Understanding Graphenes Thermal Properties - Case Study Example

Understanding graphene’s thermal properties: A phonon perspective December 17, Table of Contents 3 Introduction 4 2.Scope of this paper and main objectives 4 3. The structure of graphene 5 4.Mechanisms of heat conduction in graphene 8 6.A correlation between the 2-D and 3-Dwith respect to thermal conductivity 12 8.Conclusion 13 Abstract Graphene, as 2D structure, has attained great attention from various researchers and scientists in matter physics and materials science due to its extraordinary and unique thermal properties. Ultimately, the study and analysis of the properties of graphene owes thegreat number of applications ranging from electronic and structural uses among others. However, much of the properties as well as details pertaining graphene are still unknown[1]. 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. The heat flow in graphene can be turned on by various means such as phonon diffusing by substrates or interfaces. This research paper focuses on discussing the thermal properties of graphene paying from a phonon perspective[2]. The ability of a material to conduct heat is usually based on the atomic structure of the material and the knowledge of the thermal properties. The thermal properties of the material may change when their structure is put on the nanometer scale[3]. The divergence of the thermal conductivity in two dimensional crystals means that the anharmonicity of the crystal is not considered sufficient for the restoration of the thermal equilibrium and hence there is need for one to consider either limiting the size of the system or introducing disorder in order to have the finite value of the thermal conductivity[4]. Availability of the few layers of graphene of high quality has led to the experimentation on the evolution of the thermal properties of the dimensionality of the system from 3D to 2D[5]. The initial measurements of the thermal properties of graphene showed a thermal conductivity that is above the bulk limit of graphite Keywords: graphene, phonon, thermal conductivity, scattering, dispersion relation 1. Introduction Graphene, a recently 2-D developed allotrope of the nanocarbon, is a known as a single atomiclayer of graphite[2]. The strongest bonds are as a result of the in-plane covalent hexagonallysp2 between the carbon atoms which are significantly stronger than the sp3diamond bonding. The planes of graphene on the graphite crystal are due to weak van der Waal forces between them. The anisotropic nature of the crystals can be used to determine the thermal attributes of graphene. Basically, the 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 in order to better 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[6]. 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[5]. 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 for restoring the thermal equilibrium thus requires the need of limiting the system size or introduction of disorder to achieve the significance of the value of K[6]. Ultimately, carbon materials, in which graphene is one of them, formed a basis of study of a variety of allotropes which have a specific value as far as thermal properties are concerned[7]. 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 theoretical and experimental studies, based on heat conduction. However, there are very little details on the lattice dynamics of the graphene as well as their physical understandings/interpretation is not well clear. Thus, the main objective of this paper is to scientifically analyse/ investigates graphene’s thermal properties based on elaborated lattice dynamics fundamentals. As well, to analyse the most important property that distinguishes graphene from metals.In this paper, fundamental lattice dynamics and associated role in thermal conduction are discussed based on the available literature and using the knowledge learned from MSE 200 courseto answer some critical questions mentioned above. As such, the paper is much focused in order to avoid the 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. Ideally, 2-D crystal is an atomic plane with single layer while 100 layers are considered to be a thin film of 3-D material. Electronic structure advances drastically with various layers approaching the 3-D limit of at least 10-20 layers of graphite material[8].Figure2 illustrates the atomic arrangement of graphene and how one atom is bonded to the next atom. Figure 1: Various allotropes of carbon [9] Figure 2: The atomic structure of graphene[1] Graphene unlike other materials is uniquely identified by two thermal properties. Perfect order is a distinct property of graphene, usually located in its sheets[10]. This property means that the no atomic related defects as in the case of vacancies exist. Furthermore, this property implies that the sheets of graphene are completely pure with traces of carbon atoms being available. Secondly, the property of graphene correlates with type of unrestrained electrons[11]. It implies that the electrons at room temperature are highly charged and thus move faster as compared with electrons movement in other conducting metals or semi conducting materials[12]. It has strength of about (~ 130 GPa) and a thermal property of (~ 5000 W/m.K) which is termed as the best. In particular, the electronic structure of graphene is unique and different from metals. Graphene is a non-metal component; the electrons are basically arranged in a pi-bonds concept 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[13]. Such properties uniquely define the graphene material. 3. The Basics of conduction of heat When dealing with solid materials, heat is usually carried by acoustic phonons such that: K = Kp + Ke (1) Where Kp and Ke are the phonon and electron contributions, respectively. In materials that are solid in nature, heat is normally carried by acoustic phonons and electrons Figure 2: The thermal properties of carbon allotropes and their derivatives[14] Conductivity is explained by the presence of a strong covalent sp2 bonding which results in transfer of heat that is efficient and is achieved through lattice vibrations. The thermal conductivity of the phonon is normally expressed as: Kp = Σj ∫Cj(ω) υj2(ω)τj(ω)dω (2) Where j is the phonon polarization branch, The mean-free path (Λ) of the phonon is usually related to the time of relaxation and is given as Λ = τυ. In dealing with the approximation of the time of relation, several mechanisms of scattering, limiting Λ, are usually added, τ−1 = Στi−1, where i enumerates the scattering processes. Conduction of heat in carbon materials is normally dominated by phonons which have properties similar to those of metals[10]. It is important to point out the differences between the diffusive and ballistic phonon-transport regimes. The thermal transport regime is said to be diffusive if the size of the sample L is larger than Λ and hence the phonons undergo scattering. When the value of L < Λ, then the thermal transport is said to be ballistic[15]. Conductivity is explained by the presence of a strong covalent sp2 bonding which results in transfer of heat that is efficient and is achieved through lattice vibrations. The thermal conductivity of the phonon is normally expressed as: Kp = Σj ∫Cj(ω) υj2(ω)τj(ω)dω. (2) Where j is the phonon polarization branch, The mean-free path (Λ) of the phonon is usually related to the time of relaxation and is given as Λ = τυ. In dealing with the approximation of the time of relation, several mechanisms of scattering, limiting Λ, are usually added, τ−1 = Στi−1, where i enumerates the scattering processes[16]. Conduction of heat in carbon materials is normally dominated by phonons which have properties similar to those of metals. It is important to point out the differences between the diffusive and ballistic phonon-transport regimes[17]. The thermal transport regime is said to be diffusive if the size of the sample L is larger than Λ and hence the phonons undergo scattering. When the value of L < Λ, then the thermal transport is said to be ballistic. In materials that have nanostructures, K is normally reduced though scattering from the boundaries and this can be determined by: 1/τB = (υ/D)((1−p)/(1+p)) (3) where τB is the phonon life and 1/τB is the scattering rate of the phonon. 4. 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) (4) The formulation outlines a relationship of definite heat with v- optimum photon velocity while λ -free path. 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[3]. Essentially, 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; Where: 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 Technically, the optimum free path is correlated with relaxation of time given as Λ = τυ. This property leads to ballistic conductance at room temperature[1]. 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[9]. 2. Discussion of the specific heat of graphene Phonons components are majorly responsible for carrying heat in carbon materials. The diffusive and ballistic are two types of transport in existence[4]. 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[18].Thermal conductivity is basically termed as intrinsic if it is constrained by the crystal-lattice an-harmonicity[19]. 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 [20]. 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 an-harmonicity[13]. Engagement of the harmonic phonon leads to finite K value in 3-D which is vividly described by the Umklapp processes. The crystal degree an-harmonicity is usually depicted by the Gruneissen boundary γ, which is expressed in the Umklapp scattering rates. 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[21]. Thermal conductance of graphene, referring to (in-plane) reduces when a substrate get in touch with 2D or confined into graphene Nano-ribons (GNRs) [15]. In effect, the results are unforeseen owing to the presence of phonon propagation in thin atomic graphene hence causes sensitivity to edge perturbations [16]. 3. Thermal conductivity of Graphene consideration of the ballistic boundary threshold 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].On the other hand, 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[22]. 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[23]. 4. Thermal conveyance considering few-layer Graphene It is very vital to consider and examine the thermal properties of thin-layer of graphene as its thickness increases. 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[4].Research indicates that the suspended uncapped few-layered graphene reduces with increase in n approaching the bulk limit[16]. 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[7]. 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[25]. Illustrations of thermal conductivity of quasi-2D carbon materials considering intrinsic and extrinsic effects are as shown below. Figure 3: Thermal conductivity of graphene Nano-ribbons obtained from MD simulations as a function of n showing a similar trend[24] 5. Molecular dynamics perspective of phonon Contextually, molecular dynamics (MD) is one of the fundamental concepts in determining and calculating graphene properties such as thermal properties [26]. 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. Ideally, when 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[27]. 6. A correlation between the 2-D and 3-Dwith respect to thermal conductivity Graphene, as 2D material, is quite different from 3D dimensional materials such as graphite owing to its unique low dimensional structure as well as the strong covalent bonds hence resulting to different phonon scattering techniques which gives graphene a very high thermal conductivity as compared to other carbon allotropes[28].Obviously, graphene possess charge carriers which can travel thousands interatomic distances without being deflected or scattered [15].The 2-D crystallites are differentiable in a metastable state. They are extracted from 3-D materials while for instances of small size Read More