Determination of Diffusion Length of Carriers in Graphene Using Contactless Photoelectromagnetic Method of Investigation
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Determination of Diffusion Length of Carriers in Graphene Using Contactless Photoelectromagnetic Method of Investigations Marian Nowak1, Barbara Solecka1 and Marcin Jesionek1 1
Institute of Physics - Center for Science and Education, Silesian University of Technology, Krasińskiego 8, 40-019 Katowice, Poland ABSTRACT The photoelectromagnetic (PEM) investigations are proposed for determination of diffusion length of carriers in graphene. The presented measurements are performed in Corbino configuration using noncontact technique. The circular PEM currents are detected in an outer coil by induction if illumination intensity is periodically varied. The theoretical dependence of PEM response on magnetic field induction, intensity and spatial distribution of illumination as well as on frequency of illumination chopping is presented. Experimental PEM data are presented for graphene films grown by CVD processing on a cooper foil and transferred onto a glass substrate. The presented method of investigations should be essential for development of graphene electronic and optoelectronic devices. INTRODUCTION Outstanding properties of graphene [1] are of great importance for fundamental research as well as for a wide range of applications, e.g. in optoelectronics. Information on carrier diffusion length is necessary to optimize electronic and optoelectronic devices constructed of this material. Photoelectromagnetic (PEM) investigations are a known method of determining this parameter in semiconductors [2]. The aim of this paper is to present applicability of contactless PEM method in investigations of graphene in Corbino configuration (Fig. 1).
Figure 1. Diagramic presentation of magnetic flux (broken curves B P ) evoked by the PEM current circulating in a point-illuminated grapheme ( B - the external magnetic field, and photogenerated holes and electrons, hν - photons, solid curves - trajectories of carriers).
When a graphene sample is illuminated by a circular spot of radiation, free electrons and holes are photogenerated in the illuminated spot and diffuse in all directions in the layer. In
external magnetic field perpendicular to graphene surface the diffusing carriers are deflected by Lorentz force and the circulating PEM current flows. Under amplitude-modulated illumination of a sample the PEM current varies, and consequently the changing magnetic flux, caused by it, can induce a measurable voltage in suitably placed pick-up coils. The PEM signal depends on external magnetic field and on the gradient of concentrations of photogenerated carriers. It increases with the photogeneration rate, i.e., with illumination intensity and quantum coefficient of photogeneration of free carriers. PEM signal is also dependent on the carrier diffusion length (L=(Dτ)1/2, which is proportional to the square root of carrier mobility () multiplied by their lifetime (). THEORY The transport of electrons and holes through graphene in the presence of electric field ( E ) and steady magnetic field ( B ), under photogeneration and
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