Molecular Beam Epitaxy of Graphene on Gold Foils: Growth and Characterization

Table of Contents

Abstract

I. Introduction

II. Theory
A. Graphene
i. Properties
ii. Graphene Growth and Kinetics
B. Characterization
i. Surface Topology Analysis using Atomic Force Microscopy (AFM)
ii. Vibrational Energy States Using Raman Spectroscopy
iii. Chemical Composition using Rutherford Backscattering Spectrometry
iv. Electrical Carrier Concentration and Mobility using Hall Measurement

III. Experimental Methods
A. Growth Process
B. Transfer Process
C. Electrical Characterization
D. Material Characterization

IV. Results

V. Discussion
A. Explanation of AFM Images
B. Explanation of Raman Spectra
C. Explanation of Rutherford Backscattering Spectra
D. Explanation of Hall Measurements
E. Growth Parameters vs. Film Characteristic Trends

VI. Conclusion

VII. References

VIII. Appendix

Abstract

The application of graphene for large-area electronics requires controllable growth of single crystalline quasi-freestanding graphene films. Controllable growth of graphene films on gold foils at various temperatures using molecular beam epitaxy is shown. Film quality and electrical characteristics probed using Hall measurement, Raman spectroscopy, and Rutherford backscattering spectrometry are shown to improve at lower temperature possibly peaking at ~825˚C. Further experiments are required to assess a stronger correlation between growth parameters and film characteristics. In particular, varying carbon flux and increasing the number of growths are discussed.

I. Introduction

The 2D, sp2 -hybridized, carbon-nanosheet graphene has recently been investigated heavily for integration in modern circuits as both a conductor and semiconductor. Integration of graphene in novel circuits however requires growth of high quality, wafer-scale graphene nanosheets.

Growth of graphene on metal surfaces has been demonstrated for various substrates [1–3]. There are three methods of carbon (C) deposition on metals: segregation of C from an underlying substrate, decomposition of hydrocarbons, and elemental C deposition (physical vapor deposition). In particular, Co(0001), Ni(111), Ni(100), Ru(0001), Rh(111), Rh(100), Pd(111), Pd(100), Ir(111), Pt(111), Pt(100), Pt(110), Cu(111), and Cu(100) have exhibited single layer graphene growth[4–11]. More generally, nucleation and growth of graphene sheets on and over step edges show promise for monolayer growth on Au foils as similar results have been found on transition metals [2]. Previous work investigating large-area graphene growth on Cu(111) through chemical vapor deposition (CVD) as well as physical vapor deposition (PVD) on Cu(100) has shown that multiple grain misorientations and grain boundaries compromise overall film quality [12]. It has been shown that PVD of graphene on single crystalline Au(111) results in films with predominantly two grain orientations, thus exhibiting linear electronic dispersion relations better matched to free-standing graphene[13]. In addition, previous work has also demonstrated transferred graphene sheets from gold integrated into devices; however measured device characteristics are not promising most likely due to non-ideal transfer processes [14].

Au is attractive as a growth substrate due to its inertness, mitigating oxide-related effects. The weak interaction of Au with overlying graphene may prevent significant strain effects in graphene. The low catalytic reactivity of Au makes graphene growth by hydrocarbon decomposition difficult; thus elemental C deposition techniques are more attractive. Low-angle grain boundaries result in fewer Stone-Walles Defects and thus better film quality [13]. In particular, graphene films have also been formed on low-quality, polycrystalline, high-surface-roughness Au foils (~1 µm rms roughness over 50 µm x 50 µm area) with chemical vapor deposition and transferred for device characterization.

Au is also attractive due to its electronic properties as a substrate. Previously, modification to graphene’s electronic structure has generally been tailored by post processing of graphene films by the introduction of vacancy defects. These defects cause impurity states and donate charge, thus altering conductivity and shifting the Fermi level [15]. While impurities and defects have not explicitly been shown to occur upon growth on metals, similar charge transfer mechanisms occur due to the highly mobile electrons from the underlying metal. However, due to the relatively low chemical reactivity of Au with graphene and despite relatively higher workfunction difference than Cu and thus higher Fermi level shift in graphene, hole concentration is relatively low (~6.2x1011 holes/cm2) and thus does not significantly dope the graphene film [13]. Other work with graphene films transferred to Au thin films has revealed p-type Fermi level shift (“doping”) [16]. In particular, it has been shown that a Fermi level shift (p-type) of ~ 0.35 eV near the Dirac point occurs in the graphene band structure when near many layers of Au through first principles calculations [17]. Theoretical results have been corroborated with recent experiments Au thin films deposited on graphene sheets[18]. Thus Au shows promise for growth of films with properties close to free-standing graphene.

This work focuses on the physical vapor deposition (molecular beam epitaxy) of elemental carbon on polycrystalline Au foil. Previous work on Au foil used chemical vapor deposition and did not investigate varied growth parameters [19]. In particular, the electronic and structural properties of the graphene film under varying growth temperature will be explored. Lastly, for comparison with similar reports of graphene on Au, published transfer methods from other metals (Pt, Ru, Ir, Co, Ni, Rh, and Pd) to transfer the film to insulating surfaces and examine how electronic properties are altered and adopted. In particular, graphene mobility and carrier concentration will be characterized with Hall measurements. Electronic structure and mobility data for various process conditions will be used to show and explain trends.

II. Theory

A. Graphene

i. Properties

Monolayer graphene has attracted great attention for its robust thermal, mechanical, optical, electronic, and magnetic properties REF. Most useful and perplexing property is its Dirac-like band diagram which deviates from traditional materials. Graphene's bands follow the Dirac band dispersion as opposed to the Schrodinger dispersion relation, resulting in a linear dispersion relation and essentially no bandgap.

,

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Fig.1 Schrödinger band diagram (left). Dirac fermion band diagram (right) [20].

Electrons and holes act like massless Dirac fermions and the conduction and valence bands meet at a single point, called the Dirac point, making the effective bandgap zero. Graphene is a 2D material; more specifically, its electronic characteristics are unique. Carbon has six electrons and four valence electrons, which occupy the 2s, 2px, 2py, 2pz orbitals. The 2px and 2py orbitals combine with the 2s orbital to form 3 sp2 hybridized orbitals while the 2pz orbital mixes with 2pz orbitals of adjacent atoms to form π bonds. Various models exist to describe the electronic structure of graphene from first principles including the tight-binding model and Landau theory[21]. Although the tight-binding model only considers first order bonding (π bonds), it explains both the band structure and the formation of a bandgap due to multiple layers and various external factors [22]. Please refer to [21], [23] for further reading.

ii. Graphene Growth and Kinetics

Epitaxial growth can be described with three different modes. As initially proposed by Bauer et. al., a thin film can be formed into a layer, island or a mixture of both. Island growth, the mechanism of interest occurs when atoms preferentially attach to each other rather than the surface ( ).

For our purposes, since we are growing monolayers to few layer films, the kinetics are more complicated. It is known that graphene islands on Cu (100) and other surfaces first nucleate at surface imperfections. These islands will grow and coalesce to form larger islands until final a full film is achieved. As shown by Loginova et. al., island nucleation and growth are processes dominated by the supersaturation of carbon atoms on the surface, resulting in clusters of 5 atoms that form islands. [24]. In particular an Arrhenius relation for island growth velocity is developed:

illustration not visible in this excerpt

where Cm is a proportionality constant, Em is an activation energy, kB is the Boltzmann constant, n is the concentration of carbon atoms and neq is the equilibrium concentration of carbon atoms. The above dependence on temperature is adequate to assess the approximate structure of our film[25].

B. Characterization

i. Surface Topology Analysis using Atomic Force Microscopy (AFM)

Atomic force microscopy (AFM) is used to provide topological information about the target surface. Using a cantilever tip ~30 µm across, a class IIa laser shone at an angle on the top of the tip and a photodiode to detect the reflected laser, the apparatus can detect changes in height down to sub-nm regime.

For our purposes, a dynamic contact mode or tapping mode is used where the cantilever is oscillated at nearly its resonant frequency. Then, as the tip is moved closer to the surface, the oscillations decay due to sub-atomic forces (van der Waals forces, dipole-dipole interaction, electrostatic forces, etc.). The height of oscillation is controlled by an electronic servo motor and maintained at the diminished amplitude to ensure periodic tapping of the surface. A feedback loop is exhibited to ensure a constant oscillation height. Topological information is extracted from the force of each tap.

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Fig.2 Schematic for a standard AFM system [26]

ii. Vibrational Energy States Using Raman Spectroscopy

Another technique used is Raman spectroscopy [27]. In this technique, a high-energy laser (class III) is directed upon the sample. The incident beam causes elastic or Rayleigh scattering as well as inelastic Raman scattering. The monochromatic light from the laser has a frequency and an electric field , which interacts with a molecule with a natural vibration frequency and induces a dipole moment given by , where is the polarization. The full expression for the magnitude of the dipole moment is:

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where is the vibrational amplitude of the molecule. The first term is the elastic or Rayleigh term and the , and terms correspond to inelastic Raman scattering. It is the Raman scattering terms that distinguish materials and thus the ones of interest. A material is Raman active if the polarizability changes with vibrational amplitude, i.e[illustration not visible in this excerpt] For best results, Rayleigh scattering must be suppressed compared to Raman scattering[27].

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Fig.3 Vibrational state transitions for an arbitrary atom [28].

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Fig.4 Raman apparatus used in this study (courtesy of Prof. Wu). The box contains the optics. The source is a 488nm laser.

As seen above, Raman is indeed closely correlated to electronic structure. A characteristic Raman spectrum is given in the figure below. The spectrum is characteristic of the material. Graphene has 4 prominent peaks: At around 1582 cm-1, a peak caused by a Raman active E­2g in-plane optical mode phonon, commonly called the G line, occurs. At around 1350 cm-1, a D line peak occurs, whose amplitude determines disorder of the material. The overtone of the D line, or the D’ line (also called the 2D line) occurs around 2700 cm-1. The D’ line is explained by an electron being vertically excited from point A in the π band to point B in the π* band, then being inelastically scattered to point C and finally being inelastically scattered again back to point A. This is shown in the figure below. For a double layer, the bands split and likewise result in more possible excitations thus giving a superposition of multiple peaks in the Raman spectrum for the 2D line, broadening the peak. This trend continues for a larger number of layers[29].

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