Towards Ballistic Transport in Graphene

2017

des akademischen Grades eines Doktors der Naturwissenschaften genehmigte Dissertation vorgelegt von Dipl.-Ing.

Physical Review B, 2013

We investigate the transport of electrons in disordered and clean graphene devices. We consider a geometry where the graphene flake is contacted by narrow metallic leads. Plotting the conductance as a function of the position of one of the leads, we can approximate the probability density function of the charge flow at the edge which is used to analyze the transport properties with increasing length of the device. Moreover, we simulate scanning probe microscopy (SPM) measurements for the same devices, which can be seen as a measure for the flow of charge inside the device, thus complementing the transport calculations. We compare our analysis to theory describing transport in clean and disordered systems.

We investigate the ballistic electron transport in a monolayer graphene with configurational averaged impurities, located between two clean graphene leads. It is shown that the electron transmission are strongly dependent on the concentration of impurities and the incident energy. In turn, the conductance computed using the Landauer formalism shows a similar behavior to those found in experimental works as a function of the applied voltage for different concentrations of impurities in the limit of low temperatures. In the limit of zero bias voltage, the conductance shows a minimum value which reduces to zero for high concentration of impurities which disentangle graphene sublattices. These results can be very helpful for exploring the tunneling mechanism of electrons through doped thermodynamically stable graphene.

The discovery of graphene raises the prospect of a new class of nanoelectronic devices based on the extraordinary physical properties of this one-atom-thick layer of carbon. Unlike two-dimensional electron layers in semiconductors, where the charge carriers become immobile at low densities, the carrier mobility in graphene can remain high, even when their density vanishes at the Dirac point. However, when the graphene sample is supported on an insulating substrate, potential fluctuations induce charge puddles that obscure the Dirac point physics. Here we show that the fluctuations are significantly reduced in suspended graphene samples and we report low- temperature mobility approaching 200,000 cm2/V^2/s^2 for carrier densities below 5 x 10^9 cm^2. Such values cannot be attained in semiconductors or non-suspended graphene. Moreover, unlike graphene samples supported by a substrate, the conductivity of suspended graphene at the Dirac point is strongly dependent on temperature and approaches ballistic values at liquid helium temperatures. At higher temperatures, above 100 K, we observe the onset of thermally induced long- range scattering.

Physical Review B, 2011

The intrinsic values of the carriers mobility and density of the graphene layers inside graphite, the well known structure built on these layers in the Bernal stacking configuration, are not well known mainly because most of the research was done in rather bulk samples where lattice defects hide their intrinsic values. By measuring the electrical resistance through microfabricated constrictions in micrometer small graphite flakes of a few tens of nanometers thickness we studied the ballistic behavior of the carriers. We found that the carriers' mean free path is micrometer large with a mobility µ ≃ 6 × 10 6 cm 2 /Vs and a carrier density n ≃ 7 × 10 8 cm −2 per graphene layer at room temperature. These distinctive transport and ballistic properties have important implications for understanding the values obtained in single graphene and in graphite as well as for implementing this last in nanoelectronic devices.

Semiconductor Science and Technology, 2010

We study the effect of resonant scatterers on the local density of states in a rectangular graphene setup with metallic leads. We find that the density of states in a vicinity of the Dirac point acquires a strong position dependence due to both metallic proximity effect and impurity scattering. This effect may prevent uniform gating of weakly-doped samples. We also demonstrate that even a single-atom impurity may essentially alter electronic states at lowdoping on distances of the order of the sample size from the impurity.

Journal of Physics: Conference Series, 2012

A dynamical approach to ballistic transport in mesoscopic graphene samples of …nite length L and contact potential di¤erence with leads U is developed. It is shown that at ballistic times shorter than both relevant time scales, tL = L=vg (vg-Fermi velocity) and tU =~=(eU), the major e¤ect of electric …eld is to creates the electron-hole pairs, namely causes interband transitions. At ballistic times lager than the two scales the mechanism is very di¤erent. The conductivity has its "nonrelativistic" or intraband value equal to the one obtained within the Landauer-Butticker approach for the barrier U resulting from evanescent waves tunneling through the barrier.

arXiv: Materials Science, 2020

Pristine graphene and graphene-based heterostructures exhibit exceptionally high electron mobility and conductance if their surface contains few electron-scattering impurities. Here, we reveal a universal connection between graphene's carrier mobility and the variation of its electrical conductance with carrier density. Our model of graphene conductivity is based on a convolution of carrier density and its uncertainty, which reproduces the observed universality. Taking a single conductance measurement as input, this model accurately predicts the full shape of the conductance versus carrier density curves for a wide range of reported graphene samples. We verify the convolution model by numerically solving the Boltzmann transport equation to analyse in detail the effects of charged impurity scattering on carrier mobility. In this model, we also include optical phonons, which relax high-energy charge carriers for small impurity densities. Our numerical and analytical results both c...

2010

The intrinsic values of the carriers mobility and density of the graphene layers inside graphite, the well known structure built on these layers in the Bernal stacking configuration, are not well known mainly because most of the research was done in rather bulk samples where lattice defects hide their intrinsic values. By measuring the electrical resistance through microfabricated constrictions in

Physical Review B, 2010

The process of coherent creation of particle -hole excitations by an electric field in graphene is quantitatively described beyond linear response. We calculate the evolution of current density, number of pairs and energy in ballistic regime for electric field E using the tight binding model. While for ballistic flight times smaller than t nl ∝ E −1/2 current is linear in E and independent of time, for larger ballistic times the current increases after t nl as J ∝ E 3/2 t and finally at yet larger times (t > tB ∝ E −1 ) Bloch oscillations set in. It is shown that the number of pairs follows the 2D generalization of the Schwinger's creation rate n ∝ E 3/2 only on certain time segments with a prefactor different from that obtained using the asymptotic formula.