Chapter 1. Graphene

Simulation results for the momentum dissipation time dependence of the transmission response of graphene on quartz. Raman mapping of the relative shift in the position of the G peak of graphene transferred on quartz.

GRAPHENE

I NTRODUCTION

B AND STRUCTURE OF GRAPHENE

The two carbon atoms in graphene's unit cell each contribute four electrons and apparently form graphene's unique band structure. The long mean free path of ~0.5 µ𝑚 fits the transport of graphene in the ballistic regime and makes graphene a desirable candidate for field effect transistor (FET) applications[16].

Figure 1.2 (a) 3D energy dispersion for the two π bands in the first Brillouin zone of a hexagonal lattice of single layer graphene

O PTICAL PROPERTIES OF GRAPHENE

Interband transitions and universal absorption of graphene
Optical transmission in 2D graphene
Intraband transitions in graphene
Effect of doping on the transmission of graphene
Optical conductivity of graphene in the UV range

However, in the mid to near IR range, the optical response of graphene is mostly due to the interband transitions between the valence and conduction band.[19][20]. The sheet optical conductance of graphene for the interband phenomena can be described as.

Figure 1.5. (a) Universal absorbance and optical sheet conductivity of graphene in the energy range: 0.5-1.2 eV

METHODS

I NTRODUCTION

One of the most versatile and time-saving characterization tools in the field of graphene research is Raman spectroscopy. The last section of this chapter will discuss different Raman processes and our use of this technique to characterize the layer number, orientation, strain and intrinsic doping of graphene samples.

G RAPHENE SYNTHESIS

Mechanically exfoliated graphene
Epitaxial Graphene
Chemical Vapor Deposition (CVD) Graphene

The possibility of large-area growth, the high degree of control and reproducibility in CVD graphene production, and the inherent electrical properties that rival exfoliated graphene have made the CVD growth method one of the most viable options for transitioning graphene to industry. . In this case, the lack of bulk carbon and surface catalysis results in the self-termination of the growth process and gives uniform single-layer graphene growth [40].

CVD GRAPHENE GROWTH

CVD growth kinetics
Copper foil contamination
CVD growth recipe

SEM images of white particles on the copper foil immediately after the graphene growth process. Then we start the flow of 10 𝑆𝐶𝐶𝑀 of hydrogen and set the furnace temperature to 900°𝐶 and anneal the copper foil for 1 hour.

Figure 2.2. SEM images of white particles on the copper foil immediately after the graphene growth process

CVD GRAPHENE TRANSFER

Etching copper
PMMA removal

Another important factor that helps the etch rate is the removal of the graphene layer that grows on the bottom of the copper foil in the CVD growth process. After etching the copper foil, the PMMA + graphene floating layer must be thoroughly cleaned and cleaned of copper etchant residues.

Figure 2.3. Optical images of single layer graphene transferred on SiO 2 /Si substrate using PMMA

T HE S UBSTRATE

Surface roughness
Substrate cleaning
Passivation of the diamond samples

Since 𝜆/𝐴𝑠 is a good measure of surface roughness, Figure 2.7. b) shows the effect of surface roughness on the conformation of graphene. These images show that the compatibility of graphene with the substrate is highly dependent on the surface roughness and morphology and can range from full conformation (a) to flat alignment on top of the highest points, with minimal contact with the substrate.

Figure 2.6. Graphene transferred on nanopillars. Image in top left shows the AFM micrograph of graphene on SiO 2 nanopillars

C HARACTERIZATION

Visibility under optical microscopy
Raman spectroscopy

Phonons in graphene
Raman peaks of graphene
Nomenclature
Raman spectroscopy and graphene layer number
Raman spectroscopy and layer stacking
Raman spectroscopy and defects
Raman spectroscopy and doping in graphene

The slope of the branching anomalies can provide direct information about the electron-phonon coupling (EPC). This fact results in the dispersive nature of the frequency of the 2D peak in graphene. As discussed, due to the differences in the electronic band structure of the different stacking orders, the Raman is 2D.

Figure 2.9. (Left) Exfoliated mono and bilayer graphene transferred on SiO2/Si substrate and characterized under white light where the optical contrast provides a quick method to identify layer number.[189] (Right) Contrast plot of light wavele

C ONCLUSION

In the framework of this thesis, we use the Raman shift of the G peak to evaluate the electron/hole doping of graphene transferred to different substrates in Chapter 3. We used the average value to estimate the change in the Fermi level, which corresponds to EF= 0.27.

RELAXATION DYNAMICS OF GRAPHENE ON DIFFERENT SUBSTRATES

I NTRODUCTION

We believe that the fine polishing and sub-nm roughness of our studied substrates (sapphire, quartz and single-crystal diamond) enable a strong coupling between the photoexcited graphene carriers and the surface optical phonons of the underlying substrate. We explain the observed substrate-dependent dynamics using a multi-channel cooling picture, which includes substrate polar surface phonons (SP), graphene intrinsic optical phonons (IP) and their dissipation rate and activation time frame. The observed increase in carrier relaxation times with increasing excited carrier density further confirms the existence of an additional energy relaxation channel through substrate phonons, which can compete with intrinsic optical phonons to lower the substrate temperature. transient carriers and to reduce the lifetime of internal optical phonons.

U LTRAFAST PUMP PROBE SPECTROSCOPY OF GRAPHENE

Due to the very fast Auger processes that bridge the conduction and valence bands on a very short time scale, the separation of chemical potentials for electrons and holes is considered unimportant in our measurements. This was also contrary to the authors' expectations, where they expected the optical phonons at the surface of quartz and SiC to influence the optical phonon lifetimes and carrier relaxation times of graphene. The separation of chemical potentials for electrons and holes is considered insignificant due to the very fast Auger processes that connect the conduction and valance bands on a very short time scale.

Figure 3.2. Simulated change in the transient transmission of graphene as a function of electronic temperature for a pumping energy of 1.6 eV and an intrinsic carrier density of 1x10 12 /cm 2

U LTRAFAST TRANSIENT TRANSMISSION RESPONSE OF GRAPHENE ON QUARTZ

Experimental details
Fluence dependent dynamics of graphene on quartz
Excitation energy dependent dynamics of graphene on quartz

Using a phase-sensitive lock-in amplifier with a sensitivity of ~10-6, we can measure the pump-induced changes in transmission (ΔT) of the sample. To obtain the differential transient transmission (𝛥𝑇/𝑇0 ) we need to measure the steady state transmission 𝑇0 in the absence of the pump. Although the energy range is quite small, one can see the extent of diversity in the ultrafast dynamics.

Figure 3.4. Experimental setup for the pump probe measurements presented in this thesis

S IMULATION AND FITTING PARAMETERS

Calculated temperature dependence of the Drud scattering rate due to electron-optical phonon interactions. In the context of pump-probe experiments, optical phonon scattering of the substrate is rarely considered. Moreover, the assumed optical phonon lifetime obtained from fitting the data to the model is unphysically small (~ 100 𝑓𝑠).

Figure 3.9. Calculated temperature dependence of the Drude scattering rate due to the electron-optical phonon interactions

E FFECT OF SUBSTRATE ON THE ULTRAFAST DYNAMICS OF GRAPHENE

Simulation results of the momentum dispersion time dependence of the transmission response of graphene on quartz. The dependence of the dynamics on the static Fermi level of graphene is shown in Figure 3.13. Simulation results showing the dependence of the transient transmission of graphene (transferred on a quartz substrate) on the static Fermi level.

Figure 3.11. Fluence dependent ultrafast transmission response of graphene on: (a) diamond, (b) sapphire and (c) quartz, excited at 1.6 eV

S URFACE OPTICAL PHONON OF POLAR MATERIALS

Fröhlich coupling and the role of the separation distance
Effect of doping and polarity of the substrate
Intrinsic optical phonon vs. surface optical phonon scattering rate
Effect of SP on IOP lifetimes of graphene

In a theoretical study, Fratini et al.[134] discovered that the origin of the density-dependent mobility at room temperature in graphene is due to the carrier interactions with the optical phonons at the surface of polar materials. The sensitivity of the SP coupling to the intrinsic doping has been confirmed by a number of different studies. Based on these temperature-dependent measurements, it is concluded that the shorter lifetime of single-layer graphene is due to the additional decay channel through the surface phonons of the substrate.

Table 3.2. Static, intermediate and high frequency permittivities, surface phonon frequencies and bare Fröhlich coupling constants for different substrates

T RANSIENT TRANSMISSION IN THE PRESENCE OF SURFACE OPTICAL PHONONS

Effect of substrate on the band filling dynamics of graphene
Effect of substrate on the induced carrier absorption of graphene
Effect of substrate on the carrier relaxation times of graphene

A closer look at Figure 3.20 shows that the notable differences in the observed dynamics of graphene on different substrates are: (1) the amplitude of the positive peak, (2) the relative positive to negative peak ratio representing inter- vs intraband transition interaction ( 𝛾), and (3) relaxation times of the carriers. Normalized transmission response of graphene on diamond, quartz and sapphire for an excitation energy of 1.6 eV and a fluence of 9.6 µJ/cm2. 143] The decay constant converges towards 1.6–1.7 ps for graphene on sapphire and smoother quartz, which is in the range of the reported optical phonon lifetimes for monolayer graphene.

Figure 3.20. Transient transmission response of graphene on diamond, quartz and sapphire

C ONCLUSION

IP is the dominant energy relaxation channel, the slower tail of the experimental dynamics, and can potentially reflect the intrinsic optical phonon lifetime of graphene. For graphene on quartz 2, where the conformity of graphene and the substrate is not optimal, at high fluctuations we have 𝜏2~ 2.5 𝑝𝑠, which is comparable to the optical phonon lifetime of graphite measured with time-resolved incoherent Anti-Stokes Raman- spectroscopy. Accordingly, a multichannel cooling image involving surface phonons of the substrate and intrinsic optical phonons of graphene was used to explain the observed differences in the ultrafast transmission response of graphene on different substrates.

PHOTO RESPONSE OF CURLED GRAPHENE RIBBONS

I NTRODUCTION

In this chapter, we investigate the nature of this enhanced photoresponse in suspended CGR using optical photocurrent microscopy.

M ORPHOLOGY OF GRAPHENE

It has been shown that the deformation of sigma bonds caused by the curvature of graphene folds can result in charge transfer between the out-of-plane sigma bonds and the π-orbitals, which can alter the chemisorption and molecular adhesion of graphene.[170] Kim et al. Theoretical studies show that the long suspended bands of graphene are prone to Figure 4.2. a) Different complex folding of graphene membrane including a fourfold folding and a box folding as simulated by Kim et al. 171] (b) Figure on the left shows an AFM image of graphene on SiO2/Si substrate including folding and wrinkling of the graphene membrane.

Figure 4.3. Simulation results of twisted ribbon transformation into a coiled ribbon configuration

C URLED GRAPHENE RIBBON SYNTHESIS

One can clearly see from the top figure that the most intense curl occurs in the middle of the ribbon. We observed that focusing a high-energy electron beam on the suspended regions of a suspended graphene ribbon can lead to tearing of the membrane and scrolling of the edges in the exposed side. The inset shows a close-up of the curled area with a scale bar of 50 nm.

Figure 4.4. SEM images of three different curled graphene ribbons suspended over trenches of 5µm width

MD SIMULATIONS

To fully understand the structures of CGRs, single layer graphene was directly transferred on TEM grids coated with side carbon films and similar annealing process was adopted to form CGRs. The 2D-to-G intensity ratios are greater than 1 in the regions R1, R2, R5 and R6, indicating the presence of a single-layer graphene membrane. The broad 2D bands in the regions R3 and R4 may be the result of the interlayer interactions between different graphene layers within the CGR.

Figure 4.6. (a) SEM image of a CGR structure. The CGR was suspended across a 5 μm-wide and 5 μm-deep trench on fused silica

R AMAN S PECTROSCOPY ON CGR STRUCTURE

As we move further towards the center of the band in the R3 and R4 regions, twisting and twisting in the graphene becomes increasingly apparent and a significant decrease in the 2D to G intensity ratio is observed. The 2D bands also become broadened and asymmetric, indicating that there was a double resonance process during second-order multiple scattering cycles involved, which is a result of strong interlayer interactions between different graphene layers and differs from the case of turbostratic graphene.

P HOTOCURRENT RESPONSE IN CGR

Photocurrent setup
Results and discussion
Photocurrent generation mechanism in CGR

Schematic of energy levels and their alignment due to the built-in electric field at the graphene-metal interface. Corresponding photocurrent images of a suspended SLG device (D) and a suspended CGR device (E) respectively. Three regions (R1, R2 and R3) along the CGR were selected to study the evolution of their PV signal (𝑉𝑝𝑐=𝐼𝑝𝑐𝑅) as a function of the sweep gate voltage. d), the photovoltaic signals in the region of R3 (R1) show a strong non-monotonic dependence on the gate voltage and have a similar behavioral pattern to the calculated thermoelectric power (S), which may be due to PTE.

Figure 4.7. Schematics of the energy levels and their alignment due to the built in electric field at the graphene-metal junction

C ONCLUSION

Materials of interest
Ultrafast Pump Probe Spectroscopy (UPPS)
Time Resolved Photo Luminescence spectroscopy (TRPL)
Coherent Acoustic Phonon interferometry (CAP)

The influence of the underlying substrate on the ultrafast carrier and phonon dynamics in 2D materials and 2D heterostructures. By monitoring the relaxation of these excited carriers, we can determine not only the cooling rates of the carriers, but also the different energy relaxation pathways available to the excited electrons and the contribution of the substrate as an additional energy relaxation pathway through charge transfer or phonon coupling. Hundreds of picoseconds after photoexcitation, most of the energy from the 2D electron system moves to the lower energy 2D phonon system and the immediately available energy relaxation channel becomes the coupling of the acoustic phonon from the 2D layer to the substrate.

C ONCLUSION

Ferrari, "Electron-electron interactions and doping dependence of the two-phonon Raman intensity in graphene," Phys. Spencer, “Carrier recombination and generation rate for intravalley and gap phonon scattering in graphene,” Phys. Avouris, “Effects of polar optical and surface phonons on the optical conductivity of doped graphene,” Phys.