic types of transport. The thermal kind of transport is usually referred to as the diffusive when the size of the sample is seemingly greater than Λ implying that phonons is associated with various scattering incidences. Likewise, when the size of the sample is much less than the free path (L< Λ) the transport is referred to as ballistic [7].Thermal conductivity is basically termed as intrinsic if it is constrained by the crystal-lattice anharmonicity [13]. Such concept assumes Fourier’s law of diffusive transport. When the potential energy has terms relatively higher than the 2nd order in relation to ion displacement from the equilibrium then the crystal lattice is termed as anharmonic [22]. Principally, when the crystal is perfect, the intrinsic K limit will be reached with no impurities or defects and thus phonons will only be scattered by other photons due to anharmonicity [18]. Engagement of the anharmonic phonon leads to finite K in 3-D which is vividly described by the Umklapp processes. The crystal degree anharmonicity is usually depicted by the Gruneissen boundary γ, which is expressed in the Umklapp scattering rates of 20-22 [5]. In essence, the thermal conductivity is designated as extrinsic if and only if its constrained by extrinsic effects hence results to phonon defect scattering or phonon-rough-boundary [23]. 6. Thermal conductivity of graphene: significance of edges and substrates The in-plane thermal conductance of graphene relatively decreases when 2-D encounters a substrate or restrained into graphene Nano-ribbons (GNRs) regardless of its high temperature of the freely suspended samples [10]. The manifestation is unpredictable due to the aspect of phonon propagation in an atomically thin graphene sheet which resultantly leads to a sensitivity to surface or edge perturbations. At room temperature, the graphene reinforced by SiO2 was determined to be 600w while SiO2 encased was obtained to be 160w while for the supported GNR was approximated to be 80w [17] (see Fig. 3) Figure 3:graphene material under edges and substrates 7. The thermal conductivity of graphene ballistic limit It is a profound property, which exclusively defines graphene material. The samples in which (L ≫ λ0) implies a constant thermal conductivity k, whereas thermal conductance is inversely proportional with length, G = κA/L[12]. Conversely, quantum treatment of small amounts of graphene devices (L ≪ λ0) discloses the thermal conductance approaches a constant (Gball) which is independent of length in ballistic transport of free scattering [23]. Thereby, a firm relationship between the conductivity and conductance can be derived to which the effective thermal conductivity containing a ballistic sample should be proportional to its length; κb = (Gball/A) L, A-cross-sectional area,A = Wh. In addition, a sample size with (L ≫ λ0) implies a constant thermal conductivity k; alternatively, the graphene ballistic thermal conductance can be numerically computed based on phonon dispersion [15]. 8. Thermal transportation in few-layer Graphene It is very vital to consider and examine the thermal properties of thin-layer of graphene with increase in thickness. There are two instances; thermal transport, which is constrained by intrinsic properties of few-layered graphene of lattice such as the crystal anharmonicity while the second part, is the extrinsic effects such as phonon-boundary or defect scattering [6]. Research indicates that the suspended uncapped few-layered graphene reduces with increase in n approaching the bulk limit [24]. The evolution of K was expounded by putting intrinsic quasi-2D crystal properties into consideration as outlined by the phonon Umklapp scattering. However, an increase in the few number of graphene layers available, the phonon scattering tends to transform and thus leads to a phase-space state availability for phonon scattering hence K decreases [14]. From the top to bottom, phonon scattering is restricted in suspended few layered graphene boundaries if constant n is maintained in the layer length. A small thickness of few layer graphene (n4 implies that the boundary scattering can increment. It is also hard to maintain the constant n throughout the whole area of few layer graphene hence a K value below the graphite limit is obtained. Graphite value recuperates thicker films [26]. Illustrations of thermal conductivity of quasi-2D carbon materials considering intrinsic and extrinsic effects are as shown below. Figure 2: Thermal conductivity of graphene Nano-ribbons obtained from MD simulations as a function of n showing a similar trend 9. Features of conduction of heat in 2D crystals An investigation of the conduction of heat in graphene normally increases the matter of vagueness in defining inherent thermal conductivity mainly for 2D crystal lattices . It is widely acknowledged that K is restricted to the underlying anharmonicity of the crystal and hence are referred to as being intrinsic in nature. It has values, which are finite in 3D bulk crystals. Heat conduction in graphene is illustrated using the Klemens for the inherent Umklapp restricted thermal conductivity of underlying graphene: K = (2πγ2)−1ρm(υ4/fmT) ln(fm/fB) (7) Where fm = superior boundary of the phonon frequencies normally demarcated by the underlying phonon dispersion fB = (Mυ3fm/4πγ2kBTL)1/2 (8) M is the prevailing mass of an atom of the audio phonons. The mass is introduced by restraining the phonon mean-free pathway having graphene layer magnitude L. Moreover, Klemens ignored the influences of out-of-plane audio phonons due to the underlying stumpy group speed and great γ. The dispersion of phonon and γ in graphene are displayed in Fig. 5a and 5b, respectively. The longitudinal optical (LO), transverse optical (TO), out-of-plane optical (ZO), longitudinal acoustic (LA), transverse acoustic (TA) and out-of plane acoustic (ZA) phonon polarization branches can be seen clearly on the figures. The dependence of K on L is obtained from the model shown on Fig. 5c and 5d; γLA and γTA are the Gruneisen parameters that have been separately averaged for each branch of phonon . Figure 5: The dispersion of photon 10. Relationship between the 2-D and 3-D (key difference between metals and graphene in terms of thermal conductivity) The 2-D crystals are experimentally non-continuous with high crystal quality. Obviously, graphene possess charge carriers which can travel thousands interatomic distances without being deflected or scattered [15]. The 2-D crystallites are extinguished in a metastable state. They are extracted from 3-D materials while for instances of small size Read More